Optimize buffer_width dynamically based on FD order to improve scalability

- 用 DEBUG_NAN_CHECK 宏按需启用 NaN 检查，并在输入/宏生成器中新增 Debug_NaN_Check 配置
  - 逆度量改为先求行列式再乘法展开，减少除法；并在 Gam^i/Christoffel 处提取公共子表达式
  - 预置批量 fderivs 辅助例程，便于后续矢量化/合并导数计算
  - 将默认 MPI_processes 调整为 8

  变更涉及：

  - AMSS_NCKU_source/bssn_rhs.f90
  - generate_macrodef.py
  - AMSS_NCKU_Input.py
  - AMSS_NCKU_Input_Mini.py
  - inputfile_example/AMSS_NCKU_Input.py
  - AMSS_NCKU_source/diff_new.f90

TODO: fmisc.f90 polint()

.gitignore

@@ -1,6 +1,7 @@
 __pycache__
 GW150914
 GW150914-origin
+GW150914-mini
 docs
 *.tmp
 

AMSS_NCKU_Input.py

@@ -16,12 +16,14 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 64                             ## number of mpi processes used in the simulation
+MPI_processes    = 8                             ## number of mpi processes used in the simulation
 
 GPU_Calculation  = "no"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
 CPU_Part         = 1.0
 GPU_Part         = 0.0
+Debug_NaN_Check          = 0                       ## enable NaN checks in compute_rhs_bssn: 0 (off) or 1 (on)
+
 
 #################################################
 

AMSS_NCKU_Input_Mini.py

@@ -0,0 +1,233 @@
+
+#################################################
+##
+## This file provides the input parameters required for numerical relativity.
+## XIAOQU
+## 2024/03/19 --- 2025/09/14
+## Modified for GW150914-mini test case
+##
+#################################################
+
+import numpy    
+
+#################################################
+
+## Setting MPI processes and the output file directory
+
+File_directory   = "GW150914-mini"               ## output file directory
+Output_directory = "binary_output"               ## binary data file directory
+                                                 ## The file directory name should not be too long
+MPI_processes    = 4                             ## number of mpi processes used in the simulation (Reduced for laptop)
+
+GPU_Calculation  = "no"                          ## Use GPU or not 
+                                                 ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
+CPU_Part         = 1.0
+GPU_Part         = 0.0
+
+#################################################
+
+
+#################################################
+
+## Setting the physical system and numerical method
+
+Symmetry                 = "equatorial-symmetry"   ## Symmetry of System: choose equatorial-symmetry、no-symmetry、octant-symmetry
+Equation_Class           = "BSSN"                  ## Evolution Equation: choose "BSSN", "BSSN-EScalar", "BSSN-EM", "Z4C" 
+                                                   ## If "BSSN-EScalar" is chosen, it is necessary to set other parameters below
+Initial_Data_Method      = "Ansorg-TwoPuncture"    ## initial data method: choose "Ansorg-TwoPuncture", "Lousto-Analytical", "Cao-Analytical", "KerrSchild-Analytical"
+Time_Evolution_Method    = "runge-kutta-45"        ## time evolution method: choose "runge-kutta-45"
+Finite_Diffenence_Method = "4th-order"             ## finite-difference method: choose "2nd-order", "4th-order", "6th-order", "8th-order"
+Debug_NaN_Check          = 0                       ## enable NaN checks in compute_rhs_bssn: 0 (off) or 1 (on)
+
+#################################################
+
+
+#################################################
+
+## Setting the time evolutionary information
+
+Start_Evolution_Time     = 0.0                    ## start evolution time t0
+Final_Evolution_Time     = 100.0                  ## final evolution time t1 (Reduced for quick test)
+Check_Time               = 10.0
+Dump_Time                = 10.0                   ## time inteval dT for dumping binary data
+D2_Dump_Time             = 10.0                   ## dump the ascii data for 2d surface after dT'
+Analysis_Time            = 1.0                    ## dump the puncture position and GW psi4 after dT"
+Evolution_Step_Number    = 10000000               ## stop the calculation after the maximal step number
+Courant_Factor           = 0.5                    ## Courant Factor
+Dissipation              = 0.15                   ## Kreiss-Oliger Dissipation Strength
+
+#################################################
+
+
+#################################################
+
+## Setting the grid structure
+
+basic_grid_set    = "Patch"                          ## grid structure: choose "Patch" or "Shell-Patch"
+grid_center_set   = "Cell"                           ## grid center: chose "Cell" or "Vertex"
+
+grid_level        = 7                                ## total number of AMR grid levels (Reduced from 9)
+static_grid_level = 4                                ## number of AMR static grid levels (Reduced from 5)
+moving_grid_level = grid_level - static_grid_level   ## number of AMR moving grid levels
+
+analysis_level    = 0
+refinement_level  = 3                                ## time refinement start from this grid level
+
+largest_box_xyz_max = [320.0, 320.0, 320.0]          ## scale of the largest box
+                                                     ## not ne cess ary to be cubic for "Patch" grid s tructure
+                                                     ## need to be a cubic box for "Shell-Patch" grid structure
+largest_box_xyz_min = - numpy.array(largest_box_xyz_max)  
+
+static_grid_number = 48                              ## grid points of each static AMR grid (in x direction) (Reduced from 96)
+                                                     ## (grid points in y and z directions are automatically adjusted)
+moving_grid_number = 24                              ## grid points of each moving AMR grid (Reduced from 48)
+shell_grid_number  = [32, 32, 100]                   ## grid points of Shell-Patch grid
+                                                     ## in (phi, theta, r) direction
+devide_factor      = 2.0                             ## resolution between different grid levels dh0/dh1, only support 2.0 now
+                                                     
+
+static_grid_type   = 'Linear'                        ## AMR static grid structure , only supports "Linear"
+moving_grid_type   = 'Linear'                        ## AMR moving grid structure , only supports "Linear"
+
+quarter_sphere_number = 48                           ## grid number of 1/4 s pher ical surface (Reduced from 96)
+                                                     ## (which is needed for evaluating the spherical surface integral)
+
+#################################################
+
+
+#################################################
+
+## Setting the puncture information
+
+puncture_number       = 2                                     
+
+position_BH           = numpy.zeros( (puncture_number, 3) )   
+parameter_BH          = numpy.zeros( (puncture_number, 3) )   
+dimensionless_spin_BH = numpy.zeros( (puncture_number, 3) )   
+momentum_BH           = numpy.zeros( (puncture_number, 3) )   
+
+puncture_data_set     = "Manually"                       ## Method to give Puncture’s positions and momentum
+                                                         ## choose "Manually" or "Automatically-BBH"
+                                                         ## Prefer to choose "Manually", because "Automatically-BBH" is developing now
+
+## initial orbital distance and ellipticity for BBHs system
+## ( needed for "Automatically-BBH" case , not affect the "Manually" case )
+Distance = 10.0
+e0       = 0.0
+
+## black hole parameter (M Q* a*)
+parameter_BH[0] = [ 36.0/(36.0+29.0),  0.0,  +0.31 ]   
+parameter_BH[1] = [ 29.0/(36.0+29.0),  0.0,  -0.46 ]  
+## dimensionless spin in each direction
+dimensionless_spin_BH[0] = [ 0.0,  0.0,  +0.31 ]   
+dimensionless_spin_BH[1] = [ 0.0,  0.0,  -0.46 ]  
+
+## use Brugmann's convention
+##  -----0-----> y
+##   -      +     
+
+#---------------------------------------------
+
+## If puncture_data_set is chosen to be "Manually", it is necessary to set the position and momentum of each puncture manually
+
+## initial position for each puncture
+position_BH[0]  = [  0.0,  10.0*29.0/(36.0+29.0), 0.0 ]  
+position_BH[1]  = [  0.0, -10.0*36.0/(36.0+29.0), 0.0 ] 
+
+## initial mumentum for each puncture
+## (needed for "Manually" case, does not affect the "Automatically-BBH" case)
+momentum_BH[0]  = [ -0.09530152296974252,  -0.00084541526517121,   0.0 ]
+momentum_BH[1]  = [ +0.09530152296974252,  +0.00084541526517121,   0.0 ]
+
+
+#################################################
+
+
+#################################################
+
+## Setting the gravitational wave information
+
+GW_L_max        = 4                      ## maximal L number in gravitational wave
+GW_M_max        = 4                      ## maximal M number in gravitational wave
+Detector_Number = 12                     ## number of dector
+Detector_Rmin   = 50.0                   ## nearest dector distance
+Detector_Rmax   = 160.0                  ## farest dector distance
+
+#################################################
+
+
+#################################################
+
+## Setting the apprent horizon
+
+AHF_Find       = "no"                    ## whether to find the apparent horizon: choose "yes" or "no"
+
+AHF_Find_Every = 24
+AHF_Dump_Time  = 20.0
+
+#################################################
+
+
+#################################################
+
+## Other parameters (testing)
+## Only influence the Equation_Class = "BSSN-EScalar" case
+
+FR_a2     = 3.0        ## f(R) = R + a2 * R^2    
+FR_l2     = 10000.0
+FR_phi0   = 0.00005
+FR_r0     = 120.0
+FR_sigma0 = 8.0
+FR_Choice = 2          ## Choice options: 1 2 3 4 5
+                       ## 1: phi(r) = phi0 * Exp(-(r-r0)**2/sigma0)   
+                       ##    V(r)   = 0
+                       ## 2: phi(r) =  phi0 * a2^2/(1+a2^2)  
+                       ##    V(r)   = Exp(-8*Sqrt(PI/3)*phi(r)) * (1-Exp(4*Sqrt(PI/3)*phi(r)))**2 / (32*PI*a2)
+                       ## 3: Schrodinger-Newton gived by system phi(r) 
+                       ##    V(r)   = Exp(-8*Sqrt(PI/3)*phi(r)) * (1-Exp(4*Sqrt(PI/3)*phi(r)))**2 / (32*PI*a2)
+                       ## 4: phi(r) = phi0 * 0.5 * ( tanh((r+r0)/sigma0) - tanh((r-r0)/sigma0) )  
+                       ##    V(r)   = 0
+                       ##    f(R)   = R + a2*R^2  with a2 = +oo
+                       ## 5: phi(r) = phi0 * Exp(-(r-r0)**2/sigma)   
+                       ##    V(r)   = 0
+
+#################################################
+
+
+#################################################
+
+## Other parameters (testing)
+## (please do not change if not necessary)
+
+boundary_choice = "BAM-choice"     ## Sommerfeld boundary condition : choose "BAM-choice" or "Shibata-choice" 
+                                   ## prefer "BAM-choice"
+
+gauge_choice  = 0                  ## gauge choice
+                                   ## 0: B^i gauge
+                                   ## 1: David's puncture gauge
+                                   ## 2: MB B^i gauge               
+                                   ## 3: RIT B^i gauge
+                                   ## 4: MB beta gauge 
+                                   ## 5: RIT beta gauge 
+                                   ## 6: MGB1 B^i gauge
+                                   ## 7: MGB2 B^i gauge
+                                   ## prefer 0 or 1
+                                   
+tetrad_type  = 2                   ## tetradtype 
+                                   ##  v:r; u: phi; w: theta
+                                   ##      v^a = (x,y,z)
+                                   ## 0: orthonormal order: v,u,w
+                                   ##    v^a = (x,y,z)   
+                                   ##    m = (phi - i theta)/sqrt(2) 
+                                   ##    following Frans, Eq.(8) of  PRD 75, 124018(2007)
+                                   ## 1: orthonormal order: w,u,v
+                                   ##    m = (theta + i phi)/sqrt(2) 
+                                   ##    following Sperhake, Eq.(3.2) of  PRD 85, 124062(2012)    
+                                   ## 2: orthonormal order: v,u,w
+                                   ##    v_a = (x,y,z)
+                                   ##    m = (phi - i theta)/sqrt(2) 
+                                   ##    following Frans, Eq.(8) of  PRD 75, 124018(2007)
+                                   ## this version recommend set to 2
+                                   ## prefer 2
+                                   
+#################################################

AMSS_NCKU_MiniProgram.py

@@ -0,0 +1,224 @@
+##################################################################
+##
+## AMSS-NCKU Numerical Relativity Mini Test Program
+## Author: Assistant (based on Xiaoqu's code)
+## 2026/01/20
+##
+## This script runs a scaled-down version of the GW150914 test case
+## suitable for laptop testing.
+##
+##################################################################
+
+import os
+import shutil
+import sys
+import time
+
+# --- Context Manager for Input File Swapping ---
+class InputFileSwapper:
+    def __init__(self, mini_file="AMSS_NCKU_Input_Mini.py", target_file="AMSS_NCKU_Input.py"):
+        self.mini_file = mini_file
+        self.target_file = target_file
+        self.backup_file = target_file + ".bak"
+        self.swapped = False
+
+    def __enter__(self):
+        print(f"[MiniProgram] Swapping {self.target_file} with {self.mini_file}...")
+        if os.path.exists(self.target_file):
+            shutil.move(self.target_file, self.backup_file)
+        shutil.copy(self.mini_file, self.target_file)
+        self.swapped = True
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        if self.swapped:
+            print(f"[MiniProgram] Restoring original {self.target_file}...")
+            os.remove(self.target_file)
+            if os.path.exists(self.backup_file):
+                shutil.move(self.backup_file, self.target_file)
+
+def main():
+    # Use the swapper to ensure all imported modules see the mini configuration
+    with InputFileSwapper():
+        
+        # Import modules AFTER swapping input file
+        try:
+            import AMSS_NCKU_Input as input_data
+            import print_information
+            import setup
+            import numerical_grid
+            import generate_macrodef
+            import makefile_and_run
+            import generate_TwoPuncture_input
+            import renew_puncture_parameter
+            import plot_xiaoqu
+            import plot_GW_strain_amplitude_xiaoqu
+        except ImportError as e:
+            print(f"Error importing modules: {e}")
+            return
+
+        print_information.print_program_introduction()
+        
+        print("\n" + "#"*60)
+        print(" RUNNING MINI TEST CASE: GW150914-mini")
+        print("#"*60 + "\n")
+
+        # --- Directory Setup ---
+        File_directory = os.path.join(input_data.File_directory)
+        
+        if os.path.exists(File_directory):
+            print(f" Output directory '{File_directory}' exists. Removing for mini test...")
+            shutil.rmtree(File_directory, ignore_errors=True)
+        
+        os.mkdir(File_directory)
+        shutil.copy("AMSS_NCKU_Input.py", File_directory) # Copies the current (mini) input
+
+        output_directory = os.path.join(File_directory, "AMSS_NCKU_output")
+        os.mkdir(output_directory)
+
+        binary_results_directory = os.path.join(output_directory, input_data.Output_directory)
+        os.mkdir(binary_results_directory)
+
+        figure_directory = os.path.join(File_directory, "figure")
+        os.mkdir(figure_directory)
+
+        print(" Output directories generated.\n")
+
+        # --- Setup and Input Generation ---
+        setup.print_input_data(File_directory)
+        setup.generate_AMSSNCKU_input()
+        setup.print_puncture_information()
+
+        print("\n Generating AMSS-NCKU input parfile...")
+        numerical_grid.append_AMSSNCKU_cgh_input()
+        
+        print("\n Plotting initial grid...")
+        numerical_grid.plot_initial_grid()
+
+        print("\n Generating macro files...")
+        generate_macrodef.generate_macrodef_h()
+        generate_macrodef.generate_macrodef_fh()
+        
+        # --- Compilation Preparation ---
+        print("\n Preparing to compile and run...")
+        
+        AMSS_NCKU_source_path = "AMSS_NCKU_source"
+        AMSS_NCKU_source_copy = os.path.join(File_directory, "AMSS_NCKU_source_copy")
+
+        if not os.path.exists(AMSS_NCKU_source_path):
+             print(" Error: AMSS_NCKU_source not found! Please run in the project root.")
+             return
+
+        shutil.copytree(AMSS_NCKU_source_path, AMSS_NCKU_source_copy)
+        
+        macrodef_h_path  = os.path.join(File_directory, "macrodef.h") 
+        macrodef_fh_path = os.path.join(File_directory, "macrodef.fh") 
+
+        shutil.copy2(macrodef_h_path,  AMSS_NCKU_source_copy)
+        shutil.copy2(macrodef_fh_path, AMSS_NCKU_source_copy)
+
+        # --- Compilation ---
+        cwd = os.getcwd()
+        os.chdir(AMSS_NCKU_source_copy)
+        
+        print(" Compiling ABE...")
+        makefile_and_run.makefile_ABE()
+        
+        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ): 
+            print(" Compiling TwoPunctureABE...")
+            makefile_and_run.makefile_TwoPunctureABE()
+            
+        os.chdir(cwd)
+
+        # --- Copy Executables ---
+        if (input_data.GPU_Calculation == "no"):
+            ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
+        else:
+            ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
+            
+        if not os.path.exists(ABE_file):
+            print(" Error: ABE executable compilation failed.")
+            return
+            
+        shutil.copy2(ABE_file, output_directory)
+
+        TwoPuncture_file = os.path.join(AMSS_NCKU_source_copy, "TwoPunctureABE")
+        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
+            if not os.path.exists(TwoPuncture_file):
+                print(" Error: TwoPunctureABE compilation failed.")
+                return
+            shutil.copy2(TwoPuncture_file, output_directory)
+
+        # --- Execution ---
+        start_time = time.time()
+        
+        if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
+             print("\n Generating TwoPuncture input...")
+             generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
+             
+             AMSS_NCKU_TwoPuncture_inputfile = 'AMSS-NCKU-TwoPuncture.input'
+             AMSS_NCKU_TwoPuncture_inputfile_path = os.path.join( File_directory, AMSS_NCKU_TwoPuncture_inputfile )
+             shutil.copy2( AMSS_NCKU_TwoPuncture_inputfile_path, os.path.join(output_directory, 'TwoPunctureinput.par') )
+             
+             print(" Running TwoPunctureABE...")
+             os.chdir(output_directory)
+             makefile_and_run.run_TwoPunctureABE()
+             os.chdir(cwd)
+
+        # Update Puncture Parameter
+        renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
+        
+        AMSS_NCKU_inputfile = 'AMSS-NCKU.input'
+        AMSS_NCKU_inputfile_path = os.path.join(File_directory, AMSS_NCKU_inputfile)
+        shutil.copy2( AMSS_NCKU_inputfile_path, os.path.join(output_directory, 'input.par') )
+        
+        print("\n Input files ready. Launching ABE...")
+        
+        os.chdir(output_directory)
+        makefile_and_run.run_ABE()
+        os.chdir(cwd)
+        
+        end_time = time.time()
+        elapsed_time = end_time - start_time
+        
+        # --- Post-processing ---
+        print("\n Copying output files for inspection...")
+        AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "setting.par")
+        if os.path.exists(AMSS_NCKU_error_file_path):
+            shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "AMSSNCKU_setting_parameter") )
+
+        AMSS_NCKU_error_file_path = os.path.join(binary_results_directory, "Error.log")
+        if os.path.exists(AMSS_NCKU_error_file_path):
+            shutil.copy( AMSS_NCKU_error_file_path, os.path.join(output_directory, "Error.log") )
+
+        for fname in ["bssn_BH.dat", "bssn_ADMQs.dat", "bssn_psi4.dat", "bssn_constraint.dat"]:
+            fpath = os.path.join(binary_results_directory, fname)
+            if os.path.exists(fpath):
+                shutil.copy(fpath, os.path.join(output_directory, fname))
+
+        # --- Plotting ---
+        print("\n Plotting results...")
+        try:
+            plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
+            plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+            plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+            
+            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 )
+
+            for i in range(input_data.Detector_Number):
+                plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+
+            for i in range(input_data.grid_level):
+                plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+                
+            plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
+        except Exception as e:
+            print(f"Warning: Plotting failed: {e}")
+
+        print(f"\n Program Cost = {elapsed_time:.2f} Seconds \n")
+        print(" AMSS-NCKU-Python simulation finished (Mini Test).\n")
+
+if __name__ == "__main__":
+    main()

