fixup! Fix load explosion: use subprocess for binary data plots to avoid thread conflict

* Seems we don't have to set so many variables, `OMP_NUM_THREADS` is enough.

Test: Annotate the code for setting other environment variables. It runs normally.

.gitignore

@@ -1,3 +1,6 @@
 __pycache__
 GW150914
 GW150914-origin
+docs
+*.tmp
+

AMSS_NCKU_ABEtest.py

@@ -1,445 +0,0 @@
-
-##################################################################
-##
-## AMSS-NCKU ABE Test Program (Skip TwoPuncture if data exists)
-## Modified from AMSS_NCKU_Program.py
-## Author: Xiaoqu
-## Modified: 2026/02/01
-##
-##################################################################
-
-
-##################################################################
-
-## Print program introduction
-
-import print_information
-
-print_information.print_program_introduction()
-
-##################################################################
-
-import AMSS_NCKU_Input as input_data
-
-##################################################################
-
-## Create directories to store program run data
-
-import os
-import shutil
-import sys
-import time
-
-## Set the output directory according to the input file
-File_directory = os.path.join(input_data.File_directory)
-
-## Check if output directory exists and if TwoPuncture data is available
-skip_twopuncture = False
-output_directory = os.path.join(File_directory, "AMSS_NCKU_output")
-binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
-
-if os.path.exists(File_directory):
-    print( " Output directory already exists." )
-    print()
-
-    # Check if TwoPuncture initial data files exist
-    if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture"):
-        twopuncture_output = os.path.join(output_directory, "TwoPunctureABE")
-        input_par = os.path.join(output_directory, "input.par")
-
-        if os.path.exists(twopuncture_output) and os.path.exists(input_par):
-            print( " Found existing TwoPuncture initial data." )
-            print( " Do you want to skip TwoPuncture phase and reuse existing data?" )
-            print( " Input 'skip' to skip TwoPuncture and start ABE directly" )
-            print( " Input 'regenerate' to regenerate everything from scratch" )
-            print()
-
-            while True:
-                try:
-                    inputvalue = input()
-                    if ( inputvalue == "skip" ):
-                        print( " Skipping TwoPuncture phase, will reuse existing initial data." )
-                        print()
-                        skip_twopuncture = True
-                        break
-                    elif ( inputvalue == "regenerate" ):
-                        print( " Regenerating everything from scratch." )
-                        print()
-                        skip_twopuncture = False
-                        break
-                    else:
-                        print( " Please input 'skip' or 'regenerate'." )
-                except ValueError:
-                    print( " Please input 'skip' or 'regenerate'." )
-        else:
-            print( " TwoPuncture initial data not found, will regenerate everything." )
-            print()
-
-    # If not skipping, remove and recreate directory
-    if not skip_twopuncture:
-        shutil.rmtree(File_directory, ignore_errors=True)
-        os.mkdir(File_directory)
-        os.mkdir(output_directory)
-        os.mkdir(binary_results_directory)
-        figure_directory = os.path.join(File_directory, "figure")
-        os.mkdir(figure_directory)
-        shutil.copy("AMSS_NCKU_Input.py", File_directory)
-        print( " Output directory has been regenerated." )
-        print()
-else:
-    # Create fresh directory structure
-    os.mkdir(File_directory)
-    shutil.copy("AMSS_NCKU_Input.py", File_directory)
-    os.mkdir(output_directory)
-    os.mkdir(binary_results_directory)
-    figure_directory = os.path.join(File_directory, "figure")
-    os.mkdir(figure_directory)
-    print( " Output directory has been generated." )
-    print()
-
-# Ensure figure directory exists
-figure_directory = os.path.join(File_directory, "figure")
-if not os.path.exists(figure_directory):
-    os.mkdir(figure_directory)
-
-##################################################################
-
-## Output related parameter information
-
-import setup
-
-## Print and save input parameter information
-setup.print_input_data( File_directory )
-
-if not skip_twopuncture:
-    setup.generate_AMSSNCKU_input()
-
-setup.print_puncture_information()
-
-
-##################################################################
-
-## Generate AMSS-NCKU program input files based on the configured parameters
-
-if not skip_twopuncture:
-    print()
-    print( " Generating the AMSS-NCKU input parfile for the ABE executable." )
-    print()
-
-    ## Generate cgh-related input files from the grid information
-
-    import numerical_grid
-
-    numerical_grid.append_AMSSNCKU_cgh_input()
-
-    print()
-    print( " The input parfile for AMSS-NCKU C++ executable file ABE has been generated." )
-    print( " However, the input relevant to TwoPuncture need to be appended later." )
-    print()
-
-
-##################################################################
-
-## Plot the initial grid configuration
-
-if not skip_twopuncture:
-    print()
-    print( " Schematically plot the numerical grid structure." )
-    print()
-
-    import numerical_grid
-    numerical_grid.plot_initial_grid()
-
-
-##################################################################
-
-## Generate AMSS-NCKU macro files according to the numerical scheme and parameters
-
-if not skip_twopuncture:
-    print()
-    print( " Automatically generating the macro file for AMSS-NCKU C++ executable file ABE " )
-    print( " (Based on the finite-difference numerical scheme) " )
-    print()
-
-    import generate_macrodef
-
-    generate_macrodef.generate_macrodef_h()
-    print( " AMSS-NCKU macro file macrodef.h has been generated. " )
-
-    generate_macrodef.generate_macrodef_fh()
-    print( " AMSS-NCKU macro file macrodef.fh has been generated. " )
-
-
-##################################################################
-
-# Compile the AMSS-NCKU program according to user requirements
-# NOTE: ABE compilation is always performed, even when skipping TwoPuncture
-
-print()
-print( " Preparing to compile and run the AMSS-NCKU code as requested " )
-print( " Compiling the AMSS-NCKU code based on the generated macro files " )
-print()
-
-AMSS_NCKU_source_path = "AMSS_NCKU_source"
-AMSS_NCKU_source_copy = os.path.join(File_directory, "AMSS_NCKU_source_copy")
-
-## If AMSS_NCKU source folder is missing, create it and prompt the user
-if not os.path.exists(AMSS_NCKU_source_path):
-    os.makedirs(AMSS_NCKU_source_path)
-    print( " The AMSS-NCKU source files are incomplete; copy all source files into ./AMSS_NCKU_source. " )
-    print( " Press Enter to continue. " )
-    inputvalue = input()
-
-# Copy AMSS-NCKU source files to prepare for compilation
-# If skipping TwoPuncture and source_copy already exists, remove it first
-if skip_twopuncture and os.path.exists(AMSS_NCKU_source_copy):
-    shutil.rmtree(AMSS_NCKU_source_copy)
-
-shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
-
-# Copy the generated macro files into the AMSS_NCKU source folder
-if not skip_twopuncture:
-    macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
-    macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
-else:
-    # When skipping TwoPuncture, use existing macro files from previous run
-    macrodef_h_path  = os.path.join(File_directory, "macrodef.h")
-    macrodef_fh_path = os.path.join(File_directory, "macrodef.fh")
-
-shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
-shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
-
-# Compile related programs
-import makefile_and_run
-
-## Change working directory to the target source copy
-os.chdir(AMSS_NCKU_source_copy)
-
-## Build the main AMSS-NCKU executable (ABE or ABEGPU)
-makefile_and_run.makefile_ABE()
-
