迁移C算子的循环融合和临时量消除

bssn_rhs(fortran): migrate C kernel loop-fusion optimizations
关闭C重写算子
2026-03-03 15:57:10 +08:00 · 2026-03-03 15:41:26 +08:00 · 2026-03-03 15:28:09 +08:00 · 2026-03-03 15:22:01 +08:00 · 2026-03-03 15:15:06 +08:00 · 2026-03-03 12:36:19 +08:00
46 changed files with 8280 additions and 2508 deletions
--- a/AMSS_NCKU_ABEtest.py
+++ b/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()
 ##################################################################
--- a/AMSS_NCKU_Program.py
+++ b/AMSS_NCKU_Program.py
@@ -8,6 +8,14 @@
 ##
 ##################################################################
 ## Guard against re-execution by multiprocessing child processes.
 ## Without this, using 'spawn' or 'forkserver' context would cause every
 ## worker to re-run the entire script, spawning exponentially more
 ## workers (fork bomb).
 if __name__ != '__main__':
    import sys as _sys
    _sys.exit(0)
 ##################################################################
@@ -262,6 +270,12 @@ if not os.path.exists( ABE_file ):
 ## Copy the executable ABE (or ABEGPU) into the run directory
 shutil.copy2(ABE_file, output_directory)
 ## Copy interp load balance profile if present (for optimize pass)
 interp_lb_profile = os.path.join(AMSS_NCKU_source_copy, "interp_lb_profile.bin")
 if os.path.exists(interp_lb_profile):
    shutil.copy2(interp_lb_profile, output_directory)
    print( " Copied interp_lb_profile.bin to run directory " )
 ###########################
 ## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
@@ -424,26 +438,31 @@ print(
 import plot_xiaoqu
 import plot_GW_strain_amplitude_xiaoqu
 from parallel_plot_helper import run_plot_tasks_parallel
 plot_tasks = []
 ## Plot black hole trajectory
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
 ## Plot black hole separation vs. time
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
 ## Plot gravitational waveforms (psi4 and strain amplitude)
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
-    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
 ## Plot ADM mass evolution
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
 ## Plot Hamiltonian constraint violation over time
 for i in range(input_data.grid_level):
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
 run_plot_tasks_parallel(plot_tasks)
 ## Plot stored binary data
 plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
--- a/AMSS_NCKU_Verify_ASC26.py
+++ b/AMSS_NCKU_Verify_ASC26.py
@@ -1,9 +1,13 @@
 #!/usr/bin/env python3
 """
-AMSS-NCKU GW150914 Simulation Regression Test Script
+AMSS-NCKU GW150914 Simulation Regression Test Script (Comprehensive Version)
 Verification Requirements:
-1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
+1. RMS errors < 1% for:
   - 3D Vector Total RMS
   - X Component RMS
   - Y Component RMS
   - Z Component RMS
 2. ADM constraint violation < 2 (Grid Level 0)
 RMS Calculation Method:
@@ -57,79 +61,62 @@ def load_constraint_data(filepath):
                data.append([float(x) for x in parts[:8]])
    return np.array(data)
-
+def calculate_all_rms_errors(bh_data_ref, bh_data_target):
 def calculate_rms_error(bh_data_ref, bh_data_target):
    """
-    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
+    Calculate 3D Vector RMS and component-wise RMS (X, Y, Z) independently.
-
+    Uses r = sqrt(x^2 + y^2) as the denominator for all error normalizations.
-    This function computes the RMS error independently for BH1 and BH2 trajectories,
+    Returns the maximum error between BH1 and BH2 for each category.
    then returns the maximum of the two as the final RMS error metric.
    For each black hole, the RMS is calculated as:
        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
    where:
        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
    Args:
        bh_data_ref: Reference (baseline) trajectory data
        bh_data_target: Target (optimized) trajectory data
    Returns:
        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
        error: Error message if any
    """
    # Align data: truncate to the length of the shorter dataset
    M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
    if M < 10:
        return None, "Insufficient data points for comparison"
-    # Extract XY coordinates for both black holes
+    results = {}
    x1_ref = bh_data_ref['x1'][:M]
    y1_ref = bh_data_ref['y1'][:M]
    x2_ref = bh_data_ref['x2'][:M]
    y2_ref = bh_data_ref['y2'][:M]
-    x1_new = bh_data_target['x1'][:M]
+    for bh in ['1', '2']:
-    y1_new = bh_data_target['y1'][:M]
+        x_r, y_r, z_r = bh_data_ref[f'x{bh}'][:M], bh_data_ref[f'y{bh}'][:M], bh_data_ref[f'z{bh}'][:M]
-    x2_new = bh_data_target['x2'][:M]
+        x_n, y_n, z_n = bh_data_target[f'x{bh}'][:M], bh_data_target[f'y{bh}'][:M], bh_data_target[f'z{bh}'][:M]
    y2_new = bh_data_target['y2'][:M]
-    # Calculate RMS for BH1
+        # 核心修改：根据组委会的邮件指示，分母统一使用 r = sqrt(x^2 + y^2)
-    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
+        r_ref = np.sqrt(x_r**2 + y_r**2)
-    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
+        r_new = np.sqrt(x_n**2 + y_n**2)
-    r1_new = np.sqrt(x1_new**2 + y1_new**2)
+        denom_max = np.maximum(r_ref, r_new)
    r1_max = np.maximum(r1_ref, r1_new)
-    # Calculate RMS for BH2
+        valid = denom_max > 1e-15
-    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
+        if np.sum(valid) < 10:
-    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
+            results[f'BH{bh}'] = { '3D_Vector': 0.0, 'X_Component': 0.0, 'Y_Component': 0.0, 'Z_Component': 0.0 }
-    r2_new = np.sqrt(x2_new**2 + y2_new**2)
+            continue
    r2_max = np.maximum(r2_ref, r2_new)
-    # Avoid division by zero for BH1
+        def calc_rms(delta):
-    valid_mask1 = r1_max > 1e-15
+            # 将对应分量的偏差除以统一的轨道半径分母 denom_max
-    if np.sum(valid_mask1) < 10:
+            return np.sqrt(np.mean((delta[valid] / denom_max[valid])**2)) * 100
        return None, "Insufficient valid data points for BH1"
-    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
+        # 1. Total 3D Vector RMS
-    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+        delta_vec = np.sqrt((x_r - x_n)**2 + (y_r - y_n)**2 + (z_r - z_n)**2)
        rms_3d = calc_rms(delta_vec)
-    # Avoid division by zero for BH2
+        # 2. Component-wise RMS (分离计算各轴，但共用半径分母)
-    valid_mask2 = r2_max > 1e-15
+        rms_x = calc_rms(np.abs(x_r - x_n))
-    if np.sum(valid_mask2) < 10:
+        rms_y = calc_rms(np.abs(y_r - y_n))
-        return None, "Insufficient valid data points for BH2"
+        rms_z = calc_rms(np.abs(z_r - z_n))
-    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
+        results[f'BH{bh}'] = {
-    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+            '3D_Vector': rms_3d,
            'X_Component': rms_x,
            'Y_Component': rms_y,
            'Z_Component': rms_z
        }
-    # Final RMS is the maximum of BH1 and BH2
+    # 获取 BH1 和 BH2 中的最大误差
-    rms_final = max(rms_bh1, rms_bh2)
+    max_rms = {
-
+        '3D_Vector': max(results['BH1']['3D_Vector'], results['BH2']['3D_Vector']),
-    return rms_final, None
+        'X_Component': max(results['BH1']['X_Component'], results['BH2']['X_Component']),
        'Y_Component': max(results['BH1']['Y_Component'], results['BH2']['Y_Component']),
        'Z_Component': max(results['BH1']['Z_Component'], results['BH2']['Z_Component'])
    }
    return max_rms, None
 def analyze_constraint_violation(constraint_data, n_levels=9):
    """
@@ -155,34 +142,32 @@ def analyze_constraint_violation(constraint_data, n_levels=9):
 def print_header():
    """Print report header"""
    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "   AMSS-NCKU GW150914 Simulation Regression Test Report" + Color.RESET)
+    print(Color.BOLD + "   AMSS-NCKU GW150914 Comprehensive Regression Test" + Color.RESET)
    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-
+def print_rms_results(rms_dict, error, threshold=1.0):
-def print_rms_results(rms_rel, error, threshold=1.0):
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Maximums of BH1 & BH2){Color.RESET}")
-    """Print RMS error results"""
+    print("-" * 65)
    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
    print("-" * 45)
    if error:
        print(f"   {Color.RED}Error: {error}{Color.RESET}")
        return False
-    passed = rms_rel < threshold
+    all_passed = True
    print(f"   Requirement: < {threshold}%\n")
-    print(f"   RMS relative error: {rms_rel:.4f}%")
+    for key, val in rms_dict.items():
-    print(f"   Requirement:        < {threshold}%")
+        passed = val < threshold
-    print(f"   Status:             {get_status_text(passed)}")
+        all_passed = all_passed and passed
-
+        status = get_status_text(passed)
-    return passed
+        print(f"   {key:15}: {val:8.4f}%   |   Status: {status}")
    return all_passed
 def print_constraint_results(results, threshold=2.0):
    """Print constraint violation results"""
    print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
-    print("-" * 45)
+    print("-" * 65)
    names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
    for i, name in enumerate(names):
@@ -200,7 +185,6 @@ def print_constraint_results(results, threshold=2.0):
 def print_summary(rms_passed, constraint_passed):
    """Print summary"""
    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
    print(Color.BOLD + "Verification Summary" + Color.RESET)
    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
@@ -210,7 +194,7 @@ def print_summary(rms_passed, constraint_passed):
    res_rms = get_status_text(rms_passed)
    res_con = get_status_text(constraint_passed)
-    print(f"   [1] RMS trajectory check:         {res_rms}")
+    print(f"   [1] Comprehensive RMS check:      {res_rms}")
    print(f"   [2] ADM constraint check:         {res_con}")
    final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
@@ -219,61 +203,48 @@ def print_summary(rms_passed, constraint_passed):
    return all_passed
 def main():
    # Determine target (optimized) output directory
    if len(sys.argv) > 1:
        target_dir = sys.argv[1]
    else:
        script_dir = os.path.dirname(os.path.abspath(__file__))
        target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
    # Determine reference (baseline) directory
    script_dir = os.path.dirname(os.path.abspath(__file__))
    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
    # Data file paths
    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
    # Check if files exist
    if not os.path.exists(bh_file_ref):
        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
        sys.exit(1)
    if not os.path.exists(bh_file_target):
        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Target trajectory file not found: {bh_file_target}")
        sys.exit(1)
    if not os.path.exists(constraint_file):
        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
        sys.exit(1)
    # Print header
    print_header()
    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
    # Load data
    bh_data_ref = load_bh_trajectory(bh_file_ref)
    bh_data_target = load_bh_trajectory(bh_file_target)
    constraint_data = load_constraint_data(constraint_file)
-    # Calculate RMS error
+    # Output modified RMS results
-    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
+    rms_dict, error = calculate_all_rms_errors(bh_data_ref, bh_data_target)
-    rms_passed = print_rms_results(rms_rel, error)
+    rms_passed = print_rms_results(rms_dict, error)
-    # Analyze constraint violation
+    # Output constraint results
    constraint_results = analyze_constraint_violation(constraint_data)
    constraint_passed = print_constraint_results(constraint_results)
    # Print summary
    all_passed = print_summary(rms_passed, constraint_passed)
    # Return exit code
    sys.exit(0 if all_passed else 1)
 if __name__ == "__main__":
    main()
--- a/AMSS_NCKU_source/MPatch.C
+++ b/AMSS_NCKU_source/MPatch.C
@@ -7,12 +7,178 @@
 #include <string>
 #include <cmath>
 #include <new>
 #include <vector>
 using namespace std;
 #include "misc.h"
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
 #ifdef INTERP_LB_PROFILE
 #include "interp_lb_profile.h"
 #endif
 namespace
 {
 struct InterpBlockView
 {
  Block *bp;
  double llb[dim];
  double uub[dim];
 };
 struct BlockBinIndex
 {
  int bins[dim];
  double lo[dim];
  double inv[dim];
  vector<InterpBlockView> views;
  vector<vector<int>> bin_to_blocks;
  bool valid;
  BlockBinIndex() : valid(false)
  {
    for (int i = 0; i < dim; i++)
    {
      bins[i] = 1;
      lo[i] = 0.0;
      inv[i] = 0.0;
    }
  }
 };
 inline int clamp_int(int v, int lo, int hi)
 {
  return (v < lo) ? lo : ((v > hi) ? hi : v);
 }
 inline int coord_to_bin(double x, double lo, double inv, int nb)
 {
  if (nb <= 1 || inv <= 0.0)
    return 0;
  int b = int(floor((x - lo) * inv));
  return clamp_int(b, 0, nb - 1);
 }
 inline int bin_loc(const BlockBinIndex &index, int b0, int b1, int b2)
 {
  return b0 + index.bins[0] * (b1 + index.bins[1] * b2);
 }
 inline bool point_in_block_view(const InterpBlockView &view, const double *pox, const double *DH)
 {
  for (int i = 0; i < dim; i++)
  {
    if (pox[i] - view.llb[i] < -DH[i] / 2 || pox[i] - view.uub[i] > DH[i] / 2)
      return false;
  }
  return true;
 }
 void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
 {
  index = BlockBinIndex();
  MyList<Block> *Bp = patch->blb;
  while (Bp)
  {
    Block *BP = Bp->data;
    InterpBlockView view;
    view.bp = BP;
    for (int i = 0; i < dim; i++)
    {
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
 #endif
      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
 #else
 #ifdef Cell
      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
 #else
 #error Not define Vertex nor Cell
 #endif
 #endif
    }
    index.views.push_back(view);
    if (Bp == patch->ble)
      break;
    Bp = Bp->next;
  }
  const int nblocks = int(index.views.size());
  if (nblocks <= 0)
    return;
  int bins_1d = int(ceil(pow(double(nblocks), 1.0 / 3.0)));
  bins_1d = clamp_int(bins_1d, 1, 32);
  for (int i = 0; i < dim; i++)
  {
    index.bins[i] = bins_1d;
    index.lo[i] = patch->bbox[i] + patch->lli[i] * DH[i];
    const double hi = patch->bbox[dim + i] - patch->uui[i] * DH[i];
    if (hi > index.lo[i] && bins_1d > 1)
      index.inv[i] = bins_1d / (hi - index.lo[i]);
    else
      index.inv[i] = 0.0;
  }
  index.bin_to_blocks.resize(index.bins[0] * index.bins[1] * index.bins[2]);
  for (int bi = 0; bi < nblocks; bi++)
  {
    const InterpBlockView &view = index.views[bi];
    int bmin[dim], bmax[dim];
    for (int d = 0; d < dim; d++)
    {
      const double low = view.llb[d] - DH[d] / 2;
      const double up = view.uub[d] + DH[d] / 2;
      bmin[d] = coord_to_bin(low, index.lo[d], index.inv[d], index.bins[d]);
      bmax[d] = coord_to_bin(up, index.lo[d], index.inv[d], index.bins[d]);
      if (bmax[d] < bmin[d])
      {
        int t = bmin[d];
        bmin[d] = bmax[d];
        bmax[d] = t;
      }
    }
    for (int bz = bmin[2]; bz <= bmax[2]; bz++)
      for (int by = bmin[1]; by <= bmax[1]; by++)
        for (int bx = bmin[0]; bx <= bmax[0]; bx++)
          index.bin_to_blocks[bin_loc(index, bx, by, bz)].push_back(bi);
  }
  index.valid = true;
 }
 int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
 {
  if (!index.valid)
    return -1;
  const int bx = coord_to_bin(pox[0], index.lo[0], index.inv[0], index.bins[0]);
  const int by = coord_to_bin(pox[1], index.lo[1], index.inv[1], index.bins[1]);
  const int bz = coord_to_bin(pox[2], index.lo[2], index.inv[2], index.bins[2]);
  const vector<int> &cand = index.bin_to_blocks[bin_loc(index, bx, by, bz)];
  for (size_t ci = 0; ci < cand.size(); ci++)
  {
    const int bi = cand[ci];
    if (point_in_block_view(index.views[bi], pox, DH))
      return bi;
  }
  // Fallback to full scan for numerical edge cases around bin boundaries.
  for (size_t bi = 0; bi < index.views.size(); bi++)
    if (point_in_block_view(index.views[bi], pox, DH))
      return int(bi);
  return -1;
 }
 } // namespace
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -341,8 +507,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
                          double *Shellf, int Symmetry)
 {
  // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
-  int myrank;
+  int myrank, nprocs;
  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
  int ordn = 2 * ghost_width;
  MyList<var> *varl;
@@ -354,24 +521,20 @@ void Patch::Interp_Points(MyList<var> *VarList,
    varl = varl->next;
  }
-  double *shellf;
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
  shellf = new 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
+  // owner_rank[j] records which MPI rank owns point j
-  int *weight;
+  // All ranks traverse the same block list so they all agree on ownership
-  weight = new int[NN];
+  int *owner_rank;
-  memset(weight, 0, sizeof(int) * NN);
+  owner_rank = new int[NN];
-
+  for (int j = 0; j < NN; j++)
-  double *DH, *llb, *uub;
+    owner_rank[j] = -1;
  DH = new double[dim];
  double DH[dim];
  for (int i = 0; i < dim; i++)
  {
    DH[i] = getdX(i);
-  }
+  BlockBinIndex block_index;
-  llb = new double[dim];
+  build_block_bin_index(this, DH, block_index);
  uub = new double[dim];
  for (int j = 0; j < NN; j++) // run along points
  {
@@ -394,165 +557,350 @@ void Patch::Interp_Points(MyList<var> *VarList,
      }
    }
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
    while (notfind && Bp) // run along Blocks
    {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
      for (int i = 0; i < dim; i++)
      {
-// NOTE: our dividing structure is (exclude ghost)
+        //---> interpolation
-// -1 0
+        varl = VarList;
-//       1  2
+        int k = 0;
-// so (0,1) does not belong to any part for vertex structure
+        while (varl) // run along variables
 // here we put (0,0.5) to left part and (0.5,1) to right part
 // BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
 #endif
        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
 #else
 #ifdef Cell
        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
 #else
 #error Not define Vertex nor Cell
 #endif
 #endif
        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
        {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
          varl = varl->next;
          k++;
        }
      }
      if (flag)
      {
        notfind = false;
        if (myrank == BP->rank)
        {
          //---> interpolation
          varl = VarList;
          int k = 0;
          while (varl) // run along variables
          {
            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
            varl = varl->next;
            k++;
          }
          weight[j] = 1;
        }
      }
      if (Bp == ble)
        break;
      Bp = Bp->next;
    }
  }
-  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  // Replace MPI_Allreduce with per-owner MPI_Bcast:
-  int *Weight;
+  // Group consecutive points by owner rank and broadcast each group.
-  Weight = new int[NN];
+  // Since each point's data is non-zero only on the owner rank,
-  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  // Bcast from owner is equivalent to Allreduce(MPI_SUM) but much cheaper.
  //  misc::tillherecheck("print me");
  for (int i = 0; i < NN; i++)
  {
-    if (Weight[i] > 1)
+    int j = 0;
    while (j < NN)
    {
-      if (myrank == 0)
+      int cur_owner = owner_rank[j];
-        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
+      if (cur_owner < 0)
-      for (int j = 0; j < num_var; j++)
+      {
-        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+        if (myrank == 0)
        {
          cout << "ERROR: Patch::Interp_Points fails to find point (";
          for (int d = 0; d < dim; d++)
          {
            cout << XX[d][j];
            if (d < dim - 1)
              cout << ",";
            else
              cout << ")";
          }
          cout << " on Patch (";
          for (int d = 0; d < dim; d++)
          {
            cout << bbox[d] << "+" << lli[d] * DH[d];
            if (d < dim - 1)
              cout << ",";
            else
              cout << ")--";
          }
          cout << "(";
          for (int d = 0; d < dim; d++)
          {
            cout << bbox[dim + d] << "-" << uui[d] * DH[d];
            if (d < dim - 1)
              cout << ",";
            else
              cout << ")" << endl;
          }
          MPI_Abort(MPI_COMM_WORLD, 1);
        }
        j++;
        continue;
      }
      // Find contiguous run of points with the same owner
      int jstart = j;
      while (j < NN && owner_rank[j] == cur_owner)
        j++;
      int count = (j - jstart) * num_var;
      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner, MPI_COMM_WORLD);
    }
-    else if (Weight[i] == 0 && myrank == 0)
+  }
  delete[] owner_rank;
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                          int NN, double **XX,
                          double *Shellf, int Symmetry,
                          int Nmin_consumer, int Nmax_consumer)
 {
  // Targeted point-to-point overload: each owner sends each point only to
  // the one rank that needs it for integration (consumer), reducing
  // communication volume by ~nprocs times compared to the Bcast version.
