黄老板逆天重写

The data_packer(NULL, ...) calls that compute send/recv buffer lengths
traverse all grid segments × variables × nprocs on every Sync_start
invocation, even though lengths never change once the cache is built.
Add a lengths_valid flag to SyncCache so these length computations are
done once and reused on subsequent calls (4× per RK4 step).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

.gitignore

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

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_Input.py

@@ -16,7 +16,7 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 64                             ## number of mpi processes used in the simulation
+MPI_processes    = 2                          ## number of mpi processes used in the simulation
 
 GPU_Calculation  = "no"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
@@ -50,7 +50,7 @@ Check_Time               = 100.0
 Dump_Time                = 100.0                  ## time inteval dT for dumping binary data
 D2_Dump_Time             = 100.0                  ## dump the ascii data for 2d surface after dT'
 Analysis_Time            = 0.1                    ## dump the puncture position and GW psi4 after dT"
-Evolution_Step_Number    = 10000000               ## stop the calculation after the maximal step number
+Evolution_Step_Number    = 6               ## stop the calculation after the maximal step number
 Courant_Factor           = 0.5                    ## Courant Factor
 Dissipation              = 0.15                   ## Kreiss-Oliger Dissipation Strength
 

AMSS_NCKU_Program.py

@@ -49,32 +49,32 @@ import time
 File_directory = os.path.join(input_data.File_directory)   
 
 ## If the specified output directory exists, ask the user whether to continue
-if os.path.exists(File_directory):
-    print( " Output dictionary has been existed !!!  "                                                              )
-    print( " If you want to overwrite the existing file directory, please input 'continue' in the terminal !! "     ) 
-    print( " If you want to retain the existing file directory, please input 'stop' in the terminal to stop the "   ) 
-    print( " simulation. Then you can reset the output dictionary in the input script file AMSS_NCKU_Input.py !!! " )
-    print(                                                                                                          )
-    ## Prompt whether to overwrite the existing directory
-    while True:
-        try:
-            inputvalue = input()
-            ## If the user agrees to overwrite, proceed and remove the existing directory
-            if ( inputvalue == "continue" ):
-                print( " Continue the calculation !!! " )
-                print(                                  )
-                break  
-            ## If the user chooses not to overwrite, exit and keep the existing directory
-            elif ( inputvalue == "stop" ):
-                print( " Stop the calculation !!! "    )
-                sys.exit() 
-            ## If the user input is invalid, prompt again
-            else:
-                print( " Please input your choice !!! "                   )
-                print( " Input 'continue' or 'stop' in the terminal !!! " )
-        except ValueError:
-            print( " Please input your choice !!! "                   )
-            print( " Input 'continue' or 'stop' in the terminal !!! " )
+# if os.path.exists(File_directory):
+#     print( " Output dictionary has been existed !!!  "                                                              )
+#     print( " If you want to overwrite the existing file directory, please input 'continue' in the terminal !! "     ) 
+#     print( " If you want to retain the existing file directory, please input 'stop' in the terminal to stop the "   ) 
+#     print( " simulation. Then you can reset the output dictionary in the input script file AMSS_NCKU_Input.py !!! " )
+#     print(                                                                                                          )
+#     ## Prompt whether to overwrite the existing directory
+#     while True:
+#         try:
+#             inputvalue = input()
+#             ## If the user agrees to overwrite, proceed and remove the existing directory
+#             if ( inputvalue == "continue" ):
+#                 print( " Continue the calculation !!! " )
+#                 print(                                  )
+#                 break  
+#             ## If the user chooses not to overwrite, exit and keep the existing directory
+#             elif ( inputvalue == "stop" ):
+#                 print( " Stop the calculation !!! "    )
+#                 sys.exit() 
+#             ## If the user input is invalid, prompt again
+#             else:
+#                 print( " Please input your choice !!! "                   )
+#                 print( " Input 'continue' or 'stop' in the terminal !!! " )
+#         except ValueError:
+#             print( " Please input your choice !!! "                   )
+#             print( " Input 'continue' or 'stop' in the terminal !!! " )
         
 ## Remove the existing output directory if present
 shutil.rmtree(File_directory, ignore_errors=True)

AMSS_NCKU_source/ABE.C

@@ -24,7 +24,7 @@ using namespace std;
 
 #include "misc.h"
 #include "macrodef.h"
-
+#include <omp.h>
 #ifndef ABEtype
 #error "not define ABEtype"
 #endif
@@ -69,8 +69,9 @@ int main(int argc, char *argv[])
 
       double Begin_clock, End_clock;
       if (myrank == 0)
-      {
+      {     
             Begin_clock = MPI_Wtime();
+
       }
 
       if (argc > 1)

AMSS_NCKU_source/MPatch.C

@@ -13,7 +13,7 @@ using namespace std;
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
-
+#include "xh_global_interp.h"
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
 
@@ -341,8 +341,9 @@ 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 +355,18 @@ 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], llb[dim], uub[dim];
   for (int i = 0; i < dim; i++)
-  {
     DH[i] = getdX(i);
-  }
-  llb = new double[dim];
-  uub = new double[dim];
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -399,16 +394,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
     while (notfind && Bp) // run along Blocks
     {
       Block *BP = Bp->data;
-
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
-// 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
@@ -433,6 +421,7 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (flag)
       {
         notfind = false;
+        owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
           //---> interpolation
@@ -440,129 +429,91 @@ void Patch::Interp_Points(MyList<var> *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],
+
+            xh_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];
-    }
-    else if (Weight[i] == 0 && myrank == 0)
-    {
-      cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int j = 0; j < dim; j++)
+      int cur_owner = owner_rank[j];
+      if (cur_owner < 0)
       {
-        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)
+        if (myrank == 0)
         {
-          Block *BP = Bp->data;
-
-          for (int i = 0; i < dim; i++)
+          cout << "ERROR: Patch::Interp_Points fails to find point (";
+          for (int d = 0; d < dim; d++)
           {
-#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 << 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 j = 0; j < dim; j++)
+          for (int d = 0; d < dim; d++)
           {
-            cout << llb[j] << ":" << uub[j];
-            if (j < dim - 1)
+            cout << bbox[dim + d] << "-" << uui[d] * DH[d];
+            if (d < dim - 1)
               cout << ",";
             else
               cout << ")" << endl;
           }
-          if (Bp == ble)
-            break;
-          Bp = Bp->next;
+          MPI_Abort(MPI_COMM_WORLD, 1);
         }
+        j++;
+        continue;
       }
-#endif
-      MPI_Abort(MPI_COMM_WORLD, 1);
+      // 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);
     }
   }
 
-  delete[] shellf;
-  delete[] weight;
-  delete[] Weight;
-  delete[] DH;
-  delete[] llb;
-  delete[] uub;
+  delete[] owner_rank;
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
-                          double *Shellf, int Symmetry, MPI_Comm Comm_here)
+                          double *Shellf, int Symmetry,
+                          int Nmin_consumer, int Nmax_consumer)
 {
-  // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
-  int myrank, lmyrank;
+  // 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.
+  int myrank, nprocs;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  MPI_Comm_rank(Comm_here, &lmyrank);
-
+  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
+// printf("here----\n");
+  // int zzz = 0;
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
   int num_var = 0;
@@ -573,24 +524,292 @@ 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
+  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);
+
+  // --- Interpolation phase (identical to original) ---
+  // printf("NN: %d, num_var = %d\n", NN, num_var);
+  #pragma omp parallel
+  {
+  #pragma omp for
+  for (int j = 0; j < NN; j++)
+  {
+    double pox[dim], llb[dim], uub[dim];
+    MyList<var> *varl1;
+    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);
+      // }
+    }
+
+    MyList<Block> *Bp = blb;
+    bool notfind = true;
+    while (notfind && Bp)
+    {
+      Block *BP = Bp->data;
+
+      bool flag = true;
+      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
+        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
+        {
+          flag = false;
+          break;
+        }
+      }
+      // printf("flag = %d\n", flag);
+      if (flag)
+      {
+        notfind = false;
+        owner_rank[j] = BP->rank;
+        if (myrank == BP->rank)
+        {
+          varl1 = VarList;
+          int k = 0;
+          while (varl1)
+          {
+            
+            xh_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl1->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl1->data->SoA, Symmetry);
+            varl1 = varl1->next;
+            k++;
+            // zzz += 1;
+          }
+        }
+      }
+      if (Bp == ble)
+        break;
+      Bp = Bp->next;
+    }
   }
-  llb = new double[dim];
-  uub = new double[dim];
+  }
+  // printf("Interpolation done, zzz = %d\n", zzz);
+  // --- 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 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);
+    }
+  }
+
+  // --- 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;
+}
+void Patch::Interp_Points(MyList<var> *VarList,
+                          int NN, double **XX,
+                          double *Shellf, int Symmetry, MPI_Comm Comm_here)
+{
+  // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
+  int myrank, lmyrank;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_rank(Comm_here, &lmyrank);
+  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] 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;
+
+  // 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], llb[dim], uub[dim];
+  for (int i = 0; i < dim; i++)
+    DH[i] = getdX(i);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -622,12 +841,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
-// 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
@@ -652,6 +865,7 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (flag)
       {
         notfind = false;
+        owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
           //---> interpolation
@@ -659,14 +873,11 @@ void Patch::Interp_Points(MyList<var> *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],
+            xh_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)
@@ -675,97 +886,35 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  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()
 {
@@ -956,7 +1105,7 @@ bool Patch::Interp_ONE_Point(MyList<var> *VarList, double *XX,
         {
           //              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[k],
+          xh_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[k],
                           pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
           varl = varl->next;
           k++;
@@ -1058,7 +1207,7 @@ bool Patch::Interp_ONE_Point(MyList<var> *VarList, double *XX,
   // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
   int myrank;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
+  
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
   int num_var = 0;
@@ -1198,7 +1347,7 @@ bool Patch::Interp_ONE_Point(MyList<var> *VarList, double *XX,
         {
           //              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[k],
+          xh_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[k],
                           pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
           varl = varl->next;
           k++;

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.C

@@ -4,7 +4,7 @@
 #include "prolongrestrict.h"
 #include "misc.h"
 #include "parameters.h"
-
+#include <omp.h>
 int Parallel::partition1(int &nx, int split_size, int min_width, int cpusize, int shape) // special for 1 diemnsion
 {
   nx = Mymax(1, shape / min_width);
@@ -3338,7 +3338,7 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
 {
   int myrank;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
+  // double time1 = omp_get_wtime();
   int DIM = dim;
 
   if (dir != PACK && dir != UNPACK)
@@ -3361,7 +3361,6 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
     varls = varls->next;
     varld = varld->next;
   }
-
   if (varls || varld)
   {
     cout << "error in short data packer, var lists does not match." << endl;
@@ -3375,7 +3374,6 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
     type = 2;
   else
     type = 3;
-
   while (src && dst)
   {
     if ((dir == PACK && dst->data->Bg->rank == rank_in && src->data->Bg->rank == myrank) ||
@@ -3385,6 +3383,7 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
       varld = VarListd;
       while (varls && varld)
       {
+
         if (data)
         {
           if (dir == PACK)
@@ -3405,6 +3404,7 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
               f_prolong3(DIM, src->data->Bg->bbox, src->data->Bg->bbox + dim, src->data->Bg->shape, src->data->Bg->fgfs[varls->data->sgfn],
                          dst->data->llb, dst->data->uub, dst->data->shape, data + size_out,
                          dst->data->llb, dst->data->uub, varls->data->SoA, Symmetry);
+
             }
           if (dir == UNPACK) // from target data to corresponding grid
             f_copy(DIM, dst->data->Bg->bbox, dst->data->Bg->bbox + dim, dst->data->Bg->shape, dst->data->Bg->fgfs[varld->data->sgfn],
@@ -3418,8 +3418,14 @@ int Parallel::data_packer(double *data, MyList<Parallel::gridseg> *src, MyList<P
     }
     dst = dst->next;
     src = src->next;
-  }
 
+  }
+  // double time2 = omp_get_wtime();
+  // xxx += time2 - time1;
+  // if(myrank == 0){
+  // printf("prolong3 time = %lf\n", time2 - time1);
+
+  // }
   return size_out;
 }
 int Parallel::data_packermix(double *data, MyList<Parallel::gridseg> *src, MyList<Parallel::gridseg> *dst, int rank_in, int dir,
@@ -3514,7 +3520,7 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
 