AMSS_NCKU_Program.py

@@ -8,14 +8,6 @@
 ##
 ##################################################################
 
-## 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)
-
 
 ##################################################################
 
@@ -270,12 +262,6 @@ if not os.path.exists( ABE_file ):
 ## Copy the executable ABE (or ABEGPU) into the run directory
 shutil.copy2(ABE_file, output_directory)
 
-## Copy interp load balance profile if present (for optimize pass)
-interp_lb_profile = os.path.join(AMSS_NCKU_source_copy, "interp_lb_profile.bin")
-if os.path.exists(interp_lb_profile):
-    shutil.copy2(interp_lb_profile, output_directory)
-    print( " Copied interp_lb_profile.bin to run directory " )
-
 ###########################
 
 ## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory
@@ -438,31 +424,26 @@ 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_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
-plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
+plot_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_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
+plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
 
 ## Plot gravitational waveforms (psi4 and strain amplitude)
 for i in range(input_data.Detector_Number):
-    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
-    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_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_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
 
 ## Plot Hamiltonian constraint violation over time
 for i in range(input_data.grid_level):
-    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
-
-run_plot_tasks_parallel(plot_tasks)
+    plot_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 )

AMSS_NCKU_source/MPatch.C

@@ -13,9 +13,6 @@ using namespace std;
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
-#ifdef INTERP_LB_PROFILE
-#include "interp_lb_profile.h"
-#endif
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -344,9 +341,8 @@ void Patch::Interp_Points(MyList<var> *VarList,
                           double *Shellf, int Symmetry)
 {
   // NOTE: we do not Synchnize variables here, make sure of that before calling this routine
-  int myrank, nprocs;
+  int myrank;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
 
   int ordn = 2 * ghost_width;
   MyList<var> *varl;
@@ -358,18 +354,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
+  double *shellf;
+  shellf = new double[NN * num_var];
+  memset(shellf, 0, sizeof(double) * NN * num_var);
 
-  // owner_rank[j] records which MPI rank owns point j
-  // All ranks traverse the same block list so they all agree on ownership
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
+  // we use weight to monitor code, later some day we can move it for optimization
+  int *weight;
+  weight = new int[NN];
+  memset(weight, 0, sizeof(int) * NN);
+
+  double *DH, *llb, *uub;
+  DH = new double[dim];
 
-  double DH[dim], llb[dim], uub[dim];
   for (int i = 0; i < dim; i++)
+  {
     DH[i] = getdX(i);
+  }
+  llb = new double[dim];
+  uub = new double[dim];
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -401,6 +403,12 @@ void Patch::Interp_Points(MyList<var> *VarList,
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
+// NOTE: our dividing structure is (exclude ghost)
+// -1 0
+//       1  2
+// so (0,1) does not belong to any part for vertex structure
+// here we put (0,0.5) to left part and (0.5,1) to right part
+// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
@@ -425,7 +433,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (flag)
       {
         notfind = false;
-        owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
           //---> interpolation
@@ -433,11 +440,14 @@ void Patch::Interp_Points(MyList<var> *VarList,
           int k = 0;
           while (varl) // run along variables
           {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
+            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
                             pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
             varl = varl->next;
             k++;
           }
+          weight[j] = 1;
         }
       }
       if (Bp == ble)
@@ -446,128 +456,61 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  // Replace MPI_Allreduce with per-owner MPI_Bcast:
-  // Group consecutive points by owner rank and broadcast each group.
-  // Since each point's data is non-zero only on the owner rank,
-  // Bcast from owner is equivalent to Allreduce(MPI_SUM) but much cheaper.
+  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  int *Weight;
+  Weight = new int[NN];
+  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+
+  //  misc::tillherecheck("print me");
+
+  for (int i = 0; i < NN; i++)
   {
-    int j = 0;
-    while (j < NN)
-    {
-      int cur_owner = owner_rank[j];
-      if (cur_owner < 0)
+    if (Weight[i] > 1)
     {
       if (myrank == 0)
+        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
+      for (int j = 0; j < num_var; j++)
+        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
+    }
+    else if (Weight[i] == 0 && myrank == 0)
     {
       cout << "ERROR: Patch::Interp_Points fails to find point (";
-          for (int d = 0; d < dim; d++)
+      for (int j = 0; j < dim; j++)
       {
-            cout << XX[d][j];
-            if (d < dim - 1)
+        cout << XX[j][i];
+        if (j < dim - 1)
           cout << ",";
         else
           cout << ")";
       }
       cout << " on Patch (";
-          for (int d = 0; d < dim; d++)
+      for (int j = 0; j < dim; j++)
       {
-            cout << bbox[d] << "+" << lli[d] * DH[d];
-            if (d < dim - 1)
+        cout << bbox[j] << "+" << lli[j] * getdX(j);
+        if (j < dim - 1)
           cout << ",";
         else
           cout << ")--";
       }
       cout << "(";
-          for (int d = 0; d < dim; d++)
+      for (int j = 0; j < dim; j++)
       {
-            cout << bbox[dim + d] << "-" << uui[d] * DH[d];
-            if (d < dim - 1)
+        cout << bbox[dim + j] << "-" << uui[j] * getdX(j);
+        if (j < dim - 1)
           cout << ",";
         else
           cout << ")" << endl;
       }
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        j++;
-        continue;
-      }
-      // Find contiguous run of points with the same owner
-      int jstart = j;
-      while (j < NN && owner_rank[j] == cur_owner)
-        j++;
-      int count = (j - jstart) * num_var;
-      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner, MPI_COMM_WORLD);
-    }
-  }
-
-  delete[] owner_rank;
-}
-void Patch::Interp_Points(MyList<var> *VarList,
-                          int NN, double **XX,
-                          double *Shellf, int Symmetry,
-                          int Nmin_consumer, int Nmax_consumer)
-{
-  // Targeted point-to-point overload: each owner sends each point only to
-  // the one rank that needs it for integration (consumer), reducing
-  // communication volume by ~nprocs times compared to the Bcast version.
-#ifdef INTERP_LB_PROFILE
-  double t_interp_start = MPI_Wtime();
-#endif
-  int myrank, nprocs;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
-
-  int ordn = 2 * ghost_width;
-  MyList<var> *varl;
-  int num_var = 0;
-  varl = VarList;
-  while (varl)
+#if 0
+       checkBlock();
+#else
+      cout << "splited domains:" << endl;
       {
-    num_var++;
-    varl = varl->next;
-  }
-
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
-
-  // owner_rank[j] records which MPI rank owns point j
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
-
-  double DH[dim], llb[dim], uub[dim];
-  for (int i = 0; i < dim; i++)
-    DH[i] = getdX(i);
-
-  // --- Interpolation phase (identical to original) ---
-  for (int j = 0; j < NN; j++)
-  {
-    double pox[dim];
-    for (int i = 0; i < dim; i++)
-    {
-      pox[i] = XX[i][j];
-      if (myrank == 0 && (XX[i][j] < bbox[i] + lli[i] * DH[i] || XX[i][j] > bbox[dim + i] - uui[i] * DH[i]))
-      {
-        cout << "Patch::Interp_Points: point (";
-        for (int k = 0; k < dim; k++)
-        {
-          cout << XX[k][j];
-          if (k < dim - 1)
-            cout << ",";
-          else
-            cout << ") is out of current Patch." << endl;
-        }
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
         MyList<Block> *Bp = blb;
-    bool notfind = true;
-    while (notfind && Bp)
+        while (Bp)
         {
           Block *BP = Bp->data;
 
-      bool flag = true;
           for (int i = 0; i < dim; i++)
           {
 #ifdef Vertex
@@ -584,222 +527,32 @@ void Patch::Interp_Points(MyList<var> *VarList,
 #error Not define Vertex nor Cell
 #endif
 #endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
-        {
-          flag = false;
-          break;
           }
-      }
-
-      if (flag)
+          cout << "(";
+          for (int j = 0; j < dim; j++)
           {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          varl = VarList;
-          int k = 0;
-          while (varl)
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
+            cout << llb[j] << ":" << uub[j];
+            if (j < dim - 1)
+              cout << ",";
+            else
+              cout << ")" << endl;
           }
           if (Bp == ble)
             break;
           Bp = Bp->next;
         }
       }
-
-#ifdef INTERP_LB_PROFILE
-  double t_interp_end = MPI_Wtime();
-  double t_interp_local = t_interp_end - t_interp_start;
 #endif
-
-  // --- Error check for unfound points ---
-  for (int j = 0; j < NN; j++)
-  {
-    if (owner_rank[j] < 0 && myrank == 0)
-    {
-      cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int d = 0; d < dim; d++)
-      {
-        cout << XX[d][j];
-        if (d < dim - 1)
-          cout << ",";
-        else
-          cout << ")";
-      }
-      cout << " on Patch (";
-      for (int d = 0; d < dim; d++)
-      {
-        cout << bbox[d] << "+" << lli[d] * DH[d];
-        if (d < dim - 1)
-          cout << ",";
-        else
-          cout << ")--";
-      }
-      cout << "(";
-      for (int d = 0; d < dim; d++)
-      {
-        cout << bbox[dim + d] << "-" << uui[d] * DH[d];
-        if (d < dim - 1)
-          cout << ",";
-        else
-          cout << ")" << endl;
-      }
       MPI_Abort(MPI_COMM_WORLD, 1);
     }
   }
 
-  // --- Targeted point-to-point communication phase ---
-  // Compute consumer_rank[j] using the same deterministic formula as surface_integral
-  int *consumer_rank = new int[NN];
-  {
-    int mp = NN / nprocs;
-    int Lp = NN - nprocs * mp;
-    for (int j = 0; j < NN; j++)
-    {
-      if (j < Lp * (mp + 1))
-        consumer_rank[j] = j / (mp + 1);
-      else
-        consumer_rank[j] = Lp + (j - Lp * (mp + 1)) / mp;
-    }
-  }
-
-  // Count sends and recvs per rank
-  int *send_count = new int[nprocs];
-  int *recv_count = new int[nprocs];
-  memset(send_count, 0, sizeof(int) * nprocs);
-  memset(recv_count, 0, sizeof(int) * nprocs);
-
-  for (int j = 0; j < NN; j++)
-  {
-    int own = owner_rank[j];
-    int con = consumer_rank[j];
-    if (own == con)
-      continue; // local — no communication needed
-    if (own == myrank)
-      send_count[con]++;
-    if (con == myrank)
-      recv_count[own]++;
-  }
-
-  // Build send buffers: for each destination rank, pack (index, data) pairs
-  // Each entry: 1 int (point index j) + num_var doubles
-  int total_send = 0, total_recv = 0;
-  int *send_offset = new int[nprocs];
-  int *recv_offset = new int[nprocs];
-  for (int r = 0; r < nprocs; r++)
-  {
-    send_offset[r] = total_send;
-    total_send += send_count[r];
-    recv_offset[r] = total_recv;
-    total_recv += recv_count[r];
-  }
-
-  // Pack send buffers: each message contains (j, data[0..num_var-1]) per point
-  int stride = 1 + num_var; // 1 double for index + num_var doubles for data
-  double *sendbuf = new double[total_send * stride];
-  double *recvbuf = new double[total_recv * stride];
-
-  // Temporary counters for packing
-  int *pack_pos = new int[nprocs];
-  memset(pack_pos, 0, sizeof(int) * nprocs);
-
-  for (int j = 0; j < NN; j++)
-  {
-    int own = owner_rank[j];
-    int con = consumer_rank[j];
-    if (own != myrank || con == myrank)
-      continue;
-    int pos = (send_offset[con] + pack_pos[con]) * stride;
-    sendbuf[pos] = (double)j; // point index
-    for (int v = 0; v < num_var; v++)
-      sendbuf[pos + 1 + v] = Shellf[j * num_var + v];
-    pack_pos[con]++;
-  }
-
-  // Post non-blocking recvs and sends
-  int n_req = 0;
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (recv_count[r] > 0) n_req++;
-    if (send_count[r] > 0) n_req++;
-  }
-
-  MPI_Request *reqs = new MPI_Request[n_req];
-  int req_idx = 0;
-
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (recv_count[r] > 0)
-    {
-      MPI_Irecv(recvbuf + recv_offset[r] * stride,
-                recv_count[r] * stride, MPI_DOUBLE,
-                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
-    }
-  }
-  for (int r = 0; r < nprocs; r++)
-  {
-    if (send_count[r] > 0)
-    {
-      MPI_Isend(sendbuf + send_offset[r] * stride,
-                send_count[r] * stride, MPI_DOUBLE,
-                r, 0, MPI_COMM_WORLD, &reqs[req_idx++]);
-    }
-  }
-
-  if (n_req > 0)
-    MPI_Waitall(n_req, reqs, MPI_STATUSES_IGNORE);
-
-  // Unpack recv buffers into Shellf
-  for (int i = 0; i < total_recv; i++)
-  {
-    int pos = i * stride;
-    int j = (int)recvbuf[pos];
-    for (int v = 0; v < num_var; v++)
-      Shellf[j * num_var + v] = recvbuf[pos + 1 + v];
-  }
-
-  delete[] reqs;
-  delete[] sendbuf;
-  delete[] recvbuf;
-  delete[] pack_pos;
-  delete[] send_offset;
-  delete[] recv_offset;
-  delete[] send_count;
-  delete[] recv_count;
-  delete[] consumer_rank;
-  delete[] owner_rank;
-
-#ifdef INTERP_LB_PROFILE
-  {
-    static bool profile_written = false;
-    if (!profile_written) {
-      double *all_times = nullptr;
-      if (myrank == 0) all_times = new double[nprocs];
-      MPI_Gather(&t_interp_local, 1, MPI_DOUBLE,
-                 all_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
-      if (myrank == 0) {
-        int heavy[64];
-        int nh = InterpLBProfile::identify_heavy_ranks(
-            all_times, nprocs, 2.5, heavy, 64);
-        InterpLBProfile::write_profile(
-            "interp_lb_profile.bin", nprocs,
-            all_times, heavy, nh, 2.5);
-        printf("[InterpLB] Profile written: %d heavy ranks\n", nh);
-        for (int i = 0; i < nh; i++)
-          printf("  Heavy rank %d: %.6f s\n", heavy[i], all_times[heavy[i]]);
-        delete[] all_times;
-      }
-      profile_written = true;
-    }
-  }
-#endif
+  delete[] shellf;
+  delete[] weight;
+  delete[] Weight;
+  delete[] DH;
+  delete[] llb;
+  delete[] uub;
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
@@ -820,22 +573,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
+  double *shellf;
+  shellf = new double[NN * num_var];
+  memset(shellf, 0, sizeof(double) * NN * num_var);
 
-  // owner_rank[j] stores the global rank that owns point j
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
+  // we use weight to monitor code, later some day we can move it for optimization
+  int *weight;
+  weight = new int[NN];
+  memset(weight, 0, sizeof(int) * NN);
 
-  // Build global-to-local rank translation for Comm_here
-  MPI_Group world_group, local_group;
-  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
-  MPI_Comm_group(Comm_here, &local_group);
+  double *DH, *llb, *uub;
+  DH = new double[dim];
 
-  double DH[dim], llb[dim], uub[dim];
   for (int i = 0; i < dim; i++)
+  {
     DH[i] = getdX(i);
+  }
+  llb = new double[dim];
+  uub = new double[dim];
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -867,6 +622,12 @@ void Patch::Interp_Points(MyList<var> *VarList,
       bool flag = true;
       for (int i = 0; i < dim; i++)
       {
+// NOTE: our dividing structure is (exclude ghost)
+// -1 0
+//       1  2
+// so (0,1) does not belong to any part for vertex structure
+// here we put (0,0.5) to left part and (0.5,1) to right part
+// BUT for cell structure the bbox is (-1.5,0.5) and (0.5,2.5), there is no missing region at all
 #ifdef Vertex
 #ifdef Cell
 #error Both Cell and Vertex are defined
@@ -891,7 +652,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (flag)
       {
         notfind = false;
-        owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
           //---> interpolation
@@ -899,11 +659,14 @@ void Patch::Interp_Points(MyList<var> *VarList,
           int k = 0;
           while (varl) // run along variables
           {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+            //              shellf[j*num_var+k] = Parallel::global_interp(dim,BP->shape,BP->X,BP->fgfs[varl->data->sgfn],
+            //	  		                                    pox,ordn,varl->data->SoA,Symmetry);
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], shellf[j * num_var + k],
                             pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
             varl = varl->next;
             k++;
           }
+          weight[j] = 1;
         }
       }
       if (Bp == ble)
@@ -912,35 +675,97 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  // Collect unique global owner ranks and translate to local ranks in Comm_here
-  // Then broadcast each owner's points via MPI_Bcast on Comm_here
-  {
-    int j = 0;
-    while (j < NN)
-    {
-      int cur_owner_global = owner_rank[j];
-      if (cur_owner_global < 0)
-      {
-        // Point not found — skip (error check disabled for sub-communicator levels)
-        j++;
-        continue;
-      }
-      // Translate global rank to local rank in Comm_here
-      int cur_owner_local;
-      MPI_Group_translate_ranks(world_group, 1, &cur_owner_global, local_group, &cur_owner_local);
+  MPI_Allreduce(shellf, Shellf, NN * num_var, MPI_DOUBLE, MPI_SUM, Comm_here);
+  int *Weight;
+  Weight = new int[NN];
+  MPI_Allreduce(weight, Weight, NN, MPI_INT, MPI_SUM, Comm_here);
 