 #ifdef INTERP_LB_PROFILE
  double t_interp_start = MPI_Wtime();
 #endif
  int myrank, nprocs;
  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
  int ordn = 2 * ghost_width;
  MyList<var> *varl;
  int num_var = 0;
  varl = VarList;
  while (varl)
  {
    num_var++;
    varl = varl->next;
  }
  memset(Shellf, 0, sizeof(double) * NN * num_var);
  // owner_rank[j] records which MPI rank owns point j
  int *owner_rank;
  owner_rank = new int[NN];
  for (int j = 0; j < NN; j++)
    owner_rank[j] = -1;
  double DH[dim];
  for (int i = 0; i < dim; i++)
    DH[i] = getdX(i);
  BlockBinIndex block_index;
  build_block_bin_index(this, DH, block_index);
  // --- Interpolation phase (identical to original) ---
  for (int j = 0; j < NN; j++)
  {
    double pox[dim];
    for (int i = 0; i < dim; i++)
    {
      pox[i] = XX[i][j];
      if (myrank == 0 && (XX[i][j] < bbox[i] + lli[i] * DH[i] || XX[i][j] > bbox[dim + i] - uui[i] * DH[i]))
      {
        cout << "Patch::Interp_Points: point (";
        for (int k = 0; k < dim; k++)
        {
          cout << XX[k][j];
          if (k < dim - 1)
            cout << ",";
          else
            cout << ") is out of current Patch." << endl;
        }
        MPI_Abort(MPI_COMM_WORLD, 1);
      }
    }
    const int block_i = find_block_index_for_point(block_index, pox, DH);
    if (block_i >= 0)
    {
      Block *BP = block_index.views[block_i].bp;
      owner_rank[j] = BP->rank;
      if (myrank == BP->rank)
      {
        varl = VarList;
        int k = 0;
        while (varl)
        {
          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
          varl = varl->next;
          k++;
        }
      }
    }
  }
 #ifdef INTERP_LB_PROFILE
  double t_interp_end = MPI_Wtime();
  double t_interp_local = t_interp_end - t_interp_start;
 #endif
  // --- Error check for unfound points ---
  for (int j = 0; j < NN; j++)
  {
    if (owner_rank[j] < 0 && myrank == 0)
    {
      cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
      {
-        cout << XX[j][i];
+        cout << XX[d][j];
-        if (j < dim - 1)
+        if (d < dim - 1)
          cout << ",";
        else
          cout << ")";
      }
      cout << " on Patch (";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
      {
-        cout << bbox[j] << "+" << lli[j] * getdX(j);
+        cout << bbox[d] << "+" << lli[d] * DH[d];
-        if (j < dim - 1)
+        if (d < dim - 1)
          cout << ",";
        else
          cout << ")--";
      }
      cout << "(";
-      for (int j = 0; j < dim; j++)
+      for (int d = 0; d < dim; d++)
      {
-        cout << bbox[dim + j] << "-" << uui[j] * getdX(j);
+        cout << bbox[dim + d] << "-" << uui[d] * DH[d];
-        if (j < dim - 1)
+        if (d < dim - 1)
          cout << ",";
        else
          cout << ")" << endl;
      }
 #if 0
       checkBlock();
 #else
      cout << "splited domains:" << endl;
      {
        MyList<Block> *Bp = blb;
        while (Bp)
        {
          Block *BP = Bp->data;
          for (int i = 0; i < dim; i++)
          {
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
 #endif
            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
 #else
 #ifdef Cell
            llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
            uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
 #else
 #error Not define Vertex nor Cell
 #endif
 #endif
          }
          cout << "(";
          for (int j = 0; j < dim; j++)
          {
            cout << llb[j] << ":" << uub[j];
            if (j < dim - 1)
              cout << ",";
            else
              cout << ")" << endl;
          }
          if (Bp == ble)
            break;
          Bp = Bp->next;
        }
      }
 #endif
      MPI_Abort(MPI_COMM_WORLD, 1);
    }
  }
-  delete[] shellf;
+  // --- Targeted point-to-point communication phase ---
-  delete[] weight;
+  // Compute consumer_rank[j] using the same deterministic formula as surface_integral
-  delete[] Weight;
+  int *consumer_rank = new int[NN];
-  delete[] DH;
+  {
-  delete[] llb;
+    int mp = NN / nprocs;
-  delete[] uub;
+    int Lp = NN - nprocs * mp;
    for (int j = 0; j < NN; j++)
    {
      if (j < Lp * (mp + 1))
        consumer_rank[j] = j / (mp + 1);
      else
        consumer_rank[j] = Lp + (j - Lp * (mp + 1)) / mp;
    }
  }
  // Count sends and recvs per rank
  int *send_count = new int[nprocs];
  int *recv_count = new int[nprocs];
  memset(send_count, 0, sizeof(int) * nprocs);
  memset(recv_count, 0, sizeof(int) * nprocs);
  for (int j = 0; j < NN; j++)
  {
    int own = owner_rank[j];
    int con = consumer_rank[j];
    if (own == con)
      continue; // local — no communication needed
    if (own == myrank)
      send_count[con]++;
    if (con == myrank)
      recv_count[own]++;
  }
  // Build send buffers: for each destination rank, pack (index, data) pairs
  // Each entry: 1 int (point index j) + num_var doubles
  int total_send = 0, total_recv = 0;
  int *send_offset = new int[nprocs];
  int *recv_offset = new int[nprocs];
  for (int r = 0; r < nprocs; r++)
  {
    send_offset[r] = total_send;
    total_send += send_count[r];
    recv_offset[r] = total_recv;
    total_recv += recv_count[r];
  }
  // Pack send buffers: each message contains (j, data[0..num_var-1]) per point
  int stride = 1 + num_var; // 1 double for index + num_var doubles for data
  double *sendbuf = new double[total_send * stride];
  double *recvbuf = new double[total_recv * stride];
  // Temporary counters for packing
  int *pack_pos = new int[nprocs];
  memset(pack_pos, 0, sizeof(int) * nprocs);
  for (int j = 0; j < NN; j++)
  {
    int own = owner_rank[j];
    int con = consumer_rank[j];
    if (own != myrank || con == myrank)
      continue;
    int pos = (send_offset[con] + pack_pos[con]) * stride;
    sendbuf[pos] = (double)j; // point index
    for (int v = 0; v < num_var; v++)
      sendbuf[pos + 1 + v] = Shellf[j * num_var + v];
    pack_pos[con]++;
  }
  // Post non-blocking recvs and sends
  int n_req = 0;
  for (int r = 0; r < nprocs; r++)
  {
    if (recv_count[r] > 0) n_req++;
    if (send_count[r] > 0) n_req++;
  }
  MPI_Request *reqs = new MPI_Request[n_req];
  int req_idx = 0;
  for (int r = 0; r < nprocs; r++)
  {
    if (recv_count[r] > 0)
    {
      MPI_Irecv(recvbuf + recv_offset[r] * stride,
                recv_count[r] * stride, MPI_DOUBLE,
                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
    }
  }
  for (int r = 0; r < nprocs; r++)
  {
    if (send_count[r] > 0)
    {
      MPI_Isend(sendbuf + send_offset[r] * stride,
                send_count[r] * stride, MPI_DOUBLE,
                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
    }
  }
  if (n_req > 0)
    MPI_Waitall(n_req, reqs, MPI_STATUSES_IGNORE);
  // Unpack recv buffers into Shellf
  for (int i = 0; i < total_recv; i++)
  {
    int pos = i * stride;
    int j = (int)recvbuf[pos];
    for (int v = 0; v < num_var; v++)
      Shellf[j * num_var + v] = recvbuf[pos + 1 + v];
  }
  delete[] reqs;
  delete[] sendbuf;
  delete[] recvbuf;
  delete[] pack_pos;
  delete[] send_offset;
  delete[] recv_offset;
  delete[] send_count;
  delete[] recv_count;
  delete[] consumer_rank;
  delete[] owner_rank;
 #ifdef INTERP_LB_PROFILE
  {
    static bool profile_written = false;
    if (!profile_written) {
      double *all_times = nullptr;
      if (myrank == 0) all_times = new double[nprocs];
      MPI_Gather(&t_interp_local, 1, MPI_DOUBLE,
                 all_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
      if (myrank == 0) {
        int heavy[64];
        int nh = InterpLBProfile::identify_heavy_ranks(
            all_times, nprocs, 2.5, heavy, 64);
        InterpLBProfile::write_profile(
            "interp_lb_profile.bin", nprocs,
            all_times, heavy, nh, 2.5);
        printf("[InterpLB] Profile written: %d heavy ranks\n", nh);
        for (int i = 0; i < nh; i++)
          printf("  Heavy rank %d: %.6f s\n", heavy[i], all_times[heavy[i]]);
        delete[] all_times;
      }
      profile_written = true;
    }
  }
 #endif
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                          int NN, double **XX,
@@ -573,24 +921,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
    varl = varl->next;
  }
-  double *shellf;
+  memset(Shellf, 0, sizeof(double) * NN * num_var);
  shellf = new 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
+  // owner_rank[j] stores the global rank that owns point j
-  int *weight;
+  int *owner_rank;
-  weight = new int[NN];
+  owner_rank = new int[NN];
-  memset(weight, 0, sizeof(int) * NN);
+  for (int j = 0; j < NN; j++)
    owner_rank[j] = -1;
-  double *DH, *llb, *uub;
+  // Build global-to-local rank translation for Comm_here
-  DH = new double[dim];
+  MPI_Group world_group, local_group;
  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
  MPI_Comm_group(Comm_here, &local_group);
  double DH[dim];
  for (int i = 0; i < dim; i++)
  {
    DH[i] = getdX(i);
-  }
+  BlockBinIndex block_index;
-  llb = new double[dim];
+  build_block_bin_index(this, DH, block_index);
  uub = new double[dim];
  for (int j = 0; j < NN; j++) // run along points
  {
@@ -613,159 +961,56 @@ void Patch::Interp_Points(MyList<var> *VarList,
      }
    }
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
    while (notfind && Bp) // run along Blocks
    {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
      for (int i = 0; i < dim; i++)
      {
-// NOTE: our dividing structure is (exclude ghost)
+        //---> interpolation
-// -1 0
+        varl = VarList;
-//       1  2
+        int k = 0;
-// so (0,1) does not belong to any part for vertex structure
+        while (varl) // run along variables
 // here we put (0,0.5) to left part and (0.5,1) to right part
 // BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
 #endif
        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
 #else
 #ifdef Cell
        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
 #else
 #error Not define Vertex nor Cell
 #endif
 #endif
        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
        {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
          varl = varl->next;
          k++;
        }
      }
      if (flag)
      {
        notfind = false;
        if (myrank == BP->rank)
        {
          //---> interpolation
          varl = VarList;
          int k = 0;
          while (varl) // run along variables
          {
            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
            varl = varl->next;
            k++;
          }
          weight[j] = 1;
        }
      }
      if (Bp == ble)
        break;
      Bp = Bp->next;
    }
  }
-  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, Comm_here);
+  // Collect unique global owner ranks and translate to local ranks in Comm_here
-  int *Weight;
+  // Then broadcast each owner's points via MPI_Bcast on Comm_here
  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++)
  {
-    if (Weight[i] > 1)
+    int j = 0;
    while (j < NN)
    {
-      if (lmyrank == 0)
+      int cur_owner_global = owner_rank[j];
-        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
+      if (cur_owner_global < 0)
-      for (int j = 0; j < num_var; j++)
+      {
-        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+        // 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;
+  MPI_Group_free(&world_group);
-  delete[] weight;
+  MPI_Group_free(&local_group);
-  delete[] Weight;
+  delete[] owner_rank;
  delete[] DH;
  delete[] llb;
  delete[] uub;
 }
 void Patch::checkBlock()
 {
--- a/AMSS_NCKU_source/MPatch.h
+++ b/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);
--- a/AMSS_NCKU_source/Parallel.C
+++ b/AMSS_NCKU_source/Parallel.C
--- a/AMSS_NCKU_source/Parallel.h
+++ b/AMSS_NCKU_source/Parallel.h
@@ -32,6 +32,16 @@ namespace Parallel
  int partition2(int *nxy, int split_size, int *min_width, int cpusize, int *shape); // special for 2 diemnsions
  int partition3(int *nxyz, int split_size, int *min_width, int cpusize, int *shape);
  MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0); // produce corresponding Blocks
  MyList<Block> *distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0);
  Block* splitHotspotBlock(MyList<Block>* &BlL, int _dim,
                           int ib0_orig, int ib3_orig,
                           int jb1_orig, int jb4_orig,
                           int kb2_orig, int kb5_orig,
                           Patch* PP, int r_left, int r_right,
                           int ingfsi, int fngfsi, bool periodic,
                           Block* &split_first_block, Block* &split_last_block);
  Block* createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
                           int block_id, int ingfsi, int fngfsi, int lev);
  void KillBlocks(MyList<Patch> *PatchLIST);
  void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
@@ -81,6 +91,49 @@ namespace Parallel
                   int Symmetry);
  void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
  void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
  struct SyncCache {
    bool valid;
    int cpusize;
    MyList<gridseg> **combined_src;
    MyList<gridseg> **combined_dst;
    int *send_lengths;
    int *recv_lengths;
    double **send_bufs;
    double **recv_bufs;
    int *send_buf_caps;
    int *recv_buf_caps;
    MPI_Request *reqs;
    MPI_Status *stats;
    int max_reqs;
    bool lengths_valid;
    int *tc_req_node;
    int *tc_req_is_recv;
    int *tc_completed;
    SyncCache();
    void invalidate();
    void destroy();
  };
  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
                       MyList<var> *VarList1, MyList<var> *VarList2,
                       int Symmetry, SyncCache &cache);
  struct AsyncSyncState {
    int req_no;
    bool active;
    int *req_node;
    int *req_is_recv;
    int pending_recv;
    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
  };
  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
                  SyncCache &cache, AsyncSyncState &state);
  void Sync_finish(SyncCache &cache, AsyncSyncState &state,
                   MyList<var> *VarList, int Symmetry);
  void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                   int Symmetry);
@@ -93,6 +146,15 @@ namespace Parallel
  void OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                      MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                      int Symmetry);
  void Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                       MyList<var> *VarList1, MyList<var> *VarList2,
                       int Symmetry, SyncCache &cache);
  void OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                          MyList<var> *VarList1, MyList<var> *VarList2,
                          int Symmetry, SyncCache &cache);
  void OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                             MyList<var> *VarList1, MyList<var> *VarList2,
                             int Symmetry, SyncCache &cache);
  void Prolong(Patch *Patc, Patch *Patf,
               MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
               int Symmetry);
--- a/AMSS_NCKU_source/bssn_class.C
+++ b/AMSS_NCKU_source/bssn_class.C
--- a/AMSS_NCKU_source/bssn_class.h
+++ b/AMSS_NCKU_source/bssn_class.h
@@ -126,6 +126,13 @@ 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]
       Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
       Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong
       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
       monitor *ConVMonitor;
       surface_integral *Waveshell;
--- a/AMSS_NCKU_source/bssn_rhs.f90
+++ b/AMSS_NCKU_source/bssn_rhs.f90
--- a/AMSS_NCKU_source/bssn_rhs_c.C
+++ b/AMSS_NCKU_source/bssn_rhs_c.C
--- a/AMSS_NCKU_source/cgh.C
+++ b/AMSS_NCKU_source/cgh.C
@@ -130,7 +130,11 @@ void cgh::compose_cgh(int nprocs)
  for (int lev = 0; lev < levels; lev++)
  {
    checkPatchList(PatL[lev], false);
 #ifdef INTERP_LB_OPTIMIZE
    Parallel::distribute_optimize(PatL[lev], nprocs, ingfs, fngfs, false);
 #else
    Parallel::distribute(PatL[lev], nprocs, ingfs, fngfs, false);
 #endif
 #if (RPB == 1)
    // we need distributed box of PatL[lev] and PatL[lev-1]
    if (lev > 0)
@@ -1301,13 +1305,13 @@ bool cgh::Interp_One_Point(MyList<var> *VarList,
 }
-void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+bool cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                          MyList<var> *OldList, MyList<var> *StateList,
                          MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                          monitor *ErrorMonitor)
 {
  if (lev < movls)
-    return;
+    return false;
 #if (0)
  // #if (PSTR == 1 || PSTR == 2)
@@ -1396,7 +1400,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
      for (bhi = 0; bhi < BH_num; bhi++)
        delete[] tmpPorg[bhi];
      delete[] tmpPorg;
-      return;
+      return false;
    }
    // x direction
    rr = (Porg0[bhi][0] - handle[lev][grd][0]) / dX;
@@ -1500,6 +1504,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
  for (int bhi = 0; bhi < BH_num; bhi++)
    delete[] tmpPorg[bhi];
  delete[] tmpPorg;
  return tot_flag;
 }
--- a/AMSS_NCKU_source/cgh.h
+++ b/AMSS_NCKU_source/cgh.h
@@ -74,7 +74,7 @@ public:
                               MyList<var> *OldList, MyList<var> *StateList,
                               MyList<var> *FutureList, MyList<var> *tmList,
                               int Symmetry, bool BB);
-   void Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+   bool Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                        MyList<var> *OldList, MyList<var> *StateList,
                        MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                        monitor *ErrorMonitor);
--- a/AMSS_NCKU_source/diff_new.f90
+++ b/AMSS_NCKU_source/diff_new.f90
@@ -69,10 +69,12 @@
  fy = ZEO
  fz = ZEO
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
 !DIR$ UNROLL PARTIAL(4)
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
-! x direction   
+! x direction
        if(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
@@ -371,6 +373,8 @@
  fxz = ZEO
  fyz = ZEO
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
 !DIR$ UNROLL PARTIAL(4)
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
@@ -1000,7 +1004,86 @@
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 #if 0  
 ! x direction   
        if(i+2 <= imax .and. i-2 >= imin)then
 !
 !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
 !  fx(i) = ---------------------------------------------
 !                             12 dx
      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
    elseif(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
 !  fx(i) = --------------------------------
 !                     2 dx
      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
 ! set imax and imin 0
    endif
 ! y direction   
        if(j+2 <= jmax .and. j-2 >= jmin)then
      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
    elseif(j+1 <= jmax .and. j-1 >= jmin)then
     fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
 ! set jmax and jmin 0
    endif
 ! z direction   
        if(k+2 <= kmax .and. k-2 >= kmin)then
      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
    elseif(k+1 <= kmax .and. k-1 >= kmin)then
      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
 ! set kmax and kmin 0
    endif
 #elif 0
 ! x direction   
        if(i+2 <= imax .and. i-2 >= imin)then
 !