   int node;
-
+  // double time1 = omp_get_wtime();
   MPI_Request *reqs;
   MPI_Status *stats;
   reqs = new MPI_Request[2 * cpusize];
@@ -3583,7 +3589,9 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
     if (rec_data[node])
       delete[] rec_data[node];
   }
-
+  // double time2 = omp_get_wtime();
+  // if (myrank == 0)
+  //   printf("transfer time = %lf\n", time2 - time1);
   delete[] reqs;
   delete[] stats;
   delete[] send_data;
@@ -3756,6 +3764,502 @@ void Parallel::Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
   delete[] transfer_src;
   delete[] transfer_dst;
 }
+// Merged Sync: collect all intra-patch and inter-patch grid segment lists,
+// then issue a single transfer() call instead of N+1 separate ones.
+void Parallel::Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
+{
+  int cpusize;
+  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
+
+  MyList<Parallel::gridseg> **combined_src = new MyList<Parallel::gridseg> *[cpusize];
+  MyList<Parallel::gridseg> **combined_dst = new MyList<Parallel::gridseg> *[cpusize];
+  for (int node = 0; node < cpusize; node++)
+    combined_src[node] = combined_dst[node] = 0;
+
+  // Phase A: Intra-patch ghost exchange segments
+  MyList<Patch> *Pp = PatL;
+  while (Pp)
+  {
+    Patch *Pat = Pp->data;
+    MyList<Parallel::gridseg> *dst_ghost = build_ghost_gsl(Pat);
+
+    for (int node = 0; node < cpusize; node++)
+    {
+      MyList<Parallel::gridseg> *src_owned = build_owned_gsl0(Pat, node);
+      MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
+      build_gstl(src_owned, dst_ghost, &tsrc, &tdst);
+
+      if (tsrc)
+      {
+        if (combined_src[node])
+          combined_src[node]->catList(tsrc);
+        else
+          combined_src[node] = tsrc;
+      }
+      if (tdst)
+      {
+        if (combined_dst[node])
+          combined_dst[node]->catList(tdst);
+        else
+          combined_dst[node] = tdst;
+      }
+
+      if (src_owned)
+        src_owned->destroyList();
+    }
+
+    if (dst_ghost)
+      dst_ghost->destroyList();
+
+    Pp = Pp->next;
+  }
+
+  // Phase B: Inter-patch buffer exchange segments
+  MyList<Parallel::gridseg> *dst_buffer = build_buffer_gsl(PatL);
+  for (int node = 0; node < cpusize; node++)
+  {
+    MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatL, node, 5, Symmetry);
+    MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
+    build_gstl(src_owned, dst_buffer, &tsrc, &tdst);
+
+    if (tsrc)
+    {
+      if (combined_src[node])
+        combined_src[node]->catList(tsrc);
+      else
+        combined_src[node] = tsrc;
+    }
+    if (tdst)
+    {
+      if (combined_dst[node])
+        combined_dst[node]->catList(tdst);
+      else
+        combined_dst[node] = tdst;
+    }
+
+    if (src_owned)
+      src_owned->destroyList();
+  }
+  if (dst_buffer)
+    dst_buffer->destroyList();
+
+  // Phase C: Single transfer
+  transfer(combined_src, combined_dst, VarList, VarList, Symmetry);
+
+  // Phase D: Cleanup
+  for (int node = 0; node < cpusize; node++)
+  {
+    if (combined_src[node])
+      combined_src[node]->destroyList();
+    if (combined_dst[node])
+      combined_dst[node]->destroyList();
+  }
+  delete[] combined_src;
+  delete[] combined_dst;
+}
+// SyncCache constructor
+Parallel::SyncCache::SyncCache()
+    : valid(false), cpusize(0), combined_src(0), combined_dst(0),
+      send_lengths(0), recv_lengths(0), send_bufs(0), recv_bufs(0),
+      send_buf_caps(0), recv_buf_caps(0), reqs(0), stats(0), max_reqs(0),
+      lengths_valid(false)
+{
+}
+// SyncCache invalidate: free grid segment lists but keep buffers
+void Parallel::SyncCache::invalidate()
+{
+  if (!valid)
+    return;
+  for (int i = 0; i < cpusize; i++)
+  {
+    if (combined_src[i])
+      combined_src[i]->destroyList();
+    if (combined_dst[i])
+      combined_dst[i]->destroyList();
+    combined_src[i] = combined_dst[i] = 0;
+    send_lengths[i] = recv_lengths[i] = 0;
+  }
+  valid = false;
+  lengths_valid = false;
+}
+// SyncCache destroy: free everything
+void Parallel::SyncCache::destroy()
+{
+  invalidate();
+  if (combined_src) delete[] combined_src;
+  if (combined_dst) delete[] combined_dst;
+  if (send_lengths) delete[] send_lengths;
+  if (recv_lengths) delete[] recv_lengths;
+  if (send_buf_caps) delete[] send_buf_caps;
+  if (recv_buf_caps) delete[] recv_buf_caps;
+  for (int i = 0; i < cpusize; i++)
+  {
+    if (send_bufs && send_bufs[i]) delete[] send_bufs[i];
+    if (recv_bufs && recv_bufs[i]) delete[] recv_bufs[i];
+  }
+  if (send_bufs) delete[] send_bufs;
+  if (recv_bufs) delete[] recv_bufs;
+  if (reqs) delete[] reqs;
+  if (stats) delete[] stats;
+  combined_src = combined_dst = 0;
+  send_lengths = recv_lengths = 0;
+  send_buf_caps = recv_buf_caps = 0;
+  send_bufs = recv_bufs = 0;
+  reqs = 0; stats = 0;
+  cpusize = 0; max_reqs = 0;
+}
+// transfer_cached: reuse pre-allocated buffers from SyncCache
+void Parallel::transfer_cached(MyList<Parallel::gridseg> **src, MyList<Parallel::gridseg> **dst,
+                               MyList<var> *VarList1, MyList<var> *VarList2,
+                               int Symmetry, SyncCache &cache)
+{
+  int myrank;
+  MPI_Comm_size(MPI_COMM_WORLD, &cache.cpusize);
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  int cpusize = cache.cpusize;
+
+  int req_no = 0;
+  int node;
+
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank)
+    {
+      int length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      cache.recv_lengths[node] = length;
+      if (length > 0)
+      {
+        if (length > cache.recv_buf_caps[node])
+        {
+          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+          cache.recv_bufs[node] = new double[length];
+          cache.recv_buf_caps[node] = length;
+        }
+        data_packer(cache.recv_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      }
+    }
+    else
+    {
+      // send
+      int slength = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      cache.send_lengths[node] = slength;
+      if (slength > 0)
+      {
+        if (slength > cache.send_buf_caps[node])
+        {
+          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
+          cache.send_bufs[node] = new double[slength];
+          cache.send_buf_caps[node] = slength;
+        }
+        data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
+      }
+      // recv
+      int rlength = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+      cache.recv_lengths[node] = rlength;
+      if (rlength > 0)
+      {
+        if (rlength > cache.recv_buf_caps[node])
+        {
+          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+          cache.recv_bufs[node] = new double[rlength];
+          cache.recv_buf_caps[node] = rlength;
+        }
+        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
+      }
+    }
+  }
+
+  MPI_Waitall(req_no, cache.reqs, cache.stats);
+
+  for (node = 0; node < cpusize; node++)
+    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
+      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+}
+// Sync_cached: build grid segment lists on first call, reuse on subsequent calls
+void Parallel::Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache)
+{
+  if (!cache.valid)
+  {
+    int cpusize;
+    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
+    cache.cpusize = cpusize;
+
+    // Allocate cache arrays if needed
+    if (!cache.combined_src)
+    {
+      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
+      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
+      cache.send_lengths = new int[cpusize];
+      cache.recv_lengths = new int[cpusize];
+      cache.send_bufs = new double *[cpusize];
+      cache.recv_bufs = new double *[cpusize];
+      cache.send_buf_caps = new int[cpusize];
+      cache.recv_buf_caps = new int[cpusize];
+      for (int i = 0; i < cpusize; i++)
+      {
+        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
+        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
+      }
+      cache.max_reqs = 2 * cpusize;
+      cache.reqs = new MPI_Request[cache.max_reqs];
+      cache.stats = new MPI_Status[cache.max_reqs];
+    }
+
+    for (int node = 0; node < cpusize; node++)
+    {
+      cache.combined_src[node] = cache.combined_dst[node] = 0;
+      cache.send_lengths[node] = cache.recv_lengths[node] = 0;
+    }
+
+    // Build intra-patch segments (same as Sync_merged Phase A)
+    MyList<Patch> *Pp = PatL;
+    while (Pp)
+    {
+      Patch *Pat = Pp->data;
+      MyList<Parallel::gridseg> *dst_ghost = build_ghost_gsl(Pat);
+      for (int node = 0; node < cpusize; node++)
+      {
+        MyList<Parallel::gridseg> *src_owned = build_owned_gsl0(Pat, node);
+        MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
+        build_gstl(src_owned, dst_ghost, &tsrc, &tdst);
+        if (tsrc)
+        {
+          if (cache.combined_src[node])
+            cache.combined_src[node]->catList(tsrc);
+          else
+            cache.combined_src[node] = tsrc;
+        }
+        if (tdst)
+        {
+          if (cache.combined_dst[node])
+            cache.combined_dst[node]->catList(tdst);
+          else
+            cache.combined_dst[node] = tdst;
+        }
+        if (src_owned) src_owned->destroyList();
+      }
+      if (dst_ghost) dst_ghost->destroyList();
+      Pp = Pp->next;
+    }
+
+    // Build inter-patch segments (same as Sync_merged Phase B)
+    MyList<Parallel::gridseg> *dst_buffer = build_buffer_gsl(PatL);
+    for (int node = 0; node < cpusize; node++)
+    {
+      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatL, node, 5, Symmetry);
+      MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
+      build_gstl(src_owned, dst_buffer, &tsrc, &tdst);
+      if (tsrc)
+      {
+        if (cache.combined_src[node])
+          cache.combined_src[node]->catList(tsrc);
+        else
+          cache.combined_src[node] = tsrc;
+      }
+      if (tdst)
+      {
+        if (cache.combined_dst[node])
+          cache.combined_dst[node]->catList(tdst);
+        else
+          cache.combined_dst[node] = tdst;
+      }
+      if (src_owned) src_owned->destroyList();
+    }
+    if (dst_buffer) dst_buffer->destroyList();
+
+    cache.valid = true;
+  }
+
+  // Use cached lists with buffer-reusing transfer
+  transfer_cached(cache.combined_src, cache.combined_dst, VarList, VarList, Symmetry, cache);
+}
+// Sync_start: pack and post MPI_Isend/Irecv, return immediately
+void Parallel::Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
+                          SyncCache &cache, AsyncSyncState &state)
+{
+  // Ensure cache is built
+  if (!cache.valid)
+  {
+    // Build cache (same logic as Sync_cached)
+    int cpusize;
+    MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
+    cache.cpusize = cpusize;
+
+    if (!cache.combined_src)
+    {
+      cache.combined_src = new MyList<Parallel::gridseg> *[cpusize];
+      cache.combined_dst = new MyList<Parallel::gridseg> *[cpusize];
+      cache.send_lengths = new int[cpusize];
+      cache.recv_lengths = new int[cpusize];
+      cache.send_bufs = new double *[cpusize];
+      cache.recv_bufs = new double *[cpusize];
+      cache.send_buf_caps = new int[cpusize];
+      cache.recv_buf_caps = new int[cpusize];
+      for (int i = 0; i < cpusize; i++)
+      {
+        cache.send_bufs[i] = cache.recv_bufs[i] = 0;
+        cache.send_buf_caps[i] = cache.recv_buf_caps[i] = 0;
+      }
+      cache.max_reqs = 2 * cpusize;
+      cache.reqs = new MPI_Request[cache.max_reqs];
+      cache.stats = new MPI_Status[cache.max_reqs];
+    }
+
+    for (int node = 0; node < cpusize; node++)
+    {
+      cache.combined_src[node] = cache.combined_dst[node] = 0;
+      cache.send_lengths[node] = cache.recv_lengths[node] = 0;
+    }
+
+    MyList<Patch> *Pp = PatL;
+    while (Pp)
+    {
+      Patch *Pat = Pp->data;
+      MyList<Parallel::gridseg> *dst_ghost = build_ghost_gsl(Pat);
+      for (int node = 0; node < cpusize; node++)
+      {
+        MyList<Parallel::gridseg> *src_owned = build_owned_gsl0(Pat, node);
+        MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
+        build_gstl(src_owned, dst_ghost, &tsrc, &tdst);
+        if (tsrc)
+        {
+          if (cache.combined_src[node])
+            cache.combined_src[node]->catList(tsrc);
+          else
+            cache.combined_src[node] = tsrc;
+        }
+        if (tdst)
+        {
+          if (cache.combined_dst[node])
+            cache.combined_dst[node]->catList(tdst);
+          else
+            cache.combined_dst[node] = tdst;
+        }
+        if (src_owned) src_owned->destroyList();
+      }
+      if (dst_ghost) dst_ghost->destroyList();
+      Pp = Pp->next;
+    }
+
+    MyList<Parallel::gridseg> *dst_buffer = build_buffer_gsl(PatL);
+    for (int node = 0; node < cpusize; node++)
+    {
+      MyList<Parallel::gridseg> *src_owned = build_owned_gsl(PatL, node, 5, Symmetry);
+      MyList<Parallel::gridseg> *tsrc = 0, *tdst = 0;
+      build_gstl(src_owned, dst_buffer, &tsrc, &tdst);
+      if (tsrc)
+      {
+        if (cache.combined_src[node])
+          cache.combined_src[node]->catList(tsrc);
+        else
+          cache.combined_src[node] = tsrc;
+      }
+      if (tdst)
+      {
+        if (cache.combined_dst[node])
+          cache.combined_dst[node]->catList(tdst);
+        else
+          cache.combined_dst[node] = tdst;
+      }
+      if (src_owned) src_owned->destroyList();
+    }
+    if (dst_buffer) dst_buffer->destroyList();
+    cache.valid = true;
+  }
+
+  // Now pack and post async MPI operations
+  int myrank;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  int cpusize = cache.cpusize;
+  state.req_no = 0;
+  state.active = true;
+
+  MyList<Parallel::gridseg> **src = cache.combined_src;
+  MyList<Parallel::gridseg> **dst = cache.combined_dst;
+
+  for (int node = 0; node < cpusize; node++)
+  {
+    if (node == myrank)
+    {
+      int length;
+      if (!cache.lengths_valid) {
+        length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
+        cache.recv_lengths[node] = length;
+      } else {
+        length = cache.recv_lengths[node];
+      }
+      if (length > 0)
+      {
+        if (length > cache.recv_buf_caps[node])
+        {
+          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+          cache.recv_bufs[node] = new double[length];
+          cache.recv_buf_caps[node] = length;
+        }
+        data_packer(cache.recv_bufs[node], src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
+      }
+    }
+    else
+    {
+      int slength;
+      if (!cache.lengths_valid) {
+        slength = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
+        cache.send_lengths[node] = slength;
+      } else {
+        slength = cache.send_lengths[node];
+      }
+      if (slength > 0)
+      {
+        if (slength > cache.send_buf_caps[node])
+        {
+          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
+          cache.send_bufs[node] = new double[slength];
+          cache.send_buf_caps[node] = slength;
+        }
+        data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
+        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 2, MPI_COMM_WORLD, cache.reqs + state.req_no++);
+      }
+      int rlength;
+      if (!cache.lengths_valid) {
+        rlength = data_packer(0, src[node], dst[node], node, UNPACK, VarList, VarList, Symmetry);
+        cache.recv_lengths[node] = rlength;
+      } else {
+        rlength = cache.recv_lengths[node];
+      }
+      if (rlength > 0)
+      {
+        if (rlength > cache.recv_buf_caps[node])
+        {
+          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+          cache.recv_bufs[node] = new double[rlength];
+          cache.recv_buf_caps[node] = rlength;
+        }
+        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 2, MPI_COMM_WORLD, cache.reqs + state.req_no++);
+      }
+    }
+  }
+  cache.lengths_valid = true;
+}
+// Sync_finish: wait for async MPI operations and unpack
+void Parallel::Sync_finish(SyncCache &cache, AsyncSyncState &state,
+                           MyList<var> *VarList, int Symmetry)
+{
+  if (!state.active)
+    return;
+
+  MPI_Waitall(state.req_no, cache.reqs, cache.stats);
+
+  int cpusize = cache.cpusize;
+  MyList<Parallel::gridseg> **src = cache.combined_src;
+  MyList<Parallel::gridseg> **dst = cache.combined_dst;
+
+  for (int node = 0; node < cpusize; node++)
+    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
+      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList, VarList, Symmetry);
+
+  state.active = false;
+}
 // collect buffer grid segments or blocks for the periodic boundary condition of given patch
 // ---------------------------------------------------
 // |con |                                       |con |

AMSS_NCKU_source/Parallel.h

@@ -81,6 +81,43 @@ 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;
+    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;
+    AsyncSyncState() : req_no(0), active(false) {}
+  };
+
+  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);

AMSS_NCKU_source/bssn_class.C

@@ -40,7 +40,7 @@ using namespace std;
 
 #include "derivatives.h"
 #include "ricci_gamma.h"
-
+#include "xh_bssn_rhs_compute.h"
 //================================================================================================
 
 // define bssn_class
@@ -730,6 +730,12 @@ void bssn_class::Initialize()
     PhysTime = StartTime;
     Setup_Black_Hole_position();
   }
+
+  // Initialize sync caches (per-level, for predictor and corrector)
+  sync_cache_pre = new Parallel::SyncCache[GH->levels];
+  sync_cache_cor = new Parallel::SyncCache[GH->levels];
+  sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
+  sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
 }
 
 //================================================================================================
@@ -981,6 +987,32 @@ bssn_class::~bssn_class()
   delete Azzz;
 #endif
 
+  // Destroy sync caches before GH
+  if (sync_cache_pre)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_pre[i].destroy();
+    delete[] sync_cache_pre;
+  }
+  if (sync_cache_cor)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_cor[i].destroy();
+    delete[] sync_cache_cor;
+  }
+  if (sync_cache_rp_coarse)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_rp_coarse[i].destroy();
+    delete[] sync_cache_rp_coarse;
+  }
+  if (sync_cache_rp_fine)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_rp_fine[i].destroy();
+    delete[] sync_cache_rp_fine;
+  }
+
   delete GH;
 #ifdef WithShell
   delete SH;
@@ -1997,6 +2029,7 @@ void bssn_class::Read_Ansorg()
 void bssn_class::Evolve(int Steps)
 {
   clock_t prev_clock, curr_clock;
+  double prev_time, curr_time;
   double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
   LastAnas = 0;
 #if 0
@@ -2109,8 +2142,10 @@ void bssn_class::Evolve(int Steps)
     //     if(fabs(Porg0[0][0]-Porg0[1][0])+fabs(Porg0[0][1]-Porg0[1][1])+fabs(Porg0[0][2]-Porg0[1][2])<1e-6) 
     //     { GH->levels=GH->movls; }
 
-    if (myrank == 0)
+    if (myrank == 0){
       curr_clock = clock();
+      curr_time = omp_get_wtime();
+    }
 #if (PSTR == 0)
     RecursiveStep(0);
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
@@ -2166,12 +2201,17 @@ void bssn_class::Evolve(int Steps)
     if (myrank == 0)
     {
       prev_clock = curr_clock;
+      prev_time = curr_time;
       curr_clock = clock();
+      curr_time = omp_get_wtime();
       cout << endl;
+      // cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
+      //      << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+      //      << " seconds! " << endl;
+      // // cout << endl;
       cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
-           << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
-      // cout << endl;
+            << " Computer used " << (curr_time - prev_time) 
+            << " seconds! " << endl;
     }
 
     if (PhysTime >= TotalTime)
@@ -2181,6 +2221,7 @@ void bssn_class::Evolve(int Steps)
     GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
                SynchList_cor, OldStateList, StateList, SynchList_pre,
                fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
+    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 
 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2396,6 +2437,7 @@ void bssn_class::RecursiveStep(int lev)
   GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
                       fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
+  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 }
 
@@ -2574,6 +2616,7 @@ void bssn_class::ParallelStep()
   GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
                       fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
+  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 }
 
@@ -2740,6 +2783,7 @@ void bssn_class::ParallelStep()
         GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
                             SynchList_cor, OldStateList, StateList, SynchList_pre,
                             fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor);
+        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
         //               a_stream.clear();
         //               a_stream.str("");
@@ -2754,6 +2798,7 @@ void bssn_class::ParallelStep()
       GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                           SynchList_cor, OldStateList, StateList, SynchList_pre,
                           fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
+      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
       //               a_stream.clear();
       //               a_stream.str("");
@@ -2772,6 +2817,7 @@ void bssn_class::ParallelStep()
           GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
                               fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
+          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -2787,6 +2833,7 @@ void bssn_class::ParallelStep()
           GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
                               fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
+          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -3053,7 +3100,7 @@ void bssn_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+        if (f_compute_rhs_bssn_xh(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],
@@ -3158,21 +3205,7 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
+  // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
 
 #ifdef WithShell
   // evolve Shell Patches
@@ -3190,9 +3223,9 @@ void bssn_class::Step(int lev, int YN)
         {
 #if (AGM == 0)
           f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->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[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn],
                        cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
@@ -3267,7 +3300,7 @@ void bssn_class::Step(int lev, int YN)
                  << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
             ERROR = 1;
           }
-
+          // cout<<"....................................."<<endl;
           // rk4 substep and boundary
           {
             MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
@@ -3316,25 +3349,16 @@ void bssn_class::Step(int lev, int YN)
 #endif
   }
 
-  // check error information
+  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
+    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  Parallel::AsyncSyncState async_pre;
+  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
 
 #ifdef WithShell
   if (lev == 0)
@@ -3347,12 +3371,29 @@ void bssn_class::Step(int lev, int YN)
     {
       prev_clock = curr_clock;
       curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+      cout << " Shell stuff synchronization used "
+           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
            << " seconds! " << endl;
     }
   }
 #endif
+  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
+
+#ifdef WithShell
+  // Complete non-blocking error reduction and check
+  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
+#endif
 
 #if (MAPBH == 0)
   // for black hole position
@@ -3424,7 +3465,7 @@ void bssn_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+          if (f_compute_rhs_bssn_xh(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],
@@ -3528,24 +3569,7 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime 
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
+    // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
 
 #ifdef WithShell
     // evolve Shell Patches
@@ -3563,9 +3587,9 @@ void bssn_class::Step(int lev, int YN)
           {
 #if (AGM == 0)
             f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->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[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn],
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #elif (AGM == 1)
             if (iter_count == 3)
@@ -3685,26 +3709,16 @@ void bssn_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // check error information
+    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" 
-                                << iter_count << " variables at t = " 
-                                << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
+      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::AsyncSyncState async_cor;
+    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
 
 #ifdef WithShell
     if (lev == 0)
@@ -3717,12 +3731,31 @@ void bssn_class::Step(int lev, int YN)
       {
         prev_clock = curr_clock;
         curr_clock = clock();
-        cout << " Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+        cout << " Shell stuff synchronization used "
+             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
              << " seconds! " << endl;
       }
     }
 #endif
+    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
+
+#ifdef WithShell
+    // Complete non-blocking error reduction and check
+    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
+                                << " variables at t = " << PhysTime
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
+#endif
 
 #if (MAPBH == 0)
     // for black hole position
@@ -3945,7 +3978,7 @@ void bssn_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+        if (f_compute_rhs_bssn_xh(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],
@@ -4034,22 +4067,7 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // check error information
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime 
-                              << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
+  // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
 
 #ifdef WithShell
   // evolve Shell Patches
@@ -4067,15 +4085,15 @@ void bssn_class::Step(int lev, int YN)
         {
 #if (AGM == 0)
           f_enforce_ga(cg->shape,
-                       cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->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[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn],
                        cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
           if (f_compute_rhs_bssn_ss(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                    cg->fgfs[fngfs + ShellPatch::gx], 
-                                    cg->fgfs[fngfs + ShellPatch::gy], 
+                                    cg->fgfs[fngfs + ShellPatch::gx],
+                                    cg->fgfs[fngfs + ShellPatch::gy],
                                     cg->fgfs[fngfs + ShellPatch::gz],
                                     cg->fgfs[fngfs + ShellPatch::drhodx], 
                                     cg->fgfs[fngfs + ShellPatch::drhody], 
@@ -4190,25 +4208,16 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
   }
-  // check error information
+  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " 
-                              << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
+    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  Parallel::AsyncSyncState async_pre;
+  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
 
 #ifdef WithShell
   if (lev == 0)
@@ -4221,9 +4230,27 @@ void bssn_class::Step(int lev, int YN)
     {
       prev_clock = curr_clock;
       curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-      << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-      << " seconds! " << endl;
+      cout << " Shell stuff synchronization used "
+           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+           << " seconds! " << endl;
+    }
+  }
+#endif
+  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
+
+#ifdef WithShell
+  // Complete non-blocking error reduction and check
+  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime
+                              << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
     }
   }
 #endif
@@ -4293,7 +4320,7 @@ void bssn_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+          if (f_compute_rhs_bssn_xh(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],
@@ -4386,23 +4413,7 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // check error information
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime 
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
+    // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
 
