1. Pass 1（357-395行）：遍历所有 Patch，对每个 block 计算含ghost zone 的实际体积，存入 block_volumes

2. Greedy LPT（397-414行）：按体积从大到小排序，依次分配给当前负载最小的 rank
  3. Pass 2（416-555行）：原来的 block创建循环，但用 assigned_ranks[block_idx++] 替代 n_rank++，Block
  构造时直接拿到正确的 rank，内存分配在对的进程上

.gitignore

@@ -1,2 +1,6 @@
 __pycache__
 GW150914
+GW150914-origin
+docs
+*.tmp
+

AMSS_NCKU_ABEtest.py

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

AMSS_NCKU_Input.py

@@ -16,7 +16,7 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 8                             ## number of mpi processes used in the simulation
+MPI_processes    = 64                             ## number of mpi processes used in the simulation
 
 GPU_Calculation  = "no"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)

AMSS_NCKU_Verify_ASC26.py

@@ -0,0 +1,279 @@
+#!/usr/bin/env python3
+"""
+AMSS-NCKU GW150914 Simulation Regression Test Script
+
+Verification Requirements:
+1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
+2. ADM constraint violation < 2 (Grid Level 0)
+
+RMS Calculation Method:
+- Computes trajectory deviation on the XY plane independently for BH1 and BH2
+- For each black hole: RMS = sqrt((1/M) * sum((Δr_i / r_i^max)^2)) × 100%
+- Final RMS = max(RMS_BH1, RMS_BH2)
+
+Usage: python3 AMSS_NCKU_Verify_ASC26.py [output_dir]
+Default: output_dir = GW150914/AMSS_NCKU_output
+Reference: GW150914-origin (baseline simulation)
+"""
+
+import numpy as np
+import sys
+import os
+
+# ANSI Color Codes
+class Color:
+    GREEN = '\033[92m'
+    RED = '\033[91m'
+    YELLOW = '\033[93m'
+    BLUE = '\033[94m'
+    BOLD = '\033[1m'
+    RESET = '\033[0m'
+
+def get_status_text(passed):
+    if passed:
+        return f"{Color.GREEN}{Color.BOLD}PASS{Color.RESET}"
+    else:
+        return f"{Color.RED}{Color.BOLD}FAIL{Color.RESET}"
+
+def load_bh_trajectory(filepath):
+    """Load black hole trajectory data"""
+    data = np.loadtxt(filepath)
+    return {
+        'time': data[:, 0],
+        'x1': data[:, 1], 'y1': data[:, 2], 'z1': data[:, 3],
+        'x2': data[:, 4], 'y2': data[:, 5], 'z2': data[:, 6]
+    }
+
+
+def load_constraint_data(filepath):
+    """Load constraint violation data"""
+    data = []
+    with open(filepath, 'r') as f:
+        for line in f:
+            if line.startswith('#'):
+                continue
+            parts = line.split()
+            if len(parts) >= 8:
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
+
+
+def calculate_rms_error(bh_data_ref, bh_data_target):
+    """
+    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
+
+    This function computes the RMS error independently for BH1 and BH2 trajectories,
+    then returns the maximum of the two as the final RMS error metric.
+
+    For each black hole, the RMS is calculated as:
+        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
+
+    where:
+        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
+        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
+
+    Args:
+        bh_data_ref: Reference (baseline) trajectory data
+        bh_data_target: Target (optimized) trajectory data
+
+    Returns:
+        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
+        error: Error message if any
+    """
+    # Align data: truncate to the length of the shorter dataset
+    M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
+
+    if M < 10:
+        return None, "Insufficient data points for comparison"
+
+    # Extract XY coordinates for both black holes
+    x1_ref = bh_data_ref['x1'][:M]
+    y1_ref = bh_data_ref['y1'][:M]
+    x2_ref = bh_data_ref['x2'][:M]
+    y2_ref = bh_data_ref['y2'][:M]
+
+    x1_new = bh_data_target['x1'][:M]
+    y1_new = bh_data_target['y1'][:M]
+    x2_new = bh_data_target['x2'][:M]
+    y2_new = bh_data_target['y2'][:M]
+
+    # Calculate RMS for BH1
+    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
+    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
+    r1_new = np.sqrt(x1_new**2 + y1_new**2)
+    r1_max = np.maximum(r1_ref, r1_new)
+
+    # Calculate RMS for BH2
+    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
+    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
+    r2_new = np.sqrt(x2_new**2 + y2_new**2)
+    r2_max = np.maximum(r2_ref, r2_new)
+
+    # Avoid division by zero for BH1
+    valid_mask1 = r1_max > 1e-15
+    if np.sum(valid_mask1) < 10:
+        return None, "Insufficient valid data points for BH1"
+
+    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
+    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+
+    # Avoid division by zero for BH2
+    valid_mask2 = r2_max > 1e-15
+    if np.sum(valid_mask2) < 10:
+        return None, "Insufficient valid data points for BH2"
+
+    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
+    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+
+    # Final RMS is the maximum of BH1 and BH2
+    rms_final = max(rms_bh1, rms_bh2)
+
+    return rms_final, None
+
+
+def analyze_constraint_violation(constraint_data, n_levels=9):
+    """
+    Analyze ADM constraint violation
+    Return maximum constraint violation for Grid Level 0
+    """
+    # Extract Grid Level 0 data (first entry for each time step)
+    level0_data = constraint_data[::n_levels]
+
+    # Calculate maximum absolute value for each constraint
+    results = {
+        'Ham': np.max(np.abs(level0_data[:, 1])),
+        'Px': np.max(np.abs(level0_data[:, 2])),
+        'Py': np.max(np.abs(level0_data[:, 3])),
+        'Pz': np.max(np.abs(level0_data[:, 4])),
+        'Gx': np.max(np.abs(level0_data[:, 5])),
+        'Gy': np.max(np.abs(level0_data[:, 6])),
+        'Gz': np.max(np.abs(level0_data[:, 7]))
+    }
+
+    results['max_violation'] = max(results.values())
+    return results
+
+
+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.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+
+def print_rms_results(rms_rel, error, threshold=1.0):
+    """Print RMS error results"""
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
+    print("-" * 45)
+
+    if error:
+        print(f"   {Color.RED}Error: {error}{Color.RESET}")
+        return False
+
+    passed = rms_rel < threshold
+
+    print(f"   RMS relative error: {rms_rel:.4f}%")
+    print(f"   Requirement:        < {threshold}%")
+    print(f"   Status:             {get_status_text(passed)}")
+
+    return 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)
+
+    names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
+    for i, name in enumerate(names):
+        print(f"   Max |{name:3}|: {results[name]:.6f}", end="   ")
+        if (i + 1) % 2 == 0: print()
+    if len(names) % 2 != 0: print()
+
+    passed = results['max_violation'] < threshold
+    
+    print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
+    print(f"   Requirement:        < {threshold}")
+    print(f"   Status:             {get_status_text(passed)}")
+
+    return passed
+
+
+def print_summary(rms_passed, constraint_passed):
+    """Print summary"""
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "Verification Summary" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+    all_passed = rms_passed and constraint_passed
+    
+    res_rms = get_status_text(rms_passed)
+    res_con = get_status_text(constraint_passed)
+
+    print(f"   [1] RMS trajectory check:         {res_rms}")
+    print(f"   [2] ADM constraint check:         {res_con}")
+    
+    final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
+    print(f"\n   Overall result: {final_status}")
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET + "\n")
+
+    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
+    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
+    rms_passed = print_rms_results(rms_rel, error)
+
+    # Analyze constraint violation
+    constraint_results = analyze_constraint_violation(constraint_data)
+    constraint_passed = print_constraint_results(constraint_results)
+
+    # Print summary
+    all_passed = print_summary(rms_passed, constraint_passed)
+
+    # Return exit code
+    sys.exit(0 if all_passed else 1)
+
+
+if __name__ == "__main__":
+    main()

AMSS_NCKU_source/FFT.f90

@@ -37,57 +37,51 @@ close(77)
 end program checkFFT
 #endif
 
+!-------------
+! Optimized FFT using Intel oneMKL DFTI
+! Mathematical equivalence: Standard DFT definition
+!   Forward (isign=1):  X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
+!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
+! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
 !-------------
 SUBROUTINE four1(dataa,nn,isign)
+use MKL_DFTI
 implicit none
-INTEGER::isign,nn
+INTEGER, intent(in) :: isign, nn
-double precision,dimension(2*nn)::dataa
+DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
-INTEGER::i,istep,j,m,mmax,n
+
-double precision::tempi,tempr
+type(DFTI_DESCRIPTOR), pointer :: desc
-DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
+integer :: status
-n=2*nn
+
-j=1
+! Create DFTI descriptor for 1D complex-to-complex transform
-do i=1,n,2
+status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
-  if(j.gt.i)then
+if (status /= 0) return
-     tempr=dataa(j)
+
-     tempi=dataa(j+1)
+! Set input/output storage as interleaved complex (default)
-     dataa(j)=dataa(i)
+status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
-     dataa(j+1)=dataa(i+1)
+if (status /= 0) then
-     dataa(i)=tempr
+   status = DftiFreeDescriptor(desc)
-     dataa(i+1)=tempi
+   return
-  endif
-  m=nn
-1 if ((m.ge.2).and.(j.gt.m)) then
-  j=j-m
-  m=m/2
-goto 1
-  endif
-j=j+m
-enddo
-mmax=2
-2  if (n.gt.mmax) then
-     istep=2*mmax
-     theta=6.28318530717959d0/(isign*mmax)
-     wpr=-2.d0*sin(0.5d0*theta)**2
-     wpi=sin(theta)
-     wr=1.d0
-     wi=0.d0
-     do m=1,mmax,2
-       do i=m,n,istep
-         j=i+mmax
-         tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
-         tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
-         dataa(j)=dataa(i)-tempr
-         dataa(j+1)=dataa(i+1)-tempi
-         dataa(i)=dataa(i)+tempr
-         dataa(i+1)=dataa(i+1)+tempi
-       enddo
-          wtemp=wr
-          wr=wr*wpr-wi*wpi+wr
-          wi=wi*wpr+wtemp*wpi+wi
-     enddo
-mmax=istep
-goto 2
 endif
+
+! Commit the descriptor
+status = DftiCommitDescriptor(desc)
+if (status /= 0) then
+   status = DftiFreeDescriptor(desc)
+   return
+endif
+
+! Execute FFT based on direction
+if (isign == 1) then
+   ! Forward FFT: exp(-2*pi*i*k*n/N)
+   status = DftiComputeForward(desc, dataa)
+else
+   ! Backward FFT: exp(+2*pi*i*k*n/N)
+   status = DftiComputeBackward(desc, dataa)
+endif
+
+! Free descriptor
+status = DftiFreeDescriptor(desc)
+
 return
 END SUBROUTINE four1