 !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
 !  fx(i) = ---------------------------------------------
 !                             12 dx
      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
    elseif(i+3 <= imax .and. i-1 >= imin)then
      fx(i,j,k)=d12dx*(-3.d0*fh(i-1,j,k)-1.d1*fh(i,j,k)+1.8d1*fh(i+1,j,k)-6.d0*fh(i+2,j,k)+fh(i+3,j,k))
    elseif(i+1 <= imax .and. i-3 >= imin)then
      fx(i,j,k)=d12dx*( 3.d0*fh(i+1,j,k)+1.d1*fh(i,j,k)-1.8d1*fh(i-1,j,k)+6.d0*fh(i-2,j,k)-fh(i-3,j,k))
 ! set imax and imin 0
    endif
 ! y direction   
        if(j+2 <= jmax .and. j-2 >= jmin)then
      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
    elseif(j+3 <= jmax .and. j-1 >= jmin)then
      fy(i,j,k)=d12dy*(-3.d0*fh(i,j-1,k)-1.d1*fh(i,j,k)+1.8d1*fh(i,j+1,k)-6.d0*fh(i,j+2,k)+fh(i,j+3,k))
    elseif(j+1 <= jmax .and. j-3 >= jmin)then
      fy(i,j,k)=d12dy*( 3.d0*fh(i,j+1,k)+1.d1*fh(i,j,k)-1.8d1*fh(i,j-1,k)+6.d0*fh(i,j-2,k)-fh(i,j-3,k))
 ! set jmax and jmin 0
    endif
 ! z direction   
        if(k+2 <= kmax .and. k-2 >= kmin)then
      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
    elseif(k+3 <= kmax .and. k-1 >= kmin)then
      fz(i,j,k)=d12dz*(-3.d0*fh(i,j,k-1)-1.d1*fh(i,j,k)+1.8d1*fh(i,j,k+1)-6.d0*fh(i,j,k+2)+fh(i,j,k+3))
    elseif(k+1 <= kmax .and. k-3 >= kmin)then
      fz(i,j,k)=d12dz*( 3.d0*fh(i,j,k+1)+1.d1*fh(i,j,k)-1.8d1*fh(i,j,k-1)+6.d0*fh(i,j,k-2)-fh(i,j,k-3))
 ! set kmax and kmin 0
    endif
 #else
 ! for bam comparison
   if(i+2 <= imax .and. i-2 >= imin .and. &
      j+2 <= jmax .and. j-2 >= jmin .and. &
@@ -1015,7 +1098,7 @@
      fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
   endif
-
+#endif
  enddo
  enddo
  enddo
@@ -1325,7 +1408,85 @@
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 #if 0  
 !~~~~~~ fxx
        if(i+2 <= imax .and. i-2 >= imin)then
 !
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 
   fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
                       -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
   elseif(i+1 <= imax .and. i-1 >= imin)then
 !
 !               f(i-1) - 2 f(i) + f(i+1)
 !  fxx(i) = --------------------------------
 !                         dx^2 
   fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
                      +fh(i+1,j,k)              )
   endif
 !~~~~~~ fyy
        if(j+2 <= jmax .and. j-2 >= jmin)then
   fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
                       -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
   elseif(j+1 <= jmax .and. j-1 >= jmin)then
   fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
                      +fh(i,j+1,k)              )
   endif
 !~~~~~~ fzz
        if(k+2 <= kmax .and. k-2 >= kmin)then
   fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
                       -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
   elseif(k+1 <= kmax .and. k-1 >= kmin)then
   fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
                      +fh(i,j,k+1)              )
   endif
 !~~~~~~ fxy
       if(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
 !
 !                 ( f(i-2,j-2) - 8 f(i-1,j-2) + 8 f(i+1,j-2) - f(i+2,j-2) )
 !             - 8 ( f(i-2,j-1) - 8 f(i-1,j-1) + 8 f(i+1,j-1) - f(i+2,j-1) )
 !             + 8 ( f(i-2,j+1) - 8 f(i-1,j+1) + 8 f(i+1,j+1) - f(i+2,j+1) )
 !             -   ( f(i-2,j+2) - 8 f(i-1,j+2) + 8 f(i+1,j+2) - f(i+2,j+2) )
 !  fxy(i,j) = ----------------------------------------------------------------
 !                                  144 dx dy
   fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
                       -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
                       +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
                       -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
   elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
 !                 f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1) 
 !  fxy(i,j) = -----------------------------------------------------------
 !                                      4 dx dy
   fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
   endif
 !~~~~~~ fxz
       if(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
   fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
                       -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
                       +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
                       -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
   elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
   fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
   endif
 !~~~~~~ fyz
       if(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
   fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
                       -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
                       +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
                       -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
   elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
   fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
   endif 
 #else
 ! for bam comparison
   if(i+2 <= imax .and. i-2 >= imin .and. &
      j+2 <= jmax .and. j-2 >= jmin .and. &
@@ -1361,7 +1522,7 @@
   fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
   fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
   endif
-
+#endif
   enddo
   enddo
   enddo
--- a/AMSS_NCKU_source/diff_newwb.f90
+++ b/AMSS_NCKU_source/diff_newwb.f90
@@ -33,7 +33,7 @@
  real*8 :: dX,dY,dZ
  real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
  real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
  real*8 :: d2dx,d2dy,d2dz
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -137,7 +137,7 @@
  real*8 :: dX
  real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
  real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
  real*8 :: d2dx
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1512,8 +1512,9 @@
  real*8 :: dX,dY,dZ
  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
  real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
+  integer :: i_core_min,i_core_max,j_core_min,j_core_max,k_core_min,k_core_max
  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
  real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0,  F45=4.5d1
@@ -1560,17 +1561,55 @@
  fxx = ZEO
  fyy = ZEO
-  fzz = ZEO
+  fzz = ZEO
-  fxy = ZEO
+  fxy = ZEO
-  fxz = ZEO
+  fxz = ZEO
-  fyz = ZEO
+  fyz = ZEO
-
+
-  do k=1,ex(3)
+  i_core_min = max(1, imin+2)
-  do j=1,ex(2)
+  i_core_max = min(ex(1), imax-2)
-  do i=1,ex(1)
+  j_core_min = max(1, jmin+2)
-!~~~~~~ fxx
+  j_core_max = min(ex(2), jmax-2)
-        if(i+2 <= imax .and. i-2 >= imin)then
+  k_core_min = max(1, kmin+2)
-!
+  k_core_max = min(ex(3), kmax-2)
  if(i_core_min <= i_core_max .and. j_core_min <= j_core_max .and. k_core_min <= k_core_max)then
   do k=k_core_min,k_core_max
   do j=j_core_min,j_core_max
   do i=i_core_min,i_core_max
 ! interior points always use 4th-order stencils without branch checks
      fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
                          -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
      fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
                          -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
      fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
                          -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
      fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
                          -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
                          +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
                          -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
      fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
                          -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
                          +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
                          -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
      fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
                          -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
                          +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
                          -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
   enddo
   enddo
   enddo
  endif
  do k=1,ex(3)
  do j=1,ex(2)
  do i=1,ex(1)
      if(i>=i_core_min .and. i<=i_core_max .and. &
         j>=j_core_min .and. j<=j_core_max .and. &
         k>=k_core_min .and. k<=k_core_max) cycle
 !~~~~~~ fxx
        if(i+2 <= imax .and. i-2 >= imin)then
 !
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 
--- a/AMSS_NCKU_source/fdderivs_c.C
+++ b/AMSS_NCKU_source/fdderivs_c.C
@@ -0,0 +1,186 @@
 #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;
    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 double *fh = NULL;
    static 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);
    /* 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);
    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
    for (size_t p = 0; p < all; ++p) {
        fxx[p] = ZEO; fxy[p] = ZEO; fxz[p] = ZEO;
        fyy[p] = ZEO; fyz[p] = ZEO; fzz[p] = ZEO;
    }
    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
    // only compute when x/y/z all satisfy the same-order stencil at this point.
    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 ((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[p] = Fdxdy * (
                           (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)])
                        - F8 * (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)])
                        + F8 * (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)])
                           - (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)])
                    );
                    fxz[p] = Fdxdz * (
                           (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)])
                        - F8 * (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)])
                        + F8 * (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)])
                           - (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)])
                    );
                    fyz[p] = Fdydz * (
                           (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)])
                        - F8 * (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)])
                        + F8 * (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)])
                           - (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)])
                    );
                } 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)]
                    );
                }
            }
        }
    }
    // free(fh);
 }
--- a/AMSS_NCKU_source/fderivs_c.C
+++ b/AMSS_NCKU_source/fderivs_c.C
@@ -0,0 +1,135 @@
 #include "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];
    // Fortran 1-based bounds
    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;
    // 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 double *fh = NULL;
    static 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;
    }
    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
    // only compute when x/y/z all satisfy the same-order stencil at this point.
    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 ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
                    (jF + 2 <= jmaxF && jF - 2 >= jminF) &&
                    (kF + 2 <= kmaxF && 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)]
                    );
                } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
                           (jF + 1 <= jmaxF && jF - 1 >= jminF) &&
                           (kF + 1 <= kmaxF && 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);
 }
--- a/AMSS_NCKU_source/fmisc.f90
+++ b/AMSS_NCKU_source/fmisc.f90
@@ -326,8 +326,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
-      
+      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
    funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
   enddo
   do i=0,ord-1
      funcc(:,-i,1:extc(3)) = funcc(:,i+2,1:extc(3))*SoA(2)
@@ -884,13 +883,17 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
  integer::i
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
   enddo
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
   do i=0,ord-1
      funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
   enddo
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
   do i=0,ord-1
      funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
   enddo
@@ -1108,26 +1111,177 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
+! common code for cell and vertex
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
+! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-
+#ifndef POLINT6_USE_BARYCENTRIC
-  subroutine polint(xa, ya, x, y, dy, ordn)
+#define POLINT6_USE_BARYCENTRIC 1
-  implicit none
+#endif
-
+
-  integer, intent(in) :: ordn
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
  subroutine polint6_neville(xa, ya, x, y, dy)
  implicit none
  real*8, dimension(6), intent(in) :: xa, ya
  real*8, intent(in) :: x
  real*8, intent(out) :: y, dy
  integer :: i, m, ns, n_m
  real*8, dimension(6) :: c, d, ho
  real*8 :: dif, dift, hp, h, den_val
  c = ya
  d = ya
  ho = xa - x
  ns = 1
  dif = abs(x - xa(1))
  do i = 2, 6
    dift = abs(x - xa(i))
    if (dift < dif) then
      ns = i
      dif = dift
    end if
  end do
  y = ya(ns)
  ns = ns - 1
  do m = 1, 5
    n_m = 6 - m
    do i = 1, n_m
      hp = ho(i)
      h  = ho(i+m)
      den_val = hp - h
      if (den_val == 0.0d0) then
        write(*,*) 'failure in polint for point',x
        write(*,*) 'with input points: ',xa
        stop
      end if
      den_val = (c(i+1) - d(i)) / den_val
      d(i) = h * den_val
      c(i) = hp * den_val
    end do
    if (2 * ns < n_m) then
      dy = c(ns + 1)
    else
      dy = d(ns)
      ns = ns - 1
    end if
    y = y + dy
  end do
  return
  end subroutine polint6_neville
 !DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
  subroutine polint6_barycentric(xa, ya, x, y, dy)
  implicit none
  real*8, dimension(6), intent(in) :: xa, ya
  real*8, intent(in) :: x
  real*8, intent(out) :: y, dy
  integer :: i, j
  logical :: is_uniform
  real*8, dimension(6) :: lambda
  real*8 :: dx, den_i, term, num, den, step, tol
  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
  do i = 1, 6
    if (x == xa(i)) then
      y = ya(i)
      dy = 0.d0
      return
    end if
  end do
  step = xa(2) - xa(1)
  is_uniform = (step /= 0.d0)
  if (is_uniform) then
    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
    do i = 3, 6
      if (abs((xa(i) - xa(i-1)) - step) > tol) then
        is_uniform = .false.
        exit
      end if
    end do
  end if
  if (is_uniform) then
    num = 0.d0
    den = 0.d0
    do i = 1, 6
      term = c_uniform(i) / (x - xa(i))
      num = num + term * ya(i)
      den = den + term
    end do
    y = num / den
    dy = 0.d0
    return
  end if
  do i = 1, 6
    den_i = 1.d0
    do j = 1, 6
      if (j /= i) then
        dx = xa(i) - xa(j)
        if (dx == 0.0d0) then
          write(*,*) 'failure in polint for point',x
          write(*,*) 'with input points: ',xa
          stop
        end if
        den_i = den_i * dx
      end if
    end do
    lambda(i) = 1.d0 / den_i
  end do
  num = 0.d0
  den = 0.d0
  do i = 1, 6
    term = lambda(i) / (x - xa(i))
    num = num + term * ya(i)
    den = den + term
  end do
  y = num / den
  dy = 0.d0
  return
  end subroutine polint6_barycentric
 !DIR$ ATTRIBUTES FORCEINLINE :: polint
  subroutine polint(xa, ya, x, y, dy, ordn)
  implicit none
  integer, intent(in) :: ordn
  real*8, dimension(ordn), intent(in) :: xa, ya
  real*8, intent(in) :: x
  real*8, intent(out) :: y, dy
-  integer :: i, m, ns, n_m
+  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
+  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
+  real*8 :: dif, dift, hp, h, den_val
-
+
-  c = ya
+  if (ordn == 6) then
-  d = ya
+#if POLINT6_USE_BARYCENTRIC
-  ho = xa - x
+    call polint6_barycentric(xa, ya, x, y, dy)
 #else
    call polint6_neville(xa, ya, x, y, dy)
 #endif
    return
  end if
  c = ya
  d = ya
  ho = xa - x
  ns = 1
  dif = abs(x - xa(1))
@@ -1171,13 +1325,48 @@ end subroutine d2dump
    y = y + dy
  end do
-  return
+  return
-  end subroutine polint
+  end subroutine polint
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-!
+! Compute Lagrange interpolation basis weights for one target point.
-! interpolation in 2 dimensions, follow yx order
+!------------------------------------------------------------------------------
-!
+!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
-!------------------------------------------------------------------------------
+  subroutine polint_lagrange_weights(xa, x, w, ordn)
  implicit none
  integer, intent(in) :: ordn
  real*8, dimension(1:ordn), intent(in) :: xa
  real*8, intent(in) :: x
  real*8, dimension(1:ordn), intent(out) :: w
  integer :: i, j
  real*8 :: num, den, dx
  do i = 1, ordn
    num = 1.d0
    den = 1.d0
    do j = 1, ordn
      if (j /= i) then
        dx = xa(i) - xa(j)
        if (dx == 0.0d0) then
          write(*,*) 'failure in polint for point',x
          write(*,*) 'with input points: ',xa
          stop
        end if
        num = num * (x - xa(j))
        den = den * dx
      end if
    end do
    w(i) = num / den
  end do
  return
  end subroutine polint_lagrange_weights
 !------------------------------------------------------------------------------
 !
 ! interpolation in 2 dimensions, follow yx order
 !
 !------------------------------------------------------------------------------
  subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
  implicit none
@@ -1225,11 +1414,11 @@ end subroutine d2dump
  real*8, intent(in) :: x1,x2,x3
  real*8, intent(out) :: y,dy
-#ifdef POLINT_LEGACY_ORDER
+#ifdef POLINT_LEGACY_ORDER
-  integer  :: i,j,m,n
+  integer  :: i,j,m,n
-  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
+  real*8, dimension(ordn) :: yntmp
  real*8, dimension(ordn) :: yqtmp
  m=size(x1a)
@@ -1239,29 +1428,36 @@ end subroutine d2dump
    yqtmp=ya(i,j,:)
    call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
   end do
-    yntmp=yatmp(i,:)
+    yntmp=yatmp(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
+  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
+#else
-  integer  :: j, k
+  integer  :: i, j, k
-  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: w1, w2
-  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
+  real*8 :: yx_sum, x_sum
-
+
-  do k=1,ordn
+  call polint_lagrange_weights(x1a, x1, w1, ordn)
-    do j=1,ordn
+  call polint_lagrange_weights(x2a, x2, w2, ordn)
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+
-    end do
+  do k = 1, ordn
-  end do
+    yx_sum = 0.d0
-  do k=1,ordn
+    do j = 1, ordn
-    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+      x_sum = 0.d0
-  end do
+      do i = 1, ordn
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
+        x_sum = x_sum + w1(i) * ya(i,j,k)
-#endif
+      end do
-
+      yx_sum = yx_sum + w2(j) * x_sum
-  return
+    end do
-  end subroutine polin3
+    ymtmp(k) = yx_sum
  end do
  call polint(x3a, ymtmp, x3, y, dy, ordn)
 #endif
  return
  end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
  subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1604,11 +1800,14 @@ deallocate(f_flat)
 !       ^
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3
-  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-
+  integer :: i,j,k
-  fout = C1*f1+C2*f2+C3*f3
+
-
+  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
-  return
+    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
  end do
  return
  end subroutine average2
 !-----------------------------------------------------------------------------  
--- a/AMSS_NCKU_source/interp_lb_profile.C
+++ b/AMSS_NCKU_source/interp_lb_profile.C
@@ -0,0 +1,107 @@
 #include "interp_lb_profile.h"
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 namespace InterpLBProfile {
 bool write_profile(const char *filepath, int nprocs,
                   const double *rank_times,
                   const int *heavy_ranks, int num_heavy,
                   double threshold_ratio)
 {
    FILE *fp = fopen(filepath, "wb");
    if (!fp) return false;
    ProfileHeader hdr;
    hdr.magic = MAGIC;
    hdr.version = VERSION;
    hdr.nprocs = nprocs;
    hdr.num_heavy = num_heavy;
    hdr.threshold_ratio = threshold_ratio;
    fwrite(&hdr, sizeof(hdr), 1, fp);
    fwrite(rank_times, sizeof(double), nprocs, fp);
    fwrite(heavy_ranks, sizeof(int), num_heavy, fp);
    fclose(fp);
    return true;
 }
 bool read_profile(const char *filepath, int current_nprocs,
                  int *heavy_ranks, int &num_heavy,
                  double *rank_times, MPI_Comm comm)
 {
    int myrank;
    MPI_Comm_rank(comm, &myrank);
    int valid = 0;
    ProfileHeader hdr;
    memset(&hdr, 0, sizeof(hdr));
    if (myrank == 0) {
        FILE *fp = fopen(filepath, "rb");
        if (fp) {
            if (fread(&hdr, sizeof(hdr), 1, fp) == 1 &&
                hdr.magic == MAGIC && hdr.version == VERSION &&
                hdr.nprocs == current_nprocs)
            {
                if (fread(rank_times, sizeof(double), current_nprocs, fp)
                    == (size_t)current_nprocs &&
                    fread(heavy_ranks, sizeof(int), hdr.num_heavy, fp)
                    == (size_t)hdr.num_heavy)
                {
                    num_heavy = hdr.num_heavy;
                    valid = 1;
                }
            } else if (fp) {
                printf("[InterpLB] Profile rejected: magic=0x%X version=%u "
                       "nprocs=%d (current=%d)\n",
                       hdr.magic, hdr.version, hdr.nprocs, current_nprocs);
            }
            fclose(fp);
        }
    }
    MPI_Bcast(&valid, 1, MPI_INT, 0, comm);
    if (!valid) return false;
    MPI_Bcast(&num_heavy, 1, MPI_INT, 0, comm);
    MPI_Bcast(heavy_ranks, num_heavy, MPI_INT, 0, comm);
    MPI_Bcast(rank_times, current_nprocs, MPI_DOUBLE, 0, comm);
    return true;
 }
 int identify_heavy_ranks(const double *rank_times, int nprocs,
                         double threshold_ratio,
                         int *heavy_ranks, int max_heavy)
 {
    double sum = 0;
    for (int i = 0; i < nprocs; i++) sum += rank_times[i];
    double mean = sum / nprocs;
    double threshold = threshold_ratio * mean;
    // Collect candidates
    struct RankTime { int rank; double time; };
    RankTime *candidates = new RankTime[nprocs];
    int ncand = 0;
    for (int i = 0; i < nprocs; i++) {
        if (rank_times[i] > threshold)
            candidates[ncand++] = {i, rank_times[i]};
    }
    // Sort descending by time
    std::sort(candidates, candidates + ncand,
              [](const RankTime &a, const RankTime &b) {
                  return a.time > b.time;
              });
    int count = (ncand < max_heavy) ? ncand : max_heavy;
    for (int i = 0; i < count; i++)
        heavy_ranks[i] = candidates[i].rank;
    delete[] candidates;
    return count;
 }
 } // namespace InterpLBProfile
--- a/AMSS_NCKU_source/interp_lb_profile.bin
+++ b/AMSS_NCKU_source/interp_lb_profile.bin
--- a/AMSS_NCKU_source/interp_lb_profile.h
+++ b/AMSS_NCKU_source/interp_lb_profile.h
@@ -0,0 +1,38 @@
 #ifndef INTERP_LB_PROFILE_H
 #define INTERP_LB_PROFILE_H
 #include <mpi.h>
 namespace InterpLBProfile {
 static const unsigned int MAGIC   = 0x494C4250; // "ILBP"
 static const unsigned int VERSION = 1;
 struct ProfileHeader {
    unsigned int magic;
    unsigned int version;
    int nprocs;
    int num_heavy;
    double threshold_ratio;
 };
 // Write profile file (rank 0 only)
 bool write_profile(const char *filepath, int nprocs,
                   const double *rank_times,
                   const int *heavy_ranks, int num_heavy,
                   double threshold_ratio);
 // Read profile file (rank 0 reads, then broadcasts to all)
 // Returns true if file found and valid for current nprocs
 bool read_profile(const char *filepath, int current_nprocs,
                  int *heavy_ranks, int &num_heavy,
                  double *rank_times, MPI_Comm comm);
 // Identify heavy ranks: those with time > threshold_ratio * mean
 int identify_heavy_ranks(const double *rank_times, int nprocs,
                         double threshold_ratio,
                         int *heavy_ranks, int max_heavy);
 } // namespace InterpLBProfile
 #endif /* INTERP_LB_PROFILE_H */
--- a/AMSS_NCKU_source/interp_lb_profile_data.h
+++ b/AMSS_NCKU_source/interp_lb_profile_data.h
@@ -0,0 +1,29 @@
 /* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
 /* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
 /* Auto-generated from interp_lb_profile.bin — do not edit */
 #ifndef INTERP_LB_PROFILE_DATA_H
 #define INTERP_LB_PROFILE_DATA_H
 #define INTERP_LB_NPROCS 64
 #define INTERP_LB_NUM_HEAVY 4
 static const int interp_lb_heavy_blocks[4] = {27, 35, 28, 36};
 /* Split table: {block_id, r_left, r_right} */
 static const int interp_lb_splits[4][3] = {
    {27, 26, 27},
    {35, 34, 35},
    {28, 28, 29},
    {36, 36, 37},
 };
 /* Rank remap for displaced neighbor blocks */
 static const int interp_lb_num_remaps = 4;
 static const int interp_lb_remaps[][2] = {
    {26, 25},
    {29, 30},
    {34, 33},
    {37, 38},
 };
 #endif /* INTERP_LB_PROFILE_DATA_H */
--- a/AMSS_NCKU_source/kodiss.f90
+++ b/AMSS_NCKU_source/kodiss.f90
@@ -6,6 +6,103 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 #if (ghost_width == 2)
 ! second order code
 !------------------------------------------------------------------------------------------------------------------------------
 !usual type Kreiss-Oliger type numerical dissipation
 !We support cell center only
 !  (D_+D_-)^2 =
 !   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
 ! ------------------------------------------------------
 !                       dx^4
 !------------------------------------------------------------------------------------------------------------------------------
 ! do not add dissipation near boundary
 subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
 implicit none
 ! argument variables
 integer,intent(in) :: Symmetry
 integer,dimension(3),intent(in)::ex
 real*8, dimension(1:3), intent(in) :: SoA
 double precision,intent(in),dimension(ex(1))::X
 double precision,intent(in),dimension(ex(2))::Y
 double precision,intent(in),dimension(ex(3))::Z
 double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
 double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
 real*8,intent(in) :: eps
 !~~~~~~ other variables
  real*8 :: dX,dY,dZ
  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  real*8,parameter   :: cof = 1.6d1 ! 2^4
  real*8,  parameter :: F4=4.d0,F6=6.d0
  integer::i,j,k
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
  call symmetry_bd(2,ex,f,fh,SoA)
 !   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
 ! ------------------------------------------------------
 !                       dx^4
 !  note the sign (-1)^r-1, now r=2
 !DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
 !DIR$ UNROLL PARTIAL(4)
  do k=1,ex(3)
  do j=1,ex(2)
  do i=1,ex(1)
  if(i-2 >= imin .and. i+2 <= imax .and. &
     j-2 >= jmin .and. j+2 <= jmax .and. &
     k-2 >= kmin .and. k+2 <= kmax) then
 ! x direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
                                (fh(i-2,j,k)+fh(i+2,j,k)) &
                         - F4 * (fh(i-1,j,k)+fh(i+1,j,k)) &
                         + F6 *  fh(i,j,k) )
 ! y direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
                                (fh(i,j-2,k)+fh(i,j+2,k)) &
                         - F4 * (fh(i,j-1,k)+fh(i,j+1,k)) &
                         + F6 *  fh(i,j,k) )
 ! z direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
                                (fh(i,j,k-2)+fh(i,j,k+2)) &
                         - F4 * (fh(i,j,k-1)+fh(i,j,k+1)) &
                         + F6 *  fh(i,j,k) )
  endif
  enddo
  enddo
  enddo
  return
 end subroutine kodis
 #elif (ghost_width == 3)
 ! fourth order code
 !---------------------------------------------------------------------------------------------
@@ -61,7 +158,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
  if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin = -2
  if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin = -2
-  !print*,'imin,jmin,kmin=',imin,jmin,kmin
+
  call symmetry_bd(3,ex,f,fh,SoA)
  do k=1,ex(3)
@@ -71,7 +168,28 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
  if(i-3 >= imin .and. i+3 <= imax .and. &
     j-3 >= jmin .and. j+3 <= jmax .and. &
     k-3 >= kmin .and. k+3 <= kmax) then
 #if 0     
 ! x direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (     &
                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
                          TWT* fh(i,j,k)            )
 ! y direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (     &
                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
                          TWT* fh(i,j,k)            )
 ! z direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (     &
                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
                          TWT* fh(i,j,k)            )
 #else
 ! calculation order if important ?
