taskset setting updated

Pool fh work arrays in compute_rhs_bssn to eliminate allocation churn
Add _fh variants of fderivs, fdderivs, kodis, and lopsided that accept a caller-provided fh work array instead of allocating one internally. Declare two shared work arrays in compute_rhs_bssn (fh_work2 for symmetry_bd(2) callers, fh_work3 for symmetry_bd(3) callers) and pass them to all ~84 subroutine calls, eliminating ~77 redundant automatic array allocations (~591 MB churn per RHS call, ~2.3 GB per timestep). Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
2026-02-07 22:24:02 +08:00 · 2026-02-07 21:49:12 +08:00 · 2026-02-06 21:20:35 +08:00 · 2026-02-06 19:00:35 +08:00 · 2026-02-06 18:36:29 +08:00 · 2026-02-06 17:13:39 +08:00
23 changed files with 1803 additions and 2101 deletions
--- a/.gitignore
+++ b/.gitignore
@@ -1,5 +1,6 @@
 __pycache__
 GW150914
-GW150914*
-.codex
-docs/
+GW150914-origin
+docs
+*.tmp
+
--- a/AMSS_NCKU_Program.py
+++ b/AMSS_NCKU_Program.py
@@ -9,19 +9,9 @@
 ##################################################################


-##################################################################
-
-## 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.
-if __name__ != '__main__':
-    import sys as _sys
-    _sys.exit(0)
-
-
-##################################################################
-
-## Print program introduction
+##################################################################
+
+## Print program introduction

 import print_information

@@ -432,36 +422,31 @@ print( " Plotting the txt and binary results data from the AMSS-NCKU simulation
 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 black hole separation vs. time
-plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
-
-## Plot gravitational waveforms (psi4 and strain amplitude)
-for i in range(input_data.Detector_Number):
-    plot_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 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 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 stored binary data
-plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )
+import plot_xiaoqu
+import plot_GW_strain_amplitude_xiaoqu
+
+## Plot black hole trajectory
+plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
+plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
+
+## Plot black hole separation vs. time
+plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
+
+## Plot gravitational waveforms (psi4 and strain amplitude)
+for i in range(input_data.Detector_Number):
+    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
+    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
+
+## Plot ADM mass evolution
+for i in range(input_data.Detector_Number):
+    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
+
+## Plot Hamiltonian constraint violation over time
+for i in range(input_data.grid_level):
+    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
+
+## Plot stored binary data
+plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )

 print(                                                 )
 print( f" This Program Cost = {elapsed_time} Seconds " )
--- a/AMSS_NCKU_Verify_ASC26.py
+++ b/AMSS_NCKU_Verify_ASC26.py
@@ -0,0 +1,279 @@
+#!/usr/bin/env python3
+"""
+AMSS-NCKU GW150914 Simulation Regression Test Script
+
+Verification Requirements:
+1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
+2. ADM constraint violation < 2 (Grid Level 0)
+
+RMS Calculation Method:
+- Computes trajectory deviation on the XY plane independently for BH1 and BH2
+- For each black hole: RMS = sqrt((1/M) * sum((Δr_i / r_i^max)^2)) × 100%
+- Final RMS = max(RMS_BH1, RMS_BH2)
+
+Usage: python3 AMSS_NCKU_Verify_ASC26.py [output_dir]
+Default: output_dir = GW150914/AMSS_NCKU_output
+Reference: GW150914-origin (baseline simulation)
+"""
+
+import numpy as np
+import sys
+import os
+
+# ANSI Color Codes
+class Color:
+    GREEN = '\033[92m'
+    RED = '\033[91m'
+    YELLOW = '\033[93m'
+    BLUE = '\033[94m'
+    BOLD = '\033[1m'
+    RESET = '\033[0m'
+
+def get_status_text(passed):
+    if passed:
+        return f"{Color.GREEN}{Color.BOLD}PASS{Color.RESET}"
+    else:
+        return f"{Color.RED}{Color.BOLD}FAIL{Color.RESET}"
+
+def load_bh_trajectory(filepath):
+    """Load black hole trajectory data"""
+    data = np.loadtxt(filepath)
+    return {
+        'time': data[:, 0],
+        'x1': data[:, 1], 'y1': data[:, 2], 'z1': data[:, 3],
+        'x2': data[:, 4], 'y2': data[:, 5], 'z2': data[:, 6]
+    }
+
+
+def load_constraint_data(filepath):
+    """Load constraint violation data"""
+    data = []
+    with open(filepath, 'r') as f:
+        for line in f:
+            if line.startswith('#'):
+                continue
+            parts = line.split()
+            if len(parts) >= 8:
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
+
+
+def calculate_rms_error(bh_data_ref, bh_data_target):
+    """
+    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
+
+    This function computes the RMS error independently for BH1 and BH2 trajectories,
+    then returns the maximum of the two as the final RMS error metric.
+
+    For each black hole, the RMS is calculated as:
+        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
+
+    where:
+        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
+        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
+
+    Args:
+        bh_data_ref: Reference (baseline) trajectory data
+        bh_data_target: Target (optimized) trajectory data
+
+    Returns:
+        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
+        error: Error message if any
+    """
+    # Align data: truncate to the length of the shorter dataset
+    M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
+
+    if M < 10:
+        return None, "Insufficient data points for comparison"
+
+    # Extract XY coordinates for both black holes
+    x1_ref = bh_data_ref['x1'][:M]
+    y1_ref = bh_data_ref['y1'][:M]
+    x2_ref = bh_data_ref['x2'][:M]
+    y2_ref = bh_data_ref['y2'][:M]
+
+    x1_new = bh_data_target['x1'][:M]
+    y1_new = bh_data_target['y1'][:M]
+    x2_new = bh_data_target['x2'][:M]
+    y2_new = bh_data_target['y2'][:M]
+
+    # Calculate RMS for BH1
+    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
+    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
+    r1_new = np.sqrt(x1_new**2 + y1_new**2)
+    r1_max = np.maximum(r1_ref, r1_new)
+
+    # Calculate RMS for BH2
+    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
+    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
+    r2_new = np.sqrt(x2_new**2 + y2_new**2)
+    r2_max = np.maximum(r2_ref, r2_new)
+
+    # Avoid division by zero for BH1
+    valid_mask1 = r1_max > 1e-15
+    if np.sum(valid_mask1) < 10:
+        return None, "Insufficient valid data points for BH1"
+
+    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
+    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+
+    # Avoid division by zero for BH2
+    valid_mask2 = r2_max > 1e-15
+    if np.sum(valid_mask2) < 10:
+        return None, "Insufficient valid data points for BH2"
+
+    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
+    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+
+    # Final RMS is the maximum of BH1 and BH2
+    rms_final = max(rms_bh1, rms_bh2)
+
+    return rms_final, None
+
+
+def analyze_constraint_violation(constraint_data, n_levels=9):
+    """
+    Analyze ADM constraint violation
+    Return maximum constraint violation for Grid Level 0
+    """
+    # Extract Grid Level 0 data (first entry for each time step)
+    level0_data = constraint_data[::n_levels]
+
+    # Calculate maximum absolute value for each constraint
+    results = {
+        'Ham': np.max(np.abs(level0_data[:, 1])),
+        'Px': np.max(np.abs(level0_data[:, 2])),
+        'Py': np.max(np.abs(level0_data[:, 3])),
+        'Pz': np.max(np.abs(level0_data[:, 4])),
+        'Gx': np.max(np.abs(level0_data[:, 5])),
+        'Gy': np.max(np.abs(level0_data[:, 6])),
+        'Gz': np.max(np.abs(level0_data[:, 7]))
+    }
+
+    results['max_violation'] = max(results.values())
+    return results
+
+
+def print_header():
+    """Print report header"""
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "   AMSS-NCKU GW150914 Simulation Regression Test Report" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+
+def print_rms_results(rms_rel, error, threshold=1.0):
+    """Print RMS error results"""
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
+    print("-" * 45)
+
+    if error:
+        print(f"   {Color.RED}Error: {error}{Color.RESET}")
+        return False
+
+    passed = rms_rel < threshold
+
+    print(f"   RMS relative error: {rms_rel:.4f}%")
+    print(f"   Requirement:        < {threshold}%")
+    print(f"   Status:             {get_status_text(passed)}")
+
+    return passed
+
+
+def print_constraint_results(results, threshold=2.0):
+    """Print constraint violation results"""
+    print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
+    print("-" * 45)
+
+    names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
+    for i, name in enumerate(names):
+        print(f"   Max |{name:3}|: {results[name]:.6f}", end="   ")
+        if (i + 1) % 2 == 0: print()
+    if len(names) % 2 != 0: print()
+
+    passed = results['max_violation'] < threshold
+    
+    print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
+    print(f"   Requirement:        < {threshold}")
+    print(f"   Status:             {get_status_text(passed)}")
+
+    return passed
+
+
+def print_summary(rms_passed, constraint_passed):
+    """Print summary"""
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "Verification Summary" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+    all_passed = rms_passed and constraint_passed
+    
+    res_rms = get_status_text(rms_passed)
+    res_con = get_status_text(constraint_passed)
+
+    print(f"   [1] RMS trajectory check:         {res_rms}")
+    print(f"   [2] ADM constraint check:         {res_con}")
+    
+    final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
+    print(f"\n   Overall result: {final_status}")
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET + "\n")
+
+    return all_passed
+
+
+def main():
+    # Determine target (optimized) output directory
+    if len(sys.argv) > 1:
+        target_dir = sys.argv[1]
+    else:
+        script_dir = os.path.dirname(os.path.abspath(__file__))
+        target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
+
+    # Determine reference (baseline) directory
+    script_dir = os.path.dirname(os.path.abspath(__file__))
+    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+
+    # Data file paths
+    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
+    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
+    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
+
+    # Check if files exist
+    if not os.path.exists(bh_file_ref):
+        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
+        sys.exit(1)
+
+    if not os.path.exists(bh_file_target):
+        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Target trajectory file not found: {bh_file_target}")
+        sys.exit(1)
+
+    if not os.path.exists(constraint_file):
+        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
+        sys.exit(1)
+
+    # Print header
+    print_header()
+    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+
+    # Load data
+    bh_data_ref = load_bh_trajectory(bh_file_ref)
+    bh_data_target = load_bh_trajectory(bh_file_target)
+    constraint_data = load_constraint_data(constraint_file)
+
+    # Calculate RMS error
+    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
+    rms_passed = print_rms_results(rms_rel, error)
+
+    # Analyze constraint violation
+    constraint_results = analyze_constraint_violation(constraint_data)
+    constraint_passed = print_constraint_results(constraint_results)
+
+    # Print summary
+    all_passed = print_summary(rms_passed, constraint_passed)
+
+    # Return exit code
+    sys.exit(0 if all_passed else 1)
+
+
+if __name__ == "__main__":
+    main()
--- a/AMSS_NCKU_source/FFT.f90
+++ b/AMSS_NCKU_source/FFT.f90
@@ -37,57 +37,51 @@ close(77)
 end program checkFFT
 #endif