-      // Find contiguous run of points with the same owner
-      int jstart = j;
-      while (j < NN && owner_rank[j] == cur_owner_global)
-        j++;
-      int count = (j - jstart) * num_var;
-      MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner_local, Comm_here);
+  //  misc::tillherecheck("print me");
+  //  if(lmyrank == 0) cout<<"myrank = "<<myrank<<"print me"<<endl;
+
+  for (int i = 0; i < NN; i++)
+  {
+    if (Weight[i] > 1)
+    {
+      if (lmyrank == 0)
+        cout << "WARNING: Patch::Interp_Points meets multiple weight" << endl;
+      for (int j = 0; j < num_var; j++)
+        Shellf[j + i * num_var] = Shellf[j + i * num_var] / Weight[i];
     }
+#if 0 // for not involved levels, this may fail     
+     else if(Weight[i] == 0 && lmyrank == 0)
+     {
+       cout<<"ERROR: Patch::Interp_Points fails to find point (";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<XX[j][i];
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")";
+       }
+       cout<<" on Patch (";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<bbox[j]<<"+"<<lli[j]*getdX(j);
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")--";
+       }
+       cout<<"(";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<bbox[dim+j]<<"-"<<uui[j]*getdX(j);
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")"<<endl;
+       }
+#if 0
+       checkBlock();
+#else
+  cout<<"splited domains:"<<endl;
+  {
+     MyList<Block> *Bp=blb;
+     while(Bp)
+     {
+	Block *BP=Bp->data;
+
+	for(int i=0;i<dim;i++)
+	{
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif    
+          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +(ghost_width-0.5)*DH[i];
+          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-(ghost_width-0.5)*DH[i];
+#else
+#ifdef Cell
+          llb[i] = (feq(BP->bbox[i]    ,bbox[i]    ,DH[i]/2)) ? BP->bbox[i]+lli[i]*DH[i]     : BP->bbox[i]    +ghost_width*DH[i];
+          uub[i] = (feq(BP->bbox[dim+i],bbox[dim+i],DH[i]/2)) ? BP->bbox[dim+i]-uui[i]*DH[i] : BP->bbox[dim+i]-ghost_width*DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif 
+	}       
+       cout<<"(";
+       for(int j=0;j<dim;j++)
+       {
+	  cout<<llb[j]<<":"<<uub[j];
+	  if(j<dim-1) cout<<",";
+	  else        cout<<")"<<endl;
+       }
+	if(Bp == ble) break;
+	Bp=Bp->next;
+     }
+  }
+#endif       
+       MPI_Abort(MPI_COMM_WORLD,1);
+     }
+#endif
   }
 
-  MPI_Group_free(&world_group);
-  MPI_Group_free(&local_group);
-  delete[] owner_rank;
+  delete[] shellf;
+  delete[] weight;
+  delete[] Weight;
+  delete[] DH;
+  delete[] llb;
+  delete[] uub;
 }
 void Patch::checkBlock()
 {

AMSS_NCKU_source/MPatch.h

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

AMSS_NCKU_source/Parallel.h

@@ -32,16 +32,6 @@ namespace Parallel
   int partition2(int *nxy, int split_size, int *min_width, int cpusize, int *shape); // special for 2 diemnsions
   int partition3(int *nxyz, int split_size, int *min_width, int cpusize, int *shape);
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0); // produce corresponding Blocks
-  MyList<Block> *distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0);
-  Block* splitHotspotBlock(MyList<Block>* &BlL, int _dim,
-                           int ib0_orig, int ib3_orig,
-                           int jb1_orig, int jb4_orig,
-                           int kb2_orig, int kb5_orig,
-                           Patch* PP, int r_left, int r_right,
-                           int ingfsi, int fngfsi, bool periodic,
-                           Block* &split_first_block, Block* &split_last_block);
-  Block* createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
-                           int block_id, int ingfsi, int fngfsi, int lev);
   void KillBlocks(MyList<Patch> *PatchLIST);
 
   void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));
@@ -91,43 +81,6 @@ namespace Parallel
                    int Symmetry);
   void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
   void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-
-  struct SyncCache {
-    bool valid;
-    int cpusize;
-    MyList<gridseg> **combined_src;
-    MyList<gridseg> **combined_dst;
-    int *send_lengths;
-    int *recv_lengths;
-    double **send_bufs;
-    double **recv_bufs;
-    int *send_buf_caps;
-    int *recv_buf_caps;
-    MPI_Request *reqs;
-    MPI_Status *stats;
-    int max_reqs;
-    bool lengths_valid;
-    SyncCache();
-    void invalidate();
-    void destroy();
-  };
-
-  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
-  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
-                       MyList<var> *VarList1, MyList<var> *VarList2,
-                       int Symmetry, SyncCache &cache);
-
-  struct AsyncSyncState {
-    int req_no;
-    bool active;
-    AsyncSyncState() : req_no(0), active(false) {}
-  };
-
-  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
-                  SyncCache &cache, AsyncSyncState &state);
-  void Sync_finish(SyncCache &cache, AsyncSyncState &state,
-                   MyList<var> *VarList, int Symmetry);
   void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                    int Symmetry);
@@ -140,15 +93,6 @@ namespace Parallel
   void OutBdLow2Himix(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
                       MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                       int Symmetry);
-  void Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                       MyList<var> *VarList1, MyList<var> *VarList2,
-                       int Symmetry, SyncCache &cache);
-  void OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                          MyList<var> *VarList1, MyList<var> *VarList2,
-                          int Symmetry, SyncCache &cache);
-  void OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
-                             MyList<var> *VarList1, MyList<var> *VarList2,
-                             int Symmetry, SyncCache &cache);
   void Prolong(Patch *Patc, Patch *Patf,
                MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                int Symmetry);

AMSS_NCKU_source/TwoPunctures.h

@@ -1,8 +1,7 @@
+
 #ifndef TWO_PUNCTURES_H
 #define TWO_PUNCTURES_H
 
-#include <omp.h>
-
 #define StencilSize 19
 #define N_PlaneRelax 1
 #define NRELAX 200
@@ -43,18 +42,6 @@ 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;
@@ -71,28 +58,6 @@ 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);
@@ -151,11 +116,23 @@ 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/bssn_class.C

@@ -730,12 +730,6 @@ void bssn_class::Initialize()
     PhysTime = StartTime;
     Setup_Black_Hole_position();
   }
-
-  // Initialize sync caches (per-level, for predictor and corrector)
-  sync_cache_pre = new Parallel::SyncCache[GH->levels];
-  sync_cache_cor = new Parallel::SyncCache[GH->levels];
-  sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
-  sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
 }
 
 //================================================================================================
@@ -987,32 +981,6 @@ bssn_class::~bssn_class()
   delete Azzz;
 #endif
 
-  // Destroy sync caches before GH
-  if (sync_cache_pre)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_pre[i].destroy();
-    delete[] sync_cache_pre;
-  }
-  if (sync_cache_cor)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_cor[i].destroy();
-    delete[] sync_cache_cor;
-  }
-  if (sync_cache_rp_coarse)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_rp_coarse[i].destroy();
-    delete[] sync_cache_rp_coarse;
-  }
-  if (sync_cache_rp_fine)
-  {
-    for (int i = 0; i < GH->levels; i++)
-      sync_cache_rp_fine[i].destroy();
-    delete[] sync_cache_rp_fine;
-  }
-
   delete GH;
 #ifdef WithShell
   delete SH;
@@ -2213,7 +2181,6 @@ void bssn_class::Evolve(int Steps)
     GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
                SynchList_cor, OldStateList, StateList, SynchList_pre,
                fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
-    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 
 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2426,10 +2393,9 @@ void bssn_class::RecursiveStep(int lev)
 #endif
 
 #if (REGLEV == 0)
-  if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
+  GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
-                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
 #endif
 }
 
@@ -2605,10 +2571,9 @@ void bssn_class::ParallelStep()
   delete[] tporg;
   delete[] tporgo;
 #if (REGLEV == 0)
-  if (GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
+  GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
-                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
 #endif
 }
 
@@ -2772,10 +2737,9 @@ void bssn_class::ParallelStep()
       if (lev + 1 >= GH->movls)
       {
         //	       GH->Regrid_Onelevel_aux(lev,Symmetry,BH_num,Porgbr,Porg0,
-        if (GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
+        GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
                             SynchList_cor, OldStateList, StateList, SynchList_pre,
-                            fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor))
-        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+                            fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor);
 
         //               a_stream.clear();
         //               a_stream.str("");
@@ -2787,10 +2751,9 @@ void bssn_class::ParallelStep()
     // for this level
     if (YN == 1)
     {
-      if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
+      GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                           SynchList_cor, OldStateList, StateList, SynchList_pre,
-                          fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+                          fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
 
       //               a_stream.clear();
       //               a_stream.str("");
@@ -2806,10 +2769,9 @@ void bssn_class::ParallelStep()
         if (YN == 1)
         {
           //	   GH->Regrid_Onelevel_aux(lev-2,Symmetry,BH_num,Porgbr,Porg0,
-          if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
+          GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
-                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -2822,10 +2784,9 @@ void bssn_class::ParallelStep()
         if (i % 4 == 3)
         {
           //	   GH->Regrid_Onelevel_aux(lev-2,Symmetry,BH_num,Porgbr,Porg0,
-          if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
+          GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
-                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -3197,7 +3158,21 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+  // check error information
+  {
+    int erh = ERROR;
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
 
 #ifdef WithShell
   // evolve Shell Patches
@@ -3341,16 +3316,25 @@ void bssn_class::Step(int lev, int YN)
 #endif
   }
 
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-  MPI_Request err_req;
+  // check error information
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
   }
 #endif
 
-  Parallel::AsyncSyncState async_pre;
-  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
 
 #ifdef WithShell
   if (lev == 0)
@@ -3369,23 +3353,6 @@ void bssn_class::Step(int lev, int YN)
     }
   }
 #endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
 
 #if (MAPBH == 0)
   // for black hole position
@@ -3561,7 +3528,24 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+    // check error information
+    {
+      int erh = ERROR;
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime 
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
 
 #ifdef WithShell
     // evolve Shell Patches
@@ -3701,16 +3685,26 @@ void bssn_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-    MPI_Request err_req_cor;
+    // check error information
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" 
+                                << iter_count << " variables at t = " 
+                                << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
     }
 #endif
 
-    Parallel::AsyncSyncState async_cor;
-    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #ifdef WithShell
     if (lev == 0)
@@ -3729,25 +3723,6 @@ void bssn_class::Step(int lev, int YN)
       }
     }
 #endif
-    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
-                                << " variables at t = " << PhysTime
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-#endif
 
 #if (MAPBH == 0)
     // for black hole position
@@ -4059,7 +4034,22 @@ void bssn_class::Step(int lev, int YN)
     }
     Pp = Pp->next;
   }
-  // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+  // check error information
+  {
+    int erh = ERROR;
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime 
+                              << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
 
 #ifdef WithShell
   // evolve Shell Patches
@@ -4200,16 +4190,25 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
   }
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-  MPI_Request err_req;
+  // check error information
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " 
+                              << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
   }
 #endif
 
-  Parallel::AsyncSyncState async_pre;
-  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
 
 #ifdef WithShell
   if (lev == 0)
@@ -4228,24 +4227,6 @@ void bssn_class::Step(int lev, int YN)
     }
   }
 #endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
-
-#ifdef WithShell
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
-  if (ERROR)
-  {
-    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime
-                              << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-#endif
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -4405,7 +4386,23 @@ void bssn_class::Step(int lev, int YN)
       Pp = Pp->next;
     }
 
-    // NOTE: error check deferred to after Shell Patch computation to reduce MPI_Allreduce calls
+    // check error information
+    {
+      int erh = ERROR;
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime 
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
 
 #ifdef WithShell
     // evolve Shell Patches
@@ -4545,16 +4542,25 @@ void bssn_class::Step(int lev, int YN)
         sPp = sPp->next;
       }
     }
-    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-    MPI_Request err_req_cor;
+    // check error information
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
     }
 #endif
 
-    Parallel::AsyncSyncState async_cor;
-    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #ifdef WithShell
     if (lev == 0)
@@ -4572,25 +4578,6 @@ void bssn_class::Step(int lev, int YN)
              << " seconds! " << endl;
       }
     }
-#endif
-    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
-
-#ifdef WithShell
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
-    if (ERROR)
-    {
-      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
-                                << " variables at t = " << PhysTime
-                                << ", lev = " << lev << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
 #endif
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -4956,19 +4943,11 @@ void bssn_class::Step(int lev, int YN)
 
   //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");
 
-  // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-  MPI_Request err_req;
+  // check error information
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev], &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
   }
-
-  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
-
-  Parallel::Sync_cached(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev]);
-
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
   if (ERROR)
   {
     Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
@@ -4980,6 +4959,10 @@ void bssn_class::Step(int lev, int YN)
     }
   }
 
+  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");
+
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+
 #if (MAPBH == 0)
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -5157,21 +5140,11 @@ void bssn_class::Step(int lev, int YN)
 
     //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");
 
-    // Non-blocking error reduction overlapped with Sync to hide Allreduce latency
-    MPI_Request err_req_cor;
+    // check error information
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev], &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
     }
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");
-
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev]);
-
-    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
-
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
     if (ERROR)
     {
       Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
@@ -5185,6 +5158,12 @@ 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);
+
+    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");
+
 #if (MAPBH == 0)
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
@@ -5468,11 +5447,21 @@ void bssn_class::SHStep()
 #if (PSTR == 1 || PSTR == 2)
 //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor's error check");
 #endif
-  // Non-blocking error reduction overlapped with Synch to hide Allreduce latency
-  MPI_Request err_req;
+  // check error information
   {
     int erh = ERROR;
-    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req);
+    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+  }
+
+  if (ERROR)
+  {
+    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
   }
 
   {
@@ -5490,19 +5479,6 @@ void bssn_class::SHStep()
     }
   }
 
-  // Complete non-blocking error reduction and check
-  MPI_Wait(&err_req, MPI_STATUS_IGNORE);
-  if (ERROR)
-  {
-    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
-    if (myrank == 0)
-    {
-      if (ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "find NaN in state variables on Shell Patches at t = " << PhysTime << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
   // corrector
   for (iter_count = 1; iter_count < 4; iter_count++)
   {
@@ -5645,11 +5621,21 @@ void bssn_class::SHStep()
         sPp = sPp->next;
       }
     }
-    // Non-blocking error reduction overlapped with Synch to hide Allreduce latency
-    MPI_Request err_req_cor;
+    // check error information
     {
       int erh = ERROR;
-      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
+    }
+    if (ERROR)
+    {
+      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count 
+                                << " variables at t = " << PhysTime << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
     }
 
     {
@@ -5667,20 +5653,6 @@ void bssn_class::SHStep()
       }
     }
 
-    // Complete non-blocking error reduction and check
-    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
-    if (ERROR)
-    {
-      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
-      if (myrank == 0)
-      {
-        if (ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "find NaN on Shell Patches in RK4 substep#" << iter_count
-                                << " variables at t = " << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
     sPp = SH->PatL;
     while (sPp)
     {
@@ -5809,7 +5781,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5819,11 +5791,21 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, GH->bdsul[lev], Symmetry);
@@ -5860,7 +5842,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5870,11 +5852,21 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SL, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SL, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->bdsul[lev], Symmetry);
@@ -5888,7 +5880,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
 
 #if (PSTR == 1 || PSTR == 2)
 //    a_stream.clear();
@@ -5946,14 +5938,24 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, GH->bdsul[lev], Symmetry);
@@ -5968,21 +5970,31 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SL, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SL, SL, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SL, SL, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->bdsul[lev], Symmetry);
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SL, Symmetry);
   }
 }
 
@@ -6033,14 +6045,24 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], SynchList_pre, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -6057,21 +6079,31 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],StateList,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, GH->bdsul[lev], Symmetry);
 #endif
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
   }
 }
 
@@ -6101,11 +6133,21 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
       }
 
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, SynchList_pre, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_pre,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -6114,11 +6156,21 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
     else // no time refinement levels and for all same time levels
     {
 #if (RPB == 0)
+      Ppc = GH->PatL[lev - 1];
+      while (Ppc)
+      {
+        Pp = GH->PatL[lev];
+        while (Pp)
+        {
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Hi(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
-      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+          Parallel::OutBdLow2Himix(Ppc->data, Pp->data, StateList, SynchList_cor, Symmetry);
 #endif
+          Pp = Pp->next;
+        }
+        Ppc = Ppc->next;
+      }
 #elif (RPB == 1)
       //       Parallel::OutBdLow2Hi_bam(GH->PatL[lev-1],GH->PatL[lev],StateList,SynchList_cor,Symmetry);
       Parallel::OutBdLow2Hi_bam(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, GH->bdsul[lev], Symmetry);
@@ -6134,10 +6186,10 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 #else
       Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
 #endif
-      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+      Parallel::Sync(GH->PatL[lev - 1], StateList, Symmetry);
     }
 
-    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
   }
 }
 #undef MIXOUTB

AMSS_NCKU_source/bssn_class.h

@@ -126,11 +126,6 @@ public:
        MyList<var> *OldStateList, *DumpList;
        MyList<var> *ConstraintList;
 
-       Parallel::SyncCache *sync_cache_pre;  // per-level cache for predictor sync
-       Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
-       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
-       Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
-
        monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
        monitor *ConVMonitor;
        surface_integral *Waveshell;

AMSS_NCKU_source/bssn_rhs.f90

@@ -61,7 +61,9 @@
   real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: ham_Res, movx_Res, movy_Res, movz_Res
   real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
 !  gont = 0: success; gont = 1: something wrong
-  integer::gont
+  integer::gont,i,j,k
+  real*8 :: val1, val2
+  real*8 :: det, t_gupxx, t_gupxy, t_gupxz, t_gupyy, t_gupyz, t_gupzz
 
 !~~~~~~> Other variables:
 
@@ -84,7 +86,10 @@
   real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
 
   real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
-  real*8            :: dX, dY, dZ, PI
+  real*8            :: PI
+#if (DEBUG_NAN_CHECK)
+  real*8            :: dX
+#endif
   real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
   real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
   real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
@@ -106,8 +111,8 @@
   call getpbh(BHN,Porg,Mass)
 #endif
 
-!!! sanity check (disabled in production builds for performance)
-#ifdef DEBUG
+#if (DEBUG_NAN_CHECK)
+!!! sanity check
   dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
       +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
       +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -141,10 +146,6 @@
 
   PI = dacos(-ONE)
 
-  dX = X(2) - X(1)
-  dY = Y(2) - Y(1)
-  dZ = Z(2) - Z(1)
-
   alpn1 = Lap + ONE
   chin1 = chi + ONE
   gxx = dxx + ONE
@@ -158,15 +159,15 @@
   div_beta = betaxx + betayy + betazz
 
   call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
-
-  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
-
   call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+
   call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
   call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
-  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
   call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
-  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+
+  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
 
   gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
               TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
@@ -192,71 +193,99 @@
                                        gyz * betayx +   gzz * betazx   &
                                                     -   gxz * betayy     !rhs for gij
 
