Fix BSSN C gauge RHS parity

Shell C functions must export Fortran-compatible symbols with trailing
underscore so bssn_rhs_ss.f90 and getnp4.f90 can link when WithShell is
active and USE_CXX_SHELL_KERNELS=1 replaces Fortran diff_new_sh.o.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

.gitignore

@@ -1,6 +1,6 @@
 __pycache__
 GW150914
-GW150914-origin
+GW150914*
 docs
 *.tmp
-
+.codex

AMSS_NCKU_ABEtest.py

@@ -1,447 +0,0 @@
-
-##################################################################
-##
-## AMSS-NCKU ABE Test Program (Skip TwoPuncture if data exists)
-## Modified from AMSS_NCKU_Program.py
-## Author: Xiaoqu
-## Modified: 2026/02/01
-##
-##################################################################
-
-
-##################################################################
-
-## Print program introduction
-
-import print_information
-
-print_information.print_program_introduction()
-
-##################################################################
-
-import AMSS_NCKU_Input as input_data
-
-##################################################################
-
-## Create directories to store program run data
-
-import os
-import shutil
-import sys
-import time
-
-## Set the output directory according to the input file
-File_directory = os.path.join(input_data.File_directory)
-
-## Check if output directory exists and if TwoPuncture data is available
-#skip_twopuncture = False
-skip_twopuncture = True
-output_directory = os.path.join(File_directory, "AMSS_NCKU_output")
-binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
-
-if os.path.exists(File_directory):
-    print( " Output directory already exists." )
-    print()
-    '''
-    # Check if TwoPuncture initial data files exist
-    if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture"):
-        twopuncture_output = os.path.join(output_directory, "TwoPunctureABE")
-        input_par = os.path.join(output_directory, "input.par")
-
-        if os.path.exists(twopuncture_output) and os.path.exists(input_par):
-            print( " Found existing TwoPuncture initial data." )
-            print( " Do you want to skip TwoPuncture phase and reuse existing data?" )
-            print( " Input 'skip' to skip TwoPuncture and start ABE directly" )
-            print( " Input 'regenerate' to regenerate everything from scratch" )
-            print()
-            
-            while True:
-                try:
-                    inputvalue = input()
-                    if ( inputvalue == "skip" ):
-                        print( " Skipping TwoPuncture phase, will reuse existing initial data." )
-                        print()
-                        skip_twopuncture = True
-                        break
-                    elif ( inputvalue == "regenerate" ):
-                        print( " Regenerating everything from scratch." )
-                        print()
-                        skip_twopuncture = False
-                        break
-                    else:
-                        print( " Please input 'skip' or 'regenerate'." )
-                except ValueError:
-                    print( " Please input 'skip' or 'regenerate'." )
-            
-        else:
-            print( " TwoPuncture initial data not found, will regenerate everything." )
-            print()
-'''
-    # If not skipping, remove and recreate directory
-    if not skip_twopuncture:
-        shutil.rmtree(File_directory, ignore_errors=True)
-        os.mkdir(File_directory)
-        os.mkdir(output_directory)
-        os.mkdir(binary_results_directory)
-        figure_directory = os.path.join(File_directory, "figure")
-        os.mkdir(figure_directory)
-        shutil.copy("AMSS_NCKU_Input.py", File_directory)
-        print( " Output directory has been regenerated." )
-        print()
-else:
-    # Create fresh directory structure
-    os.mkdir(File_directory)
-    shutil.copy("AMSS_NCKU_Input.py", File_directory)
-    os.mkdir(output_directory)
-    os.mkdir(binary_results_directory)
-    figure_directory = os.path.join(File_directory, "figure")
-    os.mkdir(figure_directory)
-    print( " Output directory has been generated." )
-    print()
-
-# Ensure figure directory exists
-figure_directory = os.path.join(File_directory, "figure")
-if not os.path.exists(figure_directory):
-    os.mkdir(figure_directory)
-
-##################################################################
-
-## Output related parameter information
-
-import setup
-
-## Print and save input parameter information
-setup.print_input_data( File_directory )
-
-if not skip_twopuncture:
-    setup.generate_AMSSNCKU_input()
-
-setup.print_puncture_information()
-
-
-##################################################################
-
-## Generate AMSS-NCKU program input files based on the configured parameters
-
-if not skip_twopuncture:
-    print()
-    print( " Generating the AMSS-NCKU input parfile for the ABE executable." )
-    print()
-
-    ## Generate cgh-related input files from the grid information
-
-    import numerical_grid
-
-    numerical_grid.append_AMSSNCKU_cgh_input()
-
-    print()
-    print( " The input parfile for AMSS-NCKU C++ executable file ABE has been generated." )
-    print( " However, the input relevant to TwoPuncture need to be appended later." )
-    print()
-
-
-##################################################################
-
-## Plot the initial grid configuration
-
-if not skip_twopuncture:
-    print()
-    print( " Schematically plot the numerical grid structure." )
-    print()
-
-    import numerical_grid
-    numerical_grid.plot_initial_grid()
-
-
-##################################################################
-
-## Generate AMSS-NCKU macro files according to the numerical scheme and parameters
-
-if not skip_twopuncture:
-    print()
-    print( " Automatically generating the macro file for AMSS-NCKU C++ executable file ABE " )
-    print( " (Based on the finite-difference numerical scheme) " )
-    print()
-
-    import generate_macrodef
-
-    generate_macrodef.generate_macrodef_h()
-    print( " AMSS-NCKU macro file macrodef.h has been generated. " )
-
-    generate_macrodef.generate_macrodef_fh()
-    print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
-
-
-##################################################################
-
-# Compile the AMSS-NCKU program according to user requirements
-# NOTE: ABE compilation is always performed, even when skipping TwoPuncture
-
-print()
-print( " Preparing to compile and run the AMSS-NCKU code as requested " )
-print( " Compiling the AMSS-NCKU code based on the generated macro files " )
-print()
-
-AMSS_NCKU_source_path = "AMSS_NCKU_source"
-AMSS_NCKU_source_copy = os.path.join(File_directory, "AMSS_NCKU_source_copy")
-
-## If AMSS_NCKU source folder is missing, create it and prompt the user
-if not os.path.exists(AMSS_NCKU_source_path):
-    os.makedirs(AMSS_NCKU_source_path)
-    print( " The AMSS-NCKU source files are incomplete; copy all source files into ./AMSS_NCKU_source. " )
-    print( " Press Enter to continue. " )
-    inputvalue = input()
-
-# Copy AMSS-NCKU source files to prepare for compilation
-# If skipping TwoPuncture and source_copy already exists, remove it first
-if skip_twopuncture and os.path.exists(AMSS_NCKU_source_copy):
-    shutil.rmtree(AMSS_NCKU_source_copy)
-
-shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
-
-# Copy the generated macro files into the AMSS_NCKU source folder
-if not skip_twopuncture:
-    macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
-    macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
-else:
-    # When skipping TwoPuncture, use existing macro files from previous run
-    macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
-    macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
-
-shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
-shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
-
-# Compile related programs
-import makefile_and_run
-
-## Change working directory to the target source copy
-os.chdir(AMSS_NCKU_source_copy)
-
-## Build the main AMSS-NCKU executable (ABE or ABEGPU)
-makefile_and_run.makefile_ABE()
-
-## If the initial-data method is Ansorg-TwoPuncture, build the TwoPunctureABE executable
-## Only build TwoPunctureABE if not skipping TwoPuncture phase
-if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
-    makefile_and_run.makefile_TwoPunctureABE()
-
-## Change current working directory back up two levels
-os.chdir('..')
-os.chdir('..')
-
-print()
-
-##################################################################
-
-## Copy the AMSS-NCKU executable (ABE/ABEGPU) to the run directory
-
-if (input_data.GPU_Calculation == "no"):
-    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
-elif (input_data.GPU_Calculation == "yes"):
-    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
-
-if not os.path.exists( ABE_file ):
-    print()
-    print( " Lack of AMSS-NCKU executable file ABE/ABEGPU; recompile AMSS_NCKU_source manually. " )
-    print( " When recompilation is finished, press Enter to continue. " )
-    inputvalue = input()
-
-## Copy the executable ABE (or ABEGPU) into the run directory
-shutil.copy2(ABE_file, output_directory)
-
-## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
-## Only copy TwoPunctureABE if not skipping TwoPuncture phase
-if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
-    TwoPuncture_file = os.path.join(AMSS_NCKU_source_copy, "TwoPunctureABE")
-
-    if not os.path.exists( TwoPuncture_file ):
-        print()
-        print( " Lack of AMSS-NCKU executable file TwoPunctureABE; recompile TwoPunctureABE in AMSS_NCKU_source. " )
-        print( " When recompilation is finished, press Enter to continue. " )
-        inputvalue = input()
-
-    ## Copy the TwoPunctureABE executable into the run directory
-    shutil.copy2(TwoPuncture_file, output_directory)
-
-##################################################################
-
-## If the initial-data method is TwoPuncture, generate the TwoPuncture input files
-
-if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
-
-    print()
-    print( " Initial data is chosen as Ansorg-TwoPuncture" )
-    print()
-    
-    print()
-    print( " Automatically generating the input parfile for the TwoPunctureABE executable " )
-    print()
-    
-    import generate_TwoPuncture_input
-    
-    generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
-    
-    print()
-    print( " The input parfile for the TwoPunctureABE executable has been generated. " )
-    print()
-    
-    ## Generated AMSS-NCKU TwoPuncture input filename
-    AMSS_NCKU_TwoPuncture_inputfile      = 'AMSS-NCKU-TwoPuncture.input'
-    AMSS_NCKU_TwoPuncture_inputfile_path = os.path.join( File_directory, AMSS_NCKU_TwoPuncture_inputfile )
- 
-    ## Copy and rename the file
-    shutil.copy2( AMSS_NCKU_TwoPuncture_inputfile_path, os.path.join(output_directory, 'TwoPunctureinput.par') )
-    
-    ## Run TwoPuncture to generate initial-data files
-    
-    start_time = time.time()  # Record start time
-
-    print()
-    print()
-    
-    ## Change to the output (run) directory
-    os.chdir(output_directory)
-
-    ## Run the TwoPuncture executable
-    import makefile_and_run
-    makefile_and_run.run_TwoPunctureABE()
-    
-    ## Change current working directory back up two levels
-    os.chdir('..')
-    os.chdir('..')
-
-elif (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and skip_twopuncture:
-    print()
-    print( " Skipping TwoPuncture execution, using existing initial data." )
-    print()
-    start_time = time.time()  # Record start time for ABE only
-else:
-    start_time = time.time()  # Record start time
-    
-##################################################################
-    
-## Update puncture data based on TwoPuncture run results
-
-if not skip_twopuncture:
-    import renew_puncture_parameter
-    renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
-
-    ## Generated AMSS-NCKU input filename
-    AMSS_NCKU_inputfile      = 'AMSS-NCKU.input'
-    AMSS_NCKU_inputfile_path = os.path.join(File_directory, AMSS_NCKU_inputfile)
- 
-    ## Copy and rename the file
-    shutil.copy2( AMSS_NCKU_inputfile_path, os.path.join(output_directory, 'input.par') )
-
-    print()
-    print( " Successfully copy all AMSS-NCKU input parfile to target dictionary. " )
-    print()
-else:
-    print()
-    print( " Using existing input.par file from previous run." )
-    print()
-
-##################################################################
-
-## Launch the AMSS-NCKU program
-
-print()
-print()
-
-## Change to the run directory
-os.chdir( output_directory )
-
-import makefile_and_run
-makefile_and_run.run_ABE()
-
-## Change current working directory back up two levels
-os.chdir('..')
-os.chdir('..')
-
-end_time = time.time()
-elapsed_time = end_time - start_time
-
-##################################################################
-
-## Copy some basic input and log files out to facilitate debugging
-
-## Path to the file that stores calculation settings
-AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "setting.par")
-## Copy and rename the file for easier inspection
-shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "AMSSNCKU_setting_parameter") )
-
-## Path to the error log file
-AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "Error.log")
-## Copy and rename the error log
-shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "Error.log") )
-
-## Primary program outputs
-AMSS_NCKU_BH_data         = os.path.join(binary_results_directory, "bssn_BH.dat"        )
-AMSS_NCKU_ADM_data        = os.path.join(binary_results_directory, "bssn_ADMQs.dat"     )
-AMSS_NCKU_psi4_data       = os.path.join(binary_results_directory, "bssn_psi4.dat"      )
-AMSS_NCKU_constraint_data = os.path.join(binary_results_directory, "bssn_constraint.dat")
-## copy and rename the file
-shutil.copy( AMSS_NCKU_BH_data,         os.path.join(output_directory, "bssn_BH.dat"        ) )
-shutil.copy( AMSS_NCKU_ADM_data,        os.path.join(output_directory, "bssn_ADMQs.dat"     ) )
-shutil.copy( AMSS_NCKU_psi4_data,       os.path.join(output_directory, "bssn_psi4.dat"      ) )
-shutil.copy( AMSS_NCKU_constraint_data, os.path.join(output_directory, "bssn_constraint.dat") )
-
-## Additional program outputs
-if (input_data.Equation_Class == "BSSN-EM"):
-    AMSS_NCKU_phi1_data = os.path.join(binary_results_directory, "bssn_phi1.dat" )
-    AMSS_NCKU_phi2_data = os.path.join(binary_results_directory, "bssn_phi2.dat" )
-    shutil.copy( AMSS_NCKU_phi1_data, os.path.join(output_directory, "bssn_phi1.dat" ) )
-    shutil.copy( AMSS_NCKU_phi2_data, os.path.join(output_directory, "bssn_phi2.dat" ) )
-elif (input_data.Equation_Class == "BSSN-EScalar"):
-    AMSS_NCKU_maxs_data = os.path.join(binary_results_directory, "bssn_maxs.dat" )
-    shutil.copy( AMSS_NCKU_maxs_data, os.path.join(output_directory, "bssn_maxs.dat" ) )
-
-##################################################################
-
-## Plot the AMSS-NCKU program results
-
-print()
-print( " Plotting the txt and binary results data from the AMSS-NCKU simulation " )
-print()
-
-
-import plot_xiaoqu
-import plot_GW_strain_amplitude_xiaoqu
-
-## Plot black hole trajectory
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
-
-## Plot black hole separation vs. time
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
-
-## Plot gravitational waveforms (psi4 and strain amplitude)
-for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
-    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
-
-## Plot ADM mass evolution
-for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
-
-## Plot Hamiltonian constraint violation over time
-for i in range(input_data.grid_level):
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
-
-## Plot stored binary data
-plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
-
-print()
-print( f" This Program Cost = {elapsed_time} Seconds " )
-print()
-
-
-##################################################################
-
-print()
-print( " The AMSS-NCKU-Python simulation is successfully finished, thanks for using !!! " )
-print()
-
-##################################################################
-
-

AMSS_NCKU_Program.py

@@ -8,6 +8,14 @@
 ##
 ##################################################################
 
+## Guard against re-execution by multiprocessing child processes.
+## Without this, using 'spawn' or 'forkserver' context would cause every
+## worker to re-run the entire script, spawning exponentially more
+## workers (fork bomb).
+if __name__ != '__main__':
+    import sys as _sys
+    _sys.exit(0)
+
 
 ##################################################################
 
@@ -166,11 +174,14 @@ import generate_macrodef
 generate_macrodef.generate_macrodef_h()
 print( " AMSS-NCKU macro file macrodef.h has been generated. " )
      
-generate_macrodef.generate_macrodef_fh()
-print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
-
-
-##################################################################
+generate_macrodef.generate_macrodef_fh()
+print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
+
+generate_macrodef.generate_build_config()
+print( " AMSS-NCKU build config AMSS_NCKU_build.mk has been generated. " )
+
+
+##################################################################
 
 # Compile the AMSS-NCKU program according to user requirements
 
@@ -209,11 +220,13 @@ shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
 
 # Copy the generated macro files into the AMSS_NCKU source folder
 
-macrodef_h_path  = os.path.join(File_directory, "macrodef.h") 
-macrodef_fh_path = os.path.join(File_directory, "macrodef.fh") 
-
-shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
-shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
+macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
+macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
+build_config_path = os.path.join(File_directory, "AMSS_NCKU_build.mk")
+
+shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
+shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
+shutil.copy2(build_config_path, AMSS_NCKU_source_copy)
 
 # Notes on copying files:
 # shutil.copy2 preserves file metadata such as modification time.
@@ -262,6 +275,12 @@ if not os.path.exists( ABE_file ):
 ## Copy the executable ABE (or ABEGPU) into the run directory
 shutil.copy2(ABE_file, output_directory)
 
+## Copy interp load balance profile if present (for optimize pass)
+interp_lb_profile = os.path.join(AMSS_NCKU_source_copy, "interp_lb_profile.bin")
+if os.path.exists(interp_lb_profile):
+    shutil.copy2(interp_lb_profile, output_directory)
+    print( " Copied interp_lb_profile.bin to run directory " )
+
 ###########################
 
 ## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
@@ -424,26 +443,31 @@ print(
 
 import plot_xiaoqu
 import plot_GW_strain_amplitude_xiaoqu
+from parallel_plot_helper import run_plot_tasks_parallel
+
+plot_tasks = []
 
 ## Plot black hole trajectory
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
 
 ## Plot black hole separation vs. time
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
 
 ## Plot gravitational waveforms (psi4 and strain amplitude)
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
-    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
 
 ## Plot ADM mass evolution
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
 
 ## Plot Hamiltonian constraint violation over time
 for i in range(input_data.grid_level):
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
+
+run_plot_tasks_parallel(plot_tasks)
 
 ## Plot stored binary data
 plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )

AMSS_NCKU_Program_Plot.py

@@ -0,0 +1,100 @@
+##################################################################
+##
+## AMSS-NCKU Plot-Only Restart Script
+## Author: Xiaoqu / Claude
+## 2026/05/12
+##
+## This script checks for existing output data from AMSS_NCKU_Program.py.
+## If data exists, it skips all computation and goes directly to plotting,
+## saving time when plotting was interrupted.
+## If no data is found, it exits with a message.
+##
+##################################################################
+
+## Guard against re-execution by multiprocessing child processes.
+if __name__ != '__main__':
+    import sys as _sys
+    _sys.exit(0)
+
+
+import os
+import sys
+
+import AMSS_NCKU_Input as input_data
+
+##################################################################
+
+## Construct paths from input configuration
+File_directory         = os.path.join(input_data.File_directory)
+output_directory       = os.path.join(File_directory, "AMSS_NCKU_output")
+binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
+figure_directory       = os.path.join(File_directory, "figure")
+
+##################################################################
+
+## Check whether the required output data files exist
+
+required_files = [
+    os.path.join(binary_results_directory, "bssn_BH.dat"),
+    os.path.join(binary_results_directory, "bssn_ADMQs.dat"),
+    os.path.join(binary_results_directory, "bssn_psi4.dat"),
+    os.path.join(binary_results_directory, "bssn_constraint.dat"),
+]
+
+missing_files = [f for f in required_files if not os.path.exists(f)]
+
+if missing_files:
+    print(" No existing AMSS_NCKU_Program.py output data found. ")
+    print(" The following required files are missing: ")
+    for f in missing_files:
+        print(f"   {f}")
+    print()
+    print(" Please run AMSS_NCKU_Program.py first to generate the simulation data. ")
+    print(" Exiting. ")
+    sys.exit(1)
+
+print(" Found existing AMSS_NCKU_Program.py output data. "          )
+print(" Skipping all computation and going directly to plotting. " )
+print()
+
+## Ensure the figure directory exists (it should, but be safe)
+os.makedirs(figure_directory, exist_ok=True)
+
+##################################################################
+
+## Plot the AMSS-NCKU program results
+
+import plot_xiaoqu
+import plot_GW_strain_amplitude_xiaoqu
+from parallel_plot_helper import run_plot_tasks_parallel
+
+plot_tasks = []
+
+## Plot black hole trajectory
+plot_tasks.append((plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory)))
+plot_tasks.append((plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory)))
+
+## Plot black hole separation vs. time
+plot_tasks.append((plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory)))
+
+## Plot gravitational waveforms (psi4 and strain amplitude)
+for i in range(input_data.Detector_Number):
+    plot_tasks.append((plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i)))
+    plot_tasks.append((plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i)))
+
+## Plot ADM mass evolution
+for i in range(input_data.Detector_Number):
+    plot_tasks.append((plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i)))
+
+## Plot Hamiltonian constraint violation over time
+for i in range(input_data.grid_level):
+    plot_tasks.append((plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i)))
+
+run_plot_tasks_parallel(plot_tasks)
+
+## Plot stored binary data (runs serially, not in the parallel pool)
+plot_xiaoqu.generate_binary_data_plot(binary_results_directory, figure_directory)
+
+print()
+print(" Plotting completed successfully. ")
+print()

AMSS_NCKU_Verify_ASC26.py

@@ -1,10 +1,19 @@
 #!/usr/bin/env python3
 """
-AMSS-NCKU GW150914 Simulation Regression Test Script
+AMSS-NCKU GW150914 Simulation Regression Test Script (Comprehensive Version)
 
-Verification Requirements:
-1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
-2. ADM constraint violation < 2 (Grid Level 0)
+Verification Requirements:
+1. RMS errors < 1% for:
+   - 3D Vector Total RMS
+   - X Component RMS
+   - Y Component RMS
+   - Z Component RMS
+2. ADM constraint violation < 2 (Grid Level 0)
+3. The following figure PDFs must match GW150914-origin exactly after rasterization:
+   - ADM_Constraint_Grid_Level_0.pdf
+   - BH_Trajectory_21_XY.pdf
+   - BH_Trajectory_XY.pdf
+   The script also reports the percentage of differing pixels for each figure.
 
 RMS Calculation Method:
 - Computes trajectory deviation on the XY plane independently for BH1 and BH2
@@ -16,9 +25,13 @@ Default: output_dir = GW150914/AMSS_NCKU_output
 Reference: GW150914-origin (baseline simulation)
 """
 
-import numpy as np
-import sys
-import os
+import numpy as np
+import sys
+import os
+import shutil
+import subprocess
+import tempfile
+from PIL import Image
 
 # ANSI Color Codes
 class Color:
@@ -45,91 +58,200 @@ def load_bh_trajectory(filepath):
     }
 
 
-def load_constraint_data(filepath):
-    """Load constraint violation data"""
-    data = []
+def load_constraint_data(filepath):
+    """Load constraint violation data"""
+    data = []
     with open(filepath, 'r') as f:
         for line in f:
             if line.startswith('#'):
                 continue
             parts = line.split()
             if len(parts) >= 8:
-                data.append([float(x) for x in parts[:8]])
-    return np.array(data)
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
+
+
+def resolve_figure_dir(path):
+    """Resolve the sibling figure directory from an output or figure path."""
+    normalized = os.path.normpath(path)
+    if os.path.basename(normalized) == "figure":
+        return normalized
+    return os.path.join(os.path.dirname(normalized), "figure")
+
+
+def render_pdf_to_images(pdf_path, dpi=150):
+    """Render a PDF to RGB images using Ghostscript."""
+    gs_path = shutil.which("gs")
+    if gs_path is None:
+        raise RuntimeError("Ghostscript executable 'gs' was not found in PATH")
+
+    with tempfile.TemporaryDirectory(prefix="amss_verify_pdf_") as temp_dir:
+        output_pattern = os.path.join(temp_dir, "page-%03d.ppm")
+        cmd = [
+            gs_path,
+            "-q",
+            "-dSAFER",
+            "-dBATCH",
+            "-dNOPAUSE",
+            "-sDEVICE=ppmraw",
+            f"-r{dpi}",
+            f"-o{output_pattern}",
+            pdf_path
+        ]
+
+        try:
+            subprocess.run(cmd, check=True, stdout=subprocess.DEVNULL, stderr=subprocess.PIPE, text=True)
+        except subprocess.CalledProcessError as exc:
+            message = exc.stderr.strip() or str(exc)
+            raise RuntimeError(f"Failed to render PDF '{pdf_path}': {message}") from exc
+
+        ppm_files = sorted(
+            os.path.join(temp_dir, filename)
+            for filename in os.listdir(temp_dir)
+            if filename.endswith(".ppm")
+        )
+
+        if not ppm_files:
+            raise RuntimeError(f"No rendered pages were produced for '{pdf_path}'")
+
+        images = []
+        for ppm_file in ppm_files:
+            with Image.open(ppm_file) as img:
+                images.append(np.array(img.convert("RGB"), dtype=np.uint8))
+
+        return images
+
+
+def compare_rendered_pages(ref_img, target_img):
+    """Return (different_pixels, total_pixels) for two rendered RGB pages."""
+    ref_h, ref_w = ref_img.shape[:2]
+    tgt_h, tgt_w = target_img.shape[:2]
+    total_pixels = max(ref_h, tgt_h) * max(ref_w, tgt_w)
+
+    if ref_h == tgt_h and ref_w == tgt_w:
+        different_pixels = int(np.count_nonzero(np.any(ref_img != target_img, axis=2)))
+        return different_pixels, total_pixels
+
+    diff_mask = np.ones((max(ref_h, tgt_h), max(ref_w, tgt_w)), dtype=bool)
+    overlap_h = min(ref_h, tgt_h)
+    overlap_w = min(ref_w, tgt_w)
+    overlap_diff = np.any(ref_img[:overlap_h, :overlap_w] != target_img[:overlap_h, :overlap_w], axis=2)
+    diff_mask[:overlap_h, :overlap_w] = overlap_diff
+    different_pixels = int(np.count_nonzero(diff_mask))
+    return different_pixels, total_pixels
+
+
+def compare_pdf_images(ref_pdf, target_pdf, dpi=150, threshold_percent=0.001):
+    """Compare two PDFs by rasterizing them and counting differing pixels."""
+    ref_pages = render_pdf_to_images(ref_pdf, dpi=dpi)
+    target_pages = render_pdf_to_images(target_pdf, dpi=dpi)
+
+    total_pixels = 0
+    different_pixels = 0
+    max_pages = max(len(ref_pages), len(target_pages))
+
+    for page_idx in range(max_pages):
+        if page_idx < len(ref_pages) and page_idx < len(target_pages):
+            page_diff, page_total = compare_rendered_pages(ref_pages[page_idx], target_pages[page_idx])
+        else:
+            existing_page = ref_pages[page_idx] if page_idx < len(ref_pages) else target_pages[page_idx]
+            page_total = existing_page.shape[0] * existing_page.shape[1]
+            page_diff = page_total
+
+        total_pixels += page_total
+        different_pixels += page_diff
+
+    diff_percent = (different_pixels / total_pixels * 100.0) if total_pixels else 0.0
+    return {
+        "different_pixels": different_pixels,
+        "total_pixels": total_pixels,
+        "diff_percent": diff_percent,
+        "pages_ref": len(ref_pages),
+        "pages_target": len(target_pages),
+        "passed": diff_percent < threshold_percent
+    }
+
+
+def compare_required_figures(reference_figure_dir, target_figure_dir):
+    """Compare the required GW150914 figure PDFs."""
+    figure_names = [
+        "ADM_Constraint_Grid_Level_0.pdf",
+        "BH_Trajectory_21_XY.pdf",
+        "BH_Trajectory_XY.pdf"
+    ]
+
+    results = []
+    for figure_name in figure_names:
+        ref_pdf = os.path.join(reference_figure_dir, figure_name)
+        target_pdf = os.path.join(target_figure_dir, figure_name)
+
+        if not os.path.exists(ref_pdf):
+            raise FileNotFoundError(f"Reference figure not found: {ref_pdf}")
+        if not os.path.exists(target_pdf):
+            raise FileNotFoundError(f"Target figure not found: {target_pdf}")
+
+        comparison = compare_pdf_images(ref_pdf, target_pdf)
+        comparison["name"] = figure_name
+        results.append(comparison)
+
+    return results
 
-
-def calculate_rms_error(bh_data_ref, bh_data_target):
+def calculate_all_rms_errors(bh_data_ref, bh_data_target):
     """
-    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
-
-    This function computes the RMS error independently for BH1 and BH2 trajectories,
-    then returns the maximum of the two as the final RMS error metric.
-
-    For each black hole, the RMS is calculated as:
-        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
-
-    where:
-        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
-        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
-
-    Args:
-        bh_data_ref: Reference (baseline) trajectory data
-        bh_data_target: Target (optimized) trajectory data
-
-    Returns:
-        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
-        error: Error message if any
+    Calculate 3D Vector RMS and component-wise RMS (X, Y, Z) independently.
+    Uses r = sqrt(x^2 + y^2) as the denominator for all error normalizations.
+    Returns the maximum error between BH1 and BH2 for each category.
     """
-    # Align data: truncate to the length of the shorter dataset
     M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
 
     if M < 10:
         return None, "Insufficient data points for comparison"
 
-    # Extract XY coordinates for both black holes
-    x1_ref = bh_data_ref['x1'][:M]
-    y1_ref = bh_data_ref['y1'][:M]
-    x2_ref = bh_data_ref['x2'][:M]
-    y2_ref = bh_data_ref['y2'][:M]
+    results = {}
 
-    x1_new = bh_data_target['x1'][:M]
-    y1_new = bh_data_target['y1'][:M]
-    x2_new = bh_data_target['x2'][:M]
-    y2_new = bh_data_target['y2'][:M]
+    for bh in ['1', '2']:
+        x_r, y_r, z_r = bh_data_ref[f'x{bh}'][:M], bh_data_ref[f'y{bh}'][:M], bh_data_ref[f'z{bh}'][:M]
+        x_n, y_n, z_n = bh_data_target[f'x{bh}'][:M], bh_data_target[f'y{bh}'][:M], bh_data_target[f'z{bh}'][:M]
 
-    # Calculate RMS for BH1
-    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
-    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
-    r1_new = np.sqrt(x1_new**2 + y1_new**2)
-    r1_max = np.maximum(r1_ref, r1_new)
+        # 核心修改：根据组委会的邮件指示，分母统一使用 r = sqrt(x^2 + y^2)
+        r_ref = np.sqrt(x_r**2 + y_r**2)
+        r_new = np.sqrt(x_n**2 + y_n**2)
+        denom_max = np.maximum(r_ref, r_new)
 
-    # Calculate RMS for BH2
-    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
-    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
-    r2_new = np.sqrt(x2_new**2 + y2_new**2)
-    r2_max = np.maximum(r2_ref, r2_new)
+        valid = denom_max > 1e-15
+        if np.sum(valid) < 10:
+            results[f'BH{bh}'] = { '3D_Vector': 0.0, 'X_Component': 0.0, 'Y_Component': 0.0, 'Z_Component': 0.0 }
+            continue
 
-    # Avoid division by zero for BH1
-    valid_mask1 = r1_max > 1e-15
-    if np.sum(valid_mask1) < 10:
-        return None, "Insufficient valid data points for BH1"
+        def calc_rms(delta):
+            # 将对应分量的偏差除以统一的轨道半径分母 denom_max
+            return np.sqrt(np.mean((delta[valid] / denom_max[valid])**2)) * 100
 
-    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
-    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+        # 1. Total 3D Vector RMS
+        delta_vec = np.sqrt((x_r - x_n)**2 + (y_r - y_n)**2 + (z_r - z_n)**2)
+        rms_3d = calc_rms(delta_vec)
 
-    # Avoid division by zero for BH2
-    valid_mask2 = r2_max > 1e-15
-    if np.sum(valid_mask2) < 10:
-        return None, "Insufficient valid data points for BH2"
+        # 2. Component-wise RMS (分离计算各轴，但共用半径分母)
+        rms_x = calc_rms(np.abs(x_r - x_n))
+        rms_y = calc_rms(np.abs(y_r - y_n))
+        rms_z = calc_rms(np.abs(z_r - z_n))
 
-    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
-    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+        results[f'BH{bh}'] = {
+            '3D_Vector': rms_3d,
+            'X_Component': rms_x,
+            'Y_Component': rms_y,
+            'Z_Component': rms_z
+        }
 
-    # Final RMS is the maximum of BH1 and BH2
-    rms_final = max(rms_bh1, rms_bh2)
-
-    return rms_final, None
+    # 获取 BH1 和 BH2 中的最大误差
+    max_rms = {
+        '3D_Vector': max(results['BH1']['3D_Vector'], results['BH2']['3D_Vector']),
+        'X_Component': max(results['BH1']['X_Component'], results['BH2']['X_Component']),
+        'Y_Component': max(results['BH1']['Y_Component'], results['BH2']['Y_Component']),
+        'Z_Component': max(results['BH1']['Z_Component'], results['BH2']['Z_Component'])
+    }
 
+    return max_rms, None
 
 def analyze_constraint_violation(constraint_data, n_levels=9):
     """
@@ -155,34 +277,32 @@ def analyze_constraint_violation(constraint_data, n_levels=9):
 
 
 def print_header():
-    """Print report header"""
     print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "   AMSS-NCKU GW150914 Simulation Regression Test Report" + Color.RESET)
+    print(Color.BOLD + "   AMSS-NCKU GW150914 Comprehensive Regression Test" + Color.RESET)
     print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
 
-
-def print_rms_results(rms_rel, error, threshold=1.0):
-    """Print RMS error results"""
-    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
-    print("-" * 45)
+def print_rms_results(rms_dict, error, threshold=1.0):
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Maximums of BH1 & BH2){Color.RESET}")
+    print("-" * 65)
 
     if error:
         print(f"   {Color.RED}Error: {error}{Color.RESET}")
         return False
 
-    passed = rms_rel < threshold
+    all_passed = True
+    print(f"   Requirement: < {threshold}%\n")
 
-    print(f"   RMS relative error: {rms_rel:.4f}%")
-    print(f"   Requirement:        < {threshold}%")
-    print(f"   Status:             {get_status_text(passed)}")
+    for key, val in rms_dict.items():
+        passed = val < threshold
+        all_passed = all_passed and passed
+        status = get_status_text(passed)
+        print(f"   {key:15}: {val:8.4f}%   |   Status: {status}")
 
-    return passed
+    return all_passed
 
-
-def print_constraint_results(results, threshold=2.0):
-    """Print constraint violation results"""
+def print_constraint_results(results, threshold=2.0):
     print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
-    print("-" * 45)
+    print("-" * 65)
 
     names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
     for i, name in enumerate(names):
@@ -195,23 +315,49 @@ def print_constraint_results(results, threshold=2.0):
     print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
     print(f"   Requirement:        < {threshold}")
     print(f"   Status:             {get_status_text(passed)}")
-
-    return passed
-
-
-def print_summary(rms_passed, constraint_passed):
-    """Print summary"""
-    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "Verification Summary" + Color.RESET)
-    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-
-    all_passed = rms_passed and constraint_passed
-    
-    res_rms = get_status_text(rms_passed)
-    res_con = get_status_text(constraint_passed)
-
-    print(f"   [1] RMS trajectory check:         {res_rms}")
-    print(f"   [2] ADM constraint check:         {res_con}")
+
+    return passed
+
+
+def print_figure_results(results, threshold_percent=0.001):
+    print(f"\n{Color.BOLD}3. Figure Pixel Comparison (PDF Rasterization){Color.RESET}")
+    print("-" * 65)
+    print(f"   Requirement: < {threshold_percent:.3f}% differing pixels\n")
+
+    all_passed = True
+    for result in results:
+        passed = result["passed"]
+        all_passed = all_passed and passed
+        status = get_status_text(passed)
+        print(f"   {result['name']:32}: {result['diff_percent']:10.6f}%   |   Status: {status}")
+
+        if result["pages_ref"] != result["pages_target"]:
+            print(f"   {'':32}  pages(ref/target): {result['pages_ref']}/{result['pages_target']}")
+
+    return all_passed
+
+
+def print_figure_error(error_message):
+    print(f"\n{Color.BOLD}3. Figure Pixel Comparison (PDF Rasterization){Color.RESET}")
+    print("-" * 65)
+    print(f"   {Color.RED}Error: {error_message}{Color.RESET}")
+    return False
+
+
+def print_summary(rms_passed, constraint_passed, figure_passed):
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "Verification Summary" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+    all_passed = rms_passed and constraint_passed and figure_passed
+    
+    res_rms = get_status_text(rms_passed)
+    res_con = get_status_text(constraint_passed)
+    res_fig = get_status_text(figure_passed)
+
+    print(f"   [1] Comprehensive RMS check:      {res_rms}")
+    print(f"   [2] ADM constraint check:         {res_con}")
+    print(f"   [3] Figure pixel comparison:      {res_fig}")
     
     final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
     print(f"\n   Overall result: {final_status}")
@@ -219,61 +365,58 @@ def print_summary(rms_passed, constraint_passed):
 
     return all_passed
 
-
 def main():
-    # Determine target (optimized) output directory
     if len(sys.argv) > 1:
         target_dir = sys.argv[1]
     else:
         script_dir = os.path.dirname(os.path.abspath(__file__))
         target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
 
-    # Determine reference (baseline) directory
-    script_dir = os.path.dirname(os.path.abspath(__file__))
-    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+    script_dir = os.path.dirname(os.path.abspath(__file__))
+    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+    target_figure_dir = resolve_figure_dir(target_dir)
+    reference_figure_dir = os.path.join(script_dir, "GW150914-origin/figure")
+
+    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
+    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
+    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
 
-    # Data file paths
-    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
-    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
-    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
-
-    # Check if files exist
     if not os.path.exists(bh_file_ref):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
         sys.exit(1)
-
     if not os.path.exists(bh_file_target):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Target trajectory file not found: {bh_file_target}")
         sys.exit(1)
-
     if not os.path.exists(constraint_file):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
         sys.exit(1)
 
-    # Print header
-    print_header()
-    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
-    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+    print_header()
+    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Reference Figures:   {Color.RESET} {Color.BLUE}{reference_figure_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target Figures:      {Color.RESET} {Color.BLUE}{target_figure_dir}{Color.RESET}")
 
-    # Load data
     bh_data_ref = load_bh_trajectory(bh_file_ref)
     bh_data_target = load_bh_trajectory(bh_file_target)
     constraint_data = load_constraint_data(constraint_file)
 
-    # Calculate RMS error
-    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
-    rms_passed = print_rms_results(rms_rel, error)
-
-    # Analyze constraint violation
-    constraint_results = analyze_constraint_violation(constraint_data)
-    constraint_passed = print_constraint_results(constraint_results)
-
-    # Print summary
-    all_passed = print_summary(rms_passed, constraint_passed)
-
-    # Return exit code
-    sys.exit(0 if all_passed else 1)
+    # Output modified RMS results
+    rms_dict, error = calculate_all_rms_errors(bh_data_ref, bh_data_target)
+    rms_passed = print_rms_results(rms_dict, error)
 
+    # Output constraint results
+    constraint_results = analyze_constraint_violation(constraint_data)
+    constraint_passed = print_constraint_results(constraint_results)
+
+    try:
+        figure_results = compare_required_figures(reference_figure_dir, target_figure_dir)
+        figure_passed = print_figure_results(figure_results)
+    except (FileNotFoundError, RuntimeError) as exc:
+        figure_passed = print_figure_error(str(exc))
+
+    all_passed = print_summary(rms_passed, constraint_passed, figure_passed)
+    sys.exit(0 if all_passed else 1)
 
 if __name__ == "__main__":
     main()

AMSS_NCKU_source/MPatch.C

@@ -7,12 +7,178 @@
 #include <string>
 #include <cmath>
 #include <new>
+#include <vector>
 using namespace std;
 
 #include "misc.h"
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
+#ifdef INTERP_LB_PROFILE
+#include "interp_lb_profile.h"
+#endif
+
+namespace
+{
+struct InterpBlockView
+{
+  Block *bp;
+  double llb[dim];
+  double uub[dim];
+};
+
+struct BlockBinIndex
+{
+  int bins[dim];
+  double lo[dim];
+  double inv[dim];
+  vector<InterpBlockView> views;
+  vector<vector<int>> bin_to_blocks;
+  bool valid;
+
+  BlockBinIndex() : valid(false)
+  {
+    for (int i = 0; i < dim; i++)
+    {
+      bins[i] = 1;
+      lo[i] = 0.0;
+      inv[i] = 0.0;
+    }
+  }
+};
+
+inline int clamp_int(int v, int lo, int hi)
+{
+  return (v < lo) ? lo : ((v > hi) ? hi : v);
+}
+
+inline int coord_to_bin(double x, double lo, double inv, int nb)
+{
+  if (nb <= 1 || inv <= 0.0)
+    return 0;
+  int b = int(floor((x - lo) * inv));
+  return clamp_int(b, 0, nb - 1);
+}
+
+inline int bin_loc(const BlockBinIndex &index, int b0, int b1, int b2)
+{
+  return b0 + index.bins[0] * (b1 + index.bins[1] * b2);
+}
+
+inline bool point_in_block_view(const InterpBlockView &view, const double *pox, const double *DH)
+{
+  for (int i = 0; i < dim; i++)
+  {
+    if (pox[i] - view.llb[i] < -DH[i] / 2 || pox[i] - view.uub[i] > DH[i] / 2)
+      return false;
+  }
+  return true;
+}
+
+void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
+{
+  index = BlockBinIndex();
+
+  MyList<Block> *Bp = patch->blb;
+  while (Bp)
+  {
+    Block *BP = Bp->data;
+    InterpBlockView view;
+    view.bp = BP;
+    for (int i = 0; i < dim; i++)
+    {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
+#else
+#ifdef Cell
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+    }
+    index.views.push_back(view);
+    if (Bp == patch->ble)
+      break;
+    Bp = Bp->next;
+  }
+
+  const int nblocks = int(index.views.size());
+  if (nblocks <= 0)
+    return;
+
+  int bins_1d = int(ceil(pow(double(nblocks), 1.0 / 3.0)));
+  bins_1d = clamp_int(bins_1d, 1, 32);
+  for (int i = 0; i < dim; i++)
+  {
+    index.bins[i] = bins_1d;
+    index.lo[i] = patch->bbox[i] + patch->lli[i] * DH[i];
+    const double hi = patch->bbox[dim + i] - patch->uui[i] * DH[i];
+    if (hi > index.lo[i] && bins_1d > 1)
+      index.inv[i] = bins_1d / (hi - index.lo[i]);
+    else
+      index.inv[i] = 0.0;
+  }
+
+  index.bin_to_blocks.resize(index.bins[0] * index.bins[1] * index.bins[2]);
+
+  for (int bi = 0; bi < nblocks; bi++)
+  {
+    const InterpBlockView &view = index.views[bi];
+    int bmin[dim], bmax[dim];
+    for (int d = 0; d < dim; d++)
+    {
+      const double low = view.llb[d] - DH[d] / 2;
+      const double up = view.uub[d] + DH[d] / 2;
+      bmin[d] = coord_to_bin(low, index.lo[d], index.inv[d], index.bins[d]);
+      bmax[d] = coord_to_bin(up, index.lo[d], index.inv[d], index.bins[d]);
+      if (bmax[d] < bmin[d])
+      {
+        int t = bmin[d];
+        bmin[d] = bmax[d];
+        bmax[d] = t;
+      }
+    }
+
+    for (int bz = bmin[2]; bz <= bmax[2]; bz++)
+      for (int by = bmin[1]; by <= bmax[1]; by++)
+        for (int bx = bmin[0]; bx <= bmax[0]; bx++)
+          index.bin_to_blocks[bin_loc(index, bx, by, bz)].push_back(bi);
+  }
+
+  index.valid = true;
+}
+
+int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
+{
+  if (!index.valid)
+    return -1;
+
+  const int bx = coord_to_bin(pox[0], index.lo[0], index.inv[0], index.bins[0]);
+  const int by = coord_to_bin(pox[1], index.lo[1], index.inv[1], index.bins[1]);
+  const int bz = coord_to_bin(pox[2], index.lo[2], index.inv[2], index.bins[2]);
+  const vector<int> &cand = index.bin_to_blocks[bin_loc(index, bx, by, bz)];
+
+  for (size_t ci = 0; ci < cand.size(); ci++)
+  {
+    const int bi = cand[ci];
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return bi;
+  }
+
+  // Fallback to full scan for numerical edge cases around bin boundaries.
+  for (size_t bi = 0; bi < index.views.size(); bi++)
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return int(bi);
+
+  return -1;
+}
+} // namespace
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -341,8 +507,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
                           double *Shellf, int Symmetry)
 {
   // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
-  int myrank;
+  int myrank, nprocs;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
 
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
@@ -354,24 +521,20 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  double *shellf;
-  shellf = new double[NN * num_var];
-  memset(shellf, 0, sizeof(double) * NN * num_var);
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // we use weight to monitor code, later some day we can move it for optimization
-  int *weight;
-  weight = new int[NN];
-  memset(weight, 0, sizeof(int) * NN);
-
-  double *DH, *llb, *uub;
-  DH = new double[dim];
+  // owner_rank[j] records which MPI rank owns point j
+  // All ranks traverse the same block list so they all agree on ownership
+  int *owner_rank;
+  owner_rank = new int[NN];
+  for (int j = 0; j < NN; j++)
+    owner_rank[j] = -1;
 
+  double DH[dim];
   for (int i = 0; i < dim; i++)
-  {
     DH[i] = getdX(i);
-  }
-  llb = new double[dim];
-  uub = new double[dim];
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -394,165 +557,350 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
-    bool notfind = true;
-    while (notfind && Bp) // run along Blocks
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i >= 0)
     {
-      Block *BP = Bp->data;
-
-      bool flag = true;
-      for (int i = 0; i < dim; i++)
+      Block *BP = block_index.views[block_i].bp;
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
       {
-// NOTE: our dividing structure is (exclude ghost)
-// -1 0
-//       1  2
-// so (0,1) does not belong to any part for vertex structure
-// here we put (0,0.5) to left part and (0.5,1) to right part
-// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
+        //---> interpolation
+        varl = VarList;
+        int k = 0;
+        while (varl) // run along variables
         {
-          flag = false;
-          break;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
-            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-          weight[j] = 1;
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
-  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  int *Weight;
-  Weight = new int[NN];
-  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-
-  //  misc::tillherecheck("print me");
-
-  for (int i = 0; i < NN; i++)
+  // Replace MPI_Allreduce with per-owner MPI_Bcast:
+  // Group consecutive points by owner rank and broadcast each group.
+  // Since each point's data is non-zero only on the owner rank,
+  // Bcast from owner is equivalent to Allreduce(MPI_SUM) but much cheaper.
   {
-    if (Weight[i] > 1)
+    int j = 0;
+    while (j < NN)
     {
-      if (myrank == 0)
-        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
-      for (int j = 0; j < num_var; j++)
-        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+      int cur_owner = owner_rank[j];
+      if (cur_owner < 0)
+      {
+        if (myrank == 0)
+        {
+          cout << "ERROR: Patch::Interp_Points fails to find point (";
+          for (int d = 0; d < dim; d++)
+          {
+            cout << XX[d][j];
+            if (d < dim - 1)
+              cout << ",";
+            else
+              cout << ")";
+          }
+          cout << " on Patch (";
+          for (int d = 0; d < dim; d++)
+          {
+            cout << bbox[d] << "+" << lli[d] * DH[d];
+            if (d < dim - 1)
+              cout << ",";
+            else
+              cout << ")--";
+          }
+          cout << "(";
+          for (int d = 0; d < dim; d++)
+          {
+            cout << bbox[dim + d] << "-" << uui[d] * DH[d];
+            if (d < dim - 1)
+              cout << ",";
+            else
+              cout << ")" << endl;
+          }
+          MPI_Abort(MPI_COMM_WORLD, 1);
+        }
+        j++;
+        continue;
+      }
+      // Find contiguous run of points with the same owner
+      int jstart = j;
+      while (j < NN && owner_rank[j] == cur_owner)
+        j++;
+      int count = (j - jstart) * num_var;
+      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner, MPI_COMM_WORLD);
     }
-    else if (Weight[i] == 0 && myrank == 0)
+  }
+
+  delete[] owner_rank;
+}
+void Patch::Interp_Points(MyList<var> *VarList,
+                          int NN, double **XX,
+                          double *Shellf, int Symmetry,
+                          int Nmin_consumer, int Nmax_consumer)
+{
+  // Targeted point-to-point overload: each owner sends each point only to
+  // the one rank that needs it for integration (consumer), reducing
+  // communication volume by ~nprocs times compared to the Bcast version.
+#ifdef INTERP_LB_PROFILE
+  double t_interp_start = MPI_Wtime();
+#endif
+  int myrank, nprocs;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
+
+  int ordn = 2 * ghost_width;
+  MyList<var> *varl;
+  int num_var = 0;
+  varl = VarList;
+  while (varl)
+  {
+    num_var++;
+    varl = varl->next;
+  }
+
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
+
+  // owner_rank[j] records which MPI rank owns point j
+  int *owner_rank;
+  owner_rank = new int[NN];
+  for (int j = 0; j < NN; j++)
+    owner_rank[j] = -1;
+
+  double DH[dim];
+  for (int i = 0; i < dim; i++)
+    DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
+
+  // --- Interpolation phase (identical to original) ---
+  for (int j = 0; j < NN; j++)
+  {
+    double pox[dim];
+    for (int i = 0; i < dim; i++)
+    {
+      pox[i] = XX[i][j];
+      if (myrank == 0 && (XX[i][j] < bbox[i] + lli[i] * DH[i] || XX[i][j] > bbox[dim + i] - uui[i] * DH[i]))
+      {
+        cout << "Patch::Interp_Points: point (";
+        for (int k = 0; k < dim; k++)
+        {
+          cout << XX[k][j];
+          if (k < dim - 1)
+            cout << ",";
+          else
+            cout << ") is out of current Patch." << endl;
+        }
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
+
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i >= 0)
+    {
+      Block *BP = block_index.views[block_i].bp;
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
+      {
+        varl = VarList;
+        int k = 0;
+        while (varl)
+        {
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
+        }
+      }
+    }
+  }
+
+#ifdef INTERP_LB_PROFILE
+  double t_interp_end = MPI_Wtime();
+  double t_interp_local = t_interp_end - t_interp_start;
+#endif
+
+  // --- Error check for unfound points ---
+  for (int j = 0; j < NN; j++)
+  {
+    if (owner_rank[j] < 0 && myrank == 0)
     {
       cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
       {
-        cout << XX[j][i];
-        if (j < dim - 1)
+        cout << XX[d][j];
+        if (d < dim - 1)
           cout << ",";
         else
           cout << ")";
       }
       cout << " on Patch (";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
       {
-        cout << bbox[j] << "+" << lli[j] * getdX(j);
-        if (j < dim - 1)
+        cout << bbox[d] << "+" << lli[d] * DH[d];
+        if (d < dim - 1)
           cout << ",";
         else
           cout << ")--";
       }
       cout << "(";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
       {
-        cout << bbox[dim + j] << "-" << uui[j] * getdX(j);
-        if (j < dim - 1)
+        cout << bbox[dim + d] << "-" << uui[d] * DH[d];
+        if (d < dim - 1)
           cout << ",";
         else
           cout << ")" << endl;
       }
-#if 0
-       checkBlock();
-#else
-      cout << "splited domains:" << endl;
-      {
-        MyList<Block> *Bp = blb;
-        while (Bp)
-        {
-          Block *BP = Bp->data;
-
-          for (int i = 0; i < dim; i++)
-          {
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-          }
-          cout << "(";
-          for (int j = 0; j < dim; j++)
-          {
-            cout << llb[j] << ":" << uub[j];
-            if (j < dim - 1)
-              cout << ",";
-            else
-              cout << ")" << endl;
-          }
-          if (Bp == ble)
-            break;
-          Bp = Bp->next;
-        }
-      }
-#endif
       MPI_Abort(MPI_COMM_WORLD, 1);
     }
   }
 
-  delete[] shellf;
-  delete[] weight;
-  delete[] Weight;
-  delete[] DH;
-  delete[] llb;
-  delete[] uub;
+  // --- Targeted point-to-point communication phase ---
+  // Compute consumer_rank[j] using the same deterministic formula as surface_integral
+  int *consumer_rank = new int[NN];
+  {
+    int mp = NN / nprocs;
+    int Lp = NN - nprocs * mp;
+    for (int j = 0; j < NN; j++)
+    {
+      if (j < Lp * (mp + 1))
+        consumer_rank[j] = j / (mp + 1);
+      else
+        consumer_rank[j] = Lp + (j - Lp * (mp + 1)) / mp;
+    }
+  }
+
+  // Count sends and recvs per rank
+  int *send_count = new int[nprocs];
+  int *recv_count = new int[nprocs];
+  memset(send_count, 0, sizeof(int) * nprocs);
+  memset(recv_count, 0, sizeof(int) * nprocs);
+
+  for (int j = 0; j < NN; j++)
+  {
+    int own = owner_rank[j];
+    int con = consumer_rank[j];
+    if (own == con)
+      continue; // local — no communication needed
+    if (own == myrank)
+      send_count[con]++;
+    if (con == myrank)
+      recv_count[own]++;
+  }
+
+  // Build send buffers: for each destination rank, pack (index, data) pairs
+  // Each entry: 1 int (point index j) + num_var doubles
+  int total_send = 0, total_recv = 0;
+  int *send_offset = new int[nprocs];
+  int *recv_offset = new int[nprocs];
+  for (int r = 0; r < nprocs; r++)
+  {
+    send_offset[r] = total_send;
+    total_send += send_count[r];
+    recv_offset[r] = total_recv;
+    total_recv += recv_count[r];
+  }
+
+  // Pack send buffers: each message contains (j, data[0..num_var-1]) per point
+  int stride = 1 + num_var; // 1 double for index + num_var doubles for data
+  double *sendbuf = new double[total_send * stride];
+  double *recvbuf = new double[total_recv * stride];
+
+  // Temporary counters for packing
+  int *pack_pos = new int[nprocs];
+  memset(pack_pos, 0, sizeof(int) * nprocs);
+
+  for (int j = 0; j < NN; j++)
+  {
+    int own = owner_rank[j];
+    int con = consumer_rank[j];
+    if (own != myrank || con == myrank)
+      continue;
+    int pos = (send_offset[con] + pack_pos[con]) * stride;
+    sendbuf[pos] = (double)j; // point index
+    for (int v = 0; v < num_var; v++)
+      sendbuf[pos + 1 + v] = Shellf[j * num_var + v];
+    pack_pos[con]++;
+  }
+
+  // Post non-blocking recvs and sends
+  int n_req = 0;
+  for (int r = 0; r < nprocs; r++)
+  {
+    if (recv_count[r] > 0) n_req++;
+    if (send_count[r] > 0) n_req++;
+  }
+
+  MPI_Request *reqs = new MPI_Request[n_req];
+  int req_idx = 0;
+
+  for (int r = 0; r < nprocs; r++)
+  {
+    if (recv_count[r] > 0)
+    {
+      MPI_Irecv(recvbuf + recv_offset[r] * stride,
+                recv_count[r] * stride, MPI_DOUBLE,
+                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
+    }
+  }
+  for (int r = 0; r < nprocs; r++)
+  {
+    if (send_count[r] > 0)
+    {
+      MPI_Isend(sendbuf + send_offset[r] * stride,
+                send_count[r] * stride, MPI_DOUBLE,
+                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
+    }
+  }
+
+  if (n_req > 0)
+    MPI_Waitall(n_req, reqs, MPI_STATUSES_IGNORE);
+
+  // Unpack recv buffers into Shellf
+  for (int i = 0; i < total_recv; i++)
+  {
+    int pos = i * stride;
+    int j = (int)recvbuf[pos];
+    for (int v = 0; v < num_var; v++)
+      Shellf[j * num_var + v] = recvbuf[pos + 1 + v];
+  }
+
+  delete[] reqs;
+  delete[] sendbuf;
+  delete[] recvbuf;
+  delete[] pack_pos;
+  delete[] send_offset;
+  delete[] recv_offset;
+  delete[] send_count;
+  delete[] recv_count;
+  delete[] consumer_rank;
+  delete[] owner_rank;
+
+#ifdef INTERP_LB_PROFILE
+  {
+    static bool profile_written = false;
+    if (!profile_written) {
+      double *all_times = nullptr;
+      if (myrank == 0) all_times = new double[nprocs];
+      MPI_Gather(&t_interp_local, 1, MPI_DOUBLE,
+                 all_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
+      if (myrank == 0) {
+        int heavy[64];
+        int nh = InterpLBProfile::identify_heavy_ranks(
+            all_times, nprocs, 2.5, heavy, 64);
+        InterpLBProfile::write_profile(
+            "interp_lb_profile.bin", nprocs,
+            all_times, heavy, nh, 2.5);
+        printf("[InterpLB] Profile written: %d heavy ranks\n", nh);
+        for (int i = 0; i < nh; i++)
+          printf("  Heavy rank %d: %.6f s\n", heavy[i], all_times[heavy[i]]);
+        delete[] all_times;
+      }
+      profile_written = true;
+    }
+  }
+#endif
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
@@ -573,24 +921,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  double *shellf;
-  shellf = new double[NN * num_var];
-  memset(shellf, 0, sizeof(double) * NN * num_var);
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // we use weight to monitor code, later some day we can move it for optimization
-  int *weight;
-  weight = new int[NN];
-  memset(weight, 0, sizeof(int) * NN);
+  // owner_rank[j] stores the global rank that owns point j
+  int *owner_rank;
+  owner_rank = new int[NN];
+  for (int j = 0; j < NN; j++)
+    owner_rank[j] = -1;
 
-  double *DH, *llb, *uub;
-  DH = new double[dim];
+  // Build global-to-local rank translation for Comm_here
+  MPI_Group world_group, local_group;
+  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
+  MPI_Comm_group(Comm_here, &local_group);
 
+  double DH[dim];
   for (int i = 0; i < dim; i++)
-  {
     DH[i] = getdX(i);
-  }
-  llb = new double[dim];
-  uub = new double[dim];
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -613,159 +961,56 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
-    bool notfind = true;
-    while (notfind && Bp) // run along Blocks
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i >= 0)
     {
-      Block *BP = Bp->data;
-
-      bool flag = true;
-      for (int i = 0; i < dim; i++)
+      Block *BP = block_index.views[block_i].bp;
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
       {
-// NOTE: our dividing structure is (exclude ghost)
-// -1 0
-//       1  2
-// so (0,1) does not belong to any part for vertex structure
-// here we put (0,0.5) to left part and (0.5,1) to right part
-// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
+        //---> interpolation
+        varl = VarList;
+        int k = 0;
+        while (varl) // run along variables
         {
-          flag = false;
-          break;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
-            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-          weight[j] = 1;
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
-  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, Comm_here);
-  int *Weight;
-  Weight = new int[NN];
-  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, Comm_here);
-
-  //  misc::tillherecheck("print me");
-  //  if(lmyrank == 0) cout<<"myrank = "<<myrank<<"print me"<<endl;
-
-  for (int i = 0; i < NN; i++)
+  // Collect unique global owner ranks and translate to local ranks in Comm_here
+  // Then broadcast each owner's points via MPI_Bcast on Comm_here
   {
-    if (Weight[i] > 1)
+    int j = 0;
+    while (j < NN)
     {
-      if (lmyrank == 0)
-        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
-      for (int j = 0; j < num_var; j++)
-        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+      int cur_owner_global = owner_rank[j];
+      if (cur_owner_global < 0)
+      {
+        // Point not found — skip (error check disabled for sub-communicator levels)
+        j++;
+        continue;
+      }
+      // Translate global rank to local rank in Comm_here
+      int cur_owner_local;
+      MPI_Group_translate_ranks(world_group, 1, &cur_owner_global, local_group, &cur_owner_local);
+
+      // Find contiguous run of points with the same owner
+      int jstart = j;
+      while (j < NN && owner_rank[j] == cur_owner_global)
+        j++;
+      int count = (j - jstart) * num_var;
+      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner_local, Comm_here);
     }
-#if 0 // for not involved levels, this may fail     
-     else if(Weight[i] == 0 && lmyrank == 0)
-     {
-       cout<<"ERROR: Patch::Interp_Points fails to find point (";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<XX[j][i];
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")";
-       }
-       cout<<" on Patch (";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<bbox[j]<<"+"<<lli[j]*getdX(j);
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")--";
-       }
-       cout<<"(";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<bbox[dim+j]<<"-"<<uui[j]*getdX(j);
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")"<<endl;
-       }
-#if 0
-       checkBlock();
-#else
-  cout<<"splited domains:"<<endl;
-  {
-     MyList<Block> *Bp=blb;
-     while(Bp)
-     {
-	Block *BP=Bp->data;
-
-	for(int i=0;i<dim;i++)
-	{
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif    
-          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +(ghost_width-0.5)*DH[i];
-          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-(ghost_width-0.5)*DH[i];
-#else
-#ifdef Cell
-          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +ghost_width*DH[i];
-          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-ghost_width*DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif 
-	}       
-       cout<<"(";
-       for(int j=0;j<dim;j++)
-       {
-	  cout<<llb[j]<<":"<<uub[j];
-	  if(j<dim-1) cout<<",";
-	  else        cout<<")"<<endl;
-       }
-	if(Bp == ble) break;
-	Bp=Bp->next;
-     }
-  }
-#endif       
-       MPI_Abort(MPI_COMM_WORLD,1);
-     }
-#endif
   }
 
-  delete[] shellf;
-  delete[] weight;
-  delete[] Weight;
-  delete[] DH;
-  delete[] llb;
-  delete[] uub;
+  MPI_Group_free(&world_group);
+  MPI_Group_free(&local_group);
+  delete[] owner_rank;
 }
 void Patch::checkBlock()
 {

AMSS_NCKU_source/MPatch.h

@@ -39,6 +39,10 @@ public:
 
    bool Find_Point(double *XX);
 
+   void Interp_Points(MyList<var> *VarList,
+                      int NN, double **XX,
+                      double *Shellf, int Symmetry,
+                      int Nmin_consumer, int Nmax_consumer);
    void Interp_Points(MyList<var> *VarList,
                       int NN, double **XX,
                       double *Shellf, int Symmetry, MPI_Comm Comm_here);

AMSS_NCKU_source/Parallel.h

@@ -32,6 +32,16 @@ namespace Parallel
   int partition2(int *nxy, int split_size, int *min_width, int cpusize, int *shape); // special for 2 diemnsions
   int partition3(int *nxyz, int split_size, int *min_width, int cpusize, int *shape);
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0); // produce corresponding Blocks
+  MyList<Block> *distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0);
+  Block* splitHotspotBlock(MyList<Block>* &BlL, int _dim,
+                           int ib0_orig, int ib3_orig,
+                           int jb1_orig, int jb4_orig,
+                           int kb2_orig, int kb5_orig,
+                           Patch* PP, int r_left, int r_right,
+                           int ingfsi, int fngfsi, bool periodic,
+                           Block* &split_first_block, Block* &split_last_block);
+  Block* createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
+                           int block_id, int ingfsi, int fngfsi, int lev);
   void KillBlocks(MyList<Patch> *PatchLIST);
 
   void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
@@ -81,6 +91,49 @@ namespace Parallel
                    int Symmetry);
   void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
   void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+
+  struct SyncCache {
+    bool valid;
+    int cpusize;
+    MyList<gridseg> **combined_src;
+    MyList<gridseg> **combined_dst;
+    int *send_lengths;
+    int *recv_lengths;
+    double **send_bufs;
+    double **recv_bufs;
+    int *send_buf_caps;
+    int *recv_buf_caps;
+    MPI_Request *reqs;
+    MPI_Status *stats;
+    int max_reqs;
+    bool lengths_valid;
+    int *tc_req_node;
+    int *tc_req_is_recv;
+    int *tc_completed;
+    SyncCache();
+    void invalidate();
+    void destroy();
+  };
+
+  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
+  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
+                       MyList<var> *VarList1, MyList<var> *VarList2,
+                       int Symmetry, SyncCache &cache);
+
+  struct AsyncSyncState {
+    int req_no;
+    bool active;
+    int *req_node;
+    int *req_is_recv;
+    int pending_recv;
+    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
+  };
+
+  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
+                  SyncCache &cache, AsyncSyncState &state);
+  void Sync_finish(SyncCache &cache, AsyncSyncState &state,
+                   MyList<var> *VarList, int Symmetry);
   void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                    int Symmetry);
@@ -93,6 +146,15 @@ namespace Parallel
   void OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                       MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                       int Symmetry);
+  void Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                       MyList<var> *VarList1, MyList<var> *VarList2,
+                       int Symmetry, SyncCache &cache);
+  void OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                          MyList<var> *VarList1, MyList<var> *VarList2,
+                          int Symmetry, SyncCache &cache);
+  void OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
+                             MyList<var> *VarList1, MyList<var> *VarList2,
+                             int Symmetry, SyncCache &cache);
   void Prolong(Patch *Patc, Patch *Patf,
                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                int Symmetry);
@@ -117,12 +179,13 @@ namespace Parallel
   MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
   MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
   MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
-  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
-                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
-  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
-  double L2Norm(Patch *Pat, var *vf);
-  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
-  void checkvarl(MyList<var> *pp, bool first_only);
+  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
+                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
+  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
+  double L2Norm(Patch *Pat, var *vf);
+  void L2Norm7(Patch *Pat, var **vf, double *norms);
+  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
+  void checkvarl(MyList<var> *pp, bool first_only);
   MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
   MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
   void prepare_inter_time_level(Patch *Pat,
@@ -154,11 +217,12 @@ namespace Parallel
   void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
   bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
   void checkpatchlist(MyList<Patch> *PatL, bool buflog);
-
-  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-                             int NN, double **XX,
-                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
+
+  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
+  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
+  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
+                             int NN, double **XX,
+                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
 #if (PSTR == 1 || PSTR == 2 || PSTR == 3)
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
                             bool periodic, int start_rank, int end_rank, int nodes = 0);

AMSS_NCKU_source/ShellPatch.h

@@ -102,6 +102,16 @@ public:
                  //-1: means no dumy dimension at all; 0: means rho; 1: means sigma
    };
 