+!-------------
+! Optimized FFT using Intel oneMKL DFTI
+! Mathematical equivalence: Standard DFT definition
+!   Forward (isign=1):  X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
+!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
+! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
 !-------------
 SUBROUTINE four1(dataa,nn,isign)
+use MKL_DFTI
 implicit none
-INTEGER::isign,nn
-double precision,dimension(2*nn)::dataa
-INTEGER::i,istep,j,m,mmax,n
-double precision::tempi,tempr
-DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
-n=2*nn
-j=1
-do i=1,n,2
-  if(j.gt.i)then
-     tempr=dataa(j)
-     tempi=dataa(j+1)
-     dataa(j)=dataa(i)
-     dataa(j+1)=dataa(i+1)
-     dataa(i)=tempr
-     dataa(i+1)=tempi
-  endif
-  m=nn
-1 if ((m.ge.2).and.(j.gt.m)) then
-  j=j-m
-  m=m/2
-goto 1
-  endif
-j=j+m
-enddo
-mmax=2
-2  if (n.gt.mmax) then
-     istep=2*mmax
-     theta=6.28318530717959d0/(isign*mmax)
-     wpr=-2.d0*sin(0.5d0*theta)**2
-     wpi=sin(theta)
-     wr=1.d0
-     wi=0.d0
-     do m=1,mmax,2
-       do i=m,n,istep
-         j=i+mmax
-         tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
-         tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
-         dataa(j)=dataa(i)-tempr
-         dataa(j+1)=dataa(i+1)-tempi
-         dataa(i)=dataa(i)+tempr
-         dataa(i+1)=dataa(i+1)+tempi
-       enddo
-          wtemp=wr
-          wr=wr*wpr-wi*wpi+wr
-          wi=wi*wpr+wtemp*wpi+wi
-     enddo
-mmax=istep
-goto 2
+INTEGER, intent(in) :: isign, nn
+DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
+
+type(DFTI_DESCRIPTOR), pointer :: desc
+integer :: status
+
+! Create DFTI descriptor for 1D complex-to-complex transform
+status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
+if (status /= 0) return
+
+! Set input/output storage as interleaved complex (default)
+status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
+if (status /= 0) then
+   status = DftiFreeDescriptor(desc)
+   return
 endif
+
+! Commit the descriptor
+status = DftiCommitDescriptor(desc)
+if (status /= 0) then
+   status = DftiFreeDescriptor(desc)
+   return
+endif
+
+! Execute FFT based on direction
+if (isign == 1) then
+   ! Forward FFT: exp(-2*pi*i*k*n/N)
+   status = DftiComputeForward(desc, dataa)
+else
+   ! Backward FFT: exp(+2*pi*i*k*n/N)
+   status = DftiComputeBackward(desc, dataa)
+endif
+
+! Free descriptor
+status = DftiFreeDescriptor(desc)
+
 return
 END SUBROUTINE four1
--- a/AMSS_NCKU_source/TwoPunctures.C
+++ b/AMSS_NCKU_source/TwoPunctures.C
--- a/AMSS_NCKU_source/TwoPunctures.h
+++ b/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
@@ -33,7 +32,7 @@ private:
       int npoints_A, npoints_B, npoints_phi;

       double target_M_plus, target_M_minus;
-
+       
       double admMass;

       double adm_tol;
@@ -43,17 +42,32 @@ 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;
+       // 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
       {
@@ -71,28 +85,6 @@ 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 +143,23 @@ 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)
@@ -164,4 +168,4 @@ public:
       void SpecCoef(parameters par, int ivar, double *v, double *cf);
 };

-#endif /* TWO_PUNCTURES_H */
+#endif /* TWO_PUNCTURES_H */
--- a/AMSS_NCKU_source/bssn_rhs.f90
+++ b/AMSS_NCKU_source/bssn_rhs.f90
@@ -83,6 +83,10 @@
  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
  real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz

+! shared work arrays (memory pool) to avoid repeated allocation in subroutines
+  real*8, dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh_work2  ! for fderivs_fh/fdderivs_fh (ghost_width=2)
+  real*8, dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh_work3  ! for kodis_fh/lopsided_fh (ghost_width=3)
+
  real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
  real*8            :: dX, dY, dZ, PI
  real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
@@ -106,7 +110,8 @@
  call getpbh(BHN,Porg,Mass)
 #endif

-!!! sanity check
+!!! sanity check (disabled in production builds for performance)
+#ifdef DEBUG
  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -136,6 +141,7 @@
     gont = 1
     return
  endif
+#endif

  PI = dacos(-ONE)

@@ -149,22 +155,22 @@
  gyy = dyy + ONE
  gzz = dzz + ONE

-  call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
-  call fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev)
-  call fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev)
+  call fderivs_fh(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev,fh_work2)
  
  div_beta = betaxx + betayy + betazz
 
-  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
+  call fderivs_fh(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev,fh_work2)

  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi

-  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
-  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
-  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs_fh(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev,fh_work2)

  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
@@ -282,8 +288,8 @@
          (gupyy * gupzz       + gupyz * gupyz)* Ayz

 ! Right hand side for Gam^i without shift terms...
-  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)
+  call fderivs_fh(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev,fh_work2)

   Gamx_rhs = - TWO * (   Lapx * Rxx +   Lapy * Rxy +   Lapz * Rxz ) + &
        TWO * alpn1 * (                                                &
@@ -312,12 +318,12 @@
                        Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz   + &
                TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )

-  call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
-                X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
-  call fdderivs(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,&
-                X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
-  call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
-                X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
+  call fdderivs_fh(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
+                X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev,fh_work2)
+  call fdderivs_fh(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,&
+                X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev,fh_work2)
+  call fdderivs_fh(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
+                X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev,fh_work2)

  fxx = gxxx + gxyy + gxzz
  fxy = gxyx + gyyy + gyzz
@@ -330,9 +336,9 @@
  Gamza =       gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
          TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )

-  call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
+  call fderivs_fh(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev,fh_work2)
+  call fderivs_fh(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev,fh_work2)

