Optimize bssn_rhs.f90: Fuse loops for metric inversion and Christoffel symbols to improve cache locality

- 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_source/TwoPunctures.C

@@ -5,7 +5,6 @@
 #include <cstdio>
 #include <cstdlib>
 #include <string>
-#include <cstring>
 #include <iostream>
 #include <iomanip>
 #include <fstream>
@@ -61,110 +60,13 @@ TwoPunctures::TwoPunctures(double mp, double mm, double b,
   F = dvector(0, ntotal - 1);
   allocate_derivs(&u, ntotal);
   allocate_derivs(&v, ntotal);
-
-  // Allocate workspace buffers for hot-path allocation elimination
-  int N = maximum3(n1, n2, n3);
-  int maxn = maximum2(n1, n2);
-
-  // LineRelax_be workspace (sized for n2)
-  ws_diag_be = new double[n2];
-  ws_e_be = new double[n2 - 1];
-  ws_f_be = new double[n2 - 1];
-  ws_b_be = new double[n2];
-  ws_x_be = new double[n2];
-
-  // LineRelax_al workspace (sized for n1)
-  ws_diag_al = new double[n1];
-  ws_e_al = new double[n1 - 1];
-  ws_f_al = new double[n1 - 1];
-  ws_b_al = new double[n1];
-  ws_x_al = new double[n1];
-
-  // ThomasAlgorithm workspace (sized for max(n1,n2))
-  ws_thomas_y = new double[maxn];
-
-  // JFD_times_dv workspace (sized for nvar)
-  ws_jfd_values = dvector(0, nvar - 1);
-  allocate_derivs(&ws_jfd_dU, nvar);
-  allocate_derivs(&ws_jfd_U, nvar);
-
-  // chebft_Zeros workspace (sized for N+1)
-  ws_cheb_c = dvector(0, N);
-
-  // fourft workspace (sized for N/2+1 each)
-  ws_four_a = dvector(0, N / 2);
-  ws_four_b = dvector(0, N / 2);
-
-  // Derivatives_AB3 workspace
-  ws_deriv_p = dvector(0, N);
-  ws_deriv_dp = dvector(0, N);
-  ws_deriv_d2p = dvector(0, N);
-  ws_deriv_q = dvector(0, N);
-  ws_deriv_dq = dvector(0, N);
-  ws_deriv_r = dvector(0, N);
-  ws_deriv_dr = dvector(0, N);
-  ws_deriv_indx = ivector(0, N);
-
-  // F_of_v workspace
-  ws_fov_sources = new double[n1 * n2 * n3];
-  ws_fov_values = dvector(0, nvar - 1);
-  allocate_derivs(&ws_fov_U, nvar);
-
-  // J_times_dv workspace
-  ws_jtdv_values = dvector(0, nvar - 1);
-  allocate_derivs(&ws_jtdv_dU, nvar);
-  allocate_derivs(&ws_jtdv_U, nvar);
 }
 
 TwoPunctures::~TwoPunctures()
 {
-  int const nvar = 1, n1 = npoints_A, n2 = npoints_B, n3 = npoints_phi;
-  int N = maximum3(n1, n2, n3);
-
   free_dvector(F, 0, ntotal - 1);
   free_derivs(&u, ntotal);
   free_derivs(&v, ntotal);
-
-  // Free workspace buffers
-  delete[] ws_diag_be;
-  delete[] ws_e_be;
-  delete[] ws_f_be;
-  delete[] ws_b_be;
-  delete[] ws_x_be;
-
-  delete[] ws_diag_al;
-  delete[] ws_e_al;
-  delete[] ws_f_al;
-  delete[] ws_b_al;
-  delete[] ws_x_al;
-
-  delete[] ws_thomas_y;
-
-  free_dvector(ws_jfd_values, 0, nvar - 1);
-  free_derivs(&ws_jfd_dU, nvar);
-  free_derivs(&ws_jfd_U, nvar);
-
-  free_dvector(ws_cheb_c, 0, N);
-
-  free_dvector(ws_four_a, 0, N / 2);
-  free_dvector(ws_four_b, 0, N / 2);
-
-  free_dvector(ws_deriv_p, 0, N);
-  free_dvector(ws_deriv_dp, 0, N);
-  free_dvector(ws_deriv_d2p, 0, N);
-  free_dvector(ws_deriv_q, 0, N);
-  free_dvector(ws_deriv_dq, 0, N);
-  free_dvector(ws_deriv_r, 0, N);
-  free_dvector(ws_deriv_dr, 0, N);
-  free_ivector(ws_deriv_indx, 0, N);
-
-  delete[] ws_fov_sources;
-  free_dvector(ws_fov_values, 0, nvar - 1);
-  free_derivs(&ws_fov_U, nvar);
-
-  free_dvector(ws_jtdv_values, 0, nvar - 1);
-  free_derivs(&ws_jtdv_dU, nvar);
-  free_derivs(&ws_jtdv_U, nvar);
 }
 