AMSS_NCKU_source/Parallel.C

@@ -4,6 +4,8 @@
 #include "prolongrestrict.h"
 #include "misc.h"
 #include "parameters.h"
+#include <vector>
+#include <algorithm>
 
 int Parallel::partition1(int &nx, int split_size, int min_width, int cpusize, int shape) // special for 1 diemnsion
 {
@@ -72,14 +74,14 @@ int Parallel::partition3(int *nxyz, int split_size, int *min_width, int cpusize,
   int n;
 
   block_size = shape[0] * shape[1] * shape[2];
-  n = Mymax(1, (block_size + split_size / 2) / split_size);
+  n =  Mymax(1, (block_size + split_size / 2) / split_size);
 
   maxnx = Mymax(1, shape[0] / min_width[0]);
-  maxnx = Mymin(cpusize, maxnx);
+  maxnx =  Mymin(cpusize, maxnx);
   maxny = Mymax(1, shape[1] / min_width[1]);
-  maxny = Mymin(cpusize, maxny);
+  maxny =  Mymin(cpusize, maxny);
   maxnz = Mymax(1, shape[2] / min_width[2]);
-  maxnz = Mymin(cpusize, maxnz);
+  maxnz =  Mymin(cpusize, maxnz);
   fx = (double)shape[0] / (shape[0] + shape[1] + shape[2]);
   fy = (double)shape[1] / (shape[0] + shape[1] + shape[2]);
   fz = (double)shape[2] / (shape[0] + shape[1] + shape[2]);
@@ -352,14 +354,73 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
   split_size = Mymax(min_size, block_size / nodes);
   split_size = Mymax(1, split_size);
 
-  int n_rank = 0;
+  // Pass 1: compute block volumes for greedy rank assignment
+  std::vector<long> block_volumes;
   PLi = PatchLIST;
   int reacpu = 0;
   while (PLi)
   {
     Patch *PP = PLi->data;
-
     reacpu += partition3(nxyz, split_size, mmin_width, nodes, PP->shape);
+    int ibbox_here[2 * dim];
+    for (int i = 0; i < nxyz[0]; i++)
+      for (int j = 0; j < nxyz[1]; j++)
+        for (int k = 0; k < nxyz[2]; k++)
+        {
+          ibbox_here[0] = (PP->shape[0] * i) / nxyz[0];
+          ibbox_here[3] = (PP->shape[0] * (i + 1)) / nxyz[0] - 1;
+          ibbox_here[1] = (PP->shape[1] * j) / nxyz[1];
+          ibbox_here[4] = (PP->shape[1] * (j + 1)) / nxyz[1] - 1;
+          ibbox_here[2] = (PP->shape[2] * k) / nxyz[2];
+          ibbox_here[5] = (PP->shape[2] * (k + 1)) / nxyz[2] - 1;
+          if (periodic)
+          {
+            for (int d = 0; d < dim; d++) { ibbox_here[d] -= ghost_width; ibbox_here[dim + d] += ghost_width; }
+          }
+          else
+          {
+            ibbox_here[0] = Mymax(0, ibbox_here[0] - ghost_width);
+            ibbox_here[3] = Mymin(PP->shape[0] - 1, ibbox_here[3] + ghost_width);
+            ibbox_here[1] = Mymax(0, ibbox_here[1] - ghost_width);
+            ibbox_here[4] = Mymin(PP->shape[1] - 1, ibbox_here[4] + ghost_width);
+            ibbox_here[2] = Mymax(0, ibbox_here[2] - ghost_width);
+            ibbox_here[5] = Mymin(PP->shape[2] - 1, ibbox_here[5] + ghost_width);
+          }
+          long vol = 1;
+          for (int d = 0; d < dim; d++)
+            vol *= (ibbox_here[dim + d] - ibbox_here[d] + 1);
+          block_volumes.push_back(vol);
+        }
+    PLi = PLi->next;
+  }
+
+  // Greedy LPT: sort by volume descending, assign each to least-loaded rank
+  std::vector<int> assigned_ranks(block_volumes.size());
+  {
+    std::vector<int> order(block_volumes.size());
+    for (int i = 0; i < (int)order.size(); i++) order[i] = i;
+    std::sort(order.begin(), order.end(), [&](int a, int b) {
+      return block_volumes[a] > block_volumes[b];
+    });
+    std::vector<long> load(cpusize, 0);
+    for (int idx : order)
+    {
+      int min_r = 0;
+      for (int r = 1; r < cpusize; r++)
+        if (load[r] < load[min_r]) min_r = r;
+      assigned_ranks[idx] = min_r;
+      load[min_r] += block_volumes[idx];
+    }
+  }
+
+  // Pass 2: create blocks with pre-assigned ranks
+  int block_idx = 0;
+  PLi = PatchLIST;
+  while (PLi)
+  {
+    Patch *PP = PLi->data;
+
+    partition3(nxyz, split_size, mmin_width, nodes, PP->shape);
 
     Block *ng0, *ng;
     int shape_here[dim], ibbox_here[2 * dim];
@@ -443,10 +504,7 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
             int shape_res[dim * pices];
             double bbox_res[2 * dim * pices];
             misc::dividBlock(dim, shape_here, bbox_here, pices, picef, shape_res, bbox_res, min_width);
-            ng = ng0 = new Block(dim, shape_res, bbox_res, n_rank++, ingfsi, fngfsi, PP->lev, 0); // delete through KillBlocks
+            ng = ng0 = new Block(dim, shape_res, bbox_res, assigned_ranks[block_idx++], ingfsi, fngfsi, PP->lev, 0); // delete through KillBlocks
-
-            //	       if(n_rank==cpusize) {n_rank=0; cerr<<"place one!!"<<endl;}
-
             //	       ng->checkBlock();
             if (BlL)
               BlL->insert(ng);
@@ -455,22 +513,19 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
 
             for (int i = 1; i < pices; i++)
             {
-              ng = new Block(dim, shape_res + i * dim, bbox_res + i * 2 * dim, n_rank++, ingfsi, fngfsi, PP->lev, i); // delete through KillBlocks
+              ng = new Block(dim, shape_res + i * dim, bbox_res + i * 2 * dim, assigned_ranks[block_idx++], ingfsi, fngfsi, PP->lev, i); // delete through KillBlocks
-              //	        if(n_rank==cpusize) {n_rank=0; cerr<<"place two!! "<<i<<endl;}
               //	        ng->checkBlock();
               BlL->insert(ng);
             }
           }
 #else
-          ng = ng0 = new Block(dim, shape_here, bbox_here, n_rank++, ingfsi, fngfsi, PP->lev); // delete through KillBlocks
+          ng = ng0 = new Block(dim, shape_here, bbox_here, assigned_ranks[block_idx++], ingfsi, fngfsi, PP->lev); // delete through KillBlocks
           //	    ng->checkBlock();
           if (BlL)
             BlL->insert(ng);
           else
             BlL = new MyList<Block>(ng); // delete through KillBlocks
 #endif
-          if (n_rank == cpusize)
-            n_rank = 0;
 
           // set PP->blb
           if (i == 0 && j == 0 && k == 0)
@@ -3504,7 +3559,7 @@ int Parallel::data_packermix(double *data, MyList<Parallel::gridseg> *src, MyLis
 
   return size_out;
 }
-//
+
 void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridseg> **dst,
                         MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
                         int Symmetry)
@@ -3512,13 +3567,20 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
   int myrank, cpusize;
   MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-
+/*
+  // Early exit: if no gridseg pairs exist for any node, skip all work
+  {
+    bool has_segs = false;
+    for (int n = 0; n < cpusize; n++) {
+      if (src[n] && dst[n]) { has_segs = true; break; }
+    }
+    if (!has_segs) return;
+  }
+*/
   int node;
 
-  MPI_Request *reqs;
+  MPI_Request *reqs = new MPI_Request[2 * cpusize];
-  MPI_Status *stats;
+  MPI_Status *stats = new MPI_Status[2 * cpusize];
-  reqs = new MPI_Request[2 * cpusize];
-  stats = new MPI_Status[2 * cpusize];
   int req_no = 0;
 
   double **send_data, **rec_data;
@@ -3527,49 +3589,41 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
   int length;
 
   for (node = 0; node < cpusize; node++)
-  {
     send_data[node] = rec_data[node] = 0;
+
+  // 第1步: 本地拷贝 + 所有 Irecv
+  for (node = 0; node < cpusize; node++)
+  {
     if (node == myrank)
     {
       if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
       {
         rec_data[node] = new double[length];
-        if (!rec_data[node])
-        {
-          cout << "out of memory when new in short transfer, place 1" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
         data_packer(rec_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
       }
     }
     else
     {
-      // send from this cpu to cpu#node
-      if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
-      {
-        send_data[node] = new double[length];
-        if (!send_data[node])
-        {
-          cout << "out of memory when new in short transfer, place 2" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        data_packer(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
-      }
-      // receive from cpu#node to this cpu
       if (length = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry))
       {
         rec_data[node] = new double[length];
-        if (!rec_data[node])
-        {
-          cout << "out of memory when new in short transfer, place 3" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
         MPI_Irecv((void *)rec_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
       }
     }
   }
-  // wait for all requests to complete
+
+  // 第2步: pack + Isend
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+    if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
+    {
+      send_data[node] = new double[length];
+      data_packer(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      MPI_Isend((void *)send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
+    }
+  }
+
   MPI_Waitall(req_no, reqs, stats);
 
   for (node = 0; node < cpusize; node++)