  Gamx_rhs =               Gamx_rhs +  F2o3 *  Gamxa * div_beta        - &
                     Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz  + &
@@ -375,27 +381,27 @@
  gzzz = gxz * Gamxzz + gyz * Gamyzz + gzz * Gamzzz

 !compute Ricci tensor for tilted metric
-   call fdderivs(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,symmetry,Lev)
+   call fdderivs_fh(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,symmetry,Lev,fh_work2)
   Rxx =   gupxx * fxx + gupyy * fyy + gupzz * fzz + &
         ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO

-   call fdderivs(ex,dyy,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,symmetry,Lev)
+   call fdderivs_fh(ex,dyy,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,symmetry,Lev,fh_work2)
   Ryy =   gupxx * fxx + gupyy * fyy + gupzz * fzz + &
         ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO

-   call fdderivs(ex,dzz,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,symmetry,Lev)
+   call fdderivs_fh(ex,dzz,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,symmetry,Lev,fh_work2)
   Rzz =   gupxx * fxx + gupyy * fyy + gupzz * fzz + &
         ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO

-   call fdderivs(ex,gxy,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,ANTI, ANTI,SYM ,symmetry,Lev)
+   call fdderivs_fh(ex,gxy,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,ANTI, ANTI,SYM ,symmetry,Lev,fh_work2)
   Rxy =   gupxx * fxx + gupyy * fyy + gupzz * fzz + &
         ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO

-   call fdderivs(ex,gxz,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,ANTI ,SYM ,ANTI,symmetry,Lev)
+   call fdderivs_fh(ex,gxz,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,ANTI ,SYM ,ANTI,symmetry,Lev,fh_work2)
   Rxz =   gupxx * fxx + gupyy * fyy + gupzz * fzz + &
         ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO

-   call fdderivs(ex,gyz,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,ANTI ,ANTI,symmetry,Lev)
+   call fdderivs_fh(ex,gyz,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,ANTI ,ANTI,symmetry,Lev,fh_work2)
   Ryz =   gupxx * fxx + gupyy * fyy + gupzz * fzz + &
         ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO

@@ -600,7 +606,7 @@
            Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy  + &
            Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
 !covariant second derivative of chi respect to tilted metric
-  call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fdderivs_fh(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev,fh_work2)

  fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
  fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
@@ -626,8 +632,8 @@
  Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO

 ! 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)
+  call fdderivs_fh(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
+                SYM,SYM,SYM,symmetry,Lev,fh_work2)

  gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
  gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
@@ -810,7 +816,7 @@
  betay_rhs = FF*dtSfy
  betaz_rhs = FF*dtSfz

-  call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fderivs_fh(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev,fh_work2)
  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
@@ -822,7 +828,7 @@
  betay_rhs = FF*dtSfy
  betaz_rhs = FF*dtSfz

-  call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fderivs_fh(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev,fh_work2)
  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
@@ -830,7 +836,7 @@
  dtSfy_rhs = Gamy_rhs - reta*dtSfy
  dtSfz_rhs = Gamz_rhs - reta*dtSfz
 #elif (GAUGE == 4)
-  call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fderivs_fh(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev,fh_work2)
  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
@@ -842,7 +848,7 @@
  dtSfy_rhs = ZEO
  dtSfz_rhs = ZEO
 #elif (GAUGE == 5)
-  call fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fderivs_fh(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev,fh_work2)
  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
@@ -945,51 +951,51 @@

 !!!!!!!!!advection term part

-  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_fh(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)

-  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_fh(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)

-  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_fh(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)

-  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_fh(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,fh_work3)
 !!
-  call lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided_fh(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,fh_work3)

 #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)
+  call lopsided_fh(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,fh_work3)
 #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)
+  call lopsided_fh(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,fh_work3)
+  call lopsided_fh(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,fh_work3)
 #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)
+  call kodis_fh(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps,fh_work3)
 #if 0
 #define i 42
 #define j 40
@@ -1003,7 +1009,7 @@ endif
 #undef k
 !!stop
 #endif
-  call kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps)
+  call kodis_fh(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps,fh_work3)
 #if 0
 #define i 42
 #define j 40
@@ -1017,25 +1023,25 @@ endif
 #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)
+  call kodis_fh(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps,fh_work3)

 #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)
+  call kodis_fh(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps,fh_work3)
 #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)
+  call kodis_fh(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps,fh_work3)
+  call kodis_fh(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps,fh_work3)
 #endif
 #endif

@@ -1076,12 +1082,12 @@ endif

 ! 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,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)
+  call fderivs_fh(ex,Axx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0,fh_work2)
+  call fderivs_fh(ex,Axy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0,fh_work2)
+  call fderivs_fh(ex,Axz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0,fh_work2)
+  call fderivs_fh(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0,fh_work2)
+  call fderivs_fh(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0,fh_work2)
+  call fderivs_fh(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0,fh_work2)

  gxxx = gxxx - (  Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz &
                 + Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz) - chix*Axx/chin1
--- a/AMSS_NCKU_source/diff_new.f90
+++ b/AMSS_NCKU_source/diff_new.f90
@@ -1103,6 +1103,103 @@

  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
 !
@@ -1940,6 +2037,162 @@

  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)
+  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
+
+  real*8 :: dX,dY,dZ
+  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
+  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
+
+  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)
+
+  Sdxdx =  ONE /( dX * dX )
+  Sdydy =  ONE /( dY * dY )
+  Sdzdz =  ONE /( dZ * dZ )
+
+  Fdxdx = F1o12 /( dX * dX )
+  Fdydy = F1o12 /( dY * dY )
+  Fdzdz = F1o12 /( dZ * 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
+
+  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)))
+   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))
+   endif
+#endif
+   enddo
+   enddo
+   enddo
+
+  return
+
+  end subroutine fdderivs_fh
+
 #elif (ghost_width == 4)
 ! sixth order code

--- a/AMSS_NCKU_source/enforce_algebra.f90
+++ b/AMSS_NCKU_source/enforce_algebra.f90
@@ -17,62 +17,62 @@
  real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Axx,Axy,Axz
  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, 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)
-
-    lgxx = dxx(i,j,k) + ONE
-    lgyy = dyy(i,j,k) + ONE
-    lgzz = dzz(i,j,k) + ONE
-
-    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)
-
-    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
-
-    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 * 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
+!~~~~~~~> 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, 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)
+
+    lgxx = dxx(i,j,k) + ONE
+    lgyy = dyy(i,j,k) + ONE
+    lgzz = dzz(i,j,k) + ONE
+
+    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)
+
+    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
+
+    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 * 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

  return

@@ -93,72 +93,72 @@
  real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Axx,Axy,Axz
  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, 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)
-
-! 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)
-
-    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
-
-    lscale = ONE / ( lscale ** F1o3 )
-
-    lgxx = lgxx * lscale
-    lgxy = lgxy * lscale
-    lgxz = lgxz * lscale
-    lgyy = lgyy * lscale
-    lgyz = lgyz * lscale
-    lgzz = lgzz * lscale
-
-    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
+!~~~~~~~> 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, 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)
+
+! 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)
+
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
+
+    lscale = ONE / ( lscale ** F1o3 )
+
+    lgxx = lgxx * lscale
+    lgxy = lgxy * lscale
+    lgxz = lgxz * lscale
+    lgyy = lgyy * lscale
+    lgyz = lgyz * lscale
+    lgzz = lgzz * lscale
+
+    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

  return

--- a/AMSS_NCKU_source/fmisc.f90
+++ b/AMSS_NCKU_source/fmisc.f90
@@ -324,7 +324,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+  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)
   enddo
@@ -349,7 +349,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
      funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-1-i,1:extc(2),1:extc(3))*SoA(1)
@@ -377,7 +377,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
   do i=0,ord-1
      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
      funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-1-i,1:extc(2),1:extc(3))*SoA(1)
@@ -883,20 +883,16 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)

  integer::i

-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-   do i=0,ord-1
-      funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
-   enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-   do i=0,ord-1
-      funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
-   enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
-   do i=0,ord-1
-      funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
-   enddo
+  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)
+   enddo
+   do i=0,ord-1
+      funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
+   enddo
+   do i=0,ord-1
+      funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
+   enddo

 end subroutine symmetry_bd

@@ -912,7 +908,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+  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)
      funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-i,1:extc(2),1:extc(3))*SoA(1)
@@ -940,7 +936,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)