-! invert tilted metric
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
-  gupxx =   ( gyy * gzz - gyz * gyz ) / gupzz
-  gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
-  gupxz =   ( gxy * gyz - gyy * gxz ) / gupzz
-  gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
-  gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
-  gupzz =   ( gxx * gyy - gxy * gxy ) / gupzz
+! fused loop for metric inversion and connections
+  !DIR$ SIMD
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+     ! 1. Metric Inversion
+     det = ONE / ( &
+            gxx(i,j,k) * gyy(i,j,k) * gzz(i,j,k) + 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) * gyy(i,j,k) * gxz(i,j,k) - &
+            gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k) )
+     
+     t_gupxx =   ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) * det
+     t_gupxy = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) * det
+     t_gupxz =   ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) * det
+     t_gupyy =   ( gxx(i,j,k) * gzz(i,j,k) - gxz(i,j,k) * gxz(i,j,k) ) * det
+     t_gupyz = - ( gxx(i,j,k) * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) * det
+     t_gupzz =   ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) * det
+
+     gupxx(i,j,k) = t_gupxx
+     gupxy(i,j,k) = t_gupxy
+     gupxz(i,j,k) = t_gupxz
+     gupyy(i,j,k) = t_gupyy
+     gupyz(i,j,k) = t_gupyz
+     gupzz(i,j,k) = t_gupzz
 
      if(co == 0)then
-! Gam^i_Res = Gam^i + gup^ij_,j
-  Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
-                   +gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
-                   +gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
-                   +gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
-                   +gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
-                   +gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
-                   +gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
-                   +gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
-                   +gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
-  Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
-                   +gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
-                   +gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
-                   +gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
-                   +gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
-                   +gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
-                   +gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
-                   +gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
-                   +gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
-  Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
-                   +gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
-                   +gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
-                   +gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
-                   +gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
-                   +gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
-                   +gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
-                   +gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
-                   +gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
+        Gmx_Res(i,j,k) = Gamx(i,j,k) - (t_gupxx*(t_gupxx*gxxx(i,j,k)+t_gupxy*gxyx(i,j,k)+t_gupxz*gxzx(i,j,k))&
+                         +t_gupxy*(t_gupxx*gxyx(i,j,k)+t_gupxy*gyyx(i,j,k)+t_gupxz*gyzx(i,j,k))&
+                         +t_gupxz*(t_gupxx*gxzx(i,j,k)+t_gupxy*gyzx(i,j,k)+t_gupxz*gzzx(i,j,k))&
+                         +t_gupxx*(t_gupxy*gxxy(i,j,k)+t_gupyy*gxyy(i,j,k)+t_gupyz*gxzy(i,j,k))&
+                         +t_gupxy*(t_gupxy*gxyy(i,j,k)+t_gupyy*gyyy(i,j,k)+t_gupyz*gyzy(i,j,k))&
+                         +t_gupxz*(t_gupxy*gxzy(i,j,k)+t_gupyy*gyzy(i,j,k)+t_gupyz*gzzy(i,j,k))&
+                         +t_gupxx*(t_gupxz*gxxz(i,j,k)+t_gupyz*gxyz(i,j,k)+t_gupzz*gxzz(i,j,k))&
+                         +t_gupxy*(t_gupxz*gxyz(i,j,k)+t_gupyz*gyyz(i,j,k)+t_gupzz*gyzz(i,j,k))&
+                         +t_gupxz*(t_gupxz*gxzz(i,j,k)+t_gupyz*gyzz(i,j,k)+t_gupzz*gzzz(i,j,k)))
+        Gmy_Res(i,j,k) = Gamy(i,j,k) - (t_gupxx*(t_gupxy*gxxx(i,j,k)+t_gupyy*gxyx(i,j,k)+t_gupyz*gxzx(i,j,k))&
+                         +t_gupxy*(t_gupxy*gxyx(i,j,k)+t_gupyy*gyyx(i,j,k)+t_gupyz*gyzx(i,j,k))&
+                         +t_gupxz*(t_gupxy*gxzx(i,j,k)+t_gupyy*gyzx(i,j,k)+t_gupyz*gzzx(i,j,k))&
+                         +t_gupxy*(t_gupxy*gxxy(i,j,k)+t_gupyy*gxyy(i,j,k)+t_gupyz*gxzy(i,j,k))&
+                         +t_gupyy*(t_gupxy*gxyy(i,j,k)+t_gupyy*gyyy(i,j,k)+t_gupyz*gyzy(i,j,k))&
+                         +t_gupyz*(t_gupxy*gxzy(i,j,k)+t_gupyy*gyzy(i,j,k)+t_gupyz*gzzy(i,j,k))&
+                         +t_gupxy*(t_gupxz*gxxz(i,j,k)+t_gupyz*gxyz(i,j,k)+t_gupzz*gxzz(i,j,k))&
+                         +t_gupyy*(t_gupxz*gxyz(i,j,k)+t_gupyz*gyyz(i,j,k)+t_gupzz*gyzz(i,j,k))&
+                         +t_gupyz*(t_gupxz*gxzz(i,j,k)+t_gupyz*gyzz(i,j,k)+t_gupzz*gzzz(i,j,k)))
+        Gmz_Res(i,j,k) = Gamz(i,j,k) - (t_gupxx*(t_gupxz*gxxx(i,j,k)+t_gupyz*gxyx(i,j,k)+t_gupzz*gxzx(i,j,k))&
+                         +t_gupxy*(t_gupxz*gxyx(i,j,k)+t_gupyz*gyyx(i,j,k)+t_gupzz*gyzx(i,j,k))&
+                         +t_gupxz*(t_gupxz*gxzx(i,j,k)+t_gupyz*gyzx(i,j,k)+t_gupzz*gzzx(i,j,k))&
+                         +t_gupxy*(t_gupxz*gxxy(i,j,k)+t_gupyz*gxyy(i,j,k)+t_gupzz*gxzy(i,j,k))&
+                         +t_gupyy*(t_gupxz*gxyy(i,j,k)+t_gupyz*gyyy(i,j,k)+t_gupzz*gyzy(i,j,k))&
+                         +t_gupyz*(t_gupxz*gxzy(i,j,k)+t_gupyz*gyzy(i,j,k)+t_gupzz*gzzy(i,j,k))&
+                         +t_gupxz*(t_gupxz*gxxz(i,j,k)+t_gupyz*gxyz(i,j,k)+t_gupzz*gxzz(i,j,k))&
+                         +t_gupyz*(t_gupxz*gxyz(i,j,k)+t_gupyz*gyyz(i,j,k)+t_gupzz*gyzz(i,j,k))&
+                         +t_gupzz*(t_gupxz*gxzz(i,j,k)+t_gupyz*gyzz(i,j,k)+t_gupzz*gzzz(i,j,k)))
      endif
 
-! second kind of connection
-  Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
-  Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
-  Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
+     ! 2. Christoffel Symbols
+     val1 = TWO * gxyx(i,j,k) - gxxy(i,j,k)
+     val2 = TWO * gxzx(i,j,k) - gxxz(i,j,k)
+     Gamxxx(i,j,k) =HALF*( t_gupxx*gxxx(i,j,k) + t_gupxy*val1 + t_gupxz*val2 )
+     Gamyxx(i,j,k) =HALF*( t_gupxy*gxxx(i,j,k) + t_gupyy*val1 + t_gupyz*val2 )
+     Gamzxx(i,j,k) =HALF*( t_gupxz*gxxx(i,j,k) + t_gupyz*val1 + t_gupzz*val2 )
 
-  Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
-  Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
-  Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
+     val1 = TWO * gxyy(i,j,k) - gyyx(i,j,k)
+     val2 = TWO * gyzy(i,j,k) - gyyz(i,j,k)
+     Gamxyy(i,j,k) =HALF*( t_gupxx*val1 + t_gupxy*gyyy(i,j,k) + t_gupxz*val2 )
+     Gamyyy(i,j,k) =HALF*( t_gupxy*val1 + t_gupyy*gyyy(i,j,k) + t_gupyz*val2 )
+     Gamzyy(i,j,k) =HALF*( t_gupxz*val1 + t_gupyz*gyyy(i,j,k) + t_gupzz*val2 )
 
-  Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
-  Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
-  Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
+     val1 = TWO * gxzz(i,j,k) - gzzx(i,j,k)
+     val2 = TWO * gyzz(i,j,k) - gzzy(i,j,k)
+     Gamxzz(i,j,k) =HALF*( t_gupxx*val1 + t_gupxy*val2 + t_gupxz*gzzz(i,j,k) )
+     Gamyzz(i,j,k) =HALF*( t_gupxy*val1 + t_gupyy*val2 + t_gupyz*gzzz(i,j,k) )
+     Gamzzz(i,j,k) =HALF*( t_gupxz*val1 + t_gupyz*val2 + t_gupzz*gzzz(i,j,k) )
 
-  Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
-  Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
-  Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
+     val1 = gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)
+     Gamxxy(i,j,k) =HALF*( t_gupxx*gxxy(i,j,k) + t_gupxy*gyyx(i,j,k) + t_gupxz*val1 )
+     Gamyxy(i,j,k) =HALF*( t_gupxy*gxxy(i,j,k) + t_gupyy*gyyx(i,j,k) + t_gupyz*val1 )
+     Gamzxy(i,j,k) =HALF*( t_gupxz*gxxy(i,j,k) + t_gupyz*gyyx(i,j,k) + t_gupzz*val1 )
+
+     val1 = gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)
+     Gamxxz(i,j,k) =HALF*( t_gupxx*gxxz(i,j,k) + t_gupxy*val1 + t_gupxz*gzzx(i,j,k) )
+     Gamyxz(i,j,k) =HALF*( t_gupxy*gxxz(i,j,k) + t_gupyy*val1 + t_gupyz*gzzx(i,j,k) )
+     Gamzxz(i,j,k) =HALF*( t_gupxz*gxxz(i,j,k) + t_gupyz*val1 + t_gupzz*gzzx(i,j,k) )
+
+     val1 = gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)
+     Gamxyz(i,j,k) =HALF*( t_gupxx*val1 + t_gupxy*gyyz(i,j,k) + t_gupxz*gzzy(i,j,k) )
+     Gamyyz(i,j,k) =HALF*( t_gupxy*val1 + t_gupyy*gyyz(i,j,k) + t_gupyz*gzzy(i,j,k) )
+     Gamzyz(i,j,k) =HALF*( t_gupxz*val1 + t_gupyz*gyyz(i,j,k) + t_gupzz*gzzy(i,j,k) )
+  enddo
+  enddo
+  enddo
 
-  Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
-  Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
-  Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
 
-  Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
-  Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
-  Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
 ! Raise indices of \tilde A_{ij} and store in R_ij
 
   Rxx =    gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
@@ -287,30 +316,40 @@
   call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
   call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
 
+  ! reuse fxx/fxy/fxz as temporaries for matter-source combinations
+  fxx = F2o3 * Kx + EIGHT * PI * Sx
+  fxy = F2o3 * Ky + EIGHT * PI * Sy
+  fxz = F2o3 * Kz + EIGHT * PI * Sz
+
+  ! reuse Gamxa/Gamya/Gamza as temporaries for chix*R combinations
+  Gamxa = chix * Rxx + chiy * Rxy + chiz * Rxz
+  Gamya = chix * Rxy + chiy * Ryy + chiz * Ryz
+  Gamza = chix * Rxz + chiy * Ryz + chiz * Rzz
+
    Gamx_rhs = - TWO * (   Lapx * Rxx +   Lapy * Rxy +   Lapz * Rxz ) + &
         TWO * alpn1 * (                                                &
-        -F3o2/chin1 * (   chix * Rxx +   chiy * Rxy +   chiz * Rxz ) - &
-              gupxx * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
-              gupxy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
-              gupxz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+        -F3o2 * ONE/chin1 * Gamxa - &
+              gupxx * fxx - &
+              gupxy * fxy - &
+              gupxz * fxz + &
                         Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz   + &
                 TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
 
    Gamy_rhs = - TWO * (   Lapx * Rxy +   Lapy * Ryy +   Lapz * Ryz ) + &
         TWO * alpn1 * (                                                &
-        -F3o2/chin1 * (   chix * Rxy +  chiy * Ryy +    chiz * Ryz ) - &
-              gupxy * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
-              gupyy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
-              gupyz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+        -F3o2 * ONE/chin1 * Gamya - &
+              gupxy * fxx - &
+              gupyy * fxy - &
+              gupyz * fxz + &
                         Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz   + &
                 TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
 
    Gamz_rhs = - TWO * (   Lapx * Rxz +   Lapy * Ryz +   Lapz * Rzz ) + &
         TWO * alpn1 * (                                                &
-        -F3o2/chin1 * (   chix * Rxz +  chiy * Ryz +    chiz * Rzz ) - &
-              gupxz * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
-              gupyz * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
-              gupzz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+        -F3o2 * ONE/chin1 * Gamza - &
+              gupxz * fxx - &
+              gupyz * fxy - &
+              gupzz * fxz + &
                         Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz   + &
                 TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
 
@@ -612,47 +651,47 @@
   fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
 ! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f
 
-  f =        gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
-             gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
-             gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
-       TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
-       TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
-       TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz ) 
+  f =        gupxx * ( fxx - F3o2 * ONE/chin1 * chix * chix ) + &
+             gupyy * ( fyy - F3o2 * ONE/chin1 * chiy * chiy ) + &
+             gupzz * ( fzz - F3o2 * ONE/chin1 * chiz * chiz ) + &
+       TWO * gupxy * ( fxy - F3o2 * ONE/chin1 * chix * chiy ) + &
+       TWO * gupxz * ( fxz - F3o2 * ONE/chin1 * chix * chiz ) + &
+       TWO * gupyz * ( fyz - F3o2 * ONE/chin1 * chiy * chiz ) 
 ! Add chi part to Ricci tensor:
 
-  Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * f)/chin1/TWO
-  Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * f)/chin1/TWO
-  Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/TWO
-  Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/TWO
-  Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/TWO
-  Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO
+  Rxx = Rxx + (fxx - chix*chix*ONE/chin1*HALF + gxx * f) * ONE/chin1 * HALF
+  Ryy = Ryy + (fyy - chiy*chiy*ONE/chin1*HALF + gyy * f) * ONE/chin1 * HALF
+  Rzz = Rzz + (fzz - chiz*chiz*ONE/chin1*HALF + gzz * f) * ONE/chin1 * HALF
+  Rxy = Rxy + (fxy - chix*chiy*ONE/chin1*HALF + gxy * f) * ONE/chin1 * HALF
+  Rxz = Rxz + (fxz - chix*chiz*ONE/chin1*HALF + gxz * f) * ONE/chin1 * HALF
+  Ryz = Ryz + (fyz - chiy*chiz*ONE/chin1*HALF + gyz * f) * ONE/chin1 * HALF
 
 ! covariant second derivatives of the lapse respect to physical metric
   call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
                 SYM,SYM,SYM,symmetry,Lev)
 
-  gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
-  gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
-  gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
+  gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz) * ONE/chin1
+  gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz) * ONE/chin1
+  gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz) * ONE/chin1
 ! now get physical second kind of connection
-  Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
+  Gamxxx = Gamxxx - ( TWO * chix * ONE/chin1 - gxx * gxxx )*HALF
   Gamyxx = Gamyxx - (                     - gxx * gxxy )*HALF
   Gamzxx = Gamzxx - (                     - gxx * gxxz )*HALF
   Gamxyy = Gamxyy - (                     - gyy * gxxx )*HALF
-  Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
+  Gamyyy = Gamyyy - ( TWO * chiy * ONE/chin1 - gyy * gxxy )*HALF
   Gamzyy = Gamzyy - (                     - gyy * gxxz )*HALF
   Gamxzz = Gamxzz - (                     - gzz * gxxx )*HALF
   Gamyzz = Gamyzz - (                     - gzz * gxxy )*HALF
-  Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
-  Gamxxy = Gamxxy - (  chiy        /chin1 - gxy * gxxx )*HALF
-  Gamyxy = Gamyxy - (         chix /chin1 - gxy * gxxy )*HALF
+  Gamzzz = Gamzzz - ( TWO * chiz * ONE/chin1 - gzz * gxxz )*HALF
+  Gamxxy = Gamxxy - (  chiy * ONE/chin1 - gxy * gxxx )*HALF
+  Gamyxy = Gamyxy - (  chix * ONE/chin1 - gxy * gxxy )*HALF
   Gamzxy = Gamzxy - (                     - gxy * gxxz )*HALF
-  Gamxxz = Gamxxz - (  chiz        /chin1 - gxz * gxxx )*HALF
+  Gamxxz = Gamxxz - (  chiz * ONE/chin1 - gxz * gxxx )*HALF
   Gamyxz = Gamyxz - (                     - gxz * gxxy )*HALF
-  Gamzxz = Gamzxz - (         chix /chin1 - gxz * gxxz )*HALF
+  Gamzxz = Gamzxz - (  chix * ONE/chin1 - gxz * gxxz )*HALF
   Gamxyz = Gamxyz - (                     - gyz * gxxx )*HALF
-  Gamyyz = Gamyyz - (  chiz        /chin1 - gyz * gxxy )*HALF
-  Gamzyz = Gamzyz - (         chiy /chin1 - gyz * gxxz )*HALF
+  Gamyyz = Gamyyz - (  chiz * ONE/chin1 - gyz * gxxy )*HALF
+  Gamzyz = Gamzyz - (  chiy * ONE/chin1 - gyz * gxxz )*HALF
 
   fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
   fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
@@ -695,7 +734,7 @@
        gupxz * (Axy * Azz + Ayz * Axz) + &
        gupyz * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
   f = - F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
-        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
+        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1 * ONE/chin1 * f)
   
   fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
   fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
@@ -815,7 +854,8 @@
   call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
   reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
        TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
-  reta = 1.31d0/2*dsqrt(reta/chin1)/(1-dsqrt(chin1))**2
+  fxx = dsqrt(chin1)
+  reta = 1.31d0/2*dsqrt(reta*ONE/chin1)/(ONE-fxx)**2
   dtSfx_rhs = Gamx_rhs - reta*dtSfx
   dtSfy_rhs = Gamy_rhs - reta*dtSfy
   dtSfz_rhs = Gamz_rhs - reta*dtSfz
@@ -827,7 +867,7 @@
   call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
   reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
        TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
-  reta = 1.31d0/2*dsqrt(reta/chin1)/(1-chin1)**2
+  reta = 1.31d0/2*dsqrt(reta*ONE/chin1)/(ONE-chin1)**2
   dtSfx_rhs = Gamx_rhs - reta*dtSfx
   dtSfy_rhs = Gamy_rhs - reta*dtSfy
   dtSfz_rhs = Gamz_rhs - reta*dtSfz
@@ -835,7 +875,8 @@
   call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
   reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
        TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
-  reta = 1.31d0/2*dsqrt(reta/chin1)/(1-dsqrt(chin1))**2
+  fxx = dsqrt(chin1)
+  reta = 1.31d0/2*dsqrt(reta*ONE/chin1)/(ONE-fxx)**2
   betax_rhs = FF*Gamx - reta*betax
   betay_rhs = FF*Gamy - reta*betay
   betaz_rhs = FF*Gamz - reta*betaz
@@ -847,7 +888,7 @@
   call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
   reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
        TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
-  reta = 1.31d0/2*dsqrt(reta/chin1)/(1-chin1)**2
+  reta = 1.31d0/2*dsqrt(reta*ONE/chin1)/(ONE-chin1)**2
   betax_rhs = FF*Gamx - reta*betax
   betay_rhs = FF*Gamy - reta*betay
   betaz_rhs = FF*Gamz - reta*betaz
@@ -945,60 +986,103 @@
   SSA(2)=SYM
   SSA(3)=ANTI
 