 void TwoPunctures::Solve()
@@ -753,7 +655,7 @@ void TwoPunctures::chebft_Zeros(double u[], int n, int inv)
   int k, j, isignum;
   double fac, sum, Pion, *c;
 
-  c = ws_cheb_c;
+  c = dvector(0, n);
   Pion = Pi / n;
   if (inv == 0)
   {
@@ -784,6 +686,7 @@ void TwoPunctures::chebft_Zeros(double u[], int n, int inv)
   }
   for (j = 0; j < n; j++)
     u[j] = c[j];
+  free_dvector(c, 0, n);
 }
 
 /* --------------------------------------------------------------------------*/
@@ -871,8 +774,8 @@ void TwoPunctures::fourft(double *u, int N, int inv)
   double x, x1, fac, Pi_fac, *a, *b;
 
   M = N / 2;
-  a = ws_four_a;
-  b = ws_four_b - 1; /* offset to match dvector(1,M) indexing */
+  a = dvector(0, M);
+  b = dvector(1, M); /* Actually: b=vector(1,M-1) but this is problematic if M=1*/
   fac = 1. / M;
   Pi_fac = Pi * fac;
   if (inv == 0)
@@ -921,6 +824,8 @@ void TwoPunctures::fourft(double *u, int N, int inv)
       iy = -iy;
     }
   }
+  free_dvector(a, 0, M);
+  free_dvector(b, 1, M);
 }
 
 /* -----------------------------------------*/
@@ -1213,14 +1118,14 @@ void TwoPunctures::Derivatives_AB3(int nvar, int n1, int n2, int n3, derivs v)
   double *p, *dp, *d2p, *q, *dq, *r, *dr;
 
   N = maximum3(n1, n2, n3);
-  p = ws_deriv_p;
-  dp = ws_deriv_dp;
-  d2p = ws_deriv_d2p;
-  q = ws_deriv_q;
-  dq = ws_deriv_dq;
-  r = ws_deriv_r;
-  dr = ws_deriv_dr;
-  indx = ws_deriv_indx;
+  p = dvector(0, N);
+  dp = dvector(0, N);
+  d2p = dvector(0, N);
+  q = dvector(0, N);
+  dq = dvector(0, N);
+  r = dvector(0, N);
+  dr = dvector(0, N);
+  indx = ivector(0, N);
 
   for (ivar = 0; ivar < nvar; ivar++)
   {
@@ -1303,6 +1208,14 @@ void TwoPunctures::Derivatives_AB3(int nvar, int n1, int n2, int n3, derivs v)
       }
     }
   }
+  free_dvector(p, 0, N);
+  free_dvector(dp, 0, N);
+  free_dvector(d2p, 0, N);
+  free_dvector(q, 0, N);
+  free_dvector(dq, 0, N);
+  free_dvector(r, 0, N);
+  free_dvector(dr, 0, N);
+  free_ivector(indx, 0, N);
 }
 /* --------------------------------------------------------------------------*/
 void TwoPunctures::Newton(int const nvar, int const n1, int const n2, int const n3,
@@ -1371,11 +1284,10 @@ void TwoPunctures::F_of_v(int nvar, int n1, int n2, int n3, derivs v, double *F,
   derivs U;
   double *sources;
 
-  values = ws_fov_values;
-  U = ws_fov_U;
+  values = dvector(0, nvar - 1);
+  allocate_derivs(&U, nvar);
 