  integer::i

-  funcc(1:extc(1),1:extc(2),1:extc(3)) = func
+  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)
      funcc(extc(1)+1+i,1:extc(2),1:extc(3)) = funcc(extc(1)-i,1:extc(2),1:extc(3))*SoA(1)
@@ -1111,355 +1107,162 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
-!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
-#ifndef POLINT6_USE_BARYCENTRIC
-#define POLINT6_USE_BARYCENTRIC 1
-#endif
-
-!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
-  subroutine polint6_neville(xa, ya, x, y, dy)
-  implicit none
-
-  real*8, dimension(6), intent(in) :: xa, ya
-  real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
-
-  integer :: i, m, ns, n_m
-  real*8, dimension(6) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
-
-  c = ya
-  d = ya
-  ho = xa - x
-
-  ns = 1
-  dif = abs(x - xa(1))
-
-  do i = 2, 6
-    dift = abs(x - xa(i))
-    if (dift < dif) then
-      ns = i
-      dif = dift
-    end if
-  end do
-
-  y = ya(ns)
-  ns = ns - 1
-
-  do m = 1, 5
-    n_m = 6 - m
-    do i = 1, n_m
-      hp = ho(i)
-      h  = ho(i+m)
-      den_val = hp - h
-
-      if (den_val == 0.0d0) then
-        write(*,*) 'failure in polint for point',x
-        write(*,*) 'with input points: ',xa
-        stop
-      end if
-
-      den_val = (c(i+1) - d(i)) / den_val
-
-      d(i) = h * den_val
-      c(i) = hp * den_val
-    end do
-
-    if (2 * ns < n_m) then
-      dy = c(ns + 1)
-    else
-      dy = d(ns)
-      ns = ns - 1
-    end if
-    y = y + dy
-  end do
-
-  return
-  end subroutine polint6_neville
-
-!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
-  subroutine polint6_barycentric(xa, ya, x, y, dy)
-  implicit none
-
-  real*8, dimension(6), intent(in) :: xa, ya
-  real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
-
-  integer :: i, j
-  logical :: is_uniform
-  real*8, dimension(6) :: lambda
-  real*8 :: dx, den_i, term, num, den, step, tol
-  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
-
-  do i = 1, 6
-    if (x == xa(i)) then
-      y = ya(i)
-      dy = 0.d0
-      return
-    end if
-  end do
-
-  step = xa(2) - xa(1)
-  is_uniform = (step /= 0.d0)
-  if (is_uniform) then
-    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
-    do i = 3, 6
-      if (abs((xa(i) - xa(i-1)) - step) > tol) then
-        is_uniform = .false.
-        exit
-      end if
-    end do
-  end if
-
-  if (is_uniform) then
-    num = 0.d0
-    den = 0.d0
-    do i = 1, 6
-      term = c_uniform(i) / (x - xa(i))
-      num = num + term * ya(i)
-      den = den + term
-    end do
-    y = num / den
-    dy = 0.d0
-    return
-  end if
-
-  do i = 1, 6
-    den_i = 1.d0
-    do j = 1, 6
-      if (j /= i) then
-        dx = xa(i) - xa(j)
-        if (dx == 0.0d0) then
-          write(*,*) 'failure in polint for point',x
-          write(*,*) 'with input points: ',xa
-          stop
-        end if
-        den_i = den_i * dx
-      end if
-    end do
-    lambda(i) = 1.d0 / den_i
-  end do
-
-  num = 0.d0
-  den = 0.d0
-  do i = 1, 6
-    term = lambda(i) / (x - xa(i))
-    num = num + term * ya(i)
-    den = den + term
-  end do
-
-  y = num / den
-  dy = 0.d0
-
-  return
-  end subroutine polint6_barycentric
-
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
-  subroutine polint(xa, ya, x, y, dy, ordn)
-  implicit none
-
-  integer, intent(in) :: ordn
-  real*8, dimension(ordn), intent(in) :: xa, ya
-  real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
-
-  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
-
-  if (ordn == 6) then
-#if POLINT6_USE_BARYCENTRIC
-    call polint6_barycentric(xa, ya, x, y, dy)
-#else
-    call polint6_neville(xa, ya, x, y, dy)
-#endif
-    return
-  end if
-
-  c = ya
-  d = ya
-  ho = xa - x
-
-  ns = 1
-  dif = abs(x - xa(1))
-
-  do i = 2, ordn
-    dift = abs(x - xa(i))
-    if (dift < dif) then
-      ns = i
-      dif = dift
-    end if
-  end do
-
-  y = ya(ns)
-  ns = ns - 1
-
-  do m = 1, 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)
-    else
-      dy = d(ns)
-      ns = ns - 1
-    end if
-    y = y + dy
-  end do
-
-  return
-  end subroutine polint
-!------------------------------------------------------------------------------
-! Compute Lagrange interpolation basis weights for one target point.
-!------------------------------------------------------------------------------
-!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
-  subroutine polint_lagrange_weights(xa, x, w, ordn)
-  implicit none
-
-  integer, intent(in) :: ordn
-  real*8, dimension(1:ordn), intent(in) :: xa
-  real*8, intent(in) :: x
-  real*8, dimension(1:ordn), intent(out) :: w
-
-  integer :: i, j
-  real*8 :: num, den, dx
-
-  do i = 1, ordn
-    num = 1.d0
-    den = 1.d0
-    do j = 1, ordn
-      if (j /= i) then
-        dx = xa(i) - xa(j)
-        if (dx == 0.0d0) then
-          write(*,*) 'failure in polint for point',x
-          write(*,*) 'with input points: ',xa
-          stop
-        end if
-        num = num * (x - xa(j))
-        den = den * dx
-      end if
-    end do
-    w(i) = num / den
-  end do
-
-  return
-  end subroutine polint_lagrange_weights
-!------------------------------------------------------------------------------
-!
-! interpolation in 2 dimensions, follow yx order
-!
-!------------------------------------------------------------------------------
-  subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
-  implicit none
-
-  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
-  integer  :: i,m
-  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
-
-  m=size(x1a)
-  do i=1,m
-    yntmp=ya(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
-
-  do j=1,ordn
-    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
-  end do
-  call polint(x2a, ymtmp, x2, y, dy, ordn)
-#endif
-
-  return
-  end subroutine polin2
-!------------------------------------------------------------------------------
-!
-! interpolation in 3 dimensions, follow zyx order
-!
-!------------------------------------------------------------------------------
-  subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
-  implicit none
-
-  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
-  integer  :: i,j,m,n
-  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
-  real*8, dimension(ordn) :: yqtmp
-
-  m=size(x1a)
-  n=size(x2a)
-  do i=1,m
-   do j=1,n
-    yqtmp=ya(i,j,:)
-    call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
-   end do
-    yntmp=yatmp(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: i, j, k
-  real*8, dimension(ordn) :: w1, w2
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: yx_sum, x_sum
-
-  call polint_lagrange_weights(x1a, x1, w1, ordn)
-  call polint_lagrange_weights(x2a, x2, w2, ordn)
-
-  do k = 1, ordn
-    yx_sum = 0.d0
-    do j = 1, ordn
-      x_sum = 0.d0
-      do i = 1, ordn
-        x_sum = x_sum + w1(i) * ya(i,j,k)
-      end do
-      yx_sum = yx_sum + w2(j) * x_sum
-    end do
-    ymtmp(k) = yx_sum
-  end do
-
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
-#endif
-
-  return
-  end subroutine polin3
+! common code for cell and vertex
+!------------------------------------------------------------------------------
+! Lagrangian polynomial interpolation
+!------------------------------------------------------------------------------
+
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, m, ns, n_m
+  real*8, dimension(ordn) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, ordn
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, 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)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
+  subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
+  implicit none
+
+  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
+  integer  :: i,m
+  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: yntmp
+
+  m=size(x1a)
+  do i=1,m
+    yntmp=ya(i,:)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+  end do
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do j=1,ordn
+    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
+  end do
+  call polint(x2a, ymtmp, x2, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin2
+!------------------------------------------------------------------------------
+!
+! interpolation in 3 dimensions, follow zyx order
+!
+!------------------------------------------------------------------------------
+  subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
+  implicit none
+
+  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
+  integer  :: i,j,m,n
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: yntmp
+  real*8, dimension(ordn) :: yqtmp
+
+  m=size(x1a)
+  n=size(x2a)
+  do i=1,m
+   do j=1,n
+    yqtmp=ya(i,j,:)
+    call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
+   end do
+    yntmp=yatmp(i,:)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+  end do
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
+#else
+  integer  :: j, k
+  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: ymtmp
+  real*8 :: dy_temp
+
+  do k=1,ordn
+    do j=1,ordn
+      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+    end do
+  end do
+  do k=1,ordn
+    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+  end do
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin3
 !--------------------------------------------------------------------------------------
-! calculate L2norm  
+! calculate L2norm
  subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
                          f,f_out,gw)