+   // Thread-safe search result (no pointers to shared mutable state)
+   struct PointSearchResult
+   {
+      bool found;
+      Block *Bg;
+      double gx, gy, gz; // global Cartesian coordinates
+      double lx, ly, lz; // local coordinates within the found block
+      int ssst;          // source shell-patch type (-1 = Cartesian)
+   };
+
    int myrank;
    int shape[dim];   // for (rho, sigma, R), for rho and sigma means number of points for every pi/2
    double Rrange[2]; // for Rmin and Rmax
@@ -175,6 +185,12 @@ public:
                          MyList<Patch> *Pp, double CDH[dim], MyList<pointstru> *pss);
    bool prolongpointstru(MyList<pointstru> *&psul, bool ssyn, int tsst, MyList<ss_patch> *sPp, double DH[dim],
                          MyList<Patch> *Pp, double CDH[dim], double x, double y, double z, int Symmetry, int rank_in);
+   // Read-only point search — thread-safe (no shared mutable state modified)
+   PointSearchResult prolongpointstru_search(bool ssyn, int tsst, MyList<ss_patch> *sPp, double DH[dim],
+                                             MyList<Patch> *Pp, double CDH[dim], double x, double y, double z,
+                                             int Symmetry, int rank_in);
+   // Append a search result to a linked list — use inside omp critical section
+   void prolongpointstru_append(MyList<pointstru> *&psul, const PointSearchResult &sr, int tsst);
    void setupintintstuff(int cpusize, MyList<Patch> *CPatL, int Symmetry);
    void intertransfer(MyList<pointstru> **src, MyList<pointstru> **dst,
                       MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
@@ -198,6 +214,7 @@ public:
    void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
                             char *filename, int sst);
    double L2Norm(var *vf);
+   void L2Norm7(var **vf, double *norms);
    void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
 };
 

AMSS_NCKU_source/Z4c_rhs.f90

@@ -94,29 +94,31 @@
                Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon,                    &            
                Symmetry,Lev,eps,co)
 
-#if (ABV == 0)  
-  call ricci_gamma(ex, X, Y, Z,                                      &
-               chi,                                                  &
-               dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,&
-               Gamx   ,  Gamy    ,  Gamz    , &
-               Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
-               Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
-               Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
-               Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
-               Symmetry)
-#endif
-  call constraint_bssn(ex, X, Y, Z,&
-               chi,trK, &
-               dxx,gxy,gxz,dyy,gyz,dzz, &
-               Axx,Axy,Axz,Ayy,Ayz,Azz, &
-               Gamx,Gamy,Gamz,&
-               Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
-               Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
-               Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
-               Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
-               Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
-               Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
-               Symmetry)
+  if (co == 0) then
+#if (ABV == 0)  
+    call ricci_gamma(ex, X, Y, Z,                                      &
+                 chi,                                                  &
+                 dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,&
+                 Gamx   ,  Gamy    ,  Gamz    , &
+                 Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
+                 Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
+                 Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
+                 Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
+                 Symmetry)
+#endif
+    call constraint_bssn(ex, X, Y, Z,&
+                 chi,trK, &
+                 dxx,gxy,gxz,dyy,gyz,dzz, &
+                 Axx,Axy,Axz,Ayy,Ayz,Azz, &
+                 Gamx,Gamy,Gamz,&
+                 Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
+                 Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
+                 Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
+                 Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
+                 Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
+                 Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
+                 Symmetry)
+  endif
 
   return
 
@@ -226,11 +228,12 @@
 
   call get_Z4cparameters(kappa1,kappa2,kappa3,FF,eta)
 
-!!! sanity check
-  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
-      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
-      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
-      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
+!!! sanity check
+#ifdef DEBUG
+  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
+      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
+      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
+      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
       +sum(TZ)
   if(dX.ne.dX) then
      if(sum(chi).ne.sum(chi))write(*,*)"Z4c_rhs.f90: find NaN in chi"
@@ -257,10 +260,11 @@
      if(sum(dtSfx).ne.sum(dtSfx))write(*,*)"Z4c_rhs.f90: find NaN in dtSfx"
      if(sum(dtSfy).ne.sum(dtSfy))write(*,*)"Z4c_rhs.f90: find NaN in dtSfy"
      if(sum(dtSfz).ne.sum(dtSfz))write(*,*)"Z4c_rhs.f90: find NaN in dtSfz"
-     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs.f90: find NaN in TZ"
-     gont = 1
-     return
-  endif
+     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs.f90: find NaN in TZ"
+     gont = 1
+     return
+  endif
+#endif
 
   PI = dacos(-ONE)
 
@@ -1263,30 +1267,32 @@
 
   endif
 
-#if (ABV == 0)  
-  call ricci_gamma(ex, X, Y, Z,                                      &
-               chi,                                                  &
-               dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,&
-               Gamx   ,  Gamy    ,  Gamz    , &
-               Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
-               Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
-               Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
-               Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
-               Symmetry)
-#endif
-
-  call constraint_bssn(ex, X, Y, Z,&
-               chi,trK, &
-               dxx,gxy,gxz,dyy,gyz,dzz, &
-               Axx,Axy,Axz,Ayy,Ayz,Azz, &
-               Gamx,Gamy,Gamz,&
-               Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
-               Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
-               Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
-               Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
-               Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
-               Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
-               Symmetry)
+  if (co == 0) then
+#if (ABV == 0)  
+    call ricci_gamma(ex, X, Y, Z,                                      &
+                 chi,                                                  &
+                 dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,&
+                 Gamx   ,  Gamy    ,  Gamz    , &
+                 Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
+                 Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
+                 Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
+                 Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
+                 Symmetry)
+#endif
+
+    call constraint_bssn(ex, X, Y, Z,&
+                 chi,trK, &
+                 dxx,gxy,gxz,dyy,gyz,dzz, &
+                 Axx,Axy,Axz,Ayy,Ayz,Azz, &
+                 Gamx,Gamy,Gamz,&
+                 Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
+                 Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
+                 Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
+                 Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
+                 Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
+                 Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
+                 Symmetry)
+  endif
 
   gont = 0
 

AMSS_NCKU_source/Z4c_rhs_ss.f90

@@ -121,11 +121,12 @@
 
   call get_Z4cparameters(kappa1,kappa2,kappa3,FF,eta)
 
-!!! sanity check
-  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
-      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
-      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
-      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
+!!! sanity check
+#ifdef DEBUG
+  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
+      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
+      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
+      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
       +sum(TZ)
   if(dX.ne.dX) then
      if(sum(chi).ne.sum(chi))write(*,*)"Z4c_rhs_ss.f90: find NaN in chi"
@@ -152,10 +153,11 @@
      if(sum(dtSfx).ne.sum(dtSfx))write(*,*)"Z4c_rhs_ss.f90: find NaN in dtSfx"
      if(sum(dtSfy).ne.sum(dtSfy))write(*,*)"Z4c_rhs_ss.f90: find NaN in dtSfy"
      if(sum(dtSfz).ne.sum(dtSfz))write(*,*)"Z4c_rhs_ss.f90: find NaN in dtSfz"
-     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs_ss.f90: find NaN in TZ"
-     gont = 1
-     return
-  endif
+     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs_ss.f90: find NaN in TZ"
+     gont = 1
+     return
+  endif
+#endif
 
   PI = dacos(-ONE)
 
@@ -1388,41 +1390,43 @@
   call kodis_sh(ex,crho,sigma,R,TZ,TZ_rhs,SSS,Symmetry,eps,sst)
   endif
 
-#if (ABV == 1)  
-  call ricci_gamma_ss(ex,crho,sigma,R,X, Y, Z,                                 &
-               drhodx, drhody, drhodz,                                         &
-               dsigmadx,dsigmady,dsigmadz,                                     &
-               dRdx,dRdy,dRdz,                                                 &
-               drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,                &
-               dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,    &
-               dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                            &
-               chi,                                                  &
-               dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,&
-               Gamx   ,  Gamy    ,  Gamz    , &
-               Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
-               Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
-               Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
-               Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
-               Symmetry,Lev,sst)
-  call constraint_bssn_ss(ex,crho,sigma,R,X, Y, Z,  &
-               drhodx, drhody, drhodz,                                         &
-               dsigmadx,dsigmady,dsigmadz,                                     &
-               dRdx,dRdy,dRdz,                                                 &
-               drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,                &
-               dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,    &
-               dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                            &
-               chi,trK, &
-               dxx,gxy,gxz,dyy,gyz,dzz, &
-               Axx,Axy,Axz,Ayy,Ayz,Azz, &
-               Gamx,Gamy,Gamz,&
-               Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
-               Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
-               Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
-               Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
-               Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
-               Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
-               Symmetry,Lev,sst)
-#endif
+  if (co == 0) then
+#if (ABV == 1)  
+    call ricci_gamma_ss(ex,crho,sigma,R,X, Y, Z,                               &
+                 drhodx, drhody, drhodz,                                       &
+                 dsigmadx,dsigmady,dsigmadz,                                   &
+                 dRdx,dRdy,dRdz,                                               &
+                 drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,              &
+                 dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,  &
+                 dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                          &
+                 chi,                                                          &
+                 dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,&
+                 Gamx   ,  Gamy    ,  Gamz    , &
+                 Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
+                 Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
+                 Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
+                 Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
+                 Symmetry,Lev,sst)
+#endif
+    call constraint_bssn_ss(ex,crho,sigma,R,X, Y, Z,  &
+                 drhodx, drhody, drhodz,                                       &
+                 dsigmadx,dsigmady,dsigmadz,                                   &
+                 dRdx,dRdy,dRdz,                                               &
+                 drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,              &
+                 dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,  &
+                 dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                          &
+                 chi,trK, &
+                 dxx,gxy,gxz,dyy,gyz,dzz, &
+                 Axx,Axy,Axz,Ayy,Ayz,Azz, &
+                 Gamx,Gamy,Gamz,&
+                 Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
+                 Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
+                 Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
+                 Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
+                 Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
+                 Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
+                 Symmetry,Lev,sst)
+  endif
 
   gont = 0
 

AMSS_NCKU_source/bssnEM_class.C

@@ -258,6 +258,8 @@ void bssnEM_class::Initialize()
     PhysTime = StartTime;
     Setup_Black_Hole_position();
   }
+
+  setup_transfer_caches();
 }
 
 //================================================================================================

AMSS_NCKU_source/bssnEScalar_class.C

@@ -23,8 +23,14 @@ using namespace std;
 #include "rungekutta4_rout.h"
 #include "sommerfeld_rout.h"
 #include "getnp4.h"
-#include "shellfunctions.h"
-#include "parameters.h"
+#include "shellfunctions.h"
+#include "parameters.h"
+
+#if BSSN_USE_ESCALAR_C_KERNEL
+#define BSSN_ESCALAR_RHS f_compute_rhs_bssn_escalar_c
+#else
+#define BSSN_ESCALAR_RHS f_compute_rhs_bssn_escalar
+#endif
 
 #ifdef With_AHF
 #include "derivatives.h"
@@ -74,8 +80,8 @@ bssnEScalar_class::bssnEScalar_class(double Couranti, double StartTimei, double
 
 //================================================================================================
 
-void bssnEScalar_class::Initialize()
-{
+void bssnEScalar_class::Initialize()
+{
   Sphio = new var("Sphio", ngfs++, 1, 1, 1);
   Spio = new var("Spio", ngfs++, 1, 1, 1);
   Sphi0 = new var("Sphi0", ngfs++, 1, 1, 1);
@@ -132,11 +138,14 @@ void bssnEScalar_class::Initialize()
       }
     } 
    
-  GH = new cgh(0, ngfs, Symmetry, pname, checkrun, ErrorMonitor);
-  if (checkrun)
-    CheckPoint->readcheck_cgh(PhysTime, GH, myrank, nprocs, Symmetry);
-  else
-    GH->compose_cgh(nprocs);
+  GH = new cgh(0, ngfs, Symmetry, pname, checkrun, ErrorMonitor);
+  ConstraintRefreshLevels = new int[GH->levels];
+  for (int il = 0; il < GH->levels; il++)
+    ConstraintRefreshLevels[il] = 0;
+  if (checkrun)
+    CheckPoint->readcheck_cgh(PhysTime, GH, myrank, nprocs, Symmetry);
+  else
+    GH->compose_cgh(nprocs);
 
 #ifdef WithShell
   SH = new ShellPatch(0, ngfs, pname, Symmetry, myrank, ErrorMonitor);
@@ -160,12 +169,14 @@ void bssnEScalar_class::Initialize()
   {
     CheckPoint->read_Black_Hole_position(BH_num_input, BH_num, Porg0, Pmom, Spin, Mass, Porgbr, Porg, Porg1, Porg_rhs);
   }
-  else
-  {
-    PhysTime = StartTime;
-    Setup_Black_Hole_position();
-  }
-}
+  else
+  {
+    PhysTime = StartTime;
+    Setup_Black_Hole_position();
+  }
+
+  setup_transfer_caches();
+}
 
 //================================================================================================
 
@@ -207,10 +218,10 @@ bssnEScalar_class::~bssnEScalar_class()
 
 // Read initial data solved by Ansorg, PRD 70, 064011 (2004)
 
-void bssnEScalar_class::Read_Ansorg()
-{
-  if (!checkrun)
-  {
+void bssnEScalar_class::Read_Ansorg()
+{
+  if (!checkrun)
+  {
     if (myrank == 0)
       cout << "Read initial data from Ansorg's solver,"
            << " please be sure the input parameters for black holes are puncture parameters!!" 
@@ -227,9 +238,12 @@ void bssnEScalar_class::Read_Ansorg()
         cout << "Error inputpar" << endl;
         exit(0);
       }
-    }
-    int BH_NM;
-    double *Porg_here;
+    }
+    int BH_NM;
+    double *Porg_here;
+    double *pmom_local;
+    double *spin_local;
+    double *mass_local;
     // read parameter from file
     {
       const int LEN = 256;
@@ -269,11 +283,11 @@ void bssnEScalar_class::Read_Ansorg()
       }
       inf.close();
     }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom = new double[3 * BH_NM];
-    Spin = new double[3 * BH_NM];
-    Mass = new double[BH_NM];
+
+    Porg_here = new double[3 * BH_NM];
+    pmom_local = new double[3 * BH_NM];
+    spin_local = new double[3 * BH_NM];
+    mass_local = new double[BH_NM];
     // read parameter from file
     {
       const int LEN = 256;
@@ -305,37 +319,37 @@ void bssnEScalar_class::Read_Ansorg()
         else if (status == 0)
           continue;
 
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass[sind] = atof(sval.c_str());
-          else if (skey == "Porgx")
-            Porg_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Porgy")
-            Porg_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Porgz")
-            Porg_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Spinx")
-            Spin[sind * 3] = atof(sval.c_str());
-          else if (skey == "Spiny")
-            Spin[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Spinz")
-            Spin[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Pmomx")
-            Pmom[sind * 3] = atof(sval.c_str());
-          else if (skey == "Pmomy")
-            Pmom[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Pmomz")
-            Pmom[sind * 3 + 2] = atof(sval.c_str());
-        }
-      }
-      inf.close();
+        if (sgrp == "BSSN" && sind < BH_NM)
+        {
+          if (skey == "Mass")
+            mass_local[sind] = atof(sval.c_str());
+          else if (skey == "Porgx")
+            Porg_here[sind * 3] = atof(sval.c_str());
+          else if (skey == "Porgy")
+            Porg_here[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Porgz")
+            Porg_here[sind * 3 + 2] = atof(sval.c_str());
+          else if (skey == "Spinx")
+            spin_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Spiny")
+            spin_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Spinz")
+            spin_local[sind * 3 + 2] = atof(sval.c_str());
+          else if (skey == "Pmomx")
+            pmom_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Pmomy")
+            pmom_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Pmomz")
+            pmom_local[sind * 3 + 2] = atof(sval.c_str());
+        }
+      }
+      inf.close();
     }
-    int order = 6;
-    Ansorg read_ansorg("Ansorg.psid", order);
-    // set initial data
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
+    int order = 6;
+    Ansorg read_ansorg("Ansorg.psid", order);
+    // set initial data
+    for (int lev = 0; lev < GH->levels; lev++)
+    {
       MyList<Patch> *Pp = GH->PatL[lev];
       while (Pp)
       {
@@ -358,21 +372,21 @@ void bssnEScalar_class::Read_Ansorg()
                                       cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                       cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                       cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                      cg->fgfs[Lap0->sgfn], 
-                                      cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                      cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                      cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                      Mass, Porg_here, Pmom, Spin, BH_NM);
+                                      cg->fgfs[Lap0->sgfn], 
+                                      cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
+                                      cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
+                                      cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                      mass_local, Porg_here, pmom_local, spin_local, BH_NM);
           }
           if (BL == Pp->data->ble)
             break;
           BL = BL->next;
-        }
-        Pp = Pp->next;
-      }
-    }
-#ifdef WithShell
-    // ShellPatch part
+        }
+        Pp = Pp->next;
+      }
+    }
+#ifdef WithShell
+    // ShellPatch part
     MyList<ss_patch> *Pp = SH->PatL;
     while (Pp)
     {
@@ -400,25 +414,28 @@ void bssnEScalar_class::Read_Ansorg()
                                        cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                        cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                        cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                       cg->fgfs[Lap0->sgfn], 
-                                       cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                       cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                       cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                       Mass, Porg_here, Pmom, Spin, BH_NM);
+                                       cg->fgfs[Lap0->sgfn], 
+                                       cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
+                                       cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
+                                       cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                       mass_local, Porg_here, pmom_local, spin_local, BH_NM);
         }
         if (BL == Pp->data->ble)
           break;
         BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-#endif
-
-    delete[] Porg_here;
-    // dump read_in initial data
-    //   for(int lev=0;lev<GH->levels;lev++) Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT);
-  }
-}
+      }
+      Pp = Pp->next;
+    }
+#endif
+
+    delete[] Porg_here;
+    delete[] pmom_local;
+    delete[] spin_local;
+    delete[] mass_local;
+    // dump read_in initial data
+    //   for(int lev=0;lev<GH->levels;lev++) Parallel::Dump_Data(GH->PatL[lev],StateList,0,PhysTime,dT);
+  }
+}
 
 //================================================================================================
 
@@ -432,10 +449,10 @@ void bssnEScalar_class::Read_Ansorg()
 
 // Read initial data solved by Pablo's Olliptic Phys.Rev.D 82 024005 (2010)
 
-void bssnEScalar_class::Read_Pablo()
-{
-  if (!checkrun)
-  {
+void bssnEScalar_class::Read_Pablo()
+{
+  if (!checkrun)
+  {
     if (myrank == 0)
       cout << "Read initial data from Pablo's solver,"
            << " please be sure the input parameters for black holes are puncture parameters!!" 
@@ -452,9 +469,12 @@ void bssnEScalar_class::Read_Pablo()
         cout << "Error inputpar" << endl;
         exit(0);
       }
-    }
-    int BH_NM;
-    double *Porg_here;
+    }
+    int BH_NM;
+    double *Porg_here;
+    double *pmom_local;
+    double *spin_local;
+    double *mass_local;
     // read parameter from file
     {
       const int LEN = 256;
@@ -494,11 +514,11 @@ void bssnEScalar_class::Read_Pablo()
       }
       inf.close();
     }
-
-    Porg_here = new double[3 * BH_NM];
-    Pmom = new double[3 * BH_NM];
-    Spin = new double[3 * BH_NM];
-    Mass = new double[BH_NM];
+
+    Porg_here = new double[3 * BH_NM];
+    pmom_local = new double[3 * BH_NM];
+    spin_local = new double[3 * BH_NM];
+    mass_local = new double[BH_NM];
     // read parameter from file
     {
       const int LEN = 256;
@@ -530,31 +550,31 @@ void bssnEScalar_class::Read_Pablo()
         else if (status == 0)
           continue;
 
-        if (sgrp == "BSSN" && sind < BH_NM)
-        {
-          if (skey == "Mass")
-            Mass[sind] = atof(sval.c_str());
-          else if (skey == "Porgx")
-            Porg_here[sind * 3] = atof(sval.c_str());
-          else if (skey == "Porgy")
-            Porg_here[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Porgz")
-            Porg_here[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Spinx")
-            Spin[sind * 3] = atof(sval.c_str());
-          else if (skey == "Spiny")
-            Spin[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Spinz")
-            Spin[sind * 3 + 2] = atof(sval.c_str());
-          else if (skey == "Pmomx")
-            Pmom[sind * 3] = atof(sval.c_str());
-          else if (skey == "Pmomy")
-            Pmom[sind * 3 + 1] = atof(sval.c_str());
-          else if (skey == "Pmomz")
-            Pmom[sind * 3 + 2] = atof(sval.c_str());
-        }
-      }
-      inf.close();
+        if (sgrp == "BSSN" && sind < BH_NM)
+        {
+          if (skey == "Mass")
+            mass_local[sind] = atof(sval.c_str());
+          else if (skey == "Porgx")
+            Porg_here[sind * 3] = atof(sval.c_str());
+          else if (skey == "Porgy")
+            Porg_here[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Porgz")
+            Porg_here[sind * 3 + 2] = atof(sval.c_str());
+          else if (skey == "Spinx")
+            spin_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Spiny")
+            spin_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Spinz")
+            spin_local[sind * 3 + 2] = atof(sval.c_str());
+          else if (skey == "Pmomx")
+            pmom_local[sind * 3] = atof(sval.c_str());
+          else if (skey == "Pmomy")
+            pmom_local[sind * 3 + 1] = atof(sval.c_str());
+          else if (skey == "Pmomz")
+            pmom_local[sind * 3 + 2] = atof(sval.c_str());
+        }
+      }
+      inf.close();
     }
     bool flag = false;
     int DIM = dim;
@@ -594,11 +614,11 @@ void bssnEScalar_class::Read_Pablo()
                                         cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                         cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                         cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                        cg->fgfs[Lap0->sgfn], 
-                                        cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                        cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                        cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                        Mass, Porg_here, Pmom, Spin, BH_NM);
+                                        cg->fgfs[Lap0->sgfn], 
+                                        cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
+                                        cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
+                                        cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                        mass_local, Porg_here, pmom_local, spin_local, BH_NM);
             }
             if (BL == Pp->data->ble)
               break;
@@ -658,11 +678,11 @@ void bssnEScalar_class::Read_Pablo()
                                          cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                          cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                          cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
-                                         cg->fgfs[Lap0->sgfn], 
-                                         cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
-                                         cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
-                                         cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
-                                         Mass, Porg_here, Pmom, Spin, BH_NM);
+                                         cg->fgfs[Lap0->sgfn], 
+                                         cg->fgfs[Sfx0->sgfn], cg->fgfs[Sfy0->sgfn], cg->fgfs[Sfz0->sgfn],
+                                         cg->fgfs[dtSfx0->sgfn], cg->fgfs[dtSfy0->sgfn], cg->fgfs[dtSfz0->sgfn],
+                                         cg->fgfs[Sphi0->sgfn], cg->fgfs[Spi0->sgfn],
+                                         mass_local, Porg_here, pmom_local, spin_local, BH_NM);
           }
           if (BL == Pp->data->ble)
             break;
@@ -684,10 +704,13 @@ void bssnEScalar_class::Read_Pablo()
       Pp = Pp->next;
     }
 #endif
-
-    delete[] Porg_here;
-    if (flag && myrank == 0)
-      MPI_Abort(MPI_COMM_WORLD, 1);
+
+    delete[] Porg_here;
+    delete[] pmom_local;
+    delete[] spin_local;
+    delete[] mass_local;
+    if (flag && myrank == 0)
+      MPI_Abort(MPI_COMM_WORLD, 1);
     // dump read_in initial data
     for (int lev = 0; lev < GH->levels; lev++)
       Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT);
@@ -739,10 +762,10 @@ void bssnEScalar_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn_escalar(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                       cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                       cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
+        if (BSSN_ESCALAR_RHS(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                       cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+                                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
+                                       cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                                        cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                        cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                        cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
@@ -993,11 +1016,12 @@ void bssnEScalar_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  Parallel::AsyncSyncState async_pre;
+  sync_predictor_start(lev, SynchList_pre, async_pre);
 
-#ifdef WithShell
-  if (lev == 0)
-  {
+#ifdef WithShell
+  if (lev == 0)
+  {
     clock_t prev_clock, curr_clock;
     if (myrank == 0)
       curr_clock = clock();
@@ -1009,9 +1033,10 @@ void bssnEScalar_class::Step(int lev, int YN)
       cout << " Shell stuff synchronization used " 
            << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
            << " seconds! " << endl;
-    }
-  }
-#endif
+    }
+  }
+#endif
+  sync_predictor_finish(lev, async_pre, SynchList_pre);
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -1081,10 +1106,10 @@ void bssnEScalar_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn_escalar(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                         cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
-                                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
-                                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
+          if (BSSN_ESCALAR_RHS(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                         cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
+                                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
+                                         cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
                                          cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
                                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
                                          cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
@@ -1349,11 +1374,12 @@ void bssnEScalar_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::AsyncSyncState async_cor;
+    sync_corrector_start(lev, SynchList_cor, async_cor);
 
-#ifdef WithShell
-    if (lev == 0)
-    {
+#ifdef WithShell
+    if (lev == 0)
+    {
       clock_t prev_clock, curr_clock;
       if (myrank == 0)
         curr_clock = clock();
@@ -1365,9 +1391,10 @@ void bssnEScalar_class::Step(int lev, int YN)
         cout << " Shell stuff synchronization used " 
              << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
              << " seconds! " << endl;
-      }
-    }
-#endif
+      }
+    }
+#endif
+    sync_corrector_finish(lev, async_cor, SynchList_cor);
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
     {
@@ -1835,11 +1862,14 @@ void bssnEScalar_class::AnalysisStuff_EScalar(int lev, double dT_lev)
 
 //================================================================================================
 
-void bssnEScalar_class::Interp_Constraint()
-{
-  // we do not support a_lev != 0 yet.
-  if (a_lev > 0)
-    return;
+void bssnEScalar_class::Interp_Constraint(bool infg)
+{
+  if (!infg)
+    return;
+
+  // we do not support a_lev != 0 yet.
+  if (a_lev > 0)
+    return;
 
   for (int lev = 0; lev < GH->levels; lev++)
   {
@@ -1858,10 +1888,10 @@ void bssnEScalar_class::Interp_Constraint()
           if (myrank == cg->rank)
           {
             if (lev > 0)
-              f_compute_rhs_bssn_escalar(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                         cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                         cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                         cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
+              BSSN_ESCALAR_RHS(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                         cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+                                         cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
+                                         cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                                          cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                          cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                          cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],
@@ -2078,10 +2108,10 @@ void bssnEScalar_class::Constraint_Out()
             if (myrank == cg->rank)
             {
               if (lev > 0)
-                f_compute_rhs_bssn_escalar(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                           cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
-                                           cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
-                                           cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
+                BSSN_ESCALAR_RHS(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                           cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+                                           cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
+                                           cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                                            cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                            cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
                                            cg->fgfs[Gmx0->sgfn], cg->fgfs[Gmy0->sgfn], cg->fgfs[Gmz0->sgfn],

AMSS_NCKU_source/bssnEScalar_class.h

@@ -51,7 +51,7 @@ public:
      void Compute_Psi4(int lev);
      void Step(int lev, int YN);
      void AnalysisStuff_EScalar(int lev, double dT_lev);
-     void Interp_Constraint();
+     void Interp_Constraint(bool infg);
      void Constraint_Out(); 
 
 protected:

AMSS_NCKU_source/bssn_class.h

@@ -31,11 +31,19 @@ using namespace std;
 #include "surface_integral.h"
 #include "checkpoint.h"
 
-extern void setpbh(int iBHN, double **iPBH, double *iMass, int rBHN);
-
-class bssn_class
-{
-public:
+extern void setpbh(int iBHN, double **iPBH, double *iMass, int rBHN);
+
+#ifndef BSSN_USE_TRANSFER_CACHE
+#define BSSN_USE_TRANSFER_CACHE 1
+#endif
+
+#ifndef BSSN_USE_ESCALAR_C_KERNEL
+#define BSSN_USE_ESCALAR_C_KERNEL 1
+#endif
+
+class bssn_class
+{
+public:
        int ngfs;
        int nprocs, myrank;
        cgh *GH;
@@ -45,10 +53,11 @@ public:
        int checkrun;
        char checkfilename[50];
        int Steps;
-       double StartTime, TotalTime;
-       double AnasTime, DumpTime, d2DumpTime, CheckTime;
-       double LastAnas, LastConsOut;
-       double Courant;
+       double StartTime, TotalTime;
+       double AnasTime, DumpTime, d2DumpTime, CheckTime;
+       double LastAnas, LastConsOut;
+       int *ConstraintRefreshLevels;
+       double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
        int maxl, decn;
@@ -126,9 +135,16 @@ public:
        MyList<var> *OldStateList, *DumpList;
        MyList<var> *ConstraintList;
 
-       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
-       monitor *ConVMonitor;
-       surface_integral *Waveshell;
+       Parallel::SyncCache *sync_cache_pre;  // per-level cache for predictor sync
+       Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
+       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
+       Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
+       Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
+       Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong
+
+       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
+       monitor *ConVMonitor, *TimingMonitor;
+       surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
 public:
@@ -159,14 +175,25 @@ public:
        void Setup_KerrSchild();
        void Enforce_algcon(int lev, int fg);
 
-       void testRestrict();
-       void testOutBd();
-       
-       bool check_Stdin_Abort(); 
-
-       virtual void Setup_Initial_Data_Cao();
-       virtual void Setup_Initial_Data_Lousto();
-       virtual void Initialize();
+       void testRestrict();
+       void testOutBd();
+       
+       bool check_Stdin_Abort(); 
+       bool use_transfer_cache() const;
+       void setup_transfer_caches();
+       void invalidate_transfer_caches();
+       void destroy_transfer_caches();
+       void sync_predictor_start(int lev, MyList<var> *VarList, Parallel::AsyncSyncState &async_state);
+       void sync_predictor_finish(int lev, Parallel::AsyncSyncState &async_state, MyList<var> *VarList);
+       void sync_corrector_start(int lev, MyList<var> *VarList, Parallel::AsyncSyncState &async_state);
+       void sync_corrector_finish(int lev, Parallel::AsyncSyncState &async_state, MyList<var> *VarList);
+       void sync_evolution(int lev, MyList<var> *VarList, Parallel::SyncCache *cache_array = 0);
+       void restrict_evolution(int lev, MyList<var> *src_var_list, MyList<var> *dst_var_list);
+       void outbdlow2hi_evolution(int lev, MyList<var> *src_var_list, MyList<var> *dst_var_list);
+
+       virtual void Setup_Initial_Data_Cao();
+       virtual void Setup_Initial_Data_Lousto();
+       virtual void Initialize();
        virtual void Read_Ansorg();
        virtual void Read_Pablo() {};
        virtual void Compute_Psi4(int lev);

AMSS_NCKU_source/bssn_em_rhs_c.C

@@ -0,0 +1,323 @@
+#include "macrodef.h"
+#include "bssn_rhs.h"
+#include "share_func.h"
+#include "tool.h"
+#include <cstddef>
+
+/*
+ * C 版 BSSN-EM RHS kernel — replaces empart.f90 + bssn_rhs.f90 for BSSN+Maxwell.
+ *
+ * Computes:
+ *   1. All metric and EM field derivatives
+ *   2. Physical metric, Christoffel-like terms
+ *   3. EM field RHS (E, B, Kpsi, Kphi)
+ *   4. Stress-energy tensor (rho, Si, Sij)
+ *   5. Calls f_compute_rhs_bssn (C BSSN RHS) with stress-energy
+ *   6. Advection + KO dissipation for EM fields
+ *   7. NaN check
+ */
+int f_compute_rhs_bssn_em_c(int *ex, double &T,
+                            double *X, double *Y, double *Z,
+                            double *chi, double *trK,
+                            double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                            double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                            double *Gamx, double *Gamy, double *Gamz,
+                            double *Lap, double *betax, double *betay, double *betaz,
+                            double *dtSfx, double *dtSfy, double *dtSfz,
+                            double *Ex,  double *Ey,  double *Ez,
+                            double *Bx,  double *By,  double *Bz,
+                            double *Kpsi, double *Kphi,
+                            double *Jx, double *Jy, double *Jz, double *qchar,
+                            double *chi_rhs, double *trK_rhs,
+                            double *gxx_rhs, double *gxy_rhs, double *gxz_rhs,
+                            double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                            double *Axx_rhs, double *Axy_rhs, double *Axz_rhs,
+                            double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                            double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                            double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                            double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                            double *Ex_rhs,  double *Ey_rhs,  double *Ez_rhs,
+                            double *Bx_rhs,  double *By_rhs,  double *Bz_rhs,
+                            double *Kpsi_rhs, double *Kphi_rhs,
+                            double *rho, double *Sx, double *Sy, double *Sz,
+                            double *Sxx, double *Sxy, double *Sxz,
+                            double *Syy, double *Syz, double *Szz,
+                            double *Gamxxx, double *Gamxxy, double *Gamxxz,
+                            double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                            double *Gamyxx, double *Gamyxy, double *Gamyxz,
+                            double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                            double *Gamzxx, double *Gamzxy, double *Gamzxz,
+                            double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                            double *Rxx, double *Rxy, double *Rxz,
+                            double *Ryy, double *Ryz, double *Rzz,
+                            double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                            double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                            int &Symmetry, int &Lev, double &eps, int &co)
+{
+    (void)T;
+    int gont = 0;
+    const int nx = ex[0], ny = ex[1], nz = ex[2];
+    const int all = nx * ny * nz;
+    const size_t n = (size_t)all;
+
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0, FOUR = 4.0, EIT = 8.0;
+    const double HALF = 0.5, THR = 3.0, F3o2 = 1.5, PI = 3.14159265358979323846;
+    const double SYM = 1.0, ANTI = -1.0;
+    const double kappa = 1.0;
+    const double SSS[3]={SYM,SYM,SYM},   AAS[3]={ANTI,ANTI,SYM};
+    const double ASA[3]={ANTI,SYM,ANTI}, SAA[3]={SYM,ANTI,ANTI};
+    const double ASS[3]={ANTI,SYM,SYM},   SAS[3]={SYM,ANTI,SYM};
+    const double SSA[3]={SYM,SYM,ANTI};
+
+    /* ---- allocate temporary arrays ---- */
+    double *chix = (double*)malloc(n*sizeof(double));
+    double *chiy = (double*)malloc(n*sizeof(double));
+    double *chiz = (double*)malloc(n*sizeof(double));
+    double *Exx=(double*)malloc(n*sizeof(double)),*Exy=(double*)malloc(n*sizeof(double)),*Exz=(double*)malloc(n*sizeof(double));
+    double *Eyx=(double*)malloc(n*sizeof(double)),*Eyy=(double*)malloc(n*sizeof(double)),*Eyz=(double*)malloc(n*sizeof(double));
+    double *Ezx=(double*)malloc(n*sizeof(double)),*Ezy=(double*)malloc(n*sizeof(double)),*Ezz=(double*)malloc(n*sizeof(double));
+    double *Bxx=(double*)malloc(n*sizeof(double)),*Bxy=(double*)malloc(n*sizeof(double)),*Bxz=(double*)malloc(n*sizeof(double));
+    double *Byx=(double*)malloc(n*sizeof(double)),*Byy=(double*)malloc(n*sizeof(double)),*Byz=(double*)malloc(n*sizeof(double));
+    double *Bzx=(double*)malloc(n*sizeof(double)),*Bzy=(double*)malloc(n*sizeof(double)),*Bzz=(double*)malloc(n*sizeof(double));
+    double *Kpsix=(double*)malloc(n*sizeof(double)),*Kpsiy=(double*)malloc(n*sizeof(double)),*Kpsiz=(double*)malloc(n*sizeof(double));
+    double *Kphix=(double*)malloc(n*sizeof(double)),*Kphiy=(double*)malloc(n*sizeof(double)),*Kphiz=(double*)malloc(n*sizeof(double));
+    double *Lapx=(double*)malloc(n*sizeof(double)),*Lapy=(double*)malloc(n*sizeof(double)),*Lapz=(double*)malloc(n*sizeof(double));
+    double *betaxx=(double*)malloc(n*sizeof(double)),*betaxy=(double*)malloc(n*sizeof(double)),*betaxz=(double*)malloc(n*sizeof(double));
+    double *betayx=(double*)malloc(n*sizeof(double)),*betayy=(double*)malloc(n*sizeof(double)),*betayz=(double*)malloc(n*sizeof(double));
+    double *betazx=(double*)malloc(n*sizeof(double)),*betazy=(double*)malloc(n*sizeof(double)),*betazz=(double*)malloc(n*sizeof(double));
+    double *gxxx=(double*)malloc(n*sizeof(double)),*gxxy=(double*)malloc(n*sizeof(double)),*gxxz=(double*)malloc(n*sizeof(double));
+    double *gxyx=(double*)malloc(n*sizeof(double)),*gxyy=(double*)malloc(n*sizeof(double)),*gxyz=(double*)malloc(n*sizeof(double));
+    double *gxzx=(double*)malloc(n*sizeof(double)),*gxzy=(double*)malloc(n*sizeof(double)),*gxzz=(double*)malloc(n*sizeof(double));
+    double *gyyx=(double*)malloc(n*sizeof(double)),*gyyy=(double*)malloc(n*sizeof(double)),*gyyz=(double*)malloc(n*sizeof(double));
+    double *gyzx=(double*)malloc(n*sizeof(double)),*gyzy=(double*)malloc(n*sizeof(double)),*gyzz=(double*)malloc(n*sizeof(double));
+    double *gzzx=(double*)malloc(n*sizeof(double)),*gzzy=(double*)malloc(n*sizeof(double)),*gzzz=(double*)malloc(n*sizeof(double));
+    double *gupxx=(double*)malloc(n*sizeof(double)),*gupxy=(double*)malloc(n*sizeof(double)),*gupxz=(double*)malloc(n*sizeof(double));
+    double *gupyy=(double*)malloc(n*sizeof(double)),*gupyz=(double*)malloc(n*sizeof(double)),*gupzz=(double*)malloc(n*sizeof(double));
+
+    if (!chix||!chiy||!chiz||!Exx||!Exy||!Exz||!Eyx||!Eyy||!Eyz||!Ezx||!Ezy||!Ezz||
+        !Bxx||!Bxy||!Bxz||!Byx||!Byy||!Byz||!Bzx||!Bzy||!Bzz||
+        !Kpsix||!Kpsiy||!Kpsiz||!Kphix||!Kphiy||!Kphiz||
+        !Lapx||!Lapy||!Lapz||
+        !betaxx||!betaxy||!betaxz||!betayx||!betayy||!betayz||!betazx||!betazy||!betazz||
+        !gxxx||!gxxy||!gxxz||!gxyx||!gxyy||!gxyz||!gxzx||!gxzy||!gxzz||
+        !gyyx||!gyyy||!gyyz||!gyzx||!gyzy||!gyzz||!gzzx||!gzzy||!gzzz||
+        !gupxx||!gupxy||!gupxz||!gupyy||!gupyz||!gupzz) {
+        gont = 1;
+    }
+
+    /* ==== 1. Compute all derivatives ==== */
+    if (!gont) {
+
+    /* metric derivatives */
+    fderivs(ex, Lap, Lapx, Lapy, Lapz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, betax, betaxx, betaxy, betaxz, X, Y, Z, ANTI, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, betay, betayx, betayy, betayz, X, Y, Z, SYM, ANTI, SYM, Symmetry, Lev);
+    fderivs(ex, betaz, betazx, betazy, betazz, X, Y, Z, SYM, SYM, ANTI, Symmetry, Lev);
+    fderivs(ex, chi, chix, chiy, chiz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, dxx, gxxx, gxxy, gxxz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, gxy, gxyx, gxyy, gxyz, X, Y, Z, ANTI, ANTI, SYM, Symmetry, Lev);
+    fderivs(ex, gxz, gxzx, gxzy, gxzz, X, Y, Z, ANTI, SYM, ANTI, Symmetry, Lev);
+    fderivs(ex, dyy, gyyx, gyyy, gyyz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, gyz, gyzx, gyzy, gyzz, X, Y, Z, SYM, ANTI, ANTI, Symmetry, Lev);
+    fderivs(ex, dzz, gzzx, gzzy, gzzz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+
+    /* EM field derivatives */
+    fderivs(ex, Kpsi, Kpsix, Kpsiy, Kpsiz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, Kphi, Kphix, Kphiy, Kphiz, X, Y, Z, SYM, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, Ex, Exx, Exy, Exz, X, Y, Z, ANTI, SYM, SYM, Symmetry, Lev);
+    fderivs(ex, Ey, Eyx, Eyy, Eyz, X, Y, Z, SYM, ANTI, SYM, Symmetry, Lev);
+    fderivs(ex, Ez, Ezx, Ezy, Ezz, X, Y, Z, SYM, SYM, ANTI, Symmetry, Lev);
+    fderivs(ex, Bx, Bxx, Bxy, Bxz, X, Y, Z, SYM, ANTI, ANTI, Symmetry, Lev);
+    fderivs(ex, By, Byx, Byy, Byz, X, Y, Z, ANTI, SYM, ANTI, Symmetry, Lev);
+    fderivs(ex, Bz, Bzx, Bzy, Bzz, X, Y, Z, ANTI, ANTI, SYM, Symmetry, Lev);
+
+    /* ==== 2. Compute EM RHS and stress-energy ==== */
+    const double F1o4PI = ONE / (FOUR * PI);
+    for (size_t i = 0; i < n; ++i) {
+        const double alpn1 = Lap[i] + ONE;
+        const double chin1 = chi[i] + ONE;
+        const double chi3o2 = sqrt(chin1) * chin1;  // chi^{3/2}
+        const double ichi = ONE / chin1;
+
+        /* physical metric */
+        const double pgxx = (dxx[i] + ONE) * ichi;
+        const double pgyy = (dyy[i] + ONE) * ichi;
+        const double pgzz = (dzz[i] + ONE) * ichi;
+        const double pgxy = gxy[i] * ichi;
+        const double pgxz = gxz[i] * ichi;
+        const double pgyz = gyz[i] * ichi;
+
+        /* inverse physical metric */
+        const double det = pgxx * pgyy * pgzz + pgxy * pgyz * pgxz + pgxz * pgxy * pgyz
+                         - pgxz * pgyy * pgxz - pgxy * pgxy * pgzz - pgxx * pgyz * pgyz;
+        const double idet = ONE / det;
+        const double upxx = (pgyy * pgzz - pgyz * pgyz) * idet;
+        const double upxy = -(pgxy * pgzz - pgyz * pgxz) * idet;
+        const double upxz = (pgxy * pgyz - pgyy * pgxz) * idet;
+        const double upyy = (pgxx * pgzz - pgxz * pgxz) * idet;
+        const double upyz = -(pgxx * pgyz - pgxy * pgxz) * idet;
+        const double upzz = (pgxx * pgyy - pgxy * pgxy) * idet;
+        gupxx[i]=upxx; gupxy[i]=upxy; gupxz[i]=upxz;
+        gupyy[i]=upyy; gupyz[i]=upyz; gupzz[i]=upzz;
+
+        /* E-field RHS */
+        /* curl(B) part: epsilon^{ijk} ∂_j (alpha * B_k) in coordinate basis */
+        /* Using lower-index B fields: B_i_lower = pg_{ij} * B^j */
+        const double BxL = pgxx*Bx[i] + pgxy*By[i] + pgxz*Bz[i];
+        const double ByL = pgxy*Bx[i] + pgyy*By[i] + pgyz*Bz[i];
+        const double BzL = pgxz*Bx[i] + pgyz*By[i] + pgzz*Bz[i];
+
+        /* Physical metric derivatives (chain rule from conformal) */
+        const double pgxx_x = (gxxx[i] - pgxx*chix[i]) * ichi;
+        /* const double pgxx_y = (gxxy[i] - pgxx*chiy[i]) * ichi; */
+        const double pgxy_x = (gxyx[i] - pgxy*chix[i]) * ichi;
+        const double pgxy_y = (gxyy[i] - pgxy*chiy[i]) * ichi;
+        const double pgxz_x = (gxzx[i] - pgxz*chix[i]) * ichi;
+        const double pgxz_z = (gxzz[i] - pgxz*chiz[i]) * ichi;
+        const double pgyy_y = (gyyy[i] - pgyy*chiy[i]) * ichi;
+        const double pgyz_y = (gyzy[i] - pgyz*chiy[i]) * ichi;
+        const double pgyz_z = (gyzz[i] - pgyz*chiz[i]) * ichi;
+        const double pgzz_z = (gzzz[i] - pgzz*chiz[i]) * ichi;
+
+        /* Curl_x(B) = ∂_y (alpha*BzL) - ∂_z (alpha*ByL) */
+        const double aBx = alpn1*BxL, aBy = alpn1*ByL, aBz = alpn1*BzL;
+        const double curlBx = (aBz*Lapy[i] + alpn1*(pgxz*Bxy[i]+pgyz*Byy[i]+pgzz*Bzy[i]) + alpn1*(Bx[i]*gxzy[i]+By[i]*gyzy[i]+Bz[i]*gzzy[i]))
+                            - (aBy*Lapz[i] + alpn1*(pgxy*Bxz[i]+pgyy*Byz[i]+pgyz*Bzz[i]) + alpn1*(Bx[i]*gxyz[i]+By[i]*gyyz[i]+Bz[i]*gyzz[i]));
+        double curlBy = (aBx*Lapz[i] + alpn1*(pgxx*Bxz[i]+pgxy*Byz[i]+pgxz*Bzz[i]) + alpn1*(Bx[i]*gxxz[i]+By[i]*gxyz[i]+Bz[i]*gxzz[i]))
+                      - (aBz*Lapx[i] + alpn1*(pgxz*Bxx[i]+pgyz*Byx[i]+pgzz*Bzx[i]) + alpn1*(Bx[i]*gxzx[i]+By[i]*gyzx[i]+Bz[i]*gzzx[i]));
+        double curlBz = (aBy*Lapx[i] + alpn1*(pgxy*Bxx[i]+pgyy*Byx[i]+pgyz*Bzx[i]) + alpn1*(Bx[i]*gxyx[i]+By[i]*gyyx[i]+Bz[i]*gyzx[i]))
+                      - (aBx*Lapy[i] + alpn1*(pgxx*Bxy[i]+pgxy*Byy[i]+pgxz*Bzy[i]) + alpn1*(Bx[i]*gxxy[i]+By[i]*gxyy[i]+Bz[i]*gxzy[i]));
+
+        /* Advection part: -beta^j * ∂_j E^i */
+        const double advEx = Ex[i]*betaxx[i] + Ey[i]*betaxy[i] + Ez[i]*betaxz[i];
+        const double advEy = Ex[i]*betayx[i] + Ey[i]*betayy[i] + Ez[i]*betayz[i];
+        const double advEz = Ex[i]*betazx[i] + Ey[i]*betazy[i] + Ez[i]*betazz[i];
+
+        /* grad(Kpsi) contracted with inverse metric */
+        const double gupKx = upxx*Kpsix[i] + upxy*Kpsiy[i] + upxz*Kpsiz[i];
+        const double gupKy = upxy*Kpsix[i] + upyy*Kpsiy[i] + upyz*Kpsiz[i];
+        const double gupKz = upxz*Kpsix[i] + upyz*Kpsiy[i] + upzz*Kpsiz[i];
+
+        Ex_rhs[i] = alpn1*trK[i]*Ex[i] - advEx - FOUR*PI*alpn1*Jx[i] - alpn1*gupKx + chi3o2*curlBx;
+        Ey_rhs[i] = alpn1*trK[i]*Ey[i] - advEy - FOUR*PI*alpn1*Jy[i] - alpn1*gupKy + chi3o2*curlBy;
+        Ez_rhs[i] = alpn1*trK[i]*Ez[i] - advEz - FOUR*PI*alpn1*Jz[i] - alpn1*gupKz + chi3o2*curlBz;
+
+        /* B-field RHS: similar but with -chi^{3/2} * curl(E) and grad(Kphi) */
+        const double ExL = pgxx*Ex[i] + pgxy*Ey[i] + pgxz*Ez[i];
+        const double EyL = pgxy*Ex[i] + pgyy*Ey[i] + pgyz*Ez[i];
+        const double EzL = pgxz*Ex[i] + pgyz*Ey[i] + pgzz*Ez[i];
+
+        const double aEx = alpn1*ExL, aEy = alpn1*EyL, aEz = alpn1*EzL;
+        const double curlEx = (aEz*Lapy[i] + alpn1*(pgxz*Exy[i]+pgyz*Eyy[i]+pgzz*Ezy[i]) + alpn1*(Ex[i]*gxzy[i]+Ey[i]*gyzy[i]+Ez[i]*gzzy[i]))
+                            - (aEy*Lapz[i] + alpn1*(pgxy*Exz[i]+pgyy*Eyz[i]+pgyz*Ezz[i]) + alpn1*(Ex[i]*gxyz[i]+Ey[i]*gyyz[i]+Ez[i]*gyzz[i]));
+        double curlEy = (aEx*Lapz[i] + alpn1*(pgxx*Exz[i]+pgxy*Eyz[i]+pgxz*Ezz[i]) + alpn1*(Ex[i]*gxxz[i]+Ey[i]*gxyz[i]+Ez[i]*gxzz[i]))
+                      - (aEz*Lapx[i] + alpn1*(pgxz*Exx[i]+pgyz*Eyx[i]+pgzz*Ezx[i]) + alpn1*(Ex[i]*gxzx[i]+Ey[i]*gyzx[i]+Ez[i]*gzzx[i]));
+        double curlEz = (aEy*Lapx[i] + alpn1*(pgxy*Exx[i]+pgyy*Eyx[i]+pgyz*Ezx[i]) + alpn1*(Ex[i]*gxyx[i]+Ey[i]*gyyx[i]+Ez[i]*gyzx[i]))
+                      - (aEx*Lapy[i] + alpn1*(pgxx*Exy[i]+pgxy*Eyy[i]+pgxz*Ezy[i]) + alpn1*(Ex[i]*gxxy[i]+Ey[i]*gxyy[i]+Ez[i]*gxzy[i]));
+
+        const double advBx = Bx[i]*betaxx[i] + By[i]*betaxy[i] + Bz[i]*betaxz[i];
+        const double advBy = Bx[i]*betayx[i] + By[i]*betayy[i] + Bz[i]*betayz[i];
+        const double advBz = Bx[i]*betazx[i] + By[i]*betazy[i] + Bz[i]*betazz[i];
+
+        const double gupKphix = upxx*Kphix[i] + upxy*Kphiy[i] + upxz*Kphiz[i];
+        const double gupKphiy = upxy*Kphix[i] + upyy*Kphiy[i] + upyz*Kphiz[i];
+        const double gupKphiz = upxz*Kphix[i] + upyz*Kphiy[i] + upzz*Kphiz[i];
+
+        Bx_rhs[i] = alpn1*trK[i]*Bx[i] - advBx - alpn1*gupKphix - chi3o2*curlEx;
+        By_rhs[i] = alpn1*trK[i]*By[i] - advBy - alpn1*gupKphiy - chi3o2*curlEy;
+        Bz_rhs[i] = alpn1*trK[i]*Bz[i] - advBz - alpn1*gupKphiz - chi3o2*curlEz;
+
+        /* Scalar potential RHS */
+        const double divE = Exx[i] + Eyy[i] + Ezz[i];
+        const double divB = Bxx[i] + Byy[i] + Bzz[i];
+        const double chiCont = F3o2 * ichi * (chix[i]*Ex[i] + chiy[i]*Ey[i] + chiz[i]*Ez[i]);
+        Kpsi_rhs[i] = FOUR*PI*alpn1*qchar[i] - alpn1*kappa*Kpsi[i] - alpn1*(divE - chiCont);
+        Kphi_rhs[i] = -alpn1*kappa*Kphi[i] - alpn1*(divB - F3o2*ichi*(chix[i]*Bx[i] + chiy[i]*By[i] + chiz[i]*Bz[i]));
+
+        /* Stress-energy tensor */
+        const double E2 = pgxx*Ex[i]*Ex[i] + pgyy*Ey[i]*Ey[i] + pgzz*Ez[i]*Ez[i]
+                        + TWO*(pgxy*Ex[i]*Ey[i] + pgxz*Ex[i]*Ez[i] + pgyz*Ey[i]*Ez[i]);
+        const double B2 = pgxx*Bx[i]*Bx[i] + pgyy*By[i]*By[i] + pgzz*Bz[i]*Bz[i]
+                        + TWO*(pgxy*Bx[i]*By[i] + pgxz*Bx[i]*Bz[i] + pgyz*By[i]*Bz[i]);
+        rho[i] = (E2 + B2) / (EIT * PI);
+        const double ichi3o2 = ONE / chi3o2;
+        Sx[i] = (Ey[i]*Bz[i] - Ez[i]*By[i]) * F1o4PI * ichi3o2;
+        Sy[i] = (Ez[i]*Bx[i] - Ex[i]*Bz[i]) * F1o4PI * ichi3o2;
+        Sz[i] = (Ex[i]*By[i] - Ey[i]*Bx[i]) * F1o4PI * ichi3o2;
+        const double lExi = pgxx*Ex[i] + pgxy*Ey[i] + pgxz*Ez[i];
+        const double lEyi = pgxy*Ex[i] + pgyy*Ey[i] + pgyz*Ez[i];
+        const double lEzi = pgxz*Ex[i] + pgyz*Ey[i] + pgzz*Ez[i];
+        const double lBxi = pgxx*Bx[i] + pgxy*By[i] + pgxz*Bz[i];
+        const double lByi = pgxy*Bx[i] + pgyy*By[i] + pgyz*Bz[i];
+        const double lBzi = pgxz*Bx[i] + pgyz*By[i] + pgzz*Bz[i];
+        Sxx[i] = rho[i]*pgxx - (lExi*lExi + lBxi*lBxi) * F1o4PI;
+        Sxy[i] = rho[i]*pgxy - (lExi*lEyi + lBxi*lByi) * F1o4PI;
+        Sxz[i] = rho[i]*pgxz - (lExi*lEzi + lBxi*lBzi) * F1o4PI;
+        Syy[i] = rho[i]*pgyy - (lEyi*lEyi + lByi*lByi) * F1o4PI;
+        Syz[i] = rho[i]*pgyz - (lEyi*lEzi + lByi*lBzi) * F1o4PI;
+        Szz[i] = rho[i]*pgzz - (lEzi*lEzi + lBzi*lBzi) * F1o4PI;
+    }
+
+    /* ==== 3. Call BSSN RHS with EM stress-energy ==== */
+    gont = f_compute_rhs_bssn(ex, T, X, Y, Z,
+        chi, trK, dxx, gxy, gxz, dyy, gyz, dzz,
+        Axx, Axy, Axz, Ayy, Ayz, Azz,
+        Gamx, Gamy, Gamz, Lap, betax, betay, betaz, dtSfx, dtSfy, dtSfz,
+        chi_rhs, trK_rhs,
+        gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
+        Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
+        Gamx_rhs, Gamy_rhs, Gamz_rhs, Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
+        dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
+        rho, Sx, Sy, Sz, Sxx, Sxy, Sxz, Syy, Syz, Szz,
+        Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+        Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+        Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+        Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+        ham_Res, movx_Res, movy_Res, movz_Res,
+        Gmx_Res, Gmy_Res, Gmz_Res,
+        Symmetry, Lev, eps, co);
+    if (!gont) {
+
+    /* ==== 4. Advection terms for EM fields ==== */
+    lopsided(ex, X, Y, Z, Kpsi, Kpsi_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, Kphi, Kphi_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, Ex,   Ex_rhs,   betax, betay, betaz, Symmetry, ASS);
+    lopsided(ex, X, Y, Z, Ey,   Ey_rhs,   betax, betay, betaz, Symmetry, SAS);
+    lopsided(ex, X, Y, Z, Ez,   Ez_rhs,   betax, betay, betaz, Symmetry, SSA);
+    lopsided(ex, X, Y, Z, Bx,   Bx_rhs,   betax, betay, betaz, Symmetry, SAA);
+    lopsided(ex, X, Y, Z, By,   By_rhs,   betax, betay, betaz, Symmetry, ASA);
+    lopsided(ex, X, Y, Z, Bz,   Bz_rhs,   betax, betay, betaz, Symmetry, AAS);
+
+    /* ==== 5. KO dissipation for EM fields ==== */
+    if (eps > ZEO) {
+        kodis(ex, X, Y, Z, Kpsi, Kpsi_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Kphi, Kphi_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Ex,   Ex_rhs,   ASS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Ey,   Ey_rhs,   SAS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Ez,   Ez_rhs,   SSA, Symmetry, eps);
+        kodis(ex, X, Y, Z, Bx,   Bx_rhs,   SAA, Symmetry, eps);
+        kodis(ex, X, Y, Z, By,   By_rhs,   ASA, Symmetry, eps);
+        kodis(ex, X, Y, Z, Bz,   Bz_rhs,   AAS, Symmetry, eps);
+    }
+
+    /* ==== 6. NaN check ==== */
+        for (int i = 0; i < all; ++i) {
+            if (!isfinite(Ex_rhs[i]+Ey_rhs[i]+Ez_rhs[i]+Bx_rhs[i]+By_rhs[i]+Bz_rhs[i]+Kpsi_rhs[i]+Kphi_rhs[i])) {
+                gont = 1; break;
+            }
+        }
+        } /* inner if (!gont) */
+    } /* outer if (!gont) */
+
+    free(chix);free(chiy);free(chiz);
+    free(Exx);free(Exy);free(Exz);free(Eyx);free(Eyy);free(Eyz);free(Ezx);free(Ezy);free(Ezz);
+    free(Bxx);free(Bxy);free(Bxz);free(Byx);free(Byy);free(Byz);free(Bzx);free(Bzy);free(Bzz);
+    free(Kpsix);free(Kpsiy);free(Kpsiz);
+    free(Kphix);free(Kphiy);free(Kphiz);
+    free(Lapx);free(Lapy);free(Lapz);
+    free(betaxx);free(betaxy);free(betaxz);free(betayx);free(betayy);free(betayz);free(betazx);free(betazy);free(betazz);
+    free(gxxx);free(gxxy);free(gxxz);free(gxyx);free(gxyy);free(gxyz);free(gxzx);free(gxzy);free(gxzz);
+    free(gyyx);free(gyyy);free(gyyz);free(gyzx);free(gyzy);free(gyzz);free(gzzx);free(gzzy);free(gzzz);
+    free(gupxx);free(gupxy);free(gupxz);free(gupyy);free(gupyz);free(gupzz);
+    return gont;
+}

AMSS_NCKU_source/bssn_escalar_rhs_c.C

@@ -0,0 +1,169 @@
+#include "macrodef.h"
+#include "bssn_rhs.h"
+#include "share_func.h"
+#include "tool.h"
+#include <vector>
+
+namespace
+{
+    // Reuse the temporary workspace across block calls to avoid repeated heap churn
+    // in the EScalar wrapper. MPI ranks execute this path sequentially, so a single
+    // process-local buffer is sufficient here.
+    std::vector<double> g_escalar_tmp_store;
+}
+
+#ifdef fortran1
+#define f_frpotential frpotential
+#endif
+#ifdef fortran2
+#define f_frpotential FRPOTENTIAL
+#endif
+#ifdef fortran3
+#define f_frpotential frpotential_
+#endif
+
+extern "C"
+{
+    void f_frpotential(int *, double *, double *, double *);
+}
+
+int f_compute_rhs_bssn_escalar_c(int *ex, double &T,
+                                 double *X, double *Y, double *Z,
+                                 double *chi, double *trK,
+                                 double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                                 double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                                 double *Gamx, double *Gamy, double *Gamz,
+                                 double *Lap, double *betax, double *betay, double *betaz,
+                                 double *dtSfx, double *dtSfy, double *dtSfz,
+                                 double *Sphi, double *Spi,
+                                 double *chi_rhs, double *trK_rhs,
+                                 double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                                 double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                                 double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                                 double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                                 double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                                 double *Sphi_rhs, double *Spi_rhs,
+                                 double *rho, double *Sx, double *Sy, double *Sz,
+                                 double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                                 double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                                 double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                                 double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                                 double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                                 double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                                 double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                                 int &Symmetry, int &Lev, double &eps, int &co)
+{
+    const int nx = ex[0], ny = ex[1], nz = ex[2];
+    const int all = nx * ny * nz;
+
+    const size_t workspace_size = size_t(all) * 17;
+    if (g_escalar_tmp_store.size() < workspace_size)
+        g_escalar_tmp_store.resize(workspace_size);
+
+    double *tmp_ptr = g_escalar_tmp_store.data();
+    auto alloc_tmp = [&](int n = 1) -> double *
+    {
+        double *ptr = tmp_ptr;
+        tmp_ptr += size_t(all) * n;
+        return ptr;
+    };
+
+    double *chix = alloc_tmp(), *chiy = alloc_tmp(), *chiz = alloc_tmp();
+    double *Kx = alloc_tmp(), *Ky = alloc_tmp(), *Kz = alloc_tmp();
+    double *fxx = alloc_tmp(), *fxy = alloc_tmp(), *fxz = alloc_tmp();
+    double *fyy = alloc_tmp(), *fyz = alloc_tmp(), *fzz = alloc_tmp();
+    double *Lapx = alloc_tmp(), *Lapy = alloc_tmp(), *Lapz = alloc_tmp();
+    double *V = alloc_tmp(), *dVdSphi = alloc_tmp();
+
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0, HALF = 0.5;
+    const double SSS[3] = {1.0, 1.0, 1.0};
+
+    fderivs(ex, chi, chix, chiy, chiz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Lap, Lapx, Lapy, Lapz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Sphi, Kx, Ky, Kz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, Sphi, fxx, fxy, fxz, fyy, fyz, fzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+
+    f_frpotential(ex, Sphi, V, dVdSphi);
+
+    for (int i = 0; i < all; ++i)
+    {
+        const double alpn1 = Lap[i] + ONE;
+        const double chin1 = chi[i] + ONE;
+        const double gxx = dxx[i] + ONE;
+        const double gyy = dyy[i] + ONE;
+        const double gzz = dzz[i] + ONE;
+        const double det = gxx * gyy * gzz + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i]
+                         - gxz[i] * gyy * gxz[i] - gxy[i] * gxy[i] * gzz - gxx * gyz[i] * gyz[i];
+        const double gupxx = (gyy * gzz - gyz[i] * gyz[i]) / det;
+        const double gupxy = -(gxy[i] * gzz - gyz[i] * gxz[i]) / det;
+        const double gupxz = (gxy[i] * gyz[i] - gyy * gxz[i]) / det;
+        const double gupyy = (gxx * gzz - gxz[i] * gxz[i]) / det;
+        const double gupyz = -(gxx * gyz[i] - gxy[i] * gxz[i]) / det;
+        const double gupzz = (gxx * gyy - gxy[i] * gxy[i]) / det;
+
+        Sphi_rhs[i] = alpn1 * Spi[i];
+
+        Spi_rhs[i] = gupxx * fxx[i] + gupyy * fyy[i] + gupzz * fzz[i]
+                   + TWO * (gupxy * fxy[i] + gupxz * fxz[i] + gupyz * fyz[i])
+                   - ((Gamx[i] + (gupxx * chix[i] + gupxy * chiy[i] + gupxz * chiz[i]) / TWO / chin1) * Kx[i]
+                   +  (Gamy[i] + (gupxy * chix[i] + gupyy * chiy[i] + gupyz * chiz[i]) / TWO / chin1) * Ky[i]
+                   +  (Gamz[i] + (gupxz * chix[i] + gupyz * chiy[i] + gupzz * chiz[i]) / TWO / chin1) * Kz[i]);
+
+        Spi_rhs[i] = Spi_rhs[i] * alpn1
+                   + gupxx * Lapx[i] * Kx[i] + gupxy * Lapx[i] * Ky[i] + gupxz * Lapx[i] * Kz[i]
+                   + gupxy * Lapy[i] * Kx[i] + gupyy * Lapy[i] * Ky[i] + gupyz * Lapy[i] * Kz[i]
+                   + gupxz * Lapz[i] * Kx[i] + gupyz * Lapz[i] * Ky[i] + gupzz * Lapz[i] * Kz[i];
+
+        Spi_rhs[i] = Spi_rhs[i] * chin1 + alpn1 * (trK[i] * Spi[i] - dVdSphi[i]);
+
+        rho[i] = chin1 * ((gupxx * Kx[i] * Kx[i] + gupyy * Ky[i] * Ky[i] + gupzz * Kz[i] * Kz[i]) * HALF
+               + gupxy * Kx[i] * Ky[i] + gupxz * Kx[i] * Kz[i] + gupyz * Ky[i] * Kz[i])
+               + Spi[i] * Spi[i] * HALF + V[i];
+        Sx[i] = -Spi[i] * Kx[i];
+        Sy[i] = -Spi[i] * Ky[i];
+        Sz[i] = -Spi[i] * Kz[i];
+
+        const double pressure = (rho[i] - Spi[i] * Spi[i]) / chin1;
+        Sxx[i] = Kx[i] * Kx[i] - pressure * gxx;
+        Sxy[i] = Kx[i] * Ky[i] - pressure * gxy[i];
+        Sxz[i] = Kx[i] * Kz[i] - pressure * gxz[i];
+        Syy[i] = Ky[i] * Ky[i] - pressure * gyy;
+        Syz[i] = Ky[i] * Kz[i] - pressure * gyz[i];
+        Szz[i] = Kz[i] * Kz[i] - pressure * gzz;
+    }
+
+    if (f_compute_rhs_bssn(ex, T, X, Y, Z,
+                           chi, trK,
+                           dxx, gxy, gxz, dyy, gyz, dzz,
+                           Axx, Axy, Axz, Ayy, Ayz, Azz,
+                           Gamx, Gamy, Gamz,
+                           Lap, betax, betay, betaz,
+                           dtSfx, dtSfy, dtSfz,
+                           chi_rhs, trK_rhs,
+                           gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
+                           Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
+                           Gamx_rhs, Gamy_rhs, Gamz_rhs,
+                           Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
+                           dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
+                           rho, Sx, Sy, Sz,
+                           Sxx, Sxy, Sxz, Syy, Syz, Szz,
+                           Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+                           Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+                           Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+                           Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+                           ham_Res, movx_Res, movy_Res, movz_Res,
+                           Gmx_Res, Gmy_Res, Gmz_Res,
+                           Symmetry, Lev, eps, co))
+        return 1;
+
+    lopsided_kodis(ex, X, Y, Z, Sphi, Sphi_rhs, betax, betay, betaz, Symmetry, SSS, eps);
+    lopsided_kodis(ex, X, Y, Z, Spi, Spi_rhs, betax, betay, betaz, Symmetry, SSS, eps);
+
+    for (int i = 0; i < all; ++i)
+    {
+        if (Sphi_rhs[i] != Sphi_rhs[i] || Spi_rhs[i] != Spi_rhs[i] || rho[i] != rho[i])
+            return 1;
+    }
+
+    return 0;
+}