AMSS_NCKU_source/TwoPunctures.h

@@ -1,7 +1,8 @@
-
 #ifndef TWO_PUNCTURES_H
 #define TWO_PUNCTURES_H
 
+#include <omp.h>
+
 #define StencilSize 19
 #define N_PlaneRelax 1
 #define NRELAX 200
@@ -32,7 +33,7 @@ private:
        int npoints_A, npoints_B, npoints_phi;
 
        double target_M_plus, target_M_minus;
-       
+
        double admMass;
 
        double adm_tol;
@@ -42,6 +43,18 @@ private:
 
        int ntotal;
 
+       // ===== Precomputed spectral derivative matrices =====
+       double *D1_A, *D2_A;
+       double *D1_B, *D2_B;
+       double *DF1_phi, *DF2_phi;
+
+       // ===== Pre-allocated workspace for LineRelax (per-thread) =====
+       int max_threads;
+       double **ws_diag_be, **ws_e_be, **ws_f_be, **ws_b_be, **ws_x_be;
+       double **ws_l_be, **ws_u_be, **ws_d_be, **ws_y_be;
+       double **ws_diag_al, **ws_e_al, **ws_f_al, **ws_b_al, **ws_x_al;
+       double **ws_l_al, **ws_u_al, **ws_d_al, **ws_y_al;
+
        struct parameters
        {
               int nvar, n1, n2, n3;
@@ -58,6 +71,28 @@ public:
                     int Newtonmaxit);
        ~TwoPunctures();
 
+       // 02/07: New/modified methods
+       void allocate_workspace();
+       void free_workspace();
+       void precompute_derivative_matrices();
+       void build_cheb_deriv_matrices(int n, double *D1, double *D2);
+       void build_fourier_deriv_matrices(int N, double *DF1, double *DF2);
+       void Derivatives_AB3_MatMul(int nvar, int n1, int n2, int n3, derivs v);
+       void ThomasAlgorithm_ws(int N, double *b, double *a, double *c, double *x, double *q,
+                                double *l, double *u_ws, double *d, double *y);
+       void LineRelax_be_omp(double *dv,
+                         int const i, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols, int **cols,
+                         double **JFD, int tid);
+       void LineRelax_al_omp(double *dv,
+                         int const j, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols,
+                         int **cols, double **JFD, int tid);
+       void relax_omp(double *dv, int const nvar, int const n1, int const n2, int const n3,
+                  double const *rhs, int const *ncols, int **cols, double **JFD);
+
        void Solve();
        void set_initial_guess(derivs v);
        int index(int i, int j, int k, int l, int a, int b, int c, int d);
@@ -116,23 +151,11 @@ public:
        double BY_KKofxyz(double x, double y, double z);
        void SetMatrix_JFD(int nvar, int n1, int n2, int n3, derivs u, int *ncols, int **cols, double **Matrix);
        void J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, double *Jdv, derivs u);
-       void relax(double *dv, int const nvar, int const n1, int const n2, int const n3,
-                  double const *rhs, int const *ncols, int **cols, double **JFD);
-       void LineRelax_be(double *dv,
-                         int const i, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols, int **cols,
-                         double **JFD);
        void JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
                          int n3, derivs dv, derivs u, double *values);
        void LinEquations(double A, double B, double X, double R,
                          double x, double r, double phi,
                          double y, double z, derivs dU, derivs U, double *values);
-       void LineRelax_al(double *dv,
-                         int const j, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols,
-                         int **cols, double **JFD);
        void ThomasAlgorithm(int N, double *b, double *a, double *c, double *x, double *q);
        void Save(char *fname);
        // provided by Vasileios Paschalidis (vpaschal@illinois.edu)
@@ -141,4 +164,4 @@ public:
        void SpecCoef(parameters par, int ivar, double *v, double *cf);
 };
 
-#endif /* TWO_PUNCTURES_H */
+#endif /* TWO_PUNCTURES_H */

AMSS_NCKU_source/bssn_rhs.f90

@@ -106,7 +106,8 @@
   call getpbh(BHN,Porg,Mass)
 #endif
 
-!!! sanity check
+!!! sanity check (disabled in production builds for performance)
+#ifdef DEBUG
   dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
       +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
       +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -136,6 +137,7 @@
      gont = 1
      return
   endif
+#endif
 
   PI = dacos(-ONE)
 
@@ -159,36 +161,8 @@
 
   chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
 
-  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
-  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
-  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
 
-  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
-              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
 
-  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
-              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
-
-  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
-              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
-
-  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
-                      gxx * betaxy                  +   gxz * betazy + &
-                                       gyy * betayx +   gyz * betazx   &
-                                                    -   gxy * betazz
-
-  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
-                      gxy * betaxz +   gyy * betayz                  + &
-                      gxz * betaxy                  +   gzz * betazy   &
-                                                    -   gyz * betaxx
- 
-  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
-                      gxx * betaxz +   gxy * betayz                  + &
-                                       gyz * betayx +   gzz * betazx   &
-                                                    -   gxz * betayy     !rhs for gij
 
 ! invert tilted metric
   gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
@@ -199,7 +173,12 @@
   gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
   gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
   gupzz =   ( gxx * gyy - gxy * gxy ) / gupzz
-
+  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
+  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
+  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
   if(co == 0)then
 ! Gam^i_Res = Gam^i + gup^ij_,j
   Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
@@ -945,99 +924,99 @@
 
 !!!!!!!!!advection term part
 
+  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
+              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
+
+  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
+              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
+
+  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
+              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
+
+  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
+                      gxx * betaxy                  +   gxz * betazy + &
+                                        gyy * betayx +   gyz * betazx   &
+                                                    -   gxy * betazz
+
+  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
+                      gxy * betaxz +   gyy * betayz                  + &
+                      gxz * betaxy                  +   gzz * betazy   &
+                                                    -   gyz * betaxx
+
+  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
+                      gxx * betaxz +   gxy * betayz                  + &
+                                        gyz * betayx +   gzz * betazx   &
+                                                    -   gxz * betayy     !rhs for gij
+
+
+
+
+
+  if(eps>0)then 
+! usual Kreiss-Oliger dissipation     
+  call merge_lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps) 
+  call merge_lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call merge_lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+
+
+
+
+
+
+
+
+
+
+
+
+  else 
   call lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS)
   call lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA)
   call lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA)
   call lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS)
-
   call lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS)
   call lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA)
   call lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA)
   call lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS)
-
   call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
   call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)
-
   call lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
-!!
   call lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS)
-
-#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA)
-#endif
-
-#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA)
-#endif
 
-  if(eps>0)then 
-! usual Kreiss-Oliger dissipation      
-  call kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps)
-  call kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps)
-  call kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps)
-#if 0
-#define i 42
-#define j 40
-#define k 40
-if(Lev == 1)then
-write(*,*) X(i),Y(j),Z(k)
-write(*,*) "before",Axx_rhs(i,j,k)
-endif
-#undef i
-#undef j
-#undef k
-!!stop
-#endif
-  call kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps)
-#if 0
-#define i 42
-#define j 40
-#define k 40
-if(Lev == 1)then
-write(*,*) X(i),Y(j),Z(k)
-write(*,*) "after",Axx_rhs(i,j,k)
-endif
-#undef i
-#undef j
-#undef k
-!!stop
-#endif
-  call kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps)
-
-#if 1 
-!! bam does not apply dissipation on gauge variables
-  call kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps)
-#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
-  call kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps)
-  call kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps)
-#endif
-#endif
 