-!!!!!!!!!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.
+!!!!!!!!!advection term part
 
-  call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS)
+  call lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA)
+  call lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA)
+  call lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS)
 
-  call lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS)
+  call lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA)
+  call lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA)
+  call lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS)
 
-  call lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)
 
-  call lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  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,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
+  call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
+  call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
+!!
   call lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS)
+
 #if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA)
 #endif
+
 #if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
   call lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS)
   call lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS)
   call lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA)
 #endif
+
+  if(eps>0)then 
+! usual Kreiss-Oliger dissipation      
+  call kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "before",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
 #endif
+  call kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "after",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
+#endif
+  call kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps)
+
+#if 1 
+!! bam does not apply dissipation on gauge variables
+  call kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps)
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+  call kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps)
+#endif
+#endif
+
+  endif
 
   if(co == 0)then
 ! ham_Res = trR + 2/3 * K^2 - A_ij * A^ij - 16 * PI * rho
@@ -1036,48 +1120,48 @@
 ! mov_Res_j = gupkj*(-1/chi d_k chi*A_ij + D_k A_ij) - 2/3 d_j trK - 8 PI s_j where D respect to physical metric
 ! store D_i A_jk - 1/chi d_i chi*A_jk in gjk_i
   call fderivs(ex,Axx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
+  call fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
+  call fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
   call fderivs(ex,Axy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0)
   call fderivs(ex,Axz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0)
-  call fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
   call fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0)
-  call fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0)
 
   gxxx = gxxx - (  Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz &
-                 + Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz) - chix*Axx/chin1
+                 + Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz) - chix*Axx*ONE/chin1
   gxyx = gxyx - (  Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz &
-                 + Gamxxx * Axy + Gamyxx * Ayy + Gamzxx * Ayz) - chix*Axy/chin1
+                 + Gamxxx * Axy + Gamyxx * Ayy + Gamzxx * Ayz) - chix*Axy*ONE/chin1
   gxzx = gxzx - (  Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz &
-                 + Gamxxx * Axz + Gamyxx * Ayz + Gamzxx * Azz) - chix*Axz/chin1
+                 + Gamxxx * Axz + Gamyxx * Ayz + Gamzxx * Azz) - chix*Axz*ONE/chin1
   gyyx = gyyx - (  Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz &
-                 + Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz) - chix*Ayy/chin1
+                 + Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz) - chix*Ayy*ONE/chin1
   gyzx = gyzx - (  Gamxxz * Axy + Gamyxz * Ayy + Gamzxz * Ayz &
-                 + Gamxxy * Axz + Gamyxy * Ayz + Gamzxy * Azz) - chix*Ayz/chin1
+                 + Gamxxy * Axz + Gamyxy * Ayz + Gamzxy * Azz) - chix*Ayz*ONE/chin1
   gzzx = gzzx - (  Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz &
-                 + Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz) - chix*Azz/chin1
+                 + Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz) - chix*Azz*ONE/chin1
   gxxy = gxxy - (  Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz &
-                 + Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz) - chiy*Axx/chin1
+                 + Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz) - chiy*Axx*ONE/chin1
   gxyy = gxyy - (  Gamxyy * Axx + Gamyyy * Axy + Gamzyy * Axz &
-                 + Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz) - chiy*Axy/chin1
+                 + Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz) - chiy*Axy*ONE/chin1
   gxzy = gxzy - (  Gamxyz * Axx + Gamyyz * Axy + Gamzyz * Axz &
-                 + Gamxxy * Axz + Gamyxy * Ayz + Gamzxy * Azz) - chiy*Axz/chin1
+                 + Gamxxy * Axz + Gamyxy * Ayz + Gamzxy * Azz) - chiy*Axz*ONE/chin1
   gyyy = gyyy - (  Gamxyy * Axy + Gamyyy * Ayy + Gamzyy * Ayz &
-                 + Gamxyy * Axy + Gamyyy * Ayy + Gamzyy * Ayz) - chiy*Ayy/chin1
+                 + Gamxyy * Axy + Gamyyy * Ayy + Gamzyy * Ayz) - chiy*Ayy*ONE/chin1
   gyzy = gyzy - (  Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz &
-                 + Gamxyy * Axz + Gamyyy * Ayz + Gamzyy * Azz) - chiy*Ayz/chin1
+                 + Gamxyy * Axz + Gamyyy * Ayz + Gamzyy * Azz) - chiy*Ayz*ONE/chin1
   gzzy = gzzy - (  Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz &
-                 + Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz) - chiy*Azz/chin1
+                 + Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz) - chiy*Azz*ONE/chin1
   gxxz = gxxz - (  Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz &
-                 + Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz) - chiz*Axx/chin1
+                 + Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz) - chiz*Axx*ONE/chin1
   gxyz = gxyz - (  Gamxyz * Axx + Gamyyz * Axy + Gamzyz * Axz &
-                 + Gamxxz * Axy + Gamyxz * Ayy + Gamzxz * Ayz) - chiz*Axy/chin1
+                 + Gamxxz * Axy + Gamyxz * Ayy + Gamzxz * Ayz) - chiz*Axy*ONE/chin1
   gxzz = gxzz - (  Gamxzz * Axx + Gamyzz * Axy + Gamzzz * Axz &
-                 + Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz) - chiz*Axz/chin1
+                 + Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz) - chiz*Axz*ONE/chin1
   gyyz = gyyz - (  Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz &
-                 + Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz) - chiz*Ayy/chin1
+                 + Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz) - chiz*Ayy*ONE/chin1
   gyzz = gyzz - (  Gamxzz * Axy + Gamyzz * Ayy + Gamzzz * Ayz &
-                 + Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz) - chiz*Ayz/chin1
+                 + Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz) - chiz*Ayz*ONE/chin1
   gzzz = gzzz - (  Gamxzz * Axz + Gamyzz * Ayz + Gamzzz * Azz &
-                 + Gamxzz * Axz + Gamyzz * Ayz + Gamzzz * Azz) - chiz*Azz/chin1
+                 + Gamxzz * Axz + Gamyzz * Ayz + Gamzzz * Azz) - chiz*Azz*ONE/chin1
 movx_Res = gupxx*gxxx + gupyy*gxyy + gupzz*gxzz &
           +gupxy*gxyx + gupxz*gxzx + gupyz*gxzy &
           +gupxy*gxxy + gupxz*gxxz + gupyz*gxyz

AMSS_NCKU_source/cgh.C

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

AMSS_NCKU_source/cgh.h

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

AMSS_NCKU_source/diff_new.f90

@@ -69,8 +69,6 @@
   fy = ZEO
   fz = ZEO
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -373,8 +371,6 @@
   fxz = ZEO
   fyz = ZEO
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)-1
   do j=1,ex(2)-1
   do i=1,ex(1)-1
@@ -1943,6 +1939,309 @@
   return
 
   end subroutine fddyz
+  subroutine fderivs_batch4(ex,f1,f2,f3,f4, &
+                            f1x,f1y,f1z,f2x,f2y,f2z,f3x,f3y,f3z,f4x,f4y,f4z, &
+                            X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+  implicit none
+
+  integer,                               intent(in ):: ex(1:3),symmetry,onoff
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f1,f2,f3,f4
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f1x,f1y,f1z
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f2x,f2y,f2z
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f3x,f3y,f3z
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f4x,f4y,f4z
+  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
+  real*8,                                intent(in ):: SYM1,SYM2,SYM3
+
+!~~~~~~ other variables
+
+  real*8 :: dX,dY,dZ
+  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh1,fh2,fh3,fh4
+  real*8, dimension(3) :: SoA
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0
+  real*8,  parameter :: TWO=2.d0,EIT=8.d0
+  real*8,  parameter :: F12=1.2d1
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
+
+  SoA(1) = SYM1
+  SoA(2) = SYM2
+  SoA(3) = SYM3
+
+  call symmetry_bd(2,ex,f1,fh1,SoA)
+  call symmetry_bd(2,ex,f2,fh2,SoA)
+  call symmetry_bd(2,ex,f3,fh3,SoA)
+  call symmetry_bd(2,ex,f4,fh4,SoA)
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  f1x = ZEO; f1y = ZEO; f1z = ZEO
+  f2x = ZEO; f2y = ZEO; f2z = ZEO
+  f3x = ZEO; f3y = ZEO; f3z = ZEO
+  f4x = ZEO; f4y = ZEO; f4z = ZEO
+
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+   if(i+2 <= imax .and. i-2 >= imin .and. &
+      j+2 <= jmax .and. j-2 >= jmin .and. &
+      k+2 <= kmax .and. k-2 >= kmin) then
+      f1x(i,j,k)=d12dx*(fh1(i-2,j,k)-EIT*fh1(i-1,j,k)+EIT*fh1(i+1,j,k)-fh1(i+2,j,k))
+      f1y(i,j,k)=d12dy*(fh1(i,j-2,k)-EIT*fh1(i,j-1,k)+EIT*fh1(i,j+1,k)-fh1(i,j+2,k))
+      f1z(i,j,k)=d12dz*(fh1(i,j,k-2)-EIT*fh1(i,j,k-1)+EIT*fh1(i,j,k+1)-fh1(i,j,k+2))
+
+      f2x(i,j,k)=d12dx*(fh2(i-2,j,k)-EIT*fh2(i-1,j,k)+EIT*fh2(i+1,j,k)-fh2(i+2,j,k))
+      f2y(i,j,k)=d12dy*(fh2(i,j-2,k)-EIT*fh2(i,j-1,k)+EIT*fh2(i,j+1,k)-fh2(i,j+2,k))
+      f2z(i,j,k)=d12dz*(fh2(i,j,k-2)-EIT*fh2(i,j,k-1)+EIT*fh2(i,j,k+1)-fh2(i,j,k+2))
+
+      f3x(i,j,k)=d12dx*(fh3(i-2,j,k)-EIT*fh3(i-1,j,k)+EIT*fh3(i+1,j,k)-fh3(i+2,j,k))
+      f3y(i,j,k)=d12dy*(fh3(i,j-2,k)-EIT*fh3(i,j-1,k)+EIT*fh3(i,j+1,k)-fh3(i,j+2,k))
+      f3z(i,j,k)=d12dz*(fh3(i,j,k-2)-EIT*fh3(i,j,k-1)+EIT*fh3(i,j,k+1)-fh3(i,j,k+2))
+
+      f4x(i,j,k)=d12dx*(fh4(i-2,j,k)-EIT*fh4(i-1,j,k)+EIT*fh4(i+1,j,k)-fh4(i+2,j,k))
+      f4y(i,j,k)=d12dy*(fh4(i,j-2,k)-EIT*fh4(i,j-1,k)+EIT*fh4(i,j+1,k)-fh4(i,j+2,k))
+      f4z(i,j,k)=d12dz*(fh4(i,j,k-2)-EIT*fh4(i,j,k-1)+EIT*fh4(i,j,k+1)-fh4(i,j,k+2))
+   elseif(i+1 <= imax .and. i-1 >= imin .and. &
+          j+1 <= jmax .and. j-1 >= jmin .and. &
+          k+1 <= kmax .and. k-1 >= kmin) then
+      f1x(i,j,k)=d2dx*(-fh1(i-1,j,k)+fh1(i+1,j,k))
+      f1y(i,j,k)=d2dy*(-fh1(i,j-1,k)+fh1(i,j+1,k))
+      f1z(i,j,k)=d2dz*(-fh1(i,j,k-1)+fh1(i,j,k+1))
+
+      f2x(i,j,k)=d2dx*(-fh2(i-1,j,k)+fh2(i+1,j,k))
+      f2y(i,j,k)=d2dy*(-fh2(i,j-1,k)+fh2(i,j+1,k))
+      f2z(i,j,k)=d2dz*(-fh2(i,j,k-1)+fh2(i,j,k+1))
+
+      f3x(i,j,k)=d2dx*(-fh3(i-1,j,k)+fh3(i+1,j,k))
+      f3y(i,j,k)=d2dy*(-fh3(i,j-1,k)+fh3(i,j+1,k))
+      f3z(i,j,k)=d2dz*(-fh3(i,j,k-1)+fh3(i,j,k+1))
+
+      f4x(i,j,k)=d2dx*(-fh4(i-1,j,k)+fh4(i+1,j,k))
+      f4y(i,j,k)=d2dy*(-fh4(i,j-1,k)+fh4(i,j+1,k))
+      f4z(i,j,k)=d2dz*(-fh4(i,j,k-1)+fh4(i,j,k+1))
+   endif
+  enddo
+  enddo
+  enddo
+
+  return
+
+  end subroutine fderivs_batch4
+!-----------------------------------------------------------------------------
+! batch first derivatives (3 fields), same symmetry setup
+!-----------------------------------------------------------------------------
+  subroutine fderivs_batch3(ex,f1,f2,f3, &
+                            f1x,f1y,f1z,f2x,f2y,f2z,f3x,f3y,f3z, &
+                            X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+  implicit none
+
+  integer,                               intent(in ):: ex(1:3),symmetry,onoff
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f1,f2,f3
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f1x,f1y,f1z
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f2x,f2y,f2z
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f3x,f3y,f3z
+  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
+  real*8,                                intent(in ):: SYM1,SYM2,SYM3
+
+!~~~~~~ other variables
+
+  real*8 :: dX,dY,dZ
+  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh1,fh2,fh3
+  real*8, dimension(3) :: SoA
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0
+  real*8,  parameter :: TWO=2.d0,EIT=8.d0
+  real*8,  parameter :: F12=1.2d1
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
+
+  SoA(1) = SYM1
+  SoA(2) = SYM2
+  SoA(3) = SYM3
+
+  call symmetry_bd(2,ex,f1,fh1,SoA)
+  call symmetry_bd(2,ex,f2,fh2,SoA)
+  call symmetry_bd(2,ex,f3,fh3,SoA)
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  f1x = ZEO; f1y = ZEO; f1z = ZEO
+  f2x = ZEO; f2y = ZEO; f2z = ZEO
+  f3x = ZEO; f3y = ZEO; f3z = ZEO
+
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+   if(i+2 <= imax .and. i-2 >= imin .and. &
+      j+2 <= jmax .and. j-2 >= jmin .and. &
+      k+2 <= kmax .and. k-2 >= kmin) then
+      f1x(i,j,k)=d12dx*(fh1(i-2,j,k)-EIT*fh1(i-1,j,k)+EIT*fh1(i+1,j,k)-fh1(i+2,j,k))
+      f1y(i,j,k)=d12dy*(fh1(i,j-2,k)-EIT*fh1(i,j-1,k)+EIT*fh1(i,j+1,k)-fh1(i,j+2,k))
+      f1z(i,j,k)=d12dz*(fh1(i,j,k-2)-EIT*fh1(i,j,k-1)+EIT*fh1(i,j,k+1)-fh1(i,j,k+2))
+
+      f2x(i,j,k)=d12dx*(fh2(i-2,j,k)-EIT*fh2(i-1,j,k)+EIT*fh2(i+1,j,k)-fh2(i+2,j,k))
+      f2y(i,j,k)=d12dy*(fh2(i,j-2,k)-EIT*fh2(i,j-1,k)+EIT*fh2(i,j+1,k)-fh2(i,j+2,k))
+      f2z(i,j,k)=d12dz*(fh2(i,j,k-2)-EIT*fh2(i,j,k-1)+EIT*fh2(i,j,k+1)-fh2(i,j,k+2))
+
+      f3x(i,j,k)=d12dx*(fh3(i-2,j,k)-EIT*fh3(i-1,j,k)+EIT*fh3(i+1,j,k)-fh3(i+2,j,k))
+      f3y(i,j,k)=d12dy*(fh3(i,j-2,k)-EIT*fh3(i,j-1,k)+EIT*fh3(i,j+1,k)-fh3(i,j+2,k))
+      f3z(i,j,k)=d12dz*(fh3(i,j,k-2)-EIT*fh3(i,j,k-1)+EIT*fh3(i,j,k+1)-fh3(i,j,k+2))
+   elseif(i+1 <= imax .and. i-1 >= imin .and. &
+          j+1 <= jmax .and. j-1 >= jmin .and. &
+          k+1 <= kmax .and. k-1 >= kmin) then
+      f1x(i,j,k)=d2dx*(-fh1(i-1,j,k)+fh1(i+1,j,k))
+      f1y(i,j,k)=d2dy*(-fh1(i,j-1,k)+fh1(i,j+1,k))
+      f1z(i,j,k)=d2dz*(-fh1(i,j,k-1)+fh1(i,j,k+1))
+
+      f2x(i,j,k)=d2dx*(-fh2(i-1,j,k)+fh2(i+1,j,k))
+      f2y(i,j,k)=d2dy*(-fh2(i,j-1,k)+fh2(i,j+1,k))
+      f2z(i,j,k)=d2dz*(-fh2(i,j,k-1)+fh2(i,j,k+1))
+
+      f3x(i,j,k)=d2dx*(-fh3(i-1,j,k)+fh3(i+1,j,k))
+      f3y(i,j,k)=d2dy*(-fh3(i,j-1,k)+fh3(i,j+1,k))
+      f3z(i,j,k)=d2dz*(-fh3(i,j,k-1)+fh3(i,j,k+1))
+   endif
+  enddo
+  enddo
+  enddo
+
+  return
+
+  end subroutine fderivs_batch3
+!-----------------------------------------------------------------------------
+! batch first derivatives (2 fields), same symmetry setup
+!-----------------------------------------------------------------------------
+  subroutine fderivs_batch2(ex,f1,f2, &
+                            f1x,f1y,f1z,f2x,f2y,f2z, &
+                            X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+  implicit none
+
+  integer,                               intent(in ):: ex(1:3),symmetry,onoff
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f1,f2
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f1x,f1y,f1z
+  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: f2x,f2y,f2z
+  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
+  real*8,                                intent(in ):: SYM1,SYM2,SYM3
+
+!~~~~~~ other variables
+
+  real*8 :: dX,dY,dZ
+  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh1,fh2
+  real*8, dimension(3) :: SoA
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
+  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
+  real*8,  parameter :: ZEO=0.d0,ONE=1.d0
+  real*8,  parameter :: TWO=2.d0,EIT=8.d0
+  real*8,  parameter :: F12=1.2d1
+
+  dX = X(2)-X(1)
+  dY = Y(2)-Y(1)
+  dZ = Z(2)-Z(1)
+
+  imax = ex(1)
+  jmax = ex(2)
+  kmax = ex(3)
+
+  imin = 1
+  jmin = 1
+  kmin = 1
+  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
+  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
+
+  SoA(1) = SYM1
+  SoA(2) = SYM2
+  SoA(3) = SYM3
+
+  call symmetry_bd(2,ex,f1,fh1,SoA)
+  call symmetry_bd(2,ex,f2,fh2,SoA)
+
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
+
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
+
+  f1x = ZEO; f1y = ZEO; f1z = ZEO
+  f2x = ZEO; f2y = ZEO; f2z = ZEO
+
+  do k=1,ex(3)-1
+  do j=1,ex(2)-1
+  do i=1,ex(1)-1
+   if(i+2 <= imax .and. i-2 >= imin .and. &
+      j+2 <= jmax .and. j-2 >= jmin .and. &
+      k+2 <= kmax .and. k-2 >= kmin) then
+      f1x(i,j,k)=d12dx*(fh1(i-2,j,k)-EIT*fh1(i-1,j,k)+EIT*fh1(i+1,j,k)-fh1(i+2,j,k))
+      f1y(i,j,k)=d12dy*(fh1(i,j-2,k)-EIT*fh1(i,j-1,k)+EIT*fh1(i,j+1,k)-fh1(i,j+2,k))
+      f1z(i,j,k)=d12dz*(fh1(i,j,k-2)-EIT*fh1(i,j,k-1)+EIT*fh1(i,j,k+1)-fh1(i,j,k+2))
+
+      f2x(i,j,k)=d12dx*(fh2(i-2,j,k)-EIT*fh2(i-1,j,k)+EIT*fh2(i+1,j,k)-fh2(i+2,j,k))
+      f2y(i,j,k)=d12dy*(fh2(i,j-2,k)-EIT*fh2(i,j-1,k)+EIT*fh2(i,j+1,k)-fh2(i,j+2,k))
+      f2z(i,j,k)=d12dz*(fh2(i,j,k-2)-EIT*fh2(i,j,k-1)+EIT*fh2(i,j,k+1)-fh2(i,j,k+2))
+   elseif(i+1 <= imax .and. i-1 >= imin .and. &
+          j+1 <= jmax .and. j-1 >= jmin .and. &
+          k+1 <= kmax .and. k-1 >= kmin) then
+      f1x(i,j,k)=d2dx*(-fh1(i-1,j,k)+fh1(i+1,j,k))
+      f1y(i,j,k)=d2dy*(-fh1(i,j-1,k)+fh1(i,j+1,k))
+      f1z(i,j,k)=d2dz*(-fh1(i,j,k-1)+fh1(i,j,k+1))
+
+      f2x(i,j,k)=d2dx*(-fh2(i-1,j,k)+fh2(i+1,j,k))
+      f2y(i,j,k)=d2dy*(-fh2(i,j-1,k)+fh2(i,j+1,k))
+      f2z(i,j,k)=d2dz*(-fh2(i,j,k-1)+fh2(i,j,k+1))
+   endif
+  enddo
+  enddo
+  enddo
+
+  return
+
+  end subroutine fderivs_batch2
 