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
@@ -88,7 +206,7 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
                          TWT* fh(i,j,k)            )/dZ )
-
+#endif
  endif
  enddo
@@ -99,6 +217,218 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
  end subroutine kodis
 #elif (ghost_width == 4)
 ! sixth order code
 !------------------------------------------------------------------------------------------------------------------------------
 !usual type Kreiss-Oliger type numerical dissipation
 !We support cell center only
 !  (D_+D_-)^4 =
 !   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
 ! ----------------------------------------------------------------------------------------------------------
 !                                              dx^8
 !------------------------------------------------------------------------------------------------------------------------------
 ! do not add dissipation near boundary
 subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
 implicit none
 ! argument variables
 integer,intent(in) :: Symmetry
 integer,dimension(3),intent(in)::ex
 real*8, dimension(1:3), intent(in) :: SoA
 double precision,intent(in),dimension(ex(1))::X
 double precision,intent(in),dimension(ex(2))::Y
 double precision,intent(in),dimension(ex(3))::Z
 double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
 double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
 real*8,intent(in) :: eps
 !~~~~~~ other variables
  real*8 :: dX,dY,dZ
  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  real*8,parameter   :: cof = 2.56d2 ! 2^8
  real*8,  parameter :: F8=8.d0,F28=2.8d1,F56=5.6d1,F70=7.d1
  integer::i,j,k
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
  call symmetry_bd(4,ex,f,fh,SoA)
 !   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
 ! ----------------------------------------------------------------------------------------------------------
 !                                              dx^8
 !  note the sign (-1)^r-1, now r=4
  do k=1,ex(3)
  do j=1,ex(2)
  do i=1,ex(1)
  if(i>imin+3 .and. i < imax-3 .and. &
     j>jmin+3 .and. j < jmax-3 .and. &
     k>kmin+3 .and. k < kmax-3) then
 ! x direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
                                (fh(i-4,j,k)+fh(i+4,j,k)) &
                         - F8 * (fh(i-3,j,k)+fh(i+3,j,k)) &
                         +F28 * (fh(i-2,j,k)+fh(i+2,j,k)) &
                         -F56 * (fh(i-1,j,k)+fh(i+1,j,k)) &
                         +F70 *  fh(i,j,k) )
 ! y direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
                                (fh(i,j-4,k)+fh(i,j+4,k)) &
                         - F8 * (fh(i,j-3,k)+fh(i,j+3,k)) &
                         +F28 * (fh(i,j-2,k)+fh(i,j+2,k)) &
                         -F56 * (fh(i,j-1,k)+fh(i,j+1,k)) &
                         +F70 *  fh(i,j,k) )
 ! z direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
                                (fh(i,j,k-4)+fh(i,j,k+4)) &
                         - F8 * (fh(i,j,k-3)+fh(i,j,k+3)) &
                         +F28 * (fh(i,j,k-2)+fh(i,j,k+2)) &
                         -F56 * (fh(i,j,k-1)+fh(i,j,k+1)) &
                         +F70 *  fh(i,j,k) )
  endif
  enddo
  enddo
  enddo
  return
 end subroutine kodis
 #elif (ghost_width == 5)
 ! eighth order code
 !------------------------------------------------------------------------------------------------------------------------------
 !usual type Kreiss-Oliger type numerical dissipation
 !We support cell center only
 ! Note the notation D_+ and D_- [P240 of B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time
 ! Dependent Problems and Difference Methods (Wiley, New York, 1995).]
 ! D_+ = (f(i+1) - f(i))/h
 ! D_- = (f(i) - f(i-1))/h
 ! then we have D_+D_- = D_-D_+ = (f(i+1) - 2f(i) + f(i-1))/h^2
 ! for nth order accurate finite difference code, we need r =n/2+1
 !              D_+^rD_-^r = (D_+D_-)^r 
 ! following the tradiation of PRD 77, 024027 (BB's calibration paper, Eq.(64),
 !  correct some typo according to above book) :
 ! + eps*(-1)^(r-1)*h^(2r-1)/2^(2r)*(D_+D_-)^r 
 !
 !
 ! this is for 8th order accurate finite difference scheme
 !  (D_+D_-)^5 =
 !  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
 ! -------------------------------------------------------------------------------------------------------------------------------
 !                                                              dx^10
 !---------------------------------------------------------------------------------------------------------------------------------
 ! do not add dissipation near boundary
 subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
 implicit none
 ! argument variables
 integer,intent(in) :: Symmetry
 integer,dimension(3),intent(in)::ex
 real*8, dimension(1:3), intent(in) :: SoA
 double precision,intent(in),dimension(ex(1))::X
 double precision,intent(in),dimension(ex(2))::Y
 double precision,intent(in),dimension(ex(3))::Z
 double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
 double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
 real*8,intent(in) :: eps
 !~~~~~~ other variables
  real*8 :: dX,dY,dZ
  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  real*8,parameter   :: cof = 1.024d3 ! 2^2r = 2^10
  real*8,  parameter :: F10=1.d1,F45=4.5d1,F120=1.2d2,F210=2.1d2,F252=2.52d2
  integer::i,j,k
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
  call symmetry_bd(5,ex,f,fh,SoA)
 !  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
 ! -------------------------------------------------------------------------------------------------------------------------------
 !                                                              dx^10
 !  note the sign (-1)^r-1, now r=5
  do k=1,ex(3)
  do j=1,ex(2)
  do i=1,ex(1)
  if(i>imin+4 .and. i < imax-4 .and. &
     j>jmin+4 .and. j < jmax-4 .and. &
     k>kmin+4 .and. k < kmax-4) then
 ! x direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (      &
                                 (fh(i-5,j,k)+fh(i+5,j,k)) &
                         - F10 * (fh(i-4,j,k)+fh(i+4,j,k)) &
                         + F45 * (fh(i-3,j,k)+fh(i+3,j,k)) &
                         - F120* (fh(i-2,j,k)+fh(i+2,j,k)) &
                         + F210* (fh(i-1,j,k)+fh(i+1,j,k)) &
                         - F252 * fh(i,j,k) )
 ! y direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (      &
                                 (fh(i,j-5,k)+fh(i,j+5,k)) &
                         - F10 * (fh(i,j-4,k)+fh(i,j+4,k)) &
                         + F45 * (fh(i,j-3,k)+fh(i,j+3,k)) &
                         - F120* (fh(i,j-2,k)+fh(i,j+2,k)) &
                         + F210* (fh(i,j-1,k)+fh(i,j+1,k)) &
                         - F252 * fh(i,j,k) )
 ! z direction
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (      &
                                 (fh(i,j,k-5)+fh(i,j,k+5)) &
                         - F10 * (fh(i,j,k-4)+fh(i,j,k+4)) &
                         + F45 * (fh(i,j,k-3)+fh(i,j,k+3)) &
                         - F120* (fh(i,j,k-2)+fh(i,j,k+2)) &
                         + F210* (fh(i,j,k-1)+fh(i,j,k+1)) &
                         - F252 * fh(i,j,k) )
  endif
  enddo
  enddo
  enddo
  return
 end subroutine kodis
 #endif  
--- a/AMSS_NCKU_source/kodiss_c.C
+++ b/AMSS_NCKU_source/kodiss_c.C
@@ -0,0 +1,117 @@
 #include "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;
    double *fh = (double*)malloc(fh_size * sizeof(double));
    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, ...
     */
    // 收紧循环范围：只遍历满足 iF±3/jF±3/kF±3 条件的内部点
    // iF-3 >= iminF => iF >= iminF+3 => i0 >= iminF+2 (因为 iF=i0+1)
    // iF+3 <= imaxF => iF <= imaxF-3 => i0 <= imaxF-4
    const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
    const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
    const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
    const int i0_hi = imaxF - 4;  // inclusive
    const int j0_hi = jmaxF - 4;
    const int k0_hi = kmaxF - 4;
    if (i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi) {
        free(fh);
        return;
    }
    for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
        const int kF = k0 + 1;
        for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
            const int jF = j0 + 1;
            for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
                const int iF = i0 + 1;
                    const size_t p = idx_ex(i0, j0, k0, ex);
                    // 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);
 }
--- a/AMSS_NCKU_source/lopsided_c.C
+++ b/AMSS_NCKU_source/lopsided_c.C
@@ -0,0 +1,255 @@
 #include "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;
    double *fh = (double*)malloc(fh_size * sizeof(double));
    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);
 }
--- a/AMSS_NCKU_source/lopsided_kodis_c.C
+++ b/AMSS_NCKU_source/lopsided_kodis_c.C
@@ -0,0 +1,248 @@
 #include "tool.h"
 /*
 * Combined advection (lopsided) + KO dissipation (kodis).
 * Uses one shared symmetry_bd buffer per call.
 */
 void lopsided_kodis(const int ex[3],
                    const double *X, const double *Y, const double *Z,
                    const double *f, double *f_rhs,
                    const double *Sfx, const double *Sfy, const double *Sfz,
                    int Symmetry, const double SoA[3], double eps)
 {
    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
    const double F6 = 6.0, F18 = 18.0;
    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
    const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
    const double cof = 64.0; // 2^6
    const int NO_SYMM = 0, EQ_SYMM = 1;
    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
    const double dX = X[1] - X[0];
    const double dY = Y[1] - Y[0];
    const double dZ = Z[1] - Z[0];
    const double d12dx = ONE / F12 / dX;
    const double d12dy = ONE / F12 / dY;
    const double d12dz = ONE / F12 / dZ;
    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 = -2;
    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
    // fh for Fortran-style domain (-2:ex1,-2:ex2,-2:ex3)
    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;
    double *fh = (double*)malloc(fh_size * sizeof(double));
    if (!fh) return;
    symmetry_bd(3, ex, f, fh, SoA);
    // Advection (same stencil logic as lopsided_c.C)
    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
        const int kF = k0 + 1;
        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
            const int jF = j0 + 1;
            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
                const int iF = i0 + 1;
                const size_t p = idx_ex(i0, j0, k0, ex);
                const double sfx = Sfx[p];
                if (sfx > ZEO) {
                    if (i0 <= ex1 - 4) {
                        f_rhs[p] += sfx * d12dx *
                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
                    } else if (i0 <= ex1 - 3) {
                        f_rhs[p] += sfx * d12dx *
                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
                    } else if (i0 <= ex1 - 2) {
                        f_rhs[p] -= sfx * d12dx *
                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
                    }
                } else if (sfx < ZEO) {
                    if ((i0 - 2) >= iminF) {
                        f_rhs[p] -= sfx * d12dx *
                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
                    } else if ((i0 - 1) >= iminF) {
                        f_rhs[p] += sfx * d12dx *
                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
                    } else if (i0 >= iminF) {
                        f_rhs[p] += sfx * d12dx *
                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
                    }
                }
                const double sfy = Sfy[p];
                if (sfy > ZEO) {
                    if (j0 <= ex2 - 4) {
                        f_rhs[p] += sfy * d12dy *
                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
                    } else if (j0 <= ex2 - 3) {
                        f_rhs[p] += sfy * d12dy *
                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
                    } else if (j0 <= ex2 - 2) {
                        f_rhs[p] -= sfy * d12dy *
                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
                    }
                } else if (sfy < ZEO) {
                    if ((j0 - 2) >= jminF) {
                        f_rhs[p] -= sfy * d12dy *
                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
                    } else if ((j0 - 1) >= jminF) {
                        f_rhs[p] += sfy * d12dy *
                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
                    } else if (j0 >= jminF) {
                        f_rhs[p] += sfy * d12dy *
                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
                    }
                }
                const double sfz = Sfz[p];
                if (sfz > ZEO) {
                    if (k0 <= ex3 - 4) {
                        f_rhs[p] += sfz * d12dz *
                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
                    } else if (k0 <= ex3 - 3) {
                        f_rhs[p] += sfz * d12dz *
                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
                    } else if (k0 <= ex3 - 2) {
                        f_rhs[p] -= sfz * d12dz *
                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
                    }
                } else if (sfz < ZEO) {
                    if ((k0 - 2) >= kminF) {
                        f_rhs[p] -= sfz * d12dz *
                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
                    } else if ((k0 - 1) >= kminF) {
                        f_rhs[p] += sfz * d12dz *
                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
                    } else if (k0 >= kminF) {
                        f_rhs[p] += sfz * d12dz *
                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
                    }
                }
            }
        }
    }
    // KO dissipation (same domain restriction as kodiss_c.C)
    if (eps > ZEO) {
        const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
        const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
        const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
        const int i0_hi = imaxF - 4; // inclusive
        const int j0_hi = jmaxF - 4;
        const int k0_hi = kmaxF - 4;
        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
                const int kF = k0 + 1;
                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
                    const int jF = j0 + 1;
                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
                        const int iF = i0 + 1;
                        const size_t p = idx_ex(i0, j0, k0, ex);
                        const double Dx_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;
                        f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
                    }
                }
            }
        }
    }
    free(fh);
 }
--- a/AMSS_NCKU_source/lopsidediff.f90
+++ b/AMSS_NCKU_source/lopsidediff.f90
@@ -7,7 +7,163 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 #if (ghost_width == 2)
 ! second order code
 !-----------------------------------------------------------------------------
 !         v
 ! D f = ------[ - 3 f  + 4 f   - f     ]
 !  i     2dx         i      i+v   i+2v
 !
 ! where
 !
 !        i
 !      |B |
 ! v = -----
 !        i
 !       B
 !