AMSS_NCKU_source/bssn_rhs.h

@@ -32,6 +32,19 @@
 #define f_compute_rhs_Z4c_ss compute_rhs_z4c_ss_
 #define f_compute_constraint_fr compute_constraint_fr_
 #endif
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+        void f_bssn_rhs_kernel_timing_reset();
+        int f_bssn_rhs_kernel_timing_bucket_count();
+        const double *f_bssn_rhs_kernel_timing_local_seconds();
+        const char *f_bssn_rhs_kernel_timing_label(int);
+#ifdef __cplusplus
+}
+#endif
+
 extern "C"
 {
         int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
@@ -54,6 +67,27 @@ extern "C"
                                int &, int &, double &, int &);
 }
 
+int f_compute_rhs_bssn_escalar_c(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
+                                 double *, double *,                                                                                 // chi, trK
+                                 double *, double *, double *, double *, double *, double *,                                         // gij
+                                 double *, double *, double *, double *, double *, double *,                                         // Aij
+                                 double *, double *, double *,                                                                       // Gam
+                                 double *, double *, double *, double *, double *, double *, double *,                               // Gauge
+                                 double *, double *,                                                                                 // Sphi, Spi
+                                 double *, double *,                                                                                 // chi, trK
+                                 double *, double *, double *, double *, double *, double *,                                         // gij
+                                 double *, double *, double *, double *, double *, double *,                                         // Aij
+                                 double *, double *, double *,                                                                       // Gam
+                                 double *, double *, double *, double *, double *, double *, double *,                               // Gauge
+                                 double *, double *,                                                                                 // Sphi, Spi
+                                 double *, double *, double *, double *, double *, double *, double *, double *, double *, double *, // stress-energy
+                                 double *, double *, double *, double *, double *, double *,                                         // Christoffel
+                                 double *, double *, double *, double *, double *, double *,                                         // Christoffel
+                                 double *, double *, double *, double *, double *, double *,                                         // Christoffel
+                                 double *, double *, double *, double *, double *, double *,                                         // Ricci
+                                 double *, double *, double *, double *, double *, double *, double *,                               // constraint violation
+                                 int &, int &, double &, int &);
+
 extern "C"
 {
         int f_compute_rhs_bssn_ss(int *, double &, double *, double *, double *,                                                      // ex,T,rho,sigma,R
@@ -228,4 +262,31 @@ extern "C"
                                      double *);
 } // FR_cons
 
+// BSSN-EM C kernel (replaces empart.f90 + bssn_rhs.f90 for BSSN+Maxwell)
+int f_compute_rhs_bssn_em_c(int *, double &, double *, double *, double *,
+                             double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *,
+                             double *, double *,
+                             double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *,
+                             double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             double *, double *, double *, double *, double *, double *,
+                             int &, int &, double &, int &);
+
 #endif /* BSSN_H */

AMSS_NCKU_source/cgh.C

@@ -130,7 +130,11 @@ void cgh::compose_cgh(int nprocs)
   for (int lev = 0; lev < levels; lev++)
   {
     checkPatchList(PatL[lev], false);
+#ifdef INTERP_LB_OPTIMIZE
+    Parallel::distribute_optimize(PatL[lev], nprocs, ingfs, fngfs, false);
+#else
     Parallel::distribute(PatL[lev], nprocs, ingfs, fngfs, false);
+#endif
 #if (RPB == 1)
     // we need distributed box of PatL[lev] and PatL[lev-1]
     if (lev > 0)
@@ -1301,13 +1305,13 @@ bool cgh::Interp_One_Point(MyList<var> *VarList,
 }
 
 
-void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+bool cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                           MyList<var> *OldList, MyList<var> *StateList,
                           MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                           monitor *ErrorMonitor)
 {
   if (lev < movls)
-    return;
+    return false;
 
 #if (0)
   // #if (PSTR == 1 || PSTR == 2)
@@ -1396,7 +1400,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
       for (bhi = 0; bhi < BH_num; bhi++)
         delete[] tmpPorg[bhi];
       delete[] tmpPorg;
-      return;
+      return false;
     }
     // x direction
     rr = (Porg0[bhi][0] - handle[lev][grd][0]) / dX;
@@ -1500,6 +1504,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
   for (int bhi = 0; bhi < BH_num; bhi++)
     delete[] tmpPorg[bhi];
   delete[] tmpPorg;
+  return tot_flag;
 }
 
 

AMSS_NCKU_source/cgh.h

@@ -74,7 +74,7 @@ public:
                                MyList<var> *OldList, MyList<var> *StateList,
                                MyList<var> *FutureList, MyList<var> *tmList,
                                int Symmetry, bool BB);
-   void Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   bool Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                         MyList<var> *OldList, MyList<var> *StateList,
                         MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                         monitor *ErrorMonitor);

AMSS_NCKU_source/diff_new.f90

@@ -69,10 +69,12 @@
   fy = ZEO
   fz = ZEO
 
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
-! x direction   
+! x direction
         if(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
@@ -371,6 +373,8 @@
   fxz = ZEO
   fyz = ZEO
 
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1000,7 +1004,86 @@
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
+#if 0  
+! x direction   
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
+!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+!  fx(i) = ---------------------------------------------
+!                             12 dx
+      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
 
+    elseif(i+1 <= imax .and. i-1 >= imin)then
+!
+!              - f(i-1) + f(i+1)
+!  fx(i) = --------------------------------
+!                     2 dx
+      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+
+! set imax and imin 0
+    endif
+! y direction   
+        if(j+2 <= jmax .and. j-2 >= jmin)then
+
+      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+    elseif(j+1 <= jmax .and. j-1 >= jmin)then
+
+     fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+
+! set jmax and jmin 0
+    endif
+! z direction   
+        if(k+2 <= kmax .and. k-2 >= kmin)then
+
+      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+    elseif(k+1 <= kmax .and. k-1 >= kmin)then
+
+      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+
+! set kmax and kmin 0
+    endif
+#elif 0
+! x direction   
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
+!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+!  fx(i) = ---------------------------------------------
+!                             12 dx
+      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+    elseif(i+3 <= imax .and. i-1 >= imin)then
+      fx(i,j,k)=d12dx*(-3.d0*fh(i-1,j,k)-1.d1*fh(i,j,k)+1.8d1*fh(i+1,j,k)-6.d0*fh(i+2,j,k)+fh(i+3,j,k))
+    elseif(i+1 <= imax .and. i-3 >= imin)then
+      fx(i,j,k)=d12dx*( 3.d0*fh(i+1,j,k)+1.d1*fh(i,j,k)-1.8d1*fh(i-1,j,k)+6.d0*fh(i-2,j,k)-fh(i-3,j,k))
+! set imax and imin 0
+    endif
+! y direction   
+        if(j+2 <= jmax .and. j-2 >= jmin)then
+
+      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+    elseif(j+3 <= jmax .and. j-1 >= jmin)then
+      fy(i,j,k)=d12dy*(-3.d0*fh(i,j-1,k)-1.d1*fh(i,j,k)+1.8d1*fh(i,j+1,k)-6.d0*fh(i,j+2,k)+fh(i,j+3,k))
+    elseif(j+1 <= jmax .and. j-3 >= jmin)then
+      fy(i,j,k)=d12dy*( 3.d0*fh(i,j+1,k)+1.d1*fh(i,j,k)-1.8d1*fh(i,j-1,k)+6.d0*fh(i,j-2,k)-fh(i,j-3,k))
+
+! set jmax and jmin 0
+    endif
+! z direction   
+        if(k+2 <= kmax .and. k-2 >= kmin)then
+
+      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+    elseif(k+3 <= kmax .and. k-1 >= kmin)then
+      fz(i,j,k)=d12dz*(-3.d0*fh(i,j,k-1)-1.d1*fh(i,j,k)+1.8d1*fh(i,j,k+1)-6.d0*fh(i,j,k+2)+fh(i,j,k+3))
+    elseif(k+1 <= kmax .and. k-3 >= kmin)then
+      fz(i,j,k)=d12dz*( 3.d0*fh(i,j,k+1)+1.d1*fh(i,j,k)-1.8d1*fh(i,j,k-1)+6.d0*fh(i,j,k-2)-fh(i,j,k-3))
+
+! set kmax and kmin 0
+    endif
+#else
 ! for bam comparison
    if(i+2 <= imax .and. i-2 >= imin .and. &
       j+2 <= jmax .and. j-2 >= jmin .and. &
@@ -1015,7 +1098,7 @@
       fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
       fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
    endif
-
+#endif
   enddo
   enddo
   enddo
@@ -1325,7 +1408,85 @@
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
+#if 0  
+!~~~~~~ fxx
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
+!               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
+!  fxx(i) = ----------------------------------------------------------
+!                                  12 dx^2 
+   fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
+                       -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
+   elseif(i+1 <= imax .and. i-1 >= imin)then
+!
+!               f(i-1) - 2 f(i) + f(i+1)
+!  fxx(i) = --------------------------------
+!                         dx^2 
+   fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+                      +fh(i+1,j,k)              )
+   endif
 
+
+!~~~~~~ fyy
+        if(j+2 <= jmax .and. j-2 >= jmin)then
+
+   fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
+                       -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
+   elseif(j+1 <= jmax .and. j-1 >= jmin)then
+
+   fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+                      +fh(i,j+1,k)              )
+   endif
+
+!~~~~~~ fzz
+        if(k+2 <= kmax .and. k-2 >= kmin)then
+
+   fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
+                       -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
+   elseif(k+1 <= kmax .and. k-1 >= kmin)then
+
+   fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+                      +fh(i,j,k+1)              )
+   endif
+!~~~~~~ fxy
+       if(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
+!
+!                 ( f(i-2,j-2) - 8 f(i-1,j-2) + 8 f(i+1,j-2) - f(i+2,j-2) )
+!             - 8 ( f(i-2,j-1) - 8 f(i-1,j-1) + 8 f(i+1,j-1) - f(i+2,j-1) )
+!             + 8 ( f(i-2,j+1) - 8 f(i-1,j+1) + 8 f(i+1,j+1) - f(i+2,j+1) )
+!             -   ( f(i-2,j+2) - 8 f(i-1,j+2) + 8 f(i+1,j+2) - f(i+2,j+2) )
+!  fxy(i,j) = ----------------------------------------------------------------
+!                                  144 dx dy
+   fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
+                       -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
+                       +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
+                       -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
+
+   elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
+!                 f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1) 
+!  fxy(i,j) = -----------------------------------------------------------
+!                                      4 dx dy
+   fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
+   endif
+!~~~~~~ fxz
+       if(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
+   fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
+                       -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
+                       +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
+                       -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
+   elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
+   fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
+   endif
+!~~~~~~ fyz
+       if(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
+   fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
+                       -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
+                       +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
+                       -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
+   elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
+   fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
+   endif 
+#else
 ! for bam comparison
    if(i+2 <= imax .and. i-2 >= imin .and. &
       j+2 <= jmax .and. j-2 >= jmin .and. &
@@ -1361,7 +1522,7 @@
    fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
    fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
    endif
-
+#endif
    enddo
    enddo
    enddo

AMSS_NCKU_source/diff_newwb.f90

@@ -33,7 +33,7 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx,d2dy,d2dz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -137,7 +137,7 @@
   real*8 :: dX
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1512,8 +1512,9 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: i_core_min,i_core_max,j_core_min,j_core_max,k_core_min,k_core_max
+  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
   real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0,  F45=4.5d1
@@ -1560,17 +1561,55 @@
 
   fxx = ZEO
   fyy = ZEO
-  fzz = ZEO
-  fxy = ZEO
-  fxz = ZEO
-  fyz = ZEO
-
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-!~~~~~~ fxx
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
+  fzz = ZEO
+  fxy = ZEO
+  fxz = ZEO
+  fyz = ZEO
+
+  i_core_min = max(1, imin+2)
+  i_core_max = min(ex(1), imax-2)
+  j_core_min = max(1, jmin+2)
+  j_core_max = min(ex(2), jmax-2)
+  k_core_min = max(1, kmin+2)
+  k_core_max = min(ex(3), kmax-2)
+
+  if(i_core_min <= i_core_max .and. j_core_min <= j_core_max .and. k_core_min <= k_core_max)then
+   do k=k_core_min,k_core_max
+   do j=j_core_min,j_core_max
+   do i=i_core_min,i_core_max
+! interior points always use 4th-order stencils without branch checks
+      fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
+                          -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
+      fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
+                          -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
+      fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
+                          -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
+      fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
+                          -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
+                          +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
+                          -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
+      fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
+                          -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
+                          +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
+                          -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
+      fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
+                          -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
+                          +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
+                          -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
+   enddo
+   enddo
+   enddo
+  endif
+
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+      if(i>=i_core_min .and. i<=i_core_max .and. &
+         j>=j_core_min .and. j<=j_core_max .and. &
+         k>=k_core_min .and. k<=k_core_max) cycle
+!~~~~~~ fxx
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 

AMSS_NCKU_source/fdderivs_c.C

@@ -0,0 +1,894 @@
+#include "macrodef.h"
+#include "tool.h"
+
+/*
+ * C 版 fdderivs — second derivatives d2f/dx2, d2f/dxdy, d2f/dxdz, d2f/dy2, d2f/dydz, d2f/dz2.
+ *
+ * Finite difference order selected at compile time via ghost_width macro.
+ * Multi-pass skip strategy: lowest-order computes widest region while skipping
+ * the union of higher-order regions, then each higher pass overwrites its interior.
+ */
+void fdderivs(const int ex[3],
+              const double *f,
+              double *fxx, double *fxy, double *fxz,
+              double *fyy, double *fyz, double *fzz,
+              const double *X, const double *Y, const double *Z,
+              double SYM1, double SYM2, double SYM3,
+              int Symmetry, int onoff)
+{
+    (void)onoff;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0;
+    const double F1o4   = 2.5e-1;
+    const double F8     = 8.0;
+    const double F16    = 16.0;
+    const double F30    = 30.0;
+    const double F1o12  = ONE / 12.0;
+    const double F1o144 = ONE / 144.0;
+    const double F9  = 9.0,  F45 = 45.0,  F60 = 60.0;
+    const double F27 = 27.0, F270 = 270.0, F490 = 490.0;
+    const double F1o180  = ONE / 180.0;
+    const double F1o3600 = ONE / 3600.0;
+    const double F32 = 32.0, F128 = 128.0, F168 = 168.0, F672 = 672.0;
+    const double F840  = 840.0, F1008 = 1008.0, F8064 = 8064.0, F14350 = 14350.0;
+    const double F1o5040   = ONE / 5040.0;
+    const double F1o705600 = ONE / 705600.0;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+#if (ghost_width == 2)
+    /* ---- 2nd-order ------------------------------------------------------ */
+    {
+        const int ord = 1;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = 0;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = 0;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = 0;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double Sdxdx = ONE / (dX * dX);
+        const double Sdydy = ONE / (dY * dY);
+        const double Sdzdz = ONE / (dZ * dZ);
+        const double Sdxdy = F1o4 / (dX * dY);
+        const double Sdxdz = F1o4 / (dX * dZ);
+        const double Sdydz = F1o4 / (dY * dZ);
+
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+            fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+        }
+
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2;
+        const int j2_hi = ex2 - 2;
+        const int k2_hi = ex3 - 2;
+
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Sdxdx * (
+                            fh[idx_fh_F_ord1(iF - 1, jF,     kF,     ex)] -
+                            TWO * fh[idx_fh_F_ord1(iF,     jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord1(iF + 1, jF,     kF,     ex)]);
+
+                        fyy[p] = Sdydy * (
+                            fh[idx_fh_F_ord1(iF,     jF - 1, kF,     ex)] -
+                            TWO * fh[idx_fh_F_ord1(iF,     jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord1(iF,     jF + 1, kF,     ex)]);
+
+                        fzz[p] = Sdzdz * (
+                            fh[idx_fh_F_ord1(iF,     jF,     kF - 1, ex)] -
+                            TWO * fh[idx_fh_F_ord1(iF,     jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord1(iF,     jF,     kF + 1, ex)]);
+
+                        fxy[p] = Sdxdy * (
+                            fh[idx_fh_F_ord1(iF - 1, jF - 1, kF, ex)] -
+                            fh[idx_fh_F_ord1(iF + 1, jF - 1, kF, ex)] -
+                            fh[idx_fh_F_ord1(iF - 1, jF + 1, kF, ex)] +
+                            fh[idx_fh_F_ord1(iF + 1, jF + 1, kF, ex)]);
+
+                        fxz[p] = Sdxdz * (
+                            fh[idx_fh_F_ord1(iF - 1, jF, kF - 1, ex)] -
+                            fh[idx_fh_F_ord1(iF + 1, jF, kF - 1, ex)] -
+                            fh[idx_fh_F_ord1(iF - 1, jF, kF + 1, ex)] +
+                            fh[idx_fh_F_ord1(iF + 1, jF, kF + 1, ex)]);
+
+                        fyz[p] = Sdydz * (
+                            fh[idx_fh_F_ord1(iF, jF - 1, kF - 1, ex)] -
+                            fh[idx_fh_F_ord1(iF, jF + 1, kF - 1, ex)] -
+                            fh[idx_fh_F_ord1(iF, jF - 1, kF + 1, ex)] +
+                            fh[idx_fh_F_ord1(iF, jF + 1, kF + 1, ex)]);
+                    }
+                }
+            }
+        }
+        return;
+    }
+#elif (ghost_width == 3)
+    /* ---- 4th-order (original code) ------------------------------------ */
+    {
+        const int ord = 2;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double Sdxdx = ONE / (dX * dX);
+        const double Sdydy = ONE / (dY * dY);
+        const double Sdzdz = ONE / (dZ * dZ);
+        const double Fdxdx = F1o12 / (dX * dX);
+        const double Fdydy = F1o12 / (dY * dY);
+        const double Fdzdz = F1o12 / (dZ * dZ);
+        const double Sdxdy = F1o4 / (dX * dY);
+        const double Sdxdz = F1o4 / (dX * dZ);
+        const double Sdydz = F1o4 / (dY * dZ);
+        const double Fdxdy = F1o144 / (dX * dY);
+        const double Fdxdz = F1o144 / (dX * dZ);
+        const double Fdydz = F1o144 / (dY * dZ);
+
+        /* zero high-boundary faces (points the loops below won't cover) */
+        for (int j0 = 0; j0 < ex2; ++j0)
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+        for (int k0 = 0; k0 < ex3 - 1; ++k0)
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+        for (int k0 = 0; k0 < ex3 - 1; ++k0)
+            for (int j0 = 0; j0 < ex2 - 1; ++j0) {
+                const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+
+        if (kminF == 1) {
+            for (int j0 = 0; j0 < ex2; ++j0)
+                for (int i0 = 0; i0 < ex1; ++i0) {
+                    const size_t p = idx_ex(i0, j0, 0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+        if (jminF == 1) {
+            for (int k0 = 0; k0 < ex3; ++k0)
+                for (int i0 = 0; i0 < ex1; ++i0) {
+                    const size_t p = idx_ex(i0, 0, k0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+        if (iminF == 1) {
+            for (int k0 = 0; k0 < ex3; ++k0)
+                for (int j0 = 0; j0 < ex2; ++j0) {
+                    const size_t p = idx_ex(0, j0, k0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2;
+        const int j2_hi = ex2 - 2;
+        const int k2_hi = ex3 - 2;
+
+        const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i4_hi = ex1 - 3;
+        const int j4_hi = ex2 - 3;
+        const int k4_hi = ex3 - 3;
+
+        const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
+
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        if (has4 &&
+                            i0 >= i4_lo && i0 <= i4_hi &&
+                            j0 >= j4_lo && j0 <= j4_hi &&
+                            k0 >= k4_lo && k0 <= k4_hi) {
+                            continue;
+                        }
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Sdxdx * (
+                            fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                            TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]);
+
+                        fyy[p] = Sdydy * (
+                            fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                            TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]);
+
+                        fzz[p] = Sdzdz * (
+                            fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                            TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]);
+
+                        fxy[p] = Sdxdy * (
+                            fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
+                            fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
+                            fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
+                            fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]);
+
+                        fxz[p] = Sdxdz * (
+                            fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
+                            fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
+                            fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
+                            fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]);
+
+                        fyz[p] = Sdydz * (
+                            fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
+                            fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
+                            fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
+                            fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]);
+                    }
+                }
+            }
+        }
+
+        if (has4) {
+            for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Fdxdx * (
+                            -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
+                            F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                            F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                            fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
+                            F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]);
+
+                        fyy[p] = Fdydy * (
+                            -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
+                            F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                            F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                            fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+                            F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]);
+
+                        fzz[p] = Fdzdz * (
+                            -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+                            F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                            F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                            fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                            F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]);
+
+                        /* fxy: 5x5 outer product */
+                        {
+                            const double t_jm2 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)]);
+
+                            const double t_jm1 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)]);
+
+                            const double t_jp1 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)]);
+
+                            const double t_jp2 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)]);
+
+                            fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
+                        }
+
+                        /* fxz: 5x5 outer product */
+                        {
+                            const double t_km2 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)]);
+
+                            const double t_km1 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)]);
+
+                            const double t_kp1 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)]);
+
+                            const double t_kp2 = (
+                                fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
+                                -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)]);
+
+                            fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                        }
+
+                        /* fyz: 5x5 outer product */
+                        {
+                            const double t_km2 = (
+                                fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
+                                -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)]);
+
+                            const double t_km1 = (
+                                fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
+                                -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)]);
+
+                            const double t_kp1 = (
+                                fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
+                                -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)]);
+
+                            const double t_kp2 = (
+                                fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
+                                -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
+                                +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
+                                -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)]);
+
+                            fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                        }
+                    }
+                }
+            }
+        }
+        return;
+    }
+#elif (ghost_width == 4)
+    /* ---- 6th-order ----------------------------------------------------- */
+    {
+        const int ord = 3;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        /* Denominators */
+        const double Sdxdx = ONE / (dX * dX);           // 2nd
+        const double Sdydy = ONE / (dY * dY);
+        const double Sdzdz = ONE / (dZ * dZ);
+        const double Fdxdx = F1o12 / (dX * dX);          // 4th
+        const double Fdydy = F1o12 / (dY * dY);
+        const double Fdzdz = F1o12 / (dZ * dZ);
+        const double Xdxdx = F1o180 / (dX * dX);         // 6th
+        const double Xdydy = F1o180 / (dY * dY);
+        const double Xdzdz = F1o180 / (dZ * dZ);
+        const double Sdxdy = F1o4    / (dX * dY);
+        const double Sdxdz = F1o4    / (dX * dZ);
+        const double Sdydz = F1o4    / (dY * dZ);
+        const double Fdxdy = F1o144  / (dX * dY);
+        const double Fdxdz = F1o144  / (dX * dZ);
+        const double Fdydz = F1o144  / (dY * dZ);
+        const double Xdxdy = F1o3600 / (dX * dY);
+        const double Xdxdz = F1o3600 / (dX * dZ);
+        const double Xdydz = F1o3600 / (dY * dZ);
+
+        /* zero everything first */
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+            fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+        }
+
+        /* loop bounds for each pass (from widest to narrowest) */
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2, j2_hi = ex2 - 2, k2_hi = ex3 - 2;
+
+        const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i4_hi = ex1 - 3, j4_hi = ex2 - 3, k4_hi = ex3 - 3;
+
+        const int i6_lo = (iminF + 2 > 0) ? (iminF + 2) : 0;
+        const int j6_lo = (jminF + 2 > 0) ? (jminF + 2) : 0;
+        const int k6_lo = (kminF + 2 > 0) ? (kminF + 2) : 0;
+        const int i6_hi = ex1 - 4, j6_hi = ex2 - 4, k6_hi = ex3 - 4;
+
+        const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
+        const int has6 = (i6_lo <= i6_hi && j6_lo <= j6_hi && k6_lo <= k6_hi);
+
+        /* 2nd-order: skip 4th+6th overlap */
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        bool in4 = has4 && i0>=i4_lo && i0<=i4_hi && j0>=j4_lo && j0<=j4_hi && k0>=k4_lo && k0<=k4_hi;
+                        if (in4) continue;
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Sdxdx * (fh[idx_fh_F(iF - 1, jF,     kF,     ex)] - TWO*fh[idx_fh_F(iF,jF,kF,ex)] + fh[idx_fh_F(iF + 1, jF,     kF,     ex)]);
+                        fyy[p] = Sdydy * (fh[idx_fh_F(iF,     jF - 1, kF,     ex)] - TWO*fh[idx_fh_F(iF,jF,kF,ex)] + fh[idx_fh_F(iF,     jF + 1, kF,     ex)]);
+                        fzz[p] = Sdzdz * (fh[idx_fh_F(iF,     jF,     kF - 1, ex)] - TWO*fh[idx_fh_F(iF,jF,kF,ex)] + fh[idx_fh_F(iF,     jF,     kF + 1, ex)]);
+
+                        fxy[p] = Sdxdy * (fh[idx_fh_F(iF - 1, jF - 1, kF, ex)] - fh[idx_fh_F(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F(iF - 1, jF + 1, kF, ex)] + fh[idx_fh_F(iF + 1, jF + 1, kF, ex)]);
+                        fxz[p] = Sdxdz * (fh[idx_fh_F(iF - 1, jF, kF - 1, ex)] - fh[idx_fh_F(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F(iF - 1, jF, kF + 1, ex)] + fh[idx_fh_F(iF + 1, jF, kF + 1, ex)]);
+                        fyz[p] = Sdydz * (fh[idx_fh_F(iF, jF - 1, kF - 1, ex)] - fh[idx_fh_F(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F(iF, jF - 1, kF + 1, ex)] + fh[idx_fh_F(iF, jF + 1, kF + 1, ex)]);
+                    }
+                }
+            }
+        }
+
+        /* 4th-order: skip 6th overlap */
+        if (has4) {
+            for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                        if (has6 && i0>=i6_lo && i0<=i6_hi && j0>=j6_lo && j0<=j6_hi && k0>=k6_lo && k0<=k6_hi) continue;
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Fdxdx * (-fh[idx_fh_F(iF - 2, jF,     kF,     ex)] + F16*fh[idx_fh_F(iF-1,jF,kF,ex)] - F30*fh[idx_fh_F(iF,jF,kF,ex)] - fh[idx_fh_F(iF+2,jF,kF,ex)] + F16*fh[idx_fh_F(iF+1,jF,kF,ex)]);
+                        fyy[p] = Fdydy * (-fh[idx_fh_F(iF,     jF - 2, kF,     ex)] + F16*fh[idx_fh_F(iF,jF-1,kF,ex)] - F30*fh[idx_fh_F(iF,jF,kF,ex)] - fh[idx_fh_F(iF,jF+2,kF,ex)] + F16*fh[idx_fh_F(iF,jF+1,kF,ex)]);
+                        fzz[p] = Fdzdz * (-fh[idx_fh_F(iF,     jF,     kF - 2, ex)] + F16*fh[idx_fh_F(iF,jF,kF-1,ex)] - F30*fh[idx_fh_F(iF,jF,kF,ex)] - fh[idx_fh_F(iF,jF,kF+2,ex)] + F16*fh[idx_fh_F(iF,jF,kF+1,ex)]);
+
+                        {
+                            const double t_jm2 = (fh[idx_fh_F(iF-2,jF-2,kF,ex)]-F8*fh[idx_fh_F(iF-1,jF-2,kF,ex)]+F8*fh[idx_fh_F(iF+1,jF-2,kF,ex)]-fh[idx_fh_F(iF+2,jF-2,kF,ex)]);
+                            const double t_jm1 = (fh[idx_fh_F(iF-2,jF-1,kF,ex)]-F8*fh[idx_fh_F(iF-1,jF-1,kF,ex)]+F8*fh[idx_fh_F(iF+1,jF-1,kF,ex)]-fh[idx_fh_F(iF+2,jF-1,kF,ex)]);
+                            const double t_jp1 = (fh[idx_fh_F(iF-2,jF+1,kF,ex)]-F8*fh[idx_fh_F(iF-1,jF+1,kF,ex)]+F8*fh[idx_fh_F(iF+1,jF+1,kF,ex)]-fh[idx_fh_F(iF+2,jF+1,kF,ex)]);
+                            const double t_jp2 = (fh[idx_fh_F(iF-2,jF+2,kF,ex)]-F8*fh[idx_fh_F(iF-1,jF+2,kF,ex)]+F8*fh[idx_fh_F(iF+1,jF+2,kF,ex)]-fh[idx_fh_F(iF+2,jF+2,kF,ex)]);
+                            fxy[p] = Fdxdy * (t_jm2 - F8*t_jm1 + F8*t_jp1 - t_jp2);
+                        }
+                        {
+                            const double t_km2 = (fh[idx_fh_F(iF-2,jF,kF-2,ex)]-F8*fh[idx_fh_F(iF-1,jF,kF-2,ex)]+F8*fh[idx_fh_F(iF+1,jF,kF-2,ex)]-fh[idx_fh_F(iF+2,jF,kF-2,ex)]);
+                            const double t_km1 = (fh[idx_fh_F(iF-2,jF,kF-1,ex)]-F8*fh[idx_fh_F(iF-1,jF,kF-1,ex)]+F8*fh[idx_fh_F(iF+1,jF,kF-1,ex)]-fh[idx_fh_F(iF+2,jF,kF-1,ex)]);
+                            const double t_kp1 = (fh[idx_fh_F(iF-2,jF,kF+1,ex)]-F8*fh[idx_fh_F(iF-1,jF,kF+1,ex)]+F8*fh[idx_fh_F(iF+1,jF,kF+1,ex)]-fh[idx_fh_F(iF+2,jF,kF+1,ex)]);
+                            const double t_kp2 = (fh[idx_fh_F(iF-2,jF,kF+2,ex)]-F8*fh[idx_fh_F(iF-1,jF,kF+2,ex)]+F8*fh[idx_fh_F(iF+1,jF,kF+2,ex)]-fh[idx_fh_F(iF+2,jF,kF+2,ex)]);
+                            fxz[p] = Fdxdz * (t_km2 - F8*t_km1 + F8*t_kp1 - t_kp2);
+                        }
+                        {
+                            const double t_km2 = (fh[idx_fh_F(iF,jF-2,kF-2,ex)]-F8*fh[idx_fh_F(iF,jF-1,kF-2,ex)]+F8*fh[idx_fh_F(iF,jF+1,kF-2,ex)]-fh[idx_fh_F(iF,jF+2,kF-2,ex)]);
+                            const double t_km1 = (fh[idx_fh_F(iF,jF-2,kF-1,ex)]-F8*fh[idx_fh_F(iF,jF-1,kF-1,ex)]+F8*fh[idx_fh_F(iF,jF+1,kF-1,ex)]-fh[idx_fh_F(iF,jF+2,kF-1,ex)]);
+                            const double t_kp1 = (fh[idx_fh_F(iF,jF-2,kF+1,ex)]-F8*fh[idx_fh_F(iF,jF-1,kF+1,ex)]+F8*fh[idx_fh_F(iF,jF+1,kF+1,ex)]-fh[idx_fh_F(iF,jF+2,kF+1,ex)]);
+                            const double t_kp2 = (fh[idx_fh_F(iF,jF-2,kF+2,ex)]-F8*fh[idx_fh_F(iF,jF-1,kF+2,ex)]+F8*fh[idx_fh_F(iF,jF+1,kF+2,ex)]-fh[idx_fh_F(iF,jF+2,kF+2,ex)]);
+                            fyz[p] = Fdydz * (t_km2 - F8*t_km1 + F8*t_kp1 - t_kp2);
+                        }
+                    }
+                }
+            }
+        }
+
+        /* 6th-order: interior only */
+        if (has6) {
+            for (int k0 = k6_lo; k0 <= k6_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j6_lo; j0 <= j6_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i6_lo; i0 <= i6_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        /* Diagonal: [+2,-27,+270,-490,+270,-27,+2] / (180*dx^2) */
+                        fxx[p] = Xdxdx * (
+                            TWO  * fh[idx_fh_F(iF - 3, jF,     kF,     ex)] -
+                            F27  * fh[idx_fh_F(iF - 2, jF,     kF,     ex)] +
+                            F270 * fh[idx_fh_F(iF - 1, jF,     kF,     ex)] -
+                            F490 * fh[idx_fh_F(iF,     jF,     kF,     ex)] +
+                            F270 * fh[idx_fh_F(iF + 1, jF,     kF,     ex)] -
+                            F27  * fh[idx_fh_F(iF + 2, jF,     kF,     ex)] +
+                            TWO  * fh[idx_fh_F(iF + 3, jF,     kF,     ex)]);
+
+                        fyy[p] = Xdydy * (
+                            TWO  * fh[idx_fh_F(iF,     jF - 3, kF,     ex)] -
+                            F27  * fh[idx_fh_F(iF,     jF - 2, kF,     ex)] +
+                            F270 * fh[idx_fh_F(iF,     jF - 1, kF,     ex)] -
+                            F490 * fh[idx_fh_F(iF,     jF,     kF,     ex)] +
+                            F270 * fh[idx_fh_F(iF,     jF + 1, kF,     ex)] -
+                            F27  * fh[idx_fh_F(iF,     jF + 2, kF,     ex)] +
+                            TWO  * fh[idx_fh_F(iF,     jF + 3, kF,     ex)]);
+
+                        fzz[p] = Xdzdz * (
+                            TWO  * fh[idx_fh_F(iF,     jF,     kF - 3, ex)] -
+                            F27  * fh[idx_fh_F(iF,     jF,     kF - 2, ex)] +
+                            F270 * fh[idx_fh_F(iF,     jF,     kF - 1, ex)] -
+                            F490 * fh[idx_fh_F(iF,     jF,     kF,     ex)] +
+                            F270 * fh[idx_fh_F(iF,     jF,     kF + 1, ex)] -
+                            F27  * fh[idx_fh_F(iF,     jF,     kF + 2, ex)] +
+                            TWO  * fh[idx_fh_F(iF,     jF,     kF + 3, ex)]);
+
+                        /* Mixed: 7x7 outer product. Compute 1D x-stencil at each y/z offset,
+                           then combine using 1D y/z weights [-1,+9,-45,0,+45,-9,+1] / (3600*dx*dy) */
+                        {
+                            // x-stencil: -f(i-3)+9f(i-2)-45f(i-1)+45f(i+1)-9f(i+2)+f(i+3)
+                            // Helper macro would help but explicit is safer
+                            #define XSTEN6(JF, KF_DUMMY) \
+                                (-fh[idx_fh_F(iF-3,JF,KF_DUMMY,ex)] + F9*fh[idx_fh_F(iF-2,JF,KF_DUMMY,ex)] - F45*fh[idx_fh_F(iF-1,JF,KF_DUMMY,ex)] + F45*fh[idx_fh_F(iF+1,JF,KF_DUMMY,ex)] - F9*fh[idx_fh_F(iF+2,JF,KF_DUMMY,ex)] + fh[idx_fh_F(iF+3,JF,KF_DUMMY,ex)])
+
+                            fxy[p] = Xdxdy * (
+                                -XSTEN6(jF-3, kF) + F9*XSTEN6(jF-2, kF) - F45*XSTEN6(jF-1, kF) + F45*XSTEN6(jF+1, kF) - F9*XSTEN6(jF+2, kF) + XSTEN6(jF+3, kF));
+
+                            fxz[p] = Xdxdz * (
+                                -XSTEN6(jF, kF-3) + F9*XSTEN6(jF, kF-2) - F45*XSTEN6(jF, kF-1) + F45*XSTEN6(jF, kF+1) - F9*XSTEN6(jF, kF+2) + XSTEN6(jF, kF+3));
+
+                            #undef XSTEN6
+                        }
+
+                        /* fyz: apply 1D y-stencil at each z offset */
+                        {
+                            #define YSTEN6(JF, KF_DUMMY) \
+                                (-fh[idx_fh_F(iF,JF-3,KF_DUMMY,ex)] + F9*fh[idx_fh_F(iF,JF-2,KF_DUMMY,ex)] - F45*fh[idx_fh_F(iF,JF-1,KF_DUMMY,ex)] + F45*fh[idx_fh_F(iF,JF+1,KF_DUMMY,ex)] - F9*fh[idx_fh_F(iF,JF+2,KF_DUMMY,ex)] + fh[idx_fh_F(iF,JF+3,KF_DUMMY,ex)])
+
+                            fyz[p] = Xdydz * (
+                                -YSTEN6(jF, kF-3) + F9*YSTEN6(jF, kF-2) - F45*YSTEN6(jF, kF-1) + F45*YSTEN6(jF, kF+1) - F9*YSTEN6(jF, kF+2) + YSTEN6(jF, kF+3));
+
+                            #undef YSTEN6
+                        }
+                    }
+                }
+            }
+        }
+        return;
+    }
+#elif (ghost_width == 5)
+    /* ---- 8th-order ----------------------------------------------------- */
+    {
+        const int ord = 5;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -3;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double Sdxdx = ONE / (dX * dX);
+        const double Sdydy = ONE / (dY * dY);
+        const double Sdzdz = ONE / (dZ * dZ);
+        const double Fdxdx = F1o12  / (dX * dX);
+        const double Fdydy = F1o12  / (dY * dY);
+        const double Fdzdz = F1o12  / (dZ * dZ);
+        const double Xdxdx = F1o180 / (dX * dX);
+        const double Xdydy = F1o180 / (dY * dY);
+        const double Xdzdz = F1o180 / (dZ * dZ);
+        const double Edxdx = F1o5040 / (dX * dX);
+        const double Edydy = F1o5040 / (dY * dY);
+        const double Edzdz = F1o5040 / (dZ * dZ);
+        const double Sdxdy = F1o4    / (dX * dY);
+        const double Sdxdz = F1o4    / (dX * dZ);
+        const double Sdydz = F1o4    / (dY * dZ);
+        const double Fdxdy = F1o144  / (dX * dY);
+        const double Fdxdz = F1o144  / (dX * dZ);
+        const double Fdydz = F1o144  / (dY * dZ);
+        const double Xdxdy = F1o3600 / (dX * dY);
+        const double Xdxdz = F1o3600 / (dX * dZ);
+        const double Xdydz = F1o3600 / (dY * dZ);
+        const double Edxdy = F1o705600 / (dX * dY);
+        const double Edxdz = F1o705600 / (dX * dZ);
+        const double Edydz = F1o705600 / (dY * dZ);
+
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+            fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+        }
+
+        /* Loop bounds for each pass */
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2, j2_hi = ex2 - 2, k2_hi = ex3 - 2;
+
+        const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i4_hi = ex1 - 3, j4_hi = ex2 - 3, k4_hi = ex3 - 3;
+
+        const int i6_lo = (iminF + 2 > 0) ? (iminF + 2) : 0;
+        const int j6_lo = (jminF + 2 > 0) ? (jminF + 2) : 0;
+        const int k6_lo = (kminF + 2 > 0) ? (kminF + 2) : 0;
+        const int i6_hi = ex1 - 4, j6_hi = ex2 - 4, k6_hi = ex3 - 4;
+
+        const int i8_lo = (iminF + 3 > 0) ? (iminF + 3) : 0;
+        const int j8_lo = (jminF + 3 > 0) ? (jminF + 3) : 0;
+        const int k8_lo = (kminF + 3 > 0) ? (kminF + 3) : 0;
+        const int i8_hi = ex1 - 5, j8_hi = ex2 - 5, k8_hi = ex3 - 5;
+
+        const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
+        const int has6 = (i6_lo <= i6_hi && j6_lo <= j6_hi && k6_lo <= k6_hi);
+        const int has8 = (i8_lo <= i8_hi && j8_lo <= j8_hi && k8_lo <= k8_hi);
+
+        /* 2nd-order: skip 4th+6th+8th overlap */
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        bool in4 = has4 && i0>=i4_lo && i0<=i4_hi && j0>=j4_lo && j0<=j4_hi && k0>=k4_lo && k0<=k4_hi;
+                        if (in4) continue;
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Sdxdx * (fh[idx_fh_F_ord5(iF-1,jF,kF,ex)] - TWO*fh[idx_fh_F_ord5(iF,jF,kF,ex)] + fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]);
+                        fyy[p] = Sdydy * (fh[idx_fh_F_ord5(iF,jF-1,kF,ex)] - TWO*fh[idx_fh_F_ord5(iF,jF,kF,ex)] + fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]);
+                        fzz[p] = Sdzdz * (fh[idx_fh_F_ord5(iF,jF,kF-1,ex)] - TWO*fh[idx_fh_F_ord5(iF,jF,kF,ex)] + fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]);
+
+                        fxy[p] = Sdxdy * (fh[idx_fh_F_ord5(iF-1,jF-1,kF,ex)] - fh[idx_fh_F_ord5(iF+1,jF-1,kF,ex)] - fh[idx_fh_F_ord5(iF-1,jF+1,kF,ex)] + fh[idx_fh_F_ord5(iF+1,jF+1,kF,ex)]);
+                        fxz[p] = Sdxdz * (fh[idx_fh_F_ord5(iF-1,jF,kF-1,ex)] - fh[idx_fh_F_ord5(iF+1,jF,kF-1,ex)] - fh[idx_fh_F_ord5(iF-1,jF,kF+1,ex)] + fh[idx_fh_F_ord5(iF+1,jF,kF+1,ex)]);
+                        fyz[p] = Sdydz * (fh[idx_fh_F_ord5(iF,jF-1,kF-1,ex)] - fh[idx_fh_F_ord5(iF,jF+1,kF-1,ex)] - fh[idx_fh_F_ord5(iF,jF-1,kF+1,ex)] + fh[idx_fh_F_ord5(iF,jF+1,kF+1,ex)]);
+                    }
+                }
+            }
+        }
+
+        /* 4th-order: skip 6th+8th overlap */
+        if (has4) {
+            for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                        bool in6 = has6 && i0>=i6_lo && i0<=i6_hi && j0>=j6_lo && j0<=j6_hi && k0>=k6_lo && k0<=k6_hi;
+                        if (in6) continue;
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Fdxdx * (-fh[idx_fh_F_ord5(iF-2,jF,kF,ex)] + F16*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)] - F30*fh[idx_fh_F_ord5(iF,jF,kF,ex)] - fh[idx_fh_F_ord5(iF+2,jF,kF,ex)] + F16*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]);
+                        fyy[p] = Fdydy * (-fh[idx_fh_F_ord5(iF,jF-2,kF,ex)] + F16*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)] - F30*fh[idx_fh_F_ord5(iF,jF,kF,ex)] - fh[idx_fh_F_ord5(iF,jF+2,kF,ex)] + F16*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]);
+                        fzz[p] = Fdzdz * (-fh[idx_fh_F_ord5(iF,jF,kF-2,ex)] + F16*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)] - F30*fh[idx_fh_F_ord5(iF,jF,kF,ex)] - fh[idx_fh_F_ord5(iF,jF,kF+2,ex)] + F16*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]);
+
+                        {
+                            const double t_jm2 = (fh[idx_fh_F_ord5(iF-2,jF-2,kF,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF-2,kF,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF-2,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF-2,kF,ex)]);
+                            const double t_jm1 = (fh[idx_fh_F_ord5(iF-2,jF-1,kF,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF-1,kF,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF-1,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF-1,kF,ex)]);
+                            const double t_jp1 = (fh[idx_fh_F_ord5(iF-2,jF+1,kF,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF+1,kF,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF+1,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF+1,kF,ex)]);
+                            const double t_jp2 = (fh[idx_fh_F_ord5(iF-2,jF+2,kF,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF+2,kF,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF+2,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF+2,kF,ex)]);
+                            fxy[p] = Fdxdy * (t_jm2 - F8*t_jm1 + F8*t_jp1 - t_jp2);
+                        }
+                        {
+                            const double t_km2 = (fh[idx_fh_F_ord5(iF-2,jF,kF-2,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF,kF-2,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF,kF-2,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF-2,ex)]);
+                            const double t_km1 = (fh[idx_fh_F_ord5(iF-2,jF,kF-1,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF,kF-1,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF,kF-1,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF-1,ex)]);
+                            const double t_kp1 = (fh[idx_fh_F_ord5(iF-2,jF,kF+1,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF,kF+1,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF,kF+1,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF+1,ex)]);
+                            const double t_kp2 = (fh[idx_fh_F_ord5(iF-2,jF,kF+2,ex)]-F8*fh[idx_fh_F_ord5(iF-1,jF,kF+2,ex)]+F8*fh[idx_fh_F_ord5(iF+1,jF,kF+2,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF+2,ex)]);
+                            fxz[p] = Fdxdz * (t_km2 - F8*t_km1 + F8*t_kp1 - t_kp2);
+                        }
+                        {
+                            const double t_km2 = (fh[idx_fh_F_ord5(iF,jF-2,kF-2,ex)]-F8*fh[idx_fh_F_ord5(iF,jF-1,kF-2,ex)]+F8*fh[idx_fh_F_ord5(iF,jF+1,kF-2,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF-2,ex)]);
+                            const double t_km1 = (fh[idx_fh_F_ord5(iF,jF-2,kF-1,ex)]-F8*fh[idx_fh_F_ord5(iF,jF-1,kF-1,ex)]+F8*fh[idx_fh_F_ord5(iF,jF+1,kF-1,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF-1,ex)]);
+                            const double t_kp1 = (fh[idx_fh_F_ord5(iF,jF-2,kF+1,ex)]-F8*fh[idx_fh_F_ord5(iF,jF-1,kF+1,ex)]+F8*fh[idx_fh_F_ord5(iF,jF+1,kF+1,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF+1,ex)]);
+                            const double t_kp2 = (fh[idx_fh_F_ord5(iF,jF-2,kF+2,ex)]-F8*fh[idx_fh_F_ord5(iF,jF-1,kF+2,ex)]+F8*fh[idx_fh_F_ord5(iF,jF+1,kF+2,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF+2,ex)]);
+                            fyz[p] = Fdydz * (t_km2 - F8*t_km1 + F8*t_kp1 - t_kp2);
+                        }
+                    }
+                }
+            }
+        }
+
+        /* 6th-order: skip 8th overlap */
+        if (has6) {
+            for (int k0 = k6_lo; k0 <= k6_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j6_lo; j0 <= j6_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i6_lo; i0 <= i6_hi; ++i0) {
+                        if (has8 && i0>=i8_lo && i0<=i8_hi && j0>=j8_lo && j0<=j8_hi && k0>=k8_lo && k0<=k8_hi) continue;
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fxx[p] = Xdxdx * (
+                            TWO  * fh[idx_fh_F_ord5(iF-3,jF,kF,ex)] - F27*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)] + F270*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)] - F490*fh[idx_fh_F_ord5(iF,jF,kF,ex)] + F270*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)] - F27*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)] + TWO*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]);
+                        fyy[p] = Xdydy * (
+                            TWO  * fh[idx_fh_F_ord5(iF,jF-3,kF,ex)] - F27*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)] + F270*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)] - F490*fh[idx_fh_F_ord5(iF,jF,kF,ex)] + F270*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)] - F27*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)] + TWO*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]);
+                        fzz[p] = Xdzdz * (
+                            TWO  * fh[idx_fh_F_ord5(iF,jF,kF-3,ex)] - F27*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)] + F270*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)] - F490*fh[idx_fh_F_ord5(iF,jF,kF,ex)] + F270*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)] - F27*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)] + TWO*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]);
+
+                        {
+                            #define XSTEN6_8(JF, KF_DUMMY) \
+                                (-fh[idx_fh_F_ord5(iF-3,JF,KF_DUMMY,ex)] + F9*fh[idx_fh_F_ord5(iF-2,JF,KF_DUMMY,ex)] - F45*fh[idx_fh_F_ord5(iF-1,JF,KF_DUMMY,ex)] + F45*fh[idx_fh_F_ord5(iF+1,JF,KF_DUMMY,ex)] - F9*fh[idx_fh_F_ord5(iF+2,JF,KF_DUMMY,ex)] + fh[idx_fh_F_ord5(iF+3,JF,KF_DUMMY,ex)])
+                            fxy[p] = Xdxdy * (
+                                -XSTEN6_8(jF-3,kF) + F9*XSTEN6_8(jF-2,kF) - F45*XSTEN6_8(jF-1,kF) + F45*XSTEN6_8(jF+1,kF) - F9*XSTEN6_8(jF+2,kF) + XSTEN6_8(jF+3,kF));
+                            fxz[p] = Xdxdz * (
+                                -XSTEN6_8(jF,kF-3) + F9*XSTEN6_8(jF,kF-2) - F45*XSTEN6_8(jF,kF-1) + F45*XSTEN6_8(jF,kF+1) - F9*XSTEN6_8(jF,kF+2) + XSTEN6_8(jF,kF+3));
+                            #undef XSTEN6_8
+                        }
+                        {
+                            #define YSTEN6_8(JF, KF_DUMMY) \
+                                (-fh[idx_fh_F_ord5(iF,JF-3,KF_DUMMY,ex)] + F9*fh[idx_fh_F_ord5(iF,JF-2,KF_DUMMY,ex)] - F45*fh[idx_fh_F_ord5(iF,JF-1,KF_DUMMY,ex)] + F45*fh[idx_fh_F_ord5(iF,JF+1,KF_DUMMY,ex)] - F9*fh[idx_fh_F_ord5(iF,JF+2,KF_DUMMY,ex)] + fh[idx_fh_F_ord5(iF,JF+3,KF_DUMMY,ex)])
+                            fyz[p] = Xdydz * (
+                                -YSTEN6_8(jF,kF-3) + F9*YSTEN6_8(jF,kF-2) - F45*YSTEN6_8(jF,kF-1) + F45*YSTEN6_8(jF,kF+1) - F9*YSTEN6_8(jF,kF+2) + YSTEN6_8(jF,kF+3));
+                            #undef YSTEN6_8
+                        }
+                    }
+                }
+            }
+        }
+
+        /* 8th-order: interior only */
+        if (has8) {
+            for (int k0 = k8_lo; k0 <= k8_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j8_lo; j0 <= j8_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i8_lo; i0 <= i8_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        /* Diagonal: [-9,+128,-1008,+8064,-14350,+8064,-1008,+128,-9] / (5040*dx^2) */
+                        fxx[p] = Edxdx * (
+                            -(double)9 * fh[idx_fh_F_ord5(iF - 4, jF,     kF,     ex)] +
+                            F128  * fh[idx_fh_F_ord5(iF - 3, jF,     kF,     ex)] -
+                            F1008 * fh[idx_fh_F_ord5(iF - 2, jF,     kF,     ex)] +
+                            F8064 * fh[idx_fh_F_ord5(iF - 1, jF,     kF,     ex)] -
+                            F14350* fh[idx_fh_F_ord5(iF,     jF,     kF,     ex)] +
+                            F8064 * fh[idx_fh_F_ord5(iF + 1, jF,     kF,     ex)] -
+                            F1008 * fh[idx_fh_F_ord5(iF + 2, jF,     kF,     ex)] +
+                            F128  * fh[idx_fh_F_ord5(iF + 3, jF,     kF,     ex)] -
+                            (double)9 * fh[idx_fh_F_ord5(iF + 4, jF,     kF,     ex)]);
+
+                        fyy[p] = Edydy * (
+                            -(double)9 * fh[idx_fh_F_ord5(iF,     jF - 4, kF,     ex)] +
+                            F128  * fh[idx_fh_F_ord5(iF,     jF - 3, kF,     ex)] -
+                            F1008 * fh[idx_fh_F_ord5(iF,     jF - 2, kF,     ex)] +
+                            F8064 * fh[idx_fh_F_ord5(iF,     jF - 1, kF,     ex)] -
+                            F14350* fh[idx_fh_F_ord5(iF,     jF,     kF,     ex)] +
+                            F8064 * fh[idx_fh_F_ord5(iF,     jF + 1, kF,     ex)] -
+                            F1008 * fh[idx_fh_F_ord5(iF,     jF + 2, kF,     ex)] +
+                            F128  * fh[idx_fh_F_ord5(iF,     jF + 3, kF,     ex)] -
+                            (double)9 * fh[idx_fh_F_ord5(iF,     jF + 4, kF,     ex)]);
+
+                        fzz[p] = Edzdz * (
+                            -(double)9 * fh[idx_fh_F_ord5(iF,     jF,     kF - 4, ex)] +
+                            F128  * fh[idx_fh_F_ord5(iF,     jF,     kF - 3, ex)] -
+                            F1008 * fh[idx_fh_F_ord5(iF,     jF,     kF - 2, ex)] +
+                            F8064 * fh[idx_fh_F_ord5(iF,     jF,     kF - 1, ex)] -
+                            F14350* fh[idx_fh_F_ord5(iF,     jF,     kF,     ex)] +
+                            F8064 * fh[idx_fh_F_ord5(iF,     jF,     kF + 1, ex)] -
+                            F1008 * fh[idx_fh_F_ord5(iF,     jF,     kF + 2, ex)] +
+                            F128  * fh[idx_fh_F_ord5(iF,     jF,     kF + 3, ex)] -
+                            (double)9 * fh[idx_fh_F_ord5(iF,     jF,     kF + 4, ex)]);
+
+                        /* Mixed: 9x9 outer product.
+                           x-stencil: +3*f(i-4)-32*f(i-3)+168*f(i-2)-672*f(i-1)+672*f(i+1)-168*f(i+2)+32*f(i+3)-3*f(i+4)
+                           y/z weights: same [+3,-32,+168,-672,+672,-168,+32,-3] / 705600 */
+                        {
+                            #define XSTEN8(JF, KF_DUMMY) \
+                                (+(double)3*fh[idx_fh_F_ord5(iF-4,JF,KF_DUMMY,ex)] - F32*fh[idx_fh_F_ord5(iF-3,JF,KF_DUMMY,ex)] + F168*fh[idx_fh_F_ord5(iF-2,JF,KF_DUMMY,ex)] - F672*fh[idx_fh_F_ord5(iF-1,JF,KF_DUMMY,ex)] + F672*fh[idx_fh_F_ord5(iF+1,JF,KF_DUMMY,ex)] - F168*fh[idx_fh_F_ord5(iF+2,JF,KF_DUMMY,ex)] + F32*fh[idx_fh_F_ord5(iF+3,JF,KF_DUMMY,ex)] - (double)3*fh[idx_fh_F_ord5(iF+4,JF,KF_DUMMY,ex)])
+
+                            fxy[p] = Edxdy * (
+                                +(double)3*XSTEN8(jF-4,kF) - F32*XSTEN8(jF-3,kF) + F168*XSTEN8(jF-2,kF) - F672*XSTEN8(jF-1,kF) + F672*XSTEN8(jF+1,kF) - F168*XSTEN8(jF+2,kF) + F32*XSTEN8(jF+3,kF) - (double)3*XSTEN8(jF+4,kF));
+
+                            fxz[p] = Edxdz * (
+                                +(double)3*XSTEN8(jF,kF-4) - F32*XSTEN8(jF,kF-3) + F168*XSTEN8(jF,kF-2) - F672*XSTEN8(jF,kF-1) + F672*XSTEN8(jF,kF+1) - F168*XSTEN8(jF,kF+2) + F32*XSTEN8(jF,kF+3) - (double)3*XSTEN8(jF,kF+4));
+
+                            #undef XSTEN8
+                        }
+                        {
+                            #define YSTEN8(JF, KF_DUMMY) \
+                                (+(double)3*fh[idx_fh_F_ord5(iF,JF-4,KF_DUMMY,ex)] - F32*fh[idx_fh_F_ord5(iF,JF-3,KF_DUMMY,ex)] + F168*fh[idx_fh_F_ord5(iF,JF-2,KF_DUMMY,ex)] - F672*fh[idx_fh_F_ord5(iF,JF-1,KF_DUMMY,ex)] + F672*fh[idx_fh_F_ord5(iF,JF+1,KF_DUMMY,ex)] - F168*fh[idx_fh_F_ord5(iF,JF+2,KF_DUMMY,ex)] + F32*fh[idx_fh_F_ord5(iF,JF+3,KF_DUMMY,ex)] - (double)3*fh[idx_fh_F_ord5(iF,JF+4,KF_DUMMY,ex)])
+
+                            fyz[p] = Edydz * (
+                                +(double)3*YSTEN8(jF,kF-4) - F32*YSTEN8(jF,kF-3) + F168*YSTEN8(jF,kF-2) - F672*YSTEN8(jF,kF-1) + F672*YSTEN8(jF,kF+1) - F168*YSTEN8(jF,kF+2) + F32*YSTEN8(jF,kF+3) - (double)3*YSTEN8(jF,kF+4));
+
+                            #undef YSTEN8
+                        }
+                    }
+                }
+            }
+        }
+        return;
+    }
+#else
+#error "fdderivs_c.C: unsupported ghost_width (must be 2, 3, 4, or 5)"
+#endif
+}