 #elif (ghost_width == 4)
 ! sixth order code
@@ -2081,6 +2380,9 @@
 
   end subroutine fderivs
 !-----------------------------------------------------------------------------
+! batch first derivatives (4 fields), same symmetry setup
+!-----------------------------------------------------------------------------
+!-----------------------------------------------------------------------------
 !
 ! single derivatives dx
 !

AMSS_NCKU_source/enforce_algebra.f90

@@ -19,60 +19,48 @@
 
 !~~~~~~~> Local variable:
   
-  integer :: i,j,k
-  real*8 :: lgxx,lgyy,lgzz,ldetg
-  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
-  real*8 :: ltrA,lscale
+  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
+  gxx = dxx + ONE
+  gyy = dyy + ONE
+  gzz = dzz + ONE
 
-    lgxx = dxx(i,j,k) + ONE
-    lgyy = dyy(i,j,k) + ONE
-    lgzz = dzz(i,j,k) + ONE
+  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
+  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
 
-    ldetg =  lgxx * lgyy * lgzz &
-           + 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)
+  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
 
-    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
-    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
-    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
-    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
-    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
-    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg
+  Axx = Axx - F1o3 * gxx * trA
+  Axy = Axy - F1o3 * gxy * trA
+  Axz = Axz - F1o3 * gxz * trA
+  Ayy = Ayy - F1o3 * gyy * trA
+  Ayz = Ayz - F1o3 * gyz * trA
+  Azz = Azz - F1o3 * gzz * trA
 
-    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))
+  detg = ONE / ( detg ** F1o3 ) 
   
-    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
-    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
-    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
-    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
-    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+  gxx = gxx * detg
+  gxy = gxy * detg
+  gxz = gxz * detg
+  gyy = gyy * detg
+  gyz = gyz * detg
+  gzz = gzz * detg
 
-    lscale = ONE / ( ldetg ** F1o3 )
-
-    dxx(i,j,k) = lgxx * lscale - ONE
-    gxy(i,j,k) = gxy(i,j,k) * lscale
-    gxz(i,j,k) = gxz(i,j,k) * lscale
-    dyy(i,j,k) = lgyy * lscale - ONE
-    gyz(i,j,k) = gyz(i,j,k) * lscale
-    dzz(i,j,k) = lgzz * lscale - ONE
-
-  enddo
-  enddo
-  enddo
+  dxx = gxx - ONE
+  dyy = gyy - ONE
+  dzz = gzz - ONE
 
   return
 
@@ -95,70 +83,50 @@
 
 !~~~~~~~> Local variable:
   
-  integer :: i,j,k
-  real*8 :: lgxx,lgyy,lgzz,lscale
-  real*8 :: lgxy,lgxz,lgyz
-  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
-  real*8 :: ltrA
+  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
+  gxx = dxx + ONE
+  gyy = dyy + ONE
+  gzz = dzz + ONE
+! for g
+  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
 
-! 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)
+  gupzz = ONE / ( gupzz ** F1o3 ) 
   
-    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
+  gxx = gxx * gupzz
+  gxy = gxy * gupzz
+  gxz = gxz * gupzz
+  gyy = gyy * gupzz
+  gyz = gyz * gupzz
+  gzz = gzz * gupzz
 
-    lscale = ONE / ( lscale ** F1o3 )
+  dxx = gxx - ONE
+  dyy = gyy - ONE
+  dzz = gzz - ONE
+! for A  
 
-    lgxx = lgxx * lscale
-    lgxy = lgxy * lscale
-    lgxz = lgxz * lscale
-    lgyy = lgyy * lscale
-    lgyz = lgyz * lscale
-    lgzz = lgzz * lscale
+  gupxx =   ( gyy * gzz - gyz * gyz )
+  gupxy = - ( gxy * gzz - gyz * gxz )
+  gupxz =   ( gxy * gyz - gyy * gxz )
+  gupyy =   ( gxx * gzz - gxz * gxz )
+  gupyz = - ( gxx * gyz - gxy * gxz )
+  gupzz =   ( gxx * gyy - gxy * gxy )
 
-    dxx(i,j,k) = lgxx - ONE
-    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
+  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
 
-! for A: trace-free using normalized metric (det=1, no division needed)
-    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
-    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
-    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
-    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
-    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
-    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
-
-    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
-                 + lgupzz * Azz(i,j,k) &
-         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
-                 + lgupyz * Ayz(i,j,k))
-
-    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
-    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
-    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
-    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
-    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
-
-  enddo
-  enddo
-  enddo
+  Axx = Axx - F1o3 * gxx * trA
+  Axy = Axy - F1o3 * gxy * trA
+  Axz = Axz - F1o3 * gxz * trA
+  Ayy = Ayy - F1o3 * gyy * trA
+  Ayz = Ayz - F1o3 * gyz * trA
+  Azz = Azz - F1o3 * gzz * trA
 
   return
 

AMSS_NCKU_source/fdderivs_c.C

@@ -1,268 +0,0 @@
-#include "tool.h"
-void fdderivs(const int ex[3],
-              const double *f,
-              double *fxx, double *fxy, double *fxz,
-              double *fyy, double *fyz, double *fzz,
-              const double *X, const double *Y, const double *Z,
-              double SYM1, double SYM2, double SYM3,
-              int Symmetry, int onoff)
-{
-    (void)onoff;
-
-    const int NO_SYMM = 0, EQ_SYMM = 1;
-    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0;
-    const double F1o4   = 2.5e-1;          // 1/4
-    const double F8     = 8.0;
-    const double F16    = 16.0;
-    const double F30    = 30.0;
-    const double F1o12  = ONE / 12.0;
-    const double F1o144 = ONE / 144.0;
-
-    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
-
-    const double dX = X[1] - X[0];
-    const double dY = Y[1] - Y[0];
-    const double dZ = Z[1] - Z[0];
-
-    const int imaxF = ex1;
-    const int jmaxF = ex2;
-    const int kmaxF = ex3;
-
-    int iminF = 1, jminF = 1, kminF = 1;
-    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
-    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
-    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
-
-    const double SoA[3] = { SYM1, SYM2, SYM3 };
-
-    /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */
-    const size_t nx = (size_t)ex1 + 2;
-    const size_t ny = (size_t)ex2 + 2;
-    const size_t nz = (size_t)ex3 + 2;
-    const size_t fh_size = nx * ny * nz;
-
-    static double *fh = NULL;
-    static size_t cap = 0;
-
-    if (fh_size > cap) {
-        free(fh);
-        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
-        cap = fh_size;
-    }
-    // double *fh = (double*)malloc(fh_size * sizeof(double));
-    if (!fh) return;
-
-    symmetry_bd(2, ex, f, fh, SoA);
-
-    /* 系数：按 Fortran 原式 */
-    const double Sdxdx = ONE / (dX * dX);
-    const double Sdydy = ONE / (dY * dY);
-    const double Sdzdz = ONE / (dZ * dZ);
-
-    const double Fdxdx = F1o12 / (dX * dX);
-    const double Fdydy = F1o12 / (dY * dY);
-    const double Fdzdz = F1o12 / (dZ * dZ);
-
-    const double Sdxdy = F1o4 / (dX * dY);
-    const double Sdxdz = F1o4 / (dX * dZ);
-    const double Sdydz = F1o4 / (dY * dZ);
-
-    const double Fdxdy = F1o144 / (dX * dY);
-    const double Fdxdz = F1o144 / (dX * dZ);
-    const double Fdydz = F1o144 / (dY * dZ);
-
-    /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
-    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
-    for (size_t p = 0; p < all; ++p) {
-        fxx[p] = ZEO; fyy[p] = ZEO; fzz[p] = ZEO;
-        fxy[p] = ZEO; fxz[p] = ZEO; fyz[p] = ZEO;
-    }
-
-    /*
-     * Fortran:
-     * do k=1,ex3-1
-     * do j=1,ex2-1
-     * do i=1,ex1-1
-     */
-    
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-        const int kF = k0 + 1;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-            const int jF = j0 + 1;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-                const int iF = i0 + 1;
-                const size_t p = idx_ex(i0, j0, k0, ex);
-
-                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
-                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
-                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
-                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
-                {
-                    fxx[p] = Fdxdx * (
-                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fyy[p] = Fdydy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fzz[p] = Fdzdz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-
-                    /* fxy 高阶：完全照搬 Fortran 的括号结构 */
-                    {
-                        const double t_jm2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
-
-                        const double t_jm1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
-
-                        const double t_jp1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
-
-                        const double t_jp2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
-
-                        fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
-                    }
-
-                    /* fxz 高阶 */
-                    {
-                        const double t_km2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
-
-                        const double t_km1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
-
-                        const double t_kp1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
-
-                        const double t_kp2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
-
-                        fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
-                    }
-
-                    /* fyz 高阶 */
-                    {
-                        const double t_km2 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
-
-                        const double t_km1 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
-
-                        const double t_kp1 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
-
-                        const double t_kp2 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
-
-                        fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
-                    }
-                }
-                /* 二阶分支：i±1,j±1,k±1 在范围内 */
-                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
-                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
-                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
-                {
-                    fxx[p] = Sdxdx * (
-                        fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
-                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
-                        fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fyy[p] = Sdydy * (
-                        fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
-                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
-                        fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fzz[p] = Sdzdz * (
-                        fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
-                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-
-                    fxy[p] = Sdxdy * (
-                        fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
-                        fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
-                        fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
-                        fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
-                    );
-
-                    fxz[p] = Sdxdz * (
-                        fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
-                        fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
-                        fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
-                        fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
-                    );
-
-                    fyz[p] = Sdydz * (
-                        fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
-                        fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
-                        fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
-                        fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
-                    );
-                }else{
-                    fxx[p] = 0.0;
-                    fyy[p] = 0.0;
-                    fzz[p] = 0.0;
-                    fxy[p] = 0.0;
-                    fxz[p] = 0.0;
-                    fyz[p] = 0.0;
-                }
-            }
-        }
-    }
-
-    // free(fh);
-}

AMSS_NCKU_source/fderivs_c.C

@@ -1,150 +0,0 @@
-#include "tool.h"
-
-/*
- * C 版 fderivs
- *
- * Fortran:
- * subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
- *
- * 约定：
- *   f, fx, fy, fz: ex1*ex2*ex3，按 idx_ex 布局
- *   X: ex1, Y: ex2, Z: ex3
- */
-void fderivs(const int ex[3],
-             const double *f,
-             double *fx, double *fy, double *fz,
-             const double *X, const double *Y, const double *Z,
-             double SYM1, double SYM2, double SYM3,
-             int Symmetry, int onoff)
-{
-    (void)onoff; // Fortran 里没用到
-
-    const double ZEO = 0.0, ONE = 1.0;
-    const double TWO = 2.0, EIT = 8.0;
-    const double F12 = 12.0;
-
-    const int NO_SYMM = 0, EQ_SYMM = 1; // OCTANT=2 在本子程序里不直接用
-
-    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
-
-    // dX = X(2)-X(1) -> C: X[1]-X[0]
-    const double dX = X[1] - X[0];
-    const double dY = Y[1] - Y[0];
-    const double dZ = Z[1] - Z[0];
-
-    // Fortran 1-based bounds
-    const int imaxF = ex1;
-    const int jmaxF = ex2;
-    const int kmaxF = ex3;
-
-    int iminF = 1, jminF = 1, kminF = 1;
-    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
-    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
-    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
-
-    // SoA(1:3) = SYM1,SYM2,SYM3
-    const double SoA[3] = { SYM1, SYM2, SYM3 };
-
-    // fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2
-    const size_t nx = (size_t)ex1 + 2;
-    const size_t ny = (size_t)ex2 + 2;
-    const size_t nz = (size_t)ex3 + 2;
-    const size_t fh_size = nx * ny * nz;
-    static double *fh = NULL;
-    static size_t cap = 0;
-
-    if (fh_size > cap) {
-        free(fh);
-        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
-        cap = fh_size;
-    }
-    // double *fh = (double*)malloc(fh_size * sizeof(double));
-    if (!fh) return;
-
-    // call symmetry_bd(2,ex,f,fh,SoA)
-    symmetry_bd(2, ex, f, fh, SoA);
-
-    const double d12dx = ONE / F12 / dX;
-    const double d12dy = ONE / F12 / dY;
-    const double d12dz = ONE / F12 / dZ;
-
-    const double d2dx  = ONE / TWO / dX;
-    const double d2dy  = ONE / TWO / dY;
-    const double d2dz  = ONE / TWO / dZ;
-
-    // fx = fy = fz = 0
-    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
-    for (size_t p = 0; p < all; ++p) {
-        fx[p] = ZEO;
-        fy[p] = ZEO;
-        fz[p] = ZEO;
-    }
-
-    /*
-     * Fortran loops:
-     * do k=1,ex3-1
-     * do j=1,ex2-1
-     * do i=1,ex1-1
-     *
-     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
-     */
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-        const int kF = k0 + 1;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-            const int jF = j0 + 1;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-                const int iF = i0 + 1;
-                const size_t p = idx_ex(i0, j0, k0, ex);
-
-                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
-                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
-                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
-                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
-                {
-                    fx[p] = d12dx * (
-                        fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
-                        EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                        EIT * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)]
-                    );
-
-                    fy[p] = d12dy * (
-                        fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] -
-                        EIT * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                        EIT * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)]
-                    );
-
-                    fz[p] = d12dz * (
-                        fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] -
-                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
-                    );
-                }
-                // elseif(i+1 <= imax .and. i-1 >= imin ...)
-                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
-                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
-                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
-                {
-                    fx[p] = d2dx * (
-                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fy[p] = d2dy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fz[p] = d2dz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-                }
-            }
-        }
-    }
-
-    // free(fh);
-}

AMSS_NCKU_source/fmisc.f90

@@ -324,6 +324,7 @@ 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)
@@ -349,6 +350,7 @@ 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)
@@ -377,6 +379,7 @@ 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)
@@ -883,17 +886,14 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
    enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
    enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
    enddo
@@ -912,6 +912,7 @@ 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)
@@ -940,6 +941,7 @@ 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)
@@ -1116,66 +1118,64 @@ end subroutine d2dump
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
 
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
-  subroutine polint(xa, ya, x, y, dy, ordn)
+  subroutine polint(xa,ya,x,y,dy,ordn)
+
   implicit none
 
-  integer, intent(in) :: ordn
-  real*8, dimension(ordn), intent(in) :: xa, ya
+!~~~~~~> Input Parameter:
+  integer,intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa,ya
   real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
+  real*8, intent(out) :: y,dy
 
-  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
+!~~~~~~> Other parameter:
 
-  c = ya
-  d = ya
-  ho = xa - x
+  integer :: m,n,ns
+  real*8, dimension(ordn) :: c,d,den,ho
+  real*8 :: dif,dift
 
-  ns = 1
-  dif = abs(x - xa(1))
+!~~~~~~>
 
-  do i = 2, ordn
-    dift = abs(x - xa(i))
-    if (dift < dif) then
-      ns = i
-      dif = dift
+  n=ordn
+  m=ordn
+
+  c=ya
+  d=ya
+  ho=xa-x
+
+  ns=1
+  dif=abs(x-xa(1))
+  do m=1,n
+   dift=abs(x-xa(m))
+   if(dift < dif) then
+    ns=m
+    dif=dift
    end if
   end do
 
-  y = ya(ns)
-  ns = ns - 1
-
-  do m = 1, ordn - 1
-    n_m = ordn - m
-    do i = 1, n_m
-      hp = ho(i)
-      h  = ho(i+m)
-      den_val = hp - h
-
-      if (den_val == 0.0d0) then
+  y=ya(ns)
+  ns=ns-1
+  do m=1,n-1
+    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
+    if (any(den(1:n-m) == 0.0))then
       write(*,*) 'failure in polint for point',x
       write(*,*) 'with input points: ',xa
       stop
-      end if
-
-      den_val = (c(i+1) - d(i)) / den_val
-
-      d(i) = h * den_val
-      c(i) = hp * den_val
-    end do
-
-    if (2 * ns < n_m) then
-      dy = c(ns + 1)
+    endif
+    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
+    d(1:n-m)=ho(1+m:n)*den(1:n-m)
+    c(1:n-m)=ho(1:n-m)*den(1:n-m)
+    if (2*ns < n-m) then
+      dy=c(ns+1)
     else
-      dy = d(ns)
-      ns = ns - 1
+      dy=d(ns)
+      ns=ns-1
     end if
-    y = y + dy
+    y=y+dy
   end do
 
   return
+
   end subroutine polint
 !------------------------------------------------------------------------------
 !
@@ -1183,37 +1183,35 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
+
   implicit none
 