 !-----------------------------------------------------------------------------
 subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
  implicit none
 !~~~~~~> Input parameters:
  integer, intent(in)  :: ex(1:3),Symmetry
  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
  real*8,dimension(3),intent(in) ::SoA
 !~~~~~~> local variables:
 ! note index -1,0, so we have 2 extra points
  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
  real*8 :: dX,dY,dZ
  real*8 :: d2dx,d2dy,d2dz
  real*8,  parameter :: ZEO=0.d0,ONE=1.d0,TWO=2.d0,THR=3.d0,FOUR=4.d0
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  d2dx = ONE/TWO/dX
  d2dy = ONE/TWO/dY
  d2dz = ONE/TWO/dZ
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
  call symmetry_bd(2,ex,f,fh,SoA)
 ! upper bound set ex-1 only for efficiency, 
 ! the loop body will set ex 0 also
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 ! x direction   
    if(Sfx(i,j,k) >= ZEO)then
       if( i+2 <= imax .and. i >= imin)then
 !         v
 ! D f = ------[ - 3 f  + 4 f   - f     ]
 !  i     2dx         i      i+v   i+2v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
                  Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i+1,j,k)-fh(i+2,j,k))
       elseif(i+1 <= imax .and. i >= imin)then
 !         v
 ! D f = ------[ - f  + f   ]
 !  i      dx       i    i+v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
                  Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i+1,j,k))
       endif
    elseif(Sfx(i,j,k) <= ZEO)then
      if( i-2 >= imin .and. i <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
                  Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i-1,j,k)-fh(i-2,j,k))
      elseif(i-1 >= imin .and. i <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
                  Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i-1,j,k))
      endif
 ! set imax and imin 0
    endif
 ! y direction   
    if(Sfy(i,j,k) >= ZEO)then
       if( j+2 <= jmax .and. j >= jmin)then
 !         v
 ! D f = ------[ - 3 f  + 4 f   - f     ]
 !  i     2dx         i      i+v   i+2v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
                  Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j+1,k)-fh(i,j+2,k))
       elseif(j+1 <= jmax .and. j >= jmin)then
 !         v
 ! D f = ------[ - f  + f   ]
 !  i      dx       i    i+v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
                  Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j+1,k))
       endif
    elseif(Sfy(i,j,k) <= ZEO)then
      if( j-2 >= jmin .and. j <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
                  Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j-1,k)-fh(i,j-2,k))
      elseif(j-1 >= jmin .and. j <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
                  Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j-1,k))
      endif
 ! set jmin and jmax 0
     endif
 !! z direction   
    if(Sfz(i,j,k) >= ZEO)then
      if( k+2 <= kmax .and. k >= kmin)then
 !         v
 ! D f = ------[ - 3 f  + 4 f   - f     ]
 !  i     2dx         i      i+v   i+2v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
                  Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k+1)-fh(i,j,k+2))
       elseif(k+1 <= kmax .and. k >= kmin)then
 !         v
 ! D f = ------[ - f  + f   ]
 !  i      dx       i    i+v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                           &
                  Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k+1))
       endif
    elseif(Sfz(i,j,k) <= ZEO)then
      if( k-2 >= kmin .and. k <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
                  Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k-1)-fh(i,j,k-2))
      elseif(k-1 >= kmin .and. k <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                           &
                  Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k-1))
      endif
 ! set kmin and kmax 0
     endif
  enddo
  enddo
  enddo
  return
  end subroutine lopsided
 #elif (ghost_width == 3)
 ! fourth order code
 !-----------------------------------------------------------------------------
@@ -80,7 +236,89 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 #if 0  
 !! old code
 ! x direction   
    if(Sfx(i,j,k) >= ZEO .and. i+3 <= imax .and. i-1 >= imin)then
 !         v
 ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
 !  i     12dx       i-v      i      i+v     i+2v    i+3v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
    elseif(Sfx(i,j,k) <= ZEO .and. i-3 >= imin .and. i+1 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
     elseif(i+2 <= imax .and. i-2 >= imin)then
 !
 !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
 !  fx(i) = ---------------------------------------------
 !                             12 dx
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
     elseif(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
 !  fx(i) = --------------------------------
 !                     2 dx
     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
 ! set imax and imin 0
    endif
 ! y direction   
    if(Sfy(i,j,k) >= ZEO .and. j+3 <= jmax .and. j-1 >= jmin)then
 !         v
 ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
 !  i     12dx       i-v      i      i+v     i+2v    i+3v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
    elseif(Sfy(i,j,k) <= ZEO .and. j-3 >= jmin .and. j+1 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
     elseif(j+2 <= jmax .and. j-2 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
     elseif(j+1 <= jmax .and. j-1 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
 ! set jmin and jmax 0
     endif
 !! z direction   
    if(Sfz(i,j,k) >= ZEO .and. k+3 <= kmax .and. k-1 >= kmin)then
 !         v
 ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
 !  i     12dx       i-v      i      i+v     i+2v    i+3v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
    elseif(Sfz(i,j,k) <= ZEO .and. k-3 >= kmin .and. k+1 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
     elseif(k+2 <= kmax .and. k-2 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
     elseif(k+1 <= kmax .and. k-1 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
 ! set kmin and kmax 0
     endif
 #else
 !! new code, 2012dec27, based on bam
 ! x direction   
    if(Sfx(i,j,k) > ZEO)then
@@ -240,6 +478,7 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 ! set kmax and kmin 0
     endif
   endif
 #endif
  enddo
  enddo
  enddo
@@ -247,3 +486,612 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
  return
  end subroutine lopsided
 !-----------------------------------------------------------------------------
 ! Combined advection (lopsided) + Kreiss-Oliger dissipation (kodis)
 ! Shares the symmetry_bd buffer fh, eliminating one full-grid copy per call.
 ! Mathematically identical to calling lopsided then kodis separately.
 !-----------------------------------------------------------------------------
 subroutine lopsided_kodis(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,eps)
  implicit none
 !~~~~~~> Input parameters:
  integer, intent(in)  :: ex(1:3),Symmetry
  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
  real*8,dimension(3),intent(in) ::SoA
  real*8,intent(in) :: eps
 !~~~~~~> local variables:
 ! note index -2,-1,0, so we have 3 extra points
  real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
  real*8 :: dX,dY,dZ
  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
  real*8,  parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
  real*8,  parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
 ! kodis parameters
  real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
  real*8, parameter :: cof=6.4d1   ! 2^6
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  d12dx = ONE/F12/dX
  d12dy = ONE/F12/dY
  d12dz = ONE/F12/dZ
  d2dx = ONE/TWO/dX
  d2dy = ONE/TWO/dY
  d2dz = ONE/TWO/dZ
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
 ! Single symmetry_bd call shared by both advection and dissipation
  call symmetry_bd(3,ex,f,fh,SoA)
 ! ---- Advection (lopsided) loop ----
 ! upper bound set ex-1 only for efficiency, 
 ! the loop body will set ex 0 also
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 ! x direction   
    if(Sfx(i,j,k) > ZEO)then
      if(i+3 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
     elseif(i+2 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
     elseif(i+1 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
     endif
   elseif(Sfx(i,j,k) < ZEO)then
      if(i-3 >= imin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
     elseif(i-2 >= imin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
     elseif(i-1 >= imin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
     endif
   endif
 ! y direction   
    if(Sfy(i,j,k) > ZEO)then
      if(j+3 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
     elseif(j+2 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
     elseif(j+1 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
     endif
   elseif(Sfy(i,j,k) < ZEO)then
      if(j-3 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
     elseif(j-2 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
     elseif(j-1 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
     endif
   endif
 ! z direction   
    if(Sfz(i,j,k) > ZEO)then
      if(k+3 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
     elseif(k+2 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
     elseif(k+1 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
     endif
   elseif(Sfz(i,j,k) < ZEO)then
      if(k-3 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
     elseif(k-2 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
     elseif(k-1 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
     endif
   endif
  enddo
  enddo
  enddo
 ! ---- Dissipation (kodis) loop ----
  if(eps > ZEO) then
  do k=1,ex(3)
  do j=1,ex(2)
  do i=1,ex(1)
  if(i-3 >= imin .and. i+3 <= imax .and. &
     j-3 >= jmin .and. j+3 <= jmax .and. &
     k-3 >= kmin .and. k+3 <= kmax) then
   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
                          TWT* fh(i,j,k)            )/dX + &
                                                  (     &
                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
                          TWT* fh(i,j,k)            )/dY + &
                                                  (     &
                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
                          TWT* fh(i,j,k)            )/dZ )
  endif
  enddo
  enddo
  enddo
  endif
  return
  end subroutine lopsided_kodis
 #elif (ghost_width == 4)
 ! sixth order code
 ! Compute advection terms in right hand sides of field equations
 !         v
 ! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
 !  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
 !
 ! where
 !
 !        i
 !      |B |
 ! v = -----
 !        i
 !       B
 !
 !-----------------------------------------------------------------------------
 subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
  implicit none
 !~~~~~~> Input parameters:
  integer, intent(in)  :: ex(1:3),Symmetry
  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
  real*8,dimension(3),intent(in) ::SoA
 !~~~~~~> local variables:
  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
  real*8 :: dX,dY,dZ
  real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
  real*8,  parameter :: TWO=2.d0,F24=2.4d1,F35=3.5d1,F80=8.d1,F30=3.d1,EIT=8.d0
  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1
  real*8,  parameter ::  F10=1.d1,F77=7.7d1,F150=1.5d2,F100=1.d2,F50=5.d1,F15=1.5d1
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  d60dx = ONE/F60/dX
  d60dy = ONE/F60/dY
  d60dz = ONE/F60/dZ
  d12dx = ONE/F12/dX
  d12dy = ONE/F12/dY
  d12dz = ONE/F12/dZ
  d2dx = ONE/TWO/dX
  d2dy = ONE/TWO/dY
  d2dz = ONE/TWO/dZ
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
  call symmetry_bd(4,ex,f,fh,SoA)
 ! upper bound set ex-1 only for efficiency, 
 ! the loop body will set ex 0 also
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 ! x direction   
    if(Sfx(i,j,k) >= ZEO .and. i+4 <= imax .and. i-2 >= imin)then
 !         v
 ! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
 !  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                             &
                  Sfx(i,j,k)*d60dx*(TWO*fh(i-2,j,k)-F24*fh(i-1,j,k)-F35*fh(i,j,k)+F80*fh(i+1,j,k) &
                                   -F30*fh(i+2,j,k)+EIT*fh(i+3,j,k)-    fh(i+4,j,k))
    elseif(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-1 >= imin)then
 !         v
 ! D f = ------[-10f    - 77f  + 150f    - 100f     + 50f     -15f     + 2f    ]
 !  i     60dx      i-v      i       i+v       i+2v      i+3v     i+4v    i+5v
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
                  Sfx(i,j,k)*d60dx*(-F10*fh(i-1,j,k)-F77*fh(i  ,j,k)+F150*fh(i+1,j,k)-F100*fh(i+2,j,k) &
                                    +F50*fh(i+3,j,k)-F15*fh(i+4,j,k)+ TWO*fh(i+5,j,k))
    elseif(Sfx(i,j,k) <= ZEO .and. i-4 >= imin .and. i+2 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
                  Sfx(i,j,k)*d60dx*(TWO*fh(i+2,j,k)-F24*fh(i+1,j,k)-F35*fh(i,j,k)+F80*fh(i-1,j,k) &
                                   -F30*fh(i-2,j,k)+EIT*fh(i-3,j,k)-    fh(i-4,j,k))
    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+1 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
                  Sfx(i,j,k)*d60dx*(-F10*fh(i+1,j,k)-F77*fh(i  ,j,k)+F150*fh(i-1,j,k)-F100*fh(i-2,j,k) &
                                    +F50*fh(i-3,j,k)-F15*fh(i-4,j,k)+ TWO*fh(i-5,j,k))
     elseif(i+3 <= imax .and. i-3 >= imin)then
 !           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
 !  fx(i) = -----------------------------------------------------------------
 !                                        60 dx
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
     elseif(i+2 <= imax .and. i-2 >= imin)then
 !
 !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
 !  fx(i) = ---------------------------------------------
 !                             12 dx
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
     elseif(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
 !  fx(i) = --------------------------------
 !                     2 dx
     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
 ! set imax and imin 0
    endif
 ! y direction   
     if(Sfy(i,j,k) >= ZEO .and. j+4 <= jmax .and. j-2 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j-2,k)-F24*fh(i,j-1,k)-F35*fh(i,j,k)+F80*fh(i,j+1,k) &
                                   -F30*fh(i,j+2,k)+EIT*fh(i,j+3,k)-    fh(i,j+4,k))
     elseif(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-1 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j-1,k)-F77*fh(i,j  ,k)+F150*fh(i,j+1,k)-F100*fh(i,j+2,k) &
                                    +F50*fh(i,j+3,k)-F15*fh(i,j+4,k)+ TWO*fh(i,j+5,k))
     elseif(Sfy(i,j,k) <= ZEO .and. j-4 >= jmin .and. j+2 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j+2,k)-F24*fh(i,j+1,k)-F35*fh(i,j,k)+F80*fh(i,j-1,k) &
                                   -F30*fh(i,j-2,k)+EIT*fh(i,j-3,k)-    fh(i,j-4,k))
     elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+1 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j+1,k)-F77*fh(i,j  ,k)+F150*fh(i,j-1,k)-F100*fh(i,j-2,k) &
                                    +F50*fh(i,j-3,k)-F15*fh(i,j-4,k)+ TWO*fh(i,j-5,k))
     elseif(j+3 <= jmax .and. j-3 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
     elseif(j+2 <= jmax .and. j-2 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
     elseif(j+1 <= jmax .and. j-1 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
 ! set jmin and jmax 0
     endif
 !! z direction   
     if(Sfz(i,j,k) >= ZEO .and. k+4 <= kmax .and. k-2 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k-2)-F24*fh(i,j,k-1)-F35*fh(i,j,k)+F80*fh(i,j,k+1) &
                                   -F30*fh(i,j,k+2)+EIT*fh(i,j,k+3)-    fh(i,j,k+4))
     elseif(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-1 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k-1)-F77*fh(i,j,k  )+F150*fh(i,j,k+1)-F100*fh(i,j,k+2) &
                                    +F50*fh(i,j,k+3)-F15*fh(i,j,k+4)+ TWO*fh(i,j,k+5))
     elseif(Sfz(i,j,k) <= ZEO .and. k-4 >= kmin .and. k+2 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k+2)-F24*fh(i,j,k+1)-F35*fh(i,j,k)+F80*fh(i,j,k-1) &
                                   -F30*fh(i,j,k-2)+EIT*fh(i,j,k-3)-    fh(i,j,k-4))
     elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+1 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k+1)-F77*fh(i,j,k  )+F150*fh(i,j,k-1)-F100*fh(i,j,k-2) &
                                    +F50*fh(i,j,k-3)-F15*fh(i,j,k-4)+ TWO*fh(i,j,k-5))
     elseif(k+3 <= kmax .and. k-3 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
     elseif(k+2 <= kmax .and. k-2 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
     elseif(k+1 <= kmax .and. k-1 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
 ! set kmin and kmax 0
     endif
  enddo
  enddo
  enddo
  return
  end subroutine lopsided
 #elif (ghost_width == 5)
 ! eighth order code
 !-----------------------------------------------------------------------------
 ! PRD 77, 024034 (2008)
 ! Compute advection terms in right hand sides of field equations
 !        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
 ! D f = --------------------------------------------------------------------------------------------------------------------------
 !  i                                                             840 dx           
 !
 ! where
 !
 !        i
 !      |B |
 ! v = -----
 !        i
 !       B
 !
 !-----------------------------------------------------------------------------
 subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
  implicit none
 !~~~~~~> Input parameters:
  integer, intent(in)  :: ex(1:3),Symmetry
  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
  real*8,dimension(3),intent(in) ::SoA
 !~~~~~~> local variables:
  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
  real*8 :: dX,dY,dZ
  real*8 :: d840dx,d840dy,d840dz,d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
  real*8,  parameter :: TWO=2.d0,F30=3.d1,EIT=8.d0
  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1,F140=1.4d2,THR=3.d0
  real*8,  parameter :: F840=8.4d2,F5=5.d0,F420=4.2d2,F378=3.78d2,F1050=1.05d3
  real*8,  parameter :: F32=3.2d1,F168=1.68d2,F672=6.72d2
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
  dX = X(2)-X(1)
  dY = Y(2)-Y(1)
  dZ = Z(2)-Z(1)
  d840dx = ONE/F840/dX
  d840dy = ONE/F840/dY
  d840dz = ONE/F840/dZ
  d60dx = ONE/F60/dX
  d60dy = ONE/F60/dY
  d60dz = ONE/F60/dZ
  d12dx = ONE/F12/dX
  d12dy = ONE/F12/dY
  d12dz = ONE/F12/dZ
  d2dx = ONE/TWO/dX
  d2dy = ONE/TWO/dY
  d2dz = ONE/TWO/dZ
  imax = ex(1)
  jmax = ex(2)
  kmax = ex(3)
  imin = 1
  jmin = 1
  kmin = 1
  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
  call symmetry_bd(5,ex,f,fh,SoA)
 ! upper bound set ex-1 only for efficiency, 
 ! the loop body will set ex 0 also
  do k=1,ex(3)-1
  do j=1,ex(2)-1
  do i=1,ex(1)-1
 ! x direction   
    if(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-3 >= imin)then
 !        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
 ! D f = --------------------------------------------------------------------------------------------------------------------------
 !  i                                                             840 dx    
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
                  Sfx(i,j,k)*d840dx*(-F5*fh(i-3,j,k)+F60 *fh(i-2,j,k)-F420*fh(i-1,j,k)-F378*fh(i  ,j,k) &
                                  +F1050*fh(i+1,j,k)-F420*fh(i+2,j,k)+F140*fh(i+3,j,k)-F30 *fh(i+4,j,k)+THR*fh(i+5,j,k))
    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+3 <= imax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                          &
                  Sfx(i,j,k)*d840dx*(-F5*fh(i+3,j,k)+F60 *fh(i+2,j,k)-F420*fh(i+1,j,k)-F378*fh(i   ,j,k) &
                                  +F1050*fh(i-1,j,k)-F420*fh(i-2,j,k)+F140*fh(i-3,j,k)- F30*fh(i-4,j,k)+THR*fh(i-5,j,k))
    elseif(i+4 <= imax .and. i-4 >= imin)then
 !           3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
 !  fx(i) = -------------------------------------------------------------------------------------------------
 !                                                        840 dx
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
                  Sfx(i,j,k)*d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+    &
                                     F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
     elseif(i+3 <= imax .and. i-3 >= imin)then
 !           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
 !  fx(i) = -----------------------------------------------------------------
 !                                        60 dx
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
     elseif(i+2 <= imax .and. i-2 >= imin)then
 !
 !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
 !  fx(i) = ---------------------------------------------
 !                             12 dx
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
     elseif(i+1 <= imax .and. i-1 >= imin)then
 !