-  sources = ws_fov_sources;
-  memset(sources, 0, n1 * n2 * n3 * sizeof(double));
+  sources = (double *)calloc(n1 * n2 * n3, sizeof(double));
   if (0)
   {
     double *s_x, *s_y, *s_z;
@@ -1530,6 +1442,9 @@ void TwoPunctures::F_of_v(int nvar, int n1, int n2, int n3, derivs v, double *F,
   {
     fclose(debugfile);
   }
+  free(sources);
+  free_dvector(values, 0, nvar - 1);
+  free_derivs(&U, nvar);
 }
 /* --------------------------------------------------------------------------*/
 double TwoPunctures::norm_inf(double const *F, int const ntotal)
@@ -1935,12 +1850,11 @@ void TwoPunctures::J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, doubl
 
   Derivatives_AB3(nvar, n1, n2, n3, dv);
 
-  values = ws_jtdv_values;
-  dU = ws_jtdv_dU;
-  U = ws_jtdv_U;
-
   for (i = 0; i < n1; i++)
   {
+    values = dvector(0, nvar - 1);
+    allocate_derivs(&dU, nvar);
+    allocate_derivs(&U, nvar);
     for (j = 0; j < n2; j++)
     {
       for (k = 0; k < n3; k++)
@@ -1994,6 +1908,9 @@ void TwoPunctures::J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, doubl
         }
       }
     }
+    free_dvector(values, 0, nvar - 1);
+    free_derivs(&dU, nvar);
+    free_derivs(&U, nvar);
   }
 }
 /* --------------------------------------------------------------------------*/
@@ -2040,11 +1957,17 @@ void TwoPunctures::LineRelax_be(double *dv,
 {
   int j, m, Ic, Ip, Im, col, ivar;
 
-  double *diag = ws_diag_be;
-  double *e = ws_e_be;     /* above diagonal */
-  double *f = ws_f_be;     /* below diagonal */
-  double *b = ws_b_be;     /* rhs */
-  double *x = ws_x_be;     /* solution vector */
+  double *diag = new double[n2];
+  double *e = new double[n2 - 1]; /* above diagonal */
+  double *f = new double[n2 - 1]; /* below diagonal */
+  double *b = new double[n2];     /* rhs */
+  double *x = new double[n2];     /* solution vector */
+
+  //  gsl_vector *diag = gsl_vector_alloc(n2);
+  //  gsl_vector *e = gsl_vector_alloc(n2-1); /* above diagonal */
+  //  gsl_vector *f = gsl_vector_alloc(n2-1); /* below diagonal */
+  //  gsl_vector *b = gsl_vector_alloc(n2);   /* rhs */
+  //  gsl_vector *x = gsl_vector_alloc(n2);   /* solution vector */
 
   for (ivar = 0; ivar < nvar; ivar++)
   {
@@ -2054,35 +1977,62 @@ void TwoPunctures::LineRelax_be(double *dv,
     }
     diag[n2 - 1] = 0;
 
+    //    gsl_vector_set_zero(diag);
+    //    gsl_vector_set_zero(e);
+    //    gsl_vector_set_zero(f);
     for (j = 0; j < n2; j++)
     {
       Ip = Index(ivar, i, j + 1, k, nvar, n1, n2, n3);
       Ic = Index(ivar, i, j, k, nvar, n1, n2, n3);
       Im = Index(ivar, i, j - 1, k, nvar, n1, n2, n3);
       b[j] = rhs[Ic];
+      //      gsl_vector_set(b,j,rhs[Ic]);
       for (m = 0; m < ncols[Ic]; m++)
       {
         col = cols[Ic][m];
         if (col != Ip && col != Ic && col != Im)
           b[j] -= JFD[Ic][m] * dv[col];
+        //          *gsl_vector_ptr(b, j) -= JFD[Ic][m] * dv[col];
         else
         {
           if (col == Im && j > 0)
             f[j - 1] = JFD[Ic][m];
+          //            gsl_vector_set(f,j-1,JFD[Ic][m]);
           if (col == Ic)
             diag[j] = JFD[Ic][m];
+          //            gsl_vector_set(diag,j,JFD[Ic][m]);
           if (col == Ip && j < n2 - 1)
             e[j] = JFD[Ic][m];
+          //            gsl_vector_set(e,j,JFD[Ic][m]);
         }
       }
     }
+    //          A x = b
+    //          A = ( d_0 e_0  0   0  )
+    //              ( f_0 d_1 e_1  0  )
+    //              (  0  f_1 d_2 e_2 )
+    //              (  0   0  f_2 d_3 )
+    //
     ThomasAlgorithm(n2, f, diag, e, x, b);
+    //    gsl_linalg_solve_tridiag(diag, e, f, b, x);
     for (j = 0; j < n2; j++)
     {
       Ic = Index(ivar, i, j, k, nvar, n1, n2, n3);
       dv[Ic] = x[j];
+      //      dv[Ic] = gsl_vector_get(x, j);
     }
   }
+
+  delete[] diag;
+  delete[] e;
+  delete[] f;
+  delete[] b;
+  delete[] x;
+  //  gsl_vector_free(diag);
+  //  gsl_vector_free(e);
+  //  gsl_vector_free(f);
+  //  gsl_vector_free(b);
+  //  gsl_vector_free(x);
 }
 /* --------------------------------------------------------------------------*/
 void TwoPunctures::JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
@@ -2099,8 +2049,8 @@ void TwoPunctures::JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
       ha, ga, ga2, hb, gb, gb2, hp, gp, gp2, gagb, gagp, gbgp;
   derivs dU, U;
 