-## If the initial-data method is Ansorg-TwoPuncture, build the TwoPunctureABE executable
-## Only build TwoPunctureABE if not skipping TwoPuncture phase
-if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
-    makefile_and_run.makefile_TwoPunctureABE()
-
-## Change current working directory back up two levels
-os.chdir('..')
-os.chdir('..')
-
-print()
-
-##################################################################
-
-## Copy the AMSS-NCKU executable (ABE/ABEGPU) to the run directory
-
-if (input_data.GPU_Calculation == "no"):
-    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
-elif (input_data.GPU_Calculation == "yes"):
-    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
-
-if not os.path.exists( ABE_file ):
-    print()
-    print( " Lack of AMSS-NCKU executable file ABE/ABEGPU; recompile AMSS_NCKU_source manually. " )
-    print( " When recompilation is finished, press Enter to continue. " )
-    inputvalue = input()
-
-## Copy the executable ABE (or ABEGPU) into the run directory
-shutil.copy2(ABE_file, output_directory)
-
-## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
-## Only copy TwoPunctureABE if not skipping TwoPuncture phase
-if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
-    TwoPuncture_file = os.path.join(AMSS_NCKU_source_copy, "TwoPunctureABE")
-
-    if not os.path.exists( TwoPuncture_file ):
-        print()
-        print( " Lack of AMSS-NCKU executable file TwoPunctureABE; recompile TwoPunctureABE in AMSS_NCKU_source. " )
-        print( " When recompilation is finished, press Enter to continue. " )
-        inputvalue = input()
-
-    ## Copy the TwoPunctureABE executable into the run directory
-    shutil.copy2(TwoPuncture_file, output_directory)
-
-##################################################################
-
-## If the initial-data method is TwoPuncture, generate the TwoPuncture input files
-
-if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and not skip_twopuncture:
-
-    print()
-    print( " Initial data is chosen as Ansorg-TwoPuncture" )
-    print()
-    
-    print()
-    print( " Automatically generating the input parfile for the TwoPunctureABE executable " )
-    print()
-    
-    import generate_TwoPuncture_input
-    
-    generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
-    
-    print()
-    print( " The input parfile for the TwoPunctureABE executable has been generated. " )
-    print()
-    
-    ## Generated AMSS-NCKU TwoPuncture input filename
-    AMSS_NCKU_TwoPuncture_inputfile      = 'AMSS-NCKU-TwoPuncture.input'
-    AMSS_NCKU_TwoPuncture_inputfile_path = os.path.join( File_directory, AMSS_NCKU_TwoPuncture_inputfile )
- 
-    ## Copy and rename the file
-    shutil.copy2( AMSS_NCKU_TwoPuncture_inputfile_path, os.path.join(output_directory, 'TwoPunctureinput.par') )
-    
-    ## Run TwoPuncture to generate initial-data files
-    
-    start_time = time.time()  # Record start time
-
-    print()
-    print()
-    
-    ## Change to the output (run) directory
-    os.chdir(output_directory)
-
-    ## Run the TwoPuncture executable
-    import makefile_and_run
-    makefile_and_run.run_TwoPunctureABE()
-    
-    ## Change current working directory back up two levels
-    os.chdir('..')
-    os.chdir('..')
-
-elif (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ) and skip_twopuncture:
-    print()
-    print( " Skipping TwoPuncture execution, using existing initial data." )
-    print()
-    start_time = time.time()  # Record start time for ABE only
-else:
-    start_time = time.time()  # Record start time
-    
-##################################################################
-    
-## Update puncture data based on TwoPuncture run results
-
-if not skip_twopuncture:
-    import renew_puncture_parameter
-    renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
-
-    ## Generated AMSS-NCKU input filename
-    AMSS_NCKU_inputfile      = 'AMSS-NCKU.input'
-    AMSS_NCKU_inputfile_path = os.path.join(File_directory, AMSS_NCKU_inputfile)
- 
-    ## Copy and rename the file
-    shutil.copy2( AMSS_NCKU_inputfile_path, os.path.join(output_directory, 'input.par') )
-
-    print()
-    print( " Successfully copy all AMSS-NCKU input parfile to target dictionary. " )
-    print()
-else:
-    print()
-    print( " Using existing input.par file from previous run." )
-    print()
-
-##################################################################
-
-## Launch the AMSS-NCKU program
-
-print()
-print()
-
-## Change to the run directory
-os.chdir( output_directory )
-
-import makefile_and_run
-makefile_and_run.run_ABE()
-
-## Change current working directory back up two levels
-os.chdir('..')
-os.chdir('..')
-
-end_time = time.time()
-elapsed_time = end_time - start_time
-
-##################################################################
-
-## Copy some basic input and log files out to facilitate debugging
-
-## Path to the file that stores calculation settings
-AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "setting.par")
-## Copy and rename the file for easier inspection
-shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "AMSSNCKU_setting_parameter") )
-
-## Path to the error log file
-AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "Error.log")
-## Copy and rename the error log
-shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "Error.log") )
-
-## Primary program outputs
-AMSS_NCKU_BH_data         = os.path.join(binary_results_directory, "bssn_BH.dat"        )
-AMSS_NCKU_ADM_data        = os.path.join(binary_results_directory, "bssn_ADMQs.dat"     )
-AMSS_NCKU_psi4_data       = os.path.join(binary_results_directory, "bssn_psi4.dat"      )
-AMSS_NCKU_constraint_data = os.path.join(binary_results_directory, "bssn_constraint.dat")
-## copy and rename the file
-shutil.copy( AMSS_NCKU_BH_data,         os.path.join(output_directory, "bssn_BH.dat"        ) )
-shutil.copy( AMSS_NCKU_ADM_data,        os.path.join(output_directory, "bssn_ADMQs.dat"     ) )
-shutil.copy( AMSS_NCKU_psi4_data,       os.path.join(output_directory, "bssn_psi4.dat"      ) )
-shutil.copy( AMSS_NCKU_constraint_data, os.path.join(output_directory, "bssn_constraint.dat") )
-
-## Additional program outputs
-if (input_data.Equation_Class == "BSSN-EM"):
-    AMSS_NCKU_phi1_data = os.path.join(binary_results_directory, "bssn_phi1.dat" )
-    AMSS_NCKU_phi2_data = os.path.join(binary_results_directory, "bssn_phi2.dat" )
-    shutil.copy( AMSS_NCKU_phi1_data, os.path.join(output_directory, "bssn_phi1.dat" ) )
-    shutil.copy( AMSS_NCKU_phi2_data, os.path.join(output_directory, "bssn_phi2.dat" ) )
-elif (input_data.Equation_Class == "BSSN-EScalar"):
-    AMSS_NCKU_maxs_data = os.path.join(binary_results_directory, "bssn_maxs.dat" )
-    shutil.copy( AMSS_NCKU_maxs_data, os.path.join(output_directory, "bssn_maxs.dat" ) )
-
-##################################################################
-
-## Plot the AMSS-NCKU program results
-
-print()
-print( " Plotting the txt and binary results data from the AMSS-NCKU simulation " )
-print()
-
-
-import plot_xiaoqu
-import plot_GW_strain_amplitude_xiaoqu
-
-## Plot black hole trajectory
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
-
-## Plot black hole separation vs. time
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
-
-## Plot gravitational waveforms (psi4 and strain amplitude)
-for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
-    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
-
-## Plot ADM mass evolution
-for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
-
-## Plot Hamiltonian constraint violation over time
-for i in range(input_data.grid_level):
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
-
-## Plot stored binary data
-plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
-
-print()
-print( f" This Program Cost = {elapsed_time} Seconds " )
-print()
-
-
-##################################################################
-
-print()
-print( " The AMSS-NCKU-Python simulation is successfully finished, thanks for using !!! " )
-print()
-
-##################################################################
-
-