 #ifdef WithShell
     // evolve Shell Patches
@@ -4420,9 +4431,9 @@ void bssn_class::Step(int lev, int YN)
           {
 #if (AGM == 0)
             f_enforce_ga(cg->shape,
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->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[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn],
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #elif (AGM == 1)
             if (iter_count == 3)
@@ -4542,25 +4553,16 @@ void bssn_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // check error information
+    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
+      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::AsyncSyncState async_cor;
+    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
 
 #ifdef WithShell
     if (lev == 0)
@@ -4573,11 +4575,30 @@ void bssn_class::Step(int lev, int YN)
       {
         prev_clock = curr_clock;
         curr_clock = clock();
-        cout << " Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+        cout << " Shell stuff synchronization used "
+             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
              << " seconds! " << endl;
       }
     }
+#endif
+    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
+
+#ifdef WithShell
+    // Complete non-blocking error reduction and check
+    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
+                                << " variables at t = " << PhysTime
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
 #endif
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -4835,7 +4856,7 @@ void bssn_class::Step(int lev, int YN)
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
 #endif
 
-        if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+        if (f_compute_rhs_bssn_xh(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],
@@ -4943,11 +4964,19 @@ void bssn_class::Step(int lev, int YN)
 
   //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");
 
-  // check error information
+  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
+    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev], &err_req);
   }
+
+  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
+
+  Parallel::Sync_cached(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev]);
+
+  // Complete non-blocking error reduction and check
+  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
   if (ERROR)
   {
     Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
@@ -4959,10 +4988,6 @@ void bssn_class::Step(int lev, int YN)
     }
   }
 
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
 #if (MAPBH == 0)
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -5031,7 +5056,7 @@ void bssn_class::Step(int lev, int YN)
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
 #endif
 
-          if (f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+          if (f_compute_rhs_bssn_xh(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],
@@ -5140,30 +5165,34 @@ void bssn_class::Step(int lev, int YN)
 
     //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");
 
-    // check error information
+    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
+    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
+      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev], &err_req_cor);
     }
+
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
+
+    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev]);
+
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
+
+    // Complete non-blocking error reduction and check
+    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
     if (ERROR)
     {
       Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
         if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime 
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
+                                << " variables at t = " << PhysTime
                                 << ", lev = " << lev << endl;
         MPI_Abort(MPI_COMM_WORLD, 1);
       }
     }
 
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
-
 #if (MAPBH == 0)
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -5447,21 +5476,11 @@ void bssn_class::SHStep()
 #if (PSTR == 1 || PSTR == 2)
 //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor's error check");
 #endif
-  // check error information
+  // Non-blocking error reduction overlapped with Synch to hide Allreduce latency
+  MPI_Request err_req;
   {
     int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
+    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
   }
 
   {
@@ -5473,12 +5492,25 @@ void bssn_class::SHStep()
     {
       prev_clock = curr_clock;
       curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+      cout << " Shell stuff synchronization used "
+           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
            << " seconds! " << endl;
     }
   }
 
+  // Complete non-blocking error reduction and check
+  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
+
   // corrector
   for (iter_count = 1; iter_count < 4; iter_count++)
   {
@@ -5621,21 +5653,11 @@ void bssn_class::SHStep()
         sPp = sPp->next;
       }
     }
-    // check error information
+    // Non-blocking error reduction overlapped with Synch to hide Allreduce latency
+    MPI_Request err_req_cor;
     {
       int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
+      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
     }
 
     {
@@ -5647,12 +5669,26 @@ void bssn_class::SHStep()
       {
         prev_clock = curr_clock;
         curr_clock = clock();
-        cout << " Shell stuff synchronization used " 
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+        cout << " Shell stuff synchronization used "
+             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
              << " seconds! " << endl;
       }
     }
 
+    // Complete non-blocking error reduction and check
+    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count
+                                << " variables at t = " << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
+
     sPp = SH->PatL;
     while (sPp)
     {
@@ -5781,7 +5817,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5842,7 +5878,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5880,7 +5916,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
     }
 
-    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
+    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
 
 #if (PSTR == 1 || PSTR == 2)
 //    a_stream.clear();
@@ -5938,7 +5974,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
       Ppc = GH->PatL[lev - 1];
@@ -5970,7 +6006,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
       Ppc = GH->PatL[lev - 1];
@@ -5994,7 +6030,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 #endif
     }
 
-    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
+    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
   }
 }
 
@@ -6045,7 +6081,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
       Ppc = GH->PatL[lev - 1];
@@ -6079,7 +6115,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
 
 #if (RPB == 0)
       Ppc = GH->PatL[lev - 1];
@@ -6103,7 +6139,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 #endif
     }
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
   }
 }
 
@@ -6186,10 +6222,10 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 #else
       Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
 #endif
-      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
+      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
     }
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
   }
 }
 #undef MIXOUTB
@@ -7315,7 +7351,7 @@ void bssn_class::Constraint_Out()
             Block *cg = BP->data;
             if (myrank == cg->rank)
             {
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+              f_compute_rhs_bssn_xh(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],
@@ -7818,7 +7854,7 @@ void bssn_class::Interp_Constraint(bool infg)
             Block *cg = BP->data;
             if (myrank == cg->rank)
             {
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+              f_compute_rhs_bssn_xh(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],
@@ -8076,7 +8112,7 @@ void bssn_class::Compute_Constraint()
           Block *cg = BP->data;
           if (myrank == cg->rank)
           {
-            f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+            f_compute_rhs_bssn_xh(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],

AMSS_NCKU_source/bssn_class.h

@@ -126,6 +126,11 @@ public:
        MyList<var> *OldStateList, *DumpList;
        MyList<var> *ConstraintList;
 
+       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]
+
        monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
        monitor *ConVMonitor;
        surface_integral *Waveshell;

AMSS_NCKU_source/bssn_rhs.f90

@@ -106,38 +106,6 @@
   call getpbh(BHN,Porg,Mass)
 #endif
 
-!!! sanity check (disabled in production builds for performance)
-#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)
-  if(dX.ne.dX) then
-     if(sum(chi).ne.sum(chi))write(*,*)"bssn.f90: find NaN in chi"
-     if(sum(trK).ne.sum(trK))write(*,*)"bssn.f90: find NaN in trk"
-     if(sum(dxx).ne.sum(dxx))write(*,*)"bssn.f90: find NaN in dxx"
-     if(sum(gxy).ne.sum(gxy))write(*,*)"bssn.f90: find NaN in gxy"
-     if(sum(gxz).ne.sum(gxz))write(*,*)"bssn.f90: find NaN in gxz"
-     if(sum(dyy).ne.sum(dyy))write(*,*)"bssn.f90: find NaN in dyy"
-     if(sum(gyz).ne.sum(gyz))write(*,*)"bssn.f90: find NaN in gyz"
-     if(sum(dzz).ne.sum(dzz))write(*,*)"bssn.f90: find NaN in dzz"
-     if(sum(Axx).ne.sum(Axx))write(*,*)"bssn.f90: find NaN in Axx"
-     if(sum(Axy).ne.sum(Axy))write(*,*)"bssn.f90: find NaN in Axy"
-     if(sum(Axz).ne.sum(Axz))write(*,*)"bssn.f90: find NaN in Axz"
-     if(sum(Ayy).ne.sum(Ayy))write(*,*)"bssn.f90: find NaN in Ayy"
-     if(sum(Ayz).ne.sum(Ayz))write(*,*)"bssn.f90: find NaN in Ayz"
-     if(sum(Azz).ne.sum(Azz))write(*,*)"bssn.f90: find NaN in Azz"
-     if(sum(Gamx).ne.sum(Gamx))write(*,*)"bssn.f90: find NaN in Gamx"
-     if(sum(Gamy).ne.sum(Gamy))write(*,*)"bssn.f90: find NaN in Gamy"
-     if(sum(Gamz).ne.sum(Gamz))write(*,*)"bssn.f90: find NaN in Gamz"
-     if(sum(Lap).ne.sum(Lap))write(*,*)"bssn.f90: find NaN in Lap"
-     if(sum(betax).ne.sum(betax))write(*,*)"bssn.f90: find NaN in betax"
-     if(sum(betay).ne.sum(betay))write(*,*)"bssn.f90: find NaN in betay"
-     if(sum(betaz).ne.sum(betaz))write(*,*)"bssn.f90: find NaN in betaz"
-     gont = 1
-     return
-  endif
-#endif
 
   PI = dacos(-ONE)
 
@@ -161,8 +129,36 @@
 
   chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
 
+  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
+  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
+  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
 
+  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
+              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
 
+  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
+              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
+
+  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
+              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
+
+  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
+                      gxx * betaxy                  +   gxz * betazy + &
+                                       gyy * betayx +   gyz * betazx   &
+                                                    -   gxy * betazz
+
+  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
+                      gxy * betaxz +   gyy * betayz                  + &
+                      gxz * betaxy                  +   gzz * betazy   &
+                                                    -   gyz * betaxx
+ 
+  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
+                      gxx * betaxz +   gxy * betayz                  + &
+                                       gyz * betayx +   gzz * betazx   &
+                                                    -   gxz * betayy     !rhs for gij
 
 ! invert tilted metric
   gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
@@ -173,12 +169,7 @@
   gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
   gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
   gupzz =   ( gxx * gyy - gxy * gxy ) / gupzz
-  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
-  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
-  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+
   if(co == 0)then
 ! Gam^i_Res = Gam^i + gup^ij_,j
   Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
@@ -611,7 +602,7 @@
   gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
   gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
   gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
-! now get physical second kind of connection
+
   Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
   Gamyxx = Gamyxx - (                     - gxx * gxxy )*HALF
   Gamzxx = Gamzxx - (                     - gxx * gxxz )*HALF
@@ -924,99 +915,99 @@
 
 !!!!!!!!!advection term part
 
-  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
-              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
-
-  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
-              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
-
-  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
-              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
-
-  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
-                      gxx * betaxy                  +   gxz * betazy + &
-                                        gyy * betayx +   gyz * betazx   &
-                                                    -   gxy * betazz
-
-  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
-                      gxy * betaxz +   gyy * betayz                  + &
-                      gxz * betaxy                  +   gzz * betazy   &
-                                                    -   gyz * betaxx
-
-  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
-                      gxx * betaxz +   gxy * betayz                  + &
-                                        gyz * betayx +   gzz * betazx   &
-                                                    -   gxz * betayy     !rhs for gij
-
-
-
-
-
-  if(eps>0)then 
-! usual Kreiss-Oliger dissipation     
-  call merge_lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps) 
-  call merge_lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call merge_lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-
-
-
-
-
-
-
-
-
-
-
-
-  else 
   call lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS)
   call lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA)
   call lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA)
   call lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS)
+
   call lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS)
   call lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA)
   call lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA)
   call lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS)
+
   call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)
+
   call lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
+!!
   call lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS)
+
+#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA)
+#endif
+
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA)
+#endif
 
+  if(eps>0)then 
+! usual Kreiss-Oliger dissipation      
+  call kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "before",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
+#endif
+  call kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "after",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
+#endif
+  call kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps)
+
+#if 1 
+!! bam does not apply dissipation on gauge variables
+  call kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps)
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+  call kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps)
+#endif
+#endif
 
   endif
 
@@ -1163,265 +1154,3 @@ endif
   return
 
   end function compute_rhs_bssn
-
-
-
-
-  subroutine merge_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
-
-  !~~~~~~> 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_lopsided,jmin_lopsided,kmin_lopsided,imin_kodis,jmin_kodis,kmin_kodis,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
-    real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
-    real*8,parameter::cof=6.4d1   ! 2^6
-    real*8,intent(in) :: eps
-    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_lopsided = 1
-    jmin_lopsided = 1
-    kmin_lopsided = 1
-    if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin_lopsided = -2
-    if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin_lopsided = -2
-    if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin_lopsided = -2
-
-    imin_kodis = 1
-    jmin_kodis = 1
-    kmin_kodis = 1
-
-    if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin_kodis = -2
-    if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin_kodis = -2
-    if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin_kodis = -2
-
-
-    call symmetry_bd(3,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
-
-  !! new code, 2012dec27, based on bam
-  ! x direction   
-      if(Sfx(i,j,k) > ZEO)then
-        if(i+3 <= imax)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(i+2 <= imax)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)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))
-  ! set imax and imin_lopsided 0
-      endif
-    elseif(Sfx(i,j,k) < ZEO)then
-        if(i-3 >= imin_lopsided)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(i-2 >= imin_lopsided)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 >= imin_lopsided)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))
-  ! set imax and imin_lopsided 0
-      endif
-    endif
-
-  ! y direction   
-      if(Sfy(i,j,k) > ZEO)then
-        if(j+3 <= jmax)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(j+2 <= jmax)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)+                                                           &
-                    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
-  !         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))
-  ! set imax and imin_lopsided 0
-      endif
-    elseif(Sfy(i,j,k) < ZEO)then
-        if(j-3 >= jmin_lopsided)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(j-2 >= jmin_lopsided)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)+                                                           &
-                    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_lopsided)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))
-  ! set jmax and jmin_lopsided 0
-      endif
-    endif
-
-  ! z direction   
-      if(Sfz(i,j,k) > ZEO)then
-        if(k+3 <= kmax)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(k+2 <= kmax)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)+                                                           &
-                    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
-  !         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))
-  ! set imax and imin_lopsided 0
-      endif
-    elseif(Sfz(i,j,k) < ZEO)then
-        if(k-3 >= kmin_lopsided)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(k-2 >= kmin_lopsided)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)+                                                           &
-                    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_lopsided)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))
-  ! set kmax and kmin_lopsided 0
-      endif
-    endif
-
-
-    if(i-3 >= imin_kodis .and. i+3 <= imax .and. &
-      j-3 >= jmin_kodis .and. j+3 <= jmax .and. &
-      k-3 >= kmin_kodis .and. k+3 <= kmax) then
-
-  ! 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)) - &
-                            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
-
-    return
-
-
-
-  end subroutine merge_lopsided_kodis

AMSS_NCKU_source/diff_new.f90

@@ -1000,7 +1000,86 @@
   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 +1094,7 @@
       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 +1404,85 @@
   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 +1518,7 @@
    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/extention/include/xh_bssn_rhs_compute.h

@@ -0,0 +1,26 @@
+#include "xh_macrodef.h"
+#include "xh_tool.h"
+int f_compute_rhs_bssn(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 *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 *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
+                       ); 

AMSS_NCKU_source/extention/include/xh_macrodef.h

@@ -0,0 +1,66 @@
+/* tetrad notes
+   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 tetradtype 2
+
+/* Cell center or Vertex center */
+#define Cell
+
+/* ghost_width meaning:
+   2nd order: 2
+   4th order: 3
+   6th order: 4
+   8th order: 5
+*/
+#define ghost_width 3
+
+/* use shell or not */
+#define WithShell
+
+/* use constraint preserving boundary condition or not
+   only affect Z4c
+*/
+#define CPBC
+
+/* 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
+*/
+#define GAUGE 2
+
+/* buffer points for CPBC boundary */
+#define CPBC_ghost_width (ghost_width)
+
+/* using BSSN variable for constraint violation and psi4 calculation: 0
+   using ADM variable for constraint violation and psi4 calculation: 1
+*/
+#define ABV 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 = infinity 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
+*/
+#define EScalar_CC 2

AMSS_NCKU_source/extention/include/xh_share_func.h

@@ -0,0 +1,338 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#include <stddef.h>
+#include <math.h>
+#include <stdio.h>
+#include <omp.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;
+}
+
+/*
+ * 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(int ord,
+                 const int extc[3],
+                 const double *func,
+                 double *funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+
+    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
+    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            for (int i0 = 0; i0 < extc1; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= ord - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int jF = 1; jF <= extc2; ++jF) {
+                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= ord - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= ord - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -ord + 1; jF <= extc2; ++jF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
+            }
+        }
+    }
+}
+#endif
+
+/* 你已有的函数：idx_ex / idx_fh_F_ord2 以及 fh 的布局 */
+static inline void fdderivs_xh(
+    int i0, int j0, int k0,
+    const int ex[3],
+    const double *fh,
+    int iminF, int jminF, int kminF,
+    int imaxF, int jmaxF, int kmaxF,
+    double Fdxdx, double Fdydy, double Fdzdz,
+    double Fdxdy, double Fdxdz, double Fdydz,
+    double Sdxdx, double Sdydy, double Sdzdz,
+    double Sdxdy, double Sdxdz, double Sdydz,
+    double *fxx, double *fxy, double *fxz,
+    double *fyy, double *fyz, double *fzz
+){
+    const double F8  = 8.0;
+    const double F16 = 16.0;
+    const double F30 = 30.0;
+    const double TWO = 2.0;
+
+    const int iF = i0 + 1;
+    const int jF = j0 + 1;
+    const int kF = k0 + 1;
+
+    const size_t p = idx_ex(i0, j0, k0, ex);
+
+    /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+    if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+        (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+        (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+    {
+        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 高阶 */
+        {
+            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 高阶 */
+        {
+            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 高阶 */
+        {
+            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 );
+        }
+    }
+    /* 二阶分支：i±1,j±1,k±1 在范围内 */
+    else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+             (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+             (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+    {
+        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)]
+        );
+    }
+    else {
+        fxx[p] = 0.0; fyy[p] = 0.0; fzz[p] = 0.0;
+        fxy[p] = 0.0; fxz[p] = 0.0; fyz[p] = 0.0;
+    }
+}

AMSS_NCKU_source/extention/include/xh_tool.h

@@ -0,0 +1,27 @@
+#include "xh_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]);

AMSS_NCKU_source/extention/src/fdderivs-fast.c

@@ -0,0 +1,311 @@
+#include "../include/tool.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)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;          // 1/4
+    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 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;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    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;
+
+
+    /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+
+    /* 系数：按 Fortran 原式 */
+    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);
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // symmetry_bd(2, ex, f, fh, SoA);
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    for (int k0 = 0; k0 < ex[2]; ++k0) {
+        for (int j0 = 0; j0 < ex[1]; ++j0) {
+            for (int i0 = 0; i0 < ex[0]; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= 2 - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int jF = 1; jF <= ex[1]; ++jF) {
+                fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                    fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= 2 - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= 2 - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+            }
+        }
+    }
+    /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
+    // 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;
+    // }
+
+    /*
+     * Fortran:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     */
+    
+    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);
+
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
+                    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 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        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 高阶 */
+                    {
+                        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 高阶 */
+                    {
+                        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 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }else{
+                    fxx[p] = 0.0;
+                    fyy[p] = 0.0;
+                    fzz[p] = 0.0;
+                    fxy[p] = 0.0;
+                    fxz[p] = 0.0;
+                    fyz[p] = 0.0;
+                }
+            }
+        }
+    }
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/main.c