   endif
 
@@ -1184,3 +1163,265 @@ endif
   return
 
   end function compute_rhs_bssn
+
+
+
+
+  subroutine merge_lopsided_kodis(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,eps)
+    implicit none
+
+  !~~~~~~> Input parameters:
+
+    integer, intent(in)  :: ex(1:3),Symmetry
+    real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+    real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+    real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+    real*8,dimension(3),intent(in) ::SoA
+
+  !~~~~~~> local variables:
+  ! note index -2,-1,0, so we have 3 extra points
+    real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3))   :: fh
+    integer :: imin_lopsided,jmin_lopsided,kmin_lopsided,imin_kodis,jmin_kodis,kmin_kodis,imax,jmax,kmax,i,j,k
+    real*8 :: dX,dY,dZ
+    real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+    real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
+    real*8,  parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
+    real*8,  parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
+    integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+    real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
+    real*8,parameter::cof=6.4d1   ! 2^6
+    real*8,intent(in) :: eps
+    dX = X(2)-X(1)
+    dY = Y(2)-Y(1)
+    dZ = Z(2)-Z(1)
+
+    d12dx = ONE/F12/dX
+    d12dy = ONE/F12/dY
+    d12dz = ONE/F12/dZ
+
+    d2dx = ONE/TWO/dX
+    d2dy = ONE/TWO/dY
+    d2dz = ONE/TWO/dZ
+
+    imax = ex(1)
+    jmax = ex(2)
+    kmax = ex(3)
+
+    imin_lopsided = 1
+    jmin_lopsided = 1
+    kmin_lopsided = 1
+    if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin_lopsided = -2
+    if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin_lopsided = -2
+    if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin_lopsided = -2
+
+    imin_kodis = 1
+    jmin_kodis = 1
+    kmin_kodis = 1
+
+    if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin_kodis = -2
+    if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin_kodis = -2
+    if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin_kodis = -2
+
+
+    call symmetry_bd(3,ex,f,fh,SoA)
+
+  ! upper bound set ex-1 only for efficiency, 
+  ! the loop body will set ex 0 also
+    do k=1,ex(3)-1
+    do j=1,ex(2)-1
+    do i=1,ex(1)-1
+
+  !! new code, 2012dec27, based on bam
+  ! x direction   
+      if(Sfx(i,j,k) > ZEO)then
+        if(i+3 <= imax)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                    Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                      -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+      elseif(i+2 <= imax)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                    Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+      elseif(i+1 <= imax)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                    Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                      -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+  ! set imax and imin_lopsided 0
+      endif
+    elseif(Sfx(i,j,k) < ZEO)then
+        if(i-3 >= imin_lopsided)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                    Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                      -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+      elseif(i-2 >= imin_lopsided)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                    Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+      elseif(i-1 >= imin_lopsided)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                    Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                      -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+  ! set imax and imin_lopsided 0
+      endif
+    endif
+
+  ! y direction   
+      if(Sfy(i,j,k) > ZEO)then
+        if(j+3 <= jmax)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                    Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                      -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+      elseif(j+2 <= jmax)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                    Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+      elseif(j+1 <= jmax)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                    Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                      -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+  ! set imax and imin_lopsided 0
+      endif
+    elseif(Sfy(i,j,k) < ZEO)then
+        if(j-3 >= jmin_lopsided)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                    Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                      -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+      elseif(j-2 >= jmin_lopsided)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                    Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+      elseif(j-1 >= jmin_lopsided)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                    Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                      -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+  ! set jmax and jmin_lopsided 0
+      endif
+    endif
+
+  ! z direction   
+      if(Sfz(i,j,k) > ZEO)then
+        if(k+3 <= kmax)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                    Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                      -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+      elseif(k+2 <= kmax)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                    Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+      elseif(k+1 <= kmax)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                    Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                      -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+  ! set imax and imin_lopsided 0
+      endif
+    elseif(Sfz(i,j,k) < ZEO)then
+        if(k-3 >= kmin_lopsided)then
+  !         v
+  ! D f = ------[ - 3f    - 10f  + 18f    - 6f     + f     ]
+  !  i     12dx       i-v      i      i+v     i+2v    i+3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                    Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                      -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+      elseif(k-2 >= kmin_lopsided)then
+  !
+  !              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
+  !  fx(i) = ---------------------------------------------
+  !                             12 dx
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                    Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+      elseif(k-1 >= kmin_lopsided)then
+  !         v
+  ! D f = ------[   3f    + 10f  - 18f    + 6f     - f     ]
+  !  i     12dx       i+v      i      i-v     i-2v    i-3v
+      f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                    Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                      -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+  ! set kmax and kmin_lopsided 0
+      endif
+    endif
+
+
+    if(i-3 >= imin_kodis .and. i+3 <= imax .and. &
+      j-3 >= jmin_kodis .and. j+3 <= jmax .and. &
+      k-3 >= kmin_kodis .and. k+3 <= kmax) then
+
+  ! calculation order if important ?
+    f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
+                                (fh(i-3,j,k)+fh(i+3,j,k)) - &
+                            SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
+                            FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
+                            TWT* fh(i,j,k)            )/dX + &
+                                                    (     &
+                                (fh(i,j-3,k)+fh(i,j+3,k)) - &
+                            SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
+                            FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
+                            TWT* fh(i,j,k)            )/dY + &
+                                                    (     &
+                                (fh(i,j,k-3)+fh(i,j,k+3)) - &
+                            SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
+                            FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
+                            TWT* fh(i,j,k)            )/dZ )
+
+    endif
+
+    enddo
+    enddo
+    enddo
+
+    return
+
+
+
+  end subroutine merge_lopsided_kodis

AMSS_NCKU_source/diff_new.f90

@@ -1000,86 +1000,7 @@
   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. &
@@ -1094,7 +1015,7 @@
       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
@@ -1404,85 +1325,7 @@
   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. &
@@ -1518,7 +1361,7 @@
    fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
    fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
    endif
-#endif
+
    enddo
    enddo
    enddo

AMSS_NCKU_source/enforce_algebra.f90

@@ -18,49 +18,61 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> Local variable:
-  
+
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
+  integer :: i,j,k
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8 :: lgxx,lgyy,lgzz,ldetg
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA,lscale
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  gxx = dxx + ONE
+  do k=1,ex(3)
-  gyy = dyy + ONE
+  do j=1,ex(2)
-  gzz = dzz + ONE
+  do i=1,ex(1)
 
-  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+    lgxx = dxx(i,j,k) + ONE
-          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+    lgyy = dyy(i,j,k) + ONE
-  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
+    lgzz = dzz(i,j,k) + ONE
-  gupxy = - ( gxy * gzz - gyz * gxz ) / detg
-  gupxz =   ( gxy * gyz - gyy * gxz ) / detg
-  gupyy =   ( gxx * gzz - gxz * gxz ) / detg
-  gupyz = - ( gxx * gyz - gxy * gxz ) / detg
-  gupzz =   ( gxx * gyy - gxy * gxy ) / detg
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+    ldetg =  lgxx * lgyy * lgzz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+           + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) &
+           + gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) &
+           - gxz(i,j,k) * lgyy * gxz(i,j,k) &
+           - gxy(i,j,k) * gxy(i,j,k) * lgzz &
+           - lgxx * gyz(i,j,k) * gyz(i,j,k)
 
-  Axx = Axx - F1o3 * gxx * trA
+    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
-  Axy = Axy - F1o3 * gxy * trA
+    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
-  Axz = Axz - F1o3 * gxz * trA
+    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
-  Ayy = Ayy - F1o3 * gyy * trA
+    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
-  Ayz = Ayz - F1o3 * gyz * trA
+    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
-  Azz = Azz - F1o3 * gzz * trA
+    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg
 
-  detg = ONE / ( detg ** F1o3 ) 
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
-  
+                 + lgupzz * Azz(i,j,k) &
-  gxx = gxx * detg
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
-  gxy = gxy * detg
+                 + lgupyz * Ayz(i,j,k))
-  gxz = gxz * detg
-  gyy = gyy * detg
-  gyz = gyz * detg
-  gzz = gzz * detg
 
-  dxx = gxx - ONE
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-  dyy = gyy - ONE
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
-  dzz = gzz - ONE
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+    lscale = ONE / ( ldetg ** F1o3 )
+
+    dxx(i,j,k) = lgxx * lscale - ONE
+    gxy(i,j,k) = gxy(i,j,k) * lscale
+    gxz(i,j,k) = gxz(i,j,k) * lscale
+    dyy(i,j,k) = lgyy * lscale - ONE
+    gyz(i,j,k) = gyz(i,j,k) * lscale
+    dzz(i,j,k) = lgzz * lscale - ONE
+
+  enddo
+  enddo
+  enddo
 
   return
 
@@ -82,51 +94,71 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> Local variable:
-  
+
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
+  integer :: i,j,k
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8 :: lgxx,lgyy,lgzz,lscale
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  real*8 :: lgxy,lgxz,lgyz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  gxx = dxx + ONE
+  do k=1,ex(3)
-  gyy = dyy + ONE
+  do j=1,ex(2)
-  gzz = dzz + ONE
+  do i=1,ex(1)
-! for g
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
 
-  gupzz = ONE / ( gupzz ** F1o3 ) 
+! for g: normalize determinant first
-  
+    lgxx = dxx(i,j,k) + ONE
-  gxx = gxx * gupzz
+    lgyy = dyy(i,j,k) + ONE
-  gxy = gxy * gupzz
+    lgzz = dzz(i,j,k) + ONE
-  gxz = gxz * gupzz
+    lgxy = gxy(i,j,k)
-  gyy = gyy * gupzz
+    lgxz = gxz(i,j,k)
-  gyz = gyz * gupzz
+    lgyz = gyz(i,j,k)
-  gzz = gzz * gupzz
 
-  dxx = gxx - ONE
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-  dyy = gyy - ONE
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-  dzz = gzz - ONE
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
-! for A  
 
-  gupxx =   ( gyy * gzz - gyz * gyz )
+    lscale = ONE / ( lscale ** F1o3 )
-  gupxy = - ( gxy * gzz - gyz * gxz )
-  gupxz =   ( gxy * gyz - gyy * gxz )
-  gupyy =   ( gxx * gzz - gxz * gxz )
-  gupyz = - ( gxx * gyz - gxy * gxz )
-  gupzz =   ( gxx * gyy - gxy * gxy )
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+    lgxx = lgxx * lscale
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    lgxy = lgxy * lscale
+    lgxz = lgxz * lscale
+    lgyy = lgyy * lscale
+    lgyz = lgyz * lscale
+    lgzz = lgzz * lscale
 
-  Axx = Axx - F1o3 * gxx * trA
+    dxx(i,j,k) = lgxx - ONE
-  Axy = Axy - F1o3 * gxy * trA
+    gxy(i,j,k) = lgxy
-  Axz = Axz - F1o3 * gxz * trA
+    gxz(i,j,k) = lgxz
-  Ayy = Ayy - F1o3 * gyy * trA
+    dyy(i,j,k) = lgyy - ONE
-  Ayz = Ayz - F1o3 * gyz * trA
+    gyz(i,j,k) = lgyz
-  Azz = Azz - F1o3 * gzz * trA
+    dzz(i,j,k) = lgzz - ONE
+
+! for A: trace-free using normalized metric (det=1, no division needed)
+    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
+    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
+    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
+    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
+    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
+    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
+
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
+
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+  enddo
+  enddo
+  enddo
 
   return
 

AMSS_NCKU_source/fmisc.f90

@@ -324,10 +324,10 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   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)
@@ -350,7 +350,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   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)
@@ -379,7 +378,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   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)
@@ -886,7 +884,6 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   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+1,1:extc(2),1:extc(3))*SoA(1)
@@ -912,7 +909,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   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+1,1:extc(2),1:extc(3))*SoA(1)
@@ -941,7 +937,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   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+1,1:extc(2),1:extc(3))*SoA(1)
@@ -1118,64 +1113,65 @@ end subroutine d2dump
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
 
-  subroutine polint(xa,ya,x,y,dy,ordn)
+  subroutine polint(xa, ya, x, y, dy, ordn)
-
   implicit none
 
-!~~~~~~> Input Parameter:
+  integer, intent(in) :: ordn
-  integer,intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa, ya
-  real*8, dimension(ordn), intent(in) :: xa,ya
   real*8, intent(in) :: x
-  real*8, intent(out) :: y,dy
+  real*8, intent(out) :: y, dy
 
-!~~~~~~> Other parameter:
+  integer :: i, m, ns, n_m
+  real*8, dimension(ordn) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
 
-  integer :: m,n,ns
+  c = ya
-  real*8, dimension(ordn) :: c,d,den,ho
+  d = ya
-  real*8 :: dif,dift
+  ho = xa - x
 
-!~~~~~~>
+  ns = 1
+  dif = abs(x - xa(1))
 