AMSS_NCKU_Program.py

@@ -8,6 +8,14 @@
 ##
 ##################################################################
 
+## Guard against re-execution by multiprocessing child processes.
+## Without this, using 'spawn' or 'forkserver' context would cause every
+## worker to re-run the entire script, spawning exponentially more
+## workers (fork bomb).
+if __name__ != '__main__':
+    import sys as _sys
+    _sys.exit(0)
+
 
 ##################################################################
 
@@ -424,26 +432,31 @@ print(
 
 import plot_xiaoqu
 import plot_GW_strain_amplitude_xiaoqu
+from parallel_plot_helper import run_plot_tasks_parallel
+
+plot_tasks = []
 
 ## Plot black hole trajectory
-plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
-plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
 
 ## Plot black hole separation vs. time
-plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
 
 ## Plot gravitational waveforms (psi4 and strain amplitude)
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
-    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
 
 ## Plot ADM mass evolution
 for i in range(input_data.Detector_Number):
-    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
 
 ## Plot Hamiltonian constraint violation over time
 for i in range(input_data.grid_level):
-    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
+
+run_plot_tasks_parallel(plot_tasks)
 
 ## Plot stored binary data
 plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )

AMSS_NCKU_Verify_ASC26.py

@@ -277,4 +277,3 @@ def main():
 
 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
+! Commit the descriptor
-  j=j-m
+status = DftiCommitDescriptor(desc)
-  m=m/2
+if (status /= 0) then
-goto 1
+   status = DftiFreeDescriptor(desc)
+   return
 endif
-j=j+m
+
-enddo
+! Execute FFT based on direction
-mmax=2
+if (isign == 1) then
-2  if (n.gt.mmax) then
+   ! Forward FFT: exp(-2*pi*i*k*n/N)
-     istep=2*mmax
+   status = DftiComputeForward(desc, dataa)
-     theta=6.28318530717959d0/(isign*mmax)
+else
-     wpr=-2.d0*sin(0.5d0*theta)**2
+   ! Backward FFT: exp(+2*pi*i*k*n/N)
-     wpi=sin(theta)
+   status = DftiComputeBackward(desc, dataa)
-     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
+
+! Free descriptor
+status = DftiFreeDescriptor(desc)
+
 return
 END SUBROUTINE four1