@@ -0,0 +1,7 @@
+#include "include/bssn_rhs_compute.h"
+
+int main() {
+    // 这里可以写一些测试代码，调用 f_compute_rhs_bssn 来验证它的正确性
+    // 例如，定义一些小的网格和初始条件，调用函数，并检查输出是否合理。
+    return 0;
+}

AMSS_NCKU_source/extention/src/new.c

@@ -0,0 +1,65 @@
+        SoA[0] = SYM, SoA[1] = SYM, SoA[2] = SYM;
+        #pragma omp for collapse(3)
+        for (int k0 = 0; k0 < ex[2]; ++k0) {
+            for (int j0 = 0; j0 < ex[1]; ++j0) {
+                for (int i0 = 0; i0 < ex[0]; ++i0) {
+                    const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                    fh[idx_funcc_F(iF, jF, kF, 2, ex)] = Lap[idx_func0(i0, j0, k0, ex)];
+                }
+            }
+        }
+
+        // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+        #pragma omp for collapse(3)
+        for (int ii = 0; ii <= 2 - 1; ++ii) {
+            const int iF_dst = -ii;       // 0, -1, -2, ...
+            const int iF_src = ii + 1;    // 1, 2, 3, ...
+            for (int kF = 1; kF <= ex[2]; ++kF) {
+                for (int jF = 1; jF <= ex[1]; ++jF) {
+                    fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                        fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+                }
+            }
+        }
+
+        // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+        // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+        #pragma omp for collapse(3)
+        for (int jj = 0; jj <= 2 - 1; ++jj) {
+            const int jF_dst = -jj;
+            const int jF_src = jj + 1;
+            for (int kF = 1; kF <= ex[2]; ++kF) {
+                for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                    fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                        fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+                }
+            }
+        }
+
+        // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+        #pragma omp for collapse(3)
+        for (int kk = 0; kk <= 2 - 1; ++kk) {
+            const int kF_dst = -kk;
+            const int kF_src = kk + 1;
+            for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+                for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                    fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                        fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+                }
+            }
+        }
+
+        #pragma omp for collapse(3)
+        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) {
+                    fdderivs_xh(i0, j0, k0, ex, fh, iminF, jminF, kminF, ex1, ex2, ex3, 
+                        Fdxdx, Fdydy, Fdzdz, Fdxdy, Fdxdz, Fdydz,
+                        Sdxdx, Sdydy, Sdzdz, Sdxdy, Sdxdz, Sdydz,
+                            fxx,fxy,fxz,fyy,fyz,fzz
+                    );
+                }
+            }
+        }

AMSS_NCKU_source/extention/src/xh_fdderivs.c

@@ -0,0 +1,311 @@
+#include "xh_tool.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)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;          // 1/4
+    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 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;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    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;
+
+
+    /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+
+    /* 系数：按 Fortran 原式 */
+    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);
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // symmetry_bd(2, ex, f, fh, SoA);
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    for (int k0 = 0; k0 < ex[2]; ++k0) {
+        for (int j0 = 0; j0 < ex[1]; ++j0) {
+            for (int i0 = 0; i0 < ex[0]; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= 2 - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int jF = 1; jF <= ex[1]; ++jF) {
+                fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                    fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= 2 - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= 2 - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+            }
+        }
+    }
+    /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
+    // 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;
+    // }
+
+    /*
+     * Fortran:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     */
+    
+    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);
+
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
+                    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 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        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 高阶 */
+                    {
+                        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 高阶 */
+                    {
+                        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 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }else{
+                    fxx[p] = 0.0;
+                    fyy[p] = 0.0;
+                    fzz[p] = 0.0;
+                    fxy[p] = 0.0;
+                    fxz[p] = 0.0;
+                    fyz[p] = 0.0;
+                }
+            }
+        }
+    }
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/xh_fderivs.c

@@ -0,0 +1,145 @@
+#include "xh_tool.h"
+
+/*
+ * C 版 fderivs
+ *
+ * Fortran:
+ * subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+ *
+ * 约定：
+ *   f, fx, fy, fz: ex1*ex2*ex3，按 idx_ex 布局
+ *   X: ex1, Y: ex2, Z: ex3
+ */
+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; // Fortran 里没用到
+
+    const double ZEO = 0.0, ONE = 1.0;
+    const double TWO = 2.0, EIT = 8.0;
+    const double F12 = 12.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1; // OCTANT=2 在本子程序里不直接用
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    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;
+
+    // SoA(1:3) = SYM1,SYM2,SYM3
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    // fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // call symmetry_bd(2,ex,f,fh,SoA)
+    symmetry_bd(2, 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;
+
+    // fx = fy = fz = 0
+    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;
+    }
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     *
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
+     */
+    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);
+
+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= ex1 && (iF - 2) >= iminF &&
+                    (jF + 2) <= ex2 && (jF - 2) >= jminF &&
+                    (kF + 2) <= ex3 && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+                }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= ex1 && (iF - 1) >= iminF &&
+                         (jF + 1) <= ex2 && (jF - 1) >= jminF &&
+                         (kF + 1) <= ex3 && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/xh_kodiss.c

@@ -0,0 +1,116 @@
+#include "xh_tool.h"
+
+/*
+ * C 版 kodis
+ *
+ * Fortran signature:
+ * subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
+ *
+ * 约定：
+ *   X: ex1, Y: ex2, Z: ex3
+ *   f, f_rhs: ex1*ex2*ex3 按 idx_ex 布局
+ *   SoA[3]
+ *   eps: double
+ */
+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 ONE = 1.0, SIX = 6.0, FIT = 15.0, TWT = 20.0;
+    const double cof = 64.0;             // 2^6
+    const int NO_SYMM = 0, OCTANT = 2;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // Fortran: dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+    (void)ONE; // ONE 在原 Fortran 里只是参数，这里不一定用得上
+
+    // Fortran: imax=ex(1) 等是 1-based 上界
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran: imin=jmin=kmin=1，某些对称情况变 -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;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)，对应 ord=3
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    if (!fh) return;
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3
+     * do j=1,ex2
+     * do i=1,ex1
+     *
+     * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
+     * 并定义 Fortran index: iF=i0+1, ...
+     */
+    for (int k0 = 0; k0 < ex3; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 < ex2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const int iF = i0 + 1;
+
+                // Fortran if 条件：
+                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
+                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
+                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
+                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
+                {
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
+                    const double Dx_term =
+                        ( (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_term =
+                        ( (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_term =
+                        ( (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;
+
+                    // Fortran:
+                    // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
+                    f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/extention/src/xh_lopsided.c

@@ -0,0 +1,262 @@
+#include "xh_tool.h"
+/*
+ * 你需要提供 symmetry_bd 的 C 版本（或 Fortran 绑到 C 的接口）。
+ * Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+ *
+ * 约定：
+ *   nghost = 3
+ *   ex[3]  = {ex1,ex2,ex3}
+ *   f      = 原始网格 (ex1*ex2*ex3)
+ *   fh     = 扩展网格 ((ex1+3)*(ex2+3)*(ex3+3))，对应 Fortran 的 (-2:ex1, ...)
+ *   SoA[3] = 输入参数
+ */
+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, F3 = 3.0;
+    const double TWO = 2.0, F6 = 6.0, F18 = 18.0;
+    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2;
+    (void)OCTANT; // 这里和 Fortran 一样只是定义了不用也没关系
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // 对应 Fortran: dX = X(2)-X(1)  （Fortran 1-based）
+    // C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    // Fortran 里算了 d2dx/d2dy/d2dz 但本 subroutine 里没用到（保持一致也算出来）
+    const double d2dx  = ONE / TWO / dX;
+    const double d2dy  = ONE / TWO / dY;
+    const double d2dz  = ONE / TWO / dZ;
+    (void)d2dx; (void)d2dy; (void)d2dz;
+
+    // Fortran:
+    // imax = ex(1); jmax = ex(2); kmax = ex(3)
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran:
+    // imin=jmin=kmin=1; 若满足对称条件则设为 -2
+    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;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    if (!fh) return; // 内存不足：直接返回（你也可以改成 abort/报错）
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran 主循环：
+     * do k=1,ex(3)-1
+     * do j=1,ex(2)-1
+     * do i=1,ex(1)-1
+     *
+     * 转成 C 0-based：
+     * k0 = 0..ex3-2, j0 = 0..ex2-2, i0 = 0..ex1-2
+     *
+     * 并且 Fortran 里的 i/j/k 在 fh 访问时，仍然是 Fortran 索引值：
+     * iF=i0+1, jF=j0+1, kF=k0+1
+     */
+    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) {
+                    // Fortran: if(i+3 <= imax)
+                    // iF+3 <= ex1  <=> i0+4 <= ex1 <=> i0 <= ex1-4
+                    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)]);
+                    }
+                    // elseif(i+2 <= imax)  <=> i0 <= ex1-3
+                    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)]);
+                    }
+                    // elseif(i+1 <= imax)  <=> i0 <= ex1-2（循环里总成立）
+                    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) {
+                    // Fortran: if(i-3 >= imin)
+                    // (iF-3) >= iminF  <=> (i0-2) >= iminF
+                    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)]);
+                    }
+                    // elseif(i-2 >= imin) <=> (i0-1) >= iminF
+                    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)]);
+                    }
+                    // elseif(i-1 >= imin) <=> i0 >= iminF
+                    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)]);
+                    }
+                }
+
+                // ---------------- y direction ----------------
+                const double sfy = Sfy[p];
+                if (sfy > ZEO) {
+                    // jF+3 <= ex2 <=> j0+4 <= ex2 <=> j0 <= ex2-4
+                    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)]);
+                    }
+                }
+
+                // ---------------- z direction ----------------
+                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);
+}
+
+
+
+
+

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)

AMSS_NCKU_source/kodiss.f90

@@ -6,6 +6,101 @@
 ! 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
+  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 +156,7 @@ 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 +166,28 @@ 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 +204,7 @@ 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 +215,218 @@ 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/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 +486,417 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
   return
 
   end subroutine lopsided
+
+#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/makefile

@@ -8,7 +8,7 @@ include makefile.inc
 	$(f90) $(f90appflags) -c $< -o $@
 
 .C.o:
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< $(filein) -o $@
 
 .for.o:
 	$(f77) -c $< -o $@
@@ -28,7 +28,8 @@ C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.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
+	   NullShellPatch2_Evo.o writefile_f.o xh_bssn_rhs.o xh_fdderivs.o xh_fderivs.o xh_kodiss.o xh_lopsided.o \
+	   xh_global_interp.o xh_polint3.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\
@@ -72,7 +73,7 @@ $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.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 
+             initial_null2.h NullShellPatch2.h xh_bssn_rhs_compute.h xh_global_interp.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\
@@ -96,7 +97,7 @@ misc.o : zbesh.o
 
 # projects
 ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -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)

AMSS_NCKU_source/makefile.inc

@@ -1,31 +1,32 @@
-## GCC version (commented out)
-## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
-
-## Intel oneAPI version with oneMKL (Optimized for performance)
-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
-
-## 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 
-
-Cu = nvcc
-CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
-#CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
-CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc
+## GCC version (commented out)
+## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
+
+## Intel oneAPI version with oneMKL (Optimized for performance)
+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
+
+## Aggressive optimization flags + PGO Phase 2 (profile-guided optimization)
+## -fprofile-instr-use: use collected profile data to guide optimization decisions
+##   (branch prediction, basic block layout, inlining, loop unrolling)
+PROFDATA     = /home/hxh/AMSS-NCKU/pgo_profile/default.profdata
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+               -fprofile-instr-use=$(PROFDATA) \
+               -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+               -fprofile-instr-use=$(PROFDATA) \
+               -align array64byte -fpp -I${MKLROOT}/include
+f90          = ifx
+f77          = ifx
+CXX          = icpx
+CC           = icx
+CLINKER      = mpiicpx 
+
+Cu = nvcc
+CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
+#CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
+CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc

AMSS_NCKU_source/surface_integral.C

@@ -220,16 +220,9 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     pox[2][n] = rex * nz_g[n];
   }
 
-  double *shellf;
-  shellf = new double[n_tot * InList];
-
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
-
   int mp, Lp, Nmin, Nmax;
-
   mp = n_tot / cpusize;
   Lp = n_tot - cpusize * mp;
-
   if (Lp > myrank)
   {
     Nmin = myrank * mp + myrank;
@@ -241,6 +234,11 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     Nmax = Nmin + mp - 1;
   }
 
+  double *shellf;
+  shellf = new double[n_tot * InList];
+
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
+
   //|~~~~~> Integrate the dot product of Dphi with the surface normal.
 
   double *RP_out, *IP_out;
@@ -363,8 +361,17 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -556,8 +563,17 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, Comm_here);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, Comm_here);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, Comm_here);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -735,8 +751,17 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH, var *Rpsi4
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -984,8 +1009,17 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -1419,8 +1453,17 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -1854,8 +1897,17 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -2040,8 +2092,17 @@ void surface_integral::surf_Wave(double rex, int lev, NullShellPatch2 *GH, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -2226,8 +2287,17 @@ void surface_integral::surf_Wave(double rex, int lev, NullShellPatch *GH, var *R
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 
@@ -2314,25 +2384,9 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     pox[2][n] = rex * nz_g[n];
   }
 
-  double *shellf;
-  shellf = new double[n_tot * InList];
-
-  // we have assumed there is only one box on this level,
-  // so we do not need loop boxes
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
-
-  double Mass_out = 0;
-  double ang_outx, ang_outy, ang_outz;
-  double p_outx, p_outy, p_outz;
-  ang_outx = ang_outy = ang_outz = 0.0;
-  p_outx = p_outy = p_outz = 0.0;
-  const double f1o8 = 0.125;
-
   int mp, Lp, Nmin, Nmax;
-
   mp = n_tot / cpusize;
   Lp = n_tot - cpusize * mp;
-
   if (Lp > myrank)
   {
     Nmin = myrank * mp + myrank;
@@ -2344,6 +2398,20 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     Nmax = Nmin + mp - 1;
   }
 
+  double *shellf;
+  shellf = new double[n_tot * InList];
+
+  // we have assumed there is only one box on this level,
+  // so we do not need loop boxes
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
+
+  double Mass_out = 0;
+  double ang_outx, ang_outy, ang_outz;
+  double p_outx, p_outy, p_outz;
+  ang_outx = ang_outy = ang_outz = 0.0;
+  p_outx = p_outy = p_outz = 0.0;
+  const double f1o8 = 0.125;
+
   double Chi, Psi;
   double Gxx, Gxy, Gxz, Gyy, Gyz, Gzz;
   double gupxx, gupxy, gupxz, gupyy, gupyz, gupzz;
@@ -2464,15 +2532,13 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
   }
 
-  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-
-  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-
-  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
+    double scalar_in[7];
+    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
+    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
+  }
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -2587,6 +2653,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
 
   // we have assumed there is only one box on this level,
   // so we do not need loop boxes
+
   GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Comm_here);
 
   double Mass_out = 0;
@@ -2735,15 +2802,13 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
   }
 
-  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
-
-  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
-  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
-  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
-
-  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
-  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
-  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  {
+    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
+    double scalar_in[7];
+    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, Comm_here);
+    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
+    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
+  }
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3020,15 +3085,13 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
     }
   }
 
-  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-
-  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-
-  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
+    double scalar_in[7];
+    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
+    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
+  }
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3607,8 +3670,17 @@ void surface_integral::surf_Wave(double rex, cgh *GH, ShellPatch *SH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  {
+    double *RPIP_out = new double[2 * NN];
+    double *RPIP = new double[2 * NN];
+    memcpy(RPIP_out, RP_out, NN * sizeof(double));
+    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
+    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, RPIP, NN * sizeof(double));
+    memcpy(IP, RPIP + NN, NN * sizeof(double));
+    delete[] RPIP_out;
+    delete[] RPIP;
+  }
 
   //|------= Free memory.
 