-  dU = ws_jfd_dU;
-  U = ws_jfd_U;
+  allocate_derivs(&dU, nvar);
+  allocate_derivs(&U, nvar);
 
   if (k < 0)
     k = k + n3;
@@ -2218,6 +2168,9 @@ void TwoPunctures::JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
   LinEquations(A, B, X, R, x, r, phi, y, z, dU, U, values);
   for (ivar = 0; ivar < nvar; ivar++)
     values[ivar] *= FAC;
+
+  free_derivs(&dU, nvar);
+  free_derivs(&U, nvar);
 }
 #undef FAC
 /*-----------------------------------------------------------*/
@@ -2249,11 +2202,17 @@ void TwoPunctures::LineRelax_al(double *dv,
 {
   int i, m, Ic, Ip, Im, col, ivar;
 
-  double *diag = ws_diag_al;
-  double *e = ws_e_al;     /* above diagonal */
-  double *f = ws_f_al;     /* below diagonal */
-  double *b = ws_b_al;     /* rhs */
-  double *x = ws_x_al;     /* solution vector */
+  double *diag = new double[n1];
+  double *e = new double[n1 - 1]; /* above diagonal */
+  double *f = new double[n1 - 1]; /* below diagonal */
+  double *b = new double[n1];     /* rhs */
+  double *x = new double[n1];     /* solution vector */
+
+  //  gsl_vector *diag = gsl_vector_alloc(n1);
+  //  gsl_vector *e = gsl_vector_alloc(n1-1); /* above diagonal */
+  //  gsl_vector *f = gsl_vector_alloc(n1-1); /* below diagonal */
+  //  gsl_vector *b = gsl_vector_alloc(n1);   /* rhs */
+  //  gsl_vector *x = gsl_vector_alloc(n1);   /* solution vector */
 
   for (ivar = 0; ivar < nvar; ivar++)
   {
@@ -2263,35 +2222,57 @@ void TwoPunctures::LineRelax_al(double *dv,
     }
     diag[n1 - 1] = 0;
 