-  n=ordn
+  do i = 2, ordn
-  m=ordn
+    dift = abs(x - xa(i))
-
+    if (dift < dif) then
-  c=ya
+      ns = i
-  d=ya
+      dif = dift
-  ho=xa-x
+    end if
-
-  ns=1
-  dif=abs(x-xa(1))
-  do m=1,n
-   dift=abs(x-xa(m))
-   if(dift < dif) then
-    ns=m
-    dif=dift
-   end if
   end do
 
-  y=ya(ns)
+  y = ya(ns)
-  ns=ns-1
+  ns = ns - 1
-  do m=1,n-1
+
-    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
+  do m = 1, ordn - 1
-    if (any(den(1:n-m) == 0.0))then
+    n_m = ordn - m
-      write(*,*) 'failure in polint for point',x
+    do i = 1, n_m
-      write(*,*) 'with input points: ',xa
+      hp = ho(i)
-      stop
+      h  = ho(i+m)
-    endif
+      den_val = hp - h
-    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
+
-    d(1:n-m)=ho(1+m:n)*den(1:n-m)
+      if (den_val == 0.0d0) then
-    c(1:n-m)=ho(1:n-m)*den(1:n-m)
+        write(*,*) 'failure in polint for point',x
-    if (2*ns < n-m) then
+        write(*,*) 'with input points: ',xa
-      dy=c(ns+1)
+        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)
+      dy = d(ns)
-      ns=ns-1
+      ns = ns - 1
     end if
-    y=y+dy
+    y = y + dy
   end do
 
   return
-
   end subroutine polint
 !------------------------------------------------------------------------------
 !
@@ -1183,35 +1179,37 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
-
   implicit none
 
-!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a
   real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2
   real*8, intent(out) :: y,dy
 
-!~~~~~~> Other parameters:
+#ifdef POLINT_LEGACY_ORDER
-
   integer  :: i,m
   real*8, dimension(ordn) :: ymtmp
   real*8, dimension(ordn) :: yntmp
 
   m=size(x1a)
-  
   do i=1,m
-
     yntmp=ya(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-
   end do
-
   call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do j=1,ordn
+    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
+  end do
+  call polint(x2a, ymtmp, x2, y, dy, ordn)
+#endif
 
   return
-
   end subroutine polin2
 !------------------------------------------------------------------------------
 !
@@ -1219,18 +1217,15 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
-
   implicit none
 
-!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
   real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-!~~~~~~> Other parameters:
+#ifdef POLINT_LEGACY_ORDER
-
   integer  :: i,j,m,n
   real*8, dimension(ordn,ordn) :: yatmp
   real*8, dimension(ordn) :: ymtmp
@@ -1239,27 +1234,36 @@ end subroutine d2dump
 
   m=size(x1a)
   n=size(x2a)
-  
   do i=1,m
    do j=1,n
-
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
-
    end do
-
     yntmp=yatmp(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-
   end do
-
   call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j, k
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do k=1,ordn
+    do j=1,ordn
+      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+    end do
+  end do
+  do k=1,ordn
+    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+  end do
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
 
   return
-
   end subroutine polin3
 !--------------------------------------------------------------------------------------
-! calculate L2norm  
+! calculate L2norm
   subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
                           f,f_out,gw)
 
@@ -1276,7 +1280,9 @@ end subroutine d2dump
   real*8            :: dX, dY, dZ
   integer::imin,jmin,kmin
   integer::imax,jmax,kmax
-  integer::i,j,k
+  integer::i,j,k,n_elements
+  real*8, dimension(:), allocatable :: f_flat
+  real*8, external :: DDOT
 
   dX = X(2) - X(1)
   dY = Y(2) - Y(1)
@@ -1300,7 +1306,12 @@ if(dabs(X(1)-xmin) < dX) imin = 1
 if(dabs(Y(1)-ymin) < dY) jmin = 1
 if(dabs(Z(1)-zmin) < dZ) kmin = 1
 
-f_out = sum(f(imin:imax,jmin:jmax,kmin:kmax)*f(imin:imax,jmin:jmax,kmin:kmax))
+! Optimized with oneMKL BLAS DDOT for dot product
+n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+allocate(f_flat(n_elements))
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
+f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
@@ -1325,7 +1336,9 @@ f_out = f_out*dX*dY*dZ
   real*8            :: dX, dY, dZ
   integer::imin,jmin,kmin
   integer::imax,jmax,kmax
-  integer::i,j,k
+  integer::i,j,k,n_elements
+  real*8, dimension(:), allocatable :: f_flat
+  real*8, external :: DDOT
 
   real*8 :: PIo4
 
@@ -1388,7 +1401,12 @@ if(Symmetry==2)then
   if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif
 
-f_out = sum(f(imin:imax,jmin:jmax,kmin:kmax)*f(imin:imax,jmin:jmax,kmin:kmax))
+! Optimized with oneMKL BLAS DDOT for dot product
+n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+allocate(f_flat(n_elements))
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
+f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
@@ -1416,6 +1434,8 @@ f_out = f_out*dX*dY*dZ
   integer::imin,jmin,kmin
   integer::imax,jmax,kmax
   integer::i,j,k
+  real*8, dimension(:), allocatable :: f_flat
+  real*8, external :: DDOT
 
   real*8 :: PIo4
 
@@ -1478,11 +1498,12 @@ if(Symmetry==2)then
   if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif
 
-f_out = sum(f(imin:imax,jmin:jmax,kmin:kmax)*f(imin:imax,jmin:jmax,kmin:kmax))
+! Optimized with oneMKL BLAS DDOT for dot product
-
-f_out = f_out
-
 Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+allocate(f_flat(Nout))
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
+f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
+deallocate(f_flat)
 
   return
 
@@ -1680,6 +1701,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
   real*8, dimension(ORDN,ORDN) :: tmp2
   real*8, dimension(ORDN) :: tmp1
   real*8, dimension(3) :: SoAh
+  real*8, external :: DDOT
 
 ! +1 because c++ gives 0 for first point
   cxB = inds+1  
@@ -1715,20 +1737,21 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
      ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),cxB(3):cxT(3))
   endif 
 
+  ! Optimized with BLAS operations for better performance
+  ! First dimension: z-direction weighted sum
   tmp2=0
   do m=1,ORDN
     tmp2 = tmp2 + coef(2*ORDN+m)*ya(:,:,m)
   enddo
 
+  ! Second dimension: y-direction weighted sum
   tmp1=0
   do m=1,ORDN
     tmp1 = tmp1 + coef(ORDN+m)*tmp2(:,m)
   enddo
 
-  f_int=0
+  ! Third dimension: x-direction weighted sum using BLAS DDOT
-  do m=1,ORDN
+  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
-    f_int = f_int + coef(m)*tmp1(m)
-  enddo
 
   return
 
@@ -1758,6 +1781,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
   real*8, dimension(ORDN,ORDN) :: ya
   real*8, dimension(ORDN) :: tmp1
   real*8, dimension(2) :: SoAh
+  real*8, external :: DDOT
 
 ! +1 because c++ gives 0 for first point
   cxB = inds(1:2)+1  
@@ -1787,15 +1811,14 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
      ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),inds(3))
   endif 
 
+  ! Optimized with BLAS operations
   tmp1=0
   do m=1,ORDN
     tmp1 = tmp1 + coef(ORDN+m)*ya(:,m)
   enddo
 
-  f_int=0
+  ! Use BLAS DDOT for final weighted sum
-  do m=1,ORDN
+  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
-    f_int = f_int + coef(m)*tmp1(m)
-  enddo
 
   return
 
@@ -1826,6 +1849,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
   real*8, dimension(ORDN) :: ya
   real*8 :: SoAh
   integer,dimension(3) :: inds
+  real*8, external :: DDOT
 
 ! +1 because c++ gives 0 for first point
   inds = indsi + 1
@@ -1886,10 +1910,8 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
           write(*,*)"error in global_interpind1d, not recognized dumyd = ",dumyd
   endif
 
-  f_int=0
+  ! Optimized with BLAS DDOT for weighted sum
-  do m=1,ORDN
+  f_int = DDOT(ORDN, coef, 1, ya, 1)
-    f_int = f_int + coef(m)*ya(m)
-  enddo
 
   return
 
@@ -2121,24 +2143,38 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
 
   end function fWigner_d_function
 !----------------------------------
+! Optimized factorial function using lookup table for small N
+! and log-gamma for large N to avoid overflow
   function ffact(N) result(gont)
   implicit none
   integer,intent(in) :: N
 
   real*8 :: gont
-
   integer :: i
 
+  ! Lookup table for factorials 0! to 20! (precomputed)
+  real*8, parameter, dimension(0:20) :: fact_table = [ &
+    1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 120.d0, 720.d0, 5040.d0, 40320.d0, &
+    362880.d0, 3628800.d0, 39916800.d0, 479001600.d0, 6227020800.d0, &
+    87178291200.d0, 1307674368000.d0, 20922789888000.d0, &
+    355687428096000.d0, 6402373705728000.d0, 121645100408832000.d0, &
+    2432902008176640000.d0 ]
+
 ! sanity check
   if(N < 0)then
      write(*,*) "ffact: error input for factorial"
+     gont = 1.d0
      return
   endif
 
-  gont = 1.d0
+  ! Use lookup table for small N (fast path)
-  do i=1,N
+  if(N <= 20)then
-     gont = gont*i
+     gont = fact_table(N)
-  enddo
+  else
+     ! Use log-gamma function for large N: N! = exp(log_gamma(N+1))
+     ! This avoids overflow and is computed efficiently
+     gont = exp(log_gamma(dble(N+1)))
+  endif
 
   return
 

AMSS_NCKU_source/gaussj.C

@@ -16,115 +16,66 @@ using namespace std;
 #include <string.h>
 #include <math.h>
 #endif
-/* Linear equation solution by Gauss-Jordan elimination.
+
+// Intel oneMKL LAPACK interface
+#include <mkl_lapacke.h>
+/* Linear equation solution using Intel oneMKL LAPACK.
 a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
 containing the right-hand side vectors. On output a is
 replaced by its matrix inverse, and b is replaced by the
-corresponding set of solution vectors */
+corresponding set of solution vectors.
+
+Mathematical equivalence:
+  Solves: A * x = b  =>  x = A^(-1) * b
+  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
+  within numerical precision. */
 
 int gaussj(double *a, double *b, int n)
 {
-  double swap;
+  // Allocate pivot array and workspace
+  lapack_int *ipiv = new lapack_int[n];
+  lapack_int info;
 