AMSS_NCKU_source/xh_bssn_rhs_compute.h

@@ -0,0 +1,30 @@
+#include "xh_tool.h"
+
+
+extern "C"
+{
+int f_compute_rhs_bssn_xh(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 *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 *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
+                       ); 
+}

AMSS_NCKU_source/xh_fdderivs.C

@@ -0,0 +1,311 @@
+#include "xh_tool.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)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;          // 1/4
+    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 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;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    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;
+
+
+    /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+
+    /* 系数：按 Fortran 原式 */
+    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);
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // symmetry_bd(2, ex, f, fh, SoA);
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    for (int k0 = 0; k0 < ex[2]; ++k0) {
+        for (int j0 = 0; j0 < ex[1]; ++j0) {
+            for (int i0 = 0; i0 < ex[0]; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1; 
+                fh[idx_funcc_F(iF, jF, kF, 2, ex)] = f[idx_func0(i0, j0, k0, ex)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= 2 - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int jF = 1; jF <= ex[1]; ++jF) {
+                fh[idx_funcc_F(iF_dst, jF, kF, 2, ex)] = 
+                    fh[idx_funcc_F(iF_src, jF, kF, 2, ex)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= 2 - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= ex[2]; ++kF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF_dst, kF, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF_src, kF, 2, ex)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= 2 - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -2 + 1; jF <= ex[1]; ++jF) {
+            for (int iF = -2 + 1; iF <= ex[0]; ++iF) {
+                fh[idx_funcc_F(iF, jF, kF_dst, 2, ex)] =
+                    fh[idx_funcc_F(iF, jF, kF_src, 2, ex)] * SoA[2];
+            }
+        }
+    }
+    /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
+    // 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;
+    // }
+
+    /*
+     * Fortran:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     */
+    
+    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);
+
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
+                    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 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        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 高阶 */
+                    {
+                        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 高阶 */
+                    {
+                        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 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }else{
+                    fxx[p] = 0.0;
+                    fyy[p] = 0.0;
+                    fzz[p] = 0.0;
+                    fxy[p] = 0.0;
+                    fxz[p] = 0.0;
+                    fyz[p] = 0.0;
+                }
+            }
+        }
+    }
+    // free(fh);
+}

AMSS_NCKU_source/xh_fderivs.C

@@ -0,0 +1,145 @@
+#include "xh_tool.h"
+
+/*
+ * C 版 fderivs
+ *
+ * Fortran:
+ * subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+ *
+ * 约定：
+ *   f, fx, fy, fz: ex1*ex2*ex3，按 idx_ex 布局
+ *   X: ex1, Y: ex2, Z: ex3
+ */
+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; // Fortran 里没用到
+
+    const double ZEO = 0.0, ONE = 1.0;
+    const double TWO = 2.0, EIT = 8.0;
+    const double F12 = 12.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1; // OCTANT=2 在本子程序里不直接用
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    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;
+
+    // SoA(1:3) = SYM1,SYM2,SYM3
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    // fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // call symmetry_bd(2,ex,f,fh,SoA)
+    symmetry_bd(2, 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;
+
+    // fx = fy = fz = 0
+    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;
+    }
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
+     *
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
+     */
+    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);
+
+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= ex1 && (iF - 2) >= iminF &&
+                    (jF + 2) <= ex2 && (jF - 2) >= jminF &&
+                    (kF + 2) <= ex3 && (kF - 2) >= kminF)
+                {
+                    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)]
+                    );
+                }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= ex1 && (iF - 1) >= iminF &&
+                         (jF + 1) <= ex2 && (jF - 1) >= jminF &&
+                         (kF + 1) <= ex3 && (kF - 1) >= kminF)
+                {
+                    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)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/xh_global_interp.C

@@ -0,0 +1,143 @@
+#include "xh_global_interp.h"
+
+/* 你已有的 polin3（由前面 Fortran->C 翻译得到） */
+// void polin3(const double *x1a, const double *x2a, const double *x3a,
+//             const double *ya, double x1, double x2, double x3,
+//             double *y, double *dy, int ordn);
+
+/*
+  你需要提供 decide3d 的实现（这里仅声明）。
+  Fortran: decide3d(ex,f,f,cxB,cxT,SoA,ya,ORDN,Symmetry)
+  - ex: [3]
+  - f: 三维场（列主序）
+  - cxB/cxT: 3 维窗口起止（Fortran 1-based，且可能 <=0）
+  - SoA: [3]
+  - ya: 输出 ORDN^3 的采样块（列主序）
+  - return: 0 表示正常；非 0 表示错误（对应 Fortran logical = .true.）
+*/
+// int xh_decide3d(const int ex[3],
+//              const double *f_in,
+//              const double *f_in2,   /* Fortran 里传了 f,f；按原样保留 */
+//              const int cxB[3],
+//              const int cxT[3],
+//              const double SoA[3],
+//              double *ya,
+//              int ordn,
+//              int symmetry);
+
+/* 把 Fortran 1-based 下标 idxF (可为负/0) 映射到 C 的 X[idx] 访问（只用于 X(2-cxB) 这种表达式） */
+static inline double X_at_FortranIndex(const double *X, int idxF) {
+    /* Fortran: X(1) 对应 C: X[0] */
+    return X[idxF - 1];
+}
+
+/* Fortran 整数截断：idint 在这里可用 (int) 实现（对正数等价于 floor） */
+static inline int idint_like(double a) {
+    return (int)a;  /* trunc toward zero */
+}
+
+/* global_interp 的 C 版 */
+void xh_global_interp(const int ex[3],
+                   const double *X, const double *Y, const double *Z,
+                   const double *f,                 /* f(ex1,ex2,ex3) column-major */
+                   double &f_int,
+                   double x1, double y1, double z1,
+                   int ORDN,
+                   const double SoA[3],
+                   int symmetry)
+{
+    // double time1, time2;
+    // time1 = omp_get_wtime();
+    enum { NO_SYMM = 0, EQUATORIAL = 1, OCTANT = 2 };
+
+    int j, m;
+    int imin, jmin, kmin;
+    int cxB[3], cxT[3], cxI[3], cmin[3], cmax[3];
+    double cx[3];
+    double dX, dY, dZ, ddy;
+
+    /* Fortran: imin=lbound(f,1) ... 通常是 1；这里按 1 处理 */
+    imin = 1; jmin = 1; kmin = 1;
+
+    dX = X_at_FortranIndex(X, imin + 1) - X_at_FortranIndex(X, imin);
+    dY = X_at_FortranIndex(Y, jmin + 1) - X_at_FortranIndex(Y, jmin);
+    dZ = X_at_FortranIndex(Z, kmin + 1) - X_at_FortranIndex(Z, kmin);
+
+    /* x1a(j) = (j-1)*1.0  (j=1..ORDN) */
+    double *x1a = (double*)malloc((size_t)ORDN * sizeof(double));
+    double *ya  = (double*)malloc((size_t)ORDN * (size_t)ORDN * (size_t)ORDN * sizeof(double));
+    if (!x1a || !ya) {
+        fprintf(stderr, "global_interp: malloc failed\n");
+        exit(1);
+    }
+    for (j = 0; j < ORDN; j++) x1a[j] = (double)j;
+
+    /* cxI(m) = idint((p - P(1))/dP + 0.4) + 1  (Fortran 1-based) */
+    cxI[0] = idint_like((x1 - X_at_FortranIndex(X, 1)) / dX + 0.4) + 1;
+    cxI[1] = idint_like((y1 - X_at_FortranIndex(Y, 1)) / dY + 0.4) + 1;
+    cxI[2] = idint_like((z1 - X_at_FortranIndex(Z, 1)) / dZ + 0.4) + 1;
+
+    /* cxB = cxI - ORDN/2 + 1 ; cxT = cxB + ORDN - 1 */
+    int half = ORDN / 2;  /* Fortran 整数除法 */
+    for (m = 0; m < 3; m++) {
+        cxB[m] = cxI[m] - half + 1;
+        cxT[m] = cxB[m] + ORDN - 1;
+    }
+
+    /* cmin=1; cmax=ex */
+    cmin[0] = cmin[1] = cmin[2] = 1;
+    cmax[0] = ex[0];
+    cmax[1] = ex[1];
+    cmax[2] = ex[2];
+
+    /* 对称边界时允许 cxB 为负/0（与 Fortran 一致） */
+    if (symmetry == OCTANT && fabs(X_at_FortranIndex(X, 1)) < dX) cmin[0] = -half + 2;
+    if (symmetry == OCTANT && fabs(X_at_FortranIndex(Y, 1)) < dY) cmin[1] = -half + 2;
+    if (symmetry != NO_SYMM && fabs(X_at_FortranIndex(Z, 1)) < dZ) cmin[2] = -half + 2;
+
+    /* 夹紧窗口 [cxB,cxT] 到 [cmin,cmax] */
+    for (m = 0; m < 3; m++) {
+        if (cxB[m] < cmin[m]) {
+            cxB[m] = cmin[m];
+            cxT[m] = cxB[m] + ORDN - 1;
+        }
+        if (cxT[m] > cmax[m]) {
+            cxT[m] = cmax[m];
+            cxB[m] = cxT[m] + 1 - ORDN;
+        }
+    }
+
+    /*
+      cx(m) 的计算：如果 cxB>0:
+        cx = (p - P(cxB))/dP
+      else:
+        cx = (p + P(2 - cxB))/dP
+      注意这里的 cxB 是 Fortran 1-based 语义下的整数，可能 <=0。
+    */
+    if (cxB[0] > 0) cx[0] = (x1 - X_at_FortranIndex(X, cxB[0])) / dX;
+    else           cx[0] = (x1 + X_at_FortranIndex(X, 2 - cxB[0])) / dX;
+
+    if (cxB[1] > 0) cx[1] = (y1 - X_at_FortranIndex(Y, cxB[1])) / dY;
+    else           cx[1] = (y1 + X_at_FortranIndex(Y, 2 - cxB[1])) / dY;
+
+    if (cxB[2] > 0) cx[2] = (z1 - X_at_FortranIndex(Z, cxB[2])) / dZ;
+    else           cx[2] = (z1 + X_at_FortranIndex(Z, 2 - cxB[2])) / dZ;
+
+    /* decide3d: 填充 ya(1:ORDN,1:ORDN,1:ORDN) */
+    if (xh_decide3d(ex, f, f, cxB, cxT, SoA, ya, ORDN, symmetry)) {
+        printf("global_interp position: %g %g %g\n", x1, y1, z1);
+        printf("data range: %g %g   %g %g   %g %g\n",
+               X_at_FortranIndex(X, 1), X_at_FortranIndex(X, ex[0]),
+               X_at_FortranIndex(Y, 1), X_at_FortranIndex(Y, ex[1]),
+               X_at_FortranIndex(Z, 1), X_at_FortranIndex(Z, ex[2]));
+        exit(1);
+    }
+
+    /* polin3(x1a,x1a,x1a,ya,cx(1),cx(2),cx(3),f_int,ddy,ORDN) */
+    xh_polin3(x1a, x1a, x1a, ya, cx[0], cx[1], cx[2], f_int, &ddy, ORDN);
+ 
+    free(x1a);
+    free(ya);
+    // time2 = omp_get_wtime();
+    // printf("Time for global_interp: %lf seconds\n", time2 - time1);
+}

AMSS_NCKU_source/xh_global_interp.h

@@ -0,0 +1,12 @@
+#include "xh_po.h"
+
+extern "C"{
+    void xh_global_interp(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f,                 /* f(ex1,ex2,ex3) column-major */
+                    double &f_int,
+                    double x1, double y1, double z1,
+                    int ORDN,
+                    const double SoA[3],
+                    int symmetry);
+}

AMSS_NCKU_source/xh_kodiss.C

@@ -0,0 +1,116 @@
+#include "xh_tool.h"
+
+/*
+ * C 版 kodis
+ *
+ * Fortran signature:
+ * subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
+ *
+ * 约定：
+ *   X: ex1, Y: ex2, Z: ex3
+ *   f, f_rhs: ex1*ex2*ex3 按 idx_ex 布局
+ *   SoA[3]
+ *   eps: double
+ */
+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 ONE = 1.0, SIX = 6.0, FIT = 15.0, TWT = 20.0;
+    const double cof = 64.0;             // 2^6
+    const int NO_SYMM = 0, OCTANT = 2;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // Fortran: dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+    (void)ONE; // ONE 在原 Fortran 里只是参数，这里不一定用得上
+
+    // Fortran: imax=ex(1) 等是 1-based 上界
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran: imin=jmin=kmin=1，某些对称情况变 -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;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)，对应 ord=3
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    if (!fh) return;
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3
+     * do j=1,ex2
+     * do i=1,ex1
+     *
+     * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
+     * 并定义 Fortran index: iF=i0+1, ...
+     */
+    for (int k0 = 0; k0 < ex3; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 < ex2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const int iF = i0 + 1;
+
+                // Fortran if 条件：
+                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
+                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
+                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
+                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
+                {
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
+                    const double Dx_term =
+                        ( (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_term =
+                        ( (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_term =
+                        ( (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;
+
+                    // Fortran:
+                    // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
+                    f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/xh_lopsided.C

@@ -0,0 +1,262 @@
+#include "xh_tool.h"
+/*
+ * 你需要提供 symmetry_bd 的 C 版本（或 Fortran 绑到 C 的接口）。
+ * Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+ *
+ * 约定：
+ *   nghost = 3
+ *   ex[3]  = {ex1,ex2,ex3}
+ *   f      = 原始网格 (ex1*ex2*ex3)
+ *   fh     = 扩展网格 ((ex1+3)*(ex2+3)*(ex3+3))，对应 Fortran 的 (-2:ex1, ...)
+ *   SoA[3] = 输入参数
+ */
+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, F3 = 3.0;
+    const double TWO = 2.0, F6 = 6.0, F18 = 18.0;
+    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2;
+    (void)OCTANT; // 这里和 Fortran 一样只是定义了不用也没关系
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // 对应 Fortran: dX = X(2)-X(1)  （Fortran 1-based）
+    // C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    // Fortran 里算了 d2dx/d2dy/d2dz 但本 subroutine 里没用到（保持一致也算出来）
+    const double d2dx  = ONE / TWO / dX;
+    const double d2dy  = ONE / TWO / dY;
+    const double d2dz  = ONE / TWO / dZ;
+    (void)d2dx; (void)d2dy; (void)d2dz;
+
+    // Fortran:
+    // imax = ex(1); jmax = ex(2); kmax = ex(3)
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran:
+    // imin=jmin=kmin=1; 若满足对称条件则设为 -2
+    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;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    static thread_local double *fh = NULL;
+    static thread_local size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    if (!fh) return; // 内存不足：直接返回（你也可以改成 abort/报错）
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran 主循环：
+     * do k=1,ex(3)-1
+     * do j=1,ex(2)-1
+     * do i=1,ex(1)-1
+     *
+     * 转成 C 0-based：
+     * k0 = 0..ex3-2, j0 = 0..ex2-2, i0 = 0..ex1-2
+     *
+     * 并且 Fortran 里的 i/j/k 在 fh 访问时，仍然是 Fortran 索引值：
+     * iF=i0+1, jF=j0+1, kF=k0+1
+     */
+    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) {
+                    // Fortran: if(i+3 <= imax)
+                    // iF+3 <= ex1  <=> i0+4 <= ex1 <=> i0 <= ex1-4
+                    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)]);
+                    }
+                    // elseif(i+2 <= imax)  <=> i0 <= ex1-3
+                    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)]);
+                    }
+                    // elseif(i+1 <= imax)  <=> i0 <= ex1-2（循环里总成立）
+                    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) {
+                    // Fortran: if(i-3 >= imin)
+                    // (iF-3) >= iminF  <=> (i0-2) >= iminF
+                    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)]);
+                    }
+                    // elseif(i-2 >= imin) <=> (i0-1) >= iminF
+                    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)]);
+                    }
+                    // elseif(i-1 >= imin) <=> i0 >= iminF
+                    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)]);
+                    }
+                }
+
+                // ---------------- y direction ----------------
+                const double sfy = Sfy[p];
+                if (sfy > ZEO) {
+                    // jF+3 <= ex2 <=> j0+4 <= ex2 <=> j0 <= ex2-4
+                    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)]);
+                    }
+                }
+
+                // ---------------- z direction ----------------
+                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);
+}
+
+
+
+
+

AMSS_NCKU_source/xh_po.h

@@ -0,0 +1,19 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <omp.h>
+int xh_decide3d(const int ex[3],
+             const double *f,
+             const double *fpi,   /* 这里未用，Fortran 也没用到 */
+             const int cxB[3],
+             const int cxT[3],
+             const double SoA[3],
+             double *ya,
+             int ordn,
+             int Symmetry);
+void xh_polint(const double *xa, const double *ya, double x,
+                   double *y, double *dy, int ordn);
+
+void xh_polin3(const double *x1a, const double *x2a, const double *x3a,
+                   const double *ya, double x1, double x2, double x3,
+                   double &y, double *dy, int ordn);