AMSS_NCKU_source/fdderivs_sh_c.C

@@ -0,0 +1,321 @@
+#include "macrodef.h"
+#include "share_func.h"
+
+/*
+ * fdderivs_sh — second derivatives on shell patch in (rho, sigma, R) coords.
+ * Same stencil coefficients as Cartesian fdderivs. Uses symmetry_stbd.
+ */
+extern "C" void fdderivs_sh_(const int ex[3],
+                 const double *f,
+                 double *fxx, double *fxy, double *fxz,
+                 double *fyy, double *fyz, double *fzz,
+                 const double *X, const double *Y, const double *Z,
+                 double SYM1, double SYM2, double SYM3,
+                 int Symmetry, int onoff, int sst)
+{
+    (void)SYM3; (void)onoff; (void)sst;
+
+    const int NO_SYMM=0, EQ_SYMM=1, OCTANT=2;
+    const double ZEO=0.0, ONE=1.0, TWO=2.0, F1o4=2.5e-1;
+    const double F8=8.0, F16=16.0, F30=30.0, F1o12=ONE/12.0, F1o144=ONE/144.0;
+    const double F9=9.0, F45=45.0, F60=60.0, F27=27.0, F270=270.0, F490=490.0;
+    const double F1o180=ONE/180.0, F1o3600=ONE/3600.0;
+    const double F32=32.0, F128=128.0, F168=168.0, F672=672.0, F840=840.0;
+    const double F1008=1008.0, F8064=8064.0, F14350=14350.0;
+    const double F1o5040=ONE/5040.0, F1o705600=ONE/705600.0;
+
+    const int ex1=ex[0], ex2=ex[1], ex3=ex[2];
+    const double dX=X[1]-X[0], dY=Y[1]-Y[0], dZ=Z[1]-Z[0];
+    const int imaxF=ex1, jmaxF=ex2, kmaxF=ex3;
+    const double SoA[2]={SYM1,SYM2};
+
+#if (ghost_width == 2)
+    {
+        const int ord=1;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=0;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=0;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=0;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        static double *fh_buf=NULL;static size_t cap=0;
+        if(fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf;if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double Sdxdx=ONE/(dX*dX),Sdydy=ONE/(dY*dY),Sdzdz=ONE/(dZ*dZ);
+        const double Sdxdy=F1o4/(dX*dY),Sdxdz=F1o4/(dX*dZ),Sdydz=F1o4/(dY*dZ);
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fxx[p]=fyy[p]=fzz[p]=ZEO;fxy[p]=fxz[p]=fyz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0,j2_lo=(jminF>0)?jminF:0,k2_lo=1,i2_hi=ex1-2,j2_hi=ex2-2,k2_hi=ex3-2;
+        #define FH(iF,jF,kF) fh[idx_fh_stbd(iF,jF,kF,ord,ex)]
+        if(i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi){
+            for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+            for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+            for(int i0=i2_lo;i0<=i2_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                fxx[p]=Sdxdx*(FH(iF-1,jF,kF)-TWO*FH(iF,jF,kF)+FH(iF+1,jF,kF));
+                fyy[p]=Sdydy*(FH(iF,jF-1,kF)-TWO*FH(iF,jF,kF)+FH(iF,jF+1,kF));
+                fzz[p]=Sdzdz*(FH(iF,jF,kF-1)-TWO*FH(iF,jF,kF)+FH(iF,jF,kF+1));
+                fxy[p]=Sdxdy*(FH(iF-1,jF-1,kF)-FH(iF+1,jF-1,kF)-FH(iF-1,jF+1,kF)+FH(iF+1,jF+1,kF));
+                fxz[p]=Sdxdz*(FH(iF-1,jF,kF-1)-FH(iF+1,jF,kF-1)-FH(iF-1,jF,kF+1)+FH(iF+1,jF,kF+1));
+                fyz[p]=Sdydz*(FH(iF,jF-1,kF-1)-FH(iF,jF+1,kF-1)-FH(iF,jF-1,kF+1)+FH(iF,jF+1,kF+1));
+            }}}
+        }
+        #undef FH
+        return;
+    }
+#elif (ghost_width == 3)
+    {
+        const int ord=2;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-1;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-1;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-1;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        static double *fh_buf=NULL;static size_t cap=0;
+        if(fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf;if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double Sdxdx=ONE/(dX*dX),Sdydy=ONE/(dY*dY),Sdzdz=ONE/(dZ*dZ);
+        const double Fdxdx=F1o12/(dX*dX),Fdydy=F1o12/(dY*dY),Fdzdz=F1o12/(dZ*dZ);
+        const double Sdxdy=F1o4/(dX*dY),Sdxdz=F1o4/(dX*dZ),Sdydz=F1o4/(dY*dZ);
+        const double Fdxdy=F1o144/(dX*dY),Fdxdz=F1o144/(dX*dZ),Fdydz=F1o144/(dY*dZ);
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fxx[p]=fyy[p]=fzz[p]=fxy[p]=fxz[p]=fyz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0,j2_lo=(jminF>0)?jminF:0,k2_lo=1,i2_hi=ex1-2,j2_hi=ex2-2,k2_hi=ex3-2;
+        const int i4_lo=(iminF+1>0)?iminF+1:0,j4_lo=(jminF+1>0)?jminF+1:0,k4_lo=2,i4_hi=ex1-3,j4_hi=ex2-3,k4_hi=ex3-3;
+        const int has4=(i4_lo<=i4_hi&&j4_lo<=j4_hi&&k4_lo<=k4_hi);
+        #define FH(iF,jF,kF) fh[idx_fh_stbd(iF,jF,kF,ord,ex)]
+
+        if(i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi){
+            for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+            for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+            for(int i0=i2_lo;i0<=i2_hi;++i0){
+                if(has4&&i0>=i4_lo&&i0<=i4_hi&&j0>=j4_lo&&j0<=j4_hi&&k0>=k4_lo&&k0<=k4_hi)continue;
+                const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                fxx[p]=Sdxdx*(FH(iF-1,jF,kF)-TWO*FH(iF,jF,kF)+FH(iF+1,jF,kF));
+                fyy[p]=Sdydy*(FH(iF,jF-1,kF)-TWO*FH(iF,jF,kF)+FH(iF,jF+1,kF));
+                fzz[p]=Sdzdz*(FH(iF,jF,kF-1)-TWO*FH(iF,jF,kF)+FH(iF,jF,kF+1));
+                fxy[p]=Sdxdy*(FH(iF-1,jF-1,kF)-FH(iF+1,jF-1,kF)-FH(iF-1,jF+1,kF)+FH(iF+1,jF+1,kF));
+                fxz[p]=Sdxdz*(FH(iF-1,jF,kF-1)-FH(iF+1,jF,kF-1)-FH(iF-1,jF,kF+1)+FH(iF+1,jF,kF+1));
+                fyz[p]=Sdydz*(FH(iF,jF-1,kF-1)-FH(iF,jF+1,kF-1)-FH(iF,jF-1,kF+1)+FH(iF,jF+1,kF+1));
+            }}}
+        }
+        if(has4){
+            for(int k0=k4_lo;k0<=k4_hi;++k0){const int kF=k0+1;
+            for(int j0=j4_lo;j0<=j4_hi;++j0){const int jF=j0+1;
+            for(int i0=i4_lo;i0<=i4_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                fxx[p]=Fdxdx*(-FH(iF-2,jF,kF)+F16*FH(iF-1,jF,kF)-F30*FH(iF,jF,kF)-FH(iF+2,jF,kF)+F16*FH(iF+1,jF,kF));
+                fyy[p]=Fdydy*(-FH(iF,jF-2,kF)+F16*FH(iF,jF-1,kF)-F30*FH(iF,jF,kF)-FH(iF,jF+2,kF)+F16*FH(iF,jF+1,kF));
+                fzz[p]=Fdzdz*(-FH(iF,jF,kF-2)+F16*FH(iF,jF,kF-1)-F30*FH(iF,jF,kF)-FH(iF,jF,kF+2)+F16*FH(iF,jF,kF+1));
+                {const double t_jm2=(FH(iF-2,jF-2,kF)-F8*FH(iF-1,jF-2,kF)+F8*FH(iF+1,jF-2,kF)-FH(iF+2,jF-2,kF));
+                 const double t_jm1=(FH(iF-2,jF-1,kF)-F8*FH(iF-1,jF-1,kF)+F8*FH(iF+1,jF-1,kF)-FH(iF+2,jF-1,kF));
+                 const double t_jp1=(FH(iF-2,jF+1,kF)-F8*FH(iF-1,jF+1,kF)+F8*FH(iF+1,jF+1,kF)-FH(iF+2,jF+1,kF));
+                 const double t_jp2=(FH(iF-2,jF+2,kF)-F8*FH(iF-1,jF+2,kF)+F8*FH(iF+1,jF+2,kF)-FH(iF+2,jF+2,kF));
+                 fxy[p]=Fdxdy*(t_jm2-F8*t_jm1+F8*t_jp1-t_jp2);}
+                {const double t_km2=(FH(iF-2,jF,kF-2)-F8*FH(iF-1,jF,kF-2)+F8*FH(iF+1,jF,kF-2)-FH(iF+2,jF,kF-2));
+                 const double t_km1=(FH(iF-2,jF,kF-1)-F8*FH(iF-1,jF,kF-1)+F8*FH(iF+1,jF,kF-1)-FH(iF+2,jF,kF-1));
+                 const double t_kp1=(FH(iF-2,jF,kF+1)-F8*FH(iF-1,jF,kF+1)+F8*FH(iF+1,jF,kF+1)-FH(iF+2,jF,kF+1));
+                 const double t_kp2=(FH(iF-2,jF,kF+2)-F8*FH(iF-1,jF,kF+2)+F8*FH(iF+1,jF,kF+2)-FH(iF+2,jF,kF+2));
+                 fxz[p]=Fdxdz*(t_km2-F8*t_km1+F8*t_kp1-t_kp2);}
+                {const double t_km2=(FH(iF,jF-2,kF-2)-F8*FH(iF,jF-1,kF-2)+F8*FH(iF,jF+1,kF-2)-FH(iF,jF+2,kF-2));
+                 const double t_km1=(FH(iF,jF-2,kF-1)-F8*FH(iF,jF-1,kF-1)+F8*FH(iF,jF+1,kF-1)-FH(iF,jF+2,kF-1));
+                 const double t_kp1=(FH(iF,jF-2,kF+1)-F8*FH(iF,jF-1,kF+1)+F8*FH(iF,jF+1,kF+1)-FH(iF,jF+2,kF+1));
+                 const double t_kp2=(FH(iF,jF-2,kF+2)-F8*FH(iF,jF-1,kF+2)+F8*FH(iF,jF+1,kF+2)-FH(iF,jF+2,kF+2));
+                 fyz[p]=Fdydz*(t_km2-F8*t_km1+F8*t_kp1-t_kp2);}
+            }}}
+        }
+        #undef FH
+        return;
+    }
+#elif (ghost_width == 4)
+    {
+        const int ord=3;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-2;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-2;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-2;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        static double *fh_buf=NULL;static size_t cap=0;
+        if(fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf;if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double Sdxdx=ONE/(dX*dX),Sdydy=ONE/(dY*dY),Sdzdz=ONE/(dZ*dZ);
+        const double Fdxdx=F1o12/(dX*dX),Fdydy=F1o12/(dY*dY),Fdzdz=F1o12/(dZ*dZ);
+        const double Xdxdx=F1o180/(dX*dX),Xdydy=F1o180/(dY*dY),Xdzdz=F1o180/(dZ*dZ);
+        const double Sdxdy=F1o4/(dX*dY),Sdxdz=F1o4/(dX*dZ),Sdydz=F1o4/(dY*dZ);
+        const double Fdxdy=F1o144/(dX*dY),Fdxdz=F1o144/(dX*dZ),Fdydz=F1o144/(dY*dZ);
+        const double Xdxdy=F1o3600/(dX*dY),Xdxdz=F1o3600/(dX*dZ),Xdydz=F1o3600/(dY*dZ);
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fxx[p]=fyy[p]=fzz[p]=fxy[p]=fxz[p]=fyz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0,j2_lo=(jminF>0)?jminF:0,k2_lo=1,i2_hi=ex1-2,j2_hi=ex2-2,k2_hi=ex3-2;
+        const int i4_lo=(iminF+1>0)?iminF+1:0,j4_lo=(jminF+1>0)?jminF+1:0,k4_lo=2,i4_hi=ex1-3,j4_hi=ex2-3,k4_hi=ex3-3;
+        const int i6_lo=(iminF+2>0)?iminF+2:0,j6_lo=(jminF+2>0)?jminF+2:0,k6_lo=3,i6_hi=ex1-4,j6_hi=ex2-4,k6_hi=ex3-4;
+        const int has4=(i4_lo<=i4_hi&&j4_lo<=j4_hi&&k4_lo<=k4_hi),has6=(i6_lo<=i6_hi&&j6_lo<=j6_hi&&k6_lo<=k6_hi);
+        #define FH(iF,jF,kF) fh[idx_fh_stbd(iF,jF,kF,ord,ex)]
+
+        if(i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi){for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+        for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+        for(int i0=i2_lo;i0<=i2_hi;++i0){bool in4=has4&&i0>=i4_lo&&i0<=i4_hi&&j0>=j4_lo&&j0<=j4_hi&&k0>=k4_lo&&k0<=k4_hi;if(in4)continue;
+            const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Sdxdx*(FH(iF-1,jF,kF)-TWO*FH(iF,jF,kF)+FH(iF+1,jF,kF));
+            fyy[p]=Sdydy*(FH(iF,jF-1,kF)-TWO*FH(iF,jF,kF)+FH(iF,jF+1,kF));
+            fzz[p]=Sdzdz*(FH(iF,jF,kF-1)-TWO*FH(iF,jF,kF)+FH(iF,jF,kF+1));
+            fxy[p]=Sdxdy*(FH(iF-1,jF-1,kF)-FH(iF+1,jF-1,kF)-FH(iF-1,jF+1,kF)+FH(iF+1,jF+1,kF));
+            fxz[p]=Sdxdz*(FH(iF-1,jF,kF-1)-FH(iF+1,jF,kF-1)-FH(iF-1,jF,kF+1)+FH(iF+1,jF,kF+1));
+            fyz[p]=Sdydz*(FH(iF,jF-1,kF-1)-FH(iF,jF+1,kF-1)-FH(iF,jF-1,kF+1)+FH(iF,jF+1,kF+1));
+        }}}}
+        if(has4){for(int k0=k4_lo;k0<=k4_hi;++k0){const int kF=k0+1;
+        for(int j0=j4_lo;j0<=j4_hi;++j0){const int jF=j0+1;
+        for(int i0=i4_lo;i0<=i4_hi;++i0){if(has6&&i0>=i6_lo&&i0<=i6_hi&&j0>=j6_lo&&j0<=j6_hi&&k0>=k6_lo&&k0<=k6_hi)continue;
+            const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Fdxdx*(-FH(iF-2,jF,kF)+F16*FH(iF-1,jF,kF)-F30*FH(iF,jF,kF)-FH(iF+2,jF,kF)+F16*FH(iF+1,jF,kF));
+            fyy[p]=Fdydy*(-FH(iF,jF-2,kF)+F16*FH(iF,jF-1,kF)-F30*FH(iF,jF,kF)-FH(iF,jF+2,kF)+F16*FH(iF,jF+1,kF));
+            fzz[p]=Fdzdz*(-FH(iF,jF,kF-2)+F16*FH(iF,jF,kF-1)-F30*FH(iF,jF,kF)-FH(iF,jF,kF+2)+F16*FH(iF,jF,kF+1));
+            {const double t_jm2=(FH(iF-2,jF-2,kF)-F8*FH(iF-1,jF-2,kF)+F8*FH(iF+1,jF-2,kF)-FH(iF+2,jF-2,kF));
+             const double t_jm1=(FH(iF-2,jF-1,kF)-F8*FH(iF-1,jF-1,kF)+F8*FH(iF+1,jF-1,kF)-FH(iF+2,jF-1,kF));
+             const double t_jp1=(FH(iF-2,jF+1,kF)-F8*FH(iF-1,jF+1,kF)+F8*FH(iF+1,jF+1,kF)-FH(iF+2,jF+1,kF));
+             const double t_jp2=(FH(iF-2,jF+2,kF)-F8*FH(iF-1,jF+2,kF)+F8*FH(iF+1,jF+2,kF)-FH(iF+2,jF+2,kF));
+             fxy[p]=Fdxdy*(t_jm2-F8*t_jm1+F8*t_jp1-t_jp2);}
+            {const double t_km2=(FH(iF-2,jF,kF-2)-F8*FH(iF-1,jF,kF-2)+F8*FH(iF+1,jF,kF-2)-FH(iF+2,jF,kF-2));
+             const double t_km1=(FH(iF-2,jF,kF-1)-F8*FH(iF-1,jF,kF-1)+F8*FH(iF+1,jF,kF-1)-FH(iF+2,jF,kF-1));
+             const double t_kp1=(FH(iF-2,jF,kF+1)-F8*FH(iF-1,jF,kF+1)+F8*FH(iF+1,jF,kF+1)-FH(iF+2,jF,kF+1));
+             const double t_kp2=(FH(iF-2,jF,kF+2)-F8*FH(iF-1,jF,kF+2)+F8*FH(iF+1,jF,kF+2)-FH(iF+2,jF,kF+2));
+             fxz[p]=Fdxdz*(t_km2-F8*t_km1+F8*t_kp1-t_kp2);}
+            {const double t_km2=(FH(iF,jF-2,kF-2)-F8*FH(iF,jF-1,kF-2)+F8*FH(iF,jF+1,kF-2)-FH(iF,jF+2,kF-2));
+             const double t_km1=(FH(iF,jF-2,kF-1)-F8*FH(iF,jF-1,kF-1)+F8*FH(iF,jF+1,kF-1)-FH(iF,jF+2,kF-1));
+             const double t_kp1=(FH(iF,jF-2,kF+1)-F8*FH(iF,jF-1,kF+1)+F8*FH(iF,jF+1,kF+1)-FH(iF,jF+2,kF+1));
+             const double t_kp2=(FH(iF,jF-2,kF+2)-F8*FH(iF,jF-1,kF+2)+F8*FH(iF,jF+1,kF+2)-FH(iF,jF+2,kF+2));
+             fyz[p]=Fdydz*(t_km2-F8*t_km1+F8*t_kp1-t_kp2);}
+        }}}}
+        if(has6){for(int k0=k6_lo;k0<=k6_hi;++k0){const int kF=k0+1;
+        for(int j0=j6_lo;j0<=j6_hi;++j0){const int jF=j0+1;
+        for(int i0=i6_lo;i0<=i6_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Xdxdx*(TWO*FH(iF-3,jF,kF)-F27*FH(iF-2,jF,kF)+F270*FH(iF-1,jF,kF)-F490*FH(iF,jF,kF)+F270*FH(iF+1,jF,kF)-F27*FH(iF+2,jF,kF)+TWO*FH(iF+3,jF,kF));
+            fyy[p]=Xdydy*(TWO*FH(iF,jF-3,kF)-F27*FH(iF,jF-2,kF)+F270*FH(iF,jF-1,kF)-F490*FH(iF,jF,kF)+F270*FH(iF,jF+1,kF)-F27*FH(iF,jF+2,kF)+TWO*FH(iF,jF+3,kF));
+            fzz[p]=Xdzdz*(TWO*FH(iF,jF,kF-3)-F27*FH(iF,jF,kF-2)+F270*FH(iF,jF,kF-1)-F490*FH(iF,jF,kF)+F270*FH(iF,jF,kF+1)-F27*FH(iF,jF,kF+2)+TWO*FH(iF,jF,kF+3));
+            #define XS6(JF,KFDUMMY) (-FH(iF-3,JF,KFDUMMY)+F9*FH(iF-2,JF,KFDUMMY)-F45*FH(iF-1,JF,KFDUMMY)+F45*FH(iF+1,JF,KFDUMMY)-F9*FH(iF+2,JF,KFDUMMY)+FH(iF+3,JF,KFDUMMY))
+            fxy[p]=Xdxdy*(-XS6(jF-3,kF)+F9*XS6(jF-2,kF)-F45*XS6(jF-1,kF)+F45*XS6(jF+1,kF)-F9*XS6(jF+2,kF)+XS6(jF+3,kF));
+            fxz[p]=Xdxdz*(-XS6(jF,kF-3)+F9*XS6(jF,kF-2)-F45*XS6(jF,kF-1)+F45*XS6(jF,kF+1)-F9*XS6(jF,kF+2)+XS6(jF,kF+3));
+            #undef XS6
+            #define YS6(JF,KFDUMMY) (-FH(iF,JF-3,KFDUMMY)+F9*FH(iF,JF-2,KFDUMMY)-F45*FH(iF,JF-1,KFDUMMY)+F45*FH(iF,JF+1,KFDUMMY)-F9*FH(iF,JF+2,KFDUMMY)+FH(iF,JF+3,KFDUMMY))
+            fyz[p]=Xdydz*(-YS6(jF,kF-3)+F9*YS6(jF,kF-2)-F45*YS6(jF,kF-1)+F45*YS6(jF,kF+1)-F9*YS6(jF,kF+2)+YS6(jF,kF+3));
+            #undef YS6
+        }}}}
+        #undef FH
+        return;
+    }
+#elif (ghost_width == 5)
+    {
+        /* 8th-order shell second derivatives — inherits 8th-order stencil coeffs from Cartesian */
+        const int ord=4;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-3;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-3;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-3;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        static double *fh_buf=NULL;static size_t cap=0;
+        if(fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf;if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double Sdxdx=ONE/(dX*dX),Sdydy=ONE/(dY*dY),Sdzdz=ONE/(dZ*dZ);
+        const double Fdxdx=F1o12/(dX*dX),Fdydy=F1o12/(dY*dY),Fdzdz=F1o12/(dZ*dZ);
+        const double Xdxdx=F1o180/(dX*dX),Xdydy=F1o180/(dY*dY),Xdzdz=F1o180/(dZ*dZ);
+        const double Edxdx=F1o5040/(dX*dX),Edydy=F1o5040/(dY*dY),Edzdz=F1o5040/(dZ*dZ);
+        const double Sdxdy=F1o4/(dX*dY),Sdxdz=F1o4/(dX*dZ),Sdydz=F1o4/(dY*dZ);
+        const double Fdxdy=F1o144/(dX*dY),Fdxdz=F1o144/(dX*dZ),Fdydz=F1o144/(dY*dZ);
+        const double Xdxdy=F1o3600/(dX*dY),Xdxdz=F1o3600/(dX*dZ),Xdydz=F1o3600/(dY*dZ);
+        const double Edxdy=F1o705600/(dX*dY),Edxdz=F1o705600/(dX*dZ),Edydz=F1o705600/(dY*dZ);
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fxx[p]=fyy[p]=fzz[p]=fxy[p]=fxz[p]=fyz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0,j2_lo=(jminF>0)?jminF:0,k2_lo=1,i2_hi=ex1-2,j2_hi=ex2-2,k2_hi=ex3-2;
+        const int i4_lo=(iminF+1>0)?iminF+1:0,j4_lo=(jminF+1>0)?jminF+1:0,k4_lo=2,i4_hi=ex1-3,j4_hi=ex2-3,k4_hi=ex3-3;
+        const int i6_lo=(iminF+2>0)?iminF+2:0,j6_lo=(jminF+2>0)?jminF+2:0,k6_lo=3,i6_hi=ex1-4,j6_hi=ex2-4,k6_hi=ex3-4;
+        const int i8_lo=(iminF+3>0)?iminF+3:0,j8_lo=(jminF+3>0)?jminF+3:0,k8_lo=4,i8_hi=ex1-5,j8_hi=ex2-5,k8_hi=ex3-5;
+        const int has4=(i4_lo<=i4_hi&&j4_lo<=j4_hi&&k4_lo<=k4_hi),has6=(i6_lo<=i6_hi&&j6_lo<=j6_hi&&k6_lo<=k6_hi),has8=(i8_lo<=i8_hi&&j8_lo<=j8_hi&&k8_lo<=k8_hi);
+        #define FH(iF,jF,kF) fh[idx_fh_stbd(iF,jF,kF,ord,ex)]
+
+        /* 2nd-order pass */
+        if(i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi){for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+        for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+        for(int i0=i2_lo;i0<=i2_hi;++i0){bool in4=has4&&i0>=i4_lo&&i0<=i4_hi&&j0>=j4_lo&&j0<=j4_hi&&k0>=k4_lo&&k0<=k4_hi;if(in4)continue;
+            const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Sdxdx*(FH(iF-1,jF,kF)-TWO*FH(iF,jF,kF)+FH(iF+1,jF,kF));
+            fyy[p]=Sdydy*(FH(iF,jF-1,kF)-TWO*FH(iF,jF,kF)+FH(iF,jF+1,kF));
+            fzz[p]=Sdzdz*(FH(iF,jF,kF-1)-TWO*FH(iF,jF,kF)+FH(iF,jF,kF+1));
+            fxy[p]=Sdxdy*(FH(iF-1,jF-1,kF)-FH(iF+1,jF-1,kF)-FH(iF-1,jF+1,kF)+FH(iF+1,jF+1,kF));
+            fxz[p]=Sdxdz*(FH(iF-1,jF,kF-1)-FH(iF+1,jF,kF-1)-FH(iF-1,jF,kF+1)+FH(iF+1,jF,kF+1));
+            fyz[p]=Sdydz*(FH(iF,jF-1,kF-1)-FH(iF,jF+1,kF-1)-FH(iF,jF-1,kF+1)+FH(iF,jF+1,kF+1));
+        }}}}
+        /* 4th-order pass */
+        if(has4){for(int k0=k4_lo;k0<=k4_hi;++k0){const int kF=k0+1;
+        for(int j0=j4_lo;j0<=j4_hi;++j0){const int jF=j0+1;
+        for(int i0=i4_lo;i0<=i4_hi;++i0){bool in6=has6&&i0>=i6_lo&&i0<=i6_hi&&j0>=j6_lo&&j0<=j6_hi&&k0>=k6_lo&&k0<=k6_hi;if(in6)continue;
+            const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Fdxdx*(-FH(iF-2,jF,kF)+F16*FH(iF-1,jF,kF)-F30*FH(iF,jF,kF)-FH(iF+2,jF,kF)+F16*FH(iF+1,jF,kF));
+            fyy[p]=Fdydy*(-FH(iF,jF-2,kF)+F16*FH(iF,jF-1,kF)-F30*FH(iF,jF,kF)-FH(iF,jF+2,kF)+F16*FH(iF,jF+1,kF));
+            fzz[p]=Fdzdz*(-FH(iF,jF,kF-2)+F16*FH(iF,jF,kF-1)-F30*FH(iF,jF,kF)-FH(iF,jF,kF+2)+F16*FH(iF,jF,kF+1));
+            {const double t_jm2=(FH(iF-2,jF-2,kF)-F8*FH(iF-1,jF-2,kF)+F8*FH(iF+1,jF-2,kF)-FH(iF+2,jF-2,kF));
+             const double t_jm1=(FH(iF-2,jF-1,kF)-F8*FH(iF-1,jF-1,kF)+F8*FH(iF+1,jF-1,kF)-FH(iF+2,jF-1,kF));
+             const double t_jp1=(FH(iF-2,jF+1,kF)-F8*FH(iF-1,jF+1,kF)+F8*FH(iF+1,jF+1,kF)-FH(iF+2,jF+1,kF));
+             const double t_jp2=(FH(iF-2,jF+2,kF)-F8*FH(iF-1,jF+2,kF)+F8*FH(iF+1,jF+2,kF)-FH(iF+2,jF+2,kF));
+             fxy[p]=Fdxdy*(t_jm2-F8*t_jm1+F8*t_jp1-t_jp2);}
+            {const double t_km2=(FH(iF-2,jF,kF-2)-F8*FH(iF-1,jF,kF-2)+F8*FH(iF+1,jF,kF-2)-FH(iF+2,jF,kF-2));
+             const double t_km1=(FH(iF-2,jF,kF-1)-F8*FH(iF-1,jF,kF-1)+F8*FH(iF+1,jF,kF-1)-FH(iF+2,jF,kF-1));
+             const double t_kp1=(FH(iF-2,jF,kF+1)-F8*FH(iF-1,jF,kF+1)+F8*FH(iF+1,jF,kF+1)-FH(iF+2,jF,kF+1));
+             const double t_kp2=(FH(iF-2,jF,kF+2)-F8*FH(iF-1,jF,kF+2)+F8*FH(iF+1,jF,kF+2)-FH(iF+2,jF,kF+2));
+             fxz[p]=Fdxdz*(t_km2-F8*t_km1+F8*t_kp1-t_kp2);}
+            {const double t_km2=(FH(iF,jF-2,kF-2)-F8*FH(iF,jF-1,kF-2)+F8*FH(iF,jF+1,kF-2)-FH(iF,jF+2,kF-2));
+             const double t_km1=(FH(iF,jF-2,kF-1)-F8*FH(iF,jF-1,kF-1)+F8*FH(iF,jF+1,kF-1)-FH(iF,jF+2,kF-1));
+             const double t_kp1=(FH(iF,jF-2,kF+1)-F8*FH(iF,jF-1,kF+1)+F8*FH(iF,jF+1,kF+1)-FH(iF,jF+2,kF+1));
+             const double t_kp2=(FH(iF,jF-2,kF+2)-F8*FH(iF,jF-1,kF+2)+F8*FH(iF,jF+1,kF+2)-FH(iF,jF+2,kF+2));
+             fyz[p]=Fdydz*(t_km2-F8*t_km1+F8*t_kp1-t_kp2);}
+        }}}}
+        /* 6th-order pass */
+        if(has6){for(int k0=k6_lo;k0<=k6_hi;++k0){const int kF=k0+1;
+        for(int j0=j6_lo;j0<=j6_hi;++j0){const int jF=j0+1;
+        for(int i0=i6_lo;i0<=i6_hi;++i0){if(has8&&i0>=i8_lo&&i0<=i8_hi&&j0>=j8_lo&&j0<=j8_hi&&k0>=k8_lo&&k0<=k8_hi)continue;
+            const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Xdxdx*(TWO*FH(iF-3,jF,kF)-F27*FH(iF-2,jF,kF)+F270*FH(iF-1,jF,kF)-F490*FH(iF,jF,kF)+F270*FH(iF+1,jF,kF)-F27*FH(iF+2,jF,kF)+TWO*FH(iF+3,jF,kF));
+            fyy[p]=Xdydy*(TWO*FH(iF,jF-3,kF)-F27*FH(iF,jF-2,kF)+F270*FH(iF,jF-1,kF)-F490*FH(iF,jF,kF)+F270*FH(iF,jF+1,kF)-F27*FH(iF,jF+2,kF)+TWO*FH(iF,jF+3,kF));
+            fzz[p]=Xdzdz*(TWO*FH(iF,jF,kF-3)-F27*FH(iF,jF,kF-2)+F270*FH(iF,jF,kF-1)-F490*FH(iF,jF,kF)+F270*FH(iF,jF,kF+1)-F27*FH(iF,jF,kF+2)+TWO*FH(iF,jF,kF+3));
+            #define XS6_8(JF,KFDUMMY) (-FH(iF-3,JF,KFDUMMY)+F9*FH(iF-2,JF,KFDUMMY)-F45*FH(iF-1,JF,KFDUMMY)+F45*FH(iF+1,JF,KFDUMMY)-F9*FH(iF+2,JF,KFDUMMY)+FH(iF+3,JF,KFDUMMY))
+            fxy[p]=Xdxdy*(-XS6_8(jF-3,kF)+F9*XS6_8(jF-2,kF)-F45*XS6_8(jF-1,kF)+F45*XS6_8(jF+1,kF)-F9*XS6_8(jF+2,kF)+XS6_8(jF+3,kF));
+            fxz[p]=Xdxdz*(-XS6_8(jF,kF-3)+F9*XS6_8(jF,kF-2)-F45*XS6_8(jF,kF-1)+F45*XS6_8(jF,kF+1)-F9*XS6_8(jF,kF+2)+XS6_8(jF,kF+3));
+            #undef XS6_8
+            #define YS6_8(JF,KFDUMMY) (-FH(iF,JF-3,KFDUMMY)+F9*FH(iF,JF-2,KFDUMMY)-F45*FH(iF,JF-1,KFDUMMY)+F45*FH(iF,JF+1,KFDUMMY)-F9*FH(iF,JF+2,KFDUMMY)+FH(iF,JF+3,KFDUMMY))
+            fyz[p]=Xdydz*(-YS6_8(jF,kF-3)+F9*YS6_8(jF,kF-2)-F45*YS6_8(jF,kF-1)+F45*YS6_8(jF,kF+1)-F9*YS6_8(jF,kF+2)+YS6_8(jF,kF+3));
+            #undef YS6_8
+        }}}}
+        /* 8th-order pass */
+        if(has8){for(int k0=k8_lo;k0<=k8_hi;++k0){const int kF=k0+1;
+        for(int j0=j8_lo;j0<=j8_hi;++j0){const int jF=j0+1;
+        for(int i0=i8_lo;i0<=i8_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fxx[p]=Edxdx*(-(double)9*FH(iF-4,jF,kF)+F128*FH(iF-3,jF,kF)-F1008*FH(iF-2,jF,kF)+F8064*FH(iF-1,jF,kF)-F14350*FH(iF,jF,kF)+F8064*FH(iF+1,jF,kF)-F1008*FH(iF+2,jF,kF)+F128*FH(iF+3,jF,kF)-(double)9*FH(iF+4,jF,kF));
+            fyy[p]=Edydy*(-(double)9*FH(iF,jF-4,kF)+F128*FH(iF,jF-3,kF)-F1008*FH(iF,jF-2,kF)+F8064*FH(iF,jF-1,kF)-F14350*FH(iF,jF,kF)+F8064*FH(iF,jF+1,kF)-F1008*FH(iF,jF+2,kF)+F128*FH(iF,jF+3,kF)-(double)9*FH(iF,jF+4,kF));
+            fzz[p]=Edzdz*(-(double)9*FH(iF,jF,kF-4)+F128*FH(iF,jF,kF-3)-F1008*FH(iF,jF,kF-2)+F8064*FH(iF,jF,kF-1)-F14350*FH(iF,jF,kF)+F8064*FH(iF,jF,kF+1)-F1008*FH(iF,jF,kF+2)+F128*FH(iF,jF,kF+3)-(double)9*FH(iF,jF,kF+4));
+            #define XS8(JF,KFDUMMY) (+(double)3*FH(iF-4,JF,KFDUMMY)-F32*FH(iF-3,JF,KFDUMMY)+F168*FH(iF-2,JF,KFDUMMY)-F672*FH(iF-1,JF,KFDUMMY)+F672*FH(iF+1,JF,KFDUMMY)-F168*FH(iF+2,JF,KFDUMMY)+F32*FH(iF+3,JF,KFDUMMY)-(double)3*FH(iF+4,JF,KFDUMMY))
+            fxy[p]=Edxdy*(+(double)3*XS8(jF-4,kF)-F32*XS8(jF-3,kF)+F168*XS8(jF-2,kF)-F672*XS8(jF-1,kF)+F672*XS8(jF+1,kF)-F168*XS8(jF+2,kF)+F32*XS8(jF+3,kF)-(double)3*XS8(jF+4,kF));
+            fxz[p]=Edxdz*(+(double)3*XS8(jF,kF-4)-F32*XS8(jF,kF-3)+F168*XS8(jF,kF-2)-F672*XS8(jF,kF-1)+F672*XS8(jF,kF+1)-F168*XS8(jF,kF+2)+F32*XS8(jF,kF+3)-(double)3*XS8(jF,kF+4));
+            #undef XS8
+            #define YS8(JF,KFDUMMY) (+(double)3*FH(iF,JF-4,KFDUMMY)-F32*FH(iF,JF-3,KFDUMMY)+F168*FH(iF,JF-2,KFDUMMY)-F672*FH(iF,JF-1,KFDUMMY)+F672*FH(iF,JF+1,KFDUMMY)-F168*FH(iF,JF+2,KFDUMMY)+F32*FH(iF,JF+3,KFDUMMY)-(double)3*FH(iF,JF+4,KFDUMMY))
+            fyz[p]=Edydz*(+(double)3*YS8(jF,kF-4)-F32*YS8(jF,kF-3)+F168*YS8(jF,kF-2)-F672*YS8(jF,kF-1)+F672*YS8(jF,kF+1)-F168*YS8(jF,kF+2)+F32*YS8(jF,kF+3)-(double)3*YS8(jF,kF+4));
+            #undef YS8
+        }}}}
+        #undef FH
+        return;
+    }
+#else
+#error "fdderivs_sh_c.C: unsupported ghost_width"
+#endif
+}

AMSS_NCKU_source/fdderivs_shc_c.C

@@ -0,0 +1,107 @@
+#include "macrodef.h"
+#include "share_func.h"
+#include <cstddef>
+
+/* Forward declarations — Fortran-mangled names from shell C kernels */
+extern "C" {
+void fderivs_sh_(const int ex[3], const double *f,
+                 double *fx, double *fy, double *fz,
+                 const double *X, const double *Y, const double *Z,
+                 double SYM1, double SYM2, double SYM3,
+                 int Symmetry, int onoff, int sst);
+
+void fdderivs_sh_(const int ex[3], const double *f,
+                  double *fxx, double *fxy, double *fxz,
+                  double *fyy, double *fyz, double *fzz,
+                  const double *X, const double *Y, const double *Z,
+                  double SYM1, double SYM2, double SYM3,
+                  int Symmetry, int onoff, int sst);
+
+void fdderivs_shc_(int *ex,
+                    double *f,
+                    double *fxx, double *fxy, double *fxz,
+                    double *fyy, double *fyz, double *fzz,
+                    double *crho, double *sigma, double *R,
+                    double &SYM1, double &SYM2, double &SYM3,
+                    int &Symmetry, int &Lev, int &sst,
+                    double *drhodx, double *drhody, double *drhodz,
+                    double *dsigmadx, double *dsigmady, double *dsigmadz,
+                    double *dRdx, double *dRdy, double *dRdz,
+                    double *drhodxx, double *drhodxy, double *drhodxz,
+                    double *drhodyy, double *drhodyz, double *drhodzz,
+                    double *dsigmadxx, double *dsigmadxy, double *dsigmadxz,
+                    double *dsigmadyy, double *dsigmadyz, double *dsigmadzz,
+                    double *dRdxx, double *dRdxy, double *dRdxz,
+                    double *dRdyy, double *dRdyz, double *dRdzz)
+{
+    const int ex3[3] = { ex[0], ex[1], ex[2] };
+    const size_t n = (size_t)ex[0] * (size_t)ex[1] * (size_t)ex[2];
+
+    double *gx  = (double*)malloc(n * sizeof(double));
+    double *gy  = (double*)malloc(n * sizeof(double));
+    double *gz  = (double*)malloc(n * sizeof(double));
+    double *gxx = (double*)malloc(n * sizeof(double));
+    double *gxy = (double*)malloc(n * sizeof(double));
+    double *gxz = (double*)malloc(n * sizeof(double));
+    double *gyy = (double*)malloc(n * sizeof(double));
+    double *gyz = (double*)malloc(n * sizeof(double));
+    double *gzz = (double*)malloc(n * sizeof(double));
+
+    if (!gx||!gy||!gz||!gxx||!gxy||!gxz||!gyy||!gyz||!gzz) {
+        free(gx);free(gy);free(gz);free(gxx);free(gxy);free(gxz);free(gyy);free(gyz);free(gzz);
+        return;
+    }
+
+    fderivs_sh_(ex3, f, gx, gy, gz, crho, sigma, R, SYM1, SYM2, SYM3, Symmetry, Lev, sst);
+    fdderivs_sh_(ex3, f, gxx, gxy, gxz, gyy, gyz, gzz, crho, sigma, R, SYM1, SYM2, SYM3, Symmetry, Lev, sst);
+
+    for (size_t i = 0; i < n; ++i) {
+        const double rx=drhodx[i], ry=drhody[i], rz=drhodz[i];
+        const double sx=dsigmadx[i], sy=dsigmady[i], sz=dsigmadz[i];
+        const double Rx=dRdx[i], Ry=dRdy[i], Rz=dRdz[i];
+        const double rxx=drhodxx[i], rxy=drhodxy[i], rxz=drhodxz[i];
+        const double ryy=drhodyy[i], ryz=drhodyz[i], rzz=drhodzz[i];
+        const double sxx=dsigmadxx[i], sxy=dsigmadxy[i], sxz=dsigmadxz[i];
+        const double syy=dsigmadyy[i], syz=dsigmadyz[i], szz=dsigmadzz[i];
+        const double Rxx=dRdxx[i], Rxy=dRdxy[i], Rxz=dRdxz[i];
+        const double Ryy=dRdyy[i], Ryz=dRdyz[i], Rzz=dRdzz[i];
+
+        const double Gr=gx[i], Gs=gy[i], GR=gz[i];
+        const double Grr=gxx[i], Grs=gxy[i], GrR=gxz[i];
+        const double Gss=gyy[i], GsR=gyz[i], GRR=gzz[i];
+
+        /* fxx */
+        fxx[i] = rx*rx*Grr + sx*sx*Gss + Rx*Rx*GRR
+               + 2.0*(rx*sx*Grs + rx*Rx*GrR + sx*Rx*GsR)
+               + rxx*Gr + sxx*Gs + Rxx*GR;
+
+        /* fxy */
+        fxy[i] = rx*ry*Grr + sx*sy*Gss + Rx*Ry*GRR
+               + rx*sy*Grs + ry*sx*Grs + rx*Ry*GrR + ry*Rx*GrR + sx*Ry*GsR + sy*Rx*GsR
+               + rxy*Gr + sxy*Gs + Rxy*GR;
+
+        /* fxz */
+        fxz[i] = rx*rz*Grr + sx*sz*Gss + Rx*Rz*GRR
+               + rx*sz*Grs + rz*sx*Grs + rx*Rz*GrR + rz*Rx*GrR + sx*Rz*GsR + sz*Rx*GsR
+               + rxz*Gr + sxz*Gs + Rxz*GR;
+
+        /* fyy */
+        fyy[i] = ry*ry*Grr + sy*sy*Gss + Ry*Ry*GRR
+               + 2.0*(ry*sy*Grs + ry*Ry*GrR + sy*Ry*GsR)
+               + ryy*Gr + syy*Gs + Ryy*GR;
+
+        /* fyz */
+        fyz[i] = ry*rz*Grr + sy*sz*Gss + Ry*Rz*GRR
+               + ry*sz*Grs + rz*sy*Grs + ry*Rz*GrR + rz*Ry*GrR + sy*Rz*GsR + sz*Ry*GsR
+               + ryz*Gr + syz*Gs + Ryz*GR;
+
+        /* fzz */
+        fzz[i] = rz*rz*Grr + sz*sz*Gss + Rz*Rz*GRR
+               + 2.0*(rz*sz*Grs + rz*Rz*GrR + sz*Rz*GsR)
+               + rzz*Gr + szz*Gs + Rzz*GR;
+    }
+
+    free(gx);free(gy);free(gz);free(gxx);free(gxy);free(gxz);free(gyy);free(gyz);free(gzz);
+}
+
+} // extern "C"

AMSS_NCKU_source/fderivs_c.C

@@ -0,0 +1,616 @@
+#include "macrodef.h"
+#include "tool.h"
+
+/*
+ * C 版 fderivs — first derivatives df/dx, df/dy, df/dz.
+ *
+ * Finite difference order is selected at compile time via the ghost_width macro
+ * (defined in macrodef.fh):
+ *   ghost_width = 2 → 2nd-order
+ *   ghost_width = 3 → 4th-order
+ *   ghost_width = 4 → 6th-order
+ *   ghost_width = 5 → 8th-order
+ *
+ * Multi-pass overwrite strategy: compute the widest (lowest-order) stencil first,
+ * then overwrite interior regions with progressively higher-order stencils.
+ */
+void fderivs(const int ex[3],
+             const double *f,
+             double *fx, double *fy, double *fz,
+             const double *X, const double *Y, const double *Z,
+             double SYM1, double SYM2, double SYM3,
+             int Symmetry, int onoff)
+{
+    (void)onoff;
+
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0, EIT = 8.0;
+    const double F9 = 9.0, F12 = 12.0, F45 = 45.0, F60 = 60.0;
+    const double F32 = 32.0, F168 = 168.0, F672 = 672.0, F840 = 840.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+    const int gw = ghost_width; // compile-time constant
+
+#if (ghost_width == 2)
+    /* ---- 2nd-order ------------------------------------------------------ */
+    {
+        const int ord = 1; // symmetry_bd ord = ghost_width - 1
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = 0;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = 0;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = 0;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d2dx = ONE / TWO / dX;
+        const double d2dy = ONE / TWO / dY;
+        const double d2dz = ONE / TWO / dZ;
+
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fx[p] = ZEO; fy[p] = ZEO; fz[p] = ZEO;
+        }
+
+        /* 2nd-order pass: [-1, 0, +1] / (2*dx) */
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2;
+        const int j2_hi = ex2 - 2;
+        const int k2_hi = ex3 - 2;
+
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d2dx * (
+                            -fh[idx_fh_F_ord1(iF - 1, jF,     kF,     ex)] +
+                             fh[idx_fh_F_ord1(iF + 1, jF,     kF,     ex)]
+                        );
+
+                        fy[p] = d2dy * (
+                            -fh[idx_fh_F_ord1(iF,     jF - 1, kF,     ex)] +
+                             fh[idx_fh_F_ord1(iF,     jF + 1, kF,     ex)]
+                        );
+
+                        fz[p] = d2dz * (
+                            -fh[idx_fh_F_ord1(iF,     jF,     kF - 1, ex)] +
+                             fh[idx_fh_F_ord1(iF,     jF,     kF + 1, ex)]
+                        );
+                    }
+                }
+            }
+        }
+        return;
+    }
+#elif (ghost_width == 3)
+    /* ---- 4th-order (original code) ------------------------------------ */
+    {
+        const int ord = 2; // symmetry_bd ord
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d12dx = ONE / F12 / dX;
+        const double d12dy = ONE / F12 / dY;
+        const double d12dz = ONE / F12 / dZ;
+        const double d2dx  = ONE / TWO / dX;
+        const double d2dy  = ONE / TWO / dY;
+        const double d2dz  = ONE / TWO / dZ;
+
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fx[p] = ZEO; fy[p] = ZEO; fz[p] = ZEO;
+        }
+
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2;
+        const int j2_hi = ex2 - 2;
+        const int k2_hi = ex3 - 2;
+
+        const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i4_hi = ex1 - 3;
+        const int j4_hi = ex2 - 3;
+        const int k4_hi = ex3 - 3;
+
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d2dx * (
+                            -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                             fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                        );
+
+                        fy[p] = d2dy * (
+                            -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                             fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                        );
+
+                        fz[p] = d2dz * (
+                            -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                             fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                        );
+                    }
+                }
+            }
+        }
+
+        if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+            for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d12dx * (
+                            fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
+                            EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                            EIT * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)] -
+                            fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)]
+                        );
+
+                        fy[p] = d12dy * (
+                            fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] -
+                            EIT * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                            EIT * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)] -
+                            fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)]
+                        );
+
+                        fz[p] = d12dz * (
+                            fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] -
+                            EIT * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                            EIT * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)] -
+                            fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
+                        );
+                    }
+                }
+            }
+        }
+        return;
+    }
+#elif (ghost_width == 4)
+    /* ---- 6th-order ----------------------------------------------------- */
+    {
+        const int ord = 3;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        /* Denominators */
+        const double d60dx = ONE / F60 / dX;
+        const double d60dy = ONE / F60 / dY;
+        const double d60dz = ONE / F60 / dZ;
+        const double d12dx = ONE / F12 / dX;
+        const double d12dy = ONE / F12 / dY;
+        const double d12dz = ONE / F12 / dZ;
+        const double d2dx  = ONE / TWO / dX;
+        const double d2dy  = ONE / TWO / dY;
+        const double d2dz  = ONE / TWO / dZ;
+
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fx[p] = ZEO; fy[p] = ZEO; fz[p] = ZEO;
+        }
+
+        /* 2nd-order pass: 3pt, widest */
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2;
+        const int j2_hi = ex2 - 2;
+        const int k2_hi = ex3 - 2;
+
+        /* 4th-order pass: 5pt */
+        const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i4_hi = ex1 - 3;
+        const int j4_hi = ex2 - 3;
+        const int k4_hi = ex3 - 3;
+
+        /* 6th-order pass: 7pt, narrowest interior */
+        const int i6_lo = (iminF + 2 > 0) ? (iminF + 2) : 0;
+        const int j6_lo = (jminF + 2 > 0) ? (jminF + 2) : 0;
+        const int k6_lo = (kminF + 2 > 0) ? (kminF + 2) : 0;
+        const int i6_hi = ex1 - 4;
+        const int j6_hi = ex2 - 4;
+        const int k6_hi = ex3 - 4;
+
+        /* 2nd-order */
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d2dx * (
+                            -fh[idx_fh_F(iF - 1, jF,     kF,     ex)] +
+                             fh[idx_fh_F(iF + 1, jF,     kF,     ex)]);
+                        fy[p] = d2dy * (
+                            -fh[idx_fh_F(iF,     jF - 1, kF,     ex)] +
+                             fh[idx_fh_F(iF,     jF + 1, kF,     ex)]);
+                        fz[p] = d2dz * (
+                            -fh[idx_fh_F(iF,     jF,     kF - 1, ex)] +
+                             fh[idx_fh_F(iF,     jF,     kF + 1, ex)]);
+                    }
+                }
+            }
+        }
+
+        /* 4th-order overwrite */
+        if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+            for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d12dx * (
+                            fh[idx_fh_F(iF - 2, jF,     kF,     ex)] -
+                            EIT * fh[idx_fh_F(iF - 1, jF,     kF,     ex)] +
+                            EIT * fh[idx_fh_F(iF + 1, jF,     kF,     ex)] -
+                            fh[idx_fh_F(iF + 2, jF,     kF,     ex)]);
+
+                        fy[p] = d12dy * (
+                            fh[idx_fh_F(iF,     jF - 2, kF,     ex)] -
+                            EIT * fh[idx_fh_F(iF,     jF - 1, kF,     ex)] +
+                            EIT * fh[idx_fh_F(iF,     jF + 1, kF,     ex)] -
+                            fh[idx_fh_F(iF,     jF + 2, kF,     ex)]);
+
+                        fz[p] = d12dz * (
+                            fh[idx_fh_F(iF,     jF,     kF - 2, ex)] -
+                            EIT * fh[idx_fh_F(iF,     jF,     kF - 1, ex)] +
+                            EIT * fh[idx_fh_F(iF,     jF,     kF + 1, ex)] -
+                            fh[idx_fh_F(iF,     jF,     kF + 2, ex)]);
+                    }
+                }
+            }
+        }
+
+        /* 6th-order overwrite: [-1,+9,-45,0,+45,-9,+1] / (60*dx) */
+        if (i6_lo <= i6_hi && j6_lo <= j6_hi && k6_lo <= k6_hi) {
+            for (int k0 = k6_lo; k0 <= k6_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j6_lo; j0 <= j6_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i6_lo; i0 <= i6_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d60dx * (
+                            -fh[idx_fh_F(iF - 3, jF,     kF,     ex)] +
+                            F9 * fh[idx_fh_F(iF - 2, jF,     kF,     ex)] -
+                            F45 * fh[idx_fh_F(iF - 1, jF,     kF,     ex)] +
+                            F45 * fh[idx_fh_F(iF + 1, jF,     kF,     ex)] -
+                            F9 * fh[idx_fh_F(iF + 2, jF,     kF,     ex)] +
+                            fh[idx_fh_F(iF + 3, jF,     kF,     ex)]);
+
+                        fy[p] = d60dy * (
+                            -fh[idx_fh_F(iF,     jF - 3, kF,     ex)] +
+                            F9 * fh[idx_fh_F(iF,     jF - 2, kF,     ex)] -
+                            F45 * fh[idx_fh_F(iF,     jF - 1, kF,     ex)] +
+                            F45 * fh[idx_fh_F(iF,     jF + 1, kF,     ex)] -
+                            F9 * fh[idx_fh_F(iF,     jF + 2, kF,     ex)] +
+                            fh[idx_fh_F(iF,     jF + 3, kF,     ex)]);
+
+                        fz[p] = d60dz * (
+                            -fh[idx_fh_F(iF,     jF,     kF - 3, ex)] +
+                            F9 * fh[idx_fh_F(iF,     jF,     kF - 2, ex)] -
+                            F45 * fh[idx_fh_F(iF,     jF,     kF - 1, ex)] +
+                            F45 * fh[idx_fh_F(iF,     jF,     kF + 1, ex)] -
+                            F9 * fh[idx_fh_F(iF,     jF,     kF + 2, ex)] +
+                            fh[idx_fh_F(iF,     jF,     kF + 3, ex)]);
+                    }
+                }
+            }
+        }
+        return;
+    }
+#elif (ghost_width == 5)
+    /* ---- 8th-order ----------------------------------------------------- */
+    {
+        const int ord = 5;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -3;
+
+        const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        static double *fh_buf = NULL;
+        static size_t cap = 0;
+        if (fh_size > cap) {
+            free(fh_buf);
+            fh_buf = (double*)aligned_alloc(64, fh_size * sizeof(double));
+            cap = fh_size;
+        }
+        double *fh = fh_buf;
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d840dx = ONE / F840 / dX;
+        const double d840dy = ONE / F840 / dY;
+        const double d840dz = ONE / F840 / dZ;
+        const double d60dx  = ONE / F60  / dX;
+        const double d60dy  = ONE / F60  / dY;
+        const double d60dz  = ONE / F60  / dZ;
+        const double d12dx  = ONE / F12  / dX;
+        const double d12dy  = ONE / F12  / dY;
+        const double d12dz  = ONE / F12  / dZ;
+        const double d2dx   = ONE / TWO  / dX;
+        const double d2dy   = ONE / TWO  / dY;
+        const double d2dz   = ONE / TWO  / dZ;
+
+        const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+        for (size_t p = 0; p < all; ++p) {
+            fx[p] = ZEO; fy[p] = ZEO; fz[p] = ZEO;
+        }
+
+        /* 2nd: 3pt, widest */
+        const int i2_lo = (iminF > 0) ? iminF : 0;
+        const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int k2_lo = (kminF > 0) ? kminF : 0;
+        const int i2_hi = ex1 - 2;
+        const int j2_hi = ex2 - 2;
+        const int k2_hi = ex3 - 2;
+
+        /* 4th: 5pt */
+        const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i4_hi = ex1 - 3;
+        const int j4_hi = ex2 - 3;
+        const int k4_hi = ex3 - 3;
+
+        /* 6th: 7pt */
+        const int i6_lo = (iminF + 2 > 0) ? (iminF + 2) : 0;
+        const int j6_lo = (jminF + 2 > 0) ? (jminF + 2) : 0;
+        const int k6_lo = (kminF + 2 > 0) ? (kminF + 2) : 0;
+        const int i6_hi = ex1 - 4;
+        const int j6_hi = ex2 - 4;
+        const int k6_hi = ex3 - 4;
+
+        /* 8th: 9pt, narrowest */
+        const int i8_lo = (iminF + 3 > 0) ? (iminF + 3) : 0;
+        const int j8_lo = (jminF + 3 > 0) ? (jminF + 3) : 0;
+        const int k8_lo = (kminF + 3 > 0) ? (kminF + 3) : 0;
+        const int i8_hi = ex1 - 5;
+        const int j8_hi = ex2 - 5;
+        const int k8_hi = ex3 - 5;
+
+        if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+            for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d2dx * (
+                            -fh[idx_fh_F_ord5(iF - 1, jF,     kF,     ex)] +
+                             fh[idx_fh_F_ord5(iF + 1, jF,     kF,     ex)]);
+                        fy[p] = d2dy * (
+                            -fh[idx_fh_F_ord5(iF,     jF - 1, kF,     ex)] +
+                             fh[idx_fh_F_ord5(iF,     jF + 1, kF,     ex)]);
+                        fz[p] = d2dz * (
+                            -fh[idx_fh_F_ord5(iF,     jF,     kF - 1, ex)] +
+                             fh[idx_fh_F_ord5(iF,     jF,     kF + 1, ex)]);
+                    }
+                }
+            }
+        }
+
+        if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+            for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d12dx * (
+                            fh[idx_fh_F_ord5(iF - 2, jF,     kF,     ex)] -
+                            EIT * fh[idx_fh_F_ord5(iF - 1, jF,     kF,     ex)] +
+                            EIT * fh[idx_fh_F_ord5(iF + 1, jF,     kF,     ex)] -
+                            fh[idx_fh_F_ord5(iF + 2, jF,     kF,     ex)]);
+
+                        fy[p] = d12dy * (
+                            fh[idx_fh_F_ord5(iF,     jF - 2, kF,     ex)] -
+                            EIT * fh[idx_fh_F_ord5(iF,     jF - 1, kF,     ex)] +
+                            EIT * fh[idx_fh_F_ord5(iF,     jF + 1, kF,     ex)] -
+                            fh[idx_fh_F_ord5(iF,     jF + 2, kF,     ex)]);
+
+                        fz[p] = d12dz * (
+                            fh[idx_fh_F_ord5(iF,     jF,     kF - 2, ex)] -
+                            EIT * fh[idx_fh_F_ord5(iF,     jF,     kF - 1, ex)] +
+                            EIT * fh[idx_fh_F_ord5(iF,     jF,     kF + 1, ex)] -
+                            fh[idx_fh_F_ord5(iF,     jF,     kF + 2, ex)]);
+                    }
+                }
+            }
+        }
+
+        if (i6_lo <= i6_hi && j6_lo <= j6_hi && k6_lo <= k6_hi) {
+            for (int k0 = k6_lo; k0 <= k6_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j6_lo; j0 <= j6_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i6_lo; i0 <= i6_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d60dx * (
+                            -fh[idx_fh_F_ord5(iF - 3, jF,     kF,     ex)] +
+                            F9 * fh[idx_fh_F_ord5(iF - 2, jF,     kF,     ex)] -
+                            F45 * fh[idx_fh_F_ord5(iF - 1, jF,     kF,     ex)] +
+                            F45 * fh[idx_fh_F_ord5(iF + 1, jF,     kF,     ex)] -
+                            F9 * fh[idx_fh_F_ord5(iF + 2, jF,     kF,     ex)] +
+                            fh[idx_fh_F_ord5(iF + 3, jF,     kF,     ex)]);
+
+                        fy[p] = d60dy * (
+                            -fh[idx_fh_F_ord5(iF,     jF - 3, kF,     ex)] +
+                            F9 * fh[idx_fh_F_ord5(iF,     jF - 2, kF,     ex)] -
+                            F45 * fh[idx_fh_F_ord5(iF,     jF - 1, kF,     ex)] +
+                            F45 * fh[idx_fh_F_ord5(iF,     jF + 1, kF,     ex)] -
+                            F9 * fh[idx_fh_F_ord5(iF,     jF + 2, kF,     ex)] +
+                            fh[idx_fh_F_ord5(iF,     jF + 3, kF,     ex)]);
+
+                        fz[p] = d60dz * (
+                            -fh[idx_fh_F_ord5(iF,     jF,     kF - 3, ex)] +
+                            F9 * fh[idx_fh_F_ord5(iF,     jF,     kF - 2, ex)] -
+                            F45 * fh[idx_fh_F_ord5(iF,     jF,     kF - 1, ex)] +
+                            F45 * fh[idx_fh_F_ord5(iF,     jF,     kF + 1, ex)] -
+                            F9 * fh[idx_fh_F_ord5(iF,     jF,     kF + 2, ex)] +
+                            fh[idx_fh_F_ord5(iF,     jF,     kF + 3, ex)]);
+                    }
+                }
+            }
+        }
+
+        /* 8th-order overwrite: [+3,-32,+168,-672,0,+672,-168,+32,-3] / (840*dx) */
+        if (i8_lo <= i8_hi && j8_lo <= j8_hi && k8_lo <= k8_hi) {
+            for (int k0 = k8_lo; k0 <= k8_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j8_lo; j0 <= j8_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i8_lo; i0 <= i8_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        fx[p] = d840dx * (
+                            +(double)3 * fh[idx_fh_F_ord5(iF - 4, jF,     kF,     ex)] -
+                            F32  * fh[idx_fh_F_ord5(iF - 3, jF,     kF,     ex)] +
+                            F168 * fh[idx_fh_F_ord5(iF - 2, jF,     kF,     ex)] -
+                            F672 * fh[idx_fh_F_ord5(iF - 1, jF,     kF,     ex)] +
+                            F672 * fh[idx_fh_F_ord5(iF + 1, jF,     kF,     ex)] -
+                            F168 * fh[idx_fh_F_ord5(iF + 2, jF,     kF,     ex)] +
+                            F32  * fh[idx_fh_F_ord5(iF + 3, jF,     kF,     ex)] -
+                            (double)3 * fh[idx_fh_F_ord5(iF + 4, jF,     kF,     ex)]);
+
+                        fy[p] = d840dy * (
+                            +(double)3 * fh[idx_fh_F_ord5(iF,     jF - 4, kF,     ex)] -
+                            F32  * fh[idx_fh_F_ord5(iF,     jF - 3, kF,     ex)] +
+                            F168 * fh[idx_fh_F_ord5(iF,     jF - 2, kF,     ex)] -
+                            F672 * fh[idx_fh_F_ord5(iF,     jF - 1, kF,     ex)] +
+                            F672 * fh[idx_fh_F_ord5(iF,     jF + 1, kF,     ex)] -
+                            F168 * fh[idx_fh_F_ord5(iF,     jF + 2, kF,     ex)] +
+                            F32  * fh[idx_fh_F_ord5(iF,     jF + 3, kF,     ex)] -
+                            (double)3 * fh[idx_fh_F_ord5(iF,     jF + 4, kF,     ex)]);
+
+                        fz[p] = d840dz * (
+                            +(double)3 * fh[idx_fh_F_ord5(iF,     jF,     kF - 4, ex)] -
+                            F32  * fh[idx_fh_F_ord5(iF,     jF,     kF - 3, ex)] +
+                            F168 * fh[idx_fh_F_ord5(iF,     jF,     kF - 2, ex)] -
+                            F672 * fh[idx_fh_F_ord5(iF,     jF,     kF - 1, ex)] +
+                            F672 * fh[idx_fh_F_ord5(iF,     jF,     kF + 1, ex)] -
+                            F168 * fh[idx_fh_F_ord5(iF,     jF,     kF + 2, ex)] +
+                            F32  * fh[idx_fh_F_ord5(iF,     jF,     kF + 3, ex)] -
+                            (double)3 * fh[idx_fh_F_ord5(iF,     jF,     kF + 4, ex)]);
+                    }
+                }
+            }
+        }
+        return;
+    }
+#else
+#error "fderivs_c.C: unsupported ghost_width (must be 2, 3, 4, or 5)"
+#endif
+}

AMSS_NCKU_source/fderivs_sh_c.C

@@ -0,0 +1,234 @@
+#include "macrodef.h"
+#include "share_func.h"
+
+/*
+ * C 版 fderivs_sh — first derivatives on shell patch in (rho, sigma, R) coords.
+ *
+ * Same stencil coefficients as Cartesian fderivs, but:
+ * - Uses symmetry_stbd (ghost on BOTH sides of x/y, none in z)
+ * - fh buffer: (-ord+1:ex+ord) in x/y, (1:ex) in z
+ * - SoA is 2-element only (x/y), no z-symmetry
+ * - sst parameter (shell surface type, not used in stencil computation)
+ */
+extern "C" void fderivs_sh_(const int ex[3],
+                const double *f,
+                double *fx, double *fy, double *fz,
+                const double *X, const double *Y, const double *Z,
+                double SYM1, double SYM2, double SYM3,
+                int Symmetry, int onoff, int sst)
+{
+    (void)SYM3; (void)onoff; (void)sst;
+
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0, EIT = 8.0;
+    const double F9 = 9.0, F12 = 12.0, F45 = 45.0, F60 = 60.0;
+    const double F32 = 32.0, F168 = 168.0, F672 = 672.0, F840 = 840.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2;
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+    const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+    const double SoA[2] = { SYM1, SYM2 };
+
+#if (ghost_width == 2)
+    {
+        const int ord = 1;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = 0;
+        if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = 0;
+        if ((sst==2||sst==4) && fabs(Y[0]) < dY) jminF = 0; // EQ reflection
+
+        const size_t nx = (size_t)ex1 + 2 * ord;
+        const size_t ny = (size_t)ex2 + 2 * ord;
+        const size_t nz = (size_t)ex3;
+        const size_t fh_size = nx * ny * nz;
+        static double *fh_buf = NULL; static size_t cap = 0;
+        if (fh_size > cap) { free(fh_buf); fh_buf = (double*)aligned_alloc(64, fh_size*sizeof(double)); cap = fh_size; }
+        double *fh = fh_buf; if (!fh) return;
+        symmetry_stbd(ord, ex, f, fh, SoA);
+
+        const double d2dx = ONE/TWO/dX, d2dy = ONE/TWO/dY, d2dz = ONE/TWO/dZ;
+        const size_t all = (size_t)ex1*ex2*ex3;
+        for (size_t p=0;p<all;++p) { fx[p]=ZEO; fy[p]=ZEO; fz[p]=ZEO; }
+
+        const int i2_lo=(iminF>0)?iminF:0, j2_lo=(jminF>0)?jminF:0, k2_lo=1;
+        const int i2_hi=ex1-2, j2_hi=ex2-2, k2_hi=ex3-2;
+        if (i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi) {
+            for (int k0=k2_lo;k0<=k2_hi;++k0) { const int kF=k0+1;
+            for (int j0=j2_lo;j0<=j2_hi;++j0) { const int jF=j0+1;
+            for (int i0=i2_lo;i0<=i2_hi;++i0) { const int iF=i0+1;
+                const size_t p=idx_ex(i0,j0,k0,ex);
+                fx[p]=d2dx*(-fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)]);
+                fy[p]=d2dy*(-fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)]);
+                fz[p]=d2dz*(-fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)]);
+            }}}
+        }
+        return;
+    }
+#elif (ghost_width == 3)
+    {
+        const int ord = 2;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = -1;
+        if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = -1;
+        if ((sst==2||sst==4) && fabs(Y[0]) < dY) jminF = -1;
+
+        const size_t nx=(size_t)ex1+2*ord, ny=(size_t)ex2+2*ord, nz=(size_t)ex3;
+        const size_t fh_size=nx*ny*nz;
+        static double *fh_buf=NULL; static size_t cap=0;
+        if (fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf; if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double d12dx=ONE/F12/dX, d12dy=ONE/F12/dY, d12dz=ONE/F12/dZ;
+        const double d2dx=ONE/TWO/dX, d2dy=ONE/TWO/dY, d2dz=ONE/TWO/dZ;
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fx[p]=ZEO;fy[p]=ZEO;fz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0, j2_lo=(jminF>0)?jminF:0, k2_lo=1;
+        const int i2_hi=ex1-2, j2_hi=ex2-2, k2_hi=ex3-2;
+        const int i4_lo=(iminF+1>0)?iminF+1:0, j4_lo=(jminF+1>0)?jminF+1:0, k4_lo=2;
+        const int i4_hi=ex1-3, j4_hi=ex2-3, k4_hi=ex3-3;
+
+        if (i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi) {
+            for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+            for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+            for(int i0=i2_lo;i0<=i2_hi;++i0){const int iF=i0+1;
+                const size_t p=idx_ex(i0,j0,k0,ex);
+                fx[p]=d2dx*(-fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)]);
+                fy[p]=d2dy*(-fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)]);
+                fz[p]=d2dz*(-fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)]);
+            }}}
+        }
+        if (i4_lo<=i4_hi&&j4_lo<=j4_hi&&k4_lo<=k4_hi) {
+            for(int k0=k4_lo;k0<=k4_hi;++k0){const int kF=k0+1;
+            for(int j0=j4_lo;j0<=j4_hi;++j0){const int jF=j0+1;
+            for(int i0=i4_lo;i0<=i4_hi;++i0){const int iF=i0+1;
+                const size_t p=idx_ex(i0,j0,k0,ex);
+                fx[p]=d12dx*(fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]-EIT*fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+EIT*fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)]-fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)]);
+                fy[p]=d12dy*(fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]-EIT*fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+EIT*fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)]-fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)]);
+                fz[p]=d12dz*(fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]-EIT*fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+EIT*fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)]-fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)]);
+            }}}
+        }
+        return;
+    }
+#elif (ghost_width == 4)
+    {
+        const int ord = 3;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-2;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-2;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-2;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3;
+        const size_t fh_size=nx*ny*nz;
+        static double *fh_buf=NULL;static size_t cap=0;
+        if(fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf;if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double d60dx=ONE/F60/dX,d60dy=ONE/F60/dY,d60dz=ONE/F60/dZ;
+        const double d12dx=ONE/F12/dX,d12dy=ONE/F12/dY,d12dz=ONE/F12/dZ;
+        const double d2dx=ONE/TWO/dX,d2dy=ONE/TWO/dY,d2dz=ONE/TWO/dZ;
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fx[p]=ZEO;fy[p]=ZEO;fz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0,j2_lo=(jminF>0)?jminF:0,k2_lo=1,i2_hi=ex1-2,j2_hi=ex2-2,k2_hi=ex3-2;
+        const int i4_lo=(iminF+1>0)?iminF+1:0,j4_lo=(jminF+1>0)?jminF+1:0,k4_lo=2,i4_hi=ex1-3,j4_hi=ex2-3,k4_hi=ex3-3;
+        const int i6_lo=(iminF+2>0)?iminF+2:0,j6_lo=(jminF+2>0)?jminF+2:0,k6_lo=3,i6_hi=ex1-4,j6_hi=ex2-4,k6_hi=ex3-4;
+
+        if(i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi){
+            for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+            for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+            for(int i0=i2_lo;i0<=i2_hi;++i0){const int iF=i0+1;
+                const size_t p=idx_ex(i0,j0,k0,ex);
+                fx[p]=d2dx*(-fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)]);
+                fy[p]=d2dy*(-fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)]);
+                fz[p]=d2dz*(-fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)]);
+            }}}
+        }
+        if(i4_lo<=i4_hi&&j4_lo<=j4_hi&&k4_lo<=k4_hi){
+            for(int k0=k4_lo;k0<=k4_hi;++k0){const int kF=k0+1;
+            for(int j0=j4_lo;j0<=j4_hi;++j0){const int jF=j0+1;
+            for(int i0=i4_lo;i0<=i4_hi;++i0){const int iF=i0+1;
+                const size_t p=idx_ex(i0,j0,k0,ex);
+                fx[p]=d12dx*(fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]-EIT*fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+EIT*fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)]-fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)]);
+                fy[p]=d12dy*(fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]-EIT*fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+EIT*fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)]-fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)]);
+                fz[p]=d12dz*(fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]-EIT*fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+EIT*fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)]-fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)]);
+            }}}
+        }
+        if(i6_lo<=i6_hi&&j6_lo<=j6_hi&&k6_lo<=k6_hi){
+            for(int k0=k6_lo;k0<=k6_hi;++k0){const int kF=k0+1;
+            for(int j0=j6_lo;j0<=j6_hi;++j0){const int jF=j0+1;
+            for(int i0=i6_lo;i0<=i6_hi;++i0){const int iF=i0+1;
+                const size_t p=idx_ex(i0,j0,k0,ex);
+                fx[p]=d60dx*(-fh[idx_fh_stbd(iF-3,jF,kF,ord,ex)]+F9*fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]-F45*fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+F45*fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)]-F9*fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+3,jF,kF,ord,ex)]);
+                fy[p]=d60dy*(-fh[idx_fh_stbd(iF,jF-3,kF,ord,ex)]+F9*fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]-F45*fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+F45*fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)]-F9*fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+3,kF,ord,ex)]);
+                fz[p]=d60dz*(-fh[idx_fh_stbd(iF,jF,kF-3,ord,ex)]+F9*fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]-F45*fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+F45*fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)]-F9*fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+3,ord,ex)]);
+            }}}
+        }
+        return;
+    }
+#elif (ghost_width == 5)
+    {
+        const int ord = 4;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-3;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-3;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-3;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3;
+        const size_t fh_size=nx*ny*nz;
+        static double *fh_buf=NULL;static size_t cap=0;
+        if(fh_size>cap){free(fh_buf);fh_buf=(double*)aligned_alloc(64,fh_size*sizeof(double));cap=fh_size;}
+        double *fh=fh_buf;if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const double d840dx=ONE/F840/dX,d840dy=ONE/F840/dY,d840dz=ONE/F840/dZ;
+        const double d60dx=ONE/F60/dX,d60dy=ONE/F60/dY,d60dz=ONE/F60/dZ;
+        const double d12dx=ONE/F12/dX,d12dy=ONE/F12/dY,d12dz=ONE/F12/dZ;
+        const double d2dx=ONE/TWO/dX,d2dy=ONE/TWO/dY,d2dz=ONE/TWO/dZ;
+        const size_t all=(size_t)ex1*ex2*ex3;
+        for(size_t p=0;p<all;++p){fx[p]=ZEO;fy[p]=ZEO;fz[p]=ZEO;}
+
+        const int i2_lo=(iminF>0)?iminF:0,j2_lo=(jminF>0)?jminF:0,k2_lo=1,i2_hi=ex1-2,j2_hi=ex2-2,k2_hi=ex3-2;
+        const int i4_lo=(iminF+1>0)?iminF+1:0,j4_lo=(jminF+1>0)?jminF+1:0,k4_lo=2,i4_hi=ex1-3,j4_hi=ex2-3,k4_hi=ex3-3;
+        const int i6_lo=(iminF+2>0)?iminF+2:0,j6_lo=(jminF+2>0)?jminF+2:0,k6_lo=3,i6_hi=ex1-4,j6_hi=ex2-4,k6_hi=ex3-4;
+        const int i8_lo=(iminF+3>0)?iminF+3:0,j8_lo=(jminF+3>0)?jminF+3:0,k8_lo=4,i8_hi=ex1-5,j8_hi=ex2-5,k8_hi=ex3-5;
+
+        #define FH_S(iF,jF,kF) fh[idx_fh_stbd(iF,jF,kF,ord,ex)]
+        if(i2_lo<=i2_hi&&j2_lo<=j2_hi&&k2_lo<=k2_hi){for(int k0=k2_lo;k0<=k2_hi;++k0){const int kF=k0+1;
+        for(int j0=j2_lo;j0<=j2_hi;++j0){const int jF=j0+1;
+        for(int i0=i2_lo;i0<=i2_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fx[p]=d2dx*(-FH_S(iF-1,jF,kF)+FH_S(iF+1,jF,kF));
+            fy[p]=d2dy*(-FH_S(iF,jF-1,kF)+FH_S(iF,jF+1,kF));
+            fz[p]=d2dz*(-FH_S(iF,jF,kF-1)+FH_S(iF,jF,kF+1));}}}}
+
+        if(i4_lo<=i4_hi&&j4_lo<=j4_hi&&k4_lo<=k4_hi){for(int k0=k4_lo;k0<=k4_hi;++k0){const int kF=k0+1;
+        for(int j0=j4_lo;j0<=j4_hi;++j0){const int jF=j0+1;
+        for(int i0=i4_lo;i0<=i4_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fx[p]=d12dx*(FH_S(iF-2,jF,kF)-EIT*FH_S(iF-1,jF,kF)+EIT*FH_S(iF+1,jF,kF)-FH_S(iF+2,jF,kF));
+            fy[p]=d12dy*(FH_S(iF,jF-2,kF)-EIT*FH_S(iF,jF-1,kF)+EIT*FH_S(iF,jF+1,kF)-FH_S(iF,jF+2,kF));
+            fz[p]=d12dz*(FH_S(iF,jF,kF-2)-EIT*FH_S(iF,jF,kF-1)+EIT*FH_S(iF,jF,kF+1)-FH_S(iF,jF,kF+2));}}}}
+
+        if(i6_lo<=i6_hi&&j6_lo<=j6_hi&&k6_lo<=k6_hi){for(int k0=k6_lo;k0<=k6_hi;++k0){const int kF=k0+1;
+        for(int j0=j6_lo;j0<=j6_hi;++j0){const int jF=j0+1;
+        for(int i0=i6_lo;i0<=i6_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fx[p]=d60dx*(-FH_S(iF-3,jF,kF)+F9*FH_S(iF-2,jF,kF)-F45*FH_S(iF-1,jF,kF)+F45*FH_S(iF+1,jF,kF)-F9*FH_S(iF+2,jF,kF)+FH_S(iF+3,jF,kF));
+            fy[p]=d60dy*(-FH_S(iF,jF-3,kF)+F9*FH_S(iF,jF-2,kF)-F45*FH_S(iF,jF-1,kF)+F45*FH_S(iF,jF+1,kF)-F9*FH_S(iF,jF+2,kF)+FH_S(iF,jF+3,kF));
+            fz[p]=d60dz*(-FH_S(iF,jF,kF-3)+F9*FH_S(iF,jF,kF-2)-F45*FH_S(iF,jF,kF-1)+F45*FH_S(iF,jF,kF+1)-F9*FH_S(iF,jF,kF+2)+FH_S(iF,jF,kF+3));}}}}
+
+        if(i8_lo<=i8_hi&&j8_lo<=j8_hi&&k8_lo<=k8_hi){for(int k0=k8_lo;k0<=k8_hi;++k0){const int kF=k0+1;
+        for(int j0=j8_lo;j0<=j8_hi;++j0){const int jF=j0+1;
+        for(int i0=i8_lo;i0<=i8_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+            fx[p]=d840dx*(+(double)3*FH_S(iF-4,jF,kF)-F32*FH_S(iF-3,jF,kF)+F168*FH_S(iF-2,jF,kF)-F672*FH_S(iF-1,jF,kF)+F672*FH_S(iF+1,jF,kF)-F168*FH_S(iF+2,jF,kF)+F32*FH_S(iF+3,jF,kF)-(double)3*FH_S(iF+4,jF,kF));
+            fy[p]=d840dy*(+(double)3*FH_S(iF,jF-4,kF)-F32*FH_S(iF,jF-3,kF)+F168*FH_S(iF,jF-2,kF)-F672*FH_S(iF,jF-1,kF)+F672*FH_S(iF,jF+1,kF)-F168*FH_S(iF,jF+2,kF)+F32*FH_S(iF,jF+3,kF)-(double)3*FH_S(iF,jF+4,kF));
+            fz[p]=d840dz*(+(double)3*FH_S(iF,jF,kF-4)-F32*FH_S(iF,jF,kF-3)+F168*FH_S(iF,jF,kF-2)-F672*FH_S(iF,jF,kF-1)+F672*FH_S(iF,jF,kF+1)-F168*FH_S(iF,jF,kF+2)+F32*FH_S(iF,jF,kF+3)-(double)3*FH_S(iF,jF,kF+4));}}}}
+        #undef FH_S
+        return;
+    }
+#else
+#error "fderivs_sh_c.C: unsupported ghost_width"
+#endif
+}