-  int *indxc, *indxr, *ipiv;
+  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
-  indxc = new int[n];
+  double *a_copy = new double[n * n];
-  indxr = new int[n];
+  for (int i = 0; i < n * n; i++) {
-  ipiv = new int[n];
+    a_copy[i] = a[i];
-
-  int i, icol, irow, j, k, l, ll;
-  double big, dum, pivinv, temp;
-
-  for (j = 0; j < n; j++)
-    ipiv[j] = 0;
-  for (i = 0; i < n; i++)
-  {
-    big = 0.0;
-    for (j = 0; j < n; j++)
-      if (ipiv[j] != 1)
-        for (k = 0; k < n; k++)
-        {
-          if (ipiv[k] == 0)
-          {
-            if (fabs(a[j * n + k]) >= big)
-            {
-              big = fabs(a[j * n + k]);
-              irow = j;
-              icol = k;
-            }
-          }
-          else if (ipiv[k] > 1)
-          {
-            cout << "gaussj: Singular Matrix-1" << endl;
-            for (int ii = 0; ii < n; ii++)
-            {
-              for (int jj = 0; jj < n; jj++)
-                cout << a[ii * n + jj] << " ";
-              cout << endl;
-            }
-            return 1; // error return
-          }
-        }
-
-    ipiv[icol] = ipiv[icol] + 1;
-    if (irow != icol)
-    {
-      for (l = 0; l < n; l++)
-      {
-        swap = a[irow * n + l];
-        a[irow * n + l] = a[icol * n + l];
-        a[icol * n + l] = swap;
-      }
-
-      swap = b[irow];
-      b[irow] = b[icol];
-      b[icol] = swap;
-    }
-
-    indxr[i] = irow;
-    indxc[i] = icol;
-
-    if (a[icol * n + icol] == 0.0)
-    {
-      cout << "gaussj: Singular Matrix-2" << endl;
-      for (int ii = 0; ii < n; ii++)
-      {
-        for (int jj = 0; jj < n; jj++)
-          cout << a[ii * n + jj] << " ";
-        cout << endl;
-      }
-      return 1; // error return
-    }
-
-    pivinv = 1.0 / a[icol * n + icol];
-    a[icol * n + icol] = 1.0;
-    for (l = 0; l < n; l++)
-      a[icol * n + l] *= pivinv;
-    b[icol] *= pivinv;
-    for (ll = 0; ll < n; ll++)
-      if (ll != icol)
-      {
-        dum = a[ll * n + icol];
-        a[ll * n + icol] = 0.0;
-        for (l = 0; l < n; l++)
-          a[ll * n + l] -= a[icol * n + l] * dum;
-        b[ll] -= b[icol] * dum;
-      }
   }
 
-  for (l = n - 1; l >= 0; l--)
+  // Step 1: Solve linear system A*x = b using LU decomposition
-  {
+  // LAPACKE_dgesv uses column-major by default, but we use row-major
-    if (indxr[l] != indxc[l])
+  info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
-      for (k = 0; k < n; k++)
+
-      {
+  if (info != 0) {
-        swap = a[k * n + indxr[l]];
+    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
-        a[k * n + indxr[l]] = a[k * n + indxc[l]];
+    delete[] ipiv;
-        a[k * n + indxc[l]] = swap;
+    delete[] a_copy;
-      }
+    return 1;
+  }
+
+  // Step 2: Compute matrix inverse A^(-1) using LU factorization
+  // First do LU factorization of original matrix a
+  info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  // Then compute inverse from LU factorization
+  info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
   }
 
-  delete[] indxc;
-  delete[] indxr;
   delete[] ipiv;
+  delete[] a_copy;
 
   return 0;
 }

AMSS_NCKU_source/ilucg.f90

@@ -512,11 +512,10 @@
       IMPLICIT DOUBLE PRECISION (A-H,O-Z)
       DIMENSION V(N),W(N)
 !     SUBROUTINE TO COMPUTE DOUBLE PRECISION VECTOR DOT PRODUCT.
+!     Optimized using Intel oneMKL BLAS ddot
+!     Mathematical equivalence: DGVV = sum_{i=1}^{N} V(i)*W(i)
 
-      SUM = 0.0D0
+      DOUBLE PRECISION, EXTERNAL :: DDOT
-            DO 10 I = 1,N
+      DGVV = DDOT(N, V, 1, W, 1)
-            SUM = SUM + V(I)*W(I)
-10          CONTINUE
-      DGVV = SUM
       RETURN
       END

AMSS_NCKU_source/kodiss.f90

@@ -6,101 +6,6 @@
 ! Vertex or Cell is distinguished in routine symmetry_bd which locates in
 ! file "fmisc.f90"
 
-#if (ghost_width == 2)
-! second order code
-
-!------------------------------------------------------------------------------------------------------------------------------
-!usual type Kreiss-Oliger type numerical dissipation
-!We support cell center only
-!  (D_+D_-)^2 =
-!   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
-! ------------------------------------------------------
-!                       dx^4
-!------------------------------------------------------------------------------------------------------------------------------
-! do not add dissipation near boundary
-subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
-
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,parameter   :: cof = 1.6d1 ! 2^4
-  real*8,  parameter :: F4=4.d0,F6=6.d0
-  integer::i,j,k
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
-
-  call symmetry_bd(2,ex,f,fh,SoA)
-
-!   f(i-2) - 4 f(i-1) + 6 f(i) - 4 f(i+1) + f(i+2)
-! ------------------------------------------------------
-!                       dx^4
-
-!  note the sign (-1)^r-1, now r=2
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i-2 >= imin .and. i+2 <= imax .and. &
-     j-2 >= jmin .and. j+2 <= jmax .and. &
-     k-2 >= kmin .and. k+2 <= kmax) then
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
-                                (fh(i-2,j,k)+fh(i+2,j,k)) &
-                         - F4 * (fh(i-1,j,k)+fh(i+1,j,k)) &
-                         + F6 *  fh(i,j,k) )
-! y direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
-                                (fh(i,j-2,k)+fh(i,j+2,k)) &
-                         - F4 * (fh(i,j-1,k)+fh(i,j+1,k)) &
-                         + F6 *  fh(i,j,k) )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
-                                (fh(i,j,k-2)+fh(i,j,k+2)) &
-                         - F4 * (fh(i,j,k-1)+fh(i,j,k+1)) &
-                         + F6 *  fh(i,j,k) )
-
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-end subroutine kodis
-
-#elif (ghost_width == 3)
 ! fourth order code
 
 !---------------------------------------------------------------------------------------------
@@ -156,7 +61,7 @@ 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)
@@ -166,28 +71,7 @@ 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)) - &
@@ -204,7 +88,7 @@ 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
@@ -215,218 +99,6 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
 
   end subroutine kodis
 
-#elif (ghost_width == 4)
-! sixth order code
-!------------------------------------------------------------------------------------------------------------------------------
-!usual type Kreiss-Oliger type numerical dissipation
-!We support cell center only
-!  (D_+D_-)^4 =
-!   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
-! ----------------------------------------------------------------------------------------------------------
-!                                              dx^8
-!------------------------------------------------------------------------------------------------------------------------------
-! do not add dissipation near boundary
-subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
 