+!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a
   real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+!~~~~~~> Other parameters:
+
   integer  :: i,m
   real*8, dimension(ordn) :: ymtmp
   real*8, dimension(ordn) :: yntmp
 
   m=size(x1a)
+  
   do i=1,m
+
     yntmp=ya(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
 
-  do j=1,ordn
-    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
   end do
-  call polint(x2a, ymtmp, x2, y, dy, ordn)
-#endif
+
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
 
   return
+
   end subroutine polin2
 !------------------------------------------------------------------------------
 !
@@ -1221,15 +1219,18 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
+
   implicit none
 
+!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
   real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+!~~~~~~> Other parameters:
+
   integer  :: i,j,m,n
   real*8, dimension(ordn,ordn) :: yatmp
   real*8, dimension(ordn) :: ymtmp
@@ -1238,33 +1239,24 @@ end subroutine d2dump
 
   m=size(x1a)
   n=size(x2a)
+  
   do i=1,m
    do j=1,n
+
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
+
    end do
+
     yntmp=yatmp(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j, k
-  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
 
-  do k=1,ordn
-    do j=1,ordn
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
   end do
-  end do
-  do k=1,ordn
-    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
-  end do
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
-#endif
+
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
 
   return
+
   end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm

AMSS_NCKU_source/interp_lb_profile.C

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

AMSS_NCKU_source/interp_lb_profile.h

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

AMSS_NCKU_source/interp_lb_profile_data.h

@@ -1,27 +0,0 @@
-/* Auto-generated from interp_lb_profile.bin — do not edit */
-#ifndef INTERP_LB_PROFILE_DATA_H
-#define INTERP_LB_PROFILE_DATA_H
-
-#define INTERP_LB_NPROCS 64
-#define INTERP_LB_NUM_HEAVY 4
-
-static const int interp_lb_heavy_blocks[4] = {27, 35, 28, 36};
-
-/* Split table: {block_id, r_left, r_right} */
-static const int interp_lb_splits[4][3] = {
-    {27, 26, 27},
-    {35, 34, 35},
-    {28, 28, 29},
-    {36, 36, 37},
-};
-
-/* Rank remap for displaced neighbor blocks */
-static const int interp_lb_num_remaps = 4;
-static const int interp_lb_remaps[][2] = {
-    {26, 25},
-    {29, 30},
-    {34, 33},
-    {37, 38},
-};
-
-#endif /* INTERP_LB_PROFILE_DATA_H */

AMSS_NCKU_source/kodiss.f90

@@ -65,8 +65,6 @@ real*8,intent(in) :: eps
 !                       dx^4
 
 !  note the sign (-1)^r-1, now r=2
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-!DIR$ UNROLL PARTIAL(4)
   do k=1,ex(3)
   do j=1,ex(2)
   do i=1,ex(1)

AMSS_NCKU_source/kodiss_c.C

@@ -1,109 +0,0 @@
-#include "tool.h"
-
-/*
- * C 版 kodis
- *
- * Fortran signature:
- * subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
- *
- * 约定：
- *   X: ex1, Y: ex2, Z: ex3
- *   f, f_rhs: ex1*ex2*ex3 按 idx_ex 布局
- *   SoA[3]
- *   eps: double
- */
-void kodis(const int ex[3],
-           const double *X, const double *Y, const double *Z,
-           const double *f, double *f_rhs,
-           const double SoA[3],
-           int Symmetry, double eps)
-{
-    const double ONE = 1.0, SIX = 6.0, FIT = 15.0, TWT = 20.0;
-    const double cof = 64.0;             // 2^6
-    const int NO_SYMM = 0, OCTANT = 2;
-
-    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
-
-    // Fortran: dX = X(2)-X(1) -> C: X[1]-X[0]
-    const double dX = X[1] - X[0];
-    const double dY = Y[1] - Y[0];
-    const double dZ = Z[1] - Z[0];
-    (void)ONE; // ONE 在原 Fortran 里只是参数，这里不一定用得上
-
-    // Fortran: imax=ex(1) 等是 1-based 上界
-    const int imaxF = ex1;
-    const int jmaxF = ex2;
-    const int kmaxF = ex3;
-
-    // Fortran: imin=jmin=kmin=1，某些对称情况变 -2
-    int iminF = 1, jminF = 1, kminF = 1;
-
-    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
-    if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = -2;
-    if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = -2;
-
-    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)，对应 ord=3
-    const size_t nx = (size_t)ex1 + 3;
-    const size_t ny = (size_t)ex2 + 3;
-    const size_t nz = (size_t)ex3 + 3;
-    const size_t fh_size = nx * ny * nz;
-
-    double *fh = (double*)malloc(fh_size * sizeof(double));
-    if (!fh) return;
-
-    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
-    symmetry_bd(3, ex, f, fh, SoA);
-
-    /*
-     * Fortran loops:
-     * do k=1,ex3
-     * do j=1,ex2
-     * do i=1,ex1
-     *
-     * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
-     * 并定义 Fortran index: iF=i0+1, ...
-     */
-    for (int k0 = 0; k0 < ex3; ++k0) {
-        const int kF = k0 + 1;
-        for (int j0 = 0; j0 < ex2; ++j0) {
-            const int jF = j0 + 1;
-            for (int i0 = 0; i0 < ex1; ++i0) {
-                const int iF = i0 + 1;
-
-                // Fortran if 条件：
-                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
-                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
-                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
-                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
-                {
-                    const size_t p = idx_ex(i0, j0, k0, ex);
-
-                    // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
-                    const double Dx_term =
-                        ( (fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
-                          SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
-                          FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
-                          TWT *  fh[idx_fh_F(iF    , jF, kF, ex)] ) / dX;
-
-                    const double Dy_term =
-                        ( (fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
-                          SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
-                          FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
-                          TWT *  fh[idx_fh_F(iF, jF    , kF, ex)] ) / dY;
-
-                    const double Dz_term =
-                        ( (fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
-                          SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
-                          FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
-                          TWT *  fh[idx_fh_F(iF, jF, kF    , ex)] ) / dZ;
-
-                    // Fortran:
-                    // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
-                    f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
-                }
-            }
-        }
-    }
-
-    free(fh);
-}

AMSS_NCKU_source/lopsided_c.C

@@ -1,255 +0,0 @@
-#include "tool.h"
-/*
- * 你需要提供 symmetry_bd 的 C 版本（或 Fortran 绑到 C 的接口）。
- * Fortran: call symmetry_bd(3,ex,f,fh,SoA)
- *
- * 约定：
- *   nghost = 3
- *   ex[3]  = {ex1,ex2,ex3}
- *   f      = 原始网格 (ex1*ex2*ex3)
- *   fh     = 扩展网格 ((ex1+3)*(ex2+3)*(ex3+3))，对应 Fortran 的 (-2:ex1, ...)
- *   SoA[3] = 输入参数
- */
-void lopsided(const int ex[3],
-              const double *X, const double *Y, const double *Z,
-              const double *f, double *f_rhs,
-              const double *Sfx, const double *Sfy, const double *Sfz,
-              int Symmetry, const double SoA[3])
-{
-    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
-    const double TWO = 2.0, F6 = 6.0, F18 = 18.0;
-    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
-
-    const int NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2;
-    (void)OCTANT; // 这里和 Fortran 一样只是定义了不用也没关系
-
-    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
-
-    // 对应 Fortran: dX = X(2)-X(1)  （Fortran 1-based）
-    // C: X[1]-X[0]
-    const double dX = X[1] - X[0];
-    const double dY = Y[1] - Y[0];
-    const double dZ = Z[1] - Z[0];
-
-    const double d12dx = ONE / F12 / dX;
-    const double d12dy = ONE / F12 / dY;
-    const double d12dz = ONE / F12 / dZ;
-
-    // Fortran 里算了 d2dx/d2dy/d2dz 但本 subroutine 里没用到（保持一致也算出来）
-    const double d2dx  = ONE / TWO / dX;
-    const double d2dy  = ONE / TWO / dY;
-    const double d2dz  = ONE / TWO / dZ;
-    (void)d2dx; (void)d2dy; (void)d2dz;
-
-    // Fortran:
-    // imax = ex(1); jmax = ex(2); kmax = ex(3)
-    const int imaxF = ex1;
-    const int jmaxF = ex2;
-    const int kmaxF = ex3;
-
-    // Fortran:
-    // imin=jmin=kmin=1; 若满足对称条件则设为 -2
-    int iminF = 1, jminF = 1, kminF = 1;
-    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
-    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
-    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
-
-    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)
-    const size_t nx = (size_t)ex1 + 3;
-    const size_t ny = (size_t)ex2 + 3;
-    const size_t nz = (size_t)ex3 + 3;
-    const size_t fh_size = nx * ny * nz;
-
-    double *fh = (double*)malloc(fh_size * sizeof(double));
-    if (!fh) return; // 内存不足：直接返回（你也可以改成 abort/报错）
-
-    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
-    symmetry_bd(3, ex, f, fh, SoA);
-
-    /*
-     * Fortran 主循环：
-     * do k=1,ex(3)-1
-     * do j=1,ex(2)-1
-     * do i=1,ex(1)-1
-     *
-     * 转成 C 0-based：
-     * k0 = 0..ex3-2, j0 = 0..ex2-2, i0 = 0..ex1-2
-     *
-     * 并且 Fortran 里的 i/j/k 在 fh 访问时，仍然是 Fortran 索引值：
-     * iF=i0+1, jF=j0+1, kF=k0+1
-     */
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-        const int kF = k0 + 1;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-            const int jF = j0 + 1;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-                const int iF = i0 + 1;
-
-                const size_t p = idx_ex(i0, j0, k0, ex);
-
-                // ---------------- x direction ----------------
-                const double sfx = Sfx[p];
-                if (sfx > ZEO) {
-                    // Fortran: if(i+3 <= imax)
-                    // iF+3 <= ex1  <=> i0+4 <= ex1 <=> i0 <= ex1-4
-                    if (i0 <= ex1 - 4) {
-                        f_rhs[p] += sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
-                    }
-                    // elseif(i+2 <= imax)  <=> i0 <= ex1-3
-                    else if (i0 <= ex1 - 3) {
-                        f_rhs[p] += sfx * d12dx *
-                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
-                    }
-                    // elseif(i+1 <= imax)  <=> i0 <= ex1-2（循环里总成立）
-                    else if (i0 <= ex1 - 2) {
-                        f_rhs[p] -= sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
-                    }
-                } else if (sfx < ZEO) {
-                    // Fortran: if(i-3 >= imin)
-                    // (iF-3) >= iminF  <=> (i0-2) >= iminF
-                    if ((i0 - 2) >= iminF) {
-                        f_rhs[p] -= sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
-                    }
-                    // elseif(i-2 >= imin) <=> (i0-1) >= iminF
-                    else if ((i0 - 1) >= iminF) {
-                        f_rhs[p] += sfx * d12dx *
-                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
-                    }
-                    // elseif(i-1 >= imin) <=> i0 >= iminF
-                    else if (i0 >= iminF) {
-                        f_rhs[p] += sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
-                    }
-                }
-
-                // ---------------- y direction ----------------
-                const double sfy = Sfy[p];
-                if (sfy > ZEO) {
-                    // jF+3 <= ex2 <=> j0+4 <= ex2 <=> j0 <= ex2-4
-                    if (j0 <= ex2 - 4) {
-                        f_rhs[p] += sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
-                    } else if (j0 <= ex2 - 3) {
-                        f_rhs[p] += sfy * d12dy *
-                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
-                    } else if (j0 <= ex2 - 2) {
-                        f_rhs[p] -= sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
-                    }
-                } else if (sfy < ZEO) {
-                    if ((j0 - 2) >= jminF) {
-                        f_rhs[p] -= sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
-                    } else if ((j0 - 1) >= jminF) {
-                        f_rhs[p] += sfy * d12dy *
-                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
-                    } else if (j0 >= jminF) {
-                        f_rhs[p] += sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
-                    }
-                }
-
-                // ---------------- z direction ----------------
-                const double sfz = Sfz[p];
-                if (sfz > ZEO) {
-                    if (k0 <= ex3 - 4) {
-                        f_rhs[p] += sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
-                    } else if (k0 <= ex3 - 3) {
-                        f_rhs[p] += sfz * d12dz *
-                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
-                    } else if (k0 <= ex3 - 2) {
-                        f_rhs[p] -= sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
-                    }
-                } else if (sfz < ZEO) {
-                    if ((k0 - 2) >= kminF) {
-                        f_rhs[p] -= sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
-                    } else if ((k0 - 1) >= kminF) {
-                        f_rhs[p] += sfz * d12dz *
-                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
-                    } else if (k0 >= kminF) {
-                        f_rhs[p] += sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
-                    }
-                }
-            }
-        }
-    }
-    free(fh);
-}
-
-
-
-
-

AMSS_NCKU_source/lopsidediff.f90

@@ -487,201 +487,6 @@ 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.fh

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

AMSS_NCKU_source/macrodef.h

@@ -6,127 +6,95 @@
 
 // application parameters
 
+/// ****
+// sommerfeld boundary type
+// 0: bam, 1: shibata
 #define SommerType 0
 
+/// ****
+// for Using Gauss-Legendre quadrature in theta direction
 #define GaussInt
 
-#define ABEtype 0
-
-//#define With_AHF
-#define Psi4type 0
-
-//#define Point_Psi4
-
-#define RPS 1
-
-#define AGM 0
-
-#define RPB 0
-
-#define MAPBH 1
-
-#define PSTR 0
-
-#define REGLEV 0
-
-//#define USE_GPU
-
-//#define CHECKDETAIL
-
-//#define FAKECHECK
-
-//
-// define SommerType
-//     sommerfeld boundary type
-//     0: bam
-//     1: shibata
-//
-// define GaussInt
-//     for Using Gauss-Legendre quadrature in theta direction
-//
-// define ABEtype
+/// ****
 // 0: BSSN vacuum
 // 1: coupled to scalar field
 // 2: Z4c vacuum
 // 3: coupled to Maxwell field
 //
-// define With_AHF
+#define ABEtype 2
+
+/// ****
 // using Apparent Horizon Finder
-//
-// define Psi4type
+//#define With_AHF
+
+/// ****
 // Psi4 calculation method
 // 0: EB method
 // 1: 4-D method
 //
-// define Point_Psi4
+#define Psi4type 0
+
+/// ****
 // for Using point psi4 or not
-//
-// define RPS
+//#define Point_Psi4
+
+/// ****
 // RestrictProlong in Step (0) or after Step (1)
-//
-// define AGM
+#define RPS 1
+
+/// ****
 // Enforce algebra constraint
 // for every RK4 sub step: 0
 // only when iter_count == 3: 1
 // after routine Step: 2
-//
-// define RPB
-//     Restrict Prolong using BAM style 1 or old style 0
-//
-// define MAPBH
-//     1: move Analysis out ot 4 sub steps and treat PBH with Euler method
-//
-// define PSTR
-//     parallel structure
-//     0: level by level
-//     1: considering all levels
-//     2: as 1 but reverse the CPU order
-//     3: Frank's scheme
-//
-// define REGLEV
-//     regrid for every level or for all levels at a time
-//     0: for every level;
-//     1: for all
-//
-// define USE_GPU
-//     use gpu or not
-//
-// define CHECKDETAIL
-//     use checkpoint for every process
-//
-// define FAKECHECK
-//     use FakeCheckPrepare to write CheckPoint
-//
+#define AGM 0
 
+/// ****
+// Restrict Prolong using BAM style 1 or old style 0
+#define RPB 0
+
+/// ****
+// 1: move Analysis out ot 4 sub steps and treat PBH with Euler method
+#define MAPBH 1
+
+/// ****
+// parallel structure, 0: level by level, 1: considering all levels, 2: as 1 but reverse the CPU order, 3: Frank's scheme
+#define PSTR 0
+
+/// ****
+// regrid for every level or for all levels at a time
+// 0: for every level; 1: for all
+#define REGLEV 0
+
+/// ****
+// use gpu or not
+//#define USE_GPU
+
+/// ****
+// use checkpoint for every process
+//#define CHECKDETAIL
+
+/// ****
+// use FakeCheckPrepare to write CheckPoint
+//#define FAKECHECK
 ////================================================================
 //  some basic parameters for numerical calculation
-////================================================================
-
 #define dim 3
 
-//#define Cell or Vertex in "macrodef.fh" 
+//#define Cell or Vertex in "microdef.fh"
 
+// ******
+// buffer point number for mesh refinement interface
 #define buffer_width 6
 
+// ******
+// buffer point number shell-box interface, on shell
 #define SC_width buffer_width
-
+// buffer point number shell-box interface, on box
 #define CS_width (2*buffer_width)
 
-//
-// define Cell or Vertex in "macrodef.fh" 
-//
-// define buffer_width
-//     buffer point number for mesh refinement interface
-//
-// define SC_width buffer_width
-//     buffer point number shell-box interface, on shell
-//
-// define CS_width
-//     buffer point number shell-box interface, on box
-//
-
 #if(buffer_width < ghost_width)
-#   error we always assume buffer_width>ghost_width
+#error we always assume buffer_width>ghost_width
 #endif
 
 #define PACK 1
@@ -142,4 +110,3 @@
 #define TINY 1e-10
 
 #endif   /* MICRODEF_H */
-

AMSS_NCKU_source/makefile

@@ -2,27 +2,6 @@
 
 include makefile.inc
 
-## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
-##   make                        -> opt  (PGO-guided, maximum performance)
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
-
-ifeq ($(PGO_MODE),instrument)
-## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include
-else
-## opt (default): maximum performance with PGO profile data
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(PROFDATA) \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(PROFDATA) \
-              -align array64byte -fpp -I${MKLROOT}/include
-endif
-
 .SUFFIXES: .o .f90 .C .for .cu
 
 .f90.o:
@@ -37,54 +16,13 @@ endif
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
-# C rewrite of BSSN RHS kernel and helpers
-bssn_rhs_c.o: bssn_rhs_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-fderivs_c.o: fderivs_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-fdderivs_c.o: fdderivs_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-kodiss_c.o: kodiss_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-lopsided_c.o: lopsided_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
-TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
-TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(TP_PROFDATA) \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-
-TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
-
-TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
-
 # Input files
-
-## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
-ifeq ($(USE_CXX_KERNELS),0)
-# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES =
-else
-# C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o
-endif
-
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
 	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
 	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
            Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.o
+	   NullShellPatch2_Evo.o writefile_f.o
 	   
 C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o surface_integral.o ShellPatch.o\
@@ -94,9 +32,9 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
 	   NullShellPatch2_Evo.o \
 	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
 
-F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
 	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   rungekutta4_rout.o diff_new.o kodiss.o kodiss_sh.o\
+	   rungekutta4_rout.o bssn_rhs.o diff_new.o kodiss.o kodiss_sh.o\
 	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
 	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
            getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
@@ -107,14 +45,6 @@ F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
 	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
 	   NullNews2.o tool_f.o
 