@@ -1476,9 +1279,9 @@ end subroutine d2dump
  real*8            :: dX, dY, dZ
  integer::imin,jmin,kmin
  integer::imax,jmax,kmax
-  integer::i,j,k,n_elements
-  real*8, dimension(:), allocatable :: f_flat
-  real*8, external :: DDOT
+  integer::i,j,k,n_elements
+  real*8, dimension(:), allocatable :: f_flat
+  real*8, external :: DDOT

  dX = X(2) - X(1)
  dY = Y(2) - Y(1)
@@ -1502,91 +1305,20 @@ if(dabs(X(1)-xmin) < dX) imin = 1
 if(dabs(Y(1)-ymin) < dY) jmin = 1
 if(dabs(Z(1)-zmin) < dZ) kmin = 1

-  n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-  allocate(f_flat(n_elements))
-  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
-  f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
-  deallocate(f_flat)
+! Optimized with oneMKL BLAS DDOT for dot product
+n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+allocate(f_flat(n_elements))
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
+f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+deallocate(f_flat)

 f_out = f_out*dX*dY*dZ

  return

  end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
-  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
-
-  implicit none
-!~~~~~~> Input parameters:
-  integer,intent(in ):: ex(1:3)
-  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
-  integer,intent(in)::gw
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
-  real*8, intent(out) :: f_out(7)
-!~~~~~~> Other variables:
-
-  real*8            :: dX, dY, dZ
-  integer::imin,jmin,kmin
-  integer::imax,jmax,kmax
-  integer::i,j,k
-  real*8 :: s1,s2,s3,s4,s5,s6,s7
-
-  dX = X(2) - X(1)
-  dY = Y(2) - Y(1)
-  dZ = Z(2) - Z(1)
-
-   imin = gw+1
-   jmin = gw+1
-   kmin = gw+1
-
-   imax = ex(1) - gw
-   jmax = ex(2) - gw
-   kmax = ex(3) - gw
-
-if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
-if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
-if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
-if(dabs(X(1)-xmin) < dX) imin = 1
-if(dabs(Y(1)-ymin) < dY) jmin = 1
-if(dabs(Z(1)-zmin) < dZ) kmin = 1
-
-  s1 = 0.d0
-  s2 = 0.d0
-  s3 = 0.d0
-  s4 = 0.d0
-  s5 = 0.d0
-  s6 = 0.d0
-  s7 = 0.d0
-
-  do k=kmin,kmax
-    do j=jmin,jmax
-!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
-      do i=imin,imax
-        s1 = s1 + f1(i,j,k)*f1(i,j,k)
-        s2 = s2 + f2(i,j,k)*f2(i,j,k)
-        s3 = s3 + f3(i,j,k)*f3(i,j,k)
-        s4 = s4 + f4(i,j,k)*f4(i,j,k)
-        s5 = s5 + f5(i,j,k)*f5(i,j,k)
-        s6 = s6 + f6(i,j,k)*f6(i,j,k)
-        s7 = s7 + f7(i,j,k)*f7(i,j,k)
-      enddo
-    enddo
-  enddo
-
-  f_out(1) = s1*dX*dY*dZ
-  f_out(2) = s2*dX*dY*dZ
-  f_out(3) = s3*dX*dY*dZ
-  f_out(4) = s4*dX*dY*dZ
-  f_out(5) = s5*dX*dY*dZ
-  f_out(6) = s6*dX*dY*dZ
-  f_out(7) = s7*dX*dY*dZ
-
-  return
-
-  end subroutine l2normhelper7
-!--------------------------------------------------------------------------------------
-! calculate L2norm especially for shell Blocks
+!--------------------------------------------------------------------------------------
+! calculate L2norm especially for shell Blocks
  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
                          f,f_out,gw,ogw,Symmetry)

@@ -1603,9 +1335,9 @@ if(dabs(Z(1)-zmin) < dZ) kmin = 1
  real*8            :: dX, dY, dZ
  integer::imin,jmin,kmin
  integer::imax,jmax,kmax
-  integer::i,j,k,n_elements
-  real*8, dimension(:), allocatable :: f_flat
-  real*8, external :: DDOT
+  integer::i,j,k,n_elements
+  real*8, dimension(:), allocatable :: f_flat
+  real*8, external :: DDOT

  real*8 :: PIo4

@@ -1668,11 +1400,12 @@ if(Symmetry==2)then
  if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif

-  n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-  allocate(f_flat(n_elements))
-  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
-  f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
-  deallocate(f_flat)
+! Optimized with oneMKL BLAS DDOT for dot product
+n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+allocate(f_flat(n_elements))
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
+f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+deallocate(f_flat)

 f_out = f_out*dX*dY*dZ

@@ -1699,9 +1432,9 @@ f_out = f_out*dX*dY*dZ
  real*8            :: dX, dY, dZ
  integer::imin,jmin,kmin
  integer::imax,jmax,kmax
-  integer::i,j,k
-  real*8, dimension(:), allocatable :: f_flat
-  real*8, external :: DDOT
+  integer::i,j,k
+  real*8, dimension(:), allocatable :: f_flat
+  real*8, external :: DDOT

  real*8 :: PIo4

@@ -1764,11 +1497,12 @@ if(Symmetry==2)then
  if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif

-Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-  allocate(f_flat(Nout))
-  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
-  f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
-  deallocate(f_flat)
+! Optimized with oneMKL BLAS DDOT for dot product
+Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+allocate(f_flat(Nout))
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
+f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
+deallocate(f_flat)

  return

@@ -1869,12 +1603,9 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
 !       ^
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3

-  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-  integer :: i,j,k
-
-  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
-    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
-  end do
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
+
+  fout = C1*f1+C2*f2+C3*f3

  return

@@ -1968,8 +1699,8 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
  real*8, dimension(ORDN,ORDN,ORDN) :: ya
  real*8, dimension(ORDN,ORDN) :: tmp2
  real*8, dimension(ORDN) :: tmp1
-  real*8, dimension(3) :: SoAh
-  real*8, external :: DDOT
+  real*8, dimension(3) :: SoAh
+  real*8, external :: DDOT

 ! +1 because c++ gives 0 for first point
  cxB = inds+1  
@@ -2005,17 +1736,21 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
     ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),cxB(3):cxT(3))
  endif 

+  ! Optimized with BLAS operations for better performance
+  ! First dimension: z-direction weighted sum
  tmp2=0
  do m=1,ORDN
    tmp2 = tmp2 + coef(2*ORDN+m)*ya(:,:,m)
  enddo

+  ! Second dimension: y-direction weighted sum
  tmp1=0
  do m=1,ORDN
    tmp1 = tmp1 + coef(ORDN+m)*tmp2(:,m)
  enddo

-  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
+  ! Third dimension: x-direction weighted sum using BLAS DDOT
+  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)

  return

@@ -2044,8 +1779,8 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
  integer,dimension(2) :: cxB,cxT
  real*8, dimension(ORDN,ORDN) :: ya
  real*8, dimension(ORDN) :: tmp1
-  real*8, dimension(2) :: SoAh
-  real*8, external :: DDOT
+  real*8, dimension(2) :: SoAh
+  real*8, external :: DDOT

 ! +1 because c++ gives 0 for first point
  cxB = inds(1:2)+1  
@@ -2075,12 +1810,14 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
     ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),inds(3))
  endif 

+  ! Optimized with BLAS operations
  tmp1=0
  do m=1,ORDN
    tmp1 = tmp1 + coef(ORDN+m)*ya(:,m)
  enddo

-  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
+  ! Use BLAS DDOT for final weighted sum
+  f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)

  return

@@ -2106,12 +1843,12 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
 !~~~~~~> Other parameters:

  real*8, dimension(-ORDN+1:ex(1)+ORDN,-ORDN+1:ex(2)+ORDN,ex(3)) :: fh
-  integer :: m
-  integer :: cxB,cxT
-  real*8, dimension(ORDN) :: ya
-  real*8 :: SoAh
-  integer,dimension(3) :: inds
-  real*8, external :: DDOT
+  integer :: m
+  integer :: cxB,cxT
+  real*8, dimension(ORDN) :: ya
+  real*8 :: SoAh
+  integer,dimension(3) :: inds
+  real*8, external :: DDOT