 !              - f(i-1) + f(i+1)
 !  fx(i) = --------------------------------
 !                     2 dx
     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
 ! set imax and imin 0
    endif
 ! y direction   
    if(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-3 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j-3,k)+F60 *fh(i,j-2,k)-F420*fh(i,j-1,k)-F378*fh(i,j  ,k) &
                                  +F1050*fh(i,j+1,k)-F420*fh(i,j+2,k)+F140*fh(i,j+3,k)-F30 *fh(i,j+4,k)+THR*fh(i,j+5,k))
    elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+3 <= jmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j+3,k)+F60 *fh(i,j+2,k)-F420*fh(i,j+1,k)-F378*fh(i,j  ,k) &
                                  +F1050*fh(i,j-1,k)-F420*fh(i,j-2,k)+F140*fh(i,j-3,k)- F30*fh(i,j-4,k)+THR*fh(i,j-5,k))
    elseif(j+4 <= jmax .and. j-4 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
                  Sfy(i,j,k)*d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+    &
                                     F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
     elseif(j+3 <= jmax .and. j-3 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
     elseif(j+2 <= jmax .and. j-2 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
     elseif(j+1 <= jmax .and. j-1 >= jmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
 ! set jmin and jmax 0
     endif
 !! z direction   
    if(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-3 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k-3)+F60 *fh(i,j,k-2)-F420*fh(i,j,k-1)-F378*fh(i,j,k  ) &
                                  +F1050*fh(i,j,k+1)-F420*fh(i,j,k+2)+F140*fh(i,j,k+3)-F30 *fh(i,j,k+4)+THR*fh(i,j,k+5))
    elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+3 <= kmax)then
     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k+3)+F60 *fh(i,j,k+2)-F420*fh(i,j,k+1)-F378*fh(i,j,k  ) &
                                  +F1050*fh(i,j,k-1)-F420*fh(i,j,k-2)+F140*fh(i,j,k-3)- F30*fh(i,j,k-4)+THR*fh(i,j,k-5))
    elseif(k+4 <= kmax .and. k-4 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
                  Sfz(i,j,k)*d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+    &
                                     F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
     elseif(k+3 <= kmax .and. k-3 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
     elseif(k+2 <= kmax .and. k-2 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
     elseif(k+1 <= kmax .and. k-1 >= kmin)then
     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
 ! set kmin and kmax 0
     endif
  enddo
  enddo
  enddo
  return
  end subroutine lopsided
 #endif  
--- a/AMSS_NCKU_source/macrodef.fh
+++ b/AMSS_NCKU_source/macrodef.fh
@@ -1,83 +1,77 @@
-
+
-
+#define tetradtype 2
-#if 0
+
-note here
+#define Cell
-v:r; u: phi; w: theta
+
-tetradtype 0
+#define ghost_width 3
-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
+#define GAUGE 0
-orthonormal order: w,u,v
+
-m = (theta + i phi)/sqrt(2) following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)
+#define CPBC_ghost_width  (ghost_width)
-tetradtype 2
+
-v_a = (x,y,z)
+#define ABV 0
-orthonormal order: v,u,w
+
-m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
+#define EScalar_CC 2
-#endif
+
-#define tetradtype 2
+#if 0
-
+
-#if 0
+define tetradtype
-note here
+    v:r; u: phi; w: theta
-Cell center or Vertex center
+    tetradtype 0
-#endif
+    v^a = (x,y,z)
-#define Cell
+    orthonormal order: v,u,w
-
+    m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
-#if 0
+    tetradtype 1
-note here
+    orthonormal order: w,u,v
-2nd order: 2
+    m = (theta + i phi)/sqrt(2) following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)
-4th order: 3
+    tetradtype 2
-6th order: 4
+    v_a = (x,y,z)
-8th order: 5
+    orthonormal order: v,u,w
-#endif
+    m = (phi - i theta)/sqrt(2) following Frans, Eq.(8) of  PRD 75, 124018(2007)
-#define ghost_width 3
+
-
+define Cell or Vertex
-#if 0
+    Cell center or Vertex center
-note here
+
-use shell or not
+define ghost_width
-#endif
+    2nd order: 2
-#define WithShell
+    4th order: 3
-
+    6th order: 4
-#if 0
+    8th order: 5
-note here
+
-use constraint preserving boundary condition or not
+define WithShell
-only affect Z4c
+    use shell or not
-#endif
+
-#define CPBC
+define CPBC
-
+    use constraint preserving boundary condition or not
-#if 0
+    only affect Z4c
-note here
+    CPBC only supports WithShell
-Gauge condition type
+
-0: B^i gauge
+define GAUGE
-1: David's puncture gauge
+    0: B^i gauge
-2: MB B^i gauge
+    1: David puncture gauge
-3: RIT B^i gauge
+    2: MB B^i gauge
-4: MB beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
+    3: RIT B^i gauge
-5: RIT beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
+    4: MB beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
-6: MGB1 B^i gauge
+    5: RIT beta gauge (beta gauge not means Eq.(3) of PRD 84, 124006)
-7: MGB2 B^i gauge
+    6: MGB1 B^i gauge
-#endif
+    7: MGB2 B^i gauge
-#define GAUGE 2
+
-
+define CPBC_ghost_width  (ghost_width)
-#if 0
+    buffer points for CPBC boundary
-buffer points for CPBC boundary
+
-#endif
+define ABV
-#define CPBC_ghost_width  (ghost_width)
+    0: using BSSN variable for constraint violation and psi4 calculation
-
+    1: using ADM variable for constraint violation and psi4 calculation
-#if 0
+
-using BSSN variable for constraint violation and psi4 calculation: 0
+define EScalar_CC
-using ADM variable for constraint violation and psi4 calculation: 1
+Type of Potential and Scalar Distribution in F(R) Scalar-Tensor Theory
-#endif
+    1: Case C of 1112.3928, V=0
-#define ABV 0
+    2: shell with   phi(r) = phi0 * a2^2/(1+a2^2), f(R) = R+a2*R^2 induced V
-
+    3: ground state of Schrodinger-Newton system,  f(R) = R+a2*R^2 induced V
-#if 0
+    4: a2 = +oo and phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma) - tanh((r-r0)/sigma) )
-Type of Potential and Scalar Distribution in F(R) Scalar-Tensor Theory
+    5: shell with   phi(r) = phi0 * Exp(-(r-r0)**2/sigma), V = 0
-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
+#endif
-3: ground state of Schrodinger-Newton system, f(R) = R+a2*R^2 induced V
+
 4: a2 = oo and phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma) - tanh((r-r0)/sigma) )
 5: shell with phi(r) = phi0*Exp(-(r-r0)**2/sigma), V = 0
 #endif
 #define EScalar_CC 2
--- a/AMSS_NCKU_source/macrodef.h
+++ b/AMSS_NCKU_source/macrodef.h
@@ -1,112 +1,145 @@
-
+
-#ifndef MICRODEF_H
+#ifndef MICRODEF_H
-#define MICRODEF_H
+#define MICRODEF_H
-
+
-#include "macrodef.fh"
+#include "macrodef.fh"  
-
+
-// application parameters
+// application parameters
-
+
-/// ****
+#define SommerType 0
-// sommerfeld boundary type
+
-// 0: bam, 1: shibata
+#define GaussInt
-#define SommerType 0
+
-
+#define ABEtype 0
-/// ****
+
-// for Using Gauss-Legendre quadrature in theta direction
+//#define With_AHF
-#define GaussInt
+#define Psi4type 0
-
+
-/// ****
+//#define Point_Psi4
-// 0: BSSN vacuum
+
-// 1: coupled to scalar field
+#define RPS 1
-// 2: Z4c vacuum
+
-// 3: coupled to Maxwell field
+#define AGM 0
-//
+
-#define ABEtype 2
+#define RPB 0
-
+
-/// ****
+#define MAPBH 1
-// using Apparent Horizon Finder
+
-//#define With_AHF
+#define PSTR 0
-
+
-/// ****
+#define REGLEV 0
-// Psi4 calculation method
+
-// 0: EB method
+//#define USE_GPU
-// 1: 4-D method
+
-//
+//#define CHECKDETAIL
-#define Psi4type 0
+
-
+//#define FAKECHECK
-/// ****
+
-// for Using point psi4 or not
+//
-//#define Point_Psi4
+// define SommerType
-
+//     sommerfeld boundary type
-/// ****
+//     0: bam
-// RestrictProlong in Step (0) or after Step (1)
+//     1: shibata
-#define RPS 1
+//
-
+// define GaussInt
-/// ****
+//     for Using Gauss-Legendre quadrature in theta direction
-// Enforce algebra constraint
+//
-// for every RK4 sub step: 0
+// define ABEtype
-// only when iter_count == 3: 1
+//     0: BSSN vacuum
-// after routine Step: 2
+//     1: coupled to scalar field
-#define AGM 0
+//     2: Z4c vacuum
-
+//     3: coupled to Maxwell field
-/// ****
+//
-// Restrict Prolong using BAM style 1 or old style 0
+// define With_AHF
-#define RPB 0
+//     using Apparent Horizon Finder
-
+//
-/// ****
+// define Psi4type
-// 1: move Analysis out ot 4 sub steps and treat PBH with Euler method
+//     Psi4 calculation method
-#define MAPBH 1
+//     0: EB method
-
+//     1: 4-D method
-/// ****
+//
-// parallel structure, 0: level by level, 1: considering all levels, 2: as 1 but reverse the CPU order, 3: Frank's scheme
+// define Point_Psi4
-#define PSTR 0
+//     for Using point psi4 or not
-
+//
-/// ****
+// define RPS
-// regrid for every level or for all levels at a time
+//     RestrictProlong in Step (0) or after Step (1)
-// 0: for every level; 1: for all
+//
-#define REGLEV 0
+// define AGM
-
+//     Enforce algebra constraint
-/// ****
+//     for every RK4 sub step: 0
-// use gpu or not
+//     only when iter_count == 3: 1
-//#define USE_GPU
+//     after routine Step: 2
-
+//
-/// ****
+// define RPB
-// use checkpoint for every process
+//     Restrict Prolong using BAM style 1 or old style 0
-//#define CHECKDETAIL
+//
-
+// define MAPBH
-/// ****
+//     1: move Analysis out ot 4 sub steps and treat PBH with Euler method
-// use FakeCheckPrepare to write CheckPoint
+//
-//#define FAKECHECK
+// define PSTR
-////================================================================
+//     parallel structure
-//  some basic parameters for numerical calculation
+//     0: level by level
-#define dim 3
+//     1: considering all levels
-
+//     2: as 1 but reverse the CPU order
-//#define Cell or Vertex in "microdef.fh"
+//     3: Frank's scheme
-
+//
-// ******
+// define REGLEV
-// buffer point number for mesh refinement interface
+//     regrid for every level or for all levels at a time
-#define buffer_width 6
+//     0: for every level;
-
+//     1: for all
-// ******
+//
-// buffer point number shell-box interface, on shell
+// define USE_GPU
-#define SC_width buffer_width
+//     use gpu or not
-// buffer point number shell-box interface, on box
+//
-#define CS_width (2*buffer_width)
+// define CHECKDETAIL
-
+//     use checkpoint for every process
-#if(buffer_width < ghost_width)
+//
-#error we always assume buffer_width>ghost_width
+// define FAKECHECK
-#endif
+//     use FakeCheckPrepare to write CheckPoint
-
+//
-#define PACK 1
+
-#define UNPACK 2
+////================================================================
-
+//  some basic parameters for numerical calculation
-#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
+////================================================================
-#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
+
-
+#define dim 3
-#define feq(a,b,d) (fabs(a-b)<d)
+
-#define flt(a,b,d) ((a-b)<d)
+//#define Cell or Vertex in "macrodef.fh" 
-#define fgt(a,b,d) ((a-b)>d)
+
-
+#define buffer_width 6
-#define TINY 1e-10
+
-
+#define SC_width buffer_width
-#endif   /* MICRODEF_H */
+
 #define CS_width (2*buffer_width)
 //
 // define Cell or Vertex in "macrodef.fh" 
 //
 // define buffer_width
 //     buffer point number for mesh refinement interface
 //
 // define SC_width buffer_width
 //     buffer point number shell-box interface, on shell
 //
 // define CS_width
 //     buffer point number shell-box interface, on box
 //
 #if(buffer_width < ghost_width)
 #   error we always assume buffer_width>ghost_width
 #endif
 #define PACK 1
 #define UNPACK 2
 #define Mymax(a,b) (((a) > (b)) ? (a) : (b))
 #define Mymin(a,b) (((a) < (b)) ? (a) : (b))
 #define feq(a,b,d) (fabs(a-b)<d)
 #define flt(a,b,d) ((a-b)<d)
 #define fgt(a,b,d) ((a-b)>d)
 #define TINY 1e-10
 #endif   /* MICRODEF_H */
--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -1,6 +1,35 @@
-include makefile.inc
+include makefile.inc
 ## polint(ordn=6) kernel selector:
 ##   1 (default): barycentric fast path
 ##   0          : fallback to Neville path
 POLINT6_USE_BARY ?= 1
 POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
 ## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
 ##   make                        -> opt  (PGO-guided, maximum performance)
 ##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
 PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 ifeq ($(PGO_MODE),instrument)
 ## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
 CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
 ## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
 ## PGO has been turned off, now tested and found to be negative optimization
 ## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
 .SUFFIXES: .o .f90 .C .for .cu
@@ -16,19 +45,65 @@ include makefile.inc
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 # C rewrite of BSSN RHS kernel and helpers
 bssn_rhs_c.o: bssn_rhs_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 fderivs_c.o: fderivs_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 fdderivs_c.o: fdderivs_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 kodiss_c.o: kodiss_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 lopsided_c.o: lopsided_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 lopsided_kodis_c.o: lopsided_kodis_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 #interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
 #	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
 TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
              -fprofile-instr-use=$(TP_PROFDATA) \
              -Dfortran3 -Dnewc -I${MKLROOT}/include
 TwoPunctures.o: TwoPunctures.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 # Input files
 ## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
 ifeq ($(USE_CXX_KERNELS),0)
 # Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
 CFILES =
 else
 # C++ mode (default): C rewrite of bssn_rhs and helper kernels
 CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
 endif
 ## RK4 kernel switch (independent from USE_CXX_KERNELS)
 ifeq ($(USE_CXX_RK4),1)
 CFILES += rungekutta4_rout_c.o
 RK4_F90_OBJ =
 else
 RK4_F90_OBJ = rungekutta4_rout.o
 endif
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
           cgh.o bssn_class.o surface_integral.o ShellPatch.o\
 	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
 	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o writefile_f.o
+	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.o
 C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
           cgh.o surface_integral.o ShellPatch.o\
@@ -38,12 +113,12 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
 	   NullShellPatch2_Evo.o \
 	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
-F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   rungekutta4_rout.o bssn_rhs.o diff_new.o kodiss.o kodiss_sh.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
           fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
 	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
 	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
@@ -51,6 +126,14 @@ F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
 	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
 	   NullNews2.o tool_f.o
 ifeq ($(USE_CXX_KERNELS),0)
 # Fortran mode: include original bssn_rhs.o
 F90FILES = $(F90FILES_BASE) bssn_rhs.o
 else
 # C++ mode (default): bssn_rhs.o replaced by C++ kernel
 F90FILES = $(F90FILES_BASE)
 endif
 F77FILES = zbesh.o
 AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \
@@ -63,7 +146,7 @@ TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o
 CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
 # file dependences
-$(C++FILES) $(C++FILESGPU) $(F90FILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
+$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
 $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
@@ -86,7 +169,7 @@ $(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h
 $(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
-$(C++FILES) $(C++FILES_GPU) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
 TwoPunctureFILES: TwoPunctures.h
@@ -95,14 +178,14 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o
 # projects
-ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
+ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
-ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
+ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -8,22 +8,56 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 ## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
 ## Memory allocator switch
 ##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
 ##   0           : use system default allocator (ptmalloc)
 USE_TBBMALLOC ?= 1
 TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
 ifneq ($(wildcard $(TBBMALLOC_SO)),)
 TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
 else
 TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
 endif
 ifeq ($(USE_TBBMALLOC),1)
 LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
 endif
 ## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
 ##   opt        : (default) maximum performance with PGO profile-guided optimization
 ##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
 PGO_MODE ?= opt
 ## Interp_Points load balance profiling mode
 ##   off        : (default) no load balance instrumentation
 ##   profile    : Pass 1 — instrument Interp_Points to collect timing profile
 ##   optimize   : Pass 2 — read profile and apply block rebalancing
 INTERP_LB_MODE ?= off
 ifeq ($(INTERP_LB_MODE),profile)
 INTERP_LB_FLAGS = -DINTERP_LB_PROFILE
 else ifeq ($(INTERP_LB_MODE),optimize)
 INTERP_LB_FLAGS = -DINTERP_LB_OPTIMIZE
 else
 INTERP_LB_FLAGS =
 endif
 ## Kernel implementation switch
 ##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
 ##   0           : fall back to original Fortran kernels
 USE_CXX_KERNELS ?= 0
 ## RK4 kernel implementation switch
 ##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
 ##   0           : use original Fortran rungekutta4_rout.o
 USE_CXX_RK4 ?= 0
 ## Aggressive optimization flags:
 ## -O3: Maximum optimization
 ## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
 ## -fp-model fast=2: Aggressive floating-point optimizations
 ## -fma: Enable fused multiply-add instructions
 CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
               -Dfortran3 -Dnewc -I${MKLROOT}/include
 f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx 
+CLINKER      = mpiicpx
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
--- a/AMSS_NCKU_source/prolongrestrict_cell.f90
+++ b/AMSS_NCKU_source/prolongrestrict_cell.f90
@@ -1934,18 +1934,35 @@
 ! when if=1 -> ic=0, this is different to vertex center grid 
  real*8, dimension(-2:extc(1),-2:extc(2),-2:extc(3))   :: funcc
  integer,dimension(3) :: cxI
-  integer :: i,j,k,ii,jj,kk
+  integer :: i,j,k,ii,jj,kk,px,py,pz
  real*8, dimension(6,6) :: tmp2
  real*8, dimension(6) :: tmp1
  integer, dimension(extf(1)) :: cix
  integer, dimension(extf(2)) :: ciy
  integer, dimension(extf(3)) :: ciz
  integer, dimension(extf(1)) :: pix
  integer, dimension(extf(2)) :: piy
  integer, dimension(extf(3)) :: piz
  real*8, parameter :: C1=7.7d1/8.192d3,C2=-6.93d2/8.192d3,C3=3.465d3/4.096d3
  real*8, parameter :: C6=6.3d1/8.192d3,C5=-4.95d2/8.192d3,C4=1.155d3/4.096d3
  real*8, dimension(6,2), parameter :: WC = reshape((/&
      C1,C2,C3,C4,C5,C6,&
      C6,C5,C4,C3,C2,C1/), (/6,2/))
  integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
  integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
  integer::maxcx,maxcy,maxcz
  real*8,dimension(3) :: CD,FD
-  
+  real*8 :: tmp_yz(extc(1), 6)      ! 存储整条 X 线上 6 个 Y 轴偏置的 Z 向插值结果
  real*8 :: tmp_xyz_line(-2:extc(1))   ! 包含 X 向 6 点模板访问所需下界
  real*8 :: v1, v2, v3, v4, v5, v6
  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max,ic_min,ic_max,kc_min,kc_max
  integer :: i_lo, i_hi, j_lo, j_hi, k_lo, k_hi
  logical :: need_full_symmetry
  real*8 :: res_line
  real*8 :: tmp_z_slab(-2:extc(1), -2:extc(2))  ! 包含 Y/X 向模板访问所需下界
  if(wei.ne.3)then
     write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
     write(*,*)"dim = ",wei
@@ -2020,145 +2037,140 @@
          return
  endif
-  call symmetry_bd(3,extc,func,funcc,SoA)
+  do i = imino,imaxo
-     
+     ii = i + lbf(1) - 1
-!~~~~~~> prolongation start...
+     cix(i) = ii/2 - lbc(1) + 1
     if(ii/2*2 == ii)then
        pix(i) = 1
     else
        pix(i) = 2
     endif
  enddo
  do j = jmino,jmaxo
     jj = j + lbf(2) - 1
     ciy(j) = jj/2 - lbc(2) + 1
     if(jj/2*2 == jj)then
        piy(j) = 1
     else
        piy(j) = 2
     endif
  enddo
  do k = kmino,kmaxo
-   do j = jmino,jmaxo
+     kk = k + lbf(3) - 1
-    do i = imino,imaxo
+     ciz(k) = kk/2 - lbc(3) + 1
-       cxI(1) = i
+     if(kk/2*2 == kk)then
-       cxI(2) = j
+        piz(k) = 1
-       cxI(3) = k
+     else
-! change to coarse level reference
+        piz(k) = 2
-!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---| 
+     endif
 !|=======x===============x===============x===============x=======|
       cxI = (cxI+lbf-1)/2
 ! change to array index      
       cxI = cxI - lbc + 1
       if(any(cxI+3 > extc)) write(*,*)"error in prolong"
       ii=i+lbf(1)-1
       jj=j+lbf(2)-1
       kk=k+lbf(3)-1
 #if 0
       if(ii/2*2==ii)then
         if(jj/2*2==jj)then
           if(kk/2*2==kk)then
             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
           else
             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
           endif
         else
           if(kk/2*2==kk)then
             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
           else
             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
           endif
         endif
       else
         if(jj/2*2==jj)then
           if(kk/2*2==kk)then               
             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
           else
             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
           endif
         else
           if(kk/2*2==kk)then
             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
           else
             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
           endif
         endif
       endif
 #else 
       if(kk/2*2==kk)then
             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
       else
             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
       endif
       if(jj/2*2==jj)then
             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
       else
             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
       endif
       if(ii/2*2==ii)then
             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
       else
             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
       endif
 #endif
    enddo
   enddo
  enddo
  ic_min = minval(cix(imino:imaxo))
  ic_max = maxval(cix(imino:imaxo))
  jc_min = minval(ciy(jmino:jmaxo))
  jc_max = maxval(ciy(jmino:jmaxo))
  kc_min = minval(ciz(kmino:kmaxo))
  kc_max = maxval(ciz(kmino:kmaxo))
  maxcx = ic_max
  maxcy = jc_max
  maxcz = kc_max
  if(maxcx+3 > extc(1) .or. maxcy+3 > extc(2) .or. maxcz+3 > extc(3))then
     write(*,*)"error in prolong"
     return
  endif
  i_lo = ic_min - 2
  i_hi = ic_max + 3
  j_lo = jc_min - 2
  j_hi = jc_max + 3
  k_lo = kc_min - 2
  k_hi = kc_max + 3
  need_full_symmetry = (i_lo < 1) .or. (j_lo < 1) .or. (k_lo < 1)
  if(need_full_symmetry)then
     call symmetry_bd(3,extc,func,funcc,SoA)
  else
     funcc(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi) = func(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi)
  endif
     ! 对每个 k（pz, kc 固定）预计算 Z 向插值的 2D 切片
 do k = kmino, kmaxo
    pz = piz(k); kc = ciz(k)
    ! --- Pass 1: Z 方向，只算一次 ---
    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
        do ii = ic_min-2, ic_max+3  ! 仅需的 ii 范围（对应 cix-2:cix+3）
            tmp_z_slab(ii, iy) = sum(WC(:,pz) * funcc(ii, iy, kc-2:kc+3))
        end do
    end do
    do j = jmino, jmaxo
        py = piy(j); jc = ciy(j)
        ! --- Pass 2: Y 方向 ---
        do ii = ic_min-2, ic_max+3
            tmp_xyz_line(ii) = sum(WC(:,py) * tmp_z_slab(ii, jc-2:jc+3))
        end do
        ! --- Pass 3: X 方向 ---
        do i = imino, imaxo
            funf(i,j,k) = sum(WC(:,pix(i)) * tmp_xyz_line(cix(i)-2:cix(i)+3))
        end do
    end do
 end do
 !~~~~~~> prolongation start...