AMSS_NCKU_source/Parallel.C

@@ -3756,6 +3756,358 @@ void Parallel::Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
   delete[] transfer_src;
   delete[] transfer_dst;
 }
+//
+// Async Sync: split into SyncBegin (initiate MPI) and SyncEnd (wait + unpack)
+// This allows overlapping MPI communication with computation.
+//
+static void transfer_begin(Parallel::TransferState *ts)
+{
+  int myrank;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  int cpusize = ts->cpusize;
+
+  ts->reqs = new MPI_Request[2 * cpusize];
+  ts->stats = new MPI_Status[2 * cpusize];
+  ts->req_no = 0;
+  ts->send_data = new double *[cpusize];
+  ts->rec_data = new double *[cpusize];
+  int length;
+
+  for (int node = 0; node < cpusize; node++)
+  {
+    ts->send_data[node] = ts->rec_data[node] = 0;
+    if (node == myrank)
+    {
+      // Local copy: pack then immediately unpack (no MPI needed)
+      if ((length = Parallel::data_packer(0, ts->transfer_src[myrank], ts->transfer_dst[myrank],
+                                          node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry)))
+      {
+        double *local_data = new double[length];
+        if (!local_data)
+        {
+          cout << "out of memory in transfer_begin, local copy" << endl;
+          MPI_Abort(MPI_COMM_WORLD, 1);
+        }
+        Parallel::data_packer(local_data, ts->transfer_src[myrank], ts->transfer_dst[myrank],
+                              node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry);
+        Parallel::data_packer(local_data, ts->transfer_src[node], ts->transfer_dst[node],
+                              node, UNPACK, ts->VarList1, ts->VarList2, ts->Symmetry);
+        delete[] local_data;
+      }
+    }
+    else
+    {
+      // send from this cpu to cpu#node
+      if ((length = Parallel::data_packer(0, ts->transfer_src[myrank], ts->transfer_dst[myrank],
+                                          node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry)))
+      {
+        ts->send_data[node] = new double[length];
+        if (!ts->send_data[node])
+        {
+          cout << "out of memory in transfer_begin, send" << endl;
+          MPI_Abort(MPI_COMM_WORLD, 1);
+        }
+        Parallel::data_packer(ts->send_data[node], ts->transfer_src[myrank], ts->transfer_dst[myrank],
+                              node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry);
+        MPI_Isend((void *)ts->send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD,
+                  ts->reqs + ts->req_no++);
+      }
+      // receive from cpu#node to this cpu
+      if ((length = Parallel::data_packer(0, ts->transfer_src[node], ts->transfer_dst[node],
+                                          node, UNPACK, ts->VarList1, ts->VarList2, ts->Symmetry)))
+      {
+        ts->rec_data[node] = new double[length];
+        if (!ts->rec_data[node])
+        {
+          cout << "out of memory in transfer_begin, recv" << endl;
+          MPI_Abort(MPI_COMM_WORLD, 1);
+        }
+        MPI_Irecv((void *)ts->rec_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD,
+                  ts->reqs + ts->req_no++);
+      }
+    }
+  }
+  // NOTE: MPI_Waitall is NOT called here - that happens in transfer_end
+}
+//
+static void transfer_end(Parallel::TransferState *ts)
+{
+  // Wait for all pending MPI operations
+  MPI_Waitall(ts->req_no, ts->reqs, ts->stats);
+
+  // Unpack received data from remote ranks
+  for (int node = 0; node < ts->cpusize; node++)
+    if (ts->rec_data[node])
+      Parallel::data_packer(ts->rec_data[node], ts->transfer_src[node], ts->transfer_dst[node],
+                            node, UNPACK, ts->VarList1, ts->VarList2, ts->Symmetry);
+
+  // Cleanup MPI buffers
+  for (int node = 0; node < ts->cpusize; node++)
+  {
+    if (ts->send_data[node])
+      delete[] ts->send_data[node];
+    if (ts->rec_data[node])
+      delete[] ts->rec_data[node];
+  }
+  delete[] ts->reqs;
+  delete[] ts->stats;
+  delete[] ts->send_data;
+  delete[] ts->rec_data;
+}
+//
+Parallel::SyncHandle *Parallel::SyncBegin(Patch *Pat, MyList<var> *VarList, int Symmetry)
+{
+  int cpusize;
+  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
+
+  SyncHandle *handle = new SyncHandle;
+  handle->num_states = 1;
+  handle->states = new TransferState[1];
+
+  TransferState *ts = &handle->states[0];
+  ts->cpusize = cpusize;
+  ts->VarList1 = VarList;
+  ts->VarList2 = VarList;
+  ts->Symmetry = Symmetry;
+  ts->owns_gsl = true;
+
+  ts->dst = build_ghost_gsl(Pat);
+  ts->src = new MyList<Parallel::gridseg> *[cpusize];
+  ts->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
+  ts->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
+  for (int node = 0; node < cpusize; node++)
+  {
+    ts->src[node] = build_owned_gsl0(Pat, node);
+    build_gstl(ts->src[node], ts->dst, &ts->transfer_src[node], &ts->transfer_dst[node]);
+  }
+
+  transfer_begin(ts);
+
+  return handle;
+}
+//
+Parallel::SyncHandle *Parallel::SyncBegin(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
+{
+  int cpusize;
+  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
+
+  // Count patches
+  int num_patches = 0;
+  MyList<Patch> *Pp = PatL;
+  while (Pp) { num_patches++; Pp = Pp->next; }
+
+  SyncHandle *handle = new SyncHandle;
+  handle->num_states = num_patches + 1; // intra-patch transfers + 1 inter-patch transfer
+  handle->states = new TransferState[handle->num_states];
+
+  // Intra-patch sync: for each patch, build ghost lists and initiate transfer
+  int idx = 0;
+  Pp = PatL;
+  while (Pp)
+  {
+    TransferState *ts = &handle->states[idx];
+    ts->cpusize = cpusize;
+    ts->VarList1 = VarList;
+    ts->VarList2 = VarList;
+    ts->Symmetry = Symmetry;
+    ts->owns_gsl = true;
+
+    ts->dst = build_ghost_gsl(Pp->data);
+    ts->src = new MyList<Parallel::gridseg> *[cpusize];
+    ts->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
+    ts->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
+    for (int node = 0; node < cpusize; node++)
+    {
+      ts->src[node] = build_owned_gsl0(Pp->data, node);
+      build_gstl(ts->src[node], ts->dst, &ts->transfer_src[node], &ts->transfer_dst[node]);
+    }
+
+    transfer_begin(ts);
+
+    idx++;
+    Pp = Pp->next;
+  }
+
+  // Inter-patch sync: buffer zone exchange between patches
+  {
+    TransferState *ts = &handle->states[idx];
+    ts->cpusize = cpusize;
+    ts->VarList1 = VarList;
+    ts->VarList2 = VarList;
+    ts->Symmetry = Symmetry;
+    ts->owns_gsl = true;
+
+    ts->dst = build_buffer_gsl(PatL);
+    ts->src = new MyList<Parallel::gridseg> *[cpusize];
+    ts->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
+    ts->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
+    for (int node = 0; node < cpusize; node++)
+    {
+      ts->src[node] = build_owned_gsl(PatL, node, 5, Symmetry);
+      build_gstl(ts->src[node], ts->dst, &ts->transfer_src[node], &ts->transfer_dst[node]);
+    }
+
+    transfer_begin(ts);
+  }
+
+  return handle;
+}
+//
+void Parallel::SyncEnd(SyncHandle *handle)
+{
+  if (!handle)
+    return;
+
+  // Wait for all pending transfers and unpack
+  for (int i = 0; i < handle->num_states; i++)
+  {
+    TransferState *ts = &handle->states[i];
+    transfer_end(ts);
+
+    // Cleanup grid segment lists only if this state owns them
+    if (ts->owns_gsl)
+    {
+      if (ts->dst)
+        ts->dst->destroyList();
+      for (int node = 0; node < ts->cpusize; node++)
+      {
+        if (ts->src[node])
+          ts->src[node]->destroyList();
+        if (ts->transfer_src[node])
+          ts->transfer_src[node]->destroyList();
+        if (ts->transfer_dst[node])
+          ts->transfer_dst[node]->destroyList();
+      }
+      delete[] ts->src;
+      delete[] ts->transfer_src;
+      delete[] ts->transfer_dst;
+    }
+  }
+
+  delete[] handle->states;
+  delete handle;
+}
+//
+// SyncPreparePlan: Pre-build grid segment lists for a patch list.
+// The plan can be reused across multiple SyncBeginWithPlan calls
+// as long as the mesh topology does not change (no regridding).
+//
+Parallel::SyncPlan *Parallel::SyncPreparePlan(MyList<Patch> *PatL, int Symmetry)
+{
+  int cpusize;
+  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
+
+  // Count patches
+  int num_patches = 0;
+  MyList<Patch> *Pp = PatL;
+  while (Pp) { num_patches++; Pp = Pp->next; }
+
+  SyncPlan *plan = new SyncPlan;
+  plan->num_entries = num_patches + 1; // intra-patch + 1 inter-patch
+  plan->Symmetry = Symmetry;
+  plan->entries = new SyncPlanEntry[plan->num_entries];
+
+  // Intra-patch entries: ghost zone exchange within each patch
+  int idx = 0;
+  Pp = PatL;
+  while (Pp)
+  {
+    SyncPlanEntry *pe = &plan->entries[idx];
+    pe->cpusize = cpusize;
+    pe->dst = build_ghost_gsl(Pp->data);
+    pe->src = new MyList<Parallel::gridseg> *[cpusize];
+    pe->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
+    pe->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
+    for (int node = 0; node < cpusize; node++)
+    {
+      pe->src[node] = build_owned_gsl0(Pp->data, node);
+      build_gstl(pe->src[node], pe->dst, &pe->transfer_src[node], &pe->transfer_dst[node]);
+    }
+    idx++;
+    Pp = Pp->next;
+  }
+
+  // Inter-patch entry: buffer zone exchange between patches
+  {
+    SyncPlanEntry *pe = &plan->entries[idx];
+    pe->cpusize = cpusize;
+    pe->dst = build_buffer_gsl(PatL);
+    pe->src = new MyList<Parallel::gridseg> *[cpusize];
+    pe->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
+    pe->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
+    for (int node = 0; node < cpusize; node++)
+    {
+      pe->src[node] = build_owned_gsl(PatL, node, 5, Symmetry);
+      build_gstl(pe->src[node], pe->dst, &pe->transfer_src[node], &pe->transfer_dst[node]);
+    }
+  }
+
+  return plan;
+}
+//
+void Parallel::SyncFreePlan(SyncPlan *plan)
+{
+  if (!plan)
+    return;
+
+  for (int i = 0; i < plan->num_entries; i++)
+  {
+    SyncPlanEntry *pe = &plan->entries[i];
+    if (pe->dst)
+      pe->dst->destroyList();
+    for (int node = 0; node < pe->cpusize; node++)
+    {
+      if (pe->src[node])
+        pe->src[node]->destroyList();
+      if (pe->transfer_src[node])
+        pe->transfer_src[node]->destroyList();
+      if (pe->transfer_dst[node])
+        pe->transfer_dst[node]->destroyList();
+    }
+    delete[] pe->src;
+    delete[] pe->transfer_src;
+    delete[] pe->transfer_dst;
+  }
+  delete[] plan->entries;
+  delete plan;
+}
+//
+// SyncBeginWithPlan: Use pre-built GSLs from a SyncPlan to initiate async transfer.
+// This avoids the O(cpusize * blocks^2) cost of rebuilding GSLs on every call.
+//
+Parallel::SyncHandle *Parallel::SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList)
+{
+  return SyncBeginWithPlan(plan, VarList, VarList);
+}
+//
+Parallel::SyncHandle *Parallel::SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList1, MyList<var> *VarList2)
+{
+  SyncHandle *handle = new SyncHandle;
+  handle->num_states = plan->num_entries;
+  handle->states = new TransferState[handle->num_states];
+
+  for (int i = 0; i < plan->num_entries; i++)
+  {
+    SyncPlanEntry *pe = &plan->entries[i];
+    TransferState *ts = &handle->states[i];
+
+    ts->cpusize = pe->cpusize;
+    ts->VarList1 = VarList1;
+    ts->VarList2 = VarList2;
+    ts->Symmetry = plan->Symmetry;
+    ts->owns_gsl = false; // GSLs are owned by the plan, not this handle
+
+    // Borrow GSL pointers from the plan (do NOT free them in SyncEnd)
+    ts->transfer_src = pe->transfer_src;
+    ts->transfer_dst = pe->transfer_dst;
+    ts->src = pe->src;
+    ts->dst = pe->dst;
+
+    transfer_begin(ts);
+  }
+
+  return handle;
+}
 // collect buffer grid segments or blocks for the periodic boundary condition of given patch
 // ---------------------------------------------------
 // |con |                                       |con |