+    //    gsl_vector_set_zero(diag);
+    //    gsl_vector_set_zero(e);
+    //    gsl_vector_set_zero(f);
     for (i = 0; i < n1; i++)
     {
       Ip = Index(ivar, i + 1, j, k, nvar, n1, n2, n3);
       Ic = Index(ivar, i, j, k, nvar, n1, n2, n3);
       Im = Index(ivar, i - 1, j, k, nvar, n1, n2, n3);
       b[i] = rhs[Ic];
+      //      gsl_vector_set(b,i,rhs[Ic]);
       for (m = 0; m < ncols[Ic]; m++)
       {
         col = cols[Ic][m];
         if (col != Ip && col != Ic && col != Im)
           b[i] -= JFD[Ic][m] * dv[col];
+        //          *gsl_vector_ptr(b, i) -= JFD[Ic][m] * dv[col];
         else
         {
           if (col == Im && i > 0)
             f[i - 1] = JFD[Ic][m];
+          //            gsl_vector_set(f,i-1,JFD[Ic][m]);
           if (col == Ic)
             diag[i] = JFD[Ic][m];
+          //            gsl_vector_set(diag,i,JFD[Ic][m]);
           if (col == Ip && i < n1 - 1)
             e[i] = JFD[Ic][m];
+          //            gsl_vector_set(e,i,JFD[Ic][m]);
         }
       }
     }
     ThomasAlgorithm(n1, f, diag, e, x, b);
+    //    gsl_linalg_solve_tridiag(diag, e, f, b, x);
     for (i = 0; i < n1; i++)
     {
       Ic = Index(ivar, i, j, k, nvar, n1, n2, n3);
       dv[Ic] = x[i];
+      //      dv[Ic] = gsl_vector_get(x, i);
     }
   }
+
+  delete[] diag;
+  delete[] e;
+  delete[] f;
+  delete[] b;
+  delete[] x;
+
+  //  gsl_vector_free(diag);
+  //  gsl_vector_free(e);
+  //  gsl_vector_free(f);
+  //  gsl_vector_free(b);
+  //  gsl_vector_free(x);
 }
 /* -------------------------------------------------------------------------*/
 // a[N], b[N-1], c[N-1], x[N], q[N]
@@ -2303,29 +2284,44 @@ void TwoPunctures::LineRelax_al(double *dv,
 //"Parallel Scientific Computing in C++ and MPI" P361
 void TwoPunctures::ThomasAlgorithm(int N, double *b, double *a, double *c, double *x, double *q)
 {
-  // In-place Thomas algorithm: uses a[] as d workspace, b[] as l workspace.
-  // c[] is already u (above-diagonal). ws_thomas_y is pre-allocated workspace.
   int i;
-  double *y = ws_thomas_y;
+  double *l, *u, *d, *y;
+  l = new double[N - 1];
+  u = new double[N - 1];
+  d = new double[N];
+  y = new double[N];
+
+  /* LU Decomposition */
+  d[0] = a[0];
+  u[0] = c[0];
 
-  /* LU Decomposition (in-place: a becomes d, b becomes l) */
   for (i = 0; i < N - 2; i++)
   {
-    b[i] = b[i] / a[i];
-    a[i + 1] = a[i + 1] - b[i] * c[i];
+    l[i] = b[i] / d[i];
+    d[i + 1] = a[i + 1] - l[i] * u[i];
+    u[i + 1] = c[i + 1];
   }
-  b[N - 2] = b[N - 2] / a[N - 2];
-  a[N - 1] = a[N - 1] - b[N - 2] * c[N - 2];
+
+  l[N - 2] = b[N - 2] / d[N - 2];
+  d[N - 1] = a[N - 1] - l[N - 2] * u[N - 2];
 
   /* Forward Substitution [L][y] = [q] */
   y[0] = q[0];
   for (i = 1; i < N; i++)
-    y[i] = q[i] - b[i - 1] * y[i - 1];
+    y[i] = q[i] - l[i - 1] * y[i - 1];
 
   /* Backward Substitution [U][x] = [y] */
-  x[N - 1] = y[N - 1] / a[N - 1];
+  x[N - 1] = y[N - 1] / d[N - 1];
+
   for (i = N - 2; i >= 0; i--)
-    x[i] = (y[i] - c[i] * x[i + 1]) / a[i];
+    x[i] = (y[i] - u[i] * x[i + 1]) / d[i];
+
+  delete[] l;
+  delete[] u;
+  delete[] d;
+  delete[] y;
+
+  return;
 }
 // --------------------------------------------------------------------------*/
 // Calculates the value of v at an arbitrary position (x,y,z) if the spectral coefficients are know*/*/

AMSS_NCKU_source/TwoPunctures.h

@@ -42,33 +42,6 @@ private:
 
        int ntotal;
 