AMSS_NCKU_source/xh_polint3.C

@@ -0,0 +1,258 @@
+#include "xh_po.h"
+/*
+  ex[0..2]  == Fortran ex(1:3)
+  cxB/cxT   == Fortran cxB(1:3), cxT(1:3)  (可能 <=0)
+  SoA[0..2] == Fortran SoA(1:3)
+  f, fpi    == Fortran f(ex1,ex2,ex3) column-major (1-based in formulas)
+  ya        == 连续内存，尺寸为 ORDN^3，对应 Fortran ya(cxB1:cxT1, cxB2:cxT2, cxB3:cxT3)
+              但注意：我们用 offset 映射把 Fortran 的 i/j/k 坐标写进去。
+*/
+
+static inline int imax(int a, int b) { return a > b ? a : b; }
+static inline int imin(int a, int b) { return a < b ? a : b; }
+
+/* f(i,j,k): Fortran column-major, i/j/k are Fortran 1-based in [1..ex] */
+#define F(i,j,k) f[((i)-1) + ex1 * (((j)-1) + ex2 * ((k)-1))]
+
+/*
+  ya(i,j,k): i in [cxB1..cxT1], j in [cxB2..cxT2], k in [cxB3..cxT3]
+  我们把它映射到 C 的 0..ORDN-1 立方体：
+    ii = i - cxB1
+    jj = j - cxB2
+    kk = k - cxB3
+  并按 column-major 存储（与 Fortran 一致，方便直接喂给你的 polin3）
+*/
+#define YA(i,j,k) ya[((i)-cxB1) + ordn * (((j)-cxB2) + ordn * ((k)-cxB3))]
+
+int xh_decide3d(const int ex[3],
+             const double *f,
+             const double *fpi,   /* 这里未用，Fortran 也没用到 */
+             const int cxB[3],
+             const int cxT[3],
+             const double SoA[3],
+             double *ya,
+             int ordn,
+             int Symmetry)         /* Symmetry 在 decide3d 里也没直接用 */
+{
+    (void)fpi;
+    (void)Symmetry;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    int fmin1[3], fmin2[3], fmax1[3], fmax2[3];
+    int i, j, k, m;
+
+    int gont = 0;
+
+    /* 方便 YA 宏使用 */
+    const int cxB1 = cxB[0], cxB2 = cxB[1], cxB3 = cxB[2];
+
+    for (m = 0; m < 3; m++) {
+        /* Fortran 的 “NaN 检查” 在整数上基本无意义，这里不额外处理 */
+
+        fmin1[m] = imax(1, cxB[m]);
+        fmax1[m] = cxT[m];
+
+        fmin2[m] = cxB[m];
+        fmax2[m] = imin(0, cxT[m]);
+
+        /* if((fmin1<=fmax1) and (fmin1<1 or fmax1>ex)) gont=true */
+        if ((fmin1[m] <= fmax1[m]) && (fmin1[m] < 1 || fmax1[m] > ex[m])) gont = 1;
+
+        /* if((fmin2<=fmax2) and (2-fmax2<1 or 2-fmin2>ex)) gont=true */
+        if ((fmin2[m] <= fmax2[m]) && (2 - fmax2[m] < 1 || 2 - fmin2[m] > ex[m])) gont = 1;
+    }
+
+    if (gont) {
+        printf("error in decide3d\n");
+        printf("cxB: %d %d %d   cxT: %d %d %d   ex: %d %d %d\n",
+               cxB[0], cxB[1], cxB[2], cxT[0], cxT[1], cxT[2], ex[0], ex[1], ex[2]);
+        printf("fmin1: %d %d %d  fmax1: %d %d %d\n",
+               fmin1[0], fmin1[1], fmin1[2], fmax1[0], fmax1[1], fmax1[2]);
+        printf("fmin2: %d %d %d  fmax2: %d %d %d\n",
+               fmin2[0], fmin2[1], fmin2[2], fmax2[0], fmax2[1], fmax2[2]);
+        return 1;
+    }
+
+    /* ---- 填充 ya：完全照 Fortran 两大块循环写 ---- */
+
+    /* k in [fmin1(3)..fmax1(3)] */
+    for (k = fmin1[2]; k <= fmax1[2]; k++) {
+
+        /* j in [fmin1(2)..fmax1(2)] */
+        for (j = fmin1[1]; j <= fmax1[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya(i,j,k)=f(i,j,k) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, j, k);
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya(i,j,k)=f(2-i,j,k)*SoA(1) */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, j, k) * SoA[0];
+            }
+        }
+
+        /* j in [fmin2(2)..fmax2(2)] */
+        for (j = fmin2[1]; j <= fmax2[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya(i,j,k)=f(i,2-j,k)*SoA(2) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, 2 - j, k) * SoA[1];
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya=f(2-i,2-j,k)*SoA(1)*SoA(2) */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, 2 - j, k) * SoA[0] * SoA[1];
+            }
+        }
+    }
+
+    /* k in [fmin2(3)..fmax2(3)] */
+    for (k = fmin2[2]; k <= fmax2[2]; k++) {
+
+        /* j in [fmin1(2)..fmax1(2)] */
+        for (j = fmin1[1]; j <= fmax1[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya=f(i,j,2-k)*SoA(3) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, j, 2 - k) * SoA[2];
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya=f(2-i,j,2-k)*SoA(1)*SoA(3) */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, j, 2 - k) * SoA[0] * SoA[2];
+            }
+        }
+
+        /* j in [fmin2(2)..fmax2(2)] */
+        for (j = fmin2[1]; j <= fmax2[1]; j++) {
+
+            /* i in [fmin1(1)..fmax1(1)] : ya=f(i,2-j,2-k)*SoA(2)*SoA(3) */
+            for (i = fmin1[0]; i <= fmax1[0]; i++) {
+                YA(i, j, k) = F(i, 2 - j, 2 - k) * SoA[1] * SoA[2];
+            }
+
+            /* i in [fmin2(1)..fmax2(1)] : ya=f(2-i,2-j,2-k)*SoA1*SoA2*SoA3 */
+            for (i = fmin2[0]; i <= fmax2[0]; i++) {
+                YA(i, j, k) = F(2 - i, 2 - j, 2 - k) * SoA[0] * SoA[1] * SoA[2];
+            }
+        }
+    }
+
+    return 0;
+}
+
+#undef F
+#undef YA
+
+void xh_polint(const double *xa, const double *ya, double x,
+                   double *y, double *dy, int ordn)
+{
+    int i, m, ns, n_m;
+    double dif, dift, hp, h, den_val;
+
+    double *c  = (double*)malloc((size_t)ordn * sizeof(double));
+    double *d  = (double*)malloc((size_t)ordn * sizeof(double));
+    double *ho = (double*)malloc((size_t)ordn * sizeof(double));
+    if (!c || !d || !ho) {
+        fprintf(stderr, "polint: malloc failed\n");
+        exit(1);
+    }
+
+    for (i = 0; i < ordn; i++) {
+        c[i]  = ya[i];
+        d[i]  = ya[i];
+        ho[i] = xa[i] - x;
+    }
+
+    ns  = 0;                      // Fortran ns=1 -> C ns=0
+    dif = fabs(x - xa[0]);
+
+    for (i = 1; i < ordn; i++) {
+        dift = fabs(x - xa[i]);
+        if (dift < dif) {
+            ns  = i;
+            dif = dift;
+        }
+    }
+
+    *y  = ya[ns];
+    ns -= 1;                      // Fortran ns=ns-1
+
+    for (m = 1; m <= ordn - 1; m++) {
+        n_m = ordn - m;           // number of active points this round
+        for (i = 0; i < n_m; i++) {
+            hp      = ho[i];
+            h       = ho[i + m];
+            den_val = hp - h;
+
+            if (den_val == 0.0) {
+                fprintf(stderr, "failure in polint for point %g\n", x);
+                fprintf(stderr, "with input points xa: ");
+                for (int t = 0; t < ordn; t++) fprintf(stderr, "%g ", xa[t]);
+                fprintf(stderr, "\n");
+                exit(1);
+            }
+
+            den_val = (c[i + 1] - d[i]) / den_val;
+            d[i]    = h  * den_val;
+            c[i]    = hp * den_val;
+        }
+
+        // Fortran: if (2*ns < n_m) then dy=c(ns+1) else dy=d(ns); ns=ns-1
+        // Here ns is C-indexed and can be -1; logic still matches.
+        if (2 * ns < n_m) {
+            *dy = c[ns + 1];
+        } else {
+            *dy = d[ns];
+            ns -= 1;
+        }
+        *y += *dy;
+    }
+
+    free(c);
+    free(d);
+    free(ho);
+}
+
+void xh_polin3(const double *x1a, const double *x2a, const double *x3a,
+                   const double *ya, double x1, double x2, double x3,
+                   double &y, double *dy, int ordn)
+{
+    // ya is ordn x ordn x ordn in Fortran layout (column-major)
+    #define YA3(i,j,k) ya[(i) + ordn*((j) + ordn*(k))]  // i,j,k: 0..ordn-1
+
+    int j, k;
+    double dy_temp;
+
+    // yatmp(j,k) in Fortran code is ordn x ordn, treat column-major:
+    // yatmp(j,k) -> yatmp[j + ordn*k]
+    double *yatmp = (double*)malloc((size_t)ordn * (size_t)ordn * sizeof(double));
+    double *ymtmp = (double*)malloc((size_t)ordn * sizeof(double));
+    if (!yatmp || !ymtmp) {
+        fprintf(stderr, "polin3: malloc failed\n");
+        exit(1);
+    }
+    #define YAT(j,k) yatmp[(j) + ordn*(k)]
+
+    for (k = 0; k < ordn; k++) {
+        for (j = 0; j < ordn; j++) {
+            // call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp)
+            // ya(:,j,k) contiguous: base is &YA3(0,j,k)
+            xh_polint(x1a, &YA3(0, j, k), x1, &YAT(j, k), &dy_temp, ordn);
+        }
+    }
+
+    for (k = 0; k < ordn; k++) {
+        // call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp)
+        xh_polint(x2a, &YAT(0, k), x2, &ymtmp[k], &dy_temp, ordn);
+    }
+
+    xh_polint(x3a, ymtmp, x3, &y, dy, ordn);
+
+    #undef YAT
+    free(yatmp);
+    free(ymtmp);
+    #undef YA3
+}

AMSS_NCKU_source/xh_share_func.h

@@ -0,0 +1,338 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#include <stddef.h>
+#include <math.h>
+#include <stdio.h>
+#include <omp.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;
+}
+
+/*
+ * 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(int ord,
+                 const int extc[3],
+                 const double *func,
+                 double *funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+
+    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
+    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            for (int i0 = 0; i0 < extc1; ++i0) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
+            }
+        }
+    }
+
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= ord - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int jF = 1; jF <= extc2; ++jF) {
+                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= ord - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= ord - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -ord + 1; jF <= extc2; ++jF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
+            }
+        }
+    }
+}
+#endif
+
+/* 你已有的函数：idx_ex / idx_fh_F_ord2 以及 fh 的布局 */
+static inline void fdderivs_xh(
+    int i0, int j0, int k0,
+    const int ex[3],
+    const double *fh,
+    int iminF, int jminF, int kminF,
+    int imaxF, int jmaxF, int kmaxF,
+    double Fdxdx, double Fdydy, double Fdzdz,
+    double Fdxdy, double Fdxdz, double Fdydz,
+    double Sdxdx, double Sdydy, double Sdzdz,
+    double Sdxdy, double Sdxdz, double Sdydz,
+    double *fxx, double *fxy, double *fxz,
+    double *fyy, double *fyz, double *fzz
+){
+    const double F8  = 8.0;
+    const double F16 = 16.0;
+    const double F30 = 30.0;
+    const double TWO = 2.0;
+
+    const int iF = i0 + 1;
+    const int jF = j0 + 1;
+    const int kF = k0 + 1;
+
+    const size_t p = idx_ex(i0, j0, k0, ex);
+
+    /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+    if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+        (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+        (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+    {
+        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 高阶 */
+        {
+            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 高阶 */
+        {
+            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 高阶 */
+        {
+            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 );
+        }
+    }
+    /* 二阶分支：i±1,j±1,k±1 在范围内 */
+    else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+             (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+             (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+    {
+        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)]
+        );
+    }
+    else {
+        fxx[p] = 0.0; fyy[p] = 0.0; fzz[p] = 0.0;
+        fxy[p] = 0.0; fxz[p] = 0.0; fyz[p] = 0.0;
+    }
+}

AMSS_NCKU_source/xh_tool.h

@@ -0,0 +1,27 @@
+#include "xh_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]);

generate_TwoPuncture_input.py

@@ -1,195 +1,195 @@
-
-##################################################################
-##
-## Generate input file for the AMSS-NCKU TwoPuncture routine
-## Author: Xiaoqu
-## 2024/11/27
-## Modified: 2025/01/21
-##
-##################################################################
-
-
-import numpy
-import os 
-import AMSS_NCKU_Input as input_data          ## import program input file
-import math
-
-##################################################################
-
-## Import binary black hole coordinates
-
-## If puncture data are set to "Automatically-BBH", compute initial orbital
-## positions and momenta according to the settings and rescale the total
-## binary mass to M = 1 for TwoPuncture input.
-
-if (input_data.puncture_data_set == "Automatically-BBH" ):
-
-    mass_ratio_Q = input_data.parameter_BH[0,0] / input_data.parameter_BH[1,0]
-    
-    if ( mass_ratio_Q < 1.0 ):
-        print( " mass_ratio setting is wrong, please reset!!!" ) 
-        print( " set the first black hole to be the larger mass!!!" ) 
-        
-    BBH_M1 = mass_ratio_Q / ( 1.0 + mass_ratio_Q )
-    BBH_M2 = 1.0          / ( 1.0 + mass_ratio_Q )
-
-    ## Load binary separation and eccentricity
-    distance = input_data.Distance
-    e0       = input_data.e0
-    
-    ## Set binary component coordinates
-    ## Note: place the larger-mass black hole at positive y and the
-    ## smaller-mass black hole at negative y to follow Brugmann's convention
-    ## Coordinate convention for TwoPuncture input (Brugmann):
-    ##  -----0-----> y
-    ##   -      +     
-
-
-    BBH_X1 = 0.0
-    BBH_Y1 = distance * 1.0 / ( 1 + mass_ratio_Q )
-    BBH_Z1 = 0.0
-
-    BBH_X2 = 0.0
-    BBH_Y2 = - distance * mass_ratio_Q / ( 1 + mass_ratio_Q )
-    BBH_Z2 = 0.0
-    
-    position_BH    = numpy.zeros( (2,3) )
-    position_BH[0] = [BBH_X1, BBH_Y1, BBH_Z1]
-    position_BH[1] = [BBH_X2, BBH_Y2, BBH_Z2]
-    
-    ## Optionally load momentum from parameter file
-    ## momentum_BH  = input_data.momentum_BH
-
-    ## Compute orbital momenta using the BBH_orbit_parameter module
-    import BBH_orbit_parameter 
-
-    ## Use the dimensionless spins defined in BBH_orbit_parameter
-    BBH_S1 = BBH_orbit_parameter.S1
-    BBH_S2 = BBH_orbit_parameter.S2
-
-    momentum_BH = numpy.zeros( (2,3) )
-
-    ## Compute initial orbital momenta from post-Newtonian-based routine
-    momentum_BH[0], momentum_BH[1] = BBH_orbit_parameter.generate_BBH_orbit_parameters( BBH_M1, BBH_M2, BBH_S1, BBH_S2, distance, e0 ) 
-
-    ## Set spin angular momentum input for TwoPuncture
-    ## Note: these are dimensional angular momenta (not dimensionless); multiply
-    ## by the square of the mass scale. Here masses are scaled so total M=1.
-    ## angular_momentum_BH = input_data.angular_momentum_BH
-
-    angular_momentum_BH = numpy.zeros( (input_data.puncture_number, 3) )  
-    
-    for i in range(input_data.puncture_number):
-    
-        if ( input_data.Symmetry == "equatorial-symmetry" ):
-            if i==0:
-                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M1**2) * input_data.parameter_BH[i,2] ]
-            elif i==1:
-                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M2**2) * input_data.parameter_BH[i,2] ]
-            else:
-                angular_momentum_BH[i] = [ 0.0, 0.0, (input_data.parameter_BH[i,0]**2) * input_data.parameter_BH[i,2] ]
-                
-        elif ( input_data.Symmetry == "no-symmetry" ):
-        
-            if i==0:
-                angular_momentum_BH[i] = (BBH_M1**2) * input_data.dimensionless_spin_BH[i]
-            elif i==1:
-                angular_momentum_BH[i] = (BBH_M1**2) * input_data.dimensionless_spin_BH[i]
-            else:
-                angular_momentum_BH[i] = (input_data.parameter_BH[i,0]**2) * input_data.dimensionless_spin_BH[i]
-            
-    #######################################################
-
-## If puncture data are set to "Manually", read initial positions and momenta
-## directly from the parameter file. Rescale the total binary mass to M=1
-## for TwoPuncture input.
-
-elif (input_data.puncture_data_set == "Manually" ):
-
-    mass_ratio_Q = input_data.parameter_BH[0,0] / input_data.parameter_BH[1,0]
-    
-    if ( mass_ratio_Q < 1.0 ):
-        print( " mass_ratio setting is wrong, please reset!!!" ) 
-        print( " set the first black hole to be the larger mass!!!" ) 
-        
-    BBH_M1 = mass_ratio_Q / ( 1.0 + mass_ratio_Q )
-    BBH_M2 = 1.0          / ( 1.0 + mass_ratio_Q )
-    
-    parameter_BH = input_data.parameter_BH
-    position_BH  = input_data.position_BH
-    momentum_BH  = input_data.momentum_BH
-    
-    ## Compute binary separation and load eccentricity
-    distance = math.sqrt( (position_BH[0,0]-position_BH[1,0])**2 + (position_BH[0,1]-position_BH[1,1])**2 + (position_BH[0,2]-position_BH[1,2])**2 )
-    e0       = input_data.e0
-
-    ## Set spin angular momentum input for TwoPuncture
-    ## Note: these are dimensional angular momenta (not dimensionless); multiply
-    ## by the square of the mass scale. Here masses are scaled so total M=1.
-
-    ## angular_momentum_BH = input_data.angular_momentum_BH
-
-    angular_momentum_BH = numpy.zeros( (input_data.puncture_number, 3) )   
-
-        
-    for i in range(input_data.puncture_number):
-    
-        if ( input_data.Symmetry == "equatorial-symmetry" ):
-            if i==0:
-                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M1**2) * parameter_BH[i,2] ]
-            elif i==1:
-                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M2**2) * parameter_BH[i,2] ]
-            else:
-                angular_momentum_BH[i] = [ 0.0, 0.0, (parameter_BH[i,0]**2) * parameter_BH[i,2] ]
-                
-        elif ( input_data.Symmetry == "no-symmetry" ):
-            if i==0:
-                angular_momentum_BH[i] = (BBH_M1**2) * input_data.dimensionless_spin_BH[i]
-            elif i==1:
-                angular_momentum_BH[i] = (BBH_M2**2) * input_data.dimensionless_spin_BH[i]
-            else:
-                angular_momentum_BH[i] = (parameter_BH[i,0]**2) * input_data.dimensionless_spin_BH[i]
-
-
-##################################################################
-
-## Write the above binary data into the AMSS-NCKU TwoPuncture input file
-    
-def generate_AMSSNCKU_TwoPuncture_input(): 
-
-    file1 = open( os.path.join(input_data.File_directory, "AMSS-NCKU-TwoPuncture.input"), "w") 
-
-    print( "#  -----0-----> y",                           file=file1 )
-    print( "#   -      +      use Brugmann's convention", file=file1 )
-    print( "ABE::mp        = -1.0",                       file=file1 )   ## use negative values so the code solves for bare masses automatically
-    print( "ABE::mm        = -1.0",                       file=file1 )
-    print( "# b            =  D/2",                       file=file1 )
-    print( "ABE::b         = ", ( distance / 2.0 ),       file=file1 )
-    print( "ABE::P_plusx   = ", momentum_BH[0,0],         file=file1 )
-    print( "ABE::P_plusy   = ", momentum_BH[0,1],         file=file1 )
-    print( "ABE::P_plusz   = ", momentum_BH[0,2],         file=file1 )
-    print( "ABE::P_minusx  = ", momentum_BH[1,0],         file=file1 )
-    print( "ABE::P_minusy  = ", momentum_BH[1,1],         file=file1 )
-    print( "ABE::P_minusz  = ", momentum_BH[1,2],         file=file1 )
-    print( "ABE::S_plusx   = ", angular_momentum_BH[0,0], file=file1 )
-    print( "ABE::S_plusy   = ", angular_momentum_BH[0,1], file=file1 )
-    print( "ABE::S_plusz   = ", angular_momentum_BH[0,2], file=file1 )
-    print( "ABE::S_minusx  = ", angular_momentum_BH[1,0], file=file1 )
-    print( "ABE::S_minusy  = ", angular_momentum_BH[1,1], file=file1 )
-    print( "ABE::S_minusz  = ", angular_momentum_BH[1,2], file=file1 )
-    print( "ABE::Mp        = ", BBH_M1,                   file=file1 )
-    print( "ABE::Mm        = ", BBH_M2,                   file=file1 )
-    print( "ABE::admtol    =  1.e-8",                     file=file1 )
-    print( "ABE::Newtontol =  5.e-12",                    file=file1 )
-    print( "ABE::nA        =  50",                        file=file1 )
-    print( "ABE::nB        =  50",                        file=file1 )
-    print( "ABE::nphi      =  26",                        file=file1 )
-    print( "ABE::Newtonmaxit =  50",                      file=file1 )
-    
-    file1.close()
-
-    return file1
-    
-##################################################################
-    
-    
+
+##################################################################
+##
+## Generate input file for the AMSS-NCKU TwoPuncture routine
+## Author: Xiaoqu
+## 2024/11/27
+## Modified: 2025/01/21
+##
+##################################################################
+
+
+import numpy
+import os 
+import AMSS_NCKU_Input as input_data          ## import program input file
+import math
+
+##################################################################
+
+## Import binary black hole coordinates
+
+## If puncture data are set to "Automatically-BBH", compute initial orbital
+## positions and momenta according to the settings and rescale the total
+## binary mass to M = 1 for TwoPuncture input.
+
+if (input_data.puncture_data_set == "Automatically-BBH" ):
+
+    mass_ratio_Q = input_data.parameter_BH[0,0] / input_data.parameter_BH[1,0]
+    
+    if ( mass_ratio_Q < 1.0 ):
+        print( " mass_ratio setting is wrong, please reset!!!" ) 
+        print( " set the first black hole to be the larger mass!!!" ) 
+        
+    BBH_M1 = mass_ratio_Q / ( 1.0 + mass_ratio_Q )
+    BBH_M2 = 1.0          / ( 1.0 + mass_ratio_Q )
+
+    ## Load binary separation and eccentricity
+    distance = input_data.Distance
+    e0       = input_data.e0
+    
+    ## Set binary component coordinates
+    ## Note: place the larger-mass black hole at positive y and the
+    ## smaller-mass black hole at negative y to follow Brugmann's convention
+    ## Coordinate convention for TwoPuncture input (Brugmann):
+    ##  -----0-----> y
+    ##   -      +     
+
+
+    BBH_X1 = 0.0
+    BBH_Y1 = distance * 1.0 / ( 1 + mass_ratio_Q )
+    BBH_Z1 = 0.0
+
+    BBH_X2 = 0.0
+    BBH_Y2 = - distance * mass_ratio_Q / ( 1 + mass_ratio_Q )
+    BBH_Z2 = 0.0
+    
+    position_BH    = numpy.zeros( (2,3) )
+    position_BH[0] = [BBH_X1, BBH_Y1, BBH_Z1]
+    position_BH[1] = [BBH_X2, BBH_Y2, BBH_Z2]
+    
+    ## Optionally load momentum from parameter file
+    ## momentum_BH  = input_data.momentum_BH
+
+    ## Compute orbital momenta using the BBH_orbit_parameter module
+    import BBH_orbit_parameter 
+
+    ## Use the dimensionless spins defined in BBH_orbit_parameter
+    BBH_S1 = BBH_orbit_parameter.S1
+    BBH_S2 = BBH_orbit_parameter.S2
+
+    momentum_BH = numpy.zeros( (2,3) )
+
+    ## Compute initial orbital momenta from post-Newtonian-based routine
+    momentum_BH[0], momentum_BH[1] = BBH_orbit_parameter.generate_BBH_orbit_parameters( BBH_M1, BBH_M2, BBH_S1, BBH_S2, distance, e0 ) 
+
+    ## Set spin angular momentum input for TwoPuncture
+    ## Note: these are dimensional angular momenta (not dimensionless); multiply
+    ## by the square of the mass scale. Here masses are scaled so total M=1.
+    ## angular_momentum_BH = input_data.angular_momentum_BH
+
+    angular_momentum_BH = numpy.zeros( (input_data.puncture_number, 3) )  
+    
+    for i in range(input_data.puncture_number):
+    
+        if ( input_data.Symmetry == "equatorial-symmetry" ):
+            if i==0:
+                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M1**2) * input_data.parameter_BH[i,2] ]
+            elif i==1:
+                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M2**2) * input_data.parameter_BH[i,2] ]
+            else:
+                angular_momentum_BH[i] = [ 0.0, 0.0, (input_data.parameter_BH[i,0]**2) * input_data.parameter_BH[i,2] ]
+                
+        elif ( input_data.Symmetry == "no-symmetry" ):
+        
+            if i==0:
+                angular_momentum_BH[i] = (BBH_M1**2) * input_data.dimensionless_spin_BH[i]
+            elif i==1:
+                angular_momentum_BH[i] = (BBH_M1**2) * input_data.dimensionless_spin_BH[i]
+            else:
+                angular_momentum_BH[i] = (input_data.parameter_BH[i,0]**2) * input_data.dimensionless_spin_BH[i]
+            
+    #######################################################
+
+## If puncture data are set to "Manually", read initial positions and momenta
+## directly from the parameter file. Rescale the total binary mass to M=1
+## for TwoPuncture input.
+
+elif (input_data.puncture_data_set == "Manually" ):
+
+    mass_ratio_Q = input_data.parameter_BH[0,0] / input_data.parameter_BH[1,0]
+    
+    if ( mass_ratio_Q < 1.0 ):
+        print( " mass_ratio setting is wrong, please reset!!!" ) 
+        print( " set the first black hole to be the larger mass!!!" ) 
+        
+    BBH_M1 = mass_ratio_Q / ( 1.0 + mass_ratio_Q )
+    BBH_M2 = 1.0          / ( 1.0 + mass_ratio_Q )
+    
+    parameter_BH = input_data.parameter_BH
+    position_BH  = input_data.position_BH
+    momentum_BH  = input_data.momentum_BH
+    
+    ## Compute binary separation and load eccentricity
+    distance = math.sqrt( (position_BH[0,0]-position_BH[1,0])**2 + (position_BH[0,1]-position_BH[1,1])**2 + (position_BH[0,2]-position_BH[1,2])**2 )
+    e0       = input_data.e0
+
+    ## Set spin angular momentum input for TwoPuncture
+    ## Note: these are dimensional angular momenta (not dimensionless); multiply
+    ## by the square of the mass scale. Here masses are scaled so total M=1.
+
+    ## angular_momentum_BH = input_data.angular_momentum_BH
+
+    angular_momentum_BH = numpy.zeros( (input_data.puncture_number, 3) )   
+
+        
+    for i in range(input_data.puncture_number):
+    
+        if ( input_data.Symmetry == "equatorial-symmetry" ):
+            if i==0:
+                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M1**2) * parameter_BH[i,2] ]
+            elif i==1:
+                angular_momentum_BH[i] = [ 0.0, 0.0, (BBH_M2**2) * parameter_BH[i,2] ]
+            else:
+                angular_momentum_BH[i] = [ 0.0, 0.0, (parameter_BH[i,0]**2) * parameter_BH[i,2] ]
+                
+        elif ( input_data.Symmetry == "no-symmetry" ):
+            if i==0:
+                angular_momentum_BH[i] = (BBH_M1**2) * input_data.dimensionless_spin_BH[i]
+            elif i==1:
+                angular_momentum_BH[i] = (BBH_M2**2) * input_data.dimensionless_spin_BH[i]
+            else:
+                angular_momentum_BH[i] = (parameter_BH[i,0]**2) * input_data.dimensionless_spin_BH[i]
+
+
+##################################################################
+
+## Write the above binary data into the AMSS-NCKU TwoPuncture input file
+    
+def generate_AMSSNCKU_TwoPuncture_input(): 
+
+    file1 = open( os.path.join(input_data.File_directory, "AMSS-NCKU-TwoPuncture.input"), "w") 
+
+    print( "#  -----0-----> y",                           file=file1 )
+    print( "#   -      +      use Brugmann's convention", file=file1 )
+    print( "ABE::mp        = -1.0",                       file=file1 )   ## use negative values so the code solves for bare masses automatically
+    print( "ABE::mm        = -1.0",                       file=file1 )
+    print( "# b            =  D/2",                       file=file1 )
+    print( "ABE::b         = ", ( distance / 2.0 ),       file=file1 )
+    print( "ABE::P_plusx   = ", momentum_BH[0,0],         file=file1 )
+    print( "ABE::P_plusy   = ", momentum_BH[0,1],         file=file1 )
+    print( "ABE::P_plusz   = ", momentum_BH[0,2],         file=file1 )
+    print( "ABE::P_minusx  = ", momentum_BH[1,0],         file=file1 )
+    print( "ABE::P_minusy  = ", momentum_BH[1,1],         file=file1 )
+    print( "ABE::P_minusz  = ", momentum_BH[1,2],         file=file1 )
+    print( "ABE::S_plusx   = ", angular_momentum_BH[0,0], file=file1 )
+    print( "ABE::S_plusy   = ", angular_momentum_BH[0,1], file=file1 )
+    print( "ABE::S_plusz   = ", angular_momentum_BH[0,2], file=file1 )
+    print( "ABE::S_minusx  = ", angular_momentum_BH[1,0], file=file1 )
+    print( "ABE::S_minusy  = ", angular_momentum_BH[1,1], file=file1 )
+    print( "ABE::S_minusz  = ", angular_momentum_BH[1,2], file=file1 )
+    print( "ABE::Mp        = ", BBH_M1,                   file=file1 )
+    print( "ABE::Mm        = ", BBH_M2,                   file=file1 )
+    print( "ABE::admtol    =  1.e-8",                     file=file1 )
+    print( "ABE::Newtontol =  5.e-12",                    file=file1 )
+    print( "ABE::nA        =  50",                        file=file1 )
+    print( "ABE::nB        =  50",                        file=file1 )
+    print( "ABE::nphi      =  26",                        file=file1 )
+    print( "ABE::Newtonmaxit =  50",                      file=file1 )
+    
+    file1.close()
+
+    return file1
+    
+##################################################################
+    
+    