-ifeq ($(USE_CXX_KERNELS),0)
-# Fortran mode: include original bssn_rhs.o
-F90FILES = $(F90FILES_BASE) bssn_rhs.o
-else
-# C++ mode (default): bssn_rhs.o replaced by C++ kernel
-F90FILES = $(F90FILES_BASE)
-endif
-
 F77FILES = zbesh.o
 
 AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \
@@ -127,7 +57,7 @@ TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o
 CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
 
 # file dependences
-$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
+$(C++FILES) $(C++FILESGPU) $(F90FILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
 
 $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
@@ -150,7 +80,7 @@ $(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h
              
 $(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
 
-$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+$(C++FILES) $(C++FILES_GPU) $(AHFDOBJS) $(CUDAFILES): macrodef.h
 
 TwoPunctureFILES: TwoPunctures.h
 
@@ -159,14 +89,14 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o
 
 # projects
-ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
 	
-ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
+ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -8,31 +8,18 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 
 ## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
 
-## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
-##   opt        : (default) maximum performance with PGO profile-guided optimization
-##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
-PGO_MODE ?= opt
-
-## Interp_Points load balance profiling mode
-##   off        : (default) no load balance instrumentation
-##   profile    : Pass 1 — instrument Interp_Points to collect timing profile
-##   optimize   : Pass 2 — read profile and apply block rebalancing
-INTERP_LB_MODE ?= off
-
-ifeq ($(INTERP_LB_MODE),profile)
-INTERP_LB_FLAGS = -DINTERP_LB_PROFILE
-else ifeq ($(INTERP_LB_MODE),optimize)
-INTERP_LB_FLAGS = -DINTERP_LB_OPTIMIZE
-else
-INTERP_LB_FLAGS =
-endif
-
-## Kernel implementation switch
-##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
-##   0           : fall back to original Fortran kernels
-USE_CXX_KERNELS ?= 1
+## Aggressive optimization flags:
+## -O3: Maximum optimization
+## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
+## -fp-model fast=2: Aggressive floating-point optimizations
+## -fma: Enable fused multiply-add instructions
+## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma \
+               -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
+               -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx

AMSS_NCKU_source/share_func.h

@@ -1,146 +0,0 @@
-#ifndef SHARE_FUNC_H
-#define SHARE_FUNC_H
-
-#include <stdlib.h>
-#include <stddef.h>
-#include <math.h>
-#include <stdio.h>
-/* 主网格：0-based -> 1D */
-static inline size_t idx_ex(int i0, int j0, int k0, const int ex[3]) {
-    const int ex1 = ex[0], ex2 = ex[1];
-    return (size_t)i0 + (size_t)j0 * (size_t)ex1 + (size_t)k0 * (size_t)ex1 * (size_t)ex2;
-}
-
-/*
- * fh 对应 Fortran: fh(-1:ex1, -1:ex2, -1:ex3)
- * ord=2 => shift=1
- * iF/jF/kF 为 Fortran 索引（可为 -1,0,1..ex）
- */
-static inline size_t idx_fh_F_ord2(int iF, int jF, int kF, const int ex[3]) {
-    const int shift = 1;
-    const int nx = ex[0] + 2;      // ex1 + ord
-    const int ny = ex[1] + 2;
-
-    const int ii = iF + shift;     // 0..ex1+1
-    const int jj = jF + shift;     // 0..ex2+1
-    const int kk = kF + shift;     // 0..ex3+1
-
-    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
-}
-
-/*
- * fh 对应 Fortran: fh(-2:ex1, -2:ex2, -2:ex3)
- * ord=3 => shift=2
- * iF/jF/kF 是 Fortran 索引（可为负）
- */
-static inline size_t idx_fh_F(int iF, int jF, int kF, const int ex[3]) {
-    const int shift = 2;                 // ord=3 -> -2..ex
-    const int nx = ex[0] + 3;            // ex1 + ord
-    const int ny = ex[1] + 3;
-
-    const int ii = iF + shift;           // 0..ex1+2
-    const int jj = jF + shift;           // 0..ex2+2
-    const int kk = kF + shift;           // 0..ex3+2
-
-    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
-}
-
-/*
- * func:  (1..extc1, 1..extc2, 1..extc3)   1-based in Fortran
- * funcc: (-ord+1..extc1, -ord+1..extc2, -ord+1..extc3) in Fortran
- *
- * C 里我们把：
- *   func  视为 0-based: i0=0..extc1-1, j0=0..extc2-1, k0=0..extc3-1
- *   funcc 用“平移下标”存为一维数组：
- *     iF in [-ord+1..extc1]  -> ii = iF + (ord-1)  in [0..extc1+ord-1]
- *     总长度 nx = extc1 + ord
- *     同理 ny = extc2 + ord, nz = extc3 + ord
- */
-
-static inline size_t idx_func0(int i0, int j0, int k0, const int extc[3]) {
-    const int nx = extc[0], ny = extc[1];
-    return (size_t)i0 + (size_t)j0 * (size_t)nx + (size_t)k0 * (size_t)nx * (size_t)ny;
-}
-
-static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc[3]) {
-    const int shift = ord - 1;          // iF = -shift .. extc1
-    const int nx = extc[0] + ord;       // [-shift..extc1] 共 extc1+ord 个
-    const int ny = extc[1] + ord;
-
-    const int ii = iF + shift;          // 0..extc1+shift
-    const int jj = jF + shift;          // 0..extc2+shift
-    const int kk = kF + shift;          // 0..extc3+shift
-
-    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
-}
-
-/*
- * 等价于 Fortran:
- * funcc(1:extc1,1:extc2,1:extc3)=func
- * do i=0,ord-1
- *   funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1)
- * enddo
- * do i=0,ord-1
- *   funcc(:,-i,1:extc3) = funcc(:,i+1,1:extc3)*SoA(2)
- * enddo
- * do i=0,ord-1
- *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
- * enddo
- */
-static inline void symmetry_bd(int ord,
-                 const int extc[3],
-                 const double *func,
-                 double *funcc,
-                 const double SoA[3])
-{
-    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
-
-    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
-    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
-    for (int k0 = 0; k0 < extc3; ++k0) {
-        for (int j0 = 0; j0 < extc2; ++j0) {
-            for (int i0 = 0; i0 < extc1; ++i0) {
-                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
-                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
-            }
-        }
-    }
-
-    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
-    for (int ii = 0; ii <= ord - 1; ++ii) {
-        const int iF_dst = -ii;       // 0, -1, -2, ...
-        const int iF_src = ii + 1;    // 1, 2, 3, ...
-        for (int kF = 1; kF <= extc3; ++kF) {
-            for (int jF = 1; jF <= extc2; ++jF) {
-                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
-                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
-            }
-        }
-    }
-
-    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
-    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
-    for (int jj = 0; jj <= ord - 1; ++jj) {
-        const int jF_dst = -jj;
-        const int jF_src = jj + 1;
-        for (int kF = 1; kF <= extc3; ++kF) {
-            for (int iF = -ord + 1; iF <= extc1; ++iF) {
-                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
-                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
-            }
-        }
-    }
-
-    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
-    for (int kk = 0; kk <= ord - 1; ++kk) {
-        const int kF_dst = -kk;
-        const int kF_src = kk + 1;
-        for (int jF = -ord + 1; jF <= extc2; ++jF) {
-            for (int iF = -ord + 1; iF <= extc1; ++iF) {
-                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
-                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
-            }
-        }
-    }
-}
-#endif

AMSS_NCKU_source/surface_integral.C

@@ -220,9 +220,16 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     pox[2][n] = rex * nz_g[n];
   }
 
+  double *shellf;
+  shellf = new double[n_tot * InList];
+
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
+
   int mp, Lp, Nmin, Nmax;
+
   mp = n_tot / cpusize;
   Lp = n_tot - cpusize * mp;
+
   if (Lp > myrank)
   {
     Nmin = myrank * mp + myrank;
@@ -234,11 +241,6 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     Nmax = Nmin + mp - 1;
   }
 
-  double *shellf;
-  shellf = new double[n_tot * InList];
-
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
-
   //|~~~~~> Integrate the dot product of Dphi with the surface normal.
 
   double *RP_out, *IP_out;
@@ -361,17 +363,8 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -563,17 +556,8 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, Comm_here);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, Comm_here);
 
   //|------= Free memory.
 
@@ -751,17 +735,8 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH, var *Rpsi4
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -1009,17 +984,8 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -1453,17 +1419,8 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -1897,17 +1854,8 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -2092,17 +2040,8 @@ void surface_integral::surf_Wave(double rex, int lev, NullShellPatch2 *GH, var *
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -2287,17 +2226,8 @@ void surface_integral::surf_Wave(double rex, int lev, NullShellPatch *GH, var *R
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 
@@ -2384,9 +2314,25 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     pox[2][n] = rex * nz_g[n];
   }
 
+  double *shellf;
+  shellf = new double[n_tot * InList];
+
+  // we have assumed there is only one box on this level,
+  // so we do not need loop boxes
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
+
+  double Mass_out = 0;
+  double ang_outx, ang_outy, ang_outz;
+  double p_outx, p_outy, p_outz;
+  ang_outx = ang_outy = ang_outz = 0.0;
+  p_outx = p_outy = p_outz = 0.0;
+  const double f1o8 = 0.125;
+
   int mp, Lp, Nmin, Nmax;
+
   mp = n_tot / cpusize;
   Lp = n_tot - cpusize * mp;
+
   if (Lp > myrank)
   {
     Nmin = myrank * mp + myrank;
@@ -2398,20 +2344,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     Nmax = Nmin + mp - 1;
   }
 
-  double *shellf;
-  shellf = new double[n_tot * InList];
-
-  // we have assumed there is only one box on this level,
-  // so we do not need loop boxes
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
-
-  double Mass_out = 0;
-  double ang_outx, ang_outy, ang_outz;
-  double p_outx, p_outy, p_outz;
-  ang_outx = ang_outy = ang_outz = 0.0;
-  p_outx = p_outy = p_outz = 0.0;
-  const double f1o8 = 0.125;
-
   double Chi, Psi;
   double Gxx, Gxy, Gxz, Gyy, Gyz, Gzz;
   double gupxx, gupxy, gupxz, gupyy, gupyz, gupzz;
@@ -2532,13 +2464,15 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
   }
 
-  {
-    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-    double scalar_in[7];
-    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
-    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
-  }
+  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -2801,13 +2735,15 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
   }
 
-  {
-    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-    double scalar_in[7];
-    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, Comm_here);
-    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
-    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
-  }
+  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+
+  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+
+  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
+  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3084,13 +3020,15 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
     }
   }
 
-  {
-    double scalar_out[7] = {Mass_out, ang_outx, ang_outy, ang_outz, p_outx, p_outy, p_outz};
-    double scalar_in[7];
-    MPI_Allreduce(scalar_out, scalar_in, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    mass = scalar_in[0]; sx = scalar_in[1]; sy = scalar_in[2]; sz = scalar_in[3];
-    px = scalar_in[4]; py = scalar_in[5]; pz = scalar_in[6];
-  }
+  MPI_Allreduce(&Mass_out, &mass, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&ang_outx, &sx, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outy, &sy, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&ang_outz, &sz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  MPI_Allreduce(&p_outx, &px, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outy, &py, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(&p_outz, &pz, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3669,17 +3607,8 @@ void surface_integral::surf_Wave(double rex, cgh *GH, ShellPatch *SH,
   }
   //|------+  Communicate and sum the results from each processor.
 
-  {
-    double *RPIP_out = new double[2 * NN];
-    double *RPIP = new double[2 * NN];
-    memcpy(RPIP_out, RP_out, NN * sizeof(double));
-    memcpy(RPIP_out + NN, IP_out, NN * sizeof(double));
-    MPI_Allreduce(RPIP_out, RPIP, 2 * NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, RPIP, NN * sizeof(double));
-    memcpy(IP, RPIP + NN, NN * sizeof(double));
-    delete[] RPIP_out;
-    delete[] RPIP;
-  }
+  MPI_Allreduce(RP_out, RP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+  MPI_Allreduce(IP_out, IP, NN, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   //|------= Free memory.
 

AMSS_NCKU_source/tool.h

@@ -1,27 +0,0 @@
-#include "share_func.h"
-void fdderivs(const int ex[3],
-              const double *f,
-              double *fxx, double *fxy, double *fxz,
-              double *fyy, double *fyz, double *fzz,
-              const double *X, const double *Y, const double *Z,
-              double SYM1, double SYM2, double SYM3,
-              int Symmetry, int onoff);
-
-void fderivs(const int ex[3],
-             const double *f,
-             double *fx, double *fy, double *fz,
-             const double *X, const double *Y, const double *Z,
-             double SYM1, double SYM2, double SYM3,
-             int Symmetry, int onoff);
-
-void kodis(const int ex[3],
-           const double *X, const double *Y, const double *Z,
-           const double *f, double *f_rhs,
-           const double SoA[3],
-           int Symmetry, double eps);
-
-void lopsided(const int ex[3],
-              const double *X, const double *Y, const double *Z,
-              const double *f, double *f_rhs,
-              const double *Sfx, const double *Sfy, const double *Sfz,
-              int Symmetry, const double SoA[3]);

generate_interp_lb_header.py

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

generate_macrodef.py

@@ -253,7 +253,19 @@ def generate_macrodef_h():
     # Define macro buffer_width
     # number of buffer points for mesh-refinement interfaces
     
-    print( "#define buffer_width 6",                     file=file1 )
+    # Calculate ghost_width based on Finite_Diffenence_Method to optimize buffer_width
+    if ( input_data.Finite_Diffenence_Method == "2nd-order" ):
+        gw = 2
+    elif ( input_data.Finite_Diffenence_Method == "4th-order" ):
+        gw = 3
+    elif ( input_data.Finite_Diffenence_Method == "6th-order" ):
+        gw = 4
+    elif ( input_data.Finite_Diffenence_Method == "8th-order" ):
+        gw = 5
+    else:
+        gw = 5 # Default conservative value
+        
+    print( f"#define buffer_width {gw + 1}",      file=file1 )
     print(                                               file=file1 )
 
     # Define macro SC_width as buffer_width
@@ -392,6 +404,17 @@ def generate_macrodef_fh():
         print( "# Finite_Difference_Method #define ghost_width setting error!!!",   file=file1 )
         print(                                                   file=file1 )
 
+    # Define macro DEBUG_NAN_CHECK
+    # 0: off (default), 1: on
+
+    debug_nan_check = getattr(input_data, "Debug_NaN_Check", 0)
+    if debug_nan_check:
+        print( "#define DEBUG_NAN_CHECK 1", file=file1 )
+        print(                             file=file1 )
+    else:
+        print( "#define DEBUG_NAN_CHECK 0", file=file1 )
+        print(                             file=file1 )
+
     # Whether to use a shell-patch grid
     # use shell or not
 
@@ -514,6 +537,9 @@ def generate_macrodef_fh():
     print( "    6th order: 4",                                                                      file=file1 )
     print( "    8th order: 5",                                                                      file=file1 )
     print(                                                                                          file=file1 )
+    print( "define DEBUG_NAN_CHECK",                                                                file=file1 )
+    print( "    0: off (default), 1: on",                                                           file=file1 )
+    print(                                                                                          file=file1 )
     print( "define WithShell",                                                                      file=file1 )
     print( "    use shell or not",                                                                  file=file1 )
     print(                                                                                          file=file1 )

inputfile_example/AMSS_NCKU_Input.py

@@ -36,6 +36,7 @@ Equation_Class           = "BSSN"                  ## Evolution Equation: choose
 Initial_Data_Method      = "Ansorg-TwoPuncture"    ## initial data method: choose "Ansorg-TwoPuncture", "Lousto-Analytical", "Cao-Analytical", "KerrSchild-Analytical"
 Time_Evolution_Method    = "runge-kutta-45"        ## time evolution method: choose "runge-kutta-45"
 Finite_Diffenence_Method = "4th-order"             ## finite-difference method: choose "2nd-order", "4th-order", "6th-order", "8th-order"
+Debug_NaN_Check          = 0                       ## enable NaN checks in compute_rhs_bssn: 0 (off) or 1 (on)
 
 #################################################
 

makefile_and_run.py

@@ -10,47 +10,18 @@
 
 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 4-55,60-111"
+NUMACTL_CPU_BIND = ""
 
-def get_last_n_cores_per_socket(n=32):
-    """
-    Read CPU topology via lscpu and return a taskset -c string
-    selecting the last `n` cores of each NUMA node (socket).
-
-    Example: 2 sockets x 56 cores each, n=32 -> node0: 24-55, node1: 80-111
-    -> "taskset -c 24-55,80-111"
-    """
-    result = subprocess.run(["lscpu", "--parse=NODE,CPU"], capture_output=True, text=True)
-
-    # Build a dict: node_id -> sorted list of CPU ids
-    node_cpus = {}
-    for line in result.stdout.splitlines():
-        if line.startswith("#") or not line.strip():
-            continue
-        parts = line.split(",")
-        if len(parts) < 2:
-            continue
-        node_id, cpu_id = int(parts[0]), int(parts[1])
-        node_cpus.setdefault(node_id, []).append(cpu_id)
-
-    segments = []
-    for node_id in sorted(node_cpus):
-        cpus = sorted(node_cpus[node_id])
-        selected = cpus[-n:]          # last n cores of this socket
-        segments.append(f"{selected[0]}-{selected[-1]}")
-
-    cpu_str = ",".join(segments)
-    total = len(segments) * n
-    print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
-    return f"taskset -c {cpu_str}"
-
-
-## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
-NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
-
-## Build parallelism: match the number of bound cores
-BUILD_JOBS = 64
+## 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 = 14
 
 
 ##################################################################
@@ -69,7 +40,7 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=optimize ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
     elif (input_data.GPU_Calculation == "yes"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:
@@ -147,7 +118,6 @@ def run_ABE():
     
     if (input_data.GPU_Calculation == "no"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
-        #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
@@ -183,14 +153,13 @@ 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         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
-    TwoPuncture_command         = " ./TwoPunctureABE"
+    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output
@@ -211,9 +180,7 @@ 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

@@ -1,29 +0,0 @@
-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)

pgo_profile/PGO_Profile_Analysis.md

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

plot_GW_strain_amplitude_xiaoqu.py

@@ -11,8 +11,6 @@
 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

@@ -8,23 +8,16 @@
 ##
 #################################################
 
-## 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
+
 
 #########################################################################################
 
@@ -199,19 +192,3 @@ 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

@@ -8,8 +8,6 @@
 #################################################
 
 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
@@ -17,9 +15,6 @@ 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
 
@@ -55,40 +50,10 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
         file_list.append(x)
         print(x)
 
-    ## 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  = []
+    ## Plot each file in the list
     for filename in file_list:
         print(filename)
-        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 )
+        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
 
     print(                        )
     print( " Binary Data Plot Has been Finished " )