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
 
-!~~~~~~ other variables
 
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,parameter   :: cof = 2.56d2 ! 2^8
-  real*8,  parameter :: F8=8.d0,F28=2.8d1,F56=5.6d1,F70=7.d1
-  integer::i,j,k
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-  
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
-
-  call symmetry_bd(4,ex,f,fh,SoA)
-
-!   f(i-4) - 8 f(i-3) + 28 f(i-2) - 56 f(i-1) + 70 f(i) - 56 f(i+1) + 28 f(i+2) - 8 f(i+3) + f(i+4)
-! ----------------------------------------------------------------------------------------------------------
-!                                              dx^8
-
-!  note the sign (-1)^r-1, now r=4
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i>imin+3 .and. i < imax-3 .and. &
-     j>jmin+3 .and. j < jmax-3 .and. &
-     k>kmin+3 .and. k < kmax-3) then
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dX/cof * (     &
-                                (fh(i-4,j,k)+fh(i+4,j,k)) &
-                         - F8 * (fh(i-3,j,k)+fh(i+3,j,k)) &
-                         +F28 * (fh(i-2,j,k)+fh(i+2,j,k)) &
-                         -F56 * (fh(i-1,j,k)+fh(i+1,j,k)) &
-                         +F70 *  fh(i,j,k) )
-! y direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dY/cof * (     &
-                                (fh(i,j-4,k)+fh(i,j+4,k)) &
-                         - F8 * (fh(i,j-3,k)+fh(i,j+3,k)) &
-                         +F28 * (fh(i,j-2,k)+fh(i,j+2,k)) &
-                         -F56 * (fh(i,j-1,k)+fh(i,j+1,k)) &
-                         +F70 *  fh(i,j,k) )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) - eps/dZ/cof * (     &
-                                (fh(i,j,k-4)+fh(i,j,k+4)) &
-                         - F8 * (fh(i,j,k-3)+fh(i,j,k+3)) &
-                         +F28 * (fh(i,j,k-2)+fh(i,j,k+2)) &
-                         -F56 * (fh(i,j,k-1)+fh(i,j,k+1)) &
-                         +F70 *  fh(i,j,k) )
-
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-end subroutine kodis
-
-#elif (ghost_width == 5)
-! eighth order code
-!------------------------------------------------------------------------------------------------------------------------------
-!usual type Kreiss-Oliger type numerical dissipation
-!We support cell center only
-! Note the notation D_+ and D_- [P240 of B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time
-! Dependent Problems and Difference Methods (Wiley, New York, 1995).]
-! D_+ = (f(i+1) - f(i))/h
-! D_- = (f(i) - f(i-1))/h
-! then we have D_+D_- = D_-D_+ = (f(i+1) - 2f(i) + f(i-1))/h^2
-! for nth order accurate finite difference code, we need r =n/2+1
-!              D_+^rD_-^r = (D_+D_-)^r 
-! following the tradiation of PRD 77, 024027 (BB's calibration paper, Eq.(64),
-!  correct some typo according to above book) :
-! + eps*(-1)^(r-1)*h^(2r-1)/2^(2r)*(D_+D_-)^r 
-!
-!
-! this is for 8th order accurate finite difference scheme
-!  (D_+D_-)^5 =
-!  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
-! -------------------------------------------------------------------------------------------------------------------------------
-!                                                              dx^10
-!---------------------------------------------------------------------------------------------------------------------------------
-! do not add dissipation near boundary
-subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
-
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
-
-!~~~~~~ other variables
-
-  real*8 :: dX,dY,dZ
-  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-  real*8,parameter   :: cof = 1.024d3 ! 2^2r = 2^10
-  real*8,  parameter :: F10=1.d1,F45=4.5d1,F120=1.2d2,F210=2.1d2,F252=2.52d2
-  integer::i,j,k
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-  
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
-
-  call symmetry_bd(5,ex,f,fh,SoA)
-
-!  f(i-5) - 10 f(i-4) + 45 f(i-3) - 120 f(i-2) + 210 f(i-1) - 252 f(i) + 210 f(i+1) - 120 f(i+2) + 45 f(i+3) - 10 f(i+4) + f(i+5)
-! -------------------------------------------------------------------------------------------------------------------------------
-!                                                              dx^10
-
-!  note the sign (-1)^r-1, now r=5
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i>imin+4 .and. i < imax-4 .and. &
-     j>jmin+4 .and. j < jmax-4 .and. &
-     k>kmin+4 .and. k < kmax-4) then
-! x direction
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (      &
-                                 (fh(i-5,j,k)+fh(i+5,j,k)) &
-                         - F10 * (fh(i-4,j,k)+fh(i+4,j,k)) &
-                         + F45 * (fh(i-3,j,k)+fh(i+3,j,k)) &
-                         - F120* (fh(i-2,j,k)+fh(i+2,j,k)) &
-                         + F210* (fh(i-1,j,k)+fh(i+1,j,k)) &
-                         - F252 * fh(i,j,k) )
-! y direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (      &
-                                 (fh(i,j-5,k)+fh(i,j+5,k)) &
-                         - F10 * (fh(i,j-4,k)+fh(i,j+4,k)) &
-                         + F45 * (fh(i,j-3,k)+fh(i,j+3,k)) &
-                         - F120* (fh(i,j-2,k)+fh(i,j+2,k)) &
-                         + F210* (fh(i,j-1,k)+fh(i,j+1,k)) &
-                         - F252 * fh(i,j,k) )
-! z direction
-
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (      &
-                                 (fh(i,j,k-5)+fh(i,j,k+5)) &
-                         - F10 * (fh(i,j,k-4)+fh(i,j,k+4)) &
-                         + F45 * (fh(i,j,k-3)+fh(i,j,k+3)) &
-                         - F120* (fh(i,j,k-2)+fh(i,j,k+2)) &
-                         + F210* (fh(i,j,k-1)+fh(i,j,k+1)) &
-                         - F252 * fh(i,j,k) )
-
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-end subroutine kodis
-
-#endif  

AMSS_NCKU_source/lopsidediff.f90

@@ -7,163 +7,7 @@
 ! 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
 
 !-----------------------------------------------------------------------------
@@ -236,89 +80,7 @@ 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
@@ -478,7 +240,6 @@ 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
@@ -486,417 +247,3 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
   return
 
   end subroutine lopsided
-
-#elif (ghost_width == 4)
-! sixth order code
-! Compute advection terms in right hand sides of field equations
-!         v
-! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
-!  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
-!
-! where
-!
-!        i
-!      |B |
-! v = -----
-!        i
-!       B
-!
-!-----------------------------------------------------------------------------
-subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
-  implicit none
-
-!~~~~~~> Input parameters:
-
-  integer, intent(in)  :: ex(1:3),Symmetry
-  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
-  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
-
-  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
-  real*8,dimension(3),intent(in) ::SoA
-
-!~~~~~~> local variables:
-
-  real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: dX,dY,dZ
-  real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
-  real*8,  parameter :: TWO=2.d0,F24=2.4d1,F35=3.5d1,F80=8.d1,F30=3.d1,EIT=8.d0
-  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1
-  real*8,  parameter ::  F10=1.d1,F77=7.7d1,F150=1.5d2,F100=1.d2,F50=5.d1,F15=1.5d1
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  d60dx = ONE/F60/dX
-  d60dy = ONE/F60/dY
-  d60dz = ONE/F60/dZ
-
-  d12dx = ONE/F12/dX
-  d12dy = ONE/F12/dY
-  d12dz = ONE/F12/dZ
-
-  d2dx = ONE/TWO/dX
-  d2dy = ONE/TWO/dY
-  d2dz = ONE/TWO/dZ
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
-
-  call symmetry_bd(4,ex,f,fh,SoA)
-
-! upper bound set ex-1 only for efficiency, 
-! the loop body will set ex 0 also
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-! x direction   
-    if(Sfx(i,j,k) >= ZEO .and. i+4 <= imax .and. i-2 >= imin)then
-!         v
-! D f = ------[ 2f     - 24f    - 35f  + 80f    - 30f     + 8f     - f    ]
-!  i     60dx     i-2v      i-v      i      i+v      i+2v     i+3v    i+4v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                             &
-                  Sfx(i,j,k)*d60dx*(TWO*fh(i-2,j,k)-F24*fh(i-1,j,k)-F35*fh(i,j,k)+F80*fh(i+1,j,k) &
-                                   -F30*fh(i+2,j,k)+EIT*fh(i+3,j,k)-    fh(i+4,j,k))
-    elseif(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-1 >= imin)then
-!         v
-! D f = ------[-10f    - 77f  + 150f    - 100f     + 50f     -15f     + 2f    ]
-!  i     60dx      i-v      i       i+v       i+2v      i+3v     i+4v    i+5v
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
-                  Sfx(i,j,k)*d60dx*(-F10*fh(i-1,j,k)-F77*fh(i  ,j,k)+F150*fh(i+1,j,k)-F100*fh(i+2,j,k) &
-                                    +F50*fh(i+3,j,k)-F15*fh(i+4,j,k)+ TWO*fh(i+5,j,k))
-
-    elseif(Sfx(i,j,k) <= ZEO .and. i-4 >= imin .and. i+2 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
-                  Sfx(i,j,k)*d60dx*(TWO*fh(i+2,j,k)-F24*fh(i+1,j,k)-F35*fh(i,j,k)+F80*fh(i-1,j,k) &
-                                   -F30*fh(i-2,j,k)+EIT*fh(i-3,j,k)-    fh(i-4,j,k))
-    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+1 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
-                  Sfx(i,j,k)*d60dx*(-F10*fh(i+1,j,k)-F77*fh(i  ,j,k)+F150*fh(i-1,j,k)-F100*fh(i-2,j,k) &
-                                    +F50*fh(i-3,j,k)-F15*fh(i-4,j,k)+ TWO*fh(i-5,j,k))
-
-     elseif(i+3 <= imax .and. i-3 >= imin)then
-!           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
-!  fx(i) = -----------------------------------------------------------------
-!                                        60 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
-
-     elseif(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-
-     elseif(i+1 <= imax .and. i-1 >= imin)then
-!
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-
-! set imax and imin 0
-    endif
-
-! y direction   
-     if(Sfy(i,j,k) >= ZEO .and. j+4 <= jmax .and. j-2 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
-                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j-2,k)-F24*fh(i,j-1,k)-F35*fh(i,j,k)+F80*fh(i,j+1,k) &
-                                   -F30*fh(i,j+2,k)+EIT*fh(i,j+3,k)-    fh(i,j+4,k))
-     elseif(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-1 >= jmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
-                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j-1,k)-F77*fh(i,j  ,k)+F150*fh(i,j+1,k)-F100*fh(i,j+2,k) &
-                                    +F50*fh(i,j+3,k)-F15*fh(i,j+4,k)+ TWO*fh(i,j+5,k))
-
-     elseif(Sfy(i,j,k) <= ZEO .and. j-4 >= jmin .and. j+2 <= jmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
-                  Sfy(i,j,k)*d60dy*(TWO*fh(i,j+2,k)-F24*fh(i,j+1,k)-F35*fh(i,j,k)+F80*fh(i,j-1,k) &
-                                   -F30*fh(i,j-2,k)+EIT*fh(i,j-3,k)-    fh(i,j-4,k))
-
-     elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+1 <= jmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
-                  Sfy(i,j,k)*d60dy*(-F10*fh(i,j+1,k)-F77*fh(i,j  ,k)+F150*fh(i,j-1,k)-F100*fh(i,j-2,k) &
-                                    +F50*fh(i,j-3,k)-F15*fh(i,j-4,k)+ TWO*fh(i,j-5,k))
-
-     elseif(j+3 <= jmax .and. j-3 >= jmin)then
-          
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
-
-     elseif(j+2 <= jmax .and. j-2 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
-                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-
-     elseif(j+1 <= jmax .and. j-1 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-! set jmin and jmax 0
-     endif
-!! z direction   
-     if(Sfz(i,j,k) >= ZEO .and. k+4 <= kmax .and. k-2 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                   &
-                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k-2)-F24*fh(i,j,k-1)-F35*fh(i,j,k)+F80*fh(i,j,k+1) &
-                                   -F30*fh(i,j,k+2)+EIT*fh(i,j,k+3)-    fh(i,j,k+4))
-     elseif(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-1 >= kmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                        &
-                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k-1)-F77*fh(i,j,k  )+F150*fh(i,j,k+1)-F100*fh(i,j,k+2) &
-                                    +F50*fh(i,j,k+3)-F15*fh(i,j,k+4)+ TWO*fh(i,j,k+5))
-
-     elseif(Sfz(i,j,k) <= ZEO .and. k-4 >= kmin .and. k+2 <= kmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                   &
-                  Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k+2)-F24*fh(i,j,k+1)-F35*fh(i,j,k)+F80*fh(i,j,k-1) &
-                                   -F30*fh(i,j,k-2)+EIT*fh(i,j,k-3)-    fh(i,j,k-4))
-
-     elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+1 <= kmax)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                        &
-                  Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k+1)-F77*fh(i,j,k  )+F150*fh(i,j,k-1)-F100*fh(i,j,k-2) &
-                                    +F50*fh(i,j,k-3)-F15*fh(i,j,k-4)+ TWO*fh(i,j,k-5))
-     
-     elseif(k+3 <= kmax .and. k-3 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
-
-     elseif(k+2 <= kmax .and. k-2 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
-                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-
-     elseif(k+1 <= kmax .and. k-1 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-! set kmin and kmax 0
-     endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine lopsided
-
-#elif (ghost_width == 5)
-! eighth order code
-!-----------------------------------------------------------------------------
-! PRD 77, 024034 (2008)
-! Compute advection terms in right hand sides of field equations
-!        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
-! D f = --------------------------------------------------------------------------------------------------------------------------
-!  i                                                             840 dx           
-!
-! where
-!
-!        i
-!      |B |
-! v = -----
-!        i
-!       B
-!
-!-----------------------------------------------------------------------------
-subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
-  implicit none
-
-!~~~~~~> Input parameters:
-
-  integer, intent(in)  :: ex(1:3),Symmetry
-  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
-  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
-
-  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
-  real*8,dimension(3),intent(in) ::SoA
-
-!~~~~~~> local variables:
-
-  real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: dX,dY,dZ
-  real*8 :: d840dx,d840dy,d840dz,d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
-  real*8,  parameter :: TWO=2.d0,F30=3.d1,EIT=8.d0
-  real*8,  parameter ::  F9=9.d0,F45=4.5d1,F12=1.2d1,F140=1.4d2,THR=3.d0
-  real*8,  parameter :: F840=8.4d2,F5=5.d0,F420=4.2d2,F378=3.78d2,F1050=1.05d3
-  real*8,  parameter :: F32=3.2d1,F168=1.68d2,F672=6.72d2
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  d840dx = ONE/F840/dX
-  d840dy = ONE/F840/dY
-  d840dz = ONE/F840/dZ
-
-  d60dx = ONE/F60/dX
-  d60dy = ONE/F60/dY
-  d60dz = ONE/F60/dZ
-
-  d12dx = ONE/F12/dX
-  d12dy = ONE/F12/dY
-  d12dz = ONE/F12/dZ
-
-  d2dx = ONE/TWO/dX
-  d2dy = ONE/TWO/dY
-  d2dz = ONE/TWO/dZ
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
-
-  call symmetry_bd(5,ex,f,fh,SoA)
-
-! upper bound set ex-1 only for efficiency, 
-! the loop body will set ex 0 also
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-! x direction   
-    if(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-3 >= imin)then
-!        v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
-! D f = --------------------------------------------------------------------------------------------------------------------------
-!  i                                                             840 dx    
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
-                  Sfx(i,j,k)*d840dx*(-F5*fh(i-3,j,k)+F60 *fh(i-2,j,k)-F420*fh(i-1,j,k)-F378*fh(i  ,j,k) &
-                                  +F1050*fh(i+1,j,k)-F420*fh(i+2,j,k)+F140*fh(i+3,j,k)-F30 *fh(i+4,j,k)+THR*fh(i+5,j,k))
-
-    elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+3 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                          &
-                  Sfx(i,j,k)*d840dx*(-F5*fh(i+3,j,k)+F60 *fh(i+2,j,k)-F420*fh(i+1,j,k)-F378*fh(i   ,j,k) &
-                                  +F1050*fh(i-1,j,k)-F420*fh(i-2,j,k)+F140*fh(i-3,j,k)- F30*fh(i-4,j,k)+THR*fh(i-5,j,k))
-
-    elseif(i+4 <= imax .and. i-4 >= imin)then
-!           3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
-!  fx(i) = -------------------------------------------------------------------------------------------------
-!                                                        840 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfx(i,j,k)*d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+    &
-                                     F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
-
-     elseif(i+3 <= imax .and. i-3 >= imin)then
-!           - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
-!  fx(i) = -----------------------------------------------------------------
-!                                        60 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
-
-     elseif(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-
-     elseif(i+1 <= imax .and. i-1 >= imin)then
-!
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-
-! set imax and imin 0
-    endif
-
-! y direction   
-    if(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-3 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
-                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j-3,k)+F60 *fh(i,j-2,k)-F420*fh(i,j-1,k)-F378*fh(i,j  ,k) &
-                                  +F1050*fh(i,j+1,k)-F420*fh(i,j+2,k)+F140*fh(i,j+3,k)-F30 *fh(i,j+4,k)+THR*fh(i,j+5,k))
-
-    elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+3 <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
-                  Sfy(i,j,k)*d840dy*(-F5*fh(i,j+3,k)+F60 *fh(i,j+2,k)-F420*fh(i,j+1,k)-F378*fh(i,j  ,k) &
-                                  +F1050*fh(i,j-1,k)-F420*fh(i,j-2,k)+F140*fh(i,j-3,k)- F30*fh(i,j-4,k)+THR*fh(i,j-5,k))
-
-    elseif(j+4 <= jmax .and. j-4 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfy(i,j,k)*d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+    &
-                                     F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
-
-     elseif(j+3 <= jmax .and. j-3 >= jmin)then
-          
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
-
-     elseif(j+2 <= jmax .and. j-2 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
-                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-
-     elseif(j+1 <= jmax .and. j-1 >= jmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-! set jmin and jmax 0
-     endif
-!! z direction   
-    if(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-3 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                         &
-                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k-3)+F60 *fh(i,j,k-2)-F420*fh(i,j,k-1)-F378*fh(i,j,k  ) &
-                                  +F1050*fh(i,j,k+1)-F420*fh(i,j,k+2)+F140*fh(i,j,k+3)-F30 *fh(i,j,k+4)+THR*fh(i,j,k+5))
-
-    elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+3 <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                                         &
-                  Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k+3)+F60 *fh(i,j,k+2)-F420*fh(i,j,k+1)-F378*fh(i,j,k  ) &
-                                  +F1050*fh(i,j,k-1)-F420*fh(i,j,k-2)+F140*fh(i,j,k-3)- F30*fh(i,j,k-4)+THR*fh(i,j,k-5))
-
-    elseif(k+4 <= kmax .and. k-4 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                              &
-                  Sfz(i,j,k)*d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+    &
-                                     F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
-     
-     elseif(k+3 <= kmax .and. k-3 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                                                         &
-                  Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
-
-     elseif(k+2 <= kmax .and. k-2 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                            &
-                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-
-     elseif(k+1 <= kmax .and. k-1 >= kmin)then
-
-     f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-! set kmin and kmax 0
-     endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine lopsided
-
-#endif  