AMSS_NCKU_source/Parallel.h

@@ -81,6 +81,53 @@ namespace Parallel
                    int Symmetry);
   void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
   void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+
+  // Async Sync: overlap MPI communication with computation
+  struct TransferState
+  {
+    MPI_Request *reqs;
+    MPI_Status *stats;
+    int req_no;
+    double **send_data;
+    double **rec_data;
+    int cpusize;
+    MyList<gridseg> **transfer_src;
+    MyList<gridseg> **transfer_dst;
+    MyList<gridseg> **src;
+    MyList<gridseg> *dst;
+    MyList<var> *VarList1;
+    MyList<var> *VarList2;
+    int Symmetry;
+    bool owns_gsl; // true if this state owns and should free the GSLs
+  };
+  struct SyncHandle
+  {
+    TransferState *states;
+    int num_states;
+  };
+  SyncHandle *SyncBegin(Patch *Pat, MyList<var> *VarList, int Symmetry);
+  SyncHandle *SyncBegin(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void SyncEnd(SyncHandle *handle);
+
+  // Cached GSL plan: pre-build grid segment lists once, reuse across multiple Sync calls
+  struct SyncPlanEntry
+  {
+    int cpusize;
+    MyList<gridseg> **transfer_src;
+    MyList<gridseg> **transfer_dst;
+    MyList<gridseg> **src;
+    MyList<gridseg> *dst;
+  };
+  struct SyncPlan
+  {
+    SyncPlanEntry *entries;
+    int num_entries;
+    int Symmetry;
+  };
+  SyncPlan *SyncPreparePlan(MyList<Patch> *PatL, int Symmetry);
+  void SyncFreePlan(SyncPlan *plan);
+  SyncHandle *SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList);
+  SyncHandle *SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList1, MyList<var> *VarList2);
   void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                    int Symmetry);

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
@@ -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)

AMSS_NCKU_source/Z4c_class.C

@@ -186,6 +186,12 @@ void Z4c_class::Step(int lev, int YN)
   int ERROR = 0;
 
   MyList<ss_patch> *sPp;
+
+  // Pre-build grid segment lists once for this level's patches.
+  // These are reused across predictor + 3 corrector SyncBegin calls,
+  // avoiding O(cpusize * blocks^2) rebuild each time.
+  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
+
   // Predictor
   MyList<Patch> *Pp = GH->PatL[lev];
   while (Pp)
@@ -321,13 +327,17 @@ void Z4c_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // check error information
+  // Start async ghost zone exchange - overlaps with error check and Shell computation
+  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
+
+  // check error information (overlaps with MPI transfer)
   {
     int erh = ERROR;
     MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
   }
   if (ERROR)
   {
+    Parallel::SyncEnd(sync_pre); sync_pre = 0;
     Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
     if (myrank == 0)
     {
@@ -475,6 +485,7 @@ void Z4c_class::Step(int lev, int YN)
   }
   if (ERROR)
   {
+    Parallel::SyncEnd(sync_pre); sync_pre = 0;
     SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
     if (myrank == 0)
     {
@@ -485,7 +496,8 @@ void Z4c_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // Complete async ghost zone exchange
+  if (sync_pre) Parallel::SyncEnd(sync_pre);
 