 ! +1 because c++ gives 0 for first point
  inds = indsi + 1
@@ -2172,7 +1909,8 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
          write(*,*)"error in global_interpind1d, not recognized dumyd = ",dumyd
  endif

-  f_int = DDOT(ORDN, coef, 1, ya, 1)
+  ! Optimized with BLAS DDOT for weighted sum
+  f_int = DDOT(ORDN, coef, 1, ya, 1)

  return

@@ -2404,32 +2142,38 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)

  end function fWigner_d_function
 !----------------------------------
+! Optimized factorial function using lookup table for small N
+! and log-gamma for large N to avoid overflow
  function ffact(N) result(gont)
  implicit none
  integer,intent(in) :: N

-  real*8 :: gont
-
-  integer :: i
-  real*8, parameter, dimension(0:20) :: fact_table = [ &
-    1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 120.d0, 720.d0, 5040.d0, 40320.d0, &
-    362880.d0, 3628800.d0, 39916800.d0, 479001600.d0, 6227020800.d0, &
-    87178291200.d0, 1307674368000.d0, 20922789888000.d0, &
-    355687428096000.d0, 6402373705728000.d0, 121645100408832000.d0, &
-    2432902008176640000.d0 ]
+  real*8 :: gont
+  integer :: i
+
+  ! Lookup table for factorials 0! to 20! (precomputed)
+  real*8, parameter, dimension(0:20) :: fact_table = [ &
+    1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 120.d0, 720.d0, 5040.d0, 40320.d0, &
+    362880.d0, 3628800.d0, 39916800.d0, 479001600.d0, 6227020800.d0, &
+    87178291200.d0, 1307674368000.d0, 20922789888000.d0, &
+    355687428096000.d0, 6402373705728000.d0, 121645100408832000.d0, &
+    2432902008176640000.d0 ]

 ! sanity check
-  if(N < 0)then
-     write(*,*) "ffact: error input for factorial"
-     gont = 1.d0
-     return
-  endif
-
-  if(N <= 20)then
-     gont = fact_table(N)
-  else
-     gont = exp(log_gamma(dble(N+1)))
-  endif
+  if(N < 0)then
+     write(*,*) "ffact: error input for factorial"
+     gont = 1.d0
+     return
+  endif
+
+  ! Use lookup table for small N (fast path)
+  if(N <= 20)then
+     gont = fact_table(N)
+  else
+     ! Use log-gamma function for large N: N! = exp(log_gamma(N+1))
+     ! This avoids overflow and is computed efficiently
+     gont = exp(log_gamma(dble(N+1)))
+  endif

  return

--- a/AMSS_NCKU_source/fmisc.h
+++ b/AMSS_NCKU_source/fmisc.h
@@ -12,10 +12,9 @@
 #define f_global_interpind global_interpind
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
-#define f_l2normhelper l2normhelper
-#define f_l2normhelper7 l2normhelper7
-#define f_l2normhelper_sh l2normhelper_sh
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms
+#define f_l2normhelper l2normhelper
+#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
 #define f_average3 average3
 #define f_average2 average2
@@ -42,10 +41,9 @@
 #define f_global_interpind GLOBAL_INTERPIND
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
-#define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper7 L2NORMHELPER7
-#define f_l2normhelper_sh L2NORMHELPER_SH
-#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
+#define f_l2normhelper L2NORMHELPER
+#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
 #define f_average3 AVERAGE3
 #define f_average2 AVERAGE2
@@ -72,10 +70,9 @@
 #define f_global_interpind global_interpind_
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
-#define f_l2normhelper l2normhelper_
-#define f_l2normhelper7 l2normhelper7_
-#define f_l2normhelper_sh l2normhelper_sh_
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
+#define f_l2normhelper l2normhelper_
+#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
 #define f_average3 average3_
 #define f_average2 average2_
@@ -159,30 +156,21 @@ extern "C"
 							  int *, double *, int &, int &);
 }

-extern "C"
-{
-	void f_l2normhelper(int *, double *, double *, double *,
-						double &, double &, double &,
-						double &, double &, double &,
-						double *, double &, int &);
-}
-
-extern "C"
-{
-	void f_l2normhelper7(int *, double *, double *, double *,
-						 double &, double &, double &,
-						 double &, double &, double &,
-						 double *, double *, double *, double *,
-						 double *, double *, double *, double *, int &);
-}
-
-extern "C"
-{
-	void f_l2normhelper_sh(int *, double *, double *, double *,
-						   double &, double &, double &,
-						   double &, double &, double &,
-						   double *, double &, int &, int &, int &);
-}
+extern "C"
+{
+	void f_l2normhelper(int *, double *, double *, double *,
+						double &, double &, double &,
+						double &, double &, double &,
+						double *, double &, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper_sh(int *, double *, double *, double *,
+						   double &, double &, double &,
+						   double &, double &, double &,
+						   double *, double &, int &, int &, int &);
+}

 extern "C"
 {
--- a/AMSS_NCKU_source/gaussj.C
+++ b/AMSS_NCKU_source/gaussj.C
@@ -16,115 +16,66 @@ using namespace std;
 #include <string.h>
 #include <math.h>
 #endif
-/* Linear equation solution by Gauss-Jordan elimination.
+
+// Intel oneMKL LAPACK interface
+#include <mkl_lapacke.h>
+/* Linear equation solution using Intel oneMKL LAPACK.
 a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
 containing the right-hand side vectors. On output a is
 replaced by its matrix inverse, and b is replaced by the
-corresponding set of solution vectors */
+corresponding set of solution vectors.
+
+Mathematical equivalence:
+  Solves: A * x = b  =>  x = A^(-1) * b
+  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
+  within numerical precision. */

 int gaussj(double *a, double *b, int n)
 {
-  double swap;
+  // Allocate pivot array and workspace
+  lapack_int *ipiv = new lapack_int[n];
+  lapack_int info;

-  int *indxc, *indxr, *ipiv;
-  indxc = new int[n];
-  indxr = new int[n];
-  ipiv = new int[n];
-
-  int i, icol, irow, j, k, l, ll;
-  double big, dum, pivinv, temp;
-
-  for (j = 0; j < n; j++)
-    ipiv[j] = 0;
-  for (i = 0; i < n; i++)
-  {
-    big = 0.0;
-    for (j = 0; j < n; j++)
-      if (ipiv[j] != 1)
-        for (k = 0; k < n; k++)
-        {
-          if (ipiv[k] == 0)
-          {
-            if (fabs(a[j * n + k]) >= big)
-            {
-              big = fabs(a[j * n + k]);
-              irow = j;
-              icol = k;
-            }
-          }
-          else if (ipiv[k] > 1)
-          {
-            cout << "gaussj: Singular Matrix-1" << endl;
-            for (int ii = 0; ii < n; ii++)
-            {
-              for (int jj = 0; jj < n; jj++)
-                cout << a[ii * n + jj] << " ";
-              cout << endl;
-            }
-            return 1; // error return
-          }
-        }
-
-    ipiv[icol] = ipiv[icol] + 1;
-    if (irow != icol)
-    {
-      for (l = 0; l < n; l++)
-      {
-        swap = a[irow * n + l];
-        a[irow * n + l] = a[icol * n + l];
-        a[icol * n + l] = swap;
-      }
-
-      swap = b[irow];
-      b[irow] = b[icol];
-      b[icol] = swap;
-    }
-
-    indxr[i] = irow;
-    indxc[i] = icol;
-
-    if (a[icol * n + icol] == 0.0)
-    {
-      cout << "gaussj: Singular Matrix-2" << endl;
-      for (int ii = 0; ii < n; ii++)
-      {
-        for (int jj = 0; jj < n; jj++)
-          cout << a[ii * n + jj] << " ";
-        cout << endl;
-      }
-      return 1; // error return
-    }
-
-    pivinv = 1.0 / a[icol * n + icol];
-    a[icol * n + icol] = 1.0;
-    for (l = 0; l < n; l++)
-      a[icol * n + l] *= pivinv;
-    b[icol] *= pivinv;
-    for (ll = 0; ll < n; ll++)
-      if (ll != icol)
-      {
-        dum = a[ll * n + icol];
-        a[ll * n + icol] = 0.0;
-        for (l = 0; l < n; l++)
-          a[ll * n + l] -= a[icol * n + l] * dum;
-        b[ll] -= b[icol] * dum;
-      }
+  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
+  double *a_copy = new double[n * n];
+  for (int i = 0; i < n * n; i++) {
+    a_copy[i] = a[i];
  }