 #if 0
 do k = kmino, kmaxo
     pz = piz(k)
     kc = ciz(k)
     do j = jmino, jmaxo
        py = piy(j)
        jc = ciy(j)
 ! --- 步骤 1 & 2 融合：分段处理 X 轴，提升 Cache 命中率 ---
        ! 我们将 ii 循环逻辑重组，减少对 funcc 的跨行重复访问
        do ii = 1, extc(1)
           ! 1. 先做 Z 方向的 6 条线插值（针对当前的 ii 和当前的 6 个 iy）
           ! 我们直接在这里把 Y 方向的加权也做了，省去 tmp_yz 数组
           ! 这样 funcc 的数据读进来后立即完成所有维度的贡献，不再写回内存
           res_line = 0.0d0
           do jj = 1, 6
              iy = jc - 3 + jj
              ! 这一行代码是核心：一次性完成 Z 插值并加上 Y 的权重
              ! 编译器会把 WC(jj, py) 存在寄存器里
              res_line = res_line + WC(jj, py) * ( &
                         WC(1, pz) * funcc(ii, iy, kc-2) + &
                         WC(2, pz) * funcc(ii, iy, kc-1) + &
                         WC(3, pz) * funcc(ii, iy, kc  ) + &
                         WC(4, pz) * funcc(ii, iy, kc+1) + &
                         WC(5, pz) * funcc(ii, iy, kc+2) + &
                         WC(6, pz) * funcc(ii, iy, kc+3) )
           end do
           tmp_xyz_line(ii) = res_line
        end do
        ! 3. 【降维：X 向】最后在最内层只处理 X 方向的 6 点加权
        ! 此时每个点的计算量从原来的 200+ 次乘法降到了仅 6 次
        do i = imino, imaxo
           px = pix(i)
           ic = cix(i)
           ! 直接从预计算好的 line 中读取连续的 6 个点
           ! ic-2 到 ic+3 对应原始 6 点算子
           funf(i,j,k) = WC(1,px)*tmp_xyz_line(ic-2) + &
                         WC(2,px)*tmp_xyz_line(ic-1) + &
                         WC(3,px)*tmp_xyz_line(ic  ) + &
                         WC(4,px)*tmp_xyz_line(ic+1) + &
                         WC(5,px)*tmp_xyz_line(ic+2) + &
                         WC(6,px)*tmp_xyz_line(ic+3)
        end do
     end do
  end do
 #endif
  return
  end subroutine prolong3
@@ -2357,7 +2369,14 @@
  integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
  real*8,dimension(3) :: CD,FD
-  
+
  real*8 :: tmp_xz_plane(-1:extf(1), 6)
  real*8 :: tmp_x_line(-1:extf(1))
  integer :: fi, fj, fk, ii, jj, kk
  integer :: fi_min, fi_max, ii_lo, ii_hi
  integer :: fj_min, fj_max, fk_min, fk_max, jj_lo, jj_hi, kk_lo, kk_hi
  logical :: need_full_symmetry
  if(wei.ne.3)then
     write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
     write(*,*)"dim = ",wei
@@ -2436,9 +2455,86 @@
          stop
  endif
-  call symmetry_bd(2,extf,funf,funff,SoA)
+  ! 仅计算 X 向最终写回所需的窗口：
  ! func(i,j,k) 只访问 tmp_x_line(fi-2:fi+3)
  fi_min = 2*(imino + lbc(1) - 1) - 1 - lbf(1) + 1
  fi_max = 2*(imaxo + lbc(1) - 1) - 1 - lbf(1) + 1
  fj_min = 2*(jmino + lbc(2) - 1) - 1 - lbf(2) + 1
  fj_max = 2*(jmaxo + lbc(2) - 1) - 1 - lbf(2) + 1
  fk_min = 2*(kmino + lbc(3) - 1) - 1 - lbf(3) + 1
  fk_max = 2*(kmaxo + lbc(3) - 1) - 1 - lbf(3) + 1
  ii_lo = fi_min - 2
  ii_hi = fi_max + 3
  jj_lo = fj_min - 2
  jj_hi = fj_max + 3
  kk_lo = fk_min - 2
  kk_hi = fk_max + 3
  if(ii_lo < -1 .or. ii_hi > extf(1) .or. &
     jj_lo < -1 .or. jj_hi > extf(2) .or. &
     kk_lo < -1 .or. kk_hi > extf(3))then
      write(*,*)"restrict3: invalid stencil window"
      write(*,*)"ii=",ii_lo,ii_hi," jj=",jj_lo,jj_hi," kk=",kk_lo,kk_hi
      write(*,*)"extf=",extf
      stop
  endif
  need_full_symmetry = (ii_lo < 1) .or. (jj_lo < 1) .or. (kk_lo < 1)
  if(need_full_symmetry)then
      call symmetry_bd(2,extf,funf,funff,SoA)
  else
      funff(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi) = funf(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi)
  endif
 !~~~~~~> restriction start...
 do k = kmino, kmaxo
    fk = 2*(k + lbc(3) - 1) - 1 - lbf(3) + 1
    do j = jmino, jmaxo
        fj = 2*(j + lbc(2) - 1) - 1 - lbf(2) + 1
        ! 优化点 1: 显式展开 Z 方向计算，减少循环开销
        ! 确保 ii 循环是最内层且连续访问
        !DIR$ VECTOR ALWAYS
        do ii = ii_lo, ii_hi
            ! 预计算当前 j 对应的 6 行在 Z 方向的压缩结果
            ! 这里直接硬编码 jj 的偏移，彻底消除一层循环
            tmp_xz_plane(ii, 1) = C1*(funff(ii,fj-2,fk-2)+funff(ii,fj-2,fk+3)) + &
                                  C2*(funff(ii,fj-2,fk-1)+funff(ii,fj-2,fk+2)) + &
                                  C3*(funff(ii,fj-2,fk  )+funff(ii,fj-2,fk+1))
            tmp_xz_plane(ii, 2) = C1*(funff(ii,fj-1,fk-2)+funff(ii,fj-1,fk+3)) + &
                                  C2*(funff(ii,fj-1,fk-1)+funff(ii,fj-1,fk+2)) + &
                                  C3*(funff(ii,fj-1,fk  )+funff(ii,fj-1,fk+1))
            tmp_xz_plane(ii, 3) = C1*(funff(ii,fj  ,fk-2)+funff(ii,fj  ,fk+3)) + &
                                  C2*(funff(ii,fj  ,fk-1)+funff(ii,fj  ,fk+2)) + &
                                  C3*(funff(ii,fj  ,fk  )+funff(ii,fj  ,fk+1))
            tmp_xz_plane(ii, 4) = C1*(funff(ii,fj+1,fk-2)+funff(ii,fj+1,fk+3)) + &
                                  C2*(funff(ii,fj+1,fk-1)+funff(ii,fj+1,fk+2)) + &
                                  C3*(funff(ii,fj+1,fk  )+funff(ii,fj+1,fk+1))
            tmp_xz_plane(ii, 5) = C1*(funff(ii,fj+2,fk-2)+funff(ii,fj+2,fk+3)) + &
                                  C2*(funff(ii,fj+2,fk-1)+funff(ii,fj+2,fk+2)) + &
                                  C3*(funff(ii,fj+2,fk  )+funff(ii,fj+2,fk+1))
            tmp_xz_plane(ii, 6) = C1*(funff(ii,fj+3,fk-2)+funff(ii,fj+3,fk+3)) + &
                                  C2*(funff(ii,fj+3,fk-1)+funff(ii,fj+3,fk+2)) + &
                                  C3*(funff(ii,fj+3,fk  )+funff(ii,fj+3,fk+1))
        end do
        ! 优化点 2: 同样向量化 Y 方向压缩
        !DIR$ VECTOR ALWAYS
        do ii = ii_lo, ii_hi
            tmp_x_line(ii) = C1*(tmp_xz_plane(ii, 1) + tmp_xz_plane(ii, 6)) + &
                            C2*(tmp_xz_plane(ii, 2) + tmp_xz_plane(ii, 5)) + &
                            C3*(tmp_xz_plane(ii, 3) + tmp_xz_plane(ii, 4))
        end do
        ! 优化点 3: 最终写入，利用已经缓存在 tmp_x_line 的数据
        do i = imino, imaxo
            fi = 2*(i + lbc(1) - 1) - 1 - lbf(1) + 1
            func(i, j, k) = C1*(tmp_x_line(fi-2) + tmp_x_line(fi+3)) + &
                            C2*(tmp_x_line(fi-1) + tmp_x_line(fi+2)) + &
                            C3*(tmp_x_line(fi  ) + tmp_x_line(fi+1))
        end do
    end do
 end do
 #if 0
  do k = kmino,kmaxo
   do j = jmino,jmaxo
    do i = imino,imaxo
@@ -2462,7 +2558,7 @@
    enddo
   enddo
  enddo
-  
+#endif
  return
  end subroutine restrict3
--- a/AMSS_NCKU_source/rungekutta4_rout_c.C
+++ b/AMSS_NCKU_source/rungekutta4_rout_c.C
@@ -0,0 +1,212 @@
 #include "rungekutta4_rout.h"
 #include <cstdio>
 #include <cstdlib>
 #include <cstddef>
 #include <complex>
 #include <immintrin.h>
 namespace {
 inline void rk4_stage0(std::size_t n,
                       const double *__restrict f0,
                       const double *__restrict frhs,
                       double *__restrict f1,
                       double c) {
    std::size_t i = 0;
 #if defined(__AVX512F__)
    const __m512d vc = _mm512_set1_pd(c);
    for (; i + 7 < n; i += 8) {
        const __m512d v0 = _mm512_loadu_pd(f0 + i);
        const __m512d vr = _mm512_loadu_pd(frhs + i);
        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, vr, v0));
    }
 #elif defined(__AVX2__)
    const __m256d vc = _mm256_set1_pd(c);
    for (; i + 3 < n; i += 4) {
        const __m256d v0 = _mm256_loadu_pd(f0 + i);
        const __m256d vr = _mm256_loadu_pd(frhs + i);
        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, vr, v0));
    }
 #endif
 #pragma ivdep
    for (; i < n; ++i) {
        f1[i] = f0[i] + c * frhs[i];
    }
 }
 inline void rk4_rhs_accum(std::size_t n,
                          const double *__restrict f1,
                          double *__restrict frhs) {
    std::size_t i = 0;
 #if defined(__AVX512F__)
    const __m512d v2 = _mm512_set1_pd(2.0);
    for (; i + 7 < n; i += 8) {
        const __m512d v1 = _mm512_loadu_pd(f1 + i);
        const __m512d vrhs = _mm512_loadu_pd(frhs + i);
        _mm512_storeu_pd(frhs + i, _mm512_fmadd_pd(v2, v1, vrhs));
    }
 #elif defined(__AVX2__)
    const __m256d v2 = _mm256_set1_pd(2.0);
    for (; i + 3 < n; i += 4) {
        const __m256d v1 = _mm256_loadu_pd(f1 + i);
        const __m256d vrhs = _mm256_loadu_pd(frhs + i);
        _mm256_storeu_pd(frhs + i, _mm256_fmadd_pd(v2, v1, vrhs));
    }
 #endif
 #pragma ivdep
    for (; i < n; ++i) {
        frhs[i] = frhs[i] + 2.0 * f1[i];
    }
 }
 inline void rk4_f1_from_f0_f1(std::size_t n,
                              const double *__restrict f0,
                              double *__restrict f1,
                              double c) {
    std::size_t i = 0;
 #if defined(__AVX512F__)
    const __m512d vc = _mm512_set1_pd(c);
    for (; i + 7 < n; i += 8) {
        const __m512d v0 = _mm512_loadu_pd(f0 + i);
        const __m512d v1 = _mm512_loadu_pd(f1 + i);
        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, v1, v0));
    }
 #elif defined(__AVX2__)
    const __m256d vc = _mm256_set1_pd(c);
    for (; i + 3 < n; i += 4) {
        const __m256d v0 = _mm256_loadu_pd(f0 + i);
        const __m256d v1 = _mm256_loadu_pd(f1 + i);
        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, v1, v0));
    }
 #endif
 #pragma ivdep
    for (; i < n; ++i) {
        f1[i] = f0[i] + c * f1[i];
    }
 }
 inline void rk4_stage3(std::size_t n,
                       const double *__restrict f0,
                       double *__restrict f1,
                       const double *__restrict frhs,
                       double c) {
    std::size_t i = 0;
 #if defined(__AVX512F__)
    const __m512d vc = _mm512_set1_pd(c);
    for (; i + 7 < n; i += 8) {
        const __m512d v0 = _mm512_loadu_pd(f0 + i);
        const __m512d v1 = _mm512_loadu_pd(f1 + i);
        const __m512d vr = _mm512_loadu_pd(frhs + i);
        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, _mm512_add_pd(v1, vr), v0));
    }
 #elif defined(__AVX2__)
    const __m256d vc = _mm256_set1_pd(c);
    for (; i + 3 < n; i += 4) {
        const __m256d v0 = _mm256_loadu_pd(f0 + i);
        const __m256d v1 = _mm256_loadu_pd(f1 + i);
        const __m256d vr = _mm256_loadu_pd(frhs + i);
        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, _mm256_add_pd(v1, vr), v0));
    }
 #endif
 #pragma ivdep
    for (; i < n; ++i) {
        f1[i] = f0[i] + c * (f1[i] + frhs[i]);
    }
 }
 } // namespace
 extern "C" {
 void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
    constexpr double F1o6 = 1.0 / 6.0;
    constexpr double HLF = 0.5;
    constexpr double TWO = 2.0;
    switch (RK4) {
    case 0:
        f1 = f0 + HLF * dT * f_rhs;
        break;
    case 1:
        f_rhs = f_rhs + TWO * f1;
        f1 = f0 + HLF * dT * f1;
        break;
    case 2:
        f_rhs = f_rhs + TWO * f1;
        f1 = f0 + dT * f1;
        break;
    case 3:
        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
        break;
    default:
        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
        std::abort();
    }
 }
 void rungekutta4_cplxscalar_(double &dT,
                             std::complex<double> &f0,
                             std::complex<double> &f1,
                             std::complex<double> &f_rhs,
                             int &RK4) {
    constexpr double F1o6 = 1.0 / 6.0;
    constexpr double HLF = 0.5;
    constexpr double TWO = 2.0;
    switch (RK4) {
    case 0:
        f1 = f0 + HLF * dT * f_rhs;
        break;
    case 1:
        f_rhs = f_rhs + TWO * f1;
        f1 = f0 + HLF * dT * f1;
        break;
    case 2:
        f_rhs = f_rhs + TWO * f1;
        f1 = f0 + dT * f1;
        break;
    case 3:
        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
        break;
    default:
        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
        std::abort();
    }
 }
 int f_rungekutta4_rout(int *ex, double &dT,
                       double *f0, double *f1, double *f_rhs,
                       int &RK4) {
    const std::size_t n = static_cast<std::size_t>(ex[0]) *
                          static_cast<std::size_t>(ex[1]) *
                          static_cast<std::size_t>(ex[2]);
    const double *const __restrict f0r = f0;
    double *const __restrict f1r = f1;
    double *const __restrict frhs = f_rhs;
    if (__builtin_expect(static_cast<unsigned>(RK4) > 3u, 0)) {
        std::fprintf(stderr, "rungekutta4_rout_c: invalid RK4 stage %d\n", RK4);
        std::abort();
    }
    switch (RK4) {
    case 0:
        rk4_stage0(n, f0r, frhs, f1r, 0.5 * dT);
        break;
    case 1:
        rk4_rhs_accum(n, f1r, frhs);
        rk4_f1_from_f0_f1(n, f0r, f1r, 0.5 * dT);
        break;
    case 2:
        rk4_rhs_accum(n, f1r, frhs);
        rk4_f1_from_f0_f1(n, f0r, f1r, dT);
        break;
    default:
        rk4_stage3(n, f0r, f1r, frhs, (1.0 / 6.0) * dT);
        break;
    }
    return 0;
 }
 } // extern "C"
--- a/AMSS_NCKU_source/share_func.h
+++ b/AMSS_NCKU_source/share_func.h
@@ -0,0 +1,246 @@
 #ifndef SHARE_FUNC_H
 #define SHARE_FUNC_H
 #include <stdlib.h>
 #include <stddef.h>
 #include <math.h>
 #include <stdio.h>
 #include <string.h>
 /* 主网格：0-based -> 1D */
 static inline size_t idx_ex(int i0, int j0, int k0, const int ex[3]) {
    const int ex1 = ex[0], ex2 = ex[1];
    return (size_t)i0 + (size_t)j0 * (size_t)ex1 + (size_t)k0 * (size_t)ex1 * (size_t)ex2;
 }
 /*
 * fh 对应 Fortran: fh(-1:ex1, -1:ex2, -1:ex3)
 * ord=2 => shift=1
 * iF/jF/kF 为 Fortran 索引（可为 -1,0,1..ex）
 */
 static inline size_t idx_fh_F_ord2(int iF, int jF, int kF, const int ex[3]) {
    const int shift = 1;
    const int nx = ex[0] + 2;      // ex1 + ord
    const int ny = ex[1] + 2;
    const int ii = iF + shift;     // 0..ex1+1
    const int jj = jF + shift;     // 0..ex2+1
    const int kk = kF + shift;     // 0..ex3+1
    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
 }
 /*
 * fh 对应 Fortran: fh(-2:ex1, -2:ex2, -2:ex3)
 * ord=3 => shift=2
 * iF/jF/kF 是 Fortran 索引（可为负）
 */
 static inline size_t idx_fh_F(int iF, int jF, int kF, const int ex[3]) {
    const int shift = 2;                 // ord=3 -> -2..ex
    const int nx = ex[0] + 3;            // ex1 + ord
    const int ny = ex[1] + 3;
    const int ii = iF + shift;           // 0..ex1+2
    const int jj = jF + shift;           // 0..ex2+2
    const int kk = kF + shift;           // 0..ex3+2
    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
 }
 /*
 * func:  (1..extc1, 1..extc2, 1..extc3)   1-based in Fortran
 * funcc: (-ord+1..extc1, -ord+1..extc2, -ord+1..extc3) in Fortran
 *
 * C 里我们把：
 *   func  视为 0-based: i0=0..extc1-1, j0=0..extc2-1, k0=0..extc3-1
 *   funcc 用“平移下标”存为一维数组：
 *     iF in [-ord+1..extc1]  -> ii = iF + (ord-1)  in [0..extc1+ord-1]
 *     总长度 nx = extc1 + ord
 *     同理 ny = extc2 + ord, nz = extc3 + ord
 */
 static inline size_t idx_func0(int i0, int j0, int k0, const int extc[3]) {
    const int nx = extc[0], ny = extc[1];
    return (size_t)i0 + (size_t)j0 * (size_t)nx + (size_t)k0 * (size_t)nx * (size_t)ny;
 }
 static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc[3]) {
    const int shift = ord - 1;          // iF = -shift .. extc1
    const int nx = extc[0] + ord;       // [-shift..extc1] 共 extc1+ord 个
    const int ny = extc[1] + ord;
    const int ii = iF + shift;          // 0..extc1+shift
    const int jj = jF + shift;          // 0..extc2+shift
    const int kk = kF + shift;          // 0..extc3+shift
    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
 }
 /*
 * 等价于 Fortran:
 * funcc(1:extc1,1:extc2,1:extc3)=func
 * do i=0,ord-1
 *   funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1)
 * enddo
 * do i=0,ord-1
 *   funcc(:,-i,1:extc3) = funcc(:,i+1,1:extc3)*SoA(2)
 * enddo
 * do i=0,ord-1
 *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
 * enddo
 */
 static inline void symmetry_bd_impl(int ord,
                 int shift,
                 const int extc[3],
                 const double *__restrict func,
                 double *__restrict funcc,
                 const double SoA[3])
 {
    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
    const int nx = extc1 + ord;
    const int ny = extc2 + ord;
    const size_t snx = (size_t)nx;
    const size_t splane = (size_t)nx * (size_t)ny;
    const size_t interior_i = (size_t)shift + 1u;          /* iF = 1 */
    const size_t interior_j = ((size_t)shift + 1u) * snx;  /* jF = 1 */
    const size_t interior_k = ((size_t)shift + 1u) * splane; /* kF = 1 */
    const size_t interior0 = interior_k + interior_j + interior_i;
    /* 1) funcc(1:extc1,1:extc2,1:extc3) = func */
    for (int k0 = 0; k0 < extc3; ++k0) {
        const double *src_k = func + (size_t)k0 * (size_t)extc2 * (size_t)extc1;
        const size_t dst_k0 = interior0 + (size_t)k0 * splane;
        for (int j0 = 0; j0 < extc2; ++j0) {
            const double *src = src_k + (size_t)j0 * (size_t)extc1;
            double *dst = funcc + dst_k0 + (size_t)j0 * snx;
            memcpy(dst, src, (size_t)extc1 * sizeof(double));
        }
    }
    /* 2) funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1) */
    const double s1 = SoA[0];
    if (s1 == 1.0) {
        for (int ii = 0; ii < ord; ++ii) {
            const size_t dst_i = (size_t)(shift - ii);
            const size_t src_i = (size_t)(shift + ii + 1);
            for (int k0 = 0; k0 < extc3; ++k0) {
                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
                for (int j0 = 0; j0 < extc2; ++j0) {
                    const size_t off = kbase + (size_t)j0 * snx;
                    funcc[off + dst_i] = funcc[off + src_i];
                }
            }
        }
    } else if (s1 == -1.0) {
        for (int ii = 0; ii < ord; ++ii) {
            const size_t dst_i = (size_t)(shift - ii);
            const size_t src_i = (size_t)(shift + ii + 1);
            for (int k0 = 0; k0 < extc3; ++k0) {
                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
                for (int j0 = 0; j0 < extc2; ++j0) {
                    const size_t off = kbase + (size_t)j0 * snx;
                    funcc[off + dst_i] = -funcc[off + src_i];
                }
            }
        }
    } else {
        for (int ii = 0; ii < ord; ++ii) {
            const size_t dst_i = (size_t)(shift - ii);
            const size_t src_i = (size_t)(shift + ii + 1);
            for (int k0 = 0; k0 < extc3; ++k0) {
                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
                for (int j0 = 0; j0 < extc2; ++j0) {