 #ifdef WithShell
   if (lev == 0)
@@ -693,13 +705,17 @@ void Z4c_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // check error information
+    // Start async ghost zone exchange - overlaps with error check and Shell computation
+    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
+
+    // check error information (overlaps with MPI transfer)
     {
       int erh = ERROR;
       MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
     }
     if (ERROR)
     {
+      Parallel::SyncEnd(sync_cor); sync_cor = 0;
       Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
@@ -857,6 +873,7 @@ void Z4c_class::Step(int lev, int YN)
     }
     if (ERROR)
     {
+      Parallel::SyncEnd(sync_cor); sync_cor = 0;
       SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
@@ -868,7 +885,8 @@ void Z4c_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // Complete async ghost zone exchange
+    if (sync_cor) Parallel::SyncEnd(sync_cor);
 
 #ifdef WithShell
     if (lev == 0)
@@ -1042,6 +1060,8 @@ void Z4c_class::Step(int lev, int YN)
       Porg0[ithBH][2] = Porg1[ithBH][2];
     }
   }
+
+  Parallel::SyncFreePlan(sync_plan);
 }
 #else
 // for constraint preserving boundary (CPBC)
@@ -1075,6 +1095,10 @@ void Z4c_class::Step(int lev, int YN)
   int ERROR = 0;
 
   MyList<ss_patch> *sPp;
+
+  // Pre-build grid segment lists once for this level's patches.
+  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
+
   // Predictor
   MyList<Patch> *Pp = GH->PatL[lev];
   while (Pp)
@@ -1542,13 +1566,17 @@ void Z4c_class::Step(int lev, int YN)
   }
 #endif
   }
-  // check error information
+  // Start async ghost zone exchange - overlaps with error check
+  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
+
+  // check error information (overlaps with MPI transfer)
   {
     int erh = ERROR;
     MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
   }
   if (ERROR)
   {
+    Parallel::SyncEnd(sync_pre); sync_pre = 0;
     SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
     if (myrank == 0)
     {
@@ -1558,7 +1586,8 @@ void Z4c_class::Step(int lev, int YN)
     }
   }
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // Complete async ghost zone exchange
+  if (sync_pre) Parallel::SyncEnd(sync_pre);
 
   if (lev == 0)
   {
@@ -2103,13 +2132,17 @@ void Z4c_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // check error information
+    // Start async ghost zone exchange - overlaps with error check
+    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
+
+    // check error information (overlaps with MPI transfer)
     {
       int erh = ERROR;
       MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
     }
     if (ERROR)
     {
+      Parallel::SyncEnd(sync_cor); sync_cor = 0;
       SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
@@ -2120,7 +2153,8 @@ void Z4c_class::Step(int lev, int YN)
       }
     }
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // Complete async ghost zone exchange
+    if (sync_cor) Parallel::SyncEnd(sync_cor);
 
     if (lev == 0)
     {
@@ -2346,6 +2380,8 @@ void Z4c_class::Step(int lev, int YN)
 	  DG_List->clearList();
 	}
 #endif
+
+  Parallel::SyncFreePlan(sync_plan);
 }
 #endif
 #undef MRBD

AMSS_NCKU_source/bssn_class.C

@@ -3035,6 +3035,12 @@ void bssn_class::Step(int lev, int YN)
   int ERROR = 0;
 
   MyList<ss_patch> *sPp;
+
+  // Pre-build grid segment lists once for this level's patches.
+  // These are reused across predictor + 3 corrector SyncBegin calls,
+  // avoiding O(cpusize * blocks^2) rebuild each time.
+  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
+
   // Predictor
   MyList<Patch> *Pp = GH->PatL[lev];
   while (Pp)
@@ -3158,13 +3164,18 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // check error information
+
+  // Start async ghost zone exchange - overlaps with error check and Shell computation
+  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
+
+  // check error information (overlaps with MPI transfer)
   {
     int erh = ERROR;
     MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
   }
   if (ERROR)
   {
+    Parallel::SyncEnd(sync_pre); sync_pre = 0;
     Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
     if (myrank == 0)
     {
@@ -3324,6 +3335,7 @@ void bssn_class::Step(int lev, int YN)
 
   if (ERROR)
   {
+    Parallel::SyncEnd(sync_pre); sync_pre = 0;
     SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
     if (myrank == 0)
     {
@@ -3334,7 +3346,8 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // Complete async ghost zone exchange
+  if (sync_pre) Parallel::SyncEnd(sync_pre);
 
 #ifdef WithShell
   if (lev == 0)
@@ -3528,7 +3541,10 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // check error information
+    // Start async ghost zone exchange - overlaps with error check and Shell computation
+    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
+
+    // check error information (overlaps with MPI transfer)
     {
       int erh = ERROR;
       MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
@@ -3536,6 +3552,7 @@ void bssn_class::Step(int lev, int YN)
 
     if (ERROR)
     {
+      Parallel::SyncEnd(sync_cor); sync_cor = 0;
       Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
@@ -3692,6 +3709,7 @@ void bssn_class::Step(int lev, int YN)
     }
     if (ERROR)
     {
+      Parallel::SyncEnd(sync_cor); sync_cor = 0;
       SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
@@ -3704,7 +3722,8 @@ void bssn_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // Complete async ghost zone exchange
+    if (sync_cor) Parallel::SyncEnd(sync_cor);
 
 #ifdef WithShell
     if (lev == 0)
@@ -3895,6 +3914,8 @@ void bssn_class::Step(int lev, int YN)
       Porg0[ithBH][2] = Porg1[ithBH][2];
     }
   }
+
+  Parallel::SyncFreePlan(sync_plan);
 }
 
 //================================================================================================
@@ -4817,6 +4838,12 @@ void bssn_class::Step(int lev, int YN)
   int ERROR = 0;
 
   MyList<ss_patch> *sPp;
+
+  // Pre-build grid segment lists once for this level's patches.
+  // These are reused across predictor + 3 corrector SyncBegin calls,
+  // avoiding O(cpusize * blocks^2) rebuild each time.
+  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
+
   // Predictor
   MyList<Patch> *Pp = GH->PatL[lev];
   while (Pp)
@@ -4943,13 +4970,17 @@ void bssn_class::Step(int lev, int YN)
 
   //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");
 
-  // check error information
+  // Start async ghost zone exchange - overlaps with error check and BH position
+  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
+
+  // check error information (overlaps with MPI transfer)
   {
     int erh = ERROR;
     MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
   }
   if (ERROR)
   {
+    Parallel::SyncEnd(sync_pre); sync_pre = 0;
     Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
     if (myrank == 0)
     {
@@ -4961,7 +4992,8 @@ void bssn_class::Step(int lev, int YN)
 
   //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // Complete async ghost zone exchange
+  if (sync_pre) Parallel::SyncEnd(sync_pre);
 
 #if (MAPBH == 0)
   // for black hole position
@@ -5140,13 +5172,17 @@ void bssn_class::Step(int lev, int YN)
 
     //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");
 
-    // check error information
+    // Start async ghost zone exchange - overlaps with error check and BH position
+    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
+
+    // check error information (overlaps with MPI transfer)
     {
       int erh = ERROR;
       MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
     }
     if (ERROR)
     {
+      Parallel::SyncEnd(sync_cor); sync_cor = 0;
       Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
       if (myrank == 0)
       {
@@ -5160,7 +5196,8 @@ void bssn_class::Step(int lev, int YN)
 
     //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // Complete async ghost zone exchange
+    if (sync_cor) Parallel::SyncEnd(sync_cor);
 
     //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
 
@@ -5276,6 +5313,8 @@ void bssn_class::Step(int lev, int YN)
 
   //     if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<endl;
   //     misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"complet GH Step");
+
+  Parallel::SyncFreePlan(sync_plan);
 }
 
 //================================================================================================

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)
 
@@ -943,103 +945,60 @@
   SSA(2)=SYM
   SSA(3)=ANTI
 
-!!!!!!!!!advection term part
+!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
+! lopsided_kodis shares the symmetry_bd buffer between advection and
+! dissipation, eliminating redundant full-grid copies. For metric variables
+! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
+! so the constant offset has no effect on dissipation.
 