-  for (l = n - 1; l >= 0; l--)
-  {
-    if (indxr[l] != indxc[l])
-      for (k = 0; k < n; k++)
-      {
-        swap = a[k * n + indxr[l]];
-        a[k * n + indxr[l]] = a[k * n + indxc[l]];
-        a[k * n + indxc[l]] = swap;
-      }
+  // Step 1: Solve linear system A*x = b using LU decomposition
+  // LAPACKE_dgesv uses column-major by default, but we use row-major
+  info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  // Step 2: Compute matrix inverse A^(-1) using LU factorization
+  // First do LU factorization of original matrix a
+  info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  // Then compute inverse from LU factorization
+  info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
  }

-  delete[] indxc;
-  delete[] indxr;
  delete[] ipiv;
+  delete[] a_copy;

  return 0;
 }
--- a/AMSS_NCKU_source/ilucg.f90
+++ b/AMSS_NCKU_source/ilucg.f90
@@ -512,11 +512,10 @@
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION V(N),W(N)
 !     SUBROUTINE TO COMPUTE DOUBLE PRECISION VECTOR DOT PRODUCT.
+!     Optimized using Intel oneMKL BLAS ddot
+!     Mathematical equivalence: DGVV = sum_{i=1}^{N} V(i)*W(i)

-      SUM = 0.0D0
-            DO 10 I = 1,N
-            SUM = SUM + V(I)*W(I)
-10          CONTINUE
-      DGVV = SUM
+      DOUBLE PRECISION, EXTERNAL :: DDOT
+      DGVV = DDOT(N, V, 1, W, 1)
      RETURN
      END
--- a/AMSS_NCKU_source/kodiss.f90
+++ b/AMSS_NCKU_source/kodiss.f90
@@ -215,6 +215,99 @@ 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
 !------------------------------------------------------------------------------------------------------------------------------
--- a/AMSS_NCKU_source/lopsidediff.f90
+++ b/AMSS_NCKU_source/lopsidediff.f90
@@ -487,6 +487,160 @@ 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
--- a/AMSS_NCKU_source/macrodef.h
+++ b/AMSS_NCKU_source/macrodef.h
@@ -2,7 +2,7 @@
 #ifndef MICRODEF_H
 #define MICRODEF_H

-#include "macrodef.fh"
+#include "macrodef.fh"

 // application parameters

--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -1,25 +1,11 @@
-
-
-include makefile.inc
-
-## polint(ordn=6) kernel selector:
-##   1 (default): barycentric fast path
-##   0          : fallback to Neville path
-POLINT6_USE_BARY ?= 1
-POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
-
-ARCH_OPT = -march=x86-64-v4
-CXXAPPFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-TP_OPTFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-
-.SUFFIXES: .o .f90 .C .for .cu
-
-.f90.o:
-	$(f90) $(f90appflags) -c $< -o $@
+
+
+include makefile.inc
+
+.SUFFIXES: .o .f90 .C .for .cu
+
+.f90.o:
+	$(f90) $(f90appflags) -c $< -o $@

 .C.o:
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
@@ -27,14 +13,8 @@ TP_OPTFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
 .for.o:
 	$(f77) -c $< -o $@

-.cu.o:
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
-
-TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
-
-TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+.cu.o:
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)

 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
@@ -115,8 +95,8 @@ ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
 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)
+TwoPunctureABE: $(TwoPunctureFILES)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)

 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -1,32 +1,30 @@
-
 ## GCC version (commented out)
 ## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
 ## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
 ## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran

-## Intel oneAPI version with oneMKL
+## Intel oneAPI version with oneMKL (Optimized for performance)
 filein  = -I/usr/include/ -I${MKLROOT}/include

-## Use sequential oneMKL to avoid introducing extra OpenMP behavior into ABE.
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
-
-## Optional Intel oneTBB allocator, kept aligned with main's build environment.
-USE_TBBMALLOC ?= 1
-TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
-ifneq ($(wildcard $(TBBMALLOC_SO)),)
-TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
-else
-TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
-endif
-ifeq ($(USE_TBBMALLOC),1)
-LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
-endif
+## Using sequential MKL (OpenMP disabled for better single-threaded performance)
+## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl

+## 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 -ipo \
+               -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
+               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx
+CLINKER      = mpiicpx 

 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -11,6 +11,18 @@
 import AMSS_NCKU_Input as input_data
 import subprocess

+## 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 16-47,64-95"
+#NUMACTL_CPU_BIND = "taskset -c 0-111"
+
+## Build parallelism configuration
+## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
+## Set make -j to utilize available cores for faster builds
+BUILD_JOBS = 64
+

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

@@ -26,11 +38,11 @@ def makefile_ABE():
    print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
    print(                                                        )

-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
    if (input_data.GPU_Calculation == "no"):
-        makefile_command  = "make -j96" + " ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
    elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = "make -j4" + " ABEGPU"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
    else:
        print( " CPU/GPU numerical calculation setting is wrong " )
        print(                                                    )
@@ -67,8 +79,8 @@ def makefile_TwoPunctureABE():
    print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
    print(                                                            )
    
-    ## Build command
-    makefile_command = "make" + " TwoPunctureABE"
+    ## Build command with CPU binding to nohz_full cores
+    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"

    ## Execute the command with subprocess.Popen and stream output
    makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True) 
@@ -105,10 +117,10 @@ def run_ABE():
    ## Define the command to run; cast other values to strings as needed
    
    if (input_data.GPU_Calculation == "no"):
-        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
        mpi_command_outfile = "ABE_out.log"
    elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
        mpi_command_outfile = "ABEGPU_out.log"
 
    ## Execute the MPI command and stream output
@@ -147,7 +159,7 @@ def run_TwoPunctureABE():
    print(                                                          )
    
    ## Define the command to run
-    TwoPuncture_command         = "./TwoPunctureABE"
+    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
    TwoPuncture_command_outfile = "TwoPunctureABE_out.log"

    ## Execute the command with subprocess.Popen and stream output
--- a/parallel_plot_helper.py
+++ b/parallel_plot_helper.py
@@ -1,12 +0,0 @@
-import multiprocessing
-
-
-def run_plot_task(task):
-    func, args = task
-    return func(*args)
-
-
-def run_plot_tasks_parallel(plot_tasks):
-    ctx = multiprocessing.get_context('fork')
-    with ctx.Pool() as pool:
-        pool.map(run_plot_task, plot_tasks)
--- a/plot_GW_strain_amplitude_xiaoqu.py
+++ b/plot_GW_strain_amplitude_xiaoqu.py
@@ -8,13 +8,11 @@
 ##
 #################################################

-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
+import numpy                               ## numpy for array operations
+import scipy                               ## scipy for interpolation and signal processing
+import math
+import matplotlib.pyplot    as     plt     ## matplotlib for plotting
+import os                                  ## os for system/file operations

 import AMSS_NCKU_Input as input_data

--- a/plot_binary_data.py
+++ b/plot_binary_data.py
@@ -6,22 +6,17 @@
 ## Author: Xiaoqu
 ## Dates: 2024/10/01 --- 2025/09/14
 ##
-#################################################
-
-## Restrict OpenMP to one thread per process so that parallel
-## subprocess plotting does not multiply BLAS thread counts.
-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 numpy
+import scipy
+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


 #########################################################################################
@@ -97,9 +92,9 @@ def plot_binary_data( filename, binary_outdir, figure_outdir ):



-####################################################################################
-
-# Plot a single binary dataset (2D slices and 3D surface)
+####################################################################################
+
+# Plot a single binary dataset (2D slices and 3D surface)

 def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):

@@ -193,15 +188,7 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
    plt.savefig( os.path.join(figure_surfaceplot_outdir, figure_title + " time = " + str(time) + " surface_plot.pdf") )   # save figure
    plt.close()

-    return
-
-####################################################################################
-
-## Allow standalone subprocess execution for parallel binary-data plotting.
-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])
+    return
+
+####################################################################################

--- a/plot_xiaoqu.py
+++ b/plot_xiaoqu.py
@@ -6,20 +6,15 @@
 ## 2024/10/01 --- 2025/09/14
 ##
 #################################################
-
-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
-import os                                  ## operating system utilities
-
-import plot_binary_data
-import AMSS_NCKU_Input as input_data
-import subprocess
-import sys
-import multiprocessing
+
+import numpy                               ## numpy for array operations
+import matplotlib.pyplot    as     plt     ## matplotlib for plotting
+from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
+import glob
+import os                                  ## operating system utilities
+
+import plot_binary_data
+import AMSS_NCKU_Input as input_data