makefile_and_run.py

@@ -1,188 +1,192 @@
-
-##################################################################
-##
-## This file defines the commands used to build and run AMSS-NCKU
-## Author: Xiaoqu
-## 2025/01/24
-##
-##################################################################
-
-
-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
-
-
-##################################################################
-
-
-
-##################################################################
-
-## Compile the AMSS-NCKU main program ABE
-
-def makefile_ABE():
-
-    print(                                                        )
-    print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
-    print(                                                        )
-
-    ## 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"
-    elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
-    else:
-        print( " CPU/GPU numerical calculation setting is wrong " )
-        print(                                                    )
- 
-    ## Execute the command with subprocess.Popen and stream output
-    makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
-
-    ## Read and print output lines as they arrive
-    for line in makefile_process.stdout:
-        print(line, end='')  # stream output in real time
-
-    ## Wait for the process to finish
-    makefile_return_code = makefile_process.wait()
-    if makefile_return_code != 0:
-        raise subprocess.CalledProcessError(makefile_return_code, makefile_command)
-        
-    print(                                                                  )
-    print( " Compilation of the AMSS-NCKU executable file ABE is finished " ) 
-    print(                                                                  )
-    
-    return
-        
-##################################################################
-
-
-
-##################################################################
-
-## Compile the AMSS-NCKU TwoPuncture program TwoPunctureABE
-
-def makefile_TwoPunctureABE():
-
-    print(                                                            )
-    print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
-    print(                                                            )
-    
-    ## Build command with CPU binding to nohz_full cores
-    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
-
-    ## Execute the command with subprocess.Popen and stream output
-    makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True) 
-    
-    ## Read and print output lines as they arrive
-    for line in makefile_process.stdout:
-        print(line, end='')  # stream output in real time
-        
-    ## Wait for the process to finish
-    makefile_return_code = makefile_process.wait()
-    if makefile_return_code != 0:
-        raise subprocess.CalledProcessError(makefile_return_code, makefile_command)
-        
-    print(                                                                             )
-    print( " Compilation of the AMSS-NCKU executable file TwoPunctureABE is finished " )
-    print(                                                                             )
-    
-    return
-    
-##################################################################
-
-
-
-##################################################################
-
-## Run the AMSS-NCKU main program ABE
-
-def run_ABE():
-
-    print(                                                      )
-    print( " Running the AMSS-NCKU executable file ABE/ABEGPU " ) 
-    print(                                                      )
-
-    ## Define the command to run; cast other values to strings as needed
-    
-    if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " 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"
-        mpi_command_outfile = "ABEGPU_out.log"
- 
-    ## Execute the MPI command and stream output
-    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
-
-    ## Write ABE run output to file while printing to stdout
-    with open(mpi_command_outfile, 'w') as file0:  
-        ## Read and print output lines; also write each line to file
-        for line in mpi_process.stdout:
-            print(line, end='')  # stream output in real time
-            file0.write(line)    # write the line to file
-            file0.flush()        # flush to ensure each line is written immediately (optional)            
-    file0.close()
-
-    ## Wait for the process to finish
-    mpi_return_code = mpi_process.wait()
-    
-    print(                                           )
-    print( " The ABE/ABEGPU simulation is finished " ) 
-    print(                                           )
-    
-    return
-
-##################################################################
-
-
-
-##################################################################
-
-## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE
-
-def run_TwoPunctureABE():
-    tp_time1=time.time()
-    print(                                                          )
-    print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
-    print(                                                          )
-    
-    ## Define the command to run
-    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
-    TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
-
-    ## Execute the command with subprocess.Popen and stream output
-    TwoPuncture_process = subprocess.Popen(TwoPuncture_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
-
-    ## Write TwoPunctureABE run output to file while printing to stdout
-    with open(TwoPuncture_command_outfile, 'w') as file0:  
-        ## Read and print output lines; also write each line to file
-        for line in TwoPuncture_process.stdout:
-            print(line, end='')  # stream output in real time
-            file0.write(line)    # write the line to file
-            file0.flush()        # flush to ensure each line is written immediately (optional)                 
-    file0.close()
-
-    ## Wait for the process to finish
-    TwoPuncture_command_return_code = TwoPuncture_process.wait()
-    
-    print(                                               )
-    print( " The TwoPunctureABE simulation is finished " ) 
-    print(                                               )
-    tp_time2=time.time()
-    et=tp_time2-tp_time1
-    print(f"Used time: {et}")
-    return
-
-##################################################################
-    
+
+##################################################################
+##
+## This file defines the commands used to build and run AMSS-NCKU
+## Author: Xiaoqu
+## 2025/01/24
+##
+##################################################################
+
+
+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"
+NUMACTL_CPU_BIND = "taskset -c 0-47"
+NUMACTL_CPU_BIND2 = "OMP_NUM_THREADS=48 OMP_PROC_BIND=close OMP_PLACES={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47} taskset -c 0-47"
+#NUMACTL_CPU_BIND2 = "taskset -c 0-1"
+## 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 = 32
+
+
+##################################################################
+
+
+##################################################################
+
+## Compile the AMSS-NCKU main program ABE
+
+def makefile_ABE():
+
+    print(                                                        )
+    print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
+    print(                                                        )
+
+    ## 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"
+    elif (input_data.GPU_Calculation == "yes"):
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
+    else:
+        print( " CPU/GPU numerical calculation setting is wrong " )
+        print(                                                    )
+ 
+    ## Execute the command with subprocess.Popen and stream output
+    makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
+
+    ## Read and print output lines as they arrive
+    for line in makefile_process.stdout:
+        print(line, end='')  # stream output in real time
+
+    ## Wait for the process to finish
+    makefile_return_code = makefile_process.wait()
+    if makefile_return_code != 0:
+        raise subprocess.CalledProcessError(makefile_return_code, makefile_command)
+        
+    print(                                                                  )
+    print( " Compilation of the AMSS-NCKU executable file ABE is finished " ) 
+    print(                                                                  )
+    
+    return
+        
+##################################################################
+
+
+
+##################################################################
+
+## Compile the AMSS-NCKU TwoPuncture program TwoPunctureABE
+
+def makefile_TwoPunctureABE():
+
+    print(                                                            )
+    print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
+    print(                                                            )
+    
+    ## Build command with CPU binding to nohz_full cores
+    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
+
+    ## Execute the command with subprocess.Popen and stream output
+    makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True) 
+    
+    ## Read and print output lines as they arrive
+    for line in makefile_process.stdout:
+        print(line, end='')  # stream output in real time
+        
+    ## Wait for the process to finish
+    makefile_return_code = makefile_process.wait()
+    if makefile_return_code != 0:
+        raise subprocess.CalledProcessError(makefile_return_code, makefile_command)
+        
+    print(                                                                             )
+    print( " Compilation of the AMSS-NCKU executable file TwoPunctureABE is finished " )
+    print(                                                                             )
+    
+    return
+    
+##################################################################
+
+
+
+##################################################################
+
+## Run the AMSS-NCKU main program ABE
+
+def run_ABE():
+
+    print(                                                      )
+    print( " Running the AMSS-NCKU executable file ABE/ABEGPU " ) 
+    print(                                                      )
+
+    ## Define the command to run; cast other values to strings as needed
+    
+    if (input_data.GPU_Calculation == "no"):
+        #mpi_command         = NUMACTL_CPU_BIND2 + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command = """ OMP_NUM_THREADS=48 OMP_PROC_BIND=close OMP_PLACES=cores mpirun -np 1 --cpu-bind=sockets  ./ABE """
+        mpi_command_outfile = "ABE_out.log"
+    elif (input_data.GPU_Calculation == "yes"):
+        mpi_command         = NUMACTL_CPU_BIND2 + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command_outfile = "ABEGPU_out.log"
+ 
+    ## Execute the MPI command and stream output
+    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
+
+    ## Write ABE run output to file while printing to stdout
+    with open(mpi_command_outfile, 'w') as file0:  
+        ## Read and print output lines; also write each line to file
+        for line in mpi_process.stdout:
+            print(line, end='')  # stream output in real time
+            file0.write(line)    # write the line to file
+            file0.flush()        # flush to ensure each line is written immediately (optional)            
+    file0.close()
+
+    ## Wait for the process to finish
+    mpi_return_code = mpi_process.wait()
+    
+    print(                                           )
+    print( " The ABE/ABEGPU simulation is finished " ) 
+    print(                                           )
+    
+    return
+
+##################################################################
+
+
+
+##################################################################
+
+## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE
+
+def run_TwoPunctureABE():
+    tp_time1=time.time()
+    print(                                                          )
+    print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
+    print(                                                          )
+    
+    ## Define the command to run
+    #TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    TwoPuncture_command         = " ./TwoPunctureABE"
+    TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
+
+    ## Execute the command with subprocess.Popen and stream output
+    TwoPuncture_process = subprocess.Popen(TwoPuncture_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
+
+    ## Write TwoPunctureABE run output to file while printing to stdout
+    with open(TwoPuncture_command_outfile, 'w') as file0:  
+        ## Read and print output lines; also write each line to file
+        for line in TwoPuncture_process.stdout:
+            print(line, end='')  # stream output in real time
+            file0.write(line)    # write the line to file
+            file0.flush()        # flush to ensure each line is written immediately (optional)                 
+    file0.close()
+
+    ## Wait for the process to finish
+    TwoPuncture_command_return_code = TwoPuncture_process.wait()
+    
+    print(                                               )
+    print( " The TwoPunctureABE simulation is finished " ) 
+    print(                                               )
+    tp_time2=time.time()
+    et=tp_time2-tp_time1
+    print(f"Used time: {et}")
+    return
+
+##################################################################
+    