-  call lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS)
+  call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA)
+  call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA)
+  call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
 
-  call lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS)
+  call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA)
+  call lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA)
+  call lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
 
-  call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
 
-  call lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
+  call lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
+  call lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
+  call lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-!!
+
+#if 1 
+!! bam does not apply dissipation on gauge variables
+  call lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
+  call lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+#endif
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+  call lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
+  call lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
+  call lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
+#endif
+#else
+! No dissipation on gauge variables (advection only)
   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
 
   if(co == 0)then
 ! ham_Res = trR + 2/3 * K^2 - A_ij * A^ij - 16 * PI * rho

AMSS_NCKU_source/enforce_algebra.f90

@@ -19,48 +19,60 @@
 
 !~~~~~~~> 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) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
 
-  gxx = gxx * detg
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-  gxy = gxy * detg
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
-  gxz = gxz * detg
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
-  gyy = gyy * detg
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
-  gyz = gyz * detg
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
-  gzz = gzz * detg
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
 
-  dxx = gxx - ONE
+    lscale = ONE / ( ldetg ** F1o3 )
-  dyy = gyy - ONE
+
-  dzz = gzz - ONE
+    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
 
@@ -83,50 +95,70 @@
 
 !~~~~~~~> 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
+    lgyy = dyy(i,j,k) + ONE
+    lgzz = dzz(i,j,k) + ONE
+    lgxy = gxy(i,j,k)
+    lgxz = gxz(i,j,k)
+    lgyz = gyz(i,j,k)
 
-  gxx = gxx * gupzz
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-  gxy = gxy * gupzz
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-  gxz = gxz * gupzz
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
-  gyy = gyy * gupzz
-  gyz = gyz * gupzz
-  gzz = gzz * gupzz
 
-  dxx = gxx - ONE
+    lscale = ONE / ( lscale ** F1o3 )
-  dyy = gyy - ONE
-  dzz = gzz - ONE
-! for A  
 
-  gupxx =   ( gyy * gzz - gyz * gyz )
+    lgxx = lgxx * lscale
-  gupxy = - ( gxy * gzz - gyz * gxz )
+    lgxy = lgxy * lscale
-  gupxz =   ( gxy * gyz - gyy * gxz )
+    lgxz = lgxz * lscale
-  gupyy =   ( gxx * gzz - gxz * gxz )
+    lgyy = lgyy * lscale
-  gupyz = - ( gxx * gyz - gxy * gxz )
+    lgyz = lgyz * lscale
-  gupzz =   ( gxx * gyy - gxy * gxy )
+    lgzz = lgzz * lscale
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+    dxx(i,j,k) = lgxx - ONE
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    gxy(i,j,k) = lgxy
+    gxz(i,j,k) = lgxz
+    dyy(i,j,k) = lgyy - ONE
+    gyz(i,j,k) = lgyz
+    dzz(i,j,k) = lgzz - ONE
 
-  Axx = Axx - F1o3 * gxx * trA
+! for A: trace-free using normalized metric (det=1, no division needed)
-  Axy = Axy - F1o3 * gxy * trA
+    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
-  Axz = Axz - F1o3 * gxz * trA
+    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
-  Ayy = Ayy - F1o3 * gyy * trA
+    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
-  Ayz = Ayz - F1o3 * gyz * trA
+    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
-  Azz = Azz - F1o3 * gzz * trA
+    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

@@ -324,7 +324,6 @@ 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+2,1:extc(2),1:extc(3))*SoA(1)
@@ -350,7 +349,6 @@ 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 +377,6 @@ 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 +883,6 @@ 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 +908,6 @@ 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 +936,6 @@ 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)
@@ -1117,6 +1111,7 @@ end subroutine d2dump
 !------------------------------------------------------------------------------
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
+
   subroutine polint(xa, ya, x, y, dy, ordn)
   implicit none
 
@@ -1129,7 +1124,6 @@ end subroutine d2dump
   real*8, dimension(ordn) :: c, d, ho
   real*8 :: dif, dift, hp, h, den_val
 
-  ! Initialization
   c = ya
   d = ya
   ho = xa - x
@@ -1137,7 +1131,6 @@ end subroutine d2dump
   ns = 1
   dif = abs(x - xa(1))
 
-  ! Find the index of the closest table entry
   do i = 2, ordn
     dift = abs(x - xa(i))
     if (dift < dif) then
@@ -1149,7 +1142,6 @@ end subroutine d2dump
   y = ya(ns)
   ns = ns - 1
 
-  ! Main Neville's algorithm loop
   do m = 1, ordn - 1
     n_m = ordn - m
     do i = 1, n_m
@@ -1157,22 +1149,18 @@ end subroutine d2dump
       h  = ho(i+m)
       den_val = hp - h
 
-      ! Check for division by zero locally
       if (den_val == 0.0d0) then
         write(*,*) 'failure in polint for point',x
         write(*,*) 'with input points: ',xa
         stop
       end if
 
-      ! Reuse den_val to avoid redundant divisions
       den_val = (c(i+1) - d(i)) / den_val
 
-      ! Update c and d in place
       d(i) = h * den_val
       c(i) = hp * den_val
     end do
 
-    ! Decide which path (up or down the tableau) to take
     if (2 * ns < n_m) then
       dy = c(ns + 1)
     else
@@ -1191,24 +1179,34 @@ end subroutine d2dump
 !------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
   implicit none
+
   integer,intent(in) :: ordn
-    real*8, dimension(ordn), intent(in) :: x1a,x2a
+  real*8, dimension(1:ordn), intent(in) :: x1a,x2a
-    real*8, dimension(ordn,ordn), intent(in) :: ya
+  real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2
   real*8, intent(out) :: y,dy
 
+#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 ! Local variable to prevent overwriting result
+  real*8 :: dy_temp
 