                    const size_t off = kbase + (size_t)j0 * snx;
                    funcc[off + dst_i] = funcc[off + src_i] * s1;
                }
            }
        }
    }
    /* 3) funcc(:,-j,1:extc3) = funcc(:,j+1,1:extc3)*SoA(2) */
    const double s2 = SoA[1];
    if (s2 == 1.0) {
        for (int jj = 0; jj < ord; ++jj) {
            const size_t dst_j = (size_t)(shift - jj) * snx;
            const size_t src_j = (size_t)(shift + jj + 1) * snx;
            for (int k0 = 0; k0 < extc3; ++k0) {
                const size_t kbase = interior_k + (size_t)k0 * splane;
                double *dst = funcc + kbase + dst_j;
                const double *src = funcc + kbase + src_j;
                for (int i = 0; i < nx; ++i) dst[i] = src[i];
            }
        }
    } else if (s2 == -1.0) {
        for (int jj = 0; jj < ord; ++jj) {
            const size_t dst_j = (size_t)(shift - jj) * snx;
            const size_t src_j = (size_t)(shift + jj + 1) * snx;
            for (int k0 = 0; k0 < extc3; ++k0) {
                const size_t kbase = interior_k + (size_t)k0 * splane;
                double *dst = funcc + kbase + dst_j;
                const double *src = funcc + kbase + src_j;
                for (int i = 0; i < nx; ++i) dst[i] = -src[i];
            }
        }
    } else {
        for (int jj = 0; jj < ord; ++jj) {
            const size_t dst_j = (size_t)(shift - jj) * snx;
            const size_t src_j = (size_t)(shift + jj + 1) * snx;
            for (int k0 = 0; k0 < extc3; ++k0) {
                const size_t kbase = interior_k + (size_t)k0 * splane;
                double *dst = funcc + kbase + dst_j;
                const double *src = funcc + kbase + src_j;
                for (int i = 0; i < nx; ++i) dst[i] = src[i] * s2;
            }
        }
    }
    /* 4) funcc(:,:,-k) = funcc(:,:,k+1)*SoA(3) */
    const double s3 = SoA[2];
    if (s3 == 1.0) {
        for (int kk = 0; kk < ord; ++kk) {
            const size_t dst_k = (size_t)(shift - kk) * splane;
            const size_t src_k = (size_t)(shift + kk + 1) * splane;
            double *dst = funcc + dst_k;
            const double *src = funcc + src_k;
            for (size_t p = 0; p < splane; ++p) dst[p] = src[p];
        }
    } else if (s3 == -1.0) {
        for (int kk = 0; kk < ord; ++kk) {
            const size_t dst_k = (size_t)(shift - kk) * splane;
            const size_t src_k = (size_t)(shift + kk + 1) * splane;
            double *dst = funcc + dst_k;
            const double *src = funcc + src_k;
            for (size_t p = 0; p < splane; ++p) dst[p] = -src[p];
        }
    } else {
        for (int kk = 0; kk < ord; ++kk) {
            const size_t dst_k = (size_t)(shift - kk) * splane;
            const size_t src_k = (size_t)(shift + kk + 1) * splane;
            double *dst = funcc + dst_k;
            const double *src = funcc + src_k;
            for (size_t p = 0; p < splane; ++p) dst[p] = src[p] * s3;
        }
    }
 }
 static inline void symmetry_bd(int ord,
                 const int extc[3],
                 const double *func,
                 double *funcc,
                 const double SoA[3])
 {
    if (ord <= 0) return;
    /* Fast paths used by current C kernels: ord=2 (derivs), ord=3 (lopsided/KO). */
    if (ord == 2) {
        symmetry_bd_impl(2, 1, extc, func, funcc, SoA);
        return;
    }
    if (ord == 3) {
        symmetry_bd_impl(3, 2, extc, func, funcc, SoA);
        return;
    }
    symmetry_bd_impl(ord, ord - 1, extc, func, funcc, SoA);
 }
 #endif
--- a/AMSS_NCKU_source/surface_integral.C
+++ b/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);
+  {
-
+    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    double scalar_in[7];
-  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&ang_outz, &sz, 1, 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];
-  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);
 #ifdef GaussInt
  mass = mass * rex * rex * dphi * factor;
@@ -2735,15 +2801,13 @@ 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);
+  {
-
+    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+    double scalar_in[7];
-  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, Comm_here);
-  MPI_Allreduce(&ang_outz, &sz, 1, 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];
-  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);
 #ifdef GaussInt
  mass = mass * rex * rex * dphi * factor;
@@ -3020,15 +3084,13 @@ 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);
+  {
-
+    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    double scalar_in[7];
-  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-  MPI_Allreduce(&ang_outz, &sz, 1, 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];
-  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);
 #ifdef GaussInt
  mass = mass * rex * rex * dphi * factor;
@@ -3607,8 +3669,17 @@ 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.
--- a/AMSS_NCKU_source/tool.h
+++ b/AMSS_NCKU_source/tool.h
@@ -0,0 +1,33 @@
 #include "share_func.h"
 void fdderivs(const int ex[3],
              const double *f,
              double *fxx, double *fxy, double *fxz,
              double *fyy, double *fyz, double *fzz,
              const double *X, const double *Y, const double *Z,
              double SYM1, double SYM2, double SYM3,
              int Symmetry, int onoff);
 void fderivs(const int ex[3],
             const double *f,
             double *fx, double *fy, double *fz,
             const double *X, const double *Y, const double *Z,
             double SYM1, double SYM2, double SYM3,
             int Symmetry, int onoff);
 void kodis(const int ex[3],
           const double *X, const double *Y, const double *Z,
           const double *f, double *f_rhs,
           const double SoA[3],
           int Symmetry, double eps);
 void lopsided(const int ex[3],
              const double *X, const double *Y, const double *Z,
              const double *f, double *f_rhs,
              const double *Sfx, const double *Sfy, const double *Sfz,
              int Symmetry, const double SoA[3]);
 void lopsided_kodis(const int ex[3],
                    const double *X, const double *Y, const double *Z,
                    const double *f, double *f_rhs,
                    const double *Sfx, const double *Sfy, const double *Sfz,
                    int Symmetry, const double SoA[3], double eps);
--- a/generate_interp_lb_header.py
+++ b/generate_interp_lb_header.py
@@ -0,0 +1,72 @@
 #!/usr/bin/env python3
 """Convert interp_lb_profile.bin to a C header for compile-time embedding."""
 import struct, sys
 if len(sys.argv) < 3:
    print(f"Usage: {sys.argv[0]} <profile.bin> <output.h>")
    sys.exit(1)
 with open(sys.argv[1], 'rb') as f:
    magic, version, nprocs, num_heavy = struct.unpack('IIii', f.read(16))
    threshold = struct.unpack('d', f.read(8))[0]
    times = list(struct.unpack(f'{nprocs}d', f.read(nprocs * 8)))
    heavy = list(struct.unpack(f'{num_heavy}i', f.read(num_heavy * 4)))
 # For each heavy rank, compute split: left half -> lighter neighbor, right half -> heavy rank
 # (or vice versa depending on which neighbor is lighter)
 splits = []
 for hr in heavy:
    prev_t = times[hr - 1] if hr > 0 else 1e30
    next_t = times[hr + 1] if hr < nprocs - 1 else 1e30
    if prev_t <= next_t:
        splits.append((hr, hr - 1, hr))  # (block_id, r_left, r_right)
    else:
        splits.append((hr, hr, hr + 1))
 # Also remap the displaced neighbor blocks
 remaps = {}
 for hr, r_l, r_r in splits:
    if r_l != hr:
        # We took r_l's slot, so remap block r_l to its other neighbor
        displaced = r_l
        if displaced > 0 and displaced - 1 not in [s[0] for s in splits]:
            remaps[displaced] = displaced - 1
        elif displaced < nprocs - 1:
            remaps[displaced] = displaced + 1
    else:
        displaced = r_r
        if displaced < nprocs - 1 and displaced + 1 not in [s[0] for s in splits]:
            remaps[displaced] = displaced + 1
        elif displaced > 0:
            remaps[displaced] = displaced - 1
 with open(sys.argv[2], 'w') as out:
    out.write("/* Auto-generated from interp_lb_profile.bin — do not edit */\n")
    out.write("#ifndef INTERP_LB_PROFILE_DATA_H\n")
    out.write("#define INTERP_LB_PROFILE_DATA_H\n\n")
    out.write(f"#define INTERP_LB_NPROCS {nprocs}\n")
    out.write(f"#define INTERP_LB_NUM_HEAVY {num_heavy}\n\n")
    out.write(f"static const int interp_lb_heavy_blocks[{num_heavy}] = {{")
    out.write(", ".join(str(h) for h in heavy))
    out.write("};\n\n")
    out.write("/* Split table: {block_id, r_left, r_right} */\n")
    out.write(f"static const int interp_lb_splits[{num_heavy}][3] = {{\n")
    for bid, rl, rr in splits:
        out.write(f"    {{{bid}, {rl}, {rr}}},\n")
    out.write("};\n\n")
    out.write("/* Rank remap for displaced neighbor blocks */\n")
    out.write(f"static const int interp_lb_num_remaps = {len(remaps)};\n")
    out.write(f"static const int interp_lb_remaps[][2] = {{\n")
    for src, dst in sorted(remaps.items()):
        out.write(f"    {{{src}, {dst}}},\n")
    if not remaps:
        out.write("    {-1, -1},\n")
    out.write("};\n\n")
    out.write("#endif /* INTERP_LB_PROFILE_DATA_H */\n")
 print(f"Generated {sys.argv[2]}:")
 print(f"  {num_heavy} heavy blocks to split: {heavy}")
 for bid, rl, rr in splits:
    print(f"    block {bid}: split -> rank {rl} (left), rank {rr} (right)")
 for src, dst in sorted(remaps.items()):
    print(f"    block {src}: remap -> rank {dst}")
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -11,16 +11,47 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 import time
 ## CPU core binding configuration using taskset
 ## taskset ensures all child processes inherit the CPU affinity mask
 ## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
 ## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
 NUMACTL_CPU_BIND = "taskset -c 0-111"
-## Build parallelism configuration
+
-## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
+def get_last_n_cores_per_socket(n=32):
-## Set make -j to utilize available cores for faster builds
+    """
-BUILD_JOBS = 104
+    Read CPU topology via lscpu and return a taskset -c string
    selecting the last `n` cores of each NUMA node (socket).
    Example: 2 sockets x 56 cores each, n=32 -> node0: 24-55, node1: 80-111
    -> "taskset -c 24-55,80-111"
    """
    result = subprocess.run(["lscpu", "--parse=NODE,CPU"], capture_output=True, text=True)
    # Build a dict: node_id -> sorted list of CPU ids
    node_cpus = {}
    for line in result.stdout.splitlines():
        if line.startswith("#") or not line.strip():
            continue
        parts = line.split(",")
        if len(parts) < 2:
            continue
        node_id, cpu_id = int(parts[0]), int(parts[1])
        node_cpus.setdefault(node_id, []).append(cpu_id)
    segments = []
    for node_id in sorted(node_cpus):
        cpus = sorted(node_cpus[node_id])
        selected = cpus[-n:]          # last n cores of this socket
        segments.append(f"{selected[0]}-{selected[-1]}")
    cpu_str = ",".join(segments)
    total = len(segments) * n
    print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
    #return f"taskset -c {cpu_str}"
    return f""
 ## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
 NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
 ## Build parallelism: match the number of bound cores
 BUILD_JOBS = 64
 ##################################################################
@@ -39,7 +70,7 @@ def makefile_ABE():
    ## Build command with CPU binding to nohz_full cores
    if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
    elif (input_data.GPU_Calculation == "yes"):
        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
    else:
@@ -117,6 +148,7 @@ def run_ABE():
    if (input_data.GPU_Calculation == "no"):
        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
        #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
        mpi_command_outfile = "ABE_out.log"
    elif (input_data.GPU_Calculation == "yes"):
        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
@@ -158,7 +190,8 @@ def run_TwoPunctureABE():
    print(                                                          )
    ## Define the command to run
-    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    #TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
    TwoPuncture_command         = " ./TwoPunctureABE"
    TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
    ## Execute the command with subprocess.Popen and stream output
--- a/parallel_plot_helper.py
+++ b/parallel_plot_helper.py
@@ -0,0 +1,29 @@
 import multiprocessing
 def run_plot_task(task):
    """Execute a single plotting task.
    Parameters
    ----------
    task : tuple
        A tuple of (function, args_tuple) where function is a callable
        plotting function and args_tuple contains its arguments.
    """
    func, args = task
    return func(*args)
 def run_plot_tasks_parallel(plot_tasks):
    """Execute a list of independent plotting tasks in parallel.
    Uses the 'fork' context to create worker processes so that the main
    script is NOT re-imported/re-executed in child processes.
    Parameters
    ----------
    plot_tasks : list of tuples
        Each element is (function, args_tuple).
    """
    ctx = multiprocessing.get_context('fork')
    with ctx.Pool() as pool:
        pool.map(run_plot_task, plot_tasks)
--- a/pgo_profile/TwoPunctureABE.profdata
+++ b/pgo_profile/TwoPunctureABE.profdata
--- a/pgo_profile/default.profdata
+++ b/pgo_profile/default.profdata
--- a/pgo_profile/default_9726853898452064389_0.profdata
+++ b/pgo_profile/default_9726853898452064389_0.profdata
--- a/pgo_profile/default_9726853898452064389_0.profraw
+++ b/pgo_profile/default_9726853898452064389_0.profraw
--- a/plot_GW_strain_amplitude_xiaoqu.py
+++ b/plot_GW_strain_amplitude_xiaoqu.py
@@ -11,6 +11,8 @@
 import numpy                               ## numpy for array operations
 import scipy                               ## scipy for interpolation and signal processing
 import math
 import matplotlib
 matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 import os                                  ## os for system/file operations
--- a/plot_binary_data.py
+++ b/plot_binary_data.py
@@ -8,16 +8,23 @@
 ##
 #################################################
 ## Restrict OpenMP to one thread per process so that running
 ## many workers in parallel does not create an O(workers * BLAS_threads)
 ## thread explosion.  The variable MUST be set before numpy/scipy
 ## are imported, because the BLAS library reads them only at load time.
 import os
 os.environ.setdefault("OMP_NUM_THREADS",        "1")
 import numpy
 import scipy
 import matplotlib
 matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt
 from   matplotlib.colors    import LogNorm
 from   mpl_toolkits.mplot3d import Axes3D
 ## import torch
 import AMSS_NCKU_Input      as input_data
 import os
 #########################################################################################
@@ -192,3 +199,19 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
 ####################################################################################
 ####################################################################################
 ## Allow this module to be run as a standalone script so that each
 ## binary-data plot can be executed in a fresh subprocess whose BLAS
 ## environment variables (set above) take effect before numpy loads.
 ##
 ## Usage:  python3 plot_binary_data.py <filename> <binary_outdir> <figure_outdir>
 ####################################################################################
 if __name__ == '__main__':
    import sys
    if len(sys.argv) != 4:
        print(f"Usage: {sys.argv[0]} <filename> <binary_outdir> <figure_outdir>")
        sys.exit(1)
    plot_binary_data(sys.argv[1], sys.argv[2], sys.argv[3])
--- a/plot_xiaoqu.py
+++ b/plot_xiaoqu.py
@@ -8,6 +8,8 @@
 #################################################
 import numpy                               ## numpy for array operations
 import matplotlib
 matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
 import glob
@@ -15,6 +17,9 @@ import os                                  ## operating system utilities
 import plot_binary_data
 import AMSS_NCKU_Input as input_data
 import subprocess
 import sys
 import multiprocessing
 # plt.rcParams['text.usetex'] = True  ## enable LaTeX fonts in plots
@@ -50,10 +55,40 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
        file_list.append(x)
        print(x)
-    ## Plot each file in the list
+    ## Plot each file in parallel using subprocesses.
    ## Each subprocess is a fresh Python process where the BLAS thread-count
    ## environment variables (set at the top of plot_binary_data.py) take
    ## effect before numpy is imported.  This avoids the thread explosion
    ## that occurs when multiprocessing.Pool with 'fork' context inherits
    ## already-initialized multi-threaded BLAS from the parent.
    script = os.path.join( os.path.dirname(__file__), "plot_binary_data.py" )
    max_workers = min( multiprocessing.cpu_count(), len(file_list) ) if file_list else 0
    running = []
    failed  = []
    for filename in file_list:
        print(filename)
-        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
+        proc = subprocess.Popen(
            [sys.executable, script, filename, binary_outdir, figure_outdir],
        )
        running.append( (proc, filename) )
        ## Keep at most max_workers subprocesses active at a time
        if len(running) >= max_workers:
            p, fn = running.pop(0)
            p.wait()
            if p.returncode != 0:
                failed.append(fn)
    ## Wait for all remaining subprocesses to finish
    for p, fn in running:
        p.wait()
        if p.returncode != 0:
            failed.append(fn)
    if failed:
        print( " WARNING: the following binary data plots failed:" )
        for fn in failed:
            print( "   ", fn )
    print(                        )
    print( " Binary Data Plot Has been Finished " )