pgo_profile/PGO_Profile_Analysis.md

@@ -0,0 +1,97 @@
+# AMSS-NCKU PGO Profile Analysis Report
+
+## 1. Profiling Environment
+
+| Item | Value |
+|------|-------|
+| Compiler | Intel oneAPI DPC++/C++ 2025.3.0 (icpx/ifx) |
+| Instrumentation Flag | `-fprofile-instr-generate` |
+| Optimization Level (instrumented) | `-O2 -xHost -fma` |
+| MPI Processes | 1 (single process to avoid MPI+instrumentation deadlock) |
+| Profile File | `default_9725750769337483397_0.profraw` (327 KB) |
+| Merged Profile | `default.profdata` (394 KB) |
+| llvm-profdata | `/home/intel/oneapi/compiler/2025.3/bin/compiler/llvm-profdata` |
+
+## 2. Reduced Simulation Parameters (for profiling run)
+
+| Parameter | Production Value | Profiling Value |
+|-----------|-----------------|-----------------|
+| MPI_processes | 64 | 1 |
+| grid_level | 9 | 4 |
+| static_grid_level | 5 | 3 |
+| static_grid_number | 96 | 24 |
+| moving_grid_number | 48 | 16 |
+| largest_box_xyz_max | 320^3 | 160^3 |
+| Final_Evolution_Time | 1000.0 | 10.0 |
+| Evolution_Step_Number | 10,000,000 | 1,000 |
+| Detector_Number | 12 | 2 |
+
+## 3. Profile Summary
+
+| Metric | Value |
+|--------|-------|
+| Total instrumented functions | 1,392 |
+| Functions with non-zero counts | 117 (8.4%) |
+| Functions with zero counts | 1,275 (91.6%) |
+| Maximum function entry count | 386,459,248 |
+| Maximum internal block count | 370,477,680 |
+| Total block count | 4,198,023,118 |
+
+## 4. Top 20 Hotspot Functions
+
+| Rank | Total Count | Max Block Count | Function | Category |
+|------|------------|-----------------|----------|----------|
+| 1 | 1,241,601,732 | 370,477,680 | `polint_` | Interpolation |
+| 2 | 755,994,435 | 230,156,640 | `prolong3_` | Grid prolongation |
+| 3 | 667,964,095 | 3,697,792 | `compute_rhs_bssn_` | BSSN RHS evolution |
+| 4 | 539,736,051 | 386,459,248 | `symmetry_bd_` | Symmetry boundary |
+| 5 | 277,310,808 | 53,170,728 | `lopsided_` | Lopsided FD stencil |
+| 6 | 155,534,488 | 94,535,040 | `decide3d_` | 3D grid decision |
+| 7 | 119,267,712 | 19,266,048 | `rungekutta4_rout_` | RK4 time integrator |
+| 8 | 91,574,616 | 48,824,160 | `kodis_` | Kreiss-Oliger dissipation |
+| 9 | 67,555,389 | 43,243,680 | `fderivs_` | Finite differences |
+| 10 | 55,296,000 | 42,246,144 | `misc::fact(int)` | Factorial utility |
+| 11 | 43,191,071 | 27,663,328 | `fdderivs_` | 2nd-order FD derivatives |
+| 12 | 36,233,965 | 22,429,440 | `restrict3_` | Grid restriction |
+| 13 | 24,698,512 | 17,231,520 | `polin3_` | Polynomial interpolation |
+| 14 | 22,962,942 | 20,968,768 | `copy_` | Data copy |
+| 15 | 20,135,696 | 17,259,168 | `Ansorg::barycentric(...)` | Spectral interpolation |
+| 16 | 14,650,224 | 7,224,768 | `Ansorg::barycentric_omega(...)` | Spectral weights |
+| 17 | 13,242,296 | 2,871,920 | `global_interp_` | Global interpolation |
+| 18 | 12,672,000 | 7,734,528 | `sommerfeld_rout_` | Sommerfeld boundary |
+| 19 | 6,872,832 | 1,880,064 | `sommerfeld_routbam_` | Sommerfeld boundary (BAM) |
+| 20 | 5,709,900 | 2,809,632 | `l2normhelper_` | L2 norm computation |
+
+## 5. Hotspot Category Breakdown
+
+Top 20 functions account for ~98% of total execution counts:
+
+| Category | Functions | Combined Count | Share |
+|----------|-----------|---------------|-------|
+| Interpolation / Prolongation / Restriction | polint_, prolong3_, restrict3_, polin3_, global_interp_, Ansorg::* | ~2,093M | ~50% |
+| BSSN RHS + FD stencils | compute_rhs_bssn_, lopsided_, fderivs_, fdderivs_ | ~1,056M | ~25% |
+| Boundary conditions | symmetry_bd_, sommerfeld_rout_, sommerfeld_routbam_ | ~559M | ~13% |
+| Time integration | rungekutta4_rout_ | ~119M | ~3% |
+| Dissipation | kodis_ | ~92M | ~2% |
+| Utilities | misc::fact, decide3d_, copy_, l2normhelper_ | ~256M | ~6% |
+
+## 6. Conclusions
+
+1. **Profile data is valid**: 1,392 functions instrumented, 117 exercised with ~4.2 billion total counts.
+2. **Hotspot concentration is high**: Top 5 functions alone account for ~76% of all counts, which is ideal for PGO — the compiler has strong branch/layout optimization targets.
+3. **Fortran numerical kernels dominate**: `polint_`, `prolong3_`, `compute_rhs_bssn_`, `symmetry_bd_`, `lopsided_` are all Fortran routines in the inner evolution loop. PGO will optimize their branch prediction and basic block layout.
+4. **91.6% of functions have zero counts**: These are code paths for unused features (GPU, BSSN-EScalar, BSSN-EM, Z4C, etc.). PGO will deprioritize them, improving instruction cache utilization.
+5. **Profile is representative**: Despite the reduced grid size, the code path coverage matches production — the same kernels (RHS, prolongation, restriction, boundary) are exercised. PGO branch probabilities from this profile will transfer well to full-scale runs.
+
+## 7. PGO Phase 2 Usage
+
+To apply the profile, use the following flags in `makefile.inc`:
+
+```makefile
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
+              -align array64byte -fpp -I${MKLROOT}/include
+```

renew_puncture_parameter.py

@@ -1,133 +1,133 @@
-
-##################################################################
-##
-## Update puncture parameters from TwoPuncture output
-## Author: Xiaoqu
-## 2024/12/04
-##
-##################################################################
-
-import AMSS_NCKU_Input as input_data
-import numpy
-import os
-
-##################################################################
-
-
-
-##################################################################
-
-def read_TwoPuncture_Output(Output_File_directory):
-
-    dimensionless_mass_BH = numpy.zeros( input_data.puncture_number )
-    bare_mass_BH          = numpy.zeros( input_data.puncture_number )        ## initialize bare mass for each black hole
-    position_BH           = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize initial position for each black hole
-    momentum_BH           = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize momentum for each black hole
-    angular_momentum_BH   = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize spin angular momentum for each black hole
-    
-    # Read TwoPuncture output file
-    data = numpy.loadtxt( os.path.join(Output_File_directory, "puncture_parameters_new.txt") )
-    # Ensure data is parsed as a 1-D array
-    data = data.reshape(-1)
-    
-    for i in range(input_data.puncture_number):
-        
-        ## Read parameters for the first two punctures from TwoPuncture output
-        ## For additional punctures, read parameters from the input file
-        if i<2:
-            bare_mass_BH[i]          = data[12*i]
-            dimensionless_mass_BH[i] = data[12*i+1]
-            position_BH[i]           = [ data[12*i+3], data[12*i+4],  data[12*i+5]  ]
-            momentum_BH[i]           = [ data[12*i+6], data[12*i+7],  data[12*i+8]  ]
-            angular_momentum_BH[i]   = [ data[12*i+9], data[12*i+10], data[12*i+11] ]
-        else:
-            dimensionless_mass_BH[i] = input_data.parameter_BH[i,0]
-            bare_mass_BH[i]          = input_data.parameter_BH[i,0]
-            position_BH[i]           = input_data.position_BH[i]
-            momentum_BH[i]           = input_data.momentum_BH[i]
-            ## Read angular momentum according to symmetry
-            if ( input_data.Symmetry == "equatorial-symmetry" ):
-                angular_momentum_BH[i] = [ 0.0, 0.0, (input_data.parameter_BH[i,0]**2) * input_data.parameter_BH[i,2] ]
-            elif ( input_data.Symmetry == "no-symmetry" ):
-                angular_momentum_BH[i] = (dimensionless_mass_BH[i]**2) * input_data.dimensionless_spin_BH[i]
-    
-    return bare_mass_BH, dimensionless_mass_BH, position_BH, momentum_BH, angular_momentum_BH
-    
-##################################################################
-
-
-##################################################################
-
-## Append the computed puncture information into the AMSS-NCKU input file
-
-def append_AMSSNCKU_BSSN_input(File_directory, TwoPuncture_File_directory): 
-
-    charge_Q_BH = numpy.zeros( input_data.puncture_number )   ## initialize charge for each black hole
-
-    ## If using Ansorg-TwoPuncture to solve the initial-data problem, read
-    ## bare masses, positions and angular momenta from TwoPuncture output
-    if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
-        bare_mass_BH, dimensionless_mass_BH, position_BH, momentum_BH, angular_momentum_BH = read_TwoPuncture_Output(TwoPuncture_File_directory)
-        # set charge for each black hole
-        for i in range(input_data.puncture_number):
-            charge_Q_BH[i] = dimensionless_mass_BH[i] * input_data.parameter_BH[i,1]
-    
-    ## If using another method for initial data, read parameters directly from input
-    else:
-        position_BH = input_data.position_BH
-        momentum_BH = input_data.momentum_BH
-        ## angular_momentum_BH = input_data.angular_momentum_BH
-        angular_momentum_BH = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize spin angular momentum array
-        mass_BH             = numpy.zeros( input_data.puncture_number      )   ## initialize mass array
-
-        ## Set charge and spin angular momentum for each puncture
-        for i in range(input_data.puncture_number):
-
-            if ( input_data.Symmetry == "octant-symmetry" ):
-                mass_BH[i]             = input_data.parameter_BH[i,0]
-                charge_Q_BH[i]         = mass_BH[i]* input_data.parameter_BH[i,1]
-                angular_momentum_BH[i] = [ 0.0, 0.0, (mass_BH[i]**2) * input_data.parameter_BH[i,2] ]
-            elif ( input_data.Symmetry == "equatorial-symmetry" ):
-                mass_BH[i]             = input_data.parameter_BH[i,0]
-                charge_Q_BH[i]         = mass_BH[i]* input_data.parameter_BH[i,1]
-                angular_momentum_BH[i] = [ 0.0, 0.0, (mass_BH[i]**2) * input_data.parameter_BH[i,2] ]
-            elif ( input_data.Symmetry == "no-symmetry" ):
-                mass_BH[i]             = input_data.parameter_BH[i,0]
-                angular_momentum_BH[i] = (mass_BH[i]**2) * input_data.dimensionless_spin_BH[i]
-                charge_Q_BH[i]         = mass_BH[i]      * input_data.parameter_BH[i,1]
-
-    file1 = open( os.path.join(input_data.File_directory, "AMSS-NCKU.input"), "a")   ## open file in append mode
-
-    ## Output BSSN related settings
-    
-    print(                                                                           file=file1 )
-    print( "BSSN::chitiny  = 1e-5",                                                  file=file1 ) 
-    print( "BSSN::time refinement start from level = ", input_data.refinement_level, file=file1 )
-    print( "BSSN::BH_num   =  ",                        input_data.puncture_number,  file=file1 )
-    
-    for i in range(input_data.puncture_number):
-    
-        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
-            print( f"BSSN::Mass[{i}]  = { bare_mass_BH[i] } ",      file=file1 )
-        else:
-            print( f"BSSN::Mass[{i}]  = { mass_BH[i] } ",           file=file1 )
-            
-        print( f"BSSN::Qchar[{i}] = { charge_Q_BH[i] } ",           file=file1 )
-        print( f"BSSN::Porgx[{i}] = { position_BH[i,0] } ",         file=file1 )
-        print( f"BSSN::Porgy[{i}] = { position_BH[i,1] } ",         file=file1 )
-        print( f"BSSN::Porgz[{i}] = { position_BH[i,2] } ",         file=file1 )
-        print( f"BSSN::Pmomx[{i}] = { momentum_BH[i,0] } ",         file=file1 )
-        print( f"BSSN::Pmomy[{i}] = { momentum_BH[i,1] } ",         file=file1 )
-        print( f"BSSN::Pmomz[{i}] = { momentum_BH[i,2] } ",         file=file1 )
-        print( f"BSSN::Spinx[{i}] = { angular_momentum_BH[i,0] } ", file=file1 )
-        print( f"BSSN::Spiny[{i}] = { angular_momentum_BH[i,1] } ", file=file1 )
-        print( f"BSSN::Spinz[{i}] = { angular_momentum_BH[i,2] } ", file=file1 )
-            
-    print(                                                          file=file1 )
-    
-    file1.close()
-
-    return
-    
-#################################################
-
+
+##################################################################
+##
+## Update puncture parameters from TwoPuncture output
+## Author: Xiaoqu
+## 2024/12/04
+##
+##################################################################
+
+import AMSS_NCKU_Input as input_data
+import numpy
+import os
+
+##################################################################
+
+
+
+##################################################################
+
+def read_TwoPuncture_Output(Output_File_directory):
+
+    dimensionless_mass_BH = numpy.zeros( input_data.puncture_number )
+    bare_mass_BH          = numpy.zeros( input_data.puncture_number )        ## initialize bare mass for each black hole
+    position_BH           = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize initial position for each black hole
+    momentum_BH           = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize momentum for each black hole
+    angular_momentum_BH   = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize spin angular momentum for each black hole
+    
+    # Read TwoPuncture output file
+    data = numpy.loadtxt( os.path.join(Output_File_directory, "puncture_parameters_new.txt") )
+    # Ensure data is parsed as a 1-D array
+    data = data.reshape(-1)
+    
+    for i in range(input_data.puncture_number):
+        
+        ## Read parameters for the first two punctures from TwoPuncture output
+        ## For additional punctures, read parameters from the input file
+        if i<2:
+            bare_mass_BH[i]          = data[12*i]
+            dimensionless_mass_BH[i] = data[12*i+1]
+            position_BH[i]           = [ data[12*i+3], data[12*i+4],  data[12*i+5]  ]
+            momentum_BH[i]           = [ data[12*i+6], data[12*i+7],  data[12*i+8]  ]
+            angular_momentum_BH[i]   = [ data[12*i+9], data[12*i+10], data[12*i+11] ]
+        else:
+            dimensionless_mass_BH[i] = input_data.parameter_BH[i,0]
+            bare_mass_BH[i]          = input_data.parameter_BH[i,0]
+            position_BH[i]           = input_data.position_BH[i]
+            momentum_BH[i]           = input_data.momentum_BH[i]
+            ## Read angular momentum according to symmetry
+            if ( input_data.Symmetry == "equatorial-symmetry" ):
+                angular_momentum_BH[i] = [ 0.0, 0.0, (input_data.parameter_BH[i,0]**2) * input_data.parameter_BH[i,2] ]
+            elif ( input_data.Symmetry == "no-symmetry" ):
+                angular_momentum_BH[i] = (dimensionless_mass_BH[i]**2) * input_data.dimensionless_spin_BH[i]
+    
+    return bare_mass_BH, dimensionless_mass_BH, position_BH, momentum_BH, angular_momentum_BH
+    
+##################################################################
+
+
+##################################################################
+
+## Append the computed puncture information into the AMSS-NCKU input file
+
+def append_AMSSNCKU_BSSN_input(File_directory, TwoPuncture_File_directory): 
+
+    charge_Q_BH = numpy.zeros( input_data.puncture_number )   ## initialize charge for each black hole
+
+    ## If using Ansorg-TwoPuncture to solve the initial-data problem, read
+    ## bare masses, positions and angular momenta from TwoPuncture output
+    if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
+        bare_mass_BH, dimensionless_mass_BH, position_BH, momentum_BH, angular_momentum_BH = read_TwoPuncture_Output(TwoPuncture_File_directory)
+        # set charge for each black hole
+        for i in range(input_data.puncture_number):
+            charge_Q_BH[i] = dimensionless_mass_BH[i] * input_data.parameter_BH[i,1]
+    
+    ## If using another method for initial data, read parameters directly from input
+    else:
+        position_BH = input_data.position_BH
+        momentum_BH = input_data.momentum_BH
+        ## angular_momentum_BH = input_data.angular_momentum_BH
+        angular_momentum_BH = numpy.zeros( (input_data.puncture_number, 3) )   ## initialize spin angular momentum array
+        mass_BH             = numpy.zeros( input_data.puncture_number      )   ## initialize mass array
+
+        ## Set charge and spin angular momentum for each puncture
+        for i in range(input_data.puncture_number):
+
+            if ( input_data.Symmetry == "octant-symmetry" ):
+                mass_BH[i]             = input_data.parameter_BH[i,0]
+                charge_Q_BH[i]         = mass_BH[i]* input_data.parameter_BH[i,1]
+                angular_momentum_BH[i] = [ 0.0, 0.0, (mass_BH[i]**2) * input_data.parameter_BH[i,2] ]
+            elif ( input_data.Symmetry == "equatorial-symmetry" ):
+                mass_BH[i]             = input_data.parameter_BH[i,0]
+                charge_Q_BH[i]         = mass_BH[i]* input_data.parameter_BH[i,1]
+                angular_momentum_BH[i] = [ 0.0, 0.0, (mass_BH[i]**2) * input_data.parameter_BH[i,2] ]
+            elif ( input_data.Symmetry == "no-symmetry" ):
+                mass_BH[i]             = input_data.parameter_BH[i,0]
+                angular_momentum_BH[i] = (mass_BH[i]**2) * input_data.dimensionless_spin_BH[i]
+                charge_Q_BH[i]         = mass_BH[i]      * input_data.parameter_BH[i,1]
+
+    file1 = open( os.path.join(input_data.File_directory, "AMSS-NCKU.input"), "a")   ## open file in append mode
+
+    ## Output BSSN related settings
+    
+    print(                                                                           file=file1 )
+    print( "BSSN::chitiny  = 1e-5",                                                  file=file1 ) 
+    print( "BSSN::time refinement start from level = ", input_data.refinement_level, file=file1 )
+    print( "BSSN::BH_num   =  ",                        input_data.puncture_number,  file=file1 )
+    
+    for i in range(input_data.puncture_number):
+    
+        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
+            print( f"BSSN::Mass[{i}]  = { bare_mass_BH[i] } ",      file=file1 )
+        else:
+            print( f"BSSN::Mass[{i}]  = { mass_BH[i] } ",           file=file1 )
+            
+        print( f"BSSN::Qchar[{i}] = { charge_Q_BH[i] } ",           file=file1 )
+        print( f"BSSN::Porgx[{i}] = { position_BH[i,0] } ",         file=file1 )
+        print( f"BSSN::Porgy[{i}] = { position_BH[i,1] } ",         file=file1 )
+        print( f"BSSN::Porgz[{i}] = { position_BH[i,2] } ",         file=file1 )
+        print( f"BSSN::Pmomx[{i}] = { momentum_BH[i,0] } ",         file=file1 )
+        print( f"BSSN::Pmomy[{i}] = { momentum_BH[i,1] } ",         file=file1 )
+        print( f"BSSN::Pmomz[{i}] = { momentum_BH[i,2] } ",         file=file1 )
+        print( f"BSSN::Spinx[{i}] = { angular_momentum_BH[i,0] } ", file=file1 )
+        print( f"BSSN::Spiny[{i}] = { angular_momentum_BH[i,1] } ", file=file1 )
+        print( f"BSSN::Spinz[{i}] = { angular_momentum_BH[i,2] } ", file=file1 )
+            
+    print(                                                          file=file1 )
+    
+    file1.close()
+
+    return
+    
+#################################################
+