-       // Pre-allocated workspace buffers for hot-path allocation elimination
-       // LineRelax_be workspace (sized for n2)
-       double *ws_diag_be, *ws_e_be, *ws_f_be, *ws_b_be, *ws_x_be;
-       // LineRelax_al workspace (sized for n1)
-       double *ws_diag_al, *ws_e_al, *ws_f_al, *ws_b_al, *ws_x_al;
-       // ThomasAlgorithm workspace (sized for max(n1,n2))
-       double *ws_thomas_y;
-       // JFD_times_dv workspace (sized for nvar)
-       double *ws_jfd_values;
-       derivs ws_jfd_dU, ws_jfd_U;
-       // chebft_Zeros workspace (sized for max(n1,n2,n3)+1)
-       double *ws_cheb_c;
-       // fourft workspace (sized for max(n1,n2,n3)/2+1 each)
-       double *ws_four_a, *ws_four_b;
-       // Derivatives_AB3 workspace
-       double *ws_deriv_p, *ws_deriv_dp, *ws_deriv_d2p;
-       double *ws_deriv_q, *ws_deriv_dq;
-       double *ws_deriv_r, *ws_deriv_dr;
-       int *ws_deriv_indx;
-       // F_of_v workspace
-       double *ws_fov_sources;
-       double *ws_fov_values;
-       derivs ws_fov_U;
-       // J_times_dv workspace
-       double *ws_jtdv_values;
-       derivs ws_jtdv_dU, ws_jtdv_U;
-
        struct parameters
        {
               int nvar, n1, n2, n3;

AMSS_NCKU_source/diff_new.f90

@@ -1103,103 +1103,6 @@
 
   end subroutine fderivs
 !-----------------------------------------------------------------------------
-! fderivs variant: reuses caller-provided fh work array (memory pool)
-!-----------------------------------------------------------------------------
-  subroutine fderivs_fh(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3, &
-                         symmetry,onoff,fh)
-  implicit none
-
-  integer,                               intent(in ):: ex(1:3),symmetry,onoff
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(in ):: f
-  real*8,  dimension(ex(1),ex(2),ex(3)), intent(out):: fx,fy,fz
-  real*8,                                intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
-  real*8,                                intent(in ):: SYM1,SYM2,SYM3
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)),intent(inout):: fh
-
-  real*8 :: dX,dY,dZ
-  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,f,fh,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
-
-  fx = ZEO
-  fy = ZEO
-  fz = ZEO
-
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-#if 0
-   if(i+2 <= imax .and. i-2 >= imin)then
-      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-    elseif(i+1 <= imax .and. i-1 >= imin)then
-      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-    endif
-        if(j+2 <= jmax .and. j-2 >= jmin)then
-      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-    elseif(j+1 <= jmax .and. j-1 >= jmin)then
-     fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-    endif
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-    elseif(k+1 <= kmax .and. k-1 >= kmin)then
-      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-    endif
-#else
-   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
-      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. &
-          j+1 <= jmax .and. j-1 >= jmin .and. &
-          k+1 <= kmax .and. k-1 >= kmin) then
-      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-      fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-   endif
-#endif
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine fderivs_fh
-!-----------------------------------------------------------------------------
 !
 ! single derivatives dx
 !
@@ -2036,30 +1939,31 @@
   return
 
   end subroutine fddyz
-
-!-----------------------------------------------------------------------------
-! fdderivs variant: reuses caller-provided fh work array (memory pool)
-!-----------------------------------------------------------------------------
-  subroutine fdderivs_fh(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
-                          SYM1,SYM2,SYM3,symmetry,onoff,fh)
+  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 ):: f
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx,fxy,fxz,fyy,fyz,fzz
-  real*8,                              intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3))
-  real*8,                              intent(in ):: SYM1,SYM2,SYM3
-  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)),intent(inout):: fh
+  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  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
-  real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
+  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, TWO=2.d0, F1o4=2.5d-1
-  real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1
-  real*8, parameter :: F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
+  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)
@@ -2080,118 +1984,264 @@
   SoA(2) = SYM2
   SoA(3) = SYM3
 
-  call symmetry_bd(2,ex,f,fh,SoA)
+  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)
 
-  Sdxdx =  ONE /( dX * dX )
-  Sdydy =  ONE /( dY * dY )
-  Sdzdz =  ONE /( dZ * dZ )
+  d12dx = ONE/F12/dX
+  d12dy = ONE/F12/dY
+  d12dz = ONE/F12/dZ
 
-  Fdxdx = F1o12 /( dX * dX )
-  Fdydy = F1o12 /( dY * dY )
-  Fdzdz = F1o12 /( dZ * dZ )
+  d2dx = ONE/TWO/dX
+  d2dy = ONE/TWO/dY
+  d2dz = ONE/TWO/dZ
 