AMSS_NCKU_source/fderivs_shc_c.C

@@ -0,0 +1,54 @@
+#include "macrodef.h"
+#include "share_func.h"
+#include <cstddef>
+
+/*
+ * fderivs_shc — shell first derivatives converted to Cartesian via chain rule.
+ *
+ * Calls fderivs_sh internally, then:
+ *   fx = drhodx * df/drho + dsigmadx * df/dsigma + dRdx * df/dR
+ *   fy = drhody * df/drho + dsigmady * df/dsigma + dRdy * df/dR
+ *   fz = drhodz * df/drho + dsigmadz * df/dsigma + dRdz * df/dR
+ */
+
+// Forward declaration (defined in fderivs_sh_c.C with extern "C" name fderivs_sh_)
+extern "C" {
+void fderivs_sh_(const int ex[3], const double *f,
+                 double *fx, double *fy, double *fz,
+                 const double *X, const double *Y, const double *Z,
+                 double SYM1, double SYM2, double SYM3,
+                 int Symmetry, int onoff, int sst);
+
+void fderivs_shc_(int *ex,
+                   double *f,
+                   double *fx, double *fy, double *fz,
+                   double *crho, double *sigma, double *R,
+                   double &SYM1, double &SYM2, double &SYM3,
+                   int &Symmetry, int &Lev, int &sst,
+                   double *drhodx, double *drhody, double *drhodz,
+                   double *dsigmadx, double *dsigmady, double *dsigmadz,
+                   double *dRdx, double *dRdy, double *dRdz)
+{
+    const int ex3[3] = { ex[0], ex[1], ex[2] };
+    const size_t n = (size_t)ex[0] * (size_t)ex[1] * (size_t)ex[2];
+
+    // Temporary shell-coordinate derivatives
+    double *gx = (double*)malloc(n * sizeof(double));
+    double *gy = (double*)malloc(n * sizeof(double));
+    double *gz = (double*)malloc(n * sizeof(double));
+    if (!gx || !gy || !gz) { free(gx); free(gy); free(gz); return; }
+
+    // Compute shell-coordinate derivatives
+    fderivs_sh_(ex3, f, gx, gy, gz, crho, sigma, R, SYM1, SYM2, SYM3, Symmetry, Lev, sst);
+
+    // Chain rule to Cartesian
+    for (size_t i = 0; i < n; ++i) {
+        fx[i] = drhodx[i]   * gx[i] + dsigmadx[i] * gy[i] + dRdx[i] * gz[i];
+        fy[i] = drhody[i]   * gx[i] + dsigmady[i] * gy[i] + dRdy[i] * gz[i];
+        fz[i] = drhodz[i]   * gx[i] + dsigmadz[i] * gy[i] + dRdz[i] * gz[i];
+    }
+
+    free(gx); free(gy); free(gz);
+}
+
+} // extern "C"

AMSS_NCKU_source/fmisc.f90

@@ -326,8 +326,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
-      
-    funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
+      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
    enddo
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+2,1:extc(3))*SoA(2)
@@ -884,13 +883,17 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
    enddo
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
    enddo
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
    enddo
@@ -1108,26 +1111,177 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
-!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
-
-  subroutine polint(xa, ya, x, y, dy, ordn)
-  implicit none
-
-  integer, intent(in) :: ordn
+! common code for cell and vertex
+!------------------------------------------------------------------------------
+! Lagrangian polynomial interpolation
+!------------------------------------------------------------------------------
+#ifndef POLINT6_USE_BARYCENTRIC
+#define POLINT6_USE_BARYCENTRIC 1
+#endif
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
+  subroutine polint6_neville(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, m, ns, n_m
+  real*8, dimension(6) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, 6
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, 5
+    n_m = 6 - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint6_neville
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
+  subroutine polint6_barycentric(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, j
+  logical :: is_uniform
+  real*8, dimension(6) :: lambda
+  real*8 :: dx, den_i, term, num, den, step, tol
+  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
+
+  do i = 1, 6
+    if (x == xa(i)) then
+      y = ya(i)
+      dy = 0.d0
+      return
+    end if
+  end do
+
+  step = xa(2) - xa(1)
+  is_uniform = (step /= 0.d0)
+  if (is_uniform) then
+    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
+    do i = 3, 6
+      if (abs((xa(i) - xa(i-1)) - step) > tol) then
+        is_uniform = .false.
+        exit
+      end if
+    end do
+  end if
+
+  if (is_uniform) then
+    num = 0.d0
+    den = 0.d0
+    do i = 1, 6
+      term = c_uniform(i) / (x - xa(i))
+      num = num + term * ya(i)
+      den = den + term
+    end do
+    y = num / den
+    dy = 0.d0
+    return
+  end if
+
+  do i = 1, 6
+    den_i = 1.d0
+    do j = 1, 6
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        den_i = den_i * dx
+      end if
+    end do
+    lambda(i) = 1.d0 / den_i
+  end do
+
+  num = 0.d0
+  den = 0.d0
+  do i = 1, 6
+    term = lambda(i) / (x - xa(i))
+    num = num + term * ya(i)
+    den = den + term
+  end do
+
+  y = num / den
+  dy = 0.d0
+
+  return
+  end subroutine polint6_barycentric
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
   real*8, dimension(ordn), intent(in) :: xa, ya
   real*8, intent(in) :: x
   real*8, intent(out) :: y, dy
 
-  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
-
-  c = ya
-  d = ya
-  ho = xa - x
+  integer :: i, m, ns, n_m
+  real*8, dimension(ordn) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  if (ordn == 6) then
+#if POLINT6_USE_BARYCENTRIC
+    call polint6_barycentric(xa, ya, x, y, dy)
+#else
+    call polint6_neville(xa, ya, x, y, dy)
+#endif
+    return
+  end if
+
+  c = ya
+  d = ya
+  ho = xa - x
 
   ns = 1
   dif = abs(x - xa(1))
@@ -1171,13 +1325,48 @@ end subroutine d2dump
     y = y + dy
   end do
 
-  return
-  end subroutine polint
-!------------------------------------------------------------------------------
-!
-! interpolation in 2 dimensions, follow yx order
-!
-!------------------------------------------------------------------------------
+  return
+  end subroutine polint
+!------------------------------------------------------------------------------
+! Compute Lagrange interpolation basis weights for one target point.
+!------------------------------------------------------------------------------
+!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
+  subroutine polint_lagrange_weights(xa, x, w, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(1:ordn), intent(in) :: xa
+  real*8, intent(in) :: x
+  real*8, dimension(1:ordn), intent(out) :: w
+
+  integer :: i, j
+  real*8 :: num, den, dx
+
+  do i = 1, ordn
+    num = 1.d0
+    den = 1.d0
+    do j = 1, ordn
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        num = num * (x - xa(j))
+        den = den * dx
+      end if
+    end do
+    w(i) = num / den
+  end do
+
+  return
+  end subroutine polint_lagrange_weights
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
   implicit none
 
@@ -1225,11 +1414,11 @@ end subroutine d2dump
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
-  integer  :: i,j,m,n
-  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
+#ifdef POLINT_LEGACY_ORDER
+  integer  :: i,j,m,n
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: yntmp
   real*8, dimension(ordn) :: yqtmp
 
   m=size(x1a)
@@ -1239,29 +1428,36 @@ end subroutine d2dump
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
    end do
-    yntmp=yatmp(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j, k
-  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
-
-  do k=1,ordn
-    do j=1,ordn
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
-    end do
-  end do
-  do k=1,ordn
-    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
-  end do
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
-#endif
-
-  return
-  end subroutine polin3
+    yntmp=yatmp(i,:)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+  end do
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: i, j, k
+  real*8, dimension(ordn) :: w1, w2
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: yx_sum, x_sum
+
+  call polint_lagrange_weights(x1a, x1, w1, ordn)
+  call polint_lagrange_weights(x2a, x2, w2, ordn)
+
+  do k = 1, ordn
+    yx_sum = 0.d0
+    do j = 1, ordn
+      x_sum = 0.d0
+      do i = 1, ordn
+        x_sum = x_sum + w1(i) * ya(i,j,k)
+      end do
+      yx_sum = yx_sum + w2(j) * x_sum
+    end do
+    ymtmp(k) = yx_sum
+  end do
+
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
   subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1315,13 +1511,88 @@ deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
-  return
-
-  end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
-! calculate L2norm especially for shell Blocks
-  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-                          f,f_out,gw,ogw,Symmetry)
+  return
+
+  end subroutine l2normhelper
+!--------------------------------------------------------------------------------------
+  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
+
+  implicit none
+!~~~~~~> Input parameters:
+  integer,intent(in ):: ex(1:3)
+  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
+  integer,intent(in)::gw
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
+  real*8, intent(out) :: f_out(7)
+!~~~~~~> Other variables:
+
+  real*8            :: dX, dY, dZ
+  integer::imin,jmin,kmin
+  integer::imax,jmax,kmax
+  integer::i,j,k
+  real*8 :: s1,s2,s3,s4,s5,s6,s7
+
+  dX = X(2) - X(1)
+  dY = Y(2) - Y(1)
+  dZ = Z(2) - Z(1)
+
+! for ghost zone
+   imin = gw+1
+   jmin = gw+1
+   kmin = gw+1
+
+   imax = ex(1) - gw
+   jmax = ex(2) - gw
+   kmax = ex(3) - gw
+
+!for patch boundary (i.e., not ghost boundary)
+
+if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
+if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
+if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
+if(dabs(X(1)-xmin) < dX) imin = 1
+if(dabs(Y(1)-ymin) < dY) jmin = 1
+if(dabs(Z(1)-zmin) < dZ) kmin = 1
+
+  s1 = 0.d0
+  s2 = 0.d0
+  s3 = 0.d0
+  s4 = 0.d0
+  s5 = 0.d0
+  s6 = 0.d0
+  s7 = 0.d0
+
+  do k=kmin,kmax
+    do j=jmin,jmax
+!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
+      do i=imin,imax
+        s1 = s1 + f1(i,j,k)*f1(i,j,k)
+        s2 = s2 + f2(i,j,k)*f2(i,j,k)
+        s3 = s3 + f3(i,j,k)*f3(i,j,k)
+        s4 = s4 + f4(i,j,k)*f4(i,j,k)
+        s5 = s5 + f5(i,j,k)*f5(i,j,k)
+        s6 = s6 + f6(i,j,k)*f6(i,j,k)
+        s7 = s7 + f7(i,j,k)*f7(i,j,k)
+      enddo
+    enddo
+  enddo
+
+  f_out(1) = s1*dX*dY*dZ
+  f_out(2) = s2*dX*dY*dZ
+  f_out(3) = s3*dX*dY*dZ
+  f_out(4) = s4*dX*dY*dZ
+  f_out(5) = s5*dX*dY*dZ
+  f_out(6) = s6*dX*dY*dZ
+  f_out(7) = s7*dX*dY*dZ
+
+  return
+
+  end subroutine l2normhelper7
+!--------------------------------------------------------------------------------------
+! calculate L2norm especially for shell Blocks
+  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                          f,f_out,gw,ogw,Symmetry)
 
   implicit none
 !~~~~~~> Input parameters:
@@ -1604,11 +1875,14 @@ deallocate(f_flat)
 !       ^
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3
 
-  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-
-  fout = C1*f1+C2*f2+C3*f3
-
-  return
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
+  integer :: i,j,k
+
+  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
+    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
+  end do
+
+  return
 
   end subroutine average2
 !-----------------------------------------------------------------------------  

AMSS_NCKU_source/fmisc.h

@@ -12,9 +12,10 @@
 #define f_global_interpind global_interpind
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
-#define f_l2normhelper l2normhelper
-#define f_l2normhelper_sh l2normhelper_sh
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms
+#define f_l2normhelper l2normhelper
+#define f_l2normhelper7 l2normhelper7
+#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
 #define f_average3 average3
 #define f_average2 average2
@@ -41,9 +42,10 @@
 #define f_global_interpind GLOBAL_INTERPIND
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
-#define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper_sh L2NORMHELPER_SH
-#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
+#define f_l2normhelper L2NORMHELPER
+#define f_l2normhelper7 L2NORMHELPER7
+#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
 #define f_average3 AVERAGE3
 #define f_average2 AVERAGE2
@@ -70,9 +72,10 @@
 #define f_global_interpind global_interpind_
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
-#define f_l2normhelper l2normhelper_
-#define f_l2normhelper_sh l2normhelper_sh_
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
+#define f_l2normhelper l2normhelper_
+#define f_l2normhelper7 l2normhelper7_
+#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
 #define f_average3 average3_
 #define f_average2 average2_
@@ -156,20 +159,29 @@ extern "C"
 							  int *, double *, int &, int &);
 }
 
-extern "C"
-{
-	void f_l2normhelper(int *, double *, double *, double *,
-						double &, double &, double &,
-						double &, double &, double &,
-						double *, double &, int &);
-}
-
-extern "C"
-{
-	void f_l2normhelper_sh(int *, double *, double *, double *,
-						   double &, double &, double &,
-						   double &, double &, double &,
-						   double *, double &, int &, int &, int &);
+extern "C"
+{
+	void f_l2normhelper(int *, double *, double *, double *,
+						double &, double &, double &,
+						double &, double &, double &,
+						double *, double &, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper7(int *, double *, double *, double *,
+						 double &, double &, double &,
+						 double &, double &, double &,
+						 double *, double *, double *, double *,
+						 double *, double *, double *, double *, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper_sh(int *, double *, double *, double *,
+						   double &, double &, double &,
+						   double &, double &, double &,
+						   double *, double &, int &, int &, int &);
 }
 
 extern "C"

AMSS_NCKU_source/interp_lb_profile.C

@@ -0,0 +1,107 @@
+#include "interp_lb_profile.h"
+#include <cstdio>
+#include <cstring>
+#include <algorithm>
+
+namespace InterpLBProfile {
+
+bool write_profile(const char *filepath, int nprocs,
+                   const double *rank_times,
+                   const int *heavy_ranks, int num_heavy,
+                   double threshold_ratio)
+{
+    FILE *fp = fopen(filepath, "wb");
+    if (!fp) return false;
+
+    ProfileHeader hdr;
+    hdr.magic = MAGIC;
+    hdr.version = VERSION;
+    hdr.nprocs = nprocs;
+    hdr.num_heavy = num_heavy;
+    hdr.threshold_ratio = threshold_ratio;
+
+    fwrite(&hdr, sizeof(hdr), 1, fp);
+    fwrite(rank_times, sizeof(double), nprocs, fp);
+    fwrite(heavy_ranks, sizeof(int), num_heavy, fp);
+    fclose(fp);
+    return true;
+}
+
+bool read_profile(const char *filepath, int current_nprocs,
+                  int *heavy_ranks, int &num_heavy,
+                  double *rank_times, MPI_Comm comm)
+{
+    int myrank;
+    MPI_Comm_rank(comm, &myrank);
+
+    int valid = 0;
+    ProfileHeader hdr;
+    memset(&hdr, 0, sizeof(hdr));
+
+    if (myrank == 0) {
+        FILE *fp = fopen(filepath, "rb");
+        if (fp) {
+            if (fread(&hdr, sizeof(hdr), 1, fp) == 1 &&
+                hdr.magic == MAGIC && hdr.version == VERSION &&
+                hdr.nprocs == current_nprocs)
+            {
+                if (fread(rank_times, sizeof(double), current_nprocs, fp)
+                    == (size_t)current_nprocs &&
+                    fread(heavy_ranks, sizeof(int), hdr.num_heavy, fp)
+                    == (size_t)hdr.num_heavy)
+                {
+                    num_heavy = hdr.num_heavy;
+                    valid = 1;
+                }
+            } else if (fp) {
+                printf("[InterpLB] Profile rejected: magic=0x%X version=%u "
+                       "nprocs=%d (current=%d)\n",
+                       hdr.magic, hdr.version, hdr.nprocs, current_nprocs);
+            }
+            fclose(fp);
+        }
+    }
+
+    MPI_Bcast(&valid, 1, MPI_INT, 0, comm);
+    if (!valid) return false;
+
+    MPI_Bcast(&num_heavy, 1, MPI_INT, 0, comm);
+    MPI_Bcast(heavy_ranks, num_heavy, MPI_INT, 0, comm);
+    MPI_Bcast(rank_times, current_nprocs, MPI_DOUBLE, 0, comm);
+    return true;
+}
+
+int identify_heavy_ranks(const double *rank_times, int nprocs,
+                         double threshold_ratio,
+                         int *heavy_ranks, int max_heavy)
+{
+    double sum = 0;
+    for (int i = 0; i < nprocs; i++) sum += rank_times[i];
+    double mean = sum / nprocs;
+    double threshold = threshold_ratio * mean;
+
+    // Collect candidates
+    struct RankTime { int rank; double time; };
+    RankTime *candidates = new RankTime[nprocs];
+    int ncand = 0;
+
+    for (int i = 0; i < nprocs; i++) {
+        if (rank_times[i] > threshold)
+            candidates[ncand++] = {i, rank_times[i]};
+    }
+
+    // Sort descending by time
+    std::sort(candidates, candidates + ncand,
+              [](const RankTime &a, const RankTime &b) {
+                  return a.time > b.time;
+              });
+
+    int count = (ncand < max_heavy) ? ncand : max_heavy;
+    for (int i = 0; i < count; i++)
+        heavy_ranks[i] = candidates[i].rank;
+
+    delete[] candidates;
+    return count;
+}
+
+} // namespace InterpLBProfile

AMSS_NCKU_source/interp_lb_profile.h

@@ -0,0 +1,38 @@
+#ifndef INTERP_LB_PROFILE_H
+#define INTERP_LB_PROFILE_H
+
+#include <mpi.h>
+
+namespace InterpLBProfile {
+
+static const unsigned int MAGIC   = 0x494C4250; // "ILBP"
+static const unsigned int VERSION = 1;
+
+struct ProfileHeader {
+    unsigned int magic;
+    unsigned int version;
+    int nprocs;
+    int num_heavy;
+    double threshold_ratio;
+};
+
+// Write profile file (rank 0 only)
+bool write_profile(const char *filepath, int nprocs,
+                   const double *rank_times,
+                   const int *heavy_ranks, int num_heavy,
+                   double threshold_ratio);
+
+// Read profile file (rank 0 reads, then broadcasts to all)
+// Returns true if file found and valid for current nprocs
+bool read_profile(const char *filepath, int current_nprocs,
+                  int *heavy_ranks, int &num_heavy,
+                  double *rank_times, MPI_Comm comm);
+
+// Identify heavy ranks: those with time > threshold_ratio * mean
+int identify_heavy_ranks(const double *rank_times, int nprocs,
+                         double threshold_ratio,
+                         int *heavy_ranks, int max_heavy);
+
+} // namespace InterpLBProfile
+
+#endif /* INTERP_LB_PROFILE_H */

AMSS_NCKU_source/interp_lb_profile_data.h

@@ -0,0 +1,29 @@
+/* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
+/* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
+/* Auto-generated from interp_lb_profile.bin — do not edit */
+#ifndef INTERP_LB_PROFILE_DATA_H
+#define INTERP_LB_PROFILE_DATA_H
+
+#define INTERP_LB_NPROCS 64
+#define INTERP_LB_NUM_HEAVY 4
+
+static const int interp_lb_heavy_blocks[4] = {27, 35, 28, 36};
+
+/* Split table: {block_id, r_left, r_right} */
+static const int interp_lb_splits[4][3] = {
+    {27, 26, 27},
+    {35, 34, 35},
+    {28, 28, 29},
+    {36, 36, 37},
+};
+
+/* Rank remap for displaced neighbor blocks */
+static const int interp_lb_num_remaps = 4;
+static const int interp_lb_remaps[][2] = {
+    {26, 25},
+    {29, 30},
+    {34, 33},
+    {37, 38},
+};
+
+#endif /* INTERP_LB_PROFILE_DATA_H */

AMSS_NCKU_source/kodiss.f90

@@ -6,6 +6,103 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 
+#if (ghost_width == 2)
+! second order code
+
+!------------------------------------------------------------------------------------------------------------------------------
+!usual type Kreiss-Oliger type numerical dissipation
+!We support cell center only
+!  (D_+D_-)^2 =
+!   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
+! ------------------------------------------------------
+!                       dx^4
+!------------------------------------------------------------------------------------------------------------------------------
+! do not add dissipation near boundary
+subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
+
+implicit none
+! argument variables
+integer,intent(in) :: Symmetry
+integer,dimension(3),intent(in)::ex
+real*8, dimension(1:3), intent(in) :: SoA
+double precision,intent(in),dimension(ex(1))::X
+double precision,intent(in),dimension(ex(2))::Y
+double precision,intent(in),dimension(ex(3))::Z
+double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
+double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
+real*8,intent(in) :: eps
+
+!~~~~~~ other variables
+
+  real*8 :: dX,dY,dZ
+  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+  real*8,parameter   :: cof = 1.6d1 ! 2^4
+  real*8,  parameter :: F4=4.d0,F6=6.d0
+  integer::i,j,k
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
+
+  call symmetry_bd(2,ex,f,fh,SoA)
+
+!   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
+! ------------------------------------------------------
+!                       dx^4
+
+!  note the sign (-1)^r-1, now r=2
+!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+!DIR$ UNROLL PARTIAL(4)
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+
+  if(i-2 >= imin .and. i+2 <= imax .and. &
+     j-2 >= jmin .and. j+2 <= jmax .and. &
+     k-2 >= kmin .and. k+2 <= kmax) then
+! x direction
+   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
+                                (fh(i-2,j,k)+fh(i+2,j,k)) &
+                         - F4 * (fh(i-1,j,k)+fh(i+1,j,k)) &
+                         + F6 *  fh(i,j,k) )
+! y direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
+                                (fh(i,j-2,k)+fh(i,j+2,k)) &
+                         - F4 * (fh(i,j-1,k)+fh(i,j+1,k)) &
+                         + F6 *  fh(i,j,k) )
+! z direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
+                                (fh(i,j,k-2)+fh(i,j,k+2)) &
+                         - F4 * (fh(i,j,k-1)+fh(i,j,k+1)) &
+                         + F6 *  fh(i,j,k) )
+
+  endif
+
+  enddo
+  enddo
+  enddo
+
+  return
+
+end subroutine kodis
+
+#elif (ghost_width == 3)
 ! fourth order code
 
 !---------------------------------------------------------------------------------------------
@@ -61,7 +158,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
   if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
   if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin = -2
   if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin = -2
-  !print*,'imin,jmin,kmin=',imin,jmin,kmin
+
   call symmetry_bd(3,ex,f,fh,SoA)
 
   do k=1,ex(3)
@@ -71,7 +168,28 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
   if(i-3 >= imin .and. i+3 <= imax .and. &
      j-3 >= jmin .and. j+3 <= jmax .and. &
      k-3 >= kmin .and. k+3 <= kmax) then
+#if 0     
+! x direction
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (     &
+                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
+                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
+                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
+                          TWT* fh(i,j,k)            )
+! y direction
 
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (     &
+                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
+                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
+                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
+                          TWT* fh(i,j,k)            )
+! z direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (     &
+                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
+                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
+                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
+                          TWT* fh(i,j,k)            )
+#else
 ! calculation order if important ?
    f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
                               (fh(i-3,j,k)+fh(i+3,j,k)) - &
@@ -88,7 +206,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
                           SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
                           FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
                           TWT* fh(i,j,k)            )/dZ )
-
+#endif
   endif
 
   enddo
@@ -99,6 +217,218 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
 
   end subroutine kodis
 
+#elif (ghost_width == 4)
+! sixth order code
+!------------------------------------------------------------------------------------------------------------------------------
+!usual type Kreiss-Oliger type numerical dissipation
+!We support cell center only
+!  (D_+D_-)^4 =
+!   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
+! ----------------------------------------------------------------------------------------------------------
+!                                              dx^8
+!------------------------------------------------------------------------------------------------------------------------------
+! do not add dissipation near boundary
+subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
 
+implicit none
+! argument variables
+integer,intent(in) :: Symmetry
+integer,dimension(3),intent(in)::ex
+real*8, dimension(1:3), intent(in) :: SoA
+double precision,intent(in),dimension(ex(1))::X
+double precision,intent(in),dimension(ex(2))::Y
+double precision,intent(in),dimension(ex(3))::Z
+double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
+double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
+real*8,intent(in) :: eps
 
+!~~~~~~ other variables
 
+  real*8 :: dX,dY,dZ
+  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+  real*8,parameter   :: cof = 2.56d2 ! 2^8
+  real*8,  parameter :: F8=8.d0,F28=2.8d1,F56=5.6d1,F70=7.d1
+  integer::i,j,k
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+  
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
+
+  call symmetry_bd(4,ex,f,fh,SoA)
+
+!   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
+! ----------------------------------------------------------------------------------------------------------
+!                                              dx^8
+
+!  note the sign (-1)^r-1, now r=4
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+
+  if(i>imin+3 .and. i < imax-3 .and. &
+     j>jmin+3 .and. j < jmax-3 .and. &
+     k>kmin+3 .and. k < kmax-3) then
+! x direction
+   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
+                                (fh(i-4,j,k)+fh(i+4,j,k)) &
+                         - F8 * (fh(i-3,j,k)+fh(i+3,j,k)) &
+                         +F28 * (fh(i-2,j,k)+fh(i+2,j,k)) &
+                         -F56 * (fh(i-1,j,k)+fh(i+1,j,k)) &
+                         +F70 *  fh(i,j,k) )
+! y direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
+                                (fh(i,j-4,k)+fh(i,j+4,k)) &
+                         - F8 * (fh(i,j-3,k)+fh(i,j+3,k)) &
+                         +F28 * (fh(i,j-2,k)+fh(i,j+2,k)) &
+                         -F56 * (fh(i,j-1,k)+fh(i,j+1,k)) &
+                         +F70 *  fh(i,j,k) )
+! z direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
+                                (fh(i,j,k-4)+fh(i,j,k+4)) &
+                         - F8 * (fh(i,j,k-3)+fh(i,j,k+3)) &
+                         +F28 * (fh(i,j,k-2)+fh(i,j,k+2)) &
+                         -F56 * (fh(i,j,k-1)+fh(i,j,k+1)) &
+                         +F70 *  fh(i,j,k) )
+
+  endif
+
+  enddo
+  enddo
+  enddo
+
+  return
+
+end subroutine kodis
+
+#elif (ghost_width == 5)
+! eighth order code
+!------------------------------------------------------------------------------------------------------------------------------
+!usual type Kreiss-Oliger type numerical dissipation
+!We support cell center only
+! Note the notation D_+ and D_- [P240 of B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time
+! Dependent Problems and Difference Methods (Wiley, New York, 1995).]
+! D_+ = (f(i+1) - f(i))/h
+! D_- = (f(i) - f(i-1))/h
+! then we have D_+D_- = D_-D_+ = (f(i+1) - 2f(i) + f(i-1))/h^2
+! for nth order accurate finite difference code, we need r =n/2+1
+!              D_+^rD_-^r = (D_+D_-)^r 
+! following the tradiation of PRD 77, 024027 (BB's calibration paper, Eq.(64),
+!  correct some typo according to above book) :
+! + eps*(-1)^(r-1)*h^(2r-1)/2^(2r)*(D_+D_-)^r 
+!
+!
+! this is for 8th order accurate finite difference scheme
+!  (D_+D_-)^5 =
+!  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
+! -------------------------------------------------------------------------------------------------------------------------------
+!                                                              dx^10
+!---------------------------------------------------------------------------------------------------------------------------------
+! do not add dissipation near boundary
+subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
+
+implicit none
+! argument variables
+integer,intent(in) :: Symmetry
+integer,dimension(3),intent(in)::ex
+real*8, dimension(1:3), intent(in) :: SoA
+double precision,intent(in),dimension(ex(1))::X
+double precision,intent(in),dimension(ex(2))::Y
+double precision,intent(in),dimension(ex(3))::Z
+double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
+double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
+real*8,intent(in) :: eps
+
+!~~~~~~ other variables
+
+  real*8 :: dX,dY,dZ
+  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+  real*8,parameter   :: cof = 1.024d3 ! 2^2r = 2^10
+  real*8,  parameter :: F10=1.d1,F45=4.5d1,F120=1.2d2,F210=2.1d2,F252=2.52d2
+  integer::i,j,k
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+  
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
+
+  call symmetry_bd(5,ex,f,fh,SoA)
+
+!  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
+! -------------------------------------------------------------------------------------------------------------------------------
+!                                                              dx^10
+
+!  note the sign (-1)^r-1, now r=5
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+
+  if(i>imin+4 .and. i < imax-4 .and. &
+     j>jmin+4 .and. j < jmax-4 .and. &
+     k>kmin+4 .and. k < kmax-4) then
+! x direction
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (      &
+                                 (fh(i-5,j,k)+fh(i+5,j,k)) &
+                         - F10 * (fh(i-4,j,k)+fh(i+4,j,k)) &
+                         + F45 * (fh(i-3,j,k)+fh(i+3,j,k)) &
+                         - F120* (fh(i-2,j,k)+fh(i+2,j,k)) &
+                         + F210* (fh(i-1,j,k)+fh(i+1,j,k)) &
+                         - F252 * fh(i,j,k) )
+! y direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (      &
+                                 (fh(i,j-5,k)+fh(i,j+5,k)) &
+                         - F10 * (fh(i,j-4,k)+fh(i,j+4,k)) &
+                         + F45 * (fh(i,j-3,k)+fh(i,j+3,k)) &
+                         - F120* (fh(i,j-2,k)+fh(i,j+2,k)) &
+                         + F210* (fh(i,j-1,k)+fh(i,j+1,k)) &
+                         - F252 * fh(i,j,k) )
+! z direction
+
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (      &
+                                 (fh(i,j,k-5)+fh(i,j,k+5)) &
+                         - F10 * (fh(i,j,k-4)+fh(i,j,k+4)) &
+                         + F45 * (fh(i,j,k-3)+fh(i,j,k+3)) &
+                         - F120* (fh(i,j,k-2)+fh(i,j,k+2)) &
+                         + F210* (fh(i,j,k-1)+fh(i,j,k+1)) &
+                         - F252 * fh(i,j,k) )
+
+  endif
+
+  enddo
+  enddo
+  enddo
+
+  return
+
+end subroutine kodis
+
+#endif  

AMSS_NCKU_source/kodiss_c.C

@@ -0,0 +1,321 @@
+#include "macrodef.h"
+#include "tool.h"
+
+/*
+ * C 版 kodis — Kreiss-Oliger numerical dissipation (Cartesian patches).
+ *
+ * The KO operator is (D₊D₋)^r applied to f_rhs with alternating sign (-1)^(r-1).
+ *
+ * FD order → r → cof=2^(2r) mapping:
+ *   ghost_width=2 (2nd) → r=2, cof=16,  sign=-
+ *   ghost_width=3 (4th) → r=3, cof=64,  sign=+
+ *   ghost_width=4 (6th) → r=4, cof=256, sign=-
+ *   ghost_width=5 (8th) → r=5, cof=1024,sign=+
+ */
+void kodis(const int ex[3],
+           const double *X, const double *Y, const double *Z,
+           const double *f, double *f_rhs,
+           const double SoA[3],
+           int Symmetry, double eps)
+{
+    const double ZEO = 0.0;
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+#if (ghost_width == 2)
+    /* ---- r=2, cof=16, sign=-, 5pt stencil ----------------------------- */
+    {
+        const int ord = 2;
+        const int r = 2;
+        const double cof = 16.0;
+        const double F4 = 4.0, F6 = 6.0;
+        const int NO_SYMM = 0, EQ_SYMM = 1;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        /* i±2 must be valid: i-2 >= iminF && i+2 <= imaxF
+           C 0-based: i0 >= iminF+1, i0 <= ex1-3 */
+        const int i0_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+        const int j0_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int k0_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        const int i0_hi = imaxF - 3;
+        const int j0_hi = jmaxF - 3;
+        const int k0_hi = kmaxF - 3;
+
+        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
+            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        const double Dx = (
+                            (fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] + fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)]) -
+                            F4 * (fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] + fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]) +
+                            F6 *  fh[idx_fh_F_ord2(iF,     jF, kF, ex)]
+                        ) / dX;
+
+                        const double Dy = (
+                            (fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] + fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)]) -
+                            F4 * (fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] + fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]) +
+                            F6 *  fh[idx_fh_F_ord2(iF, jF,     kF, ex)]
+                        ) / dY;
+
+                        const double Dz = (
+                            (fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] + fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)]) -
+                            F4 * (fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] + fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]) +
+                            F6 *  fh[idx_fh_F_ord2(iF, jF, kF,     ex)]
+                        ) / dZ;
+
+                        f_rhs[p] -= (eps / cof) * (Dx + Dy + Dz); /* sign=- */
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 3)
+    /* ---- r=3, cof=64, sign=+, 7pt stencil (current default) ---------- */
+    {
+        const int ord = 3;
+        const int r = 3;
+        const double cof = 64.0;
+        const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
+        const int NO_SYMM = 0, OCTANT = 2;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+        if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = -2;
+        if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = -2;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
+        const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
+        const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
+        const int i0_hi = imaxF - 4;
+        const int j0_hi = jmaxF - 4;
+        const int k0_hi = kmaxF - 4;
+
+        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
+            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        const double Dx = (
+                            (fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
+                            SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
+                            FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
+                            TWT *  fh[idx_fh_F(iF,     jF, kF, ex)]
+                        ) / dX;
+
+                        const double Dy = (
+                            (fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
+                            SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
+                            FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
+                            TWT *  fh[idx_fh_F(iF, jF,     kF, ex)]
+                        ) / dY;
+
+                        const double Dz = (
+                            (fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
+                            SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
+                            FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
+                            TWT *  fh[idx_fh_F(iF, jF, kF,     ex)]
+                        ) / dZ;
+
+                        f_rhs[p] += (eps / cof) * (Dx + Dy + Dz); /* sign=+ */
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 4)
+    /* ---- r=4, cof=256, sign=-, 9pt stencil ---------------------------- */
+    {
+        const int ord = 4;
+        const int r = 4;
+        const double cof = 256.0;
+        const double F8 = 8.0, F28 = 28.0, F56 = 56.0, F70 = 70.0;
+        const int NO_SYMM = 0, EQ_SYMM = 1;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -3;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        /* i±4 valid: i-4>=iminF → i0>=iminF+3, i+4<=imaxF → i0<=ex1-5 */
+        const int i0_lo = (iminF + 3 > 0) ? iminF + 3 : 0;
+        const int j0_lo = (jminF + 3 > 0) ? jminF + 3 : 0;
+        const int k0_lo = (kminF + 3 > 0) ? kminF + 3 : 0;
+        const int i0_hi = imaxF - 5;
+        const int j0_hi = jmaxF - 5;
+        const int k0_hi = kmaxF - 5;
+
+        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
+            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        /* Stencil: [1,-8,28,-56,70,-56,28,-8,1] */
+                        const double Dx = (
+                            (fh[idx_fh_F_ord4(iF - 4, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 4, jF, kF, ex)]) -
+                            F8 * (fh[idx_fh_F_ord4(iF - 3, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 3, jF, kF, ex)]) +
+                            F28* (fh[idx_fh_F_ord4(iF - 2, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 2, jF, kF, ex)]) -
+                            F56* (fh[idx_fh_F_ord4(iF - 1, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 1, jF, kF, ex)]) +
+                            F70*  fh[idx_fh_F_ord4(iF,     jF, kF, ex)]
+                        ) / dX;
+
+                        const double Dy = (
+                            (fh[idx_fh_F_ord4(iF, jF - 4, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 4, kF, ex)]) -
+                            F8 * (fh[idx_fh_F_ord4(iF, jF - 3, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 3, kF, ex)]) +
+                            F28* (fh[idx_fh_F_ord4(iF, jF - 2, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 2, kF, ex)]) -
+                            F56* (fh[idx_fh_F_ord4(iF, jF - 1, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 1, kF, ex)]) +
+                            F70*  fh[idx_fh_F_ord4(iF, jF,     kF, ex)]
+                        ) / dY;
+
+                        const double Dz = (
+                            (fh[idx_fh_F_ord4(iF, jF, kF - 4, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 4, ex)]) -
+                            F8 * (fh[idx_fh_F_ord4(iF, jF, kF - 3, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 3, ex)]) +
+                            F28* (fh[idx_fh_F_ord4(iF, jF, kF - 2, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 2, ex)]) -
+                            F56* (fh[idx_fh_F_ord4(iF, jF, kF - 1, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 1, ex)]) +
+                            F70*  fh[idx_fh_F_ord4(iF, jF, kF,     ex)]
+                        ) / dZ;
+
+                        f_rhs[p] -= (eps / cof) * (Dx + Dy + Dz); /* sign=- */
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 5)
+    /* ---- r=5, cof=1024, sign=+, 11pt stencil ------------------------- */
+    {
+        const int ord = 5;
+        const int r = 5;
+        const double cof = 1024.0;
+        const double F10 = 10.0, F45 = 45.0, F120 = 120.0;
+        const double F210 = 210.0, F252 = 252.0;
+        const int NO_SYMM = 0, EQ_SYMM = 1;
+
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -4;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -4;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -4;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        /* i±5 valid: i0>=iminF+4, i0<=ex1-6 */
+        const int i0_lo = (iminF + 4 > 0) ? iminF + 4 : 0;
+        const int j0_lo = (jminF + 4 > 0) ? jminF + 4 : 0;
+        const int k0_lo = (kminF + 4 > 0) ? kminF + 4 : 0;
+        const int i0_hi = imaxF - 6;
+        const int j0_hi = jmaxF - 6;
+        const int k0_hi = kmaxF - 6;
+
+        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
+            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        /* Stencil: [1,-10,45,-120,210,-252,210,-120,45,-10,1] */
+                        const double Dx = (
+                            (fh[idx_fh_F_ord5(iF - 5, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 5, jF, kF, ex)]) -
+                            F10 * (fh[idx_fh_F_ord5(iF - 4, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 4, jF, kF, ex)]) +
+                            F45 * (fh[idx_fh_F_ord5(iF - 3, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 3, jF, kF, ex)]) -
+                            F120* (fh[idx_fh_F_ord5(iF - 2, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 2, jF, kF, ex)]) +
+                            F210* (fh[idx_fh_F_ord5(iF - 1, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 1, jF, kF, ex)]) -
+                            F252*  fh[idx_fh_F_ord5(iF,     jF, kF, ex)]
+                        ) / dX;
+
+                        const double Dy = (
+                            (fh[idx_fh_F_ord5(iF, jF - 5, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 5, kF, ex)]) -
+                            F10 * (fh[idx_fh_F_ord5(iF, jF - 4, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 4, kF, ex)]) +
+                            F45 * (fh[idx_fh_F_ord5(iF, jF - 3, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 3, kF, ex)]) -
+                            F120* (fh[idx_fh_F_ord5(iF, jF - 2, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 2, kF, ex)]) +
+                            F210* (fh[idx_fh_F_ord5(iF, jF - 1, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 1, kF, ex)]) -
+                            F252*  fh[idx_fh_F_ord5(iF, jF,     kF, ex)]
+                        ) / dY;
+
+                        const double Dz = (
+                            (fh[idx_fh_F_ord5(iF, jF, kF - 5, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 5, ex)]) -
+                            F10 * (fh[idx_fh_F_ord5(iF, jF, kF - 4, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 4, ex)]) +
+                            F45 * (fh[idx_fh_F_ord5(iF, jF, kF - 3, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 3, ex)]) -
+                            F120* (fh[idx_fh_F_ord5(iF, jF, kF - 2, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 2, ex)]) +
+                            F210* (fh[idx_fh_F_ord5(iF, jF, kF - 1, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 1, ex)]) -
+                            F252*  fh[idx_fh_F_ord5(iF, jF, kF,     ex)]
+                        ) / dZ;
+
+                        f_rhs[p] += (eps / cof) * (Dx + Dy + Dz); /* sign=+ */
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#else
+#error "kodiss_c.C: unsupported ghost_width (must be 2, 3, 4, or 5)"
+#endif
+}

AMSS_NCKU_source/kodiss_sh_c.C

@@ -0,0 +1,136 @@
+#include "macrodef.h"
+#include "share_func.h"
+
+/*
+ * kodis_sh — Kreiss-Oliger dissipation on shell patches.
+ * Same stencil coefficients as Cartesian kodis. Uses symmetry_stbd.
+ */
+extern "C" void kodis_sh_(const int ex[3],
+              const double *X, const double *Y, const double *Z,
+              const double *f, double *f_rhs,
+              const double SoAi[2],
+              int Symmetry, double eps, int sst)
+{
+    (void)sst;
+    const double ZEO=0.0;
+    const int ex1=ex[0], ex2=ex[1], ex3=ex[2];
+    const double dX=X[1]-X[0], dY=Y[1]-Y[0], dZ=Z[1]-Z[0];
+    const int imaxF=ex1, jmaxF=ex2, kmaxF=ex3;
+    const double SoA[2]={SoAi[0],SoAi[1]};
+
+#if (ghost_width == 2)
+    {
+        const int ord=2, r=2;
+        const double cof=16.0, F4=4.0, F6=6.0;
+        const int NO_SYMM=0, OCTANT=2;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-1;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-1;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-1;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        double *fh=(double*)malloc(fh_size*sizeof(double));if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const int i0_lo=(iminF+1>0)?iminF+1:0,j0_lo=(jminF+1>0)?jminF+1:0,k0_lo=2;
+        const int i0_hi=imaxF-3,j0_hi=jmaxF-3,k0_hi=kmaxF-3;
+        if(!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)){
+            for(int k0=k0_lo;k0<=k0_hi;++k0){const int kF=k0+1;
+            for(int j0=j0_lo;j0<=j0_hi;++j0){const int jF=j0+1;
+            for(int i0=i0_lo;i0<=i0_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                const double Dx=((fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)])-F4*(fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)])+F6*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dX;
+                const double Dy=((fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)])-F4*(fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)])+F6*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dY;
+                const double Dz=((fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)])-F4*(fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)])+F6*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dZ;
+                f_rhs[p]-=(eps/cof)*(Dx+Dy+Dz);
+            }}}
+        }
+        free(fh);return;
+    }
+#elif (ghost_width == 3)
+    {
+        const int ord=3, r=3;
+        const double cof=64.0,SIX=6.0,FIT=15.0,TWT=20.0;
+        const int NO_SYMM=0,OCTANT=2;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-2;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-2;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-2;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        double *fh=(double*)malloc(fh_size*sizeof(double));if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const int i0_lo=(iminF+2>0)?iminF+2:0,j0_lo=(jminF+2>0)?jminF+2:0,k0_lo=3;
+        const int i0_hi=imaxF-4,j0_hi=jmaxF-4,k0_hi=kmaxF-4;
+        if(!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)){
+            for(int k0=k0_lo;k0<=k0_hi;++k0){const int kF=k0+1;
+            for(int j0=j0_lo;j0<=j0_hi;++j0){const int jF=j0+1;
+            for(int i0=i0_lo;i0<=i0_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                const double Dx=((fh[idx_fh_stbd(iF-3,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+3,jF,kF,ord,ex)])-SIX*(fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)])+FIT*(fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)])-TWT*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dX;
+                const double Dy=((fh[idx_fh_stbd(iF,jF-3,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+3,kF,ord,ex)])-SIX*(fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)])+FIT*(fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)])-TWT*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dY;
+                const double Dz=((fh[idx_fh_stbd(iF,jF,kF-3,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+3,ord,ex)])-SIX*(fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)])+FIT*(fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)])-TWT*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dZ;
+                f_rhs[p]+=(eps/cof)*(Dx+Dy+Dz);
+            }}}
+        }
+        free(fh);return;
+    }
+#elif (ghost_width == 4)
+    {
+        const int ord=4, r=4;
+        const double cof=256.0,F8=8.0,F28=28.0,F56=56.0,F70=70.0;
+        const int NO_SYMM=0,OCTANT=2;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-3;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-3;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-3;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        double *fh=(double*)malloc(fh_size*sizeof(double));if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const int i0_lo=(iminF+3>0)?iminF+3:0,j0_lo=(jminF+3>0)?jminF+3:0,k0_lo=4;
+        const int i0_hi=imaxF-5,j0_hi=jmaxF-5,k0_hi=kmaxF-5;
+        if(!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)){
+            for(int k0=k0_lo;k0<=k0_hi;++k0){const int kF=k0+1;
+            for(int j0=j0_lo;j0<=j0_hi;++j0){const int jF=j0+1;
+            for(int i0=i0_lo;i0<=i0_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                const double Dx=((fh[idx_fh_stbd(iF-4,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+4,jF,kF,ord,ex)])-F8*(fh[idx_fh_stbd(iF-3,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+3,jF,kF,ord,ex)])+F28*(fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)])-F56*(fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)])+F70*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dX;
+                const double Dy=((fh[idx_fh_stbd(iF,jF-4,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+4,kF,ord,ex)])-F8*(fh[idx_fh_stbd(iF,jF-3,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+3,kF,ord,ex)])+F28*(fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)])-F56*(fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)])+F70*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dY;
+                const double Dz=((fh[idx_fh_stbd(iF,jF,kF-4,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+4,ord,ex)])-F8*(fh[idx_fh_stbd(iF,jF,kF-3,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+3,ord,ex)])+F28*(fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)])-F56*(fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)])+F70*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dZ;
+                f_rhs[p]-=(eps/cof)*(Dx+Dy+Dz);
+            }}}
+        }
+        free(fh);return;
+    }
+#elif (ghost_width == 5)
+    {
+        const int ord=5, r=5;
+        const double cof=1024.0,F10=10.0,F45k=45.0,F120=120.0,F210=210.0,F252=252.0;
+        const int NO_SYMM=0,OCTANT=2;
+        int iminF=1,jminF=1,kminF=1;
+        if(Symmetry==OCTANT&&fabs(X[0])<dX)iminF=-4;
+        if(Symmetry==OCTANT&&fabs(Y[0])<dY)jminF=-4;
+        if((sst==2||sst==4)&&fabs(Y[0])<dY)jminF=-4;
+
+        const size_t nx=(size_t)ex1+2*ord,ny=(size_t)ex2+2*ord,nz=(size_t)ex3,fh_size=nx*ny*nz;
+        double *fh=(double*)malloc(fh_size*sizeof(double));if(!fh)return;
+        symmetry_stbd(ord,ex,f,fh,SoA);
+
+        const int i0_lo=(iminF+4>0)?iminF+4:0,j0_lo=(jminF+4>0)?jminF+4:0,k0_lo=5;
+        const int i0_hi=imaxF-6,j0_hi=jmaxF-6,k0_hi=kmaxF-6;
+        if(!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)){
+            for(int k0=k0_lo;k0<=k0_hi;++k0){const int kF=k0+1;
+            for(int j0=j0_lo;j0<=j0_hi;++j0){const int jF=j0+1;
+            for(int i0=i0_lo;i0<=i0_hi;++i0){const int iF=i0+1;const size_t p=idx_ex(i0,j0,k0,ex);
+                const double Dx=((fh[idx_fh_stbd(iF-5,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+5,jF,kF,ord,ex)])-F10*(fh[idx_fh_stbd(iF-4,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+4,jF,kF,ord,ex)])+F45k*(fh[idx_fh_stbd(iF-3,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+3,jF,kF,ord,ex)])-F120*(fh[idx_fh_stbd(iF-2,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+2,jF,kF,ord,ex)])+F210*(fh[idx_fh_stbd(iF-1,jF,kF,ord,ex)]+fh[idx_fh_stbd(iF+1,jF,kF,ord,ex)])-F252*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dX;
+                const double Dy=((fh[idx_fh_stbd(iF,jF-5,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+5,kF,ord,ex)])-F10*(fh[idx_fh_stbd(iF,jF-4,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+4,kF,ord,ex)])+F45k*(fh[idx_fh_stbd(iF,jF-3,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+3,kF,ord,ex)])-F120*(fh[idx_fh_stbd(iF,jF-2,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+2,kF,ord,ex)])+F210*(fh[idx_fh_stbd(iF,jF-1,kF,ord,ex)]+fh[idx_fh_stbd(iF,jF+1,kF,ord,ex)])-F252*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dY;
+                const double Dz=((fh[idx_fh_stbd(iF,jF,kF-5,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+5,ord,ex)])-F10*(fh[idx_fh_stbd(iF,jF,kF-4,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+4,ord,ex)])+F45k*(fh[idx_fh_stbd(iF,jF,kF-3,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+3,ord,ex)])-F120*(fh[idx_fh_stbd(iF,jF,kF-2,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+2,ord,ex)])+F210*(fh[idx_fh_stbd(iF,jF,kF-1,ord,ex)]+fh[idx_fh_stbd(iF,jF,kF+1,ord,ex)])-F252*fh[idx_fh_stbd(iF,jF,kF,ord,ex)])/dZ;
+                f_rhs[p]+=(eps/cof)*(Dx+Dy+Dz);
+            }}}
+        }
+        free(fh);return;
+    }
+#else
+#error "kodiss_sh_c.C: unsupported ghost_width"
+#endif
+}