-    ! Optimized sequence: Loop over columns (j) 
-    ! ya(:,j) is a contiguous memory block in Fortran
   do j=1,ordn
     call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
   end do
-
-    ! Final interpolation on the results
   call polint(x2a, ymtmp, x2, y, dy, ordn)
+#endif
 
   return
   end subroutine polin2
@@ -1219,33 +1217,47 @@ subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
 !------------------------------------------------------------------------------
   subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
   implicit none
+
   integer,intent(in) :: ordn
-    real*8, dimension(ordn), intent(in) :: x1a,x2a,x3a
+  real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
-    real*8, dimension(ordn,ordn,ordn), intent(in) :: ya
+  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
 
+#ifdef POLINT_LEGACY_ORDER
+  integer  :: i,j,m,n
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: yntmp
+  real*8, dimension(ordn) :: yqtmp
+
+  m=size(x1a)
+  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
 
-    ! Sequence change: Process the contiguous first dimension (x1) first.
-    ! We loop through the 'slow' planes (j, k) to extract 'fast' columns.
   do k=1,ordn
     do j=1,ordn
-        ! ya(:,j,k) is contiguous; much faster than ya(i,j,:)
       call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
     end do
   end do
-
-    ! Now process the second dimension
   do k=1,ordn
     call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
   end do
-
-    ! Final dimension
   call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
 
   return
   end subroutine polin3
@@ -1267,7 +1279,9 @@ subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
   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)
@@ -1291,7 +1305,12 @@ 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
 
@@ -1316,7 +1335,9 @@ 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
 
@@ -1379,7 +1400,12 @@ 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
 
@@ -1407,6 +1433,8 @@ 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
 
@@ -1469,11 +1497,12 @@ 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
 
@@ -1671,6 +1700,7 @@ 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  
@@ -1706,20 +1736,21 @@ 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
 
@@ -1749,6 +1780,7 @@ 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  
@@ -1778,15 +1810,14 @@ 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
 
@@ -1817,6 +1848,7 @@ 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
@@ -1877,10 +1909,8 @@ 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
 
@@ -2112,24 +2142,38 @@ 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
 
@@ -2263,4 +2307,3 @@ subroutine find_maximum(ext,X,Y,Z,fun,val,pos,llb,uub)
   return
 
 end subroutine
-

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;
+  // Step 1: Solve linear system A*x = b using LU decomposition
-    if (irow != icol)
+  // LAPACKE_dgesv uses column-major by default, but we use row-major
-    {
+  info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
-      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];
+  if (info != 0) {
-      b[irow] = b[icol];
+    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
-      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--)
-  {
-    if (indxr[l] != indxc[l])
-      for (k = 0; k < n; k++)
-      {
-        swap = a[k * n + indxr[l]];
-        a[k * n + indxr[l]] = a[k * n + indxc[l]];
-        a[k * n + indxc[l]] = swap;
-      }
-  }
-
-  delete[] indxc;
-  delete[] indxr;
     delete[] ipiv;
+    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[] 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/lopsidediff.f90

@@ -487,6 +487,201 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 
   end subroutine lopsided
 
+!-----------------------------------------------------------------------------
+! Combined advection (lopsided) + Kreiss-Oliger dissipation (kodis)
+! Shares the symmetry_bd buffer fh, eliminating one full-grid copy per call.
+! Mathematically identical to calling lopsided then kodis separately.
+!-----------------------------------------------------------------------------
+subroutine lopsided_kodis(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,eps)
+  implicit none
+
+!~~~~~~> Input parameters:
+
+  integer, intent(in)  :: ex(1:3),Symmetry
+  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
+
+  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
+  real*8,dimension(3),intent(in) ::SoA
+  real*8,intent(in) :: eps
+
+!~~~~~~> local variables:
+! note index -2,-1,0, so we have 3 extra points
+  real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3))   :: fh
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: dX,dY,dZ
+  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
+  real*8,  parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
+  real*8,  parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+! kodis parameters
+  real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
+  real*8, parameter :: cof=6.4d1   ! 2^6
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
+
+! Single symmetry_bd call shared by both advection and dissipation
+  call symmetry_bd(3,ex,f,fh,SoA)
+
+! ---- Advection (lopsided) loop ----
+! upper bound set ex-1 only for efficiency, 
+! the loop body will set ex 0 also
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+! x direction   
+    if(Sfx(i,j,k) > ZEO)then
+      if(i+3 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+     elseif(i+2 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i+1 <= imax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+     endif
+   elseif(Sfx(i,j,k) < ZEO)then
+      if(i-3 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
+                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
+     elseif(i-2 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+
+     elseif(i-1 >= imin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
+                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
+     endif
+   endif
+
+! y direction   
+    if(Sfy(i,j,k) > ZEO)then
+      if(j+3 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+     elseif(j+2 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j+1 <= jmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+     endif
+   elseif(Sfy(i,j,k) < ZEO)then
+      if(j-3 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
+                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
+     elseif(j-2 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+
+     elseif(j-1 >= jmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
+                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
+     endif
+   endif
+
+! z direction   
+    if(Sfz(i,j,k) > ZEO)then
+      if(k+3 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+     elseif(k+2 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k+1 <= kmax)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+     endif
+   elseif(Sfz(i,j,k) < ZEO)then
+      if(k-3 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
+                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
+     elseif(k-2 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
+                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+
+     elseif(k-1 >= kmin)then
+     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
+                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
+                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
+     endif
+   endif
+  enddo
+  enddo
+  enddo
+
+! ---- Dissipation (kodis) loop ----
+  if(eps > ZEO) then
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+
+  if(i-3 >= imin .and. i+3 <= imax .and. &
+     j-3 >= jmin .and. j+3 <= jmax .and. &
+     k-3 >= kmin .and. k+3 <= kmax) then
+   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
+                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
+                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
+                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
+                          TWT* fh(i,j,k)            )/dX + &
+                                                  (     &
+                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
+                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
+                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
+                          TWT* fh(i,j,k)            )/dY + &
+                                                  (     &
+                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
+                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
+                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
+                          TWT* fh(i,j,k)            )/dZ )
+  endif
+
+  enddo
+  enddo
+  enddo
+  endif
+
+  return
+
+  end subroutine lopsided_kodis
+
 #elif (ghost_width == 4)
 ! sixth order code
 ! Compute advection terms in right hand sides of field equations

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

@@ -15,11 +15,10 @@ LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore
 ## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
 ## -fp-model fast=2: Aggressive floating-point optimizations
 ## -fma: Enable fused multiply-add instructions
-## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma \
                -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -fpp -I${MKLROOT}/include
+               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
@@ -30,4 +29,3 @@ Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
 #CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
 CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc
-

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
 
 ##################################################################

parallel_plot_helper.py

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

plot_GW_strain_amplitude_xiaoqu.py

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

plot_binary_data.py

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

plot_xiaoqu.py

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