 # plt.rcParams['text.usetex'] = True  ## enable LaTeX fonts in plots

@@ -55,37 +50,13 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
        file_list.append(x)
        print(x)

-    ## Plot each file in parallel using subprocesses.
-    ## Each subprocess starts with BLAS thread limits in plot_binary_data.py.
-    script = os.path.join( os.path.dirname(__file__), "plot_binary_data.py" )
-    max_workers = min( multiprocessing.cpu_count(), len(file_list) ) if file_list else 0
-
-    running = []
-    failed  = []
-    for filename in file_list:
-        print(filename)
-        proc = subprocess.Popen(
-            [sys.executable, script, filename, binary_outdir, figure_outdir],
-        )
-        running.append( (proc, filename) )
-        if len(running) >= max_workers:
-            p, fn = running.pop(0)
-            p.wait()
-            if p.returncode != 0:
-                failed.append(fn)
-
-    for p, fn in running:
-        p.wait()
-        if p.returncode != 0:
-            failed.append(fn)
-
-    if failed:
-        print( " WARNING: the following binary data plots failed:" )
-        for fn in failed:
-            print( "   ", fn )
-
-    print(                        )
-    print( " Binary Data Plot Has been Finished " )
+    ## Plot each file in the list
+    for filename in file_list:
+        print(filename)
+        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
+
+    print(                        )
+    print( " Binary Data Plot Has been Finished " )
    print(                                        )

    return
Author	SHA1	Message	Date
CGH0S7	6796384bf4	taskset setting updated	2026-02-07 22:24:02 +08:00
CGH0S7	c974a88d6d	Pool fh work arrays in compute_rhs_bssn to eliminate allocation churn Add _fh variants of fderivs, fdderivs, kodis, and lopsided that accept a caller-provided fh work array instead of allocating one internally. Declare two shared work arrays in compute_rhs_bssn (fh_work2 for symmetry_bd(2) callers, fh_work3 for symmetry_bd(3) callers) and pass them to all ~84 subroutine calls, eliminating ~77 redundant automatic array allocations (~591 MB churn per RHS call, ~2.3 GB per timestep). Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-07 21:49:12 +08:00
CGH0S7	09ffdb553d	Eliminate hot-path heap allocations in TwoPunctures spectral solver Pre-allocate workspace buffers as class members to remove ~8M malloc/free pairs per Newton iteration from LineRelax, ThomasAlgorithm, JFD_times_dv, J_times_dv, chebft_Zeros, fourft, Derivatives_AB3, and F_of_v. Rewrite ThomasAlgorithm to operate in-place on input arrays. Results are bit-identical; no algorithmic changes. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 21:20:35 +08:00
CGH0S7	699e443c7a	Optimize polint/polin2/polin3 interpolation for cache locality Changes: - polint: Rewrite Neville algorithm from array-slice operations to scalar loop. Mathematically identical, avoids temporary array allocations for den(1:n-m) slices. (Credit: yx-fmisc branch) - polin2: Swap interpolation order so inner loop accesses ya(:,j) (contiguous in Fortran column-major) instead of ya(i,:) (strided). Tensor product interpolation is commutative; all call sites pass identical coordinate arrays for all dimensions. - polin3: Swap interpolation order to process contiguous first dimension first: ya(:,j,k) -> yatmp(:,k) -> ymtmp(:). Same commutativity argument as polin2. Compile-time safety switch: -DPOLINT_LEGACY_ORDER restores original dimension ordering Default (no flag): uses optimized contiguous-memory ordering Usage: # Production (optimized order): make clean && make -j ABE # Fallback if results differ (original order): Add -DPOLINT_LEGACY_ORDER to f90appflags in makefile.inc Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 19:00:35 +08:00
CGH0S7	24bfa44911	Disable NaN sanity check in bssn_rhs.f90 for production builds Wrap the NaN sanity check (21 sum() full-array traversals per RHS call) with #ifdef DEBUG so it is compiled out in production builds. This eliminates 84 redundant full-array scans per timestep (21 per RHS call × 4 RK4 substages) that serve no purpose when input data is valid. Usage: - Production build (default): NaN check is disabled, no changes needed. - Debug build: add -DDEBUG to f90appflags in makefile.inc, e.g. f90appflags = -O3 ... -DDEBUG -fpp ... to re-enable the NaN sanity check. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 18:36:29 +08:00
CGH0S7	6738854a9d	Compiler-level and hot-path optimizations for GW150914 - makefile.inc: add -ipo (interprocedural optimization) and -align array64byte (64-byte array alignment for vectorization) - fmisc.f90: remove redundant funcc=0.d0 zeroing from symmetry_bd, symmetry_tbd, symmetry_stbd (~328+ full-array memsets eliminated per timestep) - enforce_algebra.f90: rewrite enforce_ag and enforce_ga as point-wise loops, replacing 12 stack-allocated 3D temporary arrays with scalar locals for better cache locality All changes are mathematically equivalent — no algorithmic modifications. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>	2026-02-06 17:13:39 +08:00
CGH0S7	223ec17a54	input updated	2026-02-06 13:57:48 +08:00
CGH0S7	26c81d8e81	makefile updated	2026-01-19 23:53:16 +08:00
CGH0S7	9deeda9831	Refactor verification method and optimize numerical kernels with oneMKL BLAS This commit transitions the verification approach from post-Newtonian theory comparison to regression testing against baseline simulations, and optimizes critical numerical kernels using Intel oneMKL BLAS routines. Verification Changes: - Replace PN theory-based RMS calculation with trajectory-based comparison - Compare optimized results against baseline (GW150914-origin) on XY plane - Compute RMS independently for BH1 and BH2, report maximum as final metric - Update documentation to reflect new regression test methodology Performance Optimizations: - Replace manual vector operations with oneMKL BLAS routines: * norm2() and scalarproduct() now use cblas_dnrm2/cblas_ddot (C++) * L2 norm calculations use DDOT for dot products (Fortran) * Interpolation weighted sums use DDOT (Fortran) - Disable OpenMP threading (switch to sequential MKL) for better performance Build Configuration: - Switch from lmkl_intel_thread to lmkl_sequential - Remove -qopenmp flags from compiler options - Maintain aggressive optimization flags (-O3, -xHost, -fp-model fast=2, -fma) Other Changes: - Update .gitignore for GW150914-origin, docs, and temporary files	2026-01-18 14:25:21 +08:00
CGH0S7	3a7bce3af2	Update Intel oneAPI configuration and CPU binding settings - Update makefile.inc with Intel oneAPI compiler flags and oneMKL linking - Configure taskset CPU binding to use nohz_full cores (4-55, 60-111) - Set build parallelism to 104 jobs for faster compilation - Update MPI process count to 48 in input configuration	2026-01-17 20:41:02 +08:00
CGH0S7	c6945bb095	Rename verify_accuracy.py to AMSS_NCKU_Verify_ASC26.py and improve visual output	2026-01-17 14:54:33 +08:00
CGH0S7	0d24f1503c	Add accuracy verification script for GW150914 simulation - Verify RMS error < 1% (black hole trajectory vs. post-Newtonian theory) - Verify ADM constraint violation < 2 (Grid Level 0) - Return exit code 0 on pass, 1 on fail Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>	2026-01-17 00:37:30 +08:00
CGH0S7	cb252f5ea2	Optimize numerical algorithms with Intel oneMKL - FFT.f90: Replace hand-written Cooley-Tukey FFT with oneMKL DFTI - ilucg.f90: Replace manual dot product loop with BLAS DDOT - gaussj.C: Replace Gauss-Jordan elimination with LAPACK dgesv/dgetri - makefile.inc: Add MKL include paths and library linking All optimizations maintain mathematical equivalence and numerical precision.	2026-01-16 10:58:11 +08:00
CGH0S7	7a76cbaafd	Add numactl CPU binding to avoid cores 0-3 and 56-59 Bind all computation processes (ABE, ABEGPU, TwoPunctureABE) to CPU cores 4-55 and 60-111 using numactl --physcpubind to prevent interference with system processes on reserved cores.	2026-01-16 10:24:46 +08:00
CGH0S7	57a7376044	Switch compiler toolchain from GCC to Intel oneAPI - makefile.inc: Replace GCC compilers with Intel oneAPI - C/C++: gcc/g++ -> icx/icpx - Fortran: gfortran -> ifx - MPI linker: mpic++ -> mpiicpx - Update LDLIBS and compiler flags accordingly - macrodef.h: Fix include path (microdef.fh -> macrodef.fh) Requires: source /home/intel/oneapi/setvars.sh before build	2026-01-15 16:32:12 +08:00