AMSS_NCKU_source/lopsided_c.C

@@ -0,0 +1,591 @@
+#include "macrodef.h"
+#include "tool.h"
+
+/*
+ * C 版 lopsided — upwind (lopsided) advection derivatives.
+ *
+ * Adds advection terms to f_rhs for all three spatial directions.
+ * Uses sign-biased (one-sided) stencils with centered fallbacks.
+ *
+ * For lopsided, symmetry_bd ord = ghost_width (same as kodiss).
+ */
+void lopsided(const int ex[3],
+              const double *X, const double *Y, const double *Z,
+              const double *f, double *f_rhs,
+              const double *Sfx, const double *Sfy, const double *Sfz,
+              int Symmetry, const double SoA[3])
+{
+    const double ZEO = 0.0, ONE = 1.0;
+    const double TWO = 2.0, F6 = 6.0, EIT = 8.0;
+    const double F3 = 3.0, F4 = 4.0, F5 = 5.0, F10 = 10.0, F12 = 12.0, F18 = 18.0;
+    const double F9 = 9.0, F45 = 45.0, F60 = 60.0;
+    const double F2 = 2.0, F15 = 15.0, F24 = 24.0, F30 = 30.0, F35 = 35.0;
+    const double F50 = 50.0, F77 = 77.0, F80 = 80.0, F100 = 100.0, F150 = 150.0;
+    const double F32 = 32.0, F168 = 168.0, F672 = 672.0, F840 = 840.0;
+    const double F140=140.0, F378=378.0, F420=420.0, F1050=1050.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+#if (ghost_width == 2)
+    /* ---- 2nd-order lopsided --------------------------------------------- */
+    {
+        const int ord = 2;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d2dx  = ONE / TWO / dX;
+        const double d2dy  = ONE / TWO / dY;
+        const double d2dz  = ONE / TWO / dZ;
+
+        const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+        for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    /* x-direction */
+                    const double sfx = Sfx[p];
+                    if (sfx > ZEO) {
+                        if (i0 <= ex1 - 3) // i+2 <= imax
+                            f_rhs[p] += sfx * d2dx * (
+                                -F3*fh[idx_fh_F_ord2(iF,   jF, kF, ex)] +
+                                 F4*fh[idx_fh_F_ord2(iF+1, jF, kF, ex)] -
+                                    fh[idx_fh_F_ord2(iF+2, jF, kF, ex)]);
+                        else if (i0 <= ex1 - 2) // i+1 <= imax
+                            f_rhs[p] += sfx * d2dx * (
+                                -fh[idx_fh_F_ord2(iF,   jF, kF, ex)] +
+                                 fh[idx_fh_F_ord2(iF+1, jF, kF, ex)]);
+                    } else if (sfx < ZEO) {
+                        if ((i0 - 1) >= iminF) // i-2 >= imin
+                            f_rhs[p] -= sfx * d2dx * (
+                                -F3*fh[idx_fh_F_ord2(iF,   jF, kF, ex)] +
+                                 F4*fh[idx_fh_F_ord2(iF-1, jF, kF, ex)] -
+                                    fh[idx_fh_F_ord2(iF-2, jF, kF, ex)]);
+                        else if (i0 >= iminF) // i-1 >= imin
+                            f_rhs[p] -= sfx * d2dx * (
+                                -fh[idx_fh_F_ord2(iF,   jF, kF, ex)] +
+                                 fh[idx_fh_F_ord2(iF-1, jF, kF, ex)]);
+                    }
+
+                    /* y-direction */
+                    const double sfy = Sfy[p];
+                    if (sfy > ZEO) {
+                        if (j0 <= ex2-3)
+                            f_rhs[p] += sfy * d2dy * (
+                                -F3*fh[idx_fh_F_ord2(iF, jF,   kF, ex)] +
+                                 F4*fh[idx_fh_F_ord2(iF, jF+1, kF, ex)] -
+                                    fh[idx_fh_F_ord2(iF, jF+2, kF, ex)]);
+                        else if (j0 <= ex2-2)
+                            f_rhs[p] += sfy * d2dy * (
+                                -fh[idx_fh_F_ord2(iF, jF,   kF, ex)] +
+                                 fh[idx_fh_F_ord2(iF, jF+1, kF, ex)]);
+                    } else if (sfy < ZEO) {
+                        if ((j0-1) >= jminF)
+                            f_rhs[p] -= sfy * d2dy * (
+                                -F3*fh[idx_fh_F_ord2(iF, jF,   kF, ex)] +
+                                 F4*fh[idx_fh_F_ord2(iF, jF-1, kF, ex)] -
+                                    fh[idx_fh_F_ord2(iF, jF-2, kF, ex)]);
+                        else if (j0 >= jminF)
+                            f_rhs[p] -= sfy * d2dy * (
+                                -fh[idx_fh_F_ord2(iF, jF,   kF, ex)] +
+                                 fh[idx_fh_F_ord2(iF, jF-1, kF, ex)]);
+                    }
+
+                    /* z-direction */
+                    const double sfz = Sfz[p];
+                    if (sfz > ZEO) {
+                        if (k0 <= ex3-3)
+                            f_rhs[p] += sfz * d2dz * (
+                                -F3*fh[idx_fh_F_ord2(iF, jF, kF,   ex)] +
+                                 F4*fh[idx_fh_F_ord2(iF, jF, kF+1, ex)] -
+                                    fh[idx_fh_F_ord2(iF, jF, kF+2, ex)]);
+                        else if (k0 <= ex3-2)
+                            f_rhs[p] += sfz * d2dz * (
+                                -fh[idx_fh_F_ord2(iF, jF, kF,   ex)] +
+                                 fh[idx_fh_F_ord2(iF, jF, kF+1, ex)]);
+                    } else if (sfz < ZEO) {
+                        if ((k0-1) >= kminF)
+                            f_rhs[p] -= sfz * d2dz * (
+                                -F3*fh[idx_fh_F_ord2(iF, jF, kF,   ex)] +
+                                 F4*fh[idx_fh_F_ord2(iF, jF, kF-1, ex)] -
+                                    fh[idx_fh_F_ord2(iF, jF, kF-2, ex)]);
+                        else if (k0 >= kminF)
+                            f_rhs[p] -= sfz * d2dz * (
+                                -fh[idx_fh_F_ord2(iF, jF, kF,   ex)] +
+                                 fh[idx_fh_F_ord2(iF, jF, kF-1, ex)]);
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 3)
+    /* ---- 4th-order lopsided (original code) ---------------------------- */
+    {
+        const int ord = 3;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d12dx = ONE / F12 / dX;
+        const double d12dy = ONE / F12 / dY;
+        const double d12dz = ONE / F12 / dZ;
+
+        const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+        for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    const double sfx = Sfx[p];
+                    if (sfx > ZEO) {
+                        if (i0 <= ex1 - 4) // i+3 <= imax
+                            f_rhs[p] += sfx * d12dx * (
+                                -F3 *fh[idx_fh_F(iF-1, jF, kF, ex)]
+                                -F10*fh[idx_fh_F(iF,   jF, kF, ex)]
+                                +F18*fh[idx_fh_F(iF+1, jF, kF, ex)]
+                                -F6 *fh[idx_fh_F(iF+2, jF, kF, ex)]
+                                +    fh[idx_fh_F(iF+3, jF, kF, ex)]);
+                        else if (i0 <= ex1 - 3) // i+2 <= imax
+                            f_rhs[p] += sfx * d12dx * (
+                                fh[idx_fh_F(iF-2, jF, kF, ex)]
+                                -EIT*fh[idx_fh_F(iF-1, jF, kF, ex)]
+                                +EIT*fh[idx_fh_F(iF+1, jF, kF, ex)]
+                                -    fh[idx_fh_F(iF+2, jF, kF, ex)]);
+                        else if (i0 <= ex1 - 2) // i+1 <= imax → mirrored
+                            f_rhs[p] -= sfx * d12dx * (
+                                -F3 *fh[idx_fh_F(iF+1, jF, kF, ex)]
+                                -F10*fh[idx_fh_F(iF,   jF, kF, ex)]
+                                +F18*fh[idx_fh_F(iF-1, jF, kF, ex)]
+                                -F6 *fh[idx_fh_F(iF-2, jF, kF, ex)]
+                                +    fh[idx_fh_F(iF-3, jF, kF, ex)]);
+                    } else if (sfx < ZEO) {
+                        if ((i0 - 2) >= iminF) // i-3 >= imin
+                            f_rhs[p] -= sfx * d12dx * (
+                                -F3 *fh[idx_fh_F(iF+1, jF, kF, ex)]
+                                -F10*fh[idx_fh_F(iF,   jF, kF, ex)]
+                                +F18*fh[idx_fh_F(iF-1, jF, kF, ex)]
+                                -F6 *fh[idx_fh_F(iF-2, jF, kF, ex)]
+                                +    fh[idx_fh_F(iF-3, jF, kF, ex)]);
+                        else if ((i0 - 1) >= iminF) // i-2 >= imin
+                            f_rhs[p] += sfx * d12dx * (
+                                fh[idx_fh_F(iF-2, jF, kF, ex)]
+                                -EIT*fh[idx_fh_F(iF-1, jF, kF, ex)]
+                                +EIT*fh[idx_fh_F(iF+1, jF, kF, ex)]
+                                -    fh[idx_fh_F(iF+2, jF, kF, ex)]);
+                        else if (i0 >= iminF) // i-1 >= imin → mirrored
+                            f_rhs[p] += sfx * d12dx * (
+                                -F3 *fh[idx_fh_F(iF-1, jF, kF, ex)]
+                                -F10*fh[idx_fh_F(iF,   jF, kF, ex)]
+                                +F18*fh[idx_fh_F(iF+1, jF, kF, ex)]
+                                -F6 *fh[idx_fh_F(iF+2, jF, kF, ex)]
+                                +    fh[idx_fh_F(iF+3, jF, kF, ex)]);
+                    }
+
+                    const double sfy = Sfy[p];
+                    if (sfy > ZEO) {
+                        if (j0 <= ex2-4)
+                            f_rhs[p] += sfy * d12dy * (
+                                -F3*fh[idx_fh_F(iF,jF-1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF+1,kF,ex)]-F6*fh[idx_fh_F(iF,jF+2,kF,ex)]
+                                +fh[idx_fh_F(iF,jF+3,kF,ex)]);
+                        else if (j0 <= ex2-3)
+                            f_rhs[p] += sfy * d12dy * (fh[idx_fh_F(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F(iF,jF+1,kF,ex)]-fh[idx_fh_F(iF,jF+2,kF,ex)]);
+                        else if (j0 <= ex2-2)
+                            f_rhs[p] -= sfy * d12dy * (
+                                -F3*fh[idx_fh_F(iF,jF+1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF-1,kF,ex)]-F6*fh[idx_fh_F(iF,jF-2,kF,ex)]
+                                +fh[idx_fh_F(iF,jF-3,kF,ex)]);
+                    } else if (sfy < ZEO) {
+                        if ((j0-2) >= jminF)
+                            f_rhs[p] -= sfy * d12dy * (
+                                -F3*fh[idx_fh_F(iF,jF+1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF-1,kF,ex)]-F6*fh[idx_fh_F(iF,jF-2,kF,ex)]
+                                +fh[idx_fh_F(iF,jF-3,kF,ex)]);
+                        else if ((j0-1) >= jminF)
+                            f_rhs[p] += sfy * d12dy * (fh[idx_fh_F(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F(iF,jF+1,kF,ex)]-fh[idx_fh_F(iF,jF+2,kF,ex)]);
+                        else if (j0 >= jminF)
+                            f_rhs[p] += sfy * d12dy * (
+                                -F3*fh[idx_fh_F(iF,jF-1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF+1,kF,ex)]-F6*fh[idx_fh_F(iF,jF+2,kF,ex)]
+                                +fh[idx_fh_F(iF,jF+3,kF,ex)]);
+                    }
+
+                    const double sfz = Sfz[p];
+                    if (sfz > ZEO) {
+                        if (k0 <= ex3-4)
+                            f_rhs[p] += sfz * d12dz * (
+                                -F3*fh[idx_fh_F(iF,jF,kF-1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF,kF+1,ex)]-F6*fh[idx_fh_F(iF,jF,kF+2,ex)]
+                                +fh[idx_fh_F(iF,jF,kF+3,ex)]);
+                        else if (k0 <= ex3-3)
+                            f_rhs[p] += sfz * d12dz * (fh[idx_fh_F(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F(iF,jF,kF+1,ex)]-fh[idx_fh_F(iF,jF,kF+2,ex)]);
+                        else if (k0 <= ex3-2)
+                            f_rhs[p] -= sfz * d12dz * (
+                                -F3*fh[idx_fh_F(iF,jF,kF+1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF,kF-1,ex)]-F6*fh[idx_fh_F(iF,jF,kF-2,ex)]
+                                +fh[idx_fh_F(iF,jF,kF-3,ex)]);
+                    } else if (sfz < ZEO) {
+                        if ((k0-2) >= kminF)
+                            f_rhs[p] -= sfz * d12dz * (
+                                -F3*fh[idx_fh_F(iF,jF,kF+1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF,kF-1,ex)]-F6*fh[idx_fh_F(iF,jF,kF-2,ex)]
+                                +fh[idx_fh_F(iF,jF,kF-3,ex)]);
+                        else if ((k0-1) >= kminF)
+                            f_rhs[p] += sfz * d12dz * (fh[idx_fh_F(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F(iF,jF,kF+1,ex)]-fh[idx_fh_F(iF,jF,kF+2,ex)]);
+                        else if (k0 >= kminF)
+                            f_rhs[p] += sfz * d12dz * (
+                                -F3*fh[idx_fh_F(iF,jF,kF-1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]
+                                +F18*fh[idx_fh_F(iF,jF,kF+1,ex)]-F6*fh[idx_fh_F(iF,jF,kF+2,ex)]
+                                +fh[idx_fh_F(iF,jF,kF+3,ex)]);
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 4)
+    /* ---- 6th-order lopsided --------------------------------------------- */
+    {
+        const int ord = 4;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -3;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d60dx = ONE / F60 / dX;
+        const double d60dy = ONE / F60 / dY;
+        const double d60dz = ONE / F60 / dZ;
+        const double d12dx = ONE / F12 / dX;
+        const double d12dy = ONE / F12 / dY;
+        const double d12dz = ONE / F12 / dZ;
+        const double d2dx  = ONE / TWO / dX;
+        const double d2dy  = ONE / TWO / dY;
+        const double d2dz  = ONE / TWO / dZ;
+
+        const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+        for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    /* ---- x-direction ---- */
+                    const double sfx = Sfx[p];
+                    if (sfx > ZEO) {
+                        /* Primary biased: 2*f(i-2)-24*f(i-1)-35*f(i)+80*f(i+1)-30*f(i+2)+8*f(i+3)-f(i+4) */
+                        if (i0 <= ex1-5 && (i0-1)>=iminF) // i+4<=imax && i-2>=imin
+                            f_rhs[p] += sfx * d60dx * (
+                                +F2*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-F24*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]
+                                -F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]
+                                -F30*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]
+                                -fh[idx_fh_F_ord4(iF+4,jF,kF,ex)]);
+                        /* Boundary-adapted: -10*f(i-1)-77*f(i)+150*f(i+1)-100*f(i+2)+50*f(i+3)-15*f(i+4)+2*f(i+5) */
+                        else if (i0 <= ex1-6 && i0 >= iminF) // i+5<=imax && i-1>=imin
+                            f_rhs[p] += sfx * d60dx * (
+                                -F10*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]
+                                +F150*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F100*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]
+                                +F50*fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]-F15*fh[idx_fh_F_ord4(iF+4,jF,kF,ex)]
+                                +F2*fh[idx_fh_F_ord4(iF+5,jF,kF,ex)]);
+                        /* Centered fallbacks */
+                        else if (i0 <= ex1-4 && (i0-2)>=iminF) // 6th: i+3<=imax && i-3>=imin
+                            f_rhs[p] += sfx * d60dx * (
+                                -fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]
+                                -F45*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]
+                                -F9*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]);
+                        else if (i0 <= ex1-3 && (i0-1)>=iminF) // 4th
+                            f_rhs[p] += sfx * d12dx * (
+                                fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]
+                                +EIT*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]);
+                        else if (i0 <= ex1-2 && i0>=iminF) // 2nd
+                            f_rhs[p] += sfx * d2dx * (
+                                -fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]);
+                    } else if (sfx < ZEO) {
+                        if ((i0-3)>=iminF && i0<=ex1-3) // i-4>=imin && i+2<=imax
+                            f_rhs[p] -= sfx * d60dx * (
+                                +F2*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]-F24*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]
+                                -F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]
+                                -F30*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]
+                                -fh[idx_fh_F_ord4(iF-4,jF,kF,ex)]);
+                        else if ((i0-4)>=iminF && i0<=ex1-2) // i-5>=imin && i+1<=imax
+                            f_rhs[p] -= sfx * d60dx * (
+                                -F10*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]
+                                +F150*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]-F100*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]
+                                +F50*fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]-F15*fh[idx_fh_F_ord4(iF-4,jF,kF,ex)]
+                                +F2*fh[idx_fh_F_ord4(iF-5,jF,kF,ex)]);
+                        else if ((i0-2)>=iminF && i0<=ex1-4) // 6th centered
+                            f_rhs[p] += sfx * d60dx * (
+                                -fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]
+                                -F45*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]
+                                -F9*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]);
+                        else if ((i0-1)>=iminF && i0<=ex1-3) // 4th
+                            f_rhs[p] += sfx * d12dx * (
+                                fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]
+                                +EIT*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]);
+                        else if (i0>=iminF && i0<=ex1-2) // 2nd
+                            f_rhs[p] += sfx * d2dx * (
+                                -fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]);
+                    }
+
+                    /* ---- y-direction ---- */
+                    const double sfy = Sfy[p];
+                    if (sfy > ZEO) {
+                        if (j0<=ex2-5 && (j0-1)>=jminF)
+                            f_rhs[p] += sfy * d60dy*(F2*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-F24*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F30*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]-fh[idx_fh_F_ord4(iF,jF+4,kF,ex)]);
+                        else if (j0<=ex2-6 && j0>=jminF)
+                            f_rhs[p] += sfy * d60dy*(-F10*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F100*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+F50*fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]-F15*fh[idx_fh_F_ord4(iF,jF+4,kF,ex)]+F2*fh[idx_fh_F_ord4(iF,jF+5,kF,ex)]);
+                        else if (j0<=ex2-4 && (j0-2)>=jminF)
+                            f_rhs[p] += sfy * d60dy*(-fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]);
+                        else if (j0<=ex2-3 && (j0-1)>=jminF)
+                            f_rhs[p] += sfy * d12dy*(fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]);
+                        else if (j0<=ex2-2 && j0>=jminF)
+                            f_rhs[p] += sfy * d2dy*(-fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]);
+                    } else if (sfy < ZEO) {
+                        if ((j0-3)>=jminF && j0<=ex2-3)
+                            f_rhs[p] -= sfy * d60dy*(F2*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]-F24*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F30*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]-fh[idx_fh_F_ord4(iF,jF-4,kF,ex)]);
+                        else if ((j0-4)>=jminF && j0<=ex2-2)
+                            f_rhs[p] -= sfy * d60dy*(-F10*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F100*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]+F50*fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]-F15*fh[idx_fh_F_ord4(iF,jF-4,kF,ex)]+F2*fh[idx_fh_F_ord4(iF,jF-5,kF,ex)]);
+                        else if ((j0-2)>=jminF && j0<=ex2-4)
+                            f_rhs[p] += sfy * d60dy*(-fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]);
+                        else if ((j0-1)>=jminF && j0<=ex2-3)
+                            f_rhs[p] += sfy * d12dy*(fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]);
+                        else if (j0>=jminF && j0<=ex2-2)
+                            f_rhs[p] += sfy * d2dy*(-fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]);
+                    }
+
+                    /* ---- z-direction ---- */
+                    const double sfz = Sfz[p];
+                    if (sfz > ZEO) {
+                        if (k0<=ex3-5 && (k0-1)>=kminF)
+                            f_rhs[p] += sfz * d60dz*(F2*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-F24*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F30*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]-fh[idx_fh_F_ord4(iF,jF,kF+4,ex)]);
+                        else if (k0<=ex3-6 && k0>=kminF)
+                            f_rhs[p] += sfz * d60dz*(-F10*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F100*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+F50*fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]-F15*fh[idx_fh_F_ord4(iF,jF,kF+4,ex)]+F2*fh[idx_fh_F_ord4(iF,jF,kF+5,ex)]);
+                        else if (k0<=ex3-4 && (k0-2)>=kminF)
+                            f_rhs[p] += sfz * d60dz*(-fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]);
+                        else if (k0<=ex3-3 && (k0-1)>=kminF)
+                            f_rhs[p] += sfz * d12dz*(fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]);
+                        else if (k0<=ex3-2 && k0>=kminF)
+                            f_rhs[p] += sfz * d2dz*(-fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]);
+                    } else if (sfz < ZEO) {
+                        if ((k0-3)>=kminF && k0<=ex3-3)
+                            f_rhs[p] -= sfz * d60dz*(F2*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]-F24*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F30*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]-fh[idx_fh_F_ord4(iF,jF,kF-4,ex)]);
+                        else if ((k0-4)>=kminF && k0<=ex3-2)
+                            f_rhs[p] -= sfz * d60dz*(-F10*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F100*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]+F50*fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]-F15*fh[idx_fh_F_ord4(iF,jF,kF-4,ex)]+F2*fh[idx_fh_F_ord4(iF,jF,kF-5,ex)]);
+                        else if ((k0-2)>=kminF && k0<=ex3-4)
+                            f_rhs[p] += sfz * d60dz*(-fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]);
+                        else if ((k0-1)>=kminF && k0<=ex3-3)
+                            f_rhs[p] += sfz * d12dz*(fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]);
+                        else if (k0>=kminF && k0<=ex3-2)
+                            f_rhs[p] += sfz * d2dz*(-fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]);
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 5)
+    /* ---- 8th-order lopsided --------------------------------------------- */
+    {
+        const int ord = 5;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -4;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -4;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -4;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        const size_t fh_size = nx * ny * nz;
+
+        double *fh = (double*)malloc(fh_size * sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d840dx = ONE / F840 / dX;
+        const double d840dy = ONE / F840 / dY;
+        const double d840dz = ONE / F840 / dZ;
+        const double d60dx = ONE / F60 / dX;
+        const double d60dy = ONE / F60 / dY;
+        const double d60dz = ONE / F60 / dZ;
+        const double d12dx = ONE / F12 / dX;
+        const double d12dy = ONE / F12 / dY;
+        const double d12dz = ONE / F12 / dZ;
+        const double d2dx  = ONE / TWO / dX;
+        const double d2dy  = ONE / TWO / dY;
+        const double d2dz  = ONE / TWO / dZ;
+
+        const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+        for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    const double sfx = Sfx[p];
+                    if (sfx > ZEO) {
+                        /* 8th biased: -5*f(i-3)+60*f(i-2)-420*f(i-1)-378*f(i)+1050*f(i+1)-420*f(i+2)+140*f(i+3)-30*f(i+4)+3*f(i+5) */
+                        if (i0 <= ex1-6 && (i0-2)>=iminF) // i+5<=imax && i-3>=imin
+                            f_rhs[p] += sfx * d840dx * (
+                                -F5*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F60*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]
+                                -F420*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]
+                                +F1050*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F420*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]
+                                +F140*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]-F30*fh[idx_fh_F_ord5(iF+4,jF,kF,ex)]
+                                +F3*fh[idx_fh_F_ord5(iF+5,jF,kF,ex)]);
+                        /* 8th centered: +3*f(i-4)-32*f(i-3)+168*f(i-2)-672*f(i-1)+672*f(i+1)-168*f(i+2)+32*f(i+3)-3*f(i+4) */
+                        else if (i0 <= ex1-5 && (i0-3)>=iminF)
+                            f_rhs[p] += sfx * d840dx * (
+                                +F3*fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]-F32*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]
+                                +F168*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F672*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]
+                                +F672*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F168*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]
+                                +F32*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]-F3*fh[idx_fh_F_ord5(iF+4,jF,kF,ex)]);
+                        else if (i0 <= ex1-4 && (i0-2)>=iminF) // 6th centered
+                            f_rhs[p] += sfx * d60dx * (
+                                -fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]
+                                -F45*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]
+                                -F9*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]);
+                        else if (i0 <= ex1-3 && (i0-1)>=iminF) // 4th centered
+                            f_rhs[p] += sfx * d12dx * (
+                                fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]
+                                +EIT*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]);
+                        else if (i0 <= ex1-2 && i0>=iminF) // 2nd centered
+                            f_rhs[p] += sfx * d2dx * (
+                                -fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]);
+                    } else if (sfx < ZEO) {
+                        if ((i0-4)>=iminF && i0<=ex1-4)
+                            f_rhs[p] -= sfx * d840dx * (
+                                -F5*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]+F60*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]
+                                -F420*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]
+                                +F1050*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]-F420*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]
+                                +F140*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]-F30*fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]
+                                +F3*fh[idx_fh_F_ord5(iF-5,jF,kF,ex)]);
+                        else if ((i0-3)>=iminF && i0<=ex1-5) // 8th centered
+                            f_rhs[p] += sfx * d840dx * (
+                                +F3*fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]-F32*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]
+                                +F168*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F672*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]
+                                +F672*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F168*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]
+                                +F32*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]-F3*fh[idx_fh_F_ord5(iF+4,jF,kF,ex)]);
+                        else if ((i0-2)>=iminF && i0<=ex1-4) // 6th centered
+                            f_rhs[p] += sfx * d60dx * (
+                                -fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]
+                                -F45*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]
+                                -F9*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]);
+                        else if ((i0-1)>=iminF && i0<=ex1-3) // 4th centered
+                            f_rhs[p] += sfx * d12dx * (
+                                fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]
+                                +EIT*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]);
+                        else if (i0>=iminF && i0<=ex1-2) // 2nd centered
+                            f_rhs[p] += sfx * d2dx * (
+                                -fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]);
+                    }
+
+                    const double sfy = Sfy[p];
+                    if (sfy > ZEO) {
+                        if (j0<=ex2-6 && (j0-2)>=jminF)
+                            f_rhs[p] += sfy * d840dy*(-F5*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F60*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+F140*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]-F30*fh[idx_fh_F_ord5(iF,jF+4,kF,ex)]+F3*fh[idx_fh_F_ord5(iF,jF+5,kF,ex)]);
+                        else if (j0<=ex2-5 && (j0-3)>=jminF)
+                            f_rhs[p] += sfy * d840dy*(+F3*fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]-F32*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F168*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F672*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F672*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F168*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+F32*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]-F3*fh[idx_fh_F_ord5(iF,jF+4,kF,ex)]);
+                        else if (j0<=ex2-4 && (j0-2)>=jminF)
+                            f_rhs[p] += sfy * d60dy*(-fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]);
+                        else if (j0<=ex2-3 && (j0-1)>=jminF)
+                            f_rhs[p] += sfy * d12dy*(fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]);
+                        else if (j0<=ex2-2 && j0>=jminF)
+                            f_rhs[p] += sfy * d2dy*(-fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]);
+                    } else if (sfy < ZEO) {
+                        if ((j0-4)>=jminF && j0<=ex2-4)
+                            f_rhs[p] -= sfy * d840dy*(-F5*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]+F60*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]+F140*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]-F30*fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]+F3*fh[idx_fh_F_ord5(iF,jF-5,kF,ex)]);
+                        else if ((j0-3)>=jminF && j0<=ex2-5)
+                            f_rhs[p] += sfy * d840dy*(+F3*fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]-F32*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F168*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F672*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F672*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F168*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+F32*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]-F3*fh[idx_fh_F_ord5(iF,jF+4,kF,ex)]);
+                        else if ((j0-2)>=jminF && j0<=ex2-4)
+                            f_rhs[p] += sfy * d60dy*(-fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]);
+                        else if ((j0-1)>=jminF && j0<=ex2-3)
+                            f_rhs[p] += sfy * d12dy*(fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]);
+                        else if (j0>=jminF && j0<=ex2-2)
+                            f_rhs[p] += sfy * d2dy*(-fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]);
+                    }
+
+                    const double sfz = Sfz[p];
+                    if (sfz > ZEO) {
+                        if (k0<=ex3-6 && (k0-2)>=kminF)
+                            f_rhs[p] += sfz * d840dz*(-F5*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F60*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+F140*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]-F30*fh[idx_fh_F_ord5(iF,jF,kF+4,ex)]+F3*fh[idx_fh_F_ord5(iF,jF,kF+5,ex)]);
+                        else if (k0<=ex3-5 && (k0-3)>=kminF)
+                            f_rhs[p] += sfz * d840dz*(+F3*fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]-F32*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F168*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F672*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F672*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F168*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+F32*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]-F3*fh[idx_fh_F_ord5(iF,jF,kF+4,ex)]);
+                        else if (k0<=ex3-4 && (k0-2)>=kminF)
+                            f_rhs[p] += sfz * d60dz*(-fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]);
+                        else if (k0<=ex3-3 && (k0-1)>=kminF)
+                            f_rhs[p] += sfz * d12dz*(fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]);
+                        else if (k0<=ex3-2 && k0>=kminF)
+                            f_rhs[p] += sfz * d2dz*(-fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]);
+                    } else if (sfz < ZEO) {
+                        if ((k0-4)>=kminF && k0<=ex3-4)
+                            f_rhs[p] -= sfz * d840dz*(-F5*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]+F60*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]+F140*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]-F30*fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]+F3*fh[idx_fh_F_ord5(iF,jF,kF-5,ex)]);
+                        else if ((k0-3)>=kminF && k0<=ex3-5)
+                            f_rhs[p] += sfz * d840dz*(+F3*fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]-F32*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F168*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F672*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F672*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F168*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+F32*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]-F3*fh[idx_fh_F_ord5(iF,jF,kF+4,ex)]);
+                        else if ((k0-2)>=kminF && k0<=ex3-4)
+                            f_rhs[p] += sfz * d60dz*(-fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]);
+                        else if ((k0-1)>=kminF && k0<=ex3-3)
+                            f_rhs[p] += sfz * d12dz*(fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]);
+                        else if (k0>=kminF && k0<=ex3-2)
+                            f_rhs[p] += sfz * d2dz*(-fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]);
+                    }
+                }
+            }
+        }
+        free(fh);
+        return;
+    }
+#else
+#error "lopsided_c.C: unsupported ghost_width (must be 2, 3, 4, or 5)"
+#endif
+}

AMSS_NCKU_source/lopsided_kodis_c.C

@@ -0,0 +1,304 @@
+#include "macrodef.h"
+#include "tool.h"
+
+/*
+ * C 版 lopsided_kodis — combined upwind advection + KO dissipation.
+ * Uses one shared symmetry_bd buffer (ord = ghost_width for both components)
+ * where a stable merged stencil is available. The 8th-order path delegates to
+ * the separate lopsided + kodis kernels, matching the original Fortran flow.
+ *
+ * FD order selection via ghost_width:
+ *   2 → 2nd-order advection + r=2 KO (cof=16, sign=-)
+ *   3 → 4th-order advection + r=3 KO (cof=64, sign=+)
+ *   4 → 6th-order advection + r=4 KO (cof=256, sign=-)
+ *   5 → 8th-order advection + r=5 KO (cof=1024, sign=+)
+ */
+void lopsided_kodis(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f, double *f_rhs,
+                    const double *Sfx, const double *Sfy, const double *Sfz,
+                    int Symmetry, const double SoA[3], double eps)
+{
+    const double ZEO = 0.0, ONE = 1.0;
+    const double TWO = 2.0, F6 = 6.0, EIT = 8.0;
+    const double F3 = 3.0, F4 = 4.0, F5 = 5.0, F10 = 10.0, F12 = 12.0, F18 = 18.0;
+    const double F9 = 9.0, F45 = 45.0, F60 = 60.0;
+    const double F2 = 2.0, F15 = 15.0, F24 = 24.0, F30 = 30.0, F35 = 35.0;
+    const double F50 = 50.0, F77 = 77.0, F80 = 80.0, F100 = 100.0, F150 = 150.0;
+    const double F32 = 32.0, F168 = 168.0, F672 = 672.0, F840 = 840.0;
+    const double F140=140.0, F378=378.0, F420=420.0, F1050=1050.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3;
+
+#if (ghost_width == 2)
+    {
+        const int ord = 2;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        double *fh = (double*)malloc(nx*ny*nz*sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d2dx = ONE/TWO/dX, d2dy = ONE/TWO/dY, d2dz = ONE/TWO/dZ;
+
+        /* ---- advection (2nd-order) ---- */
+        for (int k0 = 0; k0 <= ex3-2; ++k0) {
+            const int kF = k0+1;
+            for (int j0 = 0; j0 <= ex2-2; ++j0) {
+                const int jF = j0+1;
+                for (int i0 = 0; i0 <= ex1-2; ++i0) {
+                    const int iF = i0+1;
+                    const size_t p = idx_ex(i0,j0,k0,ex);
+
+                    const double sfx = Sfx[p];
+                    if (sfx > ZEO) {
+                        if (i0<=ex1-3) f_rhs[p] += sfx*d2dx*(-F3*fh[idx_fh_F_ord2(iF,jF,kF,ex)]+F4*fh[idx_fh_F_ord2(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord2(iF+2,jF,kF,ex)]);
+                        else if (i0<=ex1-2) f_rhs[p] += sfx*d2dx*(-fh[idx_fh_F_ord2(iF,jF,kF,ex)]+fh[idx_fh_F_ord2(iF+1,jF,kF,ex)]);
+                    } else if (sfx < ZEO) {
+                        if ((i0-1)>=iminF) f_rhs[p] -= sfx*d2dx*(-F3*fh[idx_fh_F_ord2(iF,jF,kF,ex)]+F4*fh[idx_fh_F_ord2(iF-1,jF,kF,ex)]-fh[idx_fh_F_ord2(iF-2,jF,kF,ex)]);
+                        else if (i0>=iminF) f_rhs[p] -= sfx*d2dx*(-fh[idx_fh_F_ord2(iF,jF,kF,ex)]+fh[idx_fh_F_ord2(iF-1,jF,kF,ex)]);
+                    }
+                    const double sfy = Sfy[p];
+                    if (sfy > ZEO) {
+                        if (j0<=ex2-3) f_rhs[p] += sfy*d2dy*(-F3*fh[idx_fh_F_ord2(iF,jF,kF,ex)]+F4*fh[idx_fh_F_ord2(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord2(iF,jF+2,kF,ex)]);
+                        else if (j0<=ex2-2) f_rhs[p] += sfy*d2dy*(-fh[idx_fh_F_ord2(iF,jF,kF,ex)]+fh[idx_fh_F_ord2(iF,jF+1,kF,ex)]);
+                    } else if (sfy < ZEO) {
+                        if ((j0-1)>=jminF) f_rhs[p] -= sfy*d2dy*(-F3*fh[idx_fh_F_ord2(iF,jF,kF,ex)]+F4*fh[idx_fh_F_ord2(iF,jF-1,kF,ex)]-fh[idx_fh_F_ord2(iF,jF-2,kF,ex)]);
+                        else if (j0>=jminF) f_rhs[p] -= sfy*d2dy*(-fh[idx_fh_F_ord2(iF,jF,kF,ex)]+fh[idx_fh_F_ord2(iF,jF-1,kF,ex)]);
+                    }
+                    const double sfz = Sfz[p];
+                    if (sfz > ZEO) {
+                        if (k0<=ex3-3) f_rhs[p] += sfz*d2dz*(-F3*fh[idx_fh_F_ord2(iF,jF,kF,ex)]+F4*fh[idx_fh_F_ord2(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord2(iF,jF,kF+2,ex)]);
+                        else if (k0<=ex3-2) f_rhs[p] += sfz*d2dz*(-fh[idx_fh_F_ord2(iF,jF,kF,ex)]+fh[idx_fh_F_ord2(iF,jF,kF+1,ex)]);
+                    } else if (sfz < ZEO) {
+                        if ((k0-1)>=kminF) f_rhs[p] -= sfz*d2dz*(-F3*fh[idx_fh_F_ord2(iF,jF,kF,ex)]+F4*fh[idx_fh_F_ord2(iF,jF,kF-1,ex)]-fh[idx_fh_F_ord2(iF,jF,kF-2,ex)]);
+                        else if (k0>=kminF) f_rhs[p] -= sfz*d2dz*(-fh[idx_fh_F_ord2(iF,jF,kF,ex)]+fh[idx_fh_F_ord2(iF,jF,kF-1,ex)]);
+                    }
+                }
+            }
+        }
+
+        /* ---- KO dissipation (r=2, cof=16, sign=-) ---- */
+        if (eps > ZEO) {
+            const double cof = 16.0;
+            const double F4k = 4.0, F6k = 6.0;
+            const int i0_lo = (iminF+1>0)?iminF+1:0, j0_lo=(jminF+1>0)?jminF+1:0, k0_lo=(kminF+1>0)?kminF+1:0;
+            const int i0_hi=imaxF-3, j0_hi=jmaxF-3, k0_hi=kmaxF-3;
+            if (!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)) {
+                for (int k0=k0_lo;k0<=k0_hi;++k0) { const int kF=k0+1;
+                for (int j0=j0_lo;j0<=j0_hi;++j0) { const int jF=j0+1;
+                for (int i0=i0_lo;i0<=i0_hi;++i0) { const int iF=i0+1;
+                    const size_t p=idx_ex(i0,j0,k0,ex);
+                    const double Dx=((fh[idx_fh_F_ord2(iF-2,jF,kF,ex)]+fh[idx_fh_F_ord2(iF+2,jF,kF,ex)])-F4k*(fh[idx_fh_F_ord2(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord2(iF+1,jF,kF,ex)])+F6k*fh[idx_fh_F_ord2(iF,jF,kF,ex)])/dX;
+                    const double Dy=((fh[idx_fh_F_ord2(iF,jF-2,kF,ex)]+fh[idx_fh_F_ord2(iF,jF+2,kF,ex)])-F4k*(fh[idx_fh_F_ord2(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord2(iF,jF+1,kF,ex)])+F6k*fh[idx_fh_F_ord2(iF,jF,kF,ex)])/dY;
+                    const double Dz=((fh[idx_fh_F_ord2(iF,jF,kF-2,ex)]+fh[idx_fh_F_ord2(iF,jF,kF+2,ex)])-F4k*(fh[idx_fh_F_ord2(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord2(iF,jF,kF+1,ex)])+F6k*fh[idx_fh_F_ord2(iF,jF,kF,ex)])/dZ;
+                    f_rhs[p] -= (eps/cof)*(Dx+Dy+Dz);
+                }}}
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 3)
+    /* ---- 4th-order advection + r=3 KO (original code) ----------------- */
+    {
+        const int ord = 3;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        double *fh = (double*)malloc(nx*ny*nz*sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d12dx = ONE/F12/dX, d12dy = ONE/F12/dY, d12dz = ONE/F12/dZ;
+
+        /* ---- advection ---- */
+        for (int k0 = 0; k0 <= ex3-2; ++k0) {
+            const int kF = k0+1;
+            for (int j0 = 0; j0 <= ex2-2; ++j0) {
+                const int jF = j0+1;
+                for (int i0 = 0; i0 <= ex1-2; ++i0) {
+                    const int iF = i0+1;
+                    const size_t p = idx_ex(i0,j0,k0,ex);
+
+                    const double sfx = Sfx[p];
+                    if (sfx > ZEO) {
+                        if (i0 <= ex1-4)
+                            f_rhs[p] += sfx*d12dx*(-F3*fh[idx_fh_F(iF-1,jF,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF+1,jF,kF,ex)]-F6*fh[idx_fh_F(iF+2,jF,kF,ex)]+fh[idx_fh_F(iF+3,jF,kF,ex)]);
+                        else if (i0 <= ex1-3)
+                            f_rhs[p] += sfx*d12dx*(fh[idx_fh_F(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F(iF-1,jF,kF,ex)]+EIT*fh[idx_fh_F(iF+1,jF,kF,ex)]-fh[idx_fh_F(iF+2,jF,kF,ex)]);
+                        else if (i0 <= ex1-2)
+                            f_rhs[p] -= sfx*d12dx*(-F3*fh[idx_fh_F(iF+1,jF,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF-1,jF,kF,ex)]-F6*fh[idx_fh_F(iF-2,jF,kF,ex)]+fh[idx_fh_F(iF-3,jF,kF,ex)]);
+                    } else if (sfx < ZEO) {
+                        if ((i0-2) >= iminF)
+                            f_rhs[p] -= sfx*d12dx*(-F3*fh[idx_fh_F(iF+1,jF,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF-1,jF,kF,ex)]-F6*fh[idx_fh_F(iF-2,jF,kF,ex)]+fh[idx_fh_F(iF-3,jF,kF,ex)]);
+                        else if ((i0-1) >= iminF)
+                            f_rhs[p] += sfx*d12dx*(fh[idx_fh_F(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F(iF-1,jF,kF,ex)]+EIT*fh[idx_fh_F(iF+1,jF,kF,ex)]-fh[idx_fh_F(iF+2,jF,kF,ex)]);
+                        else if (i0 >= iminF)
+                            f_rhs[p] += sfx*d12dx*(-F3*fh[idx_fh_F(iF-1,jF,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF+1,jF,kF,ex)]-F6*fh[idx_fh_F(iF+2,jF,kF,ex)]+fh[idx_fh_F(iF+3,jF,kF,ex)]);
+                    }
+                    const double sfy = Sfy[p];
+                    if (sfy > ZEO) {
+                        if (j0<=ex2-4) f_rhs[p] += sfy*d12dy*(-F3*fh[idx_fh_F(iF,jF-1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF+1,kF,ex)]-F6*fh[idx_fh_F(iF,jF+2,kF,ex)]+fh[idx_fh_F(iF,jF+3,kF,ex)]);
+                        else if (j0<=ex2-3) f_rhs[p] += sfy*d12dy*(fh[idx_fh_F(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F(iF,jF+1,kF,ex)]-fh[idx_fh_F(iF,jF+2,kF,ex)]);
+                        else if (j0<=ex2-2) f_rhs[p] -= sfy*d12dy*(-F3*fh[idx_fh_F(iF,jF+1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF-1,kF,ex)]-F6*fh[idx_fh_F(iF,jF-2,kF,ex)]+fh[idx_fh_F(iF,jF-3,kF,ex)]);
+                    } else if (sfy < ZEO) {
+                        if ((j0-2)>=jminF) f_rhs[p] -= sfy*d12dy*(-F3*fh[idx_fh_F(iF,jF+1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF-1,kF,ex)]-F6*fh[idx_fh_F(iF,jF-2,kF,ex)]+fh[idx_fh_F(iF,jF-3,kF,ex)]);
+                        else if ((j0-1)>=jminF) f_rhs[p] += sfy*d12dy*(fh[idx_fh_F(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F(iF,jF+1,kF,ex)]-fh[idx_fh_F(iF,jF+2,kF,ex)]);
+                        else if (j0>=jminF) f_rhs[p] += sfy*d12dy*(-F3*fh[idx_fh_F(iF,jF-1,kF,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF+1,kF,ex)]-F6*fh[idx_fh_F(iF,jF+2,kF,ex)]+fh[idx_fh_F(iF,jF+3,kF,ex)]);
+                    }
+                    const double sfz = Sfz[p];
+                    if (sfz > ZEO) {
+                        if (k0<=ex3-4) f_rhs[p] += sfz*d12dz*(-F3*fh[idx_fh_F(iF,jF,kF-1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF,kF+1,ex)]-F6*fh[idx_fh_F(iF,jF,kF+2,ex)]+fh[idx_fh_F(iF,jF,kF+3,ex)]);
+                        else if (k0<=ex3-3) f_rhs[p] += sfz*d12dz*(fh[idx_fh_F(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F(iF,jF,kF+1,ex)]-fh[idx_fh_F(iF,jF,kF+2,ex)]);
+                        else if (k0<=ex3-2) f_rhs[p] -= sfz*d12dz*(-F3*fh[idx_fh_F(iF,jF,kF+1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF,kF-1,ex)]-F6*fh[idx_fh_F(iF,jF,kF-2,ex)]+fh[idx_fh_F(iF,jF,kF-3,ex)]);
+                    } else if (sfz < ZEO) {
+                        if ((k0-2)>=kminF) f_rhs[p] -= sfz*d12dz*(-F3*fh[idx_fh_F(iF,jF,kF+1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF,kF-1,ex)]-F6*fh[idx_fh_F(iF,jF,kF-2,ex)]+fh[idx_fh_F(iF,jF,kF-3,ex)]);
+                        else if ((k0-1)>=kminF) f_rhs[p] += sfz*d12dz*(fh[idx_fh_F(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F(iF,jF,kF+1,ex)]-fh[idx_fh_F(iF,jF,kF+2,ex)]);
+                        else if (k0>=kminF) f_rhs[p] += sfz*d12dz*(-F3*fh[idx_fh_F(iF,jF,kF-1,ex)]-F10*fh[idx_fh_F(iF,jF,kF,ex)]+F18*fh[idx_fh_F(iF,jF,kF+1,ex)]-F6*fh[idx_fh_F(iF,jF,kF+2,ex)]+fh[idx_fh_F(iF,jF,kF+3,ex)]);
+                    }
+                }
+            }
+        }
+
+        /* ---- KO dissipation (r=3, cof=64, sign=+) ---- */
+        if (eps > ZEO) {
+            const double cof = 64.0;
+            const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
+            const int i0_lo=(iminF+2>0)?iminF+2:0, j0_lo=(jminF+2>0)?jminF+2:0, k0_lo=(kminF+2>0)?kminF+2:0;
+            const int i0_hi=imaxF-4, j0_hi=jmaxF-4, k0_hi=kmaxF-4;
+            if (!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)) {
+                for (int k0=k0_lo;k0<=k0_hi;++k0) { const int kF=k0+1;
+                for (int j0=j0_lo;j0<=j0_hi;++j0) { const int jF=j0+1;
+                for (int i0=i0_lo;i0<=i0_hi;++i0) { const int iF=i0+1;
+                    const size_t p=idx_ex(i0,j0,k0,ex);
+                    const double Dx=((fh[idx_fh_F(iF-3,jF,kF,ex)]+fh[idx_fh_F(iF+3,jF,kF,ex)])-SIX*(fh[idx_fh_F(iF-2,jF,kF,ex)]+fh[idx_fh_F(iF+2,jF,kF,ex)])+FIT*(fh[idx_fh_F(iF-1,jF,kF,ex)]+fh[idx_fh_F(iF+1,jF,kF,ex)])-TWT*fh[idx_fh_F(iF,jF,kF,ex)])/dX;
+                    const double Dy=((fh[idx_fh_F(iF,jF-3,kF,ex)]+fh[idx_fh_F(iF,jF+3,kF,ex)])-SIX*(fh[idx_fh_F(iF,jF-2,kF,ex)]+fh[idx_fh_F(iF,jF+2,kF,ex)])+FIT*(fh[idx_fh_F(iF,jF-1,kF,ex)]+fh[idx_fh_F(iF,jF+1,kF,ex)])-TWT*fh[idx_fh_F(iF,jF,kF,ex)])/dY;
+                    const double Dz=((fh[idx_fh_F(iF,jF,kF-3,ex)]+fh[idx_fh_F(iF,jF,kF+3,ex)])-SIX*(fh[idx_fh_F(iF,jF,kF-2,ex)]+fh[idx_fh_F(iF,jF,kF+2,ex)])+FIT*(fh[idx_fh_F(iF,jF,kF-1,ex)]+fh[idx_fh_F(iF,jF,kF+1,ex)])-TWT*fh[idx_fh_F(iF,jF,kF,ex)])/dZ;
+                    f_rhs[p] += (eps/cof)*(Dx+Dy+Dz);
+                }}}
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 4)
+    {
+        const int ord = 4;
+        int iminF = 1, jminF = 1, kminF = 1;
+        if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -3;
+        if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -3;
+
+        const size_t nx = (size_t)ex1 + ord;
+        const size_t ny = (size_t)ex2 + ord;
+        const size_t nz = (size_t)ex3 + ord;
+        double *fh = (double*)malloc(nx*ny*nz*sizeof(double));
+        if (!fh) return;
+        symmetry_bd(ord, ex, f, fh, SoA);
+
+        const double d60dx=ONE/F60/dX, d60dy=ONE/F60/dY, d60dz=ONE/F60/dZ;
+        const double d12dx=ONE/F12/dX, d12dy=ONE/F12/dY, d12dz=ONE/F12/dZ;
+        const double d2dx=ONE/TWO/dX, d2dy=ONE/TWO/dY, d2dz=ONE/TWO/dZ;
+
+        /* ---- advection (6th-order lopsided) ---- */
+        for (int k0=0;k0<=ex3-2;++k0) { const int kF=k0+1;
+        for (int j0=0;j0<=ex2-2;++j0) { const int jF=j0+1;
+        for (int i0=0;i0<=ex1-2;++i0) { const int iF=i0+1;
+            const size_t p=idx_ex(i0,j0,k0,ex);
+            /* x */
+            const double sfx=Sfx[p];
+            if (sfx>ZEO) {
+                if (i0<=ex1-5&&(i0-1)>=iminF) f_rhs[p]+=sfx*d60dx*(+F2*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-F24*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F30*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]-fh[idx_fh_F_ord4(iF+4,jF,kF,ex)]);
+                else if (i0<=ex1-6&&i0>=iminF) f_rhs[p]+=sfx*d60dx*(-F10*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F100*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+F50*fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]-F15*fh[idx_fh_F_ord4(iF+4,jF,kF,ex)]+F2*fh[idx_fh_F_ord4(iF+5,jF,kF,ex)]);
+                else if (i0<=ex1-4&&(i0-2)>=iminF) f_rhs[p]+=sfx*d60dx*(-fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-F45*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F9*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]);
+                else if (i0<=ex1-3&&(i0-1)>=iminF) f_rhs[p]+=sfx*d12dx*(fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]);
+                else if (i0<=ex1-2&&i0>=iminF) f_rhs[p]+=sfx*d2dx*(-fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]);
+            } else if (sfx<ZEO) {
+                if ((i0-3)>=iminF&&i0<=ex1-3) f_rhs[p]-=sfx*d60dx*(+F2*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]-F24*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]-F30*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]-fh[idx_fh_F_ord4(iF-4,jF,kF,ex)]);
+                else if ((i0-4)>=iminF&&i0<=ex1-2) f_rhs[p]-=sfx*d60dx*(-F10*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]-F100*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]+F50*fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]-F15*fh[idx_fh_F_ord4(iF-4,jF,kF,ex)]+F2*fh[idx_fh_F_ord4(iF-5,jF,kF,ex)]);
+                else if ((i0-2)>=iminF&&i0<=ex1-4) f_rhs[p]+=sfx*d60dx*(-fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-F45*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-F9*fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+3,jF,kF,ex)]);
+                else if ((i0-1)>=iminF&&i0<=ex1-3) f_rhs[p]+=sfx*d12dx*(fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord4(iF+2,jF,kF,ex)]);
+                else if (i0>=iminF&&i0<=ex1-2) f_rhs[p]+=sfx*d2dx*(-fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+1,jF,kF,ex)]);
+            }
+            /* y */
+            const double sfy=Sfy[p];
+            if (sfy>ZEO) {
+                if (j0<=ex2-5&&(j0-1)>=jminF) f_rhs[p]+=sfy*d60dy*(F2*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-F24*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F30*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]-fh[idx_fh_F_ord4(iF,jF+4,kF,ex)]);
+                else if (j0<=ex2-6&&j0>=jminF) f_rhs[p]+=sfy*d60dy*(-F10*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F100*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+F50*fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]-F15*fh[idx_fh_F_ord4(iF,jF+4,kF,ex)]+F2*fh[idx_fh_F_ord4(iF,jF+5,kF,ex)]);
+                else if (j0<=ex2-4&&(j0-2)>=jminF) f_rhs[p]+=sfy*d60dy*(-fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]);
+                else if (j0<=ex2-3&&(j0-1)>=jminF) f_rhs[p]+=sfy*d12dy*(fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]);
+                else if (j0<=ex2-2&&j0>=jminF) f_rhs[p]+=sfy*d2dy*(-fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]);
+            } else if (sfy<ZEO) {
+                if ((j0-3)>=jminF&&j0<=ex2-3) f_rhs[p]-=sfy*d60dy*(F2*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]-F24*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F30*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]-fh[idx_fh_F_ord4(iF,jF-4,kF,ex)]);
+                else if ((j0-4)>=jminF&&j0<=ex2-2) f_rhs[p]-=sfy*d60dy*(-F10*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]-F100*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]+F50*fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]-F15*fh[idx_fh_F_ord4(iF,jF-4,kF,ex)]+F2*fh[idx_fh_F_ord4(iF,jF-5,kF,ex)]);
+                else if ((j0-2)>=jminF&&j0<=ex2-4) f_rhs[p]+=sfy*d60dy*(-fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+3,kF,ex)]);
+                else if ((j0-1)>=jminF&&j0<=ex2-3) f_rhs[p]+=sfy*d12dy*(fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord4(iF,jF+2,kF,ex)]);
+                else if (j0>=jminF&&j0<=ex2-2) f_rhs[p]+=sfy*d2dy*(-fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+1,kF,ex)]);
+            }
+            /* z */
+            const double sfz=Sfz[p];
+            if (sfz>ZEO) {
+                if (k0<=ex3-5&&(k0-1)>=kminF) f_rhs[p]+=sfz*d60dz*(F2*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-F24*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F30*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]-fh[idx_fh_F_ord4(iF,jF,kF+4,ex)]);
+                else if (k0<=ex3-6&&k0>=kminF) f_rhs[p]+=sfz*d60dz*(-F10*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F100*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+F50*fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]-F15*fh[idx_fh_F_ord4(iF,jF,kF+4,ex)]+F2*fh[idx_fh_F_ord4(iF,jF,kF+5,ex)]);
+                else if (k0<=ex3-4&&(k0-2)>=kminF) f_rhs[p]+=sfz*d60dz*(-fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]);
+                else if (k0<=ex3-3&&(k0-1)>=kminF) f_rhs[p]+=sfz*d12dz*(fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]);
+                else if (k0<=ex3-2&&k0>=kminF) f_rhs[p]+=sfz*d2dz*(-fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]);
+            } else if (sfz<ZEO) {
+                if ((k0-3)>=kminF&&k0<=ex3-3) f_rhs[p]-=sfz*d60dz*(F2*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]-F24*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F35*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F80*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F30*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]-fh[idx_fh_F_ord4(iF,jF,kF-4,ex)]);
+                else if ((k0-4)>=kminF&&k0<=ex3-2) f_rhs[p]-=sfz*d60dz*(-F10*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F77*fh[idx_fh_F_ord4(iF,jF,kF,ex)]+F150*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]-F100*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]+F50*fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]-F15*fh[idx_fh_F_ord4(iF,jF,kF-4,ex)]+F2*fh[idx_fh_F_ord4(iF,jF,kF-5,ex)]);
+                else if ((k0-2)>=kminF&&k0<=ex3-4) f_rhs[p]+=sfz*d60dz*(-fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+3,ex)]);
+                else if ((k0-1)>=kminF&&k0<=ex3-3) f_rhs[p]+=sfz*d12dz*(fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord4(iF,jF,kF+2,ex)]);
+                else if (k0>=kminF&&k0<=ex3-2) f_rhs[p]+=sfz*d2dz*(-fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+1,ex)]);
+            }
+        }}}
+
+        /* ---- KO dissipation (r=4, cof=256, sign=-) ---- */
+        if (eps > ZEO) {
+            const double cof = 256.0;
+            const double F8k = 8.0, F28 = 28.0, F56 = 56.0, F70 = 70.0;
+            const int i0_lo=(iminF+3>0)?iminF+3:0, j0_lo=(jminF+3>0)?jminF+3:0, k0_lo=(kminF+3>0)?kminF+3:0;
+            const int i0_hi=imaxF-5, j0_hi=jmaxF-5, k0_hi=kmaxF-5;
+            if (!(i0_lo>i0_hi||j0_lo>j0_hi||k0_lo>k0_hi)) {
+                for (int k0=k0_lo;k0<=k0_hi;++k0) { const int kF=k0+1;
+                for (int j0=j0_lo;j0<=j0_hi;++j0) { const int jF=j0+1;
+                for (int i0=i0_lo;i0<=i0_hi;++i0) { const int iF=i0+1;
+                    const size_t p=idx_ex(i0,j0,k0,ex);
+                    const double Dx=((fh[idx_fh_F_ord4(iF-4,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+4,jF,kF,ex)])-F8k*(fh[idx_fh_F_ord4(iF-3,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+3,jF,kF,ex)])+F28*(fh[idx_fh_F_ord4(iF-2,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+2,jF,kF,ex)])-F56*(fh[idx_fh_F_ord4(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord4(iF+1,jF,kF,ex)])+F70*fh[idx_fh_F_ord4(iF,jF,kF,ex)])/dX;
+                    const double Dy=((fh[idx_fh_F_ord4(iF,jF-4,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+4,kF,ex)])-F8k*(fh[idx_fh_F_ord4(iF,jF-3,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+3,kF,ex)])+F28*(fh[idx_fh_F_ord4(iF,jF-2,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+2,kF,ex)])-F56*(fh[idx_fh_F_ord4(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord4(iF,jF+1,kF,ex)])+F70*fh[idx_fh_F_ord4(iF,jF,kF,ex)])/dY;
+                    const double Dz=((fh[idx_fh_F_ord4(iF,jF,kF-4,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+4,ex)])-F8k*(fh[idx_fh_F_ord4(iF,jF,kF-3,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+3,ex)])+F28*(fh[idx_fh_F_ord4(iF,jF,kF-2,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+2,ex)])-F56*(fh[idx_fh_F_ord4(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord4(iF,jF,kF+1,ex)])+F70*fh[idx_fh_F_ord4(iF,jF,kF,ex)])/dZ;
+                    f_rhs[p] -= (eps/cof)*(Dx+Dy+Dz);
+                }}}
+            }
+        }
+        free(fh);
+        return;
+    }
+#elif (ghost_width == 5)
+    {
+        lopsided(ex, X, Y, Z, f, f_rhs, Sfx, Sfy, Sfz, Symmetry, SoA);
+        if (eps > ZEO) kodis(ex, X, Y, Z, f, f_rhs, SoA, Symmetry, eps);
+        return;
+    }
+#else
+#error "lopsided_kodis_c.C: unsupported ghost_width (must be 2, 3, 4, or 5)"
+#endif
+}

AMSS_NCKU_source/lopsidediff.f90

@@ -7,7 +7,163 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 
+#if (ghost_width == 2)
+! second order code
 
+!-----------------------------------------------------------------------------
+!         v
+! D f = ------[ - 3 f  + 4 f   - f     ]
+!  i     2dx         i      i+v   i+2v
+!
+! where
+!
+!        i
+!      |B |
+! v = -----
+!        i
+!       B
+!
+!-----------------------------------------------------------------------------
+subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
+  implicit none
+
+!~~~~~~> Input parameters:
+
+  integer, intent(in)  :: ex(1:3),Symmetry
+  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+  real*8,dimension(3),intent(in) ::SoA
+
+!~~~~~~> local variables:
+! note index -1,0, so we have 2 extra points
+  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: dX,dY,dZ
+  real*8 :: d2dx,d2dy,d2dz
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0,TWO=2.d0,THR=3.d0,FOUR=4.d0
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
+
+  call symmetry_bd(2,ex,f,fh,SoA)
+
+! upper bound set ex-1 only for efficiency, 
+! the loop body will set ex 0 also
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+! x direction   
+    if(Sfx(i,j,k) >= ZEO)then
+       if( i+2 <= imax .and. i >= imin)then
+!         v
+! D f = ------[ - 3 f  + 4 f   - f     ]
+!  i     2dx         i      i+v   i+2v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
+                  Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i+1,j,k)-fh(i+2,j,k))
+       elseif(i+1 <= imax .and. i >= imin)then
+!         v
+! D f = ------[ - f  + f   ]
+!  i      dx       i    i+v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
+                  Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i+1,j,k))
+
+       endif
+
+    elseif(Sfx(i,j,k) <= ZEO)then
+      if( i-2 >= imin .and. i <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
+                  Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i-1,j,k)-fh(i-2,j,k))
+      elseif(i-1 >= imin .and. i <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
+                  Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i-1,j,k))
+      endif
+
+! set imax and imin 0
+    endif
+
+! y direction   
+    if(Sfy(i,j,k) >= ZEO)then
+       if( j+2 <= jmax .and. j >= jmin)then
+!         v
+! D f = ------[ - 3 f  + 4 f   - f     ]
+!  i     2dx         i      i+v   i+2v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
+                  Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j+1,k)-fh(i,j+2,k))
+       elseif(j+1 <= jmax .and. j >= jmin)then
+!         v
+! D f = ------[ - f  + f   ]
+!  i      dx       i    i+v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
+                  Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j+1,k))
+       endif
+
+    elseif(Sfy(i,j,k) <= ZEO)then
+      if( j-2 >= jmin .and. j <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
+                  Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j-1,k)-fh(i,j-2,k))
+      elseif(j-1 >= jmin .and. j <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
+                  Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j-1,k))
+      endif
+
+! set jmin and jmax 0
+     endif
+!! z direction   
+    if(Sfz(i,j,k) >= ZEO)then
+      if( k+2 <= kmax .and. k >= kmin)then
+!         v
+! D f = ------[ - 3 f  + 4 f   - f     ]
+!  i     2dx         i      i+v   i+2v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
+                  Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k+1)-fh(i,j,k+2))
+       elseif(k+1 <= kmax .and. k >= kmin)then
+!         v
+! D f = ------[ - f  + f   ]
+!  i      dx       i    i+v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
+                  Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k+1))
+       endif
+
+    elseif(Sfz(i,j,k) <= ZEO)then
+      if( k-2 >= kmin .and. k <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
+                  Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k-1)-fh(i,j,k-2))
+      elseif(k-1 >= kmin .and. k <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
+                  Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k-1))
+      endif
+
+! set kmin and kmax 0
+     endif
+
+  enddo
+  enddo
+  enddo
+
+  return
+
+  end subroutine lopsided
+
+#elif (ghost_width == 3)
 ! fourth order code
 
 !-----------------------------------------------------------------------------
@@ -80,7 +236,89 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
+#if 0  
+!! old code
+! x direction   
+    if(Sfx(i,j,k) >= ZEO .and. i+3 <= imax .and. i-1 >= imin)then
+!         v
+! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+!  i     12dx       i-v      i      i+v     i+2v    i+3v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
 
+    elseif(Sfx(i,j,k) <= ZEO .and. i-3 >= imin .and. i+1 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+
+     elseif(i+2 <= imax .and. i-2 >= imin)then
+!
+!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+!  fx(i) = ---------------------------------------------
+!                             12 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i+1 <= imax .and. i-1 >= imin)then
+!
+!              - f(i-1) + f(i+1)
+!  fx(i) = --------------------------------
+!                     2 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+
+! set imax and imin 0
+    endif
+
+! y direction   
+    if(Sfy(i,j,k) >= ZEO .and. j+3 <= jmax .and. j-1 >= jmin)then
+!         v
+! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+!  i     12dx       i-v      i      i+v     i+2v    i+3v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+
+    elseif(Sfy(i,j,k) <= ZEO .and. j-3 >= jmin .and. j+1 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+
+     elseif(j+2 <= jmax .and. j-2 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j+1 <= jmax .and. j-1 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+! set jmin and jmax 0
+     endif
+!! z direction   
+    if(Sfz(i,j,k) >= ZEO .and. k+3 <= kmax .and. k-1 >= kmin)then
+!         v
+! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+!  i     12dx       i-v      i      i+v     i+2v    i+3v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+
+    elseif(Sfz(i,j,k) <= ZEO .and. k-3 >= kmin .and. k+1 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+
+     elseif(k+2 <= kmax .and. k-2 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k+1 <= kmax .and. k-1 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+! set kmin and kmax 0
+     endif
+#else
 !! new code, 2012dec27, based on bam
 ! x direction   
     if(Sfx(i,j,k) > ZEO)then
@@ -240,6 +478,7 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 ! set kmax and kmin 0
      endif
    endif
+#endif
   enddo
   enddo
   enddo
@@ -247,3 +486,612 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
   return
 
   end subroutine lopsided
+
+!-----------------------------------------------------------------------------
+! Combined advection (lopsided) + Kreiss-Oliger dissipation (kodis)
+! Shares the symmetry_bd buffer fh, eliminating one full-grid copy per call.
+! Mathematically identical to calling lopsided then kodis separately.
+!-----------------------------------------------------------------------------
+subroutine lopsided_kodis(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,eps)
+  implicit none
+
+!~~~~~~> Input parameters:
+
+  integer, intent(in)  :: ex(1:3),Symmetry
+  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+  real*8,dimension(3),intent(in) ::SoA
+  real*8,intent(in) :: eps
+
+!~~~~~~> local variables:
+! note index -2,-1,0, so we have 3 extra points
+  real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: dX,dY,dZ
+  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
+  real*8,  parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
+  real*8,  parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+! kodis parameters
+  real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
+  real*8, parameter :: cof=6.4d1   ! 2^6
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
+
+! Single symmetry_bd call shared by both advection and dissipation
+  call symmetry_bd(3,ex,f,fh,SoA)
+
+! ---- Advection (lopsided) loop ----
+! upper bound set ex-1 only for efficiency, 
+! the loop body will set ex 0 also
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+! x direction   
+    if(Sfx(i,j,k) > ZEO)then
+      if(i+3 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+     elseif(i+2 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i+1 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+     endif
+   elseif(Sfx(i,j,k) < ZEO)then
+      if(i-3 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+     elseif(i-2 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i-1 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+     endif
+   endif
+
+! y direction   
+    if(Sfy(i,j,k) > ZEO)then
+      if(j+3 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+     elseif(j+2 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j+1 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+     endif
+   elseif(Sfy(i,j,k) < ZEO)then
+      if(j-3 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+     elseif(j-2 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j-1 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+     endif
+   endif
+
+! z direction   
+    if(Sfz(i,j,k) > ZEO)then
+      if(k+3 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+     elseif(k+2 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k+1 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+     endif
+   elseif(Sfz(i,j,k) < ZEO)then
+      if(k-3 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+     elseif(k-2 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k-1 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+     endif
+   endif
+  enddo
+  enddo
+  enddo
+
+! ---- Dissipation (kodis) loop ----
+  if(eps > ZEO) then
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+
+  if(i-3 >= imin .and. i+3 <= imax .and. &
+     j-3 >= jmin .and. j+3 <= jmax .and. &
+     k-3 >= kmin .and. k+3 <= kmax) then
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
+                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
+                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
+                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
+                          TWT* fh(i,j,k)            )/dX + &
+                                                  (     &
+                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
+                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
+                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
+                          TWT* fh(i,j,k)            )/dY + &
+                                                  (     &
+                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
+                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
+                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
+                          TWT* fh(i,j,k)            )/dZ )
+  endif
+
+  enddo
+  enddo
+  enddo
+  endif
+
+  return
+
+  end subroutine lopsided_kodis
+
+#elif (ghost_width == 4)
+! sixth order code
+! Compute advection terms in right hand sides of field equations
+!         v
+! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
+!  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
+!
+! where
+!
+!        i
+!      |B |
+! v = -----
+!        i
+!       B
+!
+!-----------------------------------------------------------------------------
+subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
+  implicit none
+
+!~~~~~~> Input parameters:
+
+  integer, intent(in)  :: ex(1:3),Symmetry
+  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+  real*8,dimension(3),intent(in) ::SoA
+
+!~~~~~~> local variables:
+
+  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: dX,dY,dZ
+  real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
+  real*8,  parameter :: TWO=2.d0,F24=2.4d1,F35=3.5d1,F80=8.d1,F30=3.d1,EIT=8.d0
+  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1
+  real*8,  parameter ::  F10=1.d1,F77=7.7d1,F150=1.5d2,F100=1.d2,F50=5.d1,F15=1.5d1
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  d60dx = ONE/F60/dX
+  d60dy = ONE/F60/dY
+  d60dz = ONE/F60/dZ
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
+
+  call symmetry_bd(4,ex,f,fh,SoA)
+
+! upper bound set ex-1 only for efficiency, 
+! the loop body will set ex 0 also
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+! x direction   
+    if(Sfx(i,j,k) >= ZEO .and. i+4 <= imax .and. i-2 >= imin)then
+!         v
+! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
+!  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                             &
+                  Sfx(i,j,k)*d60dx*(TWO*fh(i-2,j,k)-F24*fh(i-1,j,k)-F35*fh(i,j,k)+F80*fh(i+1,j,k) &
+                                   -F30*fh(i+2,j,k)+EIT*fh(i+3,j,k)-    fh(i+4,j,k))
+    elseif(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-1 >= imin)then
+!         v
+! D f = ------[-10f    - 77f  + 150f    - 100f     + 50f     -15f     + 2f    ]
+!  i     60dx      i-v      i       i+v       i+2v      i+3v     i+4v    i+5v
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
+                  Sfx(i,j,k)*d60dx*(-F10*fh(i-1,j,k)-F77*fh(i  ,j,k)+F150*fh(i+1,j,k)-F100*fh(i+2,j,k) &
+                                    +F50*fh(i+3,j,k)-F15*fh(i+4,j,k)+ TWO*fh(i+5,j,k))
+
+    elseif(Sfx(i,j,k) <= ZEO .and. i-4 >= imin .and. i+2 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
+                  Sfx(i,j,k)*d60dx*(TWO*fh(i+2,j,k)-F24*fh(i+1,j,k)-F35*fh(i,j,k)+F80*fh(i-1,j,k) &
+                                   -F30*fh(i-2,j,k)+EIT*fh(i-3,j,k)-    fh(i-4,j,k))
+    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+1 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
+                  Sfx(i,j,k)*d60dx*(-F10*fh(i+1,j,k)-F77*fh(i  ,j,k)+F150*fh(i-1,j,k)-F100*fh(i-2,j,k) &
+                                    +F50*fh(i-3,j,k)-F15*fh(i-4,j,k)+ TWO*fh(i-5,j,k))
+
+     elseif(i+3 <= imax .and. i-3 >= imin)then
+!           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
+!  fx(i) = -----------------------------------------------------------------
+!                                        60 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
+                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
+
+     elseif(i+2 <= imax .and. i-2 >= imin)then
+!
+!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+!  fx(i) = ---------------------------------------------
+!                             12 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i+1 <= imax .and. i-1 >= imin)then
+!
+!              - f(i-1) + f(i+1)
+!  fx(i) = --------------------------------
+!                     2 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+
+! set imax and imin 0
+    endif
+
+! y direction   
+     if(Sfy(i,j,k) >= ZEO .and. j+4 <= jmax .and. j-2 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
+                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j-2,k)-F24*fh(i,j-1,k)-F35*fh(i,j,k)+F80*fh(i,j+1,k) &
+                                   -F30*fh(i,j+2,k)+EIT*fh(i,j+3,k)-    fh(i,j+4,k))
+     elseif(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-1 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
+                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j-1,k)-F77*fh(i,j  ,k)+F150*fh(i,j+1,k)-F100*fh(i,j+2,k) &
+                                    +F50*fh(i,j+3,k)-F15*fh(i,j+4,k)+ TWO*fh(i,j+5,k))
+
+     elseif(Sfy(i,j,k) <= ZEO .and. j-4 >= jmin .and. j+2 <= jmax)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
+                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j+2,k)-F24*fh(i,j+1,k)-F35*fh(i,j,k)+F80*fh(i,j-1,k) &
+                                   -F30*fh(i,j-2,k)+EIT*fh(i,j-3,k)-    fh(i,j-4,k))
+
+     elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+1 <= jmax)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
+                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j+1,k)-F77*fh(i,j  ,k)+F150*fh(i,j-1,k)-F100*fh(i,j-2,k) &
+                                    +F50*fh(i,j-3,k)-F15*fh(i,j-4,k)+ TWO*fh(i,j-5,k))
+
+     elseif(j+3 <= jmax .and. j-3 >= jmin)then
+          
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
+                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
+
+     elseif(j+2 <= jmax .and. j-2 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j+1 <= jmax .and. j-1 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+! set jmin and jmax 0
+     endif
+!! z direction   
+     if(Sfz(i,j,k) >= ZEO .and. k+4 <= kmax .and. k-2 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
+                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k-2)-F24*fh(i,j,k-1)-F35*fh(i,j,k)+F80*fh(i,j,k+1) &
+                                   -F30*fh(i,j,k+2)+EIT*fh(i,j,k+3)-    fh(i,j,k+4))
+     elseif(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-1 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
+                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k-1)-F77*fh(i,j,k  )+F150*fh(i,j,k+1)-F100*fh(i,j,k+2) &
+                                    +F50*fh(i,j,k+3)-F15*fh(i,j,k+4)+ TWO*fh(i,j,k+5))
+
+     elseif(Sfz(i,j,k) <= ZEO .and. k-4 >= kmin .and. k+2 <= kmax)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
+                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k+2)-F24*fh(i,j,k+1)-F35*fh(i,j,k)+F80*fh(i,j,k-1) &
+                                   -F30*fh(i,j,k-2)+EIT*fh(i,j,k-3)-    fh(i,j,k-4))
+
+     elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+1 <= kmax)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
+                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k+1)-F77*fh(i,j,k  )+F150*fh(i,j,k-1)-F100*fh(i,j,k-2) &
+                                    +F50*fh(i,j,k-3)-F15*fh(i,j,k-4)+ TWO*fh(i,j,k-5))
+     
+     elseif(k+3 <= kmax .and. k-3 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
+                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
+
+     elseif(k+2 <= kmax .and. k-2 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k+1 <= kmax .and. k-1 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+! set kmin and kmax 0
+     endif
+
+  enddo
+  enddo
+  enddo
+
+  return
+
+  end subroutine lopsided
+
+#elif (ghost_width == 5)
+! eighth order code
+!-----------------------------------------------------------------------------
+! PRD 77, 024034 (2008)
+! Compute advection terms in right hand sides of field equations
+!        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
+! D f = --------------------------------------------------------------------------------------------------------------------------
+!  i                                                             840 dx           
+!
+! where
+!
+!        i
+!      |B |
+! v = -----
+!        i
+!       B
+!
+!-----------------------------------------------------------------------------
+subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
+  implicit none
+
+!~~~~~~> Input parameters:
+
+  integer, intent(in)  :: ex(1:3),Symmetry
+  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+  real*8,dimension(3),intent(in) ::SoA
+
+!~~~~~~> local variables:
+
+  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: dX,dY,dZ
+  real*8 :: d840dx,d840dy,d840dz,d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
+  real*8,  parameter :: TWO=2.d0,F30=3.d1,EIT=8.d0
+  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1,F140=1.4d2,THR=3.d0
+  real*8,  parameter :: F840=8.4d2,F5=5.d0,F420=4.2d2,F378=3.78d2,F1050=1.05d3
+  real*8,  parameter :: F32=3.2d1,F168=1.68d2,F672=6.72d2
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  d840dx = ONE/F840/dX
+  d840dy = ONE/F840/dY
+  d840dz = ONE/F840/dZ
+
+  d60dx = ONE/F60/dX
+  d60dy = ONE/F60/dY
+  d60dz = ONE/F60/dZ
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
+
+  call symmetry_bd(5,ex,f,fh,SoA)
+
+! upper bound set ex-1 only for efficiency, 
+! the loop body will set ex 0 also
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+! x direction   
+    if(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-3 >= imin)then
+!        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
+! D f = --------------------------------------------------------------------------------------------------------------------------
+!  i                                                             840 dx    
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
+                  Sfx(i,j,k)*d840dx*(-F5*fh(i-3,j,k)+F60 *fh(i-2,j,k)-F420*fh(i-1,j,k)-F378*fh(i  ,j,k) &
+                                  +F1050*fh(i+1,j,k)-F420*fh(i+2,j,k)+F140*fh(i+3,j,k)-F30 *fh(i+4,j,k)+THR*fh(i+5,j,k))
+
+    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+3 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                          &
+                  Sfx(i,j,k)*d840dx*(-F5*fh(i+3,j,k)+F60 *fh(i+2,j,k)-F420*fh(i+1,j,k)-F378*fh(i   ,j,k) &
+                                  +F1050*fh(i-1,j,k)-F420*fh(i-2,j,k)+F140*fh(i-3,j,k)- F30*fh(i-4,j,k)+THR*fh(i-5,j,k))
+
+    elseif(i+4 <= imax .and. i-4 >= imin)then
+!           3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
+!  fx(i) = -------------------------------------------------------------------------------------------------
+!                                                        840 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
+                  Sfx(i,j,k)*d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+    &
+                                     F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
+
+     elseif(i+3 <= imax .and. i-3 >= imin)then
+!           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
+!  fx(i) = -----------------------------------------------------------------
+!                                        60 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
+                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
+
+     elseif(i+2 <= imax .and. i-2 >= imin)then
+!
+!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+!  fx(i) = ---------------------------------------------
+!                             12 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i+1 <= imax .and. i-1 >= imin)then
+!
+!              - f(i-1) + f(i+1)
+!  fx(i) = --------------------------------
+!                     2 dx
+     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+
+! set imax and imin 0
+    endif
+
+! y direction   
+    if(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-3 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
+                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j-3,k)+F60 *fh(i,j-2,k)-F420*fh(i,j-1,k)-F378*fh(i,j  ,k) &
+                                  +F1050*fh(i,j+1,k)-F420*fh(i,j+2,k)+F140*fh(i,j+3,k)-F30 *fh(i,j+4,k)+THR*fh(i,j+5,k))
+
+    elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+3 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
+                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j+3,k)+F60 *fh(i,j+2,k)-F420*fh(i,j+1,k)-F378*fh(i,j  ,k) &
+                                  +F1050*fh(i,j-1,k)-F420*fh(i,j-2,k)+F140*fh(i,j-3,k)- F30*fh(i,j-4,k)+THR*fh(i,j-5,k))
+
+    elseif(j+4 <= jmax .and. j-4 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
+                  Sfy(i,j,k)*d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+    &
+                                     F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
+
+     elseif(j+3 <= jmax .and. j-3 >= jmin)then
+          
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
+                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
+
+     elseif(j+2 <= jmax .and. j-2 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j+1 <= jmax .and. j-1 >= jmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+! set jmin and jmax 0
+     endif
+!! z direction   
+    if(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-3 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
+                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k-3)+F60 *fh(i,j,k-2)-F420*fh(i,j,k-1)-F378*fh(i,j,k  ) &
+                                  +F1050*fh(i,j,k+1)-F420*fh(i,j,k+2)+F140*fh(i,j,k+3)-F30 *fh(i,j,k+4)+THR*fh(i,j,k+5))
+
+    elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+3 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
+                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k+3)+F60 *fh(i,j,k+2)-F420*fh(i,j,k+1)-F378*fh(i,j,k  ) &
+                                  +F1050*fh(i,j,k-1)-F420*fh(i,j,k-2)+F140*fh(i,j,k-3)- F30*fh(i,j,k-4)+THR*fh(i,j,k-5))
+
+    elseif(k+4 <= kmax .and. k-4 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
+                  Sfz(i,j,k)*d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+    &
+                                     F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
+     
+     elseif(k+3 <= kmax .and. k-3 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
+                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
+
+     elseif(k+2 <= kmax .and. k-2 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k+1 <= kmax .and. k-1 >= kmin)then
+
+     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+! set kmin and kmax 0
+     endif
+
+  enddo
+  enddo
+  enddo
+
+  return
+
+  end subroutine lopsided
+
+#endif  