-  Sdxdy = F1o4 /( dX * dY )
-  Sdxdz = F1o4 /( dX * dZ )
-  Sdydz = F1o4 /( dY * dZ )
-
-  Fdxdy = F1o144 /( dX * dY )
-  Fdxdz = F1o144 /( dX * dZ )
-  Fdydz = F1o144 /( dY * dZ )
-
-  fxx = ZEO
-  fyy = ZEO
-  fzz = ZEO
-  fxy = ZEO
-  fxz = ZEO
-  fyz = ZEO
+  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 0
-   if(i+2 <= imax .and. i-2 >= imin)then
-   fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-                       -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
-   elseif(i+1 <= imax .and. i-1 >= imin)then
-   fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k)+fh(i+1,j,k))
-   endif
-        if(j+2 <= jmax .and. j-2 >= jmin)then
-   fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-                       -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
-   elseif(j+1 <= jmax .and. j-1 >= jmin)then
-   fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k)+fh(i,j+1,k))
-   endif
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-   fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-                       -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
-   elseif(k+1 <= kmax .and. k-1 >= kmin)then
-   fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k)+fh(i,j,k+1))
-   endif
-       if(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
-   fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
-                       -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
-                       +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
-                       -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
-   fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
-   endif
-       if(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
-   fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
-                       -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
-                       +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
-                       -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
-   fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
-   endif
-       if(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
-   fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
-                       -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
-                       +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
-                       -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
-   elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
-   fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
-   endif
-#else
-! for bam comparison
    if(i+2 <= imax .and. i-2 >= imin .and. &
       j+2 <= jmax .and. j-2 >= jmin .and. &
       k+2 <= kmax .and. k-2 >= kmin) then
-   fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-                       -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
-   fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-                       -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
-   fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-                       -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
-   fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
-                       -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
-                       +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
-                       -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
-   fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
-                       -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
-                       +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
-                       -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
-   fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
-                       -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
-                       +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
-                       -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
+      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
-   fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k)+fh(i+1,j,k))
-   fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k)+fh(i,j+1,k))
-   fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k)+fh(i,j,k+1))
-   fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
-   fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
-   fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
+      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
-#endif
-   enddo
-   enddo
-   enddo
+  enddo
+  enddo
+  enddo
 
   return
 
-  end subroutine fdderivs_fh
+  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
@@ -2330,6 +2380,9 @@
 
   end subroutine fderivs
 !-----------------------------------------------------------------------------
+! batch first derivatives (4 fields), same symmetry setup
+!-----------------------------------------------------------------------------
+!-----------------------------------------------------------------------------
 !
 ! single derivatives dx
 !

AMSS_NCKU_source/enforce_algebra.f90

@@ -18,61 +18,49 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> 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 ) 
+  
+  gxx = gxx * detg
+  gxy = gxy * detg
+  gxz = gxz * detg
+  gyy = gyy * detg
+  gyz = gyz * detg
+  gzz = gzz * detg
 
-    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
-
-    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
 
@@ -94,71 +82,51 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> 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 ) 
+  
+  gxx = gxx * gupzz
+  gxy = gxy * gupzz
+  gxz = gxz * gupzz
+  gyy = gyy * gupzz
+  gyz = gyz * gupzz
+  gzz = gzz * gupzz
 
-    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
+  dxx = gxx - ONE
+  dyy = gyy - ONE
+  dzz = gzz - ONE
+! for A  
 
-    lscale = ONE / ( lscale ** F1o3 )
+  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 )
 
-    lgxx = lgxx * lscale
-    lgxy = lgxy * lscale
-    lgxz = lgxz * lscale
-    lgyy = lgyy * lscale
-    lgyz = lgyz * lscale
-    lgzz = lgzz * lscale
+  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
 
-    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
-
-! 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/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)
@@ -883,6 +886,7 @@ 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+1,1:extc(2),1:extc(3))*SoA(1)
@@ -908,6 +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)
@@ -936,6 +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)
@@ -1112,65 +1118,64 @@ end subroutine d2dump
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
 
-  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
-    end if
+  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
-        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)
+  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
+    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
 !------------------------------------------------------------------------------
 !
@@ -1178,37 +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
 !------------------------------------------------------------------------------
 !
@@ -1216,15 +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
@@ -1233,33 +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/kodiss.f90