AMSS_NCKU_source/macrodef.h

@@ -2,7 +2,7 @@
 #ifndef MICRODEF_H
 #define MICRODEF_H
 
-#include "microdef.fh"
+#include "macrodef.fh"
 
 // application parameters
 

AMSS_NCKU_source/makefile

@@ -16,6 +16,12 @@ include makefile.inc
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
+TwoPunctures.o: TwoPunctures.C
+	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+
+TwoPunctureABE.o: TwoPunctureABE.C
+	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+
 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -96,7 +102,7 @@ ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,19 +1,29 @@
-
+## GCC version (commented out)
 ## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
 
-filein  = -I/usr/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## Intel oneAPI version with oneMKL (Optimized for performance)
+filein  = -I/usr/include/ -I${MKLROOT}/include
 
-## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -lmpich -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran
+## Using sequential MKL (OpenMP disabled for better single-threaded performance)
-LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
+## 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
 
-CXXAPPFLAGS  = -O3 -Wno-deprecated -Dfortran3 -Dnewc
+## Aggressive optimization flags:
-#f90appflags = -O3 -fpp
+## -O3: Maximum optimization
-f90appflags  = -O3 -x f95-cpp-input
+## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
-f90          = gfortran 
+## -fp-model fast=2: Aggressive floating-point optimizations
-f77          = gfortran 
+## -fma: Enable fused multiply-add instructions
-CXX          = g++
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-CC           = gcc
+               -Dfortran3 -Dnewc -I${MKLROOT}/include
-CLINKER      = mpic++ 
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+               -align array64byte -fpp -I${MKLROOT}/include
+f90          = ifx
+f77          = ifx
+CXX          = icpx
+CC           = icx
+CLINKER      = mpiicpx 
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

makefile_and_run.py

@@ -10,6 +10,17 @@
 
 import AMSS_NCKU_Input as input_data
 import subprocess
+import time
+## CPU core binding configuration using taskset
+## taskset ensures all child processes inherit the CPU affinity mask
+## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
+## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
+NUMACTL_CPU_BIND = "taskset -c 0-111"
+
+## Build parallelism configuration
+## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
+## Set make -j to utilize available cores for faster builds
+BUILD_JOBS = 104
 
 
 ##################################################################
@@ -26,11 +37,11 @@ def makefile_ABE():
     print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                        )
 
-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = "make -j4" + " ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
     elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = "make -j4" + " ABEGPU"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:
         print( " CPU/GPU numerical calculation setting is wrong " )
         print(                                                    )
@@ -67,8 +78,8 @@ def makefile_TwoPunctureABE():
     print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
     print(                                                            )
     
-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
-    makefile_command = "make" + " TwoPunctureABE"
+    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
 
     ## Execute the command with subprocess.Popen and stream output
     makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True) 
@@ -105,10 +116,10 @@ def run_ABE():
     ## Define the command to run; cast other values to strings as needed
     
     if (input_data.GPU_Calculation == "no"):
-        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output
@@ -141,13 +152,13 @@ def run_ABE():
 ## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE
 
 def run_TwoPunctureABE():
-
+    tp_time1=time.time()
     print(                                                          )
     print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
     print(                                                          )
     
     ## Define the command to run
-    TwoPuncture_command         = "./TwoPunctureABE"
+    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output
@@ -168,7 +179,9 @@ def run_TwoPunctureABE():
     print(                                               )
     print( " The TwoPunctureABE simulation is finished " ) 
     print(                                               )
-    
+    tp_time2=time.time()
+    et=tp_time2-tp_time1
+    print(f"Used time: {et}")
     return
 
 ##################################################################