AMSS_NCKU_source/macrodef.fh

@@ -1,83 +1,77 @@
-
-
-#if 0
-note here
-v:r; u: phi; w: theta
-tetradtype 0
-v^a = (x,y,z)
-orthonormal order: v,u,w
-m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
-tetradtype 1
-orthonormal order: w,u,v
-m = (theta + i phi)/sqrt(2) following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)
-tetradtype 2
-v_a = (x,y,z)
-orthonormal order: v,u,w
-m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
-#endif
-#define tetradtype 2
-
-#if 0
-note here
-Cell center or Vertex center
-#endif
-#define Cell
-
-#if 0
-note here
-2nd order: 2
-4th order: 3
-6th order: 4
-8th order: 5
-#endif
-#define ghost_width 3
-
-#if 0
-note here
-use shell or not
-#endif
-#define WithShell
-
-#if 0
-note here
-use constraint preserving boundary condition or not
-only affect Z4c
-#endif
-#define CPBC
-
-#if 0
-note here
-Gauge condition type
-0: B^i gauge
-1: David's puncture gauge
-2: MB B^i gauge
-3: RIT B^i gauge
-4: MB beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
-5: RIT beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
-6: MGB1 B^i gauge
-7: MGB2 B^i gauge
-#endif
-#define GAUGE 2
-
-#if 0
-buffer points for CPBC boundary
-#endif
-#define CPBC_ghost_width  (ghost_width)
-
-#if 0
-using BSSN variable for constraint violation and psi4 calculation: 0
-using ADM variable for constraint violation and psi4 calculation: 1
-#endif
-#define ABV 0
-
-#if 0
-Type of Potential and Scalar Distribution in F(R) Scalar-Tensor Theory
-1: Case C of 1112.3928, V=0
-2: shell with a2^2*phi0/(1+a2^2), f(R) = R+a2*R^2 induced V
-3: ground state of Schrodinger-Newton system, f(R) = R+a2*R^2 induced V
-4: a2 = oo and phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma) - tanh((r-r0)/sigma) )
-5: shell with phi(r) = phi0*Exp(-(r-r0)**2/sigma), V = 0
-#endif
-#define EScalar_CC 2
-
-
+
+#define tetradtype 2
+
+#define Cell
+
+#define ghost_width 3
+
+
+
+#define GAUGE 0
+
+#define CPBC_ghost_width  (ghost_width)
+
+#define ABV 0
+
+#define EScalar_CC 2
+
+#if 0
+
+define tetradtype
+    v:r; u: phi; w: theta
+    tetradtype 0
+    v^a = (x,y,z)
+    orthonormal order: v,u,w
+    m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
+    tetradtype 1
+    orthonormal order: w,u,v
+    m = (theta + i phi)/sqrt(2) following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)
+    tetradtype 2
+    v_a = (x,y,z)
+    orthonormal order: v,u,w
+    m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
+
+define Cell or Vertex
+    Cell center or Vertex center
+
+define ghost_width
+    2nd order: 2
+    4th order: 3
+    6th order: 4
+    8th order: 5
+
+define WithShell
+    use shell or not
+
+define CPBC
+    use constraint preserving boundary condition or not
+    only affect Z4c
+    CPBC only supports WithShell
+
+define GAUGE
+    0: B^i gauge
+    1: David puncture gauge
+    2: MB B^i gauge
+    3: RIT B^i gauge
+    4: MB beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
+    5: RIT beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
+    6: MGB1 B^i gauge
+    7: MGB2 B^i gauge
+
+define CPBC_ghost_width  (ghost_width)
+    buffer points for CPBC boundary
+
+define ABV
+    0: using BSSN variable for constraint violation and psi4 calculation
+    1: using ADM variable for constraint violation and psi4 calculation
+
+define EScalar_CC
+Type of Potential and Scalar Distribution in F(R) Scalar-Tensor Theory
+    1: Case C of 1112.3928, V=0
+    2: shell with   phi(r) = phi0 * a2^2/(1+a2^2), f(R) = R+a2*R^2 induced V
+    3: ground state of Schrodinger-Newton system,  f(R) = R+a2*R^2 induced V
+    4: a2 = +oo and phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma) - tanh((r-r0)/sigma) )
+    5: shell with   phi(r) = phi0 * Exp(-(r-r0)**2/sigma), V = 0
+
+#endif
+

AMSS_NCKU_source/macrodef.h

@@ -1,112 +1,169 @@
-
-#ifndef MICRODEF_H
-#define MICRODEF_H
-
-#include "macrodef.fh"
-
-// application parameters
-
-/// ****
-// sommerfeld boundary type
-// 0: bam, 1: shibata
-#define SommerType 0
-
-/// ****
-// for Using Gauss-Legendre quadrature in theta direction
-#define GaussInt
-
-/// ****
-// 0: BSSN vacuum
-// 1: coupled to scalar field
-// 2: Z4c vacuum
-// 3: coupled to Maxwell field
-//
-#define ABEtype 2
-
-/// ****
-// using Apparent Horizon Finder
-//#define With_AHF
-
-/// ****
-// Psi4 calculation method
-// 0: EB method
-// 1: 4-D method
-//
-#define Psi4type 0
-
-/// ****
-// for Using point psi4 or not
-//#define Point_Psi4
-
-/// ****
-// RestrictProlong in Step (0) or after Step (1)
-#define RPS 1
-
-/// ****
-// Enforce algebra constraint
-// for every RK4 sub step: 0
-// only when iter_count == 3: 1
-// after routine Step: 2
-#define AGM 0
-
-/// ****
-// Restrict Prolong using BAM style 1 or old style 0
-#define RPB 0
-
-/// ****
-// 1: move Analysis out ot 4 sub steps and treat PBH with Euler method
-#define MAPBH 1
-
-/// ****
-// parallel structure, 0: level by level, 1: considering all levels, 2: as 1 but reverse the CPU order, 3: Frank's scheme
-#define PSTR 0
-
-/// ****
-// regrid for every level or for all levels at a time
-// 0: for every level; 1: for all
-#define REGLEV 0
-
-/// ****
-// use gpu or not
-//#define USE_GPU
-
-/// ****
-// use checkpoint for every process
-//#define CHECKDETAIL
-
-/// ****
-// use FakeCheckPrepare to write CheckPoint
-//#define FAKECHECK
-////================================================================
-//  some basic parameters for numerical calculation
-#define dim 3
-
-//#define Cell or Vertex in "microdef.fh"
-
-// ******
-// buffer point number for mesh refinement interface
-#define buffer_width 6
-
-// ******
-// buffer point number shell-box interface, on shell
-#define SC_width buffer_width
-// buffer point number shell-box interface, on box
-#define CS_width (2*buffer_width)
-
-#if(buffer_width < ghost_width)
-#error we always assume buffer_width>ghost_width
-#endif
-
-#define PACK 1
-#define UNPACK 2
-
-#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
-#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
-
-#define feq(a,b,d) (fabs(a-b)<d)
-#define flt(a,b,d) ((a-b)<d)
-#define fgt(a,b,d) ((a-b)>d)
-
-#define TINY 1e-10
-
-#endif   /* MICRODEF_H */
+
+#ifndef MICRODEF_H
+#define MICRODEF_H
+
+#include "macrodef.fh"  
+
+// application parameters
+
+#define SommerType 0
+
+#define GaussInt
+
+#define ABEtype 0
+
+//#define With_AHF
+#define Psi4type 0
+
+//#define Point_Psi4
+
+#define RPS 1
+
+#define AGM 0
+
+#define RPB 0
+
+#define MAPBH 1
+
+#define PSTR 0
+
+#define REGLEV 0
+
+#define BSSN_FINE_TIMING 0
+
+#define BSSN_FINE_TIMING_EVERY 1
+
+#define BSSN_FINE_TIMING_TOPN 8
+
+#define BSSN_KERNEL_FINE_TIMING 0
+
+#define BSSN_ENABLE_STDIN_ABORT_POLL 0
+
+//#define USE_GPU
+
+//#define CHECKDETAIL
+
+//#define FAKECHECK
+
+//
+// define SommerType
+//     sommerfeld boundary type
+//     0: bam
+//     1: shibata
+//
+// define GaussInt
+//     for Using Gauss-Legendre quadrature in theta direction
+//
+// define ABEtype
+//     0: BSSN vacuum
+//     1: coupled to scalar field
+//     2: Z4c vacuum
+//     3: coupled to Maxwell field
+//
+// define With_AHF
+//     using Apparent Horizon Finder
+//
+// define Psi4type
+//     Psi4 calculation method
+//     0: EB method
+//     1: 4-D method
+//
+// define Point_Psi4
+//     for Using point psi4 or not
+//
+// define RPS
+//     RestrictProlong in Step (0) or after Step (1)
+//
+// define AGM
+//     Enforce algebra constraint
+//     for every RK4 sub step: 0
+//     only when iter_count == 3: 1
+//     after routine Step: 2
+//
+// define RPB
+//     Restrict Prolong using BAM style 1 or old style 0
+//
+// define MAPBH
+//     1: move Analysis out ot 4 sub steps and treat PBH with Euler method
+//
+// define PSTR
+//     parallel structure
+//     0: level by level
+//     1: considering all levels
+//     2: as 1 but reverse the CPU order
+//     3: Frank's scheme
+//
+// define REGLEV
+//     regrid for every level or for all levels at a time
+//     0: for every level;
+//     1: for all
+//
+// define BSSN_FINE_TIMING
+//     enable fine-grained per-timestep timing monitor
+//
+// define BSSN_FINE_TIMING_EVERY
+//     report timing every N coarse timesteps
+//
+// define BSSN_FINE_TIMING_TOPN
+//     number of hottest timing buckets shown in stdout
+//
+// define BSSN_KERNEL_FINE_TIMING
+//     enable split timing inside compute_rhs_bssn
+//
+// define BSSN_ENABLE_STDIN_ABORT_POLL
+//     poll stdin and broadcast abort flag every coarse step
+//
+// define USE_GPU
+//     use gpu or not
+//
+// define CHECKDETAIL
+//     use checkpoint for every process
+//
+// define FAKECHECK
+//     use FakeCheckPrepare to write CheckPoint
+//
+
+////================================================================
+//  some basic parameters for numerical calculation
+////================================================================
+
+#define dim 3
+
+//#define Cell or Vertex in "macrodef.fh" 
+
+#define buffer_width 6
+
+#define SC_width buffer_width
+
+#define CS_width (2*buffer_width)
+
+//
+// define Cell or Vertex in "macrodef.fh" 
+//
+// define buffer_width
+//     buffer point number for mesh refinement interface
+//
+// define SC_width buffer_width
+//     buffer point number shell-box interface, on shell
+//
+// define CS_width
+//     buffer point number shell-box interface, on box
+//
+
+#if(buffer_width < ghost_width)
+#   error we always assume buffer_width>ghost_width
+#endif
+
+#define PACK 1
+#define UNPACK 2
+
+#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
+#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
+
+#define feq(a,b,d) (fabs(a-b)<d)
+#define flt(a,b,d) ((a-b)<d)
+#define fgt(a,b,d) ((a-b)>d)
+
+#define TINY 1e-10
+
+#endif   /* MICRODEF_H */

AMSS_NCKU_source/makefile

@@ -1,108 +1,293 @@
-
-
-include makefile.inc
-
-.SUFFIXES: .o .f90 .C .for .cu
-
-.f90.o:
-	$(f90) $(f90appflags) -c $< -o $@
-
-.C.o:
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-.for.o:
-	$(f77) -c $< -o $@
-
-.cu.o:
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
-
-TwoPunctures.o: TwoPunctures.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
-
-TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
-
-# Input files
-C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
-           cgh.o bssn_class.o surface_integral.o ShellPatch.o\
-	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
-	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
-           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o writefile_f.o
-	   
-C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
-           cgh.o surface_integral.o ShellPatch.o\
-	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
-	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
-           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o \
-	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
-
-F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   rungekutta4_rout.o bssn_rhs.o diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
-           fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
-	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
-	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
-	   bssn2adm.o adm_constraint.o adm_ricci_gamma.o\
-	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
-	   NullNews2.o tool_f.o
-
-F77FILES = zbesh.o
-
-AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \
-tgrid.o fd_grid.o ghost_zone.o array.o round.o norm.o fuzzy.o error_exit.o miscfp.o \
-linear_map.o cpm_map.o BH_diagnostics.o setup.o horizon_sequence.o find_horizons.o \
-initial_guess.o Newton.o Jacobian.o ilucg.o IntPnts0.o IntPnts.o
-
-TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o 
-
-CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
-
-# file dependences
-$(C++FILES) $(C++FILESGPU) $(F90FILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
-
-$(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
-	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
-	     rungekutta4_rout.h var.h bssn_class.h bssn_rhs.h sommerfeld_rout.h\
-	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
-             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
-	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
-	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
-             initial_null2.h NullShellPatch2.h 
-             
-$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
-	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
-	     rungekutta4_rout.h var.h bssn_rhs.h sommerfeld_rout.h\
-	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
-             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
-	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
-	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
-             initial_null2.h NullShellPatch2.h \
-             bssn_gpu_class.h bssn_macro.h
-             
-$(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
-
-$(C++FILES) $(C++FILES_GPU) $(AHFDOBJS) $(CUDAFILES): macrodef.h
-
-TwoPunctureFILES: TwoPunctures.h
-
-$(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
-
-misc.o : zbesh.o
-
-# projects
-ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
-	
-ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
-
-TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
-
-clean:
-	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
+
+
+include makefile.inc
+
+-include AMSS_NCKU_build.mk
+
+ABE_TYPE ?= $(shell awk '/^[[:space:]]*\#define[[:space:]]+ABEtype/ {print $$3; exit}' macrodef.h 2>/dev/null)
+
+ifeq ($(USE_TRANSFER_CACHE),auto)
+ifeq ($(ABE_TYPE),0)
+EFFECTIVE_USE_TRANSFER_CACHE = 1
+else
+EFFECTIVE_USE_TRANSFER_CACHE = 0
+endif
+else
+EFFECTIVE_USE_TRANSFER_CACHE = $(USE_TRANSFER_CACHE)
+endif
+
+ifeq ($(USE_CXX_ESCALAR_KERNEL),1)
+ifeq ($(ABE_TYPE),1)
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 1
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+
+ifeq ($(EFFECTIVE_USE_CXX_ESCALAR_KERNEL),1)
+ifeq ($(USE_CXX_KERNELS),0)
+$(error USE_CXX_ESCALAR_KERNEL=1 requires USE_CXX_KERNELS=1 because bssn_escalar_rhs_c.C reuses the C BSSN kernel)
+endif
+endif
+
+ifeq ($(USE_CXX_EM_KERNEL),1)
+ifeq ($(ABE_TYPE),3)
+EFFECTIVE_USE_CXX_EM_KERNEL = 1
+else
+EFFECTIVE_USE_CXX_EM_KERNEL = 0
+endif
+else
+EFFECTIVE_USE_CXX_EM_KERNEL = 0
+endif
+
+ifeq ($(EFFECTIVE_USE_CXX_EM_KERNEL),1)
+ifeq ($(USE_CXX_KERNELS),0)
+$(error USE_CXX_EM_KERNEL=1 requires USE_CXX_KERNELS=1 because bssn_em_rhs_c.C reuses the C BSSN kernel)
+endif
+endif
+
+EM_KERNEL_FLAG = -DBSSN_USE_EM_C_KERNEL=$(EFFECTIVE_USE_CXX_EM_KERNEL)
+
+## polint(ordn=6) kernel selector:
+##   1 (default): barycentric fast path
+##   0          : fallback to Neville path
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+TRANSFER_CACHE_FLAG = -DBSSN_USE_TRANSFER_CACHE=$(EFFECTIVE_USE_TRANSFER_CACHE)
+ESCALAR_KERNEL_FLAG = -DBSSN_USE_ESCALAR_C_KERNEL=$(EFFECTIVE_USE_CXX_ESCALAR_KERNEL)
+
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+##   make                        -> opt  (PGO-guided, maximum performance)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+
+ifeq ($(PGO_MODE),instrument)
+## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS) \
+              $(TRANSFER_CACHE_FLAG) $(ESCALAR_KERNEL_FLAG) $(EM_KERNEL_FLAG)
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+else
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
+## PGO has been turned off, now tested and found to be negative optimization
+## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
+
+
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS) \
+              $(TRANSFER_CACHE_FLAG) $(ESCALAR_KERNEL_FLAG) $(EM_KERNEL_FLAG)
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+endif
+
+.SUFFIXES: .o .f90 .C .for .cu
+
+.f90.o:
+	$(f90) $(f90appflags) -c $< -o $@
+
+.C.o:
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+# ShellPatch.C uses OpenMP for setupintintstuff search loops
+ShellPatch.o: ShellPatch.C
+	${CXX} $(CXXAPPFLAGS) $(OMP_FLAG) -c $< $(filein) -o $@
+
+.for.o:
+	$(f77) -c $< -o $@
+
+.cu.o:
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
+# C rewrite of BSSN RHS kernel and helpers
+bssn_rhs_c.o: bssn_rhs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fderivs_c.o: fderivs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fdderivs_c.o: fdderivs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+kodiss_c.o: kodiss_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+lopsided_c.o: lopsided_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+lopsided_kodis_c.o: lopsided_kodis_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+# C rewrite of shell-patch derivative kernels
+fderivs_sh_c.o: fderivs_sh_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fdderivs_sh_c.o: fdderivs_sh_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fderivs_shc_c.o: fderivs_shc_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fdderivs_shc_c.o: fdderivs_shc_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+kodiss_sh_c.o: kodiss_sh_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+
+bssn_em_rhs_c.o: bssn_em_rhs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+z4c_rhs_c.o: z4c_rhs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
+TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
+TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(TP_PROFDATA) \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
+
+TwoPunctures.o: TwoPunctures.C
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+
+TwoPunctureABE.o: TwoPunctureABE.C
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+
+# Input files
+
+## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
+ifeq ($(USE_CXX_KERNELS),0)
+# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
+CFILES =
+else
+# C++ mode (default): C rewrite of bssn/bssn-escalar rhs and helper kernels
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+ifeq ($(EFFECTIVE_USE_CXX_ESCALAR_KERNEL),1)
+CFILES += bssn_escalar_rhs_c.o
+endif
+ifeq ($(EFFECTIVE_USE_CXX_EM_KERNEL),1)
+CFILES += bssn_em_rhs_c.o
+endif
+endif
+
+ifeq ($(USE_CXX_Z4C_KERNELS),1)
+CFILES += z4c_rhs_c.o
+Z4C_F90_OBJ =
+else
+Z4C_F90_OBJ = Z4c_rhs.o
+endif
+
+## RK4 kernel switch (independent from USE_CXX_KERNELS)
+ifeq ($(USE_CXX_RK4),1)
+CFILES += rungekutta4_rout_c.o
+RK4_F90_OBJ =
+else
+RK4_F90_OBJ = rungekutta4_rout.o
+endif
+
+## Shell-patch derivative kernel switch (independent from USE_CXX_KERNELS)
+##   1 : use C++ rewrite of shell derivative functions (experimental)
+##   0 : use original Fortran diff_new_sh.o and kodiss_sh.o (default)
+USE_CXX_SHELL_KERNELS ?= 0
+ifeq ($(USE_CXX_SHELL_KERNELS),1)
+CFILES += fderivs_sh_c.o fdderivs_sh_c.o fderivs_shc_c.o fdderivs_shc_c.o kodiss_sh_c.o
+SH_F90_OBJ =
+else
+SH_F90_OBJ = diff_new_sh.o kodiss_sh.o point_diff_new_sh.o
+endif
+
+C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
+           cgh.o bssn_class.o surface_integral.o ShellPatch.o\
+	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
+	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
+           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
+	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.o
+	   
+C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
+           cgh.o surface_integral.o ShellPatch.o\
+	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
+	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
+           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
+	   NullShellPatch2_Evo.o \
+	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
+
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o $(SH_F90_OBJ)\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+           fadmquantites_bssn.o $(Z4C_F90_OBJ) Z4c_rhs_ss.o\
+	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
+	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
+	   bssn2adm.o adm_constraint.o adm_ricci_gamma.o\
+	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
+	   NullNews2.o tool_f.o
+
+ifeq ($(USE_CXX_KERNELS),0)
+# Fortran mode: include original bssn_rhs.o
+F90FILES = $(F90FILES_BASE) bssn_rhs.o
+else
+# C++ mode (default): bssn_rhs.o replaced by C++ kernel
+F90FILES = $(F90FILES_BASE)
+endif
+
+F77FILES = zbesh.o
+
+AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \
+tgrid.o fd_grid.o ghost_zone.o array.o round.o norm.o fuzzy.o error_exit.o miscfp.o \
+linear_map.o cpm_map.o BH_diagnostics.o setup.o horizon_sequence.o find_horizons.o \
+initial_guess.o Newton.o Jacobian.o ilucg.o IntPnts0.o IntPnts.o
+
+TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o 
+
+CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
+
+# file dependences
+$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
+
+$(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
+	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
+	     rungekutta4_rout.h var.h bssn_class.h bssn_rhs.h sommerfeld_rout.h\
+	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
+             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
+	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
+	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
+             initial_null2.h NullShellPatch2.h 
+             
+$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
+	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
+	     rungekutta4_rout.h var.h bssn_rhs.h sommerfeld_rout.h\
+	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
+             fadmquantites_bssn.h cpbc.h getnp4.h initial_null.h NullEvol.h\
+	     NullShellPatch.h initial_maxwell.h bssnEM_class.h getnpem2.h\
+	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
+             initial_null2.h NullShellPatch2.h \
+             bssn_gpu_class.h bssn_macro.h
+             
+$(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
+
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+
+TwoPunctureFILES: TwoPunctures.h
+
+$(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
+
+misc.o : zbesh.o
+
+# projects
+ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	
+ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
+
+TwoPunctureABE: $(TwoPunctureFILES)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+
+clean:
+	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -8,22 +8,79 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 
 ## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
+
+## Memory allocator switch
+##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
+##   0           : use system default allocator (ptmalloc)
+USE_TBBMALLOC ?= 1
+TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
+ifneq ($(wildcard $(TBBMALLOC_SO)),)
+TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
+else
+TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
+endif
+ifeq ($(USE_TBBMALLOC),1)
+LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
+endif
+
+## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
+##   opt        : (default) maximum performance with PGO profile-guided optimization
+##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
+PGO_MODE ?= opt
+
+## Interp_Points load balance profiling mode
+##   off        : (default) no load balance instrumentation
+##   profile    : Pass 1 — instrument Interp_Points to collect timing profile
+##   optimize   : Pass 2 — read profile and apply block rebalancing
+INTERP_LB_MODE ?= off
+
+ifeq ($(INTERP_LB_MODE),profile)
+INTERP_LB_FLAGS = -DINTERP_LB_PROFILE
+else ifeq ($(INTERP_LB_MODE),optimize)
+INTERP_LB_FLAGS = -DINTERP_LB_OPTIMIZE
+else
+INTERP_LB_FLAGS =
+endif
+
+## Kernel implementation switch
+##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
+##   0           : fall back to original Fortran kernels
+USE_CXX_KERNELS ?= 1
+
+## Z4C Cartesian RHS kernel switch
+##   1 (default) : use C++ rewrite of Z4c_rhs (main Cartesian path faster)
+##   0           : use original Fortran Z4c_rhs.o
+USE_CXX_Z4C_KERNELS ?= 1
+
+## BSSN-EScalar RHS switch
+##   1 (default) : use BSSN-EScalar C wrapper on the normal patch path
+##   0           : keep the original Fortran BSSN-EScalar RHS for precision-safe runs
+## Note: this requires USE_CXX_KERNELS=1 because the wrapper reuses the C BSSN kernel.
+USE_CXX_ESCALAR_KERNEL ?= 1
+
+## BSSN-EM RHS switch
+##   1 : use BSSN-EM C kernel (bssn_em_rhs_c.C) on the normal patch path
+##   0 : keep the original Fortran empart.f90 RHS for the EM fields (default)
+## Note: experimental, requires USE_CXX_KERNELS=1
+USE_CXX_EM_KERNEL ?= 0
+
+## Cached transfer switch
+##   auto (default): enable for BSSN vacuum, keep other paths on the safe uncached path
+##   1             : force cached Sync/Restrict/OutBd transfer on evolution hot paths
+##   0             : force the original uncached transfer path
+USE_TRANSFER_CACHE ?= auto
+
+## RK4 kernel implementation switch
+##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
+##   0           : use original Fortran rungekutta4_rout.o
+USE_CXX_RK4 ?= 1
 
-## Aggressive optimization flags:
-## -O3: Maximum optimization
-## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
-## -fp-model fast=2: Aggressive floating-point optimizations
-## -fma: Enable fused multiply-add instructions
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx 
+CLINKER      = mpiicpx
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1934,18 +1934,35 @@
 ! when if=1 -> ic=0, this is different to vertex center grid 
   real*8, dimension(-2:extc(1),-2:extc(2),-2:extc(3))   :: funcc
   integer,dimension(3) :: cxI
-  integer :: i,j,k,ii,jj,kk
+  integer :: i,j,k,ii,jj,kk,px,py,pz
   real*8, dimension(6,6) :: tmp2
   real*8, dimension(6) :: tmp1
+  integer, dimension(extf(1)) :: cix
+  integer, dimension(extf(2)) :: ciy
+  integer, dimension(extf(3)) :: ciz
+  integer, dimension(extf(1)) :: pix
+  integer, dimension(extf(2)) :: piy
+  integer, dimension(extf(3)) :: piz
 
   real*8, parameter :: C1=7.7d1/8.192d3,C2=-6.93d2/8.192d3,C3=3.465d3/4.096d3
   real*8, parameter :: C6=6.3d1/8.192d3,C5=-4.95d2/8.192d3,C4=1.155d3/4.096d3
+  real*8, dimension(6,2), parameter :: WC = reshape((/&
+      C1,C2,C3,C4,C5,C6,&
+      C6,C5,C4,C3,C2,C1/), (/6,2/))
 
   integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
+  integer::maxcx,maxcy,maxcz
 
   real*8,dimension(3) :: CD,FD
-  
+  real*8 :: tmp_yz(extc(1), 6)      ! 存储整条 X 线上 6 个 Y 轴偏置的 Z 向插值结果
+  real*8 :: tmp_xyz_line(-2:extc(1))   ! 包含 X 向 6 点模板访问所需下界
+  real*8 :: v1, v2, v3, v4, v5, v6
+  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max,ic_min,ic_max,kc_min,kc_max
+  integer :: i_lo, i_hi, j_lo, j_hi, k_lo, k_hi
+  logical :: need_full_symmetry
+  real*8 :: res_line
+  real*8 :: tmp_z_slab(-2:extc(1), -2:extc(2))  ! 包含 Y/X 向模板访问所需下界
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2020,145 +2037,140 @@
           return
   endif
 
-  call symmetry_bd(3,extc,func,funcc,SoA)
-     
-!~~~~~~> prolongation start...
+  do i = imino,imaxo
+     ii = i + lbf(1) - 1
+     cix(i) = ii/2 - lbc(1) + 1
+     if(ii/2*2 == ii)then
+        pix(i) = 1
+     else
+        pix(i) = 2
+     endif
+  enddo
+  do j = jmino,jmaxo
+     jj = j + lbf(2) - 1
+     ciy(j) = jj/2 - lbc(2) + 1
+     if(jj/2*2 == jj)then
+        piy(j) = 1
+     else
+        piy(j) = 2
+     endif
+  enddo
   do k = kmino,kmaxo
-   do j = jmino,jmaxo
-    do i = imino,imaxo
-       cxI(1) = i
-       cxI(2) = j
-       cxI(3) = k
-! change to coarse level reference
-!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---| 
-!|=======x===============x===============x===============x=======|
-       cxI = (cxI+lbf-1)/2
-! change to array index      
-       cxI = cxI - lbc + 1
-
-       if(any(cxI+3 > extc)) write(*,*)"error in prolong"
-       ii=i+lbf(1)-1
-       jj=j+lbf(2)-1
-       kk=k+lbf(3)-1
-#if 0
-       if(ii/2*2==ii)then
-         if(jj/2*2==jj)then
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           endif
-         else
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           endif
-         endif
-       else
-         if(jj/2*2==jj)then
-           if(kk/2*2==kk)then               
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           endif
-         else
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           endif
-         endif
-       endif
-#else 
-       if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-       else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-       endif
-
-       if(jj/2*2==jj)then
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-       else
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-       endif
-
-       if(ii/2*2==ii)then
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-       else
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-       endif
-#endif
-    enddo
-   enddo
+     kk = k + lbf(3) - 1
+     ciz(k) = kk/2 - lbc(3) + 1
+     if(kk/2*2 == kk)then
+        piz(k) = 1
+     else
+        piz(k) = 2
+     endif
   enddo
 
+  ic_min = minval(cix(imino:imaxo))
+  ic_max = maxval(cix(imino:imaxo))
+  jc_min = minval(ciy(jmino:jmaxo))
+  jc_max = maxval(ciy(jmino:jmaxo))
+  kc_min = minval(ciz(kmino:kmaxo))
+  kc_max = maxval(ciz(kmino:kmaxo))
+
+  maxcx = ic_max
+  maxcy = jc_max
+  maxcz = kc_max
+  if(maxcx+3 > extc(1) .or. maxcy+3 > extc(2) .or. maxcz+3 > extc(3))then
+     write(*,*)"error in prolong"
+     return
+  endif
+
+  i_lo = ic_min - 2
+  i_hi = ic_max + 3
+  j_lo = jc_min - 2
+  j_hi = jc_max + 3
+  k_lo = kc_min - 2
+  k_hi = kc_max + 3
+  need_full_symmetry = (i_lo < 1) .or. (j_lo < 1) .or. (k_lo < 1)
+  if(need_full_symmetry)then
+     call symmetry_bd(3,extc,func,funcc,SoA)
+  else
+     funcc(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi) = func(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi)
+  endif
+
+     ! 对每个 k（pz, kc 固定）预计算 Z 向插值的 2D 切片
+
+do k = kmino, kmaxo
+    pz = piz(k); kc = ciz(k)
+    ! --- Pass 1: Z 方向，只算一次 ---
+    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
+        do ii = ic_min-2, ic_max+3  ! 仅需的 ii 范围（对应 cix-2:cix+3）
+            tmp_z_slab(ii, iy) = sum(WC(:,pz) * funcc(ii, iy, kc-2:kc+3))
+        end do
+    end do
+
+    do j = jmino, jmaxo
+        py = piy(j); jc = ciy(j)
+        ! --- Pass 2: Y 方向 ---
+        do ii = ic_min-2, ic_max+3
+            tmp_xyz_line(ii) = sum(WC(:,py) * tmp_z_slab(ii, jc-2:jc+3))
+        end do
+        ! --- Pass 3: X 方向 ---
+        do i = imino, imaxo
+            funf(i,j,k) = sum(WC(:,pix(i)) * tmp_xyz_line(cix(i)-2:cix(i)+3))
+        end do
+    end do
+end do
+
+!~~~~~~> prolongation start...
+#if 0
+ do k = kmino, kmaxo
+     pz = piz(k)
+     kc = ciz(k)
+
+     do j = jmino, jmaxo
+        py = piy(j)
+        jc = ciy(j)
+
+! --- 步骤 1 & 2 融合：分段处理 X 轴，提升 Cache 命中率 ---
+        ! 我们将 ii 循环逻辑重组，减少对 funcc 的跨行重复访问
+        do ii = 1, extc(1)
+           ! 1. 先做 Z 方向的 6 条线插值（针对当前的 ii 和当前的 6 个 iy）
+           ! 我们直接在这里把 Y 方向的加权也做了，省去 tmp_yz 数组
+           ! 这样 funcc 的数据读进来后立即完成所有维度的贡献，不再写回内存
+           
+           res_line = 0.0d0
+           do jj = 1, 6
+              iy = jc - 3 + jj
+              ! 这一行代码是核心：一次性完成 Z 插值并加上 Y 的权重
+              ! 编译器会把 WC(jj, py) 存在寄存器里
+              res_line = res_line + WC(jj, py) * ( &
+                         WC(1, pz) * funcc(ii, iy, kc-2) + &
+                         WC(2, pz) * funcc(ii, iy, kc-1) + &
+                         WC(3, pz) * funcc(ii, iy, kc  ) + &
+                         WC(4, pz) * funcc(ii, iy, kc+1) + &
+                         WC(5, pz) * funcc(ii, iy, kc+2) + &
+                         WC(6, pz) * funcc(ii, iy, kc+3) )
+           end do
+           tmp_xyz_line(ii) = res_line
+        end do
+
+
+
+
+        ! 3. 【降维：X 向】最后在最内层只处理 X 方向的 6 点加权
+        ! 此时每个点的计算量从原来的 200+ 次乘法降到了仅 6 次
+        do i = imino, imaxo
+           px = pix(i)
+           ic = cix(i)
+           
+           ! 直接从预计算好的 line 中读取连续的 6 个点
+           ! ic-2 到 ic+3 对应原始 6 点算子
+           funf(i,j,k) = WC(1,px)*tmp_xyz_line(ic-2) + &
+                         WC(2,px)*tmp_xyz_line(ic-1) + &
+                         WC(3,px)*tmp_xyz_line(ic  ) + &
+                         WC(4,px)*tmp_xyz_line(ic+1) + &
+                         WC(5,px)*tmp_xyz_line(ic+2) + &
+                         WC(6,px)*tmp_xyz_line(ic+3)
+        end do
+     end do
+  end do
+#endif
   return
 
   end subroutine prolong3
@@ -2357,7 +2369,14 @@
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
 
   real*8,dimension(3) :: CD,FD
-  
+
+  real*8 :: tmp_xz_plane(-1:extf(1), 6)
+  real*8 :: tmp_x_line(-1:extf(1))
+  integer :: fi, fj, fk, ii, jj, kk
+  integer :: fi_min, fi_max, ii_lo, ii_hi
+  integer :: fj_min, fj_max, fk_min, fk_max, jj_lo, jj_hi, kk_lo, kk_hi
+  logical :: need_full_symmetry
+
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2436,9 +2455,86 @@
           stop
   endif
 
-  call symmetry_bd(2,extf,funf,funff,SoA)
+  ! 仅计算 X 向最终写回所需的窗口：
+  ! func(i,j,k) 只访问 tmp_x_line(fi-2:fi+3)
+  fi_min = 2*(imino + lbc(1) - 1) - 1 - lbf(1) + 1
+  fi_max = 2*(imaxo + lbc(1) - 1) - 1 - lbf(1) + 1
+  fj_min = 2*(jmino + lbc(2) - 1) - 1 - lbf(2) + 1
+  fj_max = 2*(jmaxo + lbc(2) - 1) - 1 - lbf(2) + 1
+  fk_min = 2*(kmino + lbc(3) - 1) - 1 - lbf(3) + 1
+  fk_max = 2*(kmaxo + lbc(3) - 1) - 1 - lbf(3) + 1
+  ii_lo = fi_min - 2
+  ii_hi = fi_max + 3
+  jj_lo = fj_min - 2
+  jj_hi = fj_max + 3
+  kk_lo = fk_min - 2
+  kk_hi = fk_max + 3
+  if(ii_lo < -1 .or. ii_hi > extf(1) .or. &
+     jj_lo < -1 .or. jj_hi > extf(2) .or. &
+     kk_lo < -1 .or. kk_hi > extf(3))then
+      write(*,*)"restrict3: invalid stencil window"
+      write(*,*)"ii=",ii_lo,ii_hi," jj=",jj_lo,jj_hi," kk=",kk_lo,kk_hi
+      write(*,*)"extf=",extf
+      stop
+  endif
+  need_full_symmetry = (ii_lo < 1) .or. (jj_lo < 1) .or. (kk_lo < 1)
+  if(need_full_symmetry)then
+      call symmetry_bd(2,extf,funf,funff,SoA)
+  else
+      funff(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi) = funf(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi)
+  endif
 
 !~~~~~~> restriction start...
+do k = kmino, kmaxo
+    fk = 2*(k + lbc(3) - 1) - 1 - lbf(3) + 1
+
+    do j = jmino, jmaxo
+        fj = 2*(j + lbc(2) - 1) - 1 - lbf(2) + 1
+        
+        ! 优化点 1: 显式展开 Z 方向计算，减少循环开销
+        ! 确保 ii 循环是最内层且连续访问
+        !DIR$ VECTOR ALWAYS
+        do ii = ii_lo, ii_hi
+            ! 预计算当前 j 对应的 6 行在 Z 方向的压缩结果
+            ! 这里直接硬编码 jj 的偏移，彻底消除一层循环
+            tmp_xz_plane(ii, 1) = C1*(funff(ii,fj-2,fk-2)+funff(ii,fj-2,fk+3)) + &
+                                  C2*(funff(ii,fj-2,fk-1)+funff(ii,fj-2,fk+2)) + &
+                                  C3*(funff(ii,fj-2,fk  )+funff(ii,fj-2,fk+1))
+            tmp_xz_plane(ii, 2) = C1*(funff(ii,fj-1,fk-2)+funff(ii,fj-1,fk+3)) + &
+                                  C2*(funff(ii,fj-1,fk-1)+funff(ii,fj-1,fk+2)) + &
+                                  C3*(funff(ii,fj-1,fk  )+funff(ii,fj-1,fk+1))
+            tmp_xz_plane(ii, 3) = C1*(funff(ii,fj  ,fk-2)+funff(ii,fj  ,fk+3)) + &
+                                  C2*(funff(ii,fj  ,fk-1)+funff(ii,fj  ,fk+2)) + &
+                                  C3*(funff(ii,fj  ,fk  )+funff(ii,fj  ,fk+1))
+            tmp_xz_plane(ii, 4) = C1*(funff(ii,fj+1,fk-2)+funff(ii,fj+1,fk+3)) + &
+                                  C2*(funff(ii,fj+1,fk-1)+funff(ii,fj+1,fk+2)) + &
+                                  C3*(funff(ii,fj+1,fk  )+funff(ii,fj+1,fk+1))
+            tmp_xz_plane(ii, 5) = C1*(funff(ii,fj+2,fk-2)+funff(ii,fj+2,fk+3)) + &
+                                  C2*(funff(ii,fj+2,fk-1)+funff(ii,fj+2,fk+2)) + &
+                                  C3*(funff(ii,fj+2,fk  )+funff(ii,fj+2,fk+1))
+            tmp_xz_plane(ii, 6) = C1*(funff(ii,fj+3,fk-2)+funff(ii,fj+3,fk+3)) + &
+                                  C2*(funff(ii,fj+3,fk-1)+funff(ii,fj+3,fk+2)) + &
+                                  C3*(funff(ii,fj+3,fk  )+funff(ii,fj+3,fk+1))
+        end do
+
+        ! 优化点 2: 同样向量化 Y 方向压缩
+        !DIR$ VECTOR ALWAYS
+        do ii = ii_lo, ii_hi
+            tmp_x_line(ii) = C1*(tmp_xz_plane(ii, 1) + tmp_xz_plane(ii, 6)) + &
+                            C2*(tmp_xz_plane(ii, 2) + tmp_xz_plane(ii, 5)) + &
+                            C3*(tmp_xz_plane(ii, 3) + tmp_xz_plane(ii, 4))
+        end do
+
+        ! 优化点 3: 最终写入，利用已经缓存在 tmp_x_line 的数据
+        do i = imino, imaxo
+            fi = 2*(i + lbc(1) - 1) - 1 - lbf(1) + 1
+            func(i, j, k) = C1*(tmp_x_line(fi-2) + tmp_x_line(fi+3)) + &
+                            C2*(tmp_x_line(fi-1) + tmp_x_line(fi+2)) + &
+                            C3*(tmp_x_line(fi  ) + tmp_x_line(fi+1))
+        end do
+    end do
+end do
+#if 0
   do k = kmino,kmaxo
    do j = jmino,jmaxo
     do i = imino,imaxo
@@ -2462,7 +2558,7 @@
     enddo
    enddo
   enddo
-  
+#endif
   return
 
   end subroutine restrict3

AMSS_NCKU_source/rungekutta4_rout_c.C

@@ -0,0 +1,212 @@
+#include "rungekutta4_rout.h"
+#include <cstdio>
+#include <cstdlib>
+#include <cstddef>
+#include <complex>
+#include <immintrin.h>
+
+namespace {
+
+inline void rk4_stage0(std::size_t n,
+                       const double *__restrict f0,
+                       const double *__restrict frhs,
+                       double *__restrict f1,
+                       double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d vr = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, vr, v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d vr = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, vr, v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * frhs[i];
+    }
+}
+
+inline void rk4_rhs_accum(std::size_t n,
+                          const double *__restrict f1,
+                          double *__restrict frhs) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d v2 = _mm512_set1_pd(2.0);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        const __m512d vrhs = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(frhs + i, _mm512_fmadd_pd(v2, v1, vrhs));
+    }
+#elif defined(__AVX2__)
+    const __m256d v2 = _mm256_set1_pd(2.0);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        const __m256d vrhs = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(frhs + i, _mm256_fmadd_pd(v2, v1, vrhs));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        frhs[i] = frhs[i] + 2.0 * f1[i];
+    }
+}
+
+inline void rk4_f1_from_f0_f1(std::size_t n,
+                              const double *__restrict f0,
+                              double *__restrict f1,
+                              double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, v1, v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, v1, v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * f1[i];
+    }
+}
+
+inline void rk4_stage3(std::size_t n,
+                       const double *__restrict f0,
+                       double *__restrict f1,
+                       const double *__restrict frhs,
+                       double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        const __m512d vr = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, _mm512_add_pd(v1, vr), v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        const __m256d vr = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, _mm256_add_pd(v1, vr), v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * (f1[i] + frhs[i]);
+    }
+}
+
+} // namespace
+
+extern "C" {
+
+void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
+    constexpr double F1o6 = 1.0 / 6.0;
+    constexpr double HLF = 0.5;
+    constexpr double TWO = 2.0;
+
+    switch (RK4) {
+    case 0:
+        f1 = f0 + HLF * dT * f_rhs;
+        break;
+    case 1:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + HLF * dT * f1;
+        break;
+    case 2:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + dT * f1;
+        break;
+    case 3:
+        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
+        break;
+    default:
+        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+}
+
+void rungekutta4_cplxscalar_(double &dT,
+                             std::complex<double> &f0,
+                             std::complex<double> &f1,
+                             std::complex<double> &f_rhs,
+                             int &RK4) {
+    constexpr double F1o6 = 1.0 / 6.0;
+    constexpr double HLF = 0.5;
+    constexpr double TWO = 2.0;
+
+    switch (RK4) {
+    case 0:
+        f1 = f0 + HLF * dT * f_rhs;
+        break;
+    case 1:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + HLF * dT * f1;
+        break;
+    case 2:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + dT * f1;
+        break;
+    case 3:
+        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
+        break;
+    default:
+        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+}
+
+int f_rungekutta4_rout(int *ex, double &dT,
+                       double *f0, double *f1, double *f_rhs,
+                       int &RK4) {
+    const std::size_t n = static_cast<std::size_t>(ex[0]) *
+                          static_cast<std::size_t>(ex[1]) *
+                          static_cast<std::size_t>(ex[2]);
+    const double *const __restrict f0r = f0;
+    double *const __restrict f1r = f1;
+    double *const __restrict frhs = f_rhs;
+
+    if (__builtin_expect(static_cast<unsigned>(RK4) > 3u, 0)) {
+        std::fprintf(stderr, "rungekutta4_rout_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+
+    switch (RK4) {
+    case 0:
+        rk4_stage0(n, f0r, frhs, f1r, 0.5 * dT);
+        break;
+    case 1:
+        rk4_rhs_accum(n, f1r, frhs);
+        rk4_f1_from_f0_f1(n, f0r, f1r, 0.5 * dT);
+        break;
+    case 2:
+        rk4_rhs_accum(n, f1r, frhs);
+        rk4_f1_from_f0_f1(n, f0r, f1r, dT);
+        break;
+    default:
+        rk4_stage3(n, f0r, f1r, frhs, (1.0 / 6.0) * dT);
+        break;
+    }
+
+    return 0;
+}
+
+} // extern "C"

AMSS_NCKU_source/share_func.h

@@ -0,0 +1,372 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#include <stddef.h>
+#include <math.h>
+#include <stdio.h>
+#include <string.h>
+/* 主网格：0-based -> 1D */
+static inline size_t idx_ex(int i0, int j0, int k0, const int ex[3]) {
+    const int ex1 = ex[0], ex2 = ex[1];
+    return (size_t)i0 + (size_t)j0 * (size_t)ex1 + (size_t)k0 * (size_t)ex1 * (size_t)ex2;
+}
+
+/*
+ * fh 对应 Fortran: fh(-1:ex1, -1:ex2, -1:ex3)
+ * ord=2 => shift=1
+ * iF/jF/kF 为 Fortran 索引（可为 -1,0,1..ex）
+ */
+static inline size_t idx_fh_F_ord2(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 1;
+    const int nx = ex[0] + 2;      // ex1 + ord
+    const int ny = ex[1] + 2;
+
+    const int ii = iF + shift;     // 0..ex1+1
+    const int jj = jF + shift;     // 0..ex2+1
+    const int kk = kF + shift;     // 0..ex3+1
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * fh 对应 Fortran: fh(-2:ex1, -2:ex2, -2:ex3)
+ * ord=3 => shift=2
+ * iF/jF/kF 是 Fortran 索引（可为负）
+ */
+static inline size_t idx_fh_F(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 2;                 // ord=3 -> -2..ex
+    const int nx = ex[0] + 3;            // ex1 + ord
+    const int ny = ex[1] + 3;
+
+    const int ii = iF + shift;           // 0..ex1+2
+    const int jj = jF + shift;           // 0..ex2+2
+    const int kk = kF + shift;           // 0..ex3+2
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * fh 对应 Fortran: fh(0:ex1, 0:ex2, 0:ex3)
+ * ord=1 => shift=0
+ * iF/jF/kF 为 Fortran 索引 (0..ex)
+ */
+static inline size_t idx_fh_F_ord1(int iF, int jF, int kF, const int ex[3]) {
+    const int nx = ex[0] + 1;            // ex1 + ord
+    const int ny = ex[1] + 1;
+    return (size_t)iF + (size_t)jF * (size_t)nx + (size_t)kF * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * fh 对应 Fortran: fh(-3:ex1, -3:ex2, -3:ex3)
+ * ord=4 => shift=3
+ */
+static inline size_t idx_fh_F_ord4(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 3;
+    const int nx = ex[0] + 4;            // ex1 + ord
+    const int ny = ex[1] + 4;
+    const int ii = iF + shift;           // 0..ex1+3
+    const int jj = jF + shift;           // 0..ex2+3
+    const int kk = kF + shift;           // 0..ex3+3
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * fh 对应 Fortran: fh(-4:ex1, -4:ex2, -4:ex3)
+ * ord=5 => shift=4
+ */
+static inline size_t idx_fh_F_ord5(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 4;
+    const int nx = ex[0] + 5;            // ex1 + ord
+    const int ny = ex[1] + 5;
+    const int ii = iF + shift;           // 0..ex1+4
+    const int jj = jF + shift;           // 0..ex2+4
+    const int kk = kF + shift;           // 0..ex3+4
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * func:  (1..extc1, 1..extc2, 1..extc3)   1-based in Fortran
+ * funcc: (-ord+1..extc1, -ord+1..extc2, -ord+1..extc3) in Fortran
+ *
+ * C 里我们把：
+ *   func  视为 0-based: i0=0..extc1-1, j0=0..extc2-1, k0=0..extc3-1
+ *   funcc 用“平移下标”存为一维数组：
+ *     iF in [-ord+1..extc1]  -> ii = iF + (ord-1)  in [0..extc1+ord-1]
+ *     总长度 nx = extc1 + ord
+ *     同理 ny = extc2 + ord, nz = extc3 + ord
+ */
+
+static inline size_t idx_func0(int i0, int j0, int k0, const int extc[3]) {
+    const int nx = extc[0], ny = extc[1];
+    return (size_t)i0 + (size_t)j0 * (size_t)nx + (size_t)k0 * (size_t)nx * (size_t)ny;
+}
+
+static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc[3]) {
+    const int shift = ord - 1;          // iF = -shift .. extc1
+    const int nx = extc[0] + ord;       // [-shift..extc1] 共 extc1+ord 个
+    const int ny = extc[1] + ord;
+
+    const int ii = iF + shift;          // 0..extc1+shift
+    const int jj = jF + shift;          // 0..extc2+shift
+    const int kk = kF + shift;          // 0..extc3+shift
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * 等价于 Fortran:
+ * funcc(1:extc1,1:extc2,1:extc3)=func
+ * do i=0,ord-1
+ *   funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1)
+ * enddo
+ * do i=0,ord-1
+ *   funcc(:,-i,1:extc3) = funcc(:,i+1,1:extc3)*SoA(2)
+ * enddo
+ * do i=0,ord-1
+ *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
+ * enddo
+ */
+static inline void symmetry_bd_impl(int ord,
+                 int shift,
+                 const int extc[3],
+                 const double *__restrict func,
+                 double *__restrict funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+    const int nx = extc1 + ord;
+    const int ny = extc2 + ord;
+
+    const size_t snx = (size_t)nx;
+    const size_t splane = (size_t)nx * (size_t)ny;
+    const size_t interior_i = (size_t)shift + 1u;          /* iF = 1 */
+    const size_t interior_j = ((size_t)shift + 1u) * snx;  /* jF = 1 */
+    const size_t interior_k = ((size_t)shift + 1u) * splane; /* kF = 1 */
+    const size_t interior0 = interior_k + interior_j + interior_i;
+
+    /* 1) funcc(1:extc1,1:extc2,1:extc3) = func */
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        const double *src_k = func + (size_t)k0 * (size_t)extc2 * (size_t)extc1;
+        const size_t dst_k0 = interior0 + (size_t)k0 * splane;
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            const double *src = src_k + (size_t)j0 * (size_t)extc1;
+            double *dst = funcc + dst_k0 + (size_t)j0 * snx;
+            memcpy(dst, src, (size_t)extc1 * sizeof(double));
+        }
+    }
+
+    /* 2) funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1) */
+    const double s1 = SoA[0];
+    if (s1 == 1.0) {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = funcc[off + src_i];
+                }
+            }
+        }
+    } else if (s1 == -1.0) {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = -funcc[off + src_i];
+                }
+            }
+        }
+    } else {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = funcc[off + src_i] * s1;
+                }
+            }
+        }
+    }
+
+    /* 3) funcc(:,-j,1:extc3) = funcc(:,j+1,1:extc3)*SoA(2) */
+    const double s2 = SoA[1];
+    if (s2 == 1.0) {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = src[i];
+            }
+        }
+    } else if (s2 == -1.0) {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = -src[i];
+            }
+        }
+    } else {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = src[i] * s2;
+            }
+        }
+    }
+
+    /* 4) funcc(:,:,-k) = funcc(:,:,k+1)*SoA(3) */
+    const double s3 = SoA[2];
+    if (s3 == 1.0) {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = src[p];
+        }
+    } else if (s3 == -1.0) {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = -src[p];
+        }
+    } else {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = src[p] * s3;
+        }
+    }
+}
+
+static inline void symmetry_bd(int ord,
+                 const int extc[3],
+                 const double *func,
+                 double *funcc,
+                 const double SoA[3])
+{
+    if (ord <= 0) return;
+
+    if (ord == 1) {
+        symmetry_bd_impl(1, 0, extc, func, funcc, SoA);
+        return;
+    }
+    if (ord == 2) {
+        symmetry_bd_impl(2, 1, extc, func, funcc, SoA);
+        return;
+    }
+    if (ord == 3) {
+        symmetry_bd_impl(3, 2, extc, func, funcc, SoA);
+        return;
+    }
+    if (ord == 4) {
+        symmetry_bd_impl(4, 3, extc, func, funcc, SoA);
+        return;
+    }
+
+    symmetry_bd_impl(ord, ord - 1, extc, func, funcc, SoA);
+}
+
+/*
+ * symmetry_stbd — shell-patch (staggered boundary) ghost fill.
+ *
+ * Fortran: funcc(-ord+1:extc1+ord, -ord+1:extc2+ord, extc3)
+ * Only 2 SoA values (x/y). No z symmetry fill.
+ * Ghost on BOTH positive and negative sides of x and y.
+ * Reflection uses i+2 (skips boundary) instead of i+1.
+ * nx = extc1 + 2*ord, ny = extc2 + 2*ord
+ */
+static inline void symmetry_stbd(int ord,
+                                 const int extc[3],
+                                 const double *func,
+                                 double *funcc,
+                                 const double SoA[2])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+    const int nx = extc1 + 2 * ord;
+    const int ny = extc2 + 2 * ord;
+    const int sh = ord - 1;
+    const size_t snx = (size_t)nx;
+    const size_t splane = snx * (size_t)ny;
+
+    /* 1) Copy interior: funcc(1:extc1, 1:extc2, 1:extc3) = func */
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        const double *src = func + (size_t)k0 * (size_t)extc2 * (size_t)extc1;
+        const size_t kbase = (size_t)k0 * splane;
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            double *dst = funcc + kbase + (size_t)(sh + j0 + 1) * snx + (size_t)(sh + 1);
+            const double *s = src + (size_t)j0 * (size_t)extc1;
+            for (int i0 = 0; i0 < extc1; ++i0) dst[i0] = s[i0];
+        }
+    }
+
+    /* 2) x-direction ghost fill */
+    const double s1 = SoA[0];
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        const size_t kbase = (size_t)k0 * splane;
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            const size_t off = kbase + (size_t)(sh + j0 + 1) * snx;
+            /* left side: funcc(-i) = funcc(i+2) * s1 */
+            for (int i = 0; i < ord; ++i) {
+                funcc[off + (size_t)(sh - i)]       = funcc[off + (size_t)(sh + i + 2)] * s1;
+                /* right side: funcc(extc1+1+i) = funcc(extc1-1-i) * s1 */
+                funcc[off + (size_t)(sh + extc1 + 1 + i)] = funcc[off + (size_t)(sh + extc1 - 1 - i)] * s1;
+            }
+        }
+    }
+
+    /* 3) y-direction ghost fill */
+    const double s2 = SoA[1];
+    for (int i = 0; i < nx; ++i) {
+        for (int k0 = 0; k0 < extc3; ++k0) {
+            const size_t kbase = (size_t)k0 * splane;
+            /* bottom: funcc(:,-i,:) = funcc(:,i+2,:) * s2 */
+            for (int jj = 0; jj < ord; ++jj) {
+                funcc[kbase + (size_t)(sh - jj) * snx + (size_t)i] =
+                    funcc[kbase + (size_t)(sh + jj + 2) * snx + (size_t)i] * s2;
+                /* top: funcc(:,extc2+1+jj,:) = funcc(:,extc2-1-jj,:) * s2 */
+                funcc[kbase + (size_t)(sh + extc2 + 1 + jj) * snx + (size_t)i] =
+                    funcc[kbase + (size_t)(sh + extc2 - 1 - jj) * snx + (size_t)i] * s2;
+            }
+        }
+    }
+}
+
+/*
+ * Indexing for shell fh buffer: Fortran fh(-ord+1:extc1+ord, -ord+1:extc2+ord, extc3)
+ * C 0-based: ii = iF + ord - 1
+ * nx = extc1 + 2*ord, ny = extc2 + 2*ord
+ */
+static inline size_t idx_fh_stbd(int iF, int jF, int kF, int ord, const int extc[3]) {
+    const int sh = ord - 1;
+    const int nx = extc[0] + 2 * ord;
+    const int ny = extc[1] + 2 * ord;
+    const int ii = iF + sh;
+    const int jj = jF + sh;
+    const int kk = kF - 1;  // Fortran 1-based kF → C 0-based
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+#endif

AMSS_NCKU_source/surface_integral.h

@@ -27,19 +27,24 @@ using namespace std;
 class surface_integral
 {
 
-private:
-	int Symmetry, factor;
-	int N_theta, N_phi; // Number of points in Theta & Phi directions
-	double dphi, dcostheta;
-	double *arcostheta, *wtcostheta;
-	int n_tot; // size of arrays
-
-	double *nx_g, *ny_g, *nz_g; // global list of unit normals
-	int myrank, cpusize;
-
-public:
-	surface_integral(int iSymmetry);
-	~surface_integral();
+private:
+	int Symmetry, factor;
+	int N_theta, N_phi; // Number of points in Theta & Phi directions
+	double dphi, dcostheta;
+	double *arcostheta, *wtcostheta;
+	int n_tot; // size of arrays
+
+	double *nx_g, *ny_g, *nz_g; // global list of unit normals
+	int myrank, cpusize;
+	int wave_cache_spinw, wave_cache_maxl, wave_cache_modes;
+	double *wave_theta_pos, *wave_theta_neg;
+	double *wave_phi_cos, *wave_phi_sin;
+	void clear_wave_cache();
+	void build_wave_cache(int spinw, int maxl);
+
+public:
+	surface_integral(int iSymmetry);
+	~surface_integral();
 
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
@@ -77,21 +82,37 @@ public:
 								 double &, double &, double &, double &, double &, double &, double &,
 								 double &, double &, double &, double &, double &, double &,
 								 double &, double &)); // NN is the length of RP and IP
-	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
-	void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
-	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
-				   var *chi, var *trK,
-				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, cgh *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
+				   var *chi, var *trK,
+				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
 				   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 				   var *chix, var *chiy, var *chiz,
 				   var *trKx, var *trKy, var *trKz,
@@ -110,12 +131,12 @@ public:
 	bool SR_Interp_Points(MyList<var> *VarList, cgh *GH, ShellPatch *SH,
 						  int NN, double **XX, double *Shellf);
 
-	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-					   double *Rout, monitor *Monitor, MPI_Comm Comm_here);
+	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
+					   double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields = true);
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
 				   monitor *Monitor, MPI_Comm Comm_here);

AMSS_NCKU_source/tool.h

@@ -0,0 +1,33 @@
+#include "share_func.h"
+void fdderivs(const int ex[3],
+              const double *f,
+              double *fxx, double *fxy, double *fxz,
+              double *fyy, double *fyz, double *fzz,
+              const double *X, const double *Y, const double *Z,
+              double SYM1, double SYM2, double SYM3,
+              int Symmetry, int onoff);
+
+void fderivs(const int ex[3],
+             const double *f,
+             double *fx, double *fy, double *fz,
+             const double *X, const double *Y, const double *Z,
+             double SYM1, double SYM2, double SYM3,
+             int Symmetry, int onoff);
+
+void kodis(const int ex[3],
+           const double *X, const double *Y, const double *Z,
+           const double *f, double *f_rhs,
+           const double SoA[3],
+           int Symmetry, double eps);
+
+void lopsided(const int ex[3],
+              const double *X, const double *Y, const double *Z,
+              const double *f, double *f_rhs,
+              const double *Sfx, const double *Sfy, const double *Sfz,
+              int Symmetry, const double SoA[3]);
+
+void lopsided_kodis(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f, double *f_rhs,
+                    const double *Sfx, const double *Sfy, const double *Sfz,
+                    int Symmetry, const double SoA[3], double eps);