@@ -215,99 +215,6 @@ integer, parameter :: NO_SYMM=0, OCTANT=2
 
   end subroutine kodis
 
-!-----------------------------------------------------------------------------
-! kodis variant: reuses caller-provided fh work array (memory pool)
-!-----------------------------------------------------------------------------
-subroutine kodis_fh(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps,fh)
-
-implicit none
-! argument variables
-integer,intent(in) :: Symmetry
-integer,dimension(3),intent(in)::ex
-real*8, dimension(1:3), intent(in) :: SoA
-double precision,intent(in),dimension(ex(1))::X
-double precision,intent(in),dimension(ex(2))::Y
-double precision,intent(in),dimension(ex(3))::Z
-double precision,intent(in),dimension(ex(1),ex(2),ex(3))::f
-double precision,intent(inout),dimension(ex(1),ex(2),ex(3))::f_rhs
-real*8,intent(in) :: eps
-real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)),intent(inout):: fh
-! local variables
-integer :: imin,jmin,kmin,imax,jmax,kmax
-integer :: i,j,k
-real*8  :: dX,dY,dZ
-real*8, parameter :: ONE=1.d0,SIX=6.d0,FIT=1.5d1,TWT=2.d1
-real*8,parameter::cof=6.4d1   ! 2^6
-integer, parameter :: NO_SYMM=0, OCTANT=2
-
-  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 = -2
-  if(Symmetry == OCTANT .and. dabs(X(1)) < dX) imin = -2
-  if(Symmetry == OCTANT .and. dabs(Y(1)) < dY) jmin = -2
-
-  call symmetry_bd(3,ex,f,fh,SoA)
-
-  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
-#if 0
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dX/cof * (     &
-                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
-                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
-                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
-                          TWT* fh(i,j,k)            )
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dY/cof * (     &
-                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
-                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
-                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
-                          TWT* fh(i,j,k)            )
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/dZ/cof * (     &
-                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
-                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
-                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
-                          TWT* fh(i,j,k)            )
-#else
-   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
-  endif
-
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine kodis_fh
-
 #elif (ghost_width == 4)
 ! sixth order code
 !------------------------------------------------------------------------------------------------------------------------------

AMSS_NCKU_source/lopsidediff.f90

@@ -487,160 +487,6 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
 
   end subroutine lopsided
 
-!-----------------------------------------------------------------------------
-! lopsided variant: reuses caller-provided fh work array (memory pool)
-!-----------------------------------------------------------------------------
-subroutine lopsided_fh(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,fh)
-  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,dimension(-2:ex(1),-2:ex(2),-2:ex(3)),intent(inout):: fh
-
-!~~~~~~> local variables:
-  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
-
-  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
-
-  call symmetry_bd(3,ex,f,fh,SoA)
-
-! upper bound set ex-1 only for efficiency,
-! the loop body will set ex 0 also
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-#if 0
-!! old code - same as original lopsided
-#else
-!! new code, 2012dec27, based on bam
-! 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
-#endif
-  enddo
-  enddo
-  enddo
-
-  return
-
-  end subroutine lopsided_fh
-
 #elif (ghost_width == 4)
 ! sixth order code
 ! Compute advection terms in right hand sides of field equations

AMSS_NCKU_source/makefile.inc

@@ -16,10 +16,10 @@ LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore
 ## -fp-model fast=2: Aggressive floating-point optimizations
 ## -fma: Enable fused multiply-add instructions
 ## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma \
                -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -align array64byte -fpp -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
+               -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx

generate_macrodef.py

@@ -392,6 +392,17 @@ 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 +525,9 @@ 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

@@ -35,7 +35,8 @@ Equation_Class           = "BSSN"                  ## Evolution Equation: choose
                                                    ## 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"
+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

@@ -15,13 +15,13 @@ import subprocess
 ## 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 16-47,64-95"
-#NUMACTL_CPU_BIND = "taskset -c 0-111"
+#NUMACTL_CPU_BIND = "taskset -c 4-55,60-111"
+NUMACTL_CPU_BIND = ""
 
 ## 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 = 64
+BUILD_JOBS = 14
 
 
 ##################################################################