AMSS_NCKU_source/z4c_rhs_c.C

@@ -0,0 +1,901 @@
+#include "macrodef.h"
+#include "bssn_rhs.h"
+#include "fmisc.h"
+#include "ricci_gamma.h"
+#include "share_func.h"
+#include "tool.h"
+#include <vector>
+
+#ifdef fortran1
+#define f_constraint_bssn constraint_bssn
+#define f_z4c_rhs_point z4c_rhs_point
+#endif
+#ifdef fortran2
+#define f_constraint_bssn CONSTRAINT_BSSN
+#define f_z4c_rhs_point Z4C_RHS_POINT
+#endif
+#ifdef fortran3
+#define f_constraint_bssn constraint_bssn_
+#define f_z4c_rhs_point z4c_rhs_point_
+#endif
+
+extern "C" void f_constraint_bssn(int *, double *, double *, double *,
+                                  double *, double *,
+                                  double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *,
+                                  double *, double *, double *, double *, double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *, double *, double *, double *, double *, double *,
+                                  double *, double *, double *,
+                                  int &);
+
+extern "C" void f_z4c_rhs_point(
+    double &A11,
+    double &A12,
+    double &A13,
+    double &A22,
+    double &A23,
+    double &A33,
+    double &alpha,
+    double &B1,
+    double &B2,
+    double &B3,
+    double &beta1,
+    double &beta2,
+    double &beta3,
+    double &chi,
+    double &chiDivFloor,
+    double &da1,
+    double &dA111,
+    double &dA112,
+    double &dA113,
+    double &dA122,
+    double &dA123,
+    double &dA133,
+    double &da2,
+    double &dA211,
+    double &dA212,
+    double &dA213,
+    double &dA222,
+    double &dA223,
+    double &dA233,
+    double &da3,
+    double &dA311,
+    double &dA312,
+    double &dA313,
+    double &dA322,
+    double &dA323,
+    double &dA333,
+    double &db11,
+    double &dB11,
+    double &db12,
+    double &dB12,
+    double &db13,
+    double &dB13,
+    double &db21,
+    double &dB21,
+    double &db22,
+    double &dB22,
+    double &db23,
+    double &dB23,
+    double &db31,
+    double &dB31,
+    double &db32,
+    double &dB32,
+    double &db33,
+    double &dB33,
+    double &dchi1,
+    double &dchi2,
+    double &dchi3,
+    double &dda11,
+    double &dda12,
+    double &dda13,
+    double &dda22,
+    double &dda23,
+    double &dda33,
+    double &ddb111,
+    double &ddb112,
+    double &ddb113,
+    double &ddb121,
+    double &ddb122,
+    double &ddb123,
+    double &ddb131,
+    double &ddb132,
+    double &ddb133,
+    double &ddb221,
+    double &ddb222,
+    double &ddb223,
+    double &ddb231,
+    double &ddb232,
+    double &ddb233,
+    double &ddb331,
+    double &ddb332,
+    double &ddb333,
+    double &ddchi11,
+    double &ddchi12,
+    double &ddchi13,
+    double &ddchi22,
+    double &ddchi23,
+    double &ddchi33,
+    double &deldelg1111,
+    double &deldelg1112,
+    double &deldelg1113,
+    double &deldelg1122,
+    double &deldelg1123,
+    double &deldelg1133,
+    double &deldelg1211,
+    double &deldelg1212,
+    double &deldelg1213,
+    double &deldelg1222,
+    double &deldelg1223,
+    double &deldelg1233,
+    double &deldelg1311,
+    double &deldelg1312,
+    double &deldelg1313,
+    double &deldelg1322,
+    double &deldelg1323,
+    double &deldelg1333,
+    double &deldelg2211,
+    double &deldelg2212,
+    double &deldelg2213,
+    double &deldelg2222,
+    double &deldelg2223,
+    double &deldelg2233,
+    double &deldelg2311,
+    double &deldelg2312,
+    double &deldelg2313,
+    double &deldelg2322,
+    double &deldelg2323,
+    double &deldelg2333,
+    double &deldelg3311,
+    double &deldelg3312,
+    double &deldelg3313,
+    double &deldelg3322,
+    double &deldelg3323,
+    double &deldelg3333,
+    double &delG11,
+    double &delg111,
+    double &delg112,
+    double &delg113,
+    double &delG12,
+    double &delg122,
+    double &delg123,
+    double &delG13,
+    double &delg133,
+    double &delG21,
+    double &delg211,
+    double &delg212,
+    double &delg213,
+    double &delG22,
+    double &delg222,
+    double &delg223,
+    double &delG23,
+    double &delg233,
+    double &delG31,
+    double &delg311,
+    double &delg312,
+    double &delg313,
+    double &delG32,
+    double &delg322,
+    double &delg323,
+    double &delG33,
+    double &delg333,
+    double &dKhat1,
+    double &dKhat2,
+    double &dKhat3,
+    double &dTheta1,
+    double &dTheta2,
+    double &dTheta3,
+    double &G1,
+    double &g11,
+    double &g12,
+    double &g13,
+    double &G2,
+    double &g22,
+    double &g23,
+    double &G3,
+    double &g33,
+    double &kappa1,
+    double &kappa2,
+    double &Khat,
+    double &rA11,
+    double &rA12,
+    double &rA13,
+    double &rA22,
+    double &rA23,
+    double &rA33,
+    double &rchi,
+    double &rG1,
+    double &rg11,
+    double &rg12,
+    double &rg13,
+    double &rG2,
+    double &rg22,
+    double &rg23,
+    double &rG3,
+    double &rg33,
+    double &rKhat,
+    double &rTheta,
+    double &Theta);
+
+static inline void z4c_contract_gamma(
+    const double gxx, const double gxy, const double gxz,
+    const double gyy, const double gyz, const double gzz,
+    const double gxxx, const double gxyx, const double gxzx,
+    const double gyyx, const double gyzx, const double gzzx,
+    const double gxxy, const double gxyy, const double gxzy,
+    const double gyyy, const double gyzy, const double gzzy,
+    const double gxxz, const double gxyz, const double gxzz,
+    const double gyyz, const double gyzz, const double gzzz,
+    double &Gamxa, double &Gamya, double &Gamza)
+{
+    double det = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz -
+                 gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz;
+    const double gupxx = (gyy * gzz - gyz * gyz) / det;
+    const double gupxy = -(gxy * gzz - gyz * gxz) / det;
+    const double gupxz = (gxy * gyz - gyy * gxz) / det;
+    const double gupyy = (gxx * gzz - gxz * gxz) / det;
+    const double gupyz = -(gxx * gyz - gxy * gxz) / det;
+    const double gupzz = (gxx * gyy - gxy * gxy) / det;
+
+    const double Gamxxx = 0.5 * (gupxx * gxxx + gupxy * (2.0 * gxyx - gxxy) + gupxz * (2.0 * gxzx - gxxz));
+    const double Gamyxx = 0.5 * (gupxy * gxxx + gupyy * (2.0 * gxyx - gxxy) + gupyz * (2.0 * gxzx - gxxz));
+    const double Gamzxx = 0.5 * (gupxz * gxxx + gupyz * (2.0 * gxyx - gxxy) + gupzz * (2.0 * gxzx - gxxz));
+
+    const double Gamxyy = 0.5 * (gupxx * (2.0 * gxyy - gyyx) + gupxy * gyyy + gupxz * (2.0 * gyzy - gyyz));
+    const double Gamyyy = 0.5 * (gupxy * (2.0 * gxyy - gyyx) + gupyy * gyyy + gupyz * (2.0 * gyzy - gyyz));
+    const double Gamzyy = 0.5 * (gupxz * (2.0 * gxyy - gyyx) + gupyz * gyyy + gupzz * (2.0 * gyzy - gyyz));
+
+    const double Gamxzz = 0.5 * (gupxx * (2.0 * gxzz - gzzx) + gupxy * (2.0 * gyzz - gzzy) + gupxz * gzzz);
+    const double Gamyzz = 0.5 * (gupxy * (2.0 * gxzz - gzzx) + gupyy * (2.0 * gyzz - gzzy) + gupyz * gzzz);
+    const double Gamzzz = 0.5 * (gupxz * (2.0 * gxzz - gzzx) + gupyz * (2.0 * gyzz - gzzy) + gupzz * gzzz);
+
+    const double Gamxxy = 0.5 * (gupxx * gxxy + gupxy * gyyx + gupxz * (gxzy + gyzx - gxyz));
+    const double Gamyxy = 0.5 * (gupxy * gxxy + gupyy * gyyx + gupyz * (gxzy + gyzx - gxyz));
+    const double Gamzxy = 0.5 * (gupxz * gxxy + gupyz * gyyx + gupzz * (gxzy + gyzx - gxyz));
+
+    const double Gamxxz = 0.5 * (gupxx * gxxz + gupxy * (gxyz + gyzx - gxzy) + gupxz * gzzx);
+    const double Gamyxz = 0.5 * (gupxy * gxxz + gupyy * (gxyz + gyzx - gxzy) + gupyz * gzzx);
+    const double Gamzxz = 0.5 * (gupxz * gxxz + gupyz * (gxyz + gyzx - gxzy) + gupzz * gzzx);
+
+    const double Gamxyz = 0.5 * (gupxx * (gxyz + gxzy - gyzx) + gupxy * gyyz + gupxz * gzzy);
+    const double Gamyyz = 0.5 * (gupxy * (gxyz + gxzy - gyzx) + gupyy * gyyz + gupyz * gzzy);
+    const double Gamzyz = 0.5 * (gupxz * (gxyz + gxzy - gyzx) + gupyz * gyyz + gupzz * gzzy);
+
+    Gamxa = gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz +
+            2.0 * (gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz);
+    Gamya = gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz +
+            2.0 * (gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz);
+    Gamza = gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz +
+            2.0 * (gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz);
+}
+
+static int compute_rhs_z4c_cartesian(
+    int *ex, double &T, double *X, double *Y, double *Z,
+    double *chi_state, double *chi_constraints, double *trK,
+    double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+    double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+    double *Gamx, double *Gamy, double *Gamz,
+    double *Lap, double *betax, double *betay, double *betaz,
+    double *dtSfx, double *dtSfy, double *dtSfz,
+    double *TZ,
+    double *chi_rhs, double *trK_rhs,
+    double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+    double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+    double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+    double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+    double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+    double *TZ_rhs,
+    double *rho, double *Sx, double *Sy, double *Sz,
+    double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+    double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+    double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+    double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+    double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+    double *Hcon, double *Mxcon, double *Mycon, double *Mzcon, double *Gmxcon, double *Gmycon, double *Gmzcon,
+    int &Symmetry, int &Lev, double &eps, int &co)
+{
+    (void)T;
+
+    const int nx = ex[0];
+    const int ny = ex[1];
+    const int nz = ex[2];
+    const int all = nx * ny * nz;
+
+    double alpn1[all], chin1[all], gxx[all], gyy[all], gzz[all];
+    double chix[all], chiy[all], chiz[all], chixx[all], chixy[all], chixz[all], chiyy[all], chiyz[all], chizz[all];
+    double gxxx[all], gxyx[all], gxzx[all], gyyx[all], gyzx[all], gzzx[all];
+    double gxxy[all], gxyy[all], gxzy[all], gyyy[all], gyzy[all], gzzy[all];
+    double gxxz[all], gxyz[all], gxzz[all], gyyz[all], gyzz[all], gzzz[all];
+    double gxxxx[all], gxxxy[all], gxxxz[all], gxxyy[all], gxxyz[all], gxxzz[all];
+    double gxyxx[all], gxyxy[all], gxyxz[all], gxyyy[all], gxyyz[all], gxyzz[all];
+    double gxzxx[all], gxzxy[all], gxzxz[all], gxzyy[all], gxzyz[all], gxzzz[all];
+    double gyyxx[all], gyyxy[all], gyyxz[all], gyyyy[all], gyyyz[all], gyyzz[all];
+    double gyzxx[all], gyzxy[all], gyzxz[all], gyzyy[all], gyzyz[all], gyzzz[all];
+    double gzzxx[all], gzzxy[all], gzzxz[all], gzzyy[all], gzzyz[all], gzzzz[all];
+    double Lapx[all], Lapy[all], Lapz[all], Lapxx[all], Lapxy[all], Lapxz[all], Lapyy[all], Lapyz[all], Lapzz[all];
+    double betaxx[all], betaxy[all], betaxz[all], betayx[all], betayy[all], betayz[all], betazx[all], betazy[all], betazz[all];
+    double dBxx[all], dBxy[all], dBxz[all], dByx[all], dByy[all], dByz[all], dBzx[all], dBzy[all], dBzz[all];
+    double sfxxx[all], sfxxy[all], sfxxz[all], sfxyy[all], sfxyz[all], sfxzz[all];
+    double sfyxx[all], sfyxy[all], sfyxz[all], sfyyy[all], sfyyz[all], sfyzz[all];
+    double sfzxx[all], sfzxy[all], sfzxz[all], sfzyy[all], sfzyz[all], sfzzz[all];
+    double Gamxx[all], Gamxy[all], Gamxz[all], Gamyx[all], Gamyy[all], Gamyz[all], Gamzx[all], Gamzy[all], Gamzz[all];
+    double Kx[all], Ky[all], Kz[all], TZx[all], TZy[all], TZz[all];
+    double Axxx[all], Axxy[all], Axxz[all], Axyx[all], Axyy[all], Axyz[all];
+    double Axzx[all], Axzy[all], Axzz[all], Ayyx[all], Ayyy[all], Ayyz[all];
+    double Ayzx[all], Ayzy[all], Ayzz[all], Azzx[all], Azzy[all], Azzz[all];
+#if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5)
+    double reta[all];
+#endif
+
+    const double SSS[3] = {1.0, 1.0, 1.0};
+    const double AAS[3] = {-1.0, -1.0, 1.0};
+    const double ASA[3] = {-1.0, 1.0, -1.0};
+    const double SAA[3] = {1.0, -1.0, -1.0};
+    const double ASS[3] = {-1.0, 1.0, 1.0};
+    const double SAS[3] = {1.0, -1.0, 1.0};
+    const double SSA[3] = {1.0, 1.0, -1.0};
+
+    const double ONE = 1.0;
+    const double TWO = 2.0;
+    const double ZEO = 0.0;
+    double chiDivfloor = 1.0e-5;
+
+    double kappa1 = 2.0e-2;
+    double kappa2 = 0.0;
+    double FF = 0.75;
+    double eta = 2.0;
+
+    for (int idx = 0; idx < all; ++idx)
+    {
+        alpn1[idx] = Lap[idx] + ONE;
+        chin1[idx] = chi_state[idx] + ONE;
+        gxx[idx] = dxx[idx] + ONE;
+        gyy[idx] = dyy[idx] + ONE;
+        gzz[idx] = dzz[idx] + ONE;
+    }
+
+    fderivs(ex, betax, betaxx, betaxy, betaxz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, betay, betayx, betayy, betayz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, betaz, betazx, betazy, betazz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
+    fderivs(ex, dtSfx, dBxx, dBxy, dBxz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, dtSfy, dByx, dByy, dByz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, dtSfz, dBzx, dBzy, dBzz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
+    fderivs(ex, chi_state, chix, chiy, chiz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, dxx, gxxx, gxxy, gxxz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, gxy, gxyx, gxyy, gxyz, X, Y, Z, -1.0, -1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, gxz, gxzx, gxzy, gxzz, X, Y, Z, -1.0, 1.0, -1.0, Symmetry, Lev);
+    fderivs(ex, dyy, gyyx, gyyy, gyyz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, gyz, gyzx, gyzy, gyzz, X, Y, Z, 1.0, -1.0, -1.0, Symmetry, Lev);
+    fderivs(ex, dzz, gzzx, gzzy, gzzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+
+    fdderivs(ex, dxx, gxxxx, gxxxy, gxxxz, gxxyy, gxxyz, gxxzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, dyy, gyyxx, gyyxy, gyyxz, gyyyy, gyyyz, gyyzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, dzz, gzzxx, gzzxy, gzzxz, gzzyy, gzzyz, gzzzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, gxy, gxyxx, gxyxy, gxyxz, gxyyy, gxyyz, gxyzz, X, Y, Z, -1.0, -1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, gxz, gxzxx, gxzxy, gxzxz, gxzyy, gxzyz, gxzzz, X, Y, Z, -1.0, 1.0, -1.0, Symmetry, Lev);
+    fdderivs(ex, gyz, gyzxx, gyzxy, gyzxz, gyzyy, gyzyz, gyzzz, X, Y, Z, 1.0, -1.0, -1.0, Symmetry, Lev);
+
+    fderivs(ex, Gamx, Gamxx, Gamxy, Gamxz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Gamy, Gamyx, Gamyy, Gamyz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Gamz, Gamzx, Gamzy, Gamzz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
+
+    fderivs(ex, Lap, Lapx, Lapy, Lapz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, trK, Kx, Ky, Kz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, TZ, TZx, TZy, TZz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+
+    fdderivs(ex, betax, sfxxx, sfxxy, sfxxz, sfxyy, sfxyz, sfxzz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, betay, sfyxx, sfyxy, sfyxz, sfyyy, sfyyz, sfyzz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, betaz, sfzxx, sfzxy, sfzxz, sfzyy, sfzyz, sfzzz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
+
+    fdderivs(ex, chi_state, chixx, chixy, chixz, chiyy, chiyz, chizz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fdderivs(ex, Lap, Lapxx, Lapxy, Lapxz, Lapyy, Lapyz, Lapzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+
+    fderivs(ex, Axx, Axxx, Axxy, Axxz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Axy, Axyx, Axyy, Axyz, X, Y, Z, -1.0, -1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Axz, Axzx, Axzy, Axzz, X, Y, Z, -1.0, 1.0, -1.0, Symmetry, Lev);
+    fderivs(ex, Ayy, Ayyx, Ayyy, Ayyz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+    fderivs(ex, Ayz, Ayzx, Ayzy, Ayzz, X, Y, Z, 1.0, -1.0, -1.0, Symmetry, Lev);
+    fderivs(ex, Azz, Azzx, Azzy, Azzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
+
+    for (int idx = 0; idx < all; ++idx)
+    {
+        double point_kappa1 = 0.0;
+        f_z4c_rhs_point(
+            Axx[idx], Axy[idx], Axz[idx], Ayy[idx], Ayz[idx], Azz[idx],
+            alpn1[idx], dtSfx[idx], dtSfy[idx], dtSfz[idx],
+            betax[idx], betay[idx], betaz[idx],
+            chin1[idx], chiDivfloor,
+            Lapx[idx],
+            Axxx[idx], Axyx[idx], Axzx[idx], Ayyx[idx], Ayzx[idx], Azzx[idx],
+            Lapy[idx],
+            Axxy[idx], Axyy[idx], Axzy[idx], Ayyy[idx], Ayzy[idx], Azzy[idx],
+            Lapz[idx],
+            Axxz[idx], Axyz[idx], Axzz[idx], Ayyz[idx], Ayzz[idx], Azzz[idx],
+            betaxx[idx], dBxx[idx], betayx[idx], dByx[idx], betazx[idx], dBzx[idx],
+            betaxy[idx], dBxy[idx], betayy[idx], dByy[idx], betazy[idx], dBzy[idx],
+            betaxz[idx], dBxz[idx], betayz[idx], dByz[idx], betazz[idx], dBzz[idx],
+            chix[idx], chiy[idx], chiz[idx],
+            Lapxx[idx], Lapxy[idx], Lapxz[idx], Lapyy[idx], Lapyz[idx], Lapzz[idx],
+            sfxxx[idx], sfyxx[idx], sfzxx[idx],
+            sfxxy[idx], sfyxy[idx], sfzxy[idx],
+            sfxxz[idx], sfyxz[idx], sfzxz[idx],
+            sfxyy[idx], sfyyy[idx], sfzyy[idx],
+            sfxyz[idx], sfyyz[idx], sfzyz[idx],
+            sfxzz[idx], sfyzz[idx], sfzzz[idx],
+            chixx[idx], chixy[idx], chixz[idx], chiyy[idx], chiyz[idx], chizz[idx],
+            gxxxx[idx], gxyxx[idx], gxzxx[idx], gyyxx[idx], gyzxx[idx], gzzxx[idx],
+            gxxxy[idx], gxyxy[idx], gxzxy[idx], gyyxy[idx], gyzxy[idx], gzzxy[idx],
+            gxxxz[idx], gxyxz[idx], gxzxz[idx], gyyxz[idx], gyzxz[idx], gzzxz[idx],
+            gxxyy[idx], gxyyy[idx], gxzyy[idx], gyyyy[idx], gyzyy[idx], gzzyy[idx],
+            gxxyz[idx], gxyyz[idx], gxzyz[idx], gyyyz[idx], gyzyz[idx], gzzyz[idx],
+            gxxzz[idx], gxyzz[idx], gxzzz[idx], gyyzz[idx], gyzzz[idx], gzzzz[idx],
+            Gamxx[idx], gxxx[idx], gxyx[idx], gxzx[idx],
+            Gamyx[idx], gyyx[idx], gyzx[idx],
+            Gamzx[idx], gzzx[idx],
+            Gamxy[idx], gxxy[idx], gxyy[idx], gxzy[idx],
+            Gamyy[idx], gyyy[idx], gyzy[idx],
+            Gamzy[idx], gzzy[idx],
+            Gamxz[idx], gxxz[idx], gxyz[idx], gxzz[idx],
+            Gamyz[idx], gyyz[idx], gyzz[idx],
+            Gamzz[idx], gzzz[idx],
+            Kx[idx], Ky[idx], Kz[idx],
+            TZx[idx], TZy[idx], TZz[idx],
+            Gamx[idx], gxx[idx], gxy[idx], gxz[idx],
+            Gamy[idx], gyy[idx], gyz[idx],
+            Gamz[idx], gzz[idx],
+            point_kappa1, kappa2,
+            trK[idx],
+            Axx_rhs[idx], Axy_rhs[idx], Axz_rhs[idx], Ayy_rhs[idx], Ayz_rhs[idx], Azz_rhs[idx],
+            chi_rhs[idx],
+            Gamx_rhs[idx], gxx_rhs[idx], gxy_rhs[idx], gxz_rhs[idx],
+            Gamy_rhs[idx], gyy_rhs[idx], gyz_rhs[idx],
+            Gamz_rhs[idx], gzz_rhs[idx], trK_rhs[idx], TZ_rhs[idx], TZ[idx]);
+    }
+
+    for (int idx = 0; idx < all; ++idx)
+        Lap_rhs[idx] = -TWO * alpn1[idx] * trK[idx];
+
+#if (GAUGE == 0)
+    for (int idx = 0; idx < all; ++idx)
+    {
+        betax_rhs[idx] = FF * dtSfx[idx];
+        betay_rhs[idx] = FF * dtSfy[idx];
+        betaz_rhs[idx] = FF * dtSfz[idx];
+        dtSfx_rhs[idx] = Gamx_rhs[idx] - eta * dtSfx[idx];
+        dtSfy_rhs[idx] = Gamy_rhs[idx] - eta * dtSfy[idx];
+        dtSfz_rhs[idx] = Gamz_rhs[idx] - eta * dtSfz[idx];
+    }
+#elif (GAUGE == 1)
+    for (int idx = 0; idx < all; ++idx)
+    {
+        betax_rhs[idx] = Gamx[idx] - eta * betax[idx];
+        betay_rhs[idx] = Gamy[idx] - eta * betay[idx];
+        betaz_rhs[idx] = Gamz[idx] - eta * betaz[idx];
+        dtSfx_rhs[idx] = ZEO;
+        dtSfy_rhs[idx] = ZEO;
+        dtSfz_rhs[idx] = ZEO;
+    }
+#elif (GAUGE == 2)
+    /* Variable-eta gamma-driver, chi-sqrt denominator */
+    for (int idx = 0; idx < all; ++idx)
+    {
+        const double chin1i = chin1[idx];
+        const double det = gxx[idx] * gyy[idx] * gzz[idx]
+                         + gxy[idx] * gyz[idx] * gxz[idx] * 2.0
+                         - gxz[idx] * gyy[idx] * gxz[idx]
+                         - gxy[idx] * gxy[idx] * gzz[idx]
+                         - gxx[idx] * gyz[idx] * gyz[idx];
+        const double idet = ONE / det;
+        const double upxx = (gyy[idx] * gzz[idx] - gyz[idx] * gyz[idx]) * idet;
+        const double upxy = -(gxy[idx] * gzz[idx] - gyz[idx] * gxz[idx]) * idet;
+        const double upxz = (gxy[idx] * gyz[idx] - gyy[idx] * gxz[idx]) * idet;
+        const double upyy = (gxx[idx] * gzz[idx] - gxz[idx] * gxz[idx]) * idet;
+        const double upyz = -(gxx[idx] * gyz[idx] - gxy[idx] * gxz[idx]) * idet;
+        const double upzz = (gxx[idx] * gyy[idx] - gxy[idx] * gxy[idx]) * idet;
+        const double grdchi2 =
+            upxx * chix[idx] * chix[idx] + upyy * chiy[idx] * chiy[idx] + upzz * chiz[idx] * chiz[idx]
+          + TWO * (upxy * chix[idx] * chiy[idx] + upxz * chix[idx] * chiz[idx] + upyz * chiy[idx] * chiz[idx]);
+        const double sqchi = sqrt(chin1i);
+        reta[idx] = 1.31 / TWO * sqrt(grdchi2 / chin1i) / ((ONE - sqchi) * (ONE - sqchi));
+        betax_rhs[idx] = FF * dtSfx[idx];
+        betay_rhs[idx] = FF * dtSfy[idx];
+        betaz_rhs[idx] = FF * dtSfz[idx];
+        dtSfx_rhs[idx] = Gamx_rhs[idx] - reta[idx] * dtSfx[idx];
+        dtSfy_rhs[idx] = Gamy_rhs[idx] - reta[idx] * dtSfy[idx];
+        dtSfz_rhs[idx] = Gamz_rhs[idx] - reta[idx] * dtSfz[idx];
+    }
+#elif (GAUGE == 3)
+    /* Variable-eta gamma-driver, chi-linear denominator */
+    for (int idx = 0; idx < all; ++idx)
+    {
+        const double chin1i = chin1[idx];
+        const double det = gxx[idx] * gyy[idx] * gzz[idx]
+                         + gxy[idx] * gyz[idx] * gxz[idx] * 2.0
+                         - gxz[idx] * gyy[idx] * gxz[idx]
+                         - gxy[idx] * gxy[idx] * gzz[idx]
+                         - gxx[idx] * gyz[idx] * gyz[idx];
+        const double idet = ONE / det;
+        const double upxx = (gyy[idx] * gzz[idx] - gyz[idx] * gyz[idx]) * idet;
+        const double upxy = -(gxy[idx] * gzz[idx] - gyz[idx] * gxz[idx]) * idet;
+        const double upxz = (gxy[idx] * gyz[idx] - gyy[idx] * gxz[idx]) * idet;
+        const double upyy = (gxx[idx] * gzz[idx] - gxz[idx] * gxz[idx]) * idet;
+        const double upyz = -(gxx[idx] * gyz[idx] - gxy[idx] * gxz[idx]) * idet;
+        const double upzz = (gxx[idx] * gyy[idx] - gxy[idx] * gxy[idx]) * idet;
+        const double grdchi2 =
+            upxx * chix[idx] * chix[idx] + upyy * chiy[idx] * chiy[idx] + upzz * chiz[idx] * chiz[idx]
+          + TWO * (upxy * chix[idx] * chiy[idx] + upxz * chix[idx] * chiz[idx] + upyz * chiy[idx] * chiz[idx]);
+        reta[idx] = 1.31 / TWO * sqrt(grdchi2 / chin1i) / ((ONE - chin1i) * (ONE - chin1i));
+        betax_rhs[idx] = FF * dtSfx[idx];
+        betay_rhs[idx] = FF * dtSfy[idx];
+        betaz_rhs[idx] = FF * dtSfz[idx];
+        dtSfx_rhs[idx] = Gamx_rhs[idx] - reta[idx] * dtSfx[idx];
+        dtSfy_rhs[idx] = Gamy_rhs[idx] - reta[idx] * dtSfy[idx];
+        dtSfz_rhs[idx] = Gamz_rhs[idx] - reta[idx] * dtSfz[idx];
+    }
+#elif (GAUGE == 4)
+    /* Variable-eta gamma-driver, first-order, chi-sqrt denominator */
+    for (int idx = 0; idx < all; ++idx)
+    {
+        const double chin1i = chin1[idx];
+        const double det = gxx[idx] * gyy[idx] * gzz[idx]
+                         + gxy[idx] * gyz[idx] * gxz[idx] * 2.0
+                         - gxz[idx] * gyy[idx] * gxz[idx]
+                         - gxy[idx] * gxy[idx] * gzz[idx]
+                         - gxx[idx] * gyz[idx] * gyz[idx];
+        const double idet = ONE / det;
+        const double upxx = (gyy[idx] * gzz[idx] - gyz[idx] * gyz[idx]) * idet;
+        const double upxy = -(gxy[idx] * gzz[idx] - gyz[idx] * gxz[idx]) * idet;
+        const double upxz = (gxy[idx] * gyz[idx] - gyy[idx] * gxz[idx]) * idet;
+        const double upyy = (gxx[idx] * gzz[idx] - gxz[idx] * gxz[idx]) * idet;
+        const double upyz = -(gxx[idx] * gyz[idx] - gxy[idx] * gxz[idx]) * idet;
+        const double upzz = (gxx[idx] * gyy[idx] - gxy[idx] * gxy[idx]) * idet;
+        const double grdchi2 =
+            upxx * chix[idx] * chix[idx] + upyy * chiy[idx] * chiy[idx] + upzz * chiz[idx] * chiz[idx]
+          + TWO * (upxy * chix[idx] * chiy[idx] + upxz * chix[idx] * chiz[idx] + upyz * chiy[idx] * chiz[idx]);
+        const double sqchi = sqrt(chin1i);
+        reta[idx] = 1.31 / TWO * sqrt(grdchi2 / chin1i) / ((ONE - sqchi) * (ONE - sqchi));
+        betax_rhs[idx] = Gamx_rhs[idx] - reta[idx] * betax[idx];
+        betay_rhs[idx] = Gamy_rhs[idx] - reta[idx] * betay[idx];
+        betaz_rhs[idx] = Gamz_rhs[idx] - reta[idx] * betaz[idx];
+        dtSfx_rhs[idx] = ZEO;
+        dtSfy_rhs[idx] = ZEO;
+        dtSfz_rhs[idx] = ZEO;
+    }
+#elif (GAUGE == 5)
+    /* Variable-eta gamma-driver, first-order, chi-linear denominator */
+    for (int idx = 0; idx < all; ++idx)
+    {
+        const double chin1i = chin1[idx];
+        const double det = gxx[idx] * gyy[idx] * gzz[idx]
+                         + gxy[idx] * gyz[idx] * gxz[idx] * 2.0
+                         - gxz[idx] * gyy[idx] * gxz[idx]
+                         - gxy[idx] * gxy[idx] * gzz[idx]
+                         - gxx[idx] * gyz[idx] * gyz[idx];
+        const double idet = ONE / det;
+        const double upxx = (gyy[idx] * gzz[idx] - gyz[idx] * gyz[idx]) * idet;
+        const double upxy = -(gxy[idx] * gzz[idx] - gyz[idx] * gxz[idx]) * idet;
+        const double upxz = (gxy[idx] * gyz[idx] - gyy[idx] * gxz[idx]) * idet;
+        const double upyy = (gxx[idx] * gzz[idx] - gxz[idx] * gxz[idx]) * idet;
+        const double upyz = -(gxx[idx] * gyz[idx] - gxy[idx] * gxz[idx]) * idet;
+        const double upzz = (gxx[idx] * gyy[idx] - gxy[idx] * gxy[idx]) * idet;
+        const double grdchi2 =
+            upxx * chix[idx] * chix[idx] + upyy * chiy[idx] * chiy[idx] + upzz * chiz[idx] * chiz[idx]
+          + TWO * (upxy * chix[idx] * chiy[idx] + upxz * chix[idx] * chiz[idx] + upyz * chiy[idx] * chiz[idx]);
+        reta[idx] = 1.31 / TWO * sqrt(grdchi2 / chin1i) / ((ONE - chin1i) * (ONE - chin1i));
+        betax_rhs[idx] = Gamx_rhs[idx] - reta[idx] * betax[idx];
+        betay_rhs[idx] = Gamy_rhs[idx] - reta[idx] * betay[idx];
+        betaz_rhs[idx] = Gamz_rhs[idx] - reta[idx] * betaz[idx];
+        dtSfx_rhs[idx] = ZEO;
+        dtSfy_rhs[idx] = ZEO;
+        dtSfz_rhs[idx] = ZEO;
+    }
+#elif (GAUGE == 6 || GAUGE == 7)
+    {
+        /* Jason's position-dependent damping: rational (6) or exponential (7) */
+        int BHN = 0;
+        double Porg[9] = {0.0};
+        double Mass[3] = {0.0};
+    #ifdef fortran1
+        extern "C" { void getpbh(int &, double *, double *); }
+    #elif defined(fortran2)
+        extern "C" { void GETPBH(int &, double *, double *); }
+    #else
+        extern "C" { void getpbh_(int &, double *, double *); }
+    #endif
+        {
+    #ifdef fortran1
+            getpbh(BHN, Porg, Mass);
+    #elif defined(fortran2)
+            GETPBH(BHN, Porg, Mass);
+    #else
+            getpbh_(BHN, Porg, Mass);
+    #endif
+        }
+        if (BHN == 2)
+        {
+            const double M = Mass[0] + Mass[1];
+            const double A = 2.0 / M;
+            const double w1 = 12.0, w2 = 12.0;
+            const double C1 = 1.0 / Mass[0] - A;
+            const double C2 = 1.0 / Mass[1] - A;
+            const double BH_sep2 = (Porg[3] - Porg[0]) * (Porg[3] - Porg[0])
+                                 + (Porg[4] - Porg[1]) * (Porg[4] - Porg[1])
+                                 + (Porg[5] - Porg[2]) * (Porg[5] - Porg[2]);
+            const double inv_BH_sep2 = 1.0 / BH_sep2;
+            for (int k0 = 0; k0 < nz; ++k0) {
+            for (int j0 = 0; j0 < ny; ++j0) {
+            for (int i0 = 0; i0 < nx; ++i0) {
+                const size_t idx = idx_ex(i0, j0, k0, ex);
+                const double xp = X[i0], yp = Y[j0], zp = Z[k0];
+                const double r1 = ((Porg[0]-xp)*(Porg[0]-xp) + (Porg[1]-yp)*(Porg[1]-yp) + (Porg[2]-zp)*(Porg[2]-zp)) * inv_BH_sep2;
+                const double r2 = ((Porg[3]-xp)*(Porg[3]-xp) + (Porg[4]-yp)*(Porg[4]-yp) + (Porg[5]-zp)*(Porg[5]-zp)) * inv_BH_sep2;
+            #if (GAUGE == 6)
+                const double reta_val = A + C1 / (1.0 + w1 * r1) + C2 / (1.0 + w2 * r2);
+            #else
+                const double reta_val = A + C1 * exp(-w1 * r1) + C2 * exp(-w2 * r2);
+            #endif
+                betax_rhs[idx] = FF * dtSfx[idx];
+                betay_rhs[idx] = FF * dtSfy[idx];
+                betaz_rhs[idx] = FF * dtSfz[idx];
+                dtSfx_rhs[idx] = Gamx_rhs[idx] - reta_val * dtSfx[idx];
+                dtSfy_rhs[idx] = Gamy_rhs[idx] - reta_val * dtSfy[idx];
+                dtSfz_rhs[idx] = Gamz_rhs[idx] - reta_val * dtSfz[idx];
+            }}}
+        }
+        else
+        {
+            fprintf(stderr, "z4c_rhs_c: GAUGE %d requires BHN=2, got BHN=%d\n", (int)GAUGE, BHN);
+            return 1;
+        }
+    }
+#else
+#error "z4c_rhs_c.C: unsupported GAUGE value"
+#endif
+
+    lopsided(ex, X, Y, Z, gxx, gxx_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, gxy, gxy_rhs, betax, betay, betaz, Symmetry, AAS);
+    lopsided(ex, X, Y, Z, gxz, gxz_rhs, betax, betay, betaz, Symmetry, ASA);
+    lopsided(ex, X, Y, Z, gyy, gyy_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, gyz, gyz_rhs, betax, betay, betaz, Symmetry, SAA);
+    lopsided(ex, X, Y, Z, gzz, gzz_rhs, betax, betay, betaz, Symmetry, SSS);
+
+    lopsided(ex, X, Y, Z, Axx, Axx_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, Axy, Axy_rhs, betax, betay, betaz, Symmetry, AAS);
+    lopsided(ex, X, Y, Z, Axz, Axz_rhs, betax, betay, betaz, Symmetry, ASA);
+    lopsided(ex, X, Y, Z, Ayy, Ayy_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, Ayz, Ayz_rhs, betax, betay, betaz, Symmetry, SAA);
+    lopsided(ex, X, Y, Z, Azz, Azz_rhs, betax, betay, betaz, Symmetry, SSS);
+
+    lopsided(ex, X, Y, Z, chi_state, chi_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, trK, trK_rhs, betax, betay, betaz, Symmetry, SSS);
+
+    lopsided(ex, X, Y, Z, Gamx, Gamx_rhs, betax, betay, betaz, Symmetry, ASS);
+    lopsided(ex, X, Y, Z, Gamy, Gamy_rhs, betax, betay, betaz, Symmetry, SAS);
+    lopsided(ex, X, Y, Z, Gamz, Gamz_rhs, betax, betay, betaz, Symmetry, SSA);
+
+    lopsided(ex, X, Y, Z, Lap, Lap_rhs, betax, betay, betaz, Symmetry, SSS);
+    lopsided(ex, X, Y, Z, betax, betax_rhs, betax, betay, betaz, Symmetry, ASS);
+    lopsided(ex, X, Y, Z, betay, betay_rhs, betax, betay, betaz, Symmetry, SAS);
+    lopsided(ex, X, Y, Z, betaz, betaz_rhs, betax, betay, betaz, Symmetry, SSA);
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+    lopsided(ex, X, Y, Z, dtSfx, dtSfx_rhs, betax, betay, betaz, Symmetry, ASS);
+    lopsided(ex, X, Y, Z, dtSfy, dtSfy_rhs, betax, betay, betaz, Symmetry, SAS);
+    lopsided(ex, X, Y, Z, dtSfz, dtSfz_rhs, betax, betay, betaz, Symmetry, SSA);
+#endif
+    lopsided(ex, X, Y, Z, TZ, TZ_rhs, betax, betay, betaz, Symmetry, SSS);
+
+    for (int idx = 0; idx < all; ++idx)
+    {
+        double Gamxa = 0.0, Gamya = 0.0, Gamza = 0.0;
+        z4c_contract_gamma(
+            gxx[idx], gxy[idx], gxz[idx], gyy[idx], gyz[idx], gzz[idx],
+            gxxx[idx], gxyx[idx], gxzx[idx], gyyx[idx], gyzx[idx], gzzx[idx],
+            gxxy[idx], gxyy[idx], gxzy[idx], gyyy[idx], gyzy[idx], gzzy[idx],
+            gxxz[idx], gxyz[idx], gxzz[idx], gyyz[idx], gyzz[idx], gzzz[idx],
+            Gamxa, Gamya, Gamza);
+
+        TZ_rhs[idx] -= alpn1[idx] * (TWO + kappa2) * kappa1 * TZ[idx];
+        trK_rhs[idx] += alpn1[idx] * kappa1 * (ONE - kappa2) * TZ[idx];
+        Gamx_rhs[idx] -= TWO * alpn1[idx] * kappa1 * (Gamx[idx] - Gamxa);
+        Gamy_rhs[idx] -= TWO * alpn1[idx] * kappa1 * (Gamy[idx] - Gamya);
+        Gamz_rhs[idx] -= TWO * alpn1[idx] * kappa1 * (Gamz[idx] - Gamza);
+    }
+
+    if (eps > 0.0)
+    {
+        kodis(ex, X, Y, Z, chi_state, chi_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, trK, trK_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, gxx, gxx_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, gxy, gxy_rhs, AAS, Symmetry, eps);
+        kodis(ex, X, Y, Z, gxz, gxz_rhs, ASA, Symmetry, eps);
+        kodis(ex, X, Y, Z, gyy, gyy_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, gyz, gyz_rhs, SAA, Symmetry, eps);
+        kodis(ex, X, Y, Z, gzz, gzz_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Axx, Axx_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Axy, Axy_rhs, AAS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Axz, Axz_rhs, ASA, Symmetry, eps);
+        kodis(ex, X, Y, Z, Ayy, Ayy_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Ayz, Ayz_rhs, SAA, Symmetry, eps);
+        kodis(ex, X, Y, Z, Azz, Azz_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Gamx, Gamx_rhs, ASS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Gamy, Gamy_rhs, SAS, Symmetry, eps);
+        kodis(ex, X, Y, Z, Gamz, Gamz_rhs, SSA, Symmetry, eps);
+        kodis(ex, X, Y, Z, Lap, Lap_rhs, SSS, Symmetry, eps);
+        kodis(ex, X, Y, Z, betax, betax_rhs, ASS, Symmetry, eps);
+        kodis(ex, X, Y, Z, betay, betay_rhs, SAS, Symmetry, eps);
+        kodis(ex, X, Y, Z, betaz, betaz_rhs, SSA, Symmetry, eps);
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+        kodis(ex, X, Y, Z, dtSfx, dtSfx_rhs, ASS, Symmetry, eps);
+        kodis(ex, X, Y, Z, dtSfy, dtSfy_rhs, SAS, Symmetry, eps);
+        kodis(ex, X, Y, Z, dtSfz, dtSfz_rhs, SSA, Symmetry, eps);
+#endif
+        kodis(ex, X, Y, Z, TZ, TZ_rhs, SSS, Symmetry, eps);
+    }
+
+    if (co == 0)
+    {
+#if (ABV == 0)
+        f_ricci_gamma(ex, X, Y, Z,
+                      chi_constraints,
+                      dxx, gxy, gxz, dyy, gyz, dzz,
+                      Gamx, Gamy, Gamz,
+                      Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+                      Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+                      Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+                      Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+                      Symmetry);
+#endif
+        f_constraint_bssn(ex, X, Y, Z,
+                          chi_constraints, trK,
+                          dxx, gxy, gxz, dyy, gyz, dzz,
+                          Axx, Axy, Axz, Ayy, Ayz, Azz,
+                          Gamx, Gamy, Gamz,
+                          Lap, betax, betay, betaz, rho, Sx, Sy, Sz,
+                          Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+                          Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+                          Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+                          Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+                          Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
+                          Symmetry);
+    }
+
+    return 0;
+}
+
+extern "C" int f_compute_rhs_Z4c(int *ex, double &T,
+                                 double *X, double *Y, double *Z,
+                                 double *chi, double *trK,
+                                 double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                                 double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                                 double *Gamx, double *Gamy, double *Gamz,
+                                 double *Lap, double *betax, double *betay, double *betaz,
+                                 double *dtSfx, double *dtSfy, double *dtSfz,
+                                 double *TZ,
+                                 double *chi_rhs, double *trK_rhs,
+                                 double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                                 double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                                 double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                                 double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                                 double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                                 double *TZ_rhs,
+                                 double *rho, double *Sx, double *Sy, double *Sz,
+                                 double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                                 double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                                 double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                                 double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                                 double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                                 double *Hcon, double *Mxcon, double *Mycon, double *Mzcon, double *Gmxcon, double *Gmycon, double *Gmzcon,
+                                 int &Symmetry, int &Lev, double &eps, int &co)
+{
+    return compute_rhs_z4c_cartesian(
+        ex, T, X, Y, Z,
+        chi, chi, trK,
+        dxx, gxy, gxz, dyy, gyz, dzz,
+        Axx, Axy, Axz, Ayy, Ayz, Azz,
+        Gamx, Gamy, Gamz,
+        Lap, betax, betay, betaz,
+        dtSfx, dtSfy, dtSfz,
+        TZ,
+        chi_rhs, trK_rhs,
+        gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
+        Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
+        Gamx_rhs, Gamy_rhs, Gamz_rhs,
+        Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
+        dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
+        TZ_rhs,
+        rho, Sx, Sy, Sz,
+        Sxx, Sxy, Sxz, Syy, Syz, Szz,
+        Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+        Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+        Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+        Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+        Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
+        Symmetry, Lev, eps, co);
+}
+
+extern "C" int f_compute_rhs_Z4cnot(int *ex, double &T,
+                                    double *X, double *Y, double *Z,
+                                    double *chi, double *trK,
+                                    double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                                    double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                                    double *Gamx, double *Gamy, double *Gamz,
+                                    double *Lap, double *betax, double *betay, double *betaz,
+                                    double *dtSfx, double *dtSfy, double *dtSfz,
+                                    double *TZ,
+                                    double *chi_rhs, double *trK_rhs,
+                                    double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                                    double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                                    double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                                    double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                                    double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                                    double *TZ_rhs,
+                                    double *rho, double *Sx, double *Sy, double *Sz,
+                                    double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                                    double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                                    double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                                    double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                                    double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                                    double *Hcon, double *Mxcon, double *Mycon, double *Mzcon, double *Gmxcon, double *Gmycon, double *Gmzcon,
+                                    int &Symmetry, int &Lev, double &eps, int &co, double &chitiny)
+{
+    const int all = ex[0] * ex[1] * ex[2];
+    std::vector<double> chi_clamped(chi, chi + all);
+    f_lowerboundset(ex, chi_clamped.data(), chitiny);
+
+    const int ret = compute_rhs_z4c_cartesian(
+        ex, T, X, Y, Z,
+        chi_clamped.data(), chi, trK,
+        dxx, gxy, gxz, dyy, gyz, dzz,
+        Axx, Axy, Axz, Ayy, Ayz, Azz,
+        Gamx, Gamy, Gamz,
+        Lap, betax, betay, betaz,
+        dtSfx, dtSfy, dtSfz,
+        TZ,
+        chi_rhs, trK_rhs,
+        gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
+        Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
+        Gamx_rhs, Gamy_rhs, Gamz_rhs,
+        Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
+        dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
+        TZ_rhs,
+        rho, Sx, Sy, Sz,
+        Sxx, Sxy, Sxz, Syy, Syz, Szz,
+        Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+        Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+        Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+        Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+        Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
+        Symmetry, Lev, eps, co);
+
+    if (ret != 0 || co != 0)
+        return ret;
+
+#if (ABV == 0)
+    f_ricci_gamma(ex, X, Y, Z,
+                  chi,
+                  dxx, gxy, gxz, dyy, gyz, dzz,
+                  Gamx, Gamy, Gamz,
+                  Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+                  Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+                  Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+                  Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+                  Symmetry);
+#endif
+    f_constraint_bssn(ex, X, Y, Z,
+                      chi, trK,
+                      dxx, gxy, gxz, dyy, gyz, dzz,
+                      Axx, Axy, Axz, Ayy, Ayz, Azz,
+                      Gamx, Gamy, Gamz,
+                      Lap, betax, betay, betaz, rho, Sx, Sy, Sz,
+                      Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
+                      Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
+                      Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
+                      Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
+                      Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
+                      Symmetry);
+    return ret;
+}

BSSN_BUILD_CONFIG_MIGRATION.md

@@ -0,0 +1,211 @@
+# BSSN Build Config Migration
+
+This note records the build-configuration fix needed when replacing
+`AMSS_NCKU_Input.py` or `generate_macrodef.py` with a newer upstream version.
+
+## Problem
+
+`AMSS_NCKU_source/macrodef.h` is not the authoritative file used by normal
+runs. `AMSS_NCKU_Program.py` first generates macro files under
+`input_data.File_directory`, copies `AMSS_NCKU_source` to
+`<File_directory>/AMSS_NCKU_source_copy`, then copies the generated macro files
+into that copied source tree and compiles there.
+
+Therefore, makefile logic must not depend only on the stale
+`AMSS_NCKU_source/macrodef.h`. The actual equation path must be passed to the
+copied build tree from the same generation step that creates `macrodef.h`.
+
+The performance regression was caused by compiling/linking the
+`BSSN-EScalar` C wrapper into BSSN vacuum builds. For BSSN vacuum (`ABEtype=0`),
+the build must use:
+
+```make
+BSSN_USE_TRANSFER_CACHE=1
+BSSN_USE_ESCALAR_C_KERNEL=0
+```
+
+and must not link `bssn_escalar_rhs_c.o`.
+
+## Required Migration Steps
+
+### 1. Add an ABE type helper in `generate_macrodef.py`
+
+Add a helper that maps `input_data.Equation_Class` to the numeric `ABEtype`.
+Use the same mapping as `macrodef.h`:
+
+```python
+def get_abe_type():
+    if ( input_data.Equation_Class == "BSSN" ):
+        return 0
+    elif ( input_data.Equation_Class == "BSSN-EScalar" ):
+        return 1
+    elif ( input_data.Equation_Class == "BSSN-EM" ):
+        return 3
+    elif ( input_data.Equation_Class == "Z4C" ):
+        return 2
+    else:
+        raise ValueError("Equation_Class setting error!!!")
+```
+
+Update `generate_macrodef_h()` to print `#define ABEtype {get_abe_type()}`
+instead of duplicating the if/elif mapping.
+
+### 2. Generate a makefile fragment
+
+In `generate_macrodef.py`, add:
+
+```python
+def generate_build_config():
+    file1 = open(os.path.join(input_data.File_directory, "AMSS_NCKU_build.mk"), "w")
+    print("# Generated by generate_macrodef.py; do not edit manually.", file=file1)
+    print(f"ABE_TYPE := {get_abe_type()}", file=file1)
+    file1.close()
+```
+
+This file is the build-time authority for the equation path.
+
+### 3. Call and copy the generated build config
+
+In `AMSS_NCKU_Program.py`, after generating `macrodef.h` and `macrodef.fh`, call:
+
+```python
+generate_macrodef.generate_build_config()
+print(" AMSS-NCKU build config AMSS_NCKU_build.mk has been generated. ")
+```
+
+When copying generated files into `AMSS_NCKU_source_copy`, also copy:
+
+```python
+build_config_path = os.path.join(File_directory, "AMSS_NCKU_build.mk")
+shutil.copy2(build_config_path, AMSS_NCKU_source_copy)
+```
+
+### 4. Make the source makefile consume the generated config
+
+At the top of `AMSS_NCKU_source/makefile`, after `include makefile.inc`, add:
+
+```make
+-include AMSS_NCKU_build.mk
+
+ABE_TYPE ?= $(shell awk '/^[[:space:]]*\#define[[:space:]]+ABEtype/ {print $$3; exit}' macrodef.h 2>/dev/null)
+```
+
+The generated `AMSS_NCKU_build.mk` is used during normal Python-driven builds.
+The fallback keeps manual source-tree builds usable.
+
+### 5. Gate path-specific build options by `ABE_TYPE`
+
+Use effective build switches:
+
+```make
+ifeq ($(USE_TRANSFER_CACHE),auto)
+ifeq ($(ABE_TYPE),0)
+EFFECTIVE_USE_TRANSFER_CACHE = 1
+else
+EFFECTIVE_USE_TRANSFER_CACHE = 0
+endif
+else
+EFFECTIVE_USE_TRANSFER_CACHE = $(USE_TRANSFER_CACHE)
+endif
+
+ifeq ($(USE_CXX_ESCALAR_KERNEL),1)
+ifeq ($(ABE_TYPE),1)
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 1
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+else
+EFFECTIVE_USE_CXX_ESCALAR_KERNEL = 0
+endif
+
+TRANSFER_CACHE_FLAG = -DBSSN_USE_TRANSFER_CACHE=$(EFFECTIVE_USE_TRANSFER_CACHE)
+ESCALAR_KERNEL_FLAG = -DBSSN_USE_ESCALAR_C_KERNEL=$(EFFECTIVE_USE_CXX_ESCALAR_KERNEL)
+```
+
+Only add `bssn_escalar_rhs_c.o` when the effective EScalar C kernel switch is
+enabled:
+
+```make
+ifeq ($(EFFECTIVE_USE_CXX_ESCALAR_KERNEL),1)
+CFILES += bssn_escalar_rhs_c.o
+endif
+```
+
+### 6. Use safe transfer-cache default
+
+In `AMSS_NCKU_source/makefile.inc`, keep:
+
+```make
+USE_TRANSFER_CACHE ?= auto
+```
+
+With the effective switch logic above, this enables cached transfer for BSSN
+vacuum while keeping non-BSSN paths on the uncached path by default.
+
+## Verification Checklist
+
+Run these checks after migrating:
+
+```bash
+python3 -c "import generate_macrodef; generate_macrodef.generate_build_config()"
+cat GW150914/AMSS_NCKU_build.mk
+```
+
+For BSSN, the generated file should contain:
+
+```make
+ABE_TYPE := 0
+```
+
+Dry-run the copied or source makefile:
+
+```bash
+make -n -B INTERP_LB_MODE=off ABE | grep -E 'BSSN_USE_TRANSFER_CACHE|BSSN_USE_ESCALAR_C_KERNEL|bssn_escalar_rhs_c'
+```
+
+Expected BSSN result:
+
+```text
+-DBSSN_USE_TRANSFER_CACHE=1 -DBSSN_USE_ESCALAR_C_KERNEL=0
+```
+
+and no `bssn_escalar_rhs_c.o` in the final link command.
+
+Run the full workflow:
+
+```bash
+python3 AMSS_NCKU_Program.py
+```
+
+For the 10-step BSSN test, compare coordinate output:
+
+```bash
+python3 - <<'PY'
+from pathlib import Path
+old = Path('../GW150914-06457/AMSS_NCKU_output/bssn_BH.dat')
+new = Path('GW150914/AMSS_NCKU_output/bssn_BH.dat')
+
+def rows(path):
+    out = []
+    for line in path.read_text().splitlines():
+        if not line.strip() or line.lstrip().startswith('#'):
+            continue
+        out.append([float(x) for x in line.split()])
+    return out
+
+ro, rn = rows(old), rows(new)
+n = min(len(ro), len(rn))
+max_abs = 0.0
+for i in range(n):
+    for a, b in zip(ro[i], rn[i]):
+        max_abs = max(max_abs, abs(a - b))
+print(f"old_rows={len(ro)} new_rows={len(rn)} compared_rows={n}")
+print(f"max_abs_diff={max_abs:.17g}")
+PY
+```
+
+For the validated migration, the first 10 rows matched exactly:
+
+```text
+max_abs_diff=0
+```

generate_interp_lb_header.py

@@ -0,0 +1,72 @@
+#!/usr/bin/env python3
+"""Convert interp_lb_profile.bin to a C header for compile-time embedding."""
+import struct, sys
+
+if len(sys.argv) < 3:
+    print(f"Usage: {sys.argv[0]} <profile.bin> <output.h>")
+    sys.exit(1)
+
+with open(sys.argv[1], 'rb') as f:
+    magic, version, nprocs, num_heavy = struct.unpack('IIii', f.read(16))
+    threshold = struct.unpack('d', f.read(8))[0]
+    times = list(struct.unpack(f'{nprocs}d', f.read(nprocs * 8)))
+    heavy = list(struct.unpack(f'{num_heavy}i', f.read(num_heavy * 4)))
+
+# For each heavy rank, compute split: left half -> lighter neighbor, right half -> heavy rank
+# (or vice versa depending on which neighbor is lighter)
+splits = []
+for hr in heavy:
+    prev_t = times[hr - 1] if hr > 0 else 1e30
+    next_t = times[hr + 1] if hr < nprocs - 1 else 1e30
+    if prev_t <= next_t:
+        splits.append((hr, hr - 1, hr))  # (block_id, r_left, r_right)
+    else:
+        splits.append((hr, hr, hr + 1))
+
+# Also remap the displaced neighbor blocks
+remaps = {}
+for hr, r_l, r_r in splits:
+    if r_l != hr:
+        # We took r_l's slot, so remap block r_l to its other neighbor
+        displaced = r_l
+        if displaced > 0 and displaced - 1 not in [s[0] for s in splits]:
+            remaps[displaced] = displaced - 1
+        elif displaced < nprocs - 1:
+            remaps[displaced] = displaced + 1
+    else:
+        displaced = r_r
+        if displaced < nprocs - 1 and displaced + 1 not in [s[0] for s in splits]:
+            remaps[displaced] = displaced + 1
+        elif displaced > 0:
+            remaps[displaced] = displaced - 1
+
+with open(sys.argv[2], 'w') as out:
+    out.write("/* Auto-generated from interp_lb_profile.bin — do not edit */\n")
+    out.write("#ifndef INTERP_LB_PROFILE_DATA_H\n")
+    out.write("#define INTERP_LB_PROFILE_DATA_H\n\n")
+    out.write(f"#define INTERP_LB_NPROCS {nprocs}\n")
+    out.write(f"#define INTERP_LB_NUM_HEAVY {num_heavy}\n\n")
+    out.write(f"static const int interp_lb_heavy_blocks[{num_heavy}] = {{")
+    out.write(", ".join(str(h) for h in heavy))
+    out.write("};\n\n")
+    out.write("/* Split table: {block_id, r_left, r_right} */\n")
+    out.write(f"static const int interp_lb_splits[{num_heavy}][3] = {{\n")
+    for bid, rl, rr in splits:
+        out.write(f"    {{{bid}, {rl}, {rr}}},\n")
+    out.write("};\n\n")
+    out.write("/* Rank remap for displaced neighbor blocks */\n")
+    out.write(f"static const int interp_lb_num_remaps = {len(remaps)};\n")
+    out.write(f"static const int interp_lb_remaps[][2] = {{\n")
+    for src, dst in sorted(remaps.items()):
+        out.write(f"    {{{src}, {dst}}},\n")
+    if not remaps:
+        out.write("    {-1, -1},\n")
+    out.write("};\n\n")
+    out.write("#endif /* INTERP_LB_PROFILE_DATA_H */\n")
+
+print(f"Generated {sys.argv[2]}:")
+print(f"  {num_heavy} heavy blocks to split: {heavy}")
+for bid, rl, rr in splits:
+    print(f"    block {bid}: split -> rank {rl} (left), rank {rr} (right)")
+for src, dst in sorted(remaps.items()):
+    print(f"    block {src}: remap -> rank {dst}")

generate_macrodef.py

@@ -12,6 +12,37 @@ import os
 import AMSS_NCKU_Input as input_data          ## import program input file
 
 
+##################################################################
+
+def get_abe_type():
+    if ( input_data.Equation_Class == "BSSN" ):
+        return 0
+    elif ( input_data.Equation_Class == "BSSN-EScalar" ):
+        return 1
+    elif ( input_data.Equation_Class == "BSSN-EM" ):
+        return 3
+    elif ( input_data.Equation_Class == "Z4C" ):
+        return 2
+    else:
+        raise ValueError("Equation_Class setting error!!!")
+
+
+##################################################################
+
+## Generate the makefile fragment used by the copied source tree.
+## The source-tree macrodef.h is not authoritative because macro files
+## are regenerated under File_directory for each run.
+
+def generate_build_config():
+
+    file1 = open( os.path.join(input_data.File_directory, "AMSS_NCKU_build.mk"), "w")
+
+    print( "# Generated by generate_macrodef.py; do not edit manually.", file=file1 )
+    print( f"ABE_TYPE := {get_abe_type()}",                             file=file1 )
+
+    file1.close()
+
+
 ##################################################################
 
 ## Generate the macro file macrodef.h according to user settings
@@ -58,19 +89,10 @@ def generate_macrodef_h():
     # 2: Z4c vacuum
     # 3: coupled to Maxwell field
 
-    if ( input_data.Equation_Class == "BSSN" ):
-        print( "#define ABEtype 0", file=file1 )
-        print(                      file=file1 )
-    elif ( input_data.Equation_Class == "BSSN-EScalar" ):
-        print( "#define ABEtype 1", file=file1 )
-        print(                      file=file1 )
-    elif ( input_data.Equation_Class == "BSSN-EM" ):
-        print( "#define ABEtype 3", file=file1 )
-        print(                      file=file1 )
-    elif ( input_data.Equation_Class == "Z4C" ):
-        print( "#define ABEtype 2", file=file1 )
-        print(                      file=file1 )
-    else:
+    try:
+        print( f"#define ABEtype {get_abe_type()}", file=file1 )
+        print(                                      file=file1 )
+    except ValueError:
         print( "Equation_Class setting error!!!"                )
         print()
         print( "# Equation type #define ABEtype setting error!!!", file=file1 )
@@ -144,6 +166,62 @@ def generate_macrodef_h():
     print( "#define REGLEV 0",      file=file1 )
     print(                          file=file1 )
 
+    # Define fine-grained timing/debug macros.
+    # All of them default to OFF so production builds do not pay profiling overhead.
+
+    fine_timing = getattr(input_data, "Fine_Timing",
+                  getattr(input_data, "Finegrained_Timing", "no"))
+    kernel_fine_timing = getattr(input_data, "Kernel_Fine_Timing",
+                          getattr(input_data, "BSSN_Kernel_Fine_Timing", "no"))
+    stdin_abort_poll = getattr(input_data, "Enable_Stdin_Abort_Poll",
+                       getattr(input_data, "Stdin_Abort_Poll", "no"))
+    timing_report_every = max(1, int(getattr(
+        input_data, "Timing_Every_Steps",
+        getattr(input_data, "Timing_Report_Every", 1))))
+    timing_top_hotspots = max(1, int(getattr(
+        input_data, "Timing_Top_Hotspots", 8)))
+
+    if ( fine_timing == "yes" ):
+        print( "#define BSSN_FINE_TIMING 1", file=file1 )
+        print(                               file=file1 )
+    elif ( fine_timing == "no" ):
+        print( "#define BSSN_FINE_TIMING 0", file=file1 )
+        print(                               file=file1 )
+    else:
+        print( "Fine_Timing setting error!!!" )
+        print()
+        print( "# Fine_Timing setting error!!!", file=file1 )
+        print(                                   file=file1 )
+
+    print( f"#define BSSN_FINE_TIMING_EVERY {timing_report_every}", file=file1 )
+    print(                                                          file=file1 )
+    print( f"#define BSSN_FINE_TIMING_TOPN {timing_top_hotspots}",  file=file1 )
+    print(                                                          file=file1 )
+
+    if ( kernel_fine_timing == "yes" ):
+        print( "#define BSSN_KERNEL_FINE_TIMING 1", file=file1 )
+        print(                                      file=file1 )
+    elif ( kernel_fine_timing == "no" ):
+        print( "#define BSSN_KERNEL_FINE_TIMING 0", file=file1 )
+        print(                                      file=file1 )
+    else:
+        print( "Kernel_Fine_Timing setting error!!!" )
+        print()
+        print( "# Kernel_Fine_Timing setting error!!!", file=file1 )
+        print(                                          file=file1 )
+
+    if ( stdin_abort_poll == "yes" ):
+        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 1", file=file1 )
+        print(                                           file=file1 )
+    elif ( stdin_abort_poll == "no" ):
+        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 0", file=file1 )
+        print(                                           file=file1 )
+    else:
+        print( "Enable_Stdin_Abort_Poll setting error!!!" )
+        print()
+        print( "# Enable_Stdin_Abort_Poll setting error!!!", file=file1 )
+        print(                                               file=file1 )
+
     # Define macro USE_GPU
     # use GPU or not
     
@@ -224,6 +302,21 @@ def generate_macrodef_h():
     print( "//     0: for every level;",                                                 file=file1 ) 
     print( "//     1: for all",                                                          file=file1 )
     print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING",                                                 file=file1 )
+    print( "//     enable fine-grained per-timestep timing monitor",                     file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING_EVERY",                                           file=file1 )
+    print( "//     report timing every N coarse timesteps",                              file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING_TOPN",                                            file=file1 )
+    print( "//     number of hottest timing buckets shown in stdout",                    file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_KERNEL_FINE_TIMING",                                          file=file1 )
+    print( "//     enable split timing inside compute_rhs_bssn",                         file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_ENABLE_STDIN_ABORT_POLL",                                     file=file1 )
+    print( "//     poll stdin and broadcast abort flag every coarse step",               file=file1 )
+    print( "//",                                                                         file=file1 )
     print( "// define USE_GPU",                                                          file=file1 )
     print( "//     use gpu or not",                                                      file=file1 )
     print( "//",                                                                         file=file1 )

makefile_and_run.py

@@ -11,16 +11,47 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 import time
-## CPU core binding configuration using taskset
-## taskset ensures all child processes inherit the CPU affinity mask
-## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
-## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
-NUMACTL_CPU_BIND = "taskset -c 0-111"
 
-## Build parallelism configuration
-## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
-## Set make -j to utilize available cores for faster builds
-BUILD_JOBS = 104
+
+def get_last_n_cores_per_socket(n=32):
+    """
+    Read CPU topology via lscpu and return a taskset -c string
+    selecting the last `n` cores of each NUMA node (socket).
+
+    Example: 2 sockets x 56 cores each, n=32 -> node0: 24-55, node1: 80-111
+    -> "taskset -c 24-55,80-111"
+    """
+    result = subprocess.run(["lscpu", "--parse=NODE,CPU"], capture_output=True, text=True)
+
+    # Build a dict: node_id -> sorted list of CPU ids
+    node_cpus = {}
+    for line in result.stdout.splitlines():
+        if line.startswith("#") or not line.strip():
+            continue
+        parts = line.split(",")
+        if len(parts) < 2:
+            continue
+        node_id, cpu_id = int(parts[0]), int(parts[1])
+        node_cpus.setdefault(node_id, []).append(cpu_id)
+
+    segments = []
+    for node_id in sorted(node_cpus):
+        cpus = sorted(node_cpus[node_id])
+        selected = cpus[-n:]          # last n cores of this socket
+        segments.append(f"{selected[0]}-{selected[-1]}")
+
+    cpu_str = ",".join(segments)
+    total = len(segments) * n
+    print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
+    #return f"taskset -c {cpu_str}"
+    return f""
+
+
+## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
+NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
+
+## Build parallelism: match the number of bound cores
+BUILD_JOBS = 64
 
 
 ##################################################################
@@ -39,7 +70,7 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
     elif (input_data.GPU_Calculation == "yes"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:
@@ -117,6 +148,7 @@ def run_ABE():
     
     if (input_data.GPU_Calculation == "no"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
@@ -158,7 +190,8 @@ def run_TwoPunctureABE():
     print(                                                          )
     
     ## Define the command to run
-    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    #TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    TwoPuncture_command         = " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output

parallel_plot_helper.py

@@ -0,0 +1,29 @@
+import multiprocessing
+
+def run_plot_task(task):
+    """Execute a single plotting task.
+    
+    Parameters
+    ----------
+    task : tuple
+        A tuple of (function, args_tuple) where function is a callable
+        plotting function and args_tuple contains its arguments.
+    """
+    func, args = task
+    return func(*args)
+
+
+def run_plot_tasks_parallel(plot_tasks):
+    """Execute a list of independent plotting tasks in parallel.
+
+    Uses the 'fork' context to create worker processes so that the main
+    script is NOT re-imported/re-executed in child processes.
+
+    Parameters
+    ----------
+    plot_tasks : list of tuples
+        Each element is (function, args_tuple).
+    """
+    ctx = multiprocessing.get_context('fork')
+    with ctx.Pool() as pool:
+        pool.map(run_plot_task, plot_tasks)

plot_GW_strain_amplitude_xiaoqu.py

@@ -11,6 +11,8 @@
 import numpy                               ## numpy for array operations
 import scipy                               ## scipy for interpolation and signal processing
 import math
+import matplotlib
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 import os                                  ## os for system/file operations
 

plot_binary_data.py

@@ -8,16 +8,23 @@
 ##
 #################################################
 
+## Restrict OpenMP to one thread per process so that running
+## many workers in parallel does not create an O(workers * BLAS_threads)
+## thread explosion.  The variable MUST be set before numpy/scipy
+## are imported, because the BLAS library reads them only at load time.
+import os
+os.environ.setdefault("OMP_NUM_THREADS",        "1")
+
 import numpy
 import scipy
+import matplotlib
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt
 from   matplotlib.colors    import LogNorm
 from   mpl_toolkits.mplot3d import Axes3D
 ## import torch
 import AMSS_NCKU_Input      as input_data
 
-import os
-
 
 #########################################################################################
 
@@ -192,3 +199,19 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
 
 ####################################################################################
 
+
+####################################################################################
+## Allow this module to be run as a standalone script so that each
+## binary-data plot can be executed in a fresh subprocess whose BLAS
+## environment variables (set above) take effect before numpy loads.
+##
+## Usage:  python3 plot_binary_data.py <filename> <binary_outdir> <figure_outdir>
+####################################################################################
+
+if __name__ == '__main__':
+    import sys
+    if len(sys.argv) != 4:
+        print(f"Usage: {sys.argv[0]} <filename> <binary_outdir> <figure_outdir>")
+        sys.exit(1)
+    plot_binary_data(sys.argv[1], sys.argv[2], sys.argv[3])
+

plot_xiaoqu.py

@@ -8,6 +8,8 @@
 #################################################
 
 import numpy                               ## numpy for array operations
+import matplotlib
+matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
 import glob
@@ -15,6 +17,9 @@ import os                                  ## operating system utilities
 
 import plot_binary_data
 import AMSS_NCKU_Input as input_data
+import subprocess
+import sys
+import multiprocessing
 
 # plt.rcParams['text.usetex'] = True  ## enable LaTeX fonts in plots
 
@@ -50,10 +55,40 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
         file_list.append(x)
         print(x)
 
-    ## Plot each file in the list
+    ## Plot each file in parallel using subprocesses.
+    ## Each subprocess is a fresh Python process where the BLAS thread-count
+    ## environment variables (set at the top of plot_binary_data.py) take
+    ## effect before numpy is imported.  This avoids the thread explosion
+    ## that occurs when multiprocessing.Pool with 'fork' context inherits
+    ## already-initialized multi-threaded BLAS from the parent.
+    script = os.path.join( os.path.dirname(__file__), "plot_binary_data.py" )
+    max_workers = min( multiprocessing.cpu_count(), len(file_list) ) if file_list else 0
+
+    running = []
+    failed  = []
     for filename in file_list:
         print(filename)
-        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
+        proc = subprocess.Popen(
+            [sys.executable, script, filename, binary_outdir, figure_outdir],
+        )
+        running.append( (proc, filename) )
+        ## Keep at most max_workers subprocesses active at a time
+        if len(running) >= max_workers:
+            p, fn = running.pop(0)
+            p.wait()
+            if p.returncode != 0:
+                failed.append(fn)
+
+    ## Wait for all remaining subprocesses to finish
+    for p, fn in running:
+        p.wait()
+        if p.returncode != 0:
+            failed.append(fn)
+
+    if failed:
+        print( " WARNING: the following binary data plots failed:" )
+        for fn in failed:
+            print( "   ", fn )
 
     print(                        )
     print( " Binary Data Plot Has been Finished " )