Trigger-Discipline: parallelize result plotting

Trigger-Discipline: port TwoPuncture OpenMP optimizations
.gitignore updated
2026-04-24 10:04:57 +08:00 · 2026-04-24 09:25:13 +08:00 · 2026-04-24 09:10:12 +08:00 · 2026-04-24 09:09:50 +08:00 · 2026-02-05 19:53:55 +08:00
23 changed files with 1099 additions and 1710 deletions
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,5 @@
 __pycache__
 GW150914
-GW150914-origin
-docs
-*.tmp
-
+GW150914*
+.codex
+docs/
--- a/AMSS_NCKU_Program.py
+++ b/AMSS_NCKU_Program.py
@@ -8,10 +8,12 @@
 ##
 ##################################################################

+
+##################################################################
+
 ## Guard against re-execution by multiprocessing child processes.
 ## Without this, using 'spawn' or 'forkserver' context would cause every
-## worker to re-run the entire script, spawning exponentially more
-## workers (fork bomb).
+## worker to re-run the entire script.
 if __name__ != '__main__':
    import sys as _sys
    _sys.exit(0)
--- a/AMSS_NCKU_Verify_ASC26.py
+++ b/AMSS_NCKU_Verify_ASC26.py
@@ -1,279 +0,0 @@
-#!/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
@@ -37,51 +37,57 @@ 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, 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
+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
 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/Parallel.C
+++ b/AMSS_NCKU_source/Parallel.C
@@ -3756,358 +3756,6 @@ void Parallel::Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
  delete[] transfer_src;
  delete[] transfer_dst;
 }
-//
-// Async Sync: split into SyncBegin (initiate MPI) and SyncEnd (wait + unpack)
-// This allows overlapping MPI communication with computation.
-//
-static void transfer_begin(Parallel::TransferState *ts)
-{
-  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  int cpusize = ts->cpusize;
-
-  ts->reqs = new MPI_Request[2 * cpusize];
-  ts->stats = new MPI_Status[2 * cpusize];
-  ts->req_no = 0;
-  ts->send_data = new double *[cpusize];
-  ts->rec_data = new double *[cpusize];
-  int length;
-
-  for (int node = 0; node < cpusize; node++)
-  {
-    ts->send_data[node] = ts->rec_data[node] = 0;
-    if (node == myrank)
-    {
-      // Local copy: pack then immediately unpack (no MPI needed)
-      if ((length = Parallel::data_packer(0, ts->transfer_src[myrank], ts->transfer_dst[myrank],
-                                          node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry)))
-      {
-        double *local_data = new double[length];
-        if (!local_data)
-        {
-          cout << "out of memory in transfer_begin, local copy" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        Parallel::data_packer(local_data, ts->transfer_src[myrank], ts->transfer_dst[myrank],
-                              node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry);
-        Parallel::data_packer(local_data, ts->transfer_src[node], ts->transfer_dst[node],
-                              node, UNPACK, ts->VarList1, ts->VarList2, ts->Symmetry);
-        delete[] local_data;
-      }
-    }
-    else
-    {
-      // send from this cpu to cpu#node
-      if ((length = Parallel::data_packer(0, ts->transfer_src[myrank], ts->transfer_dst[myrank],
-                                          node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry)))
-      {
-        ts->send_data[node] = new double[length];
-        if (!ts->send_data[node])
-        {
-          cout << "out of memory in transfer_begin, send" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        Parallel::data_packer(ts->send_data[node], ts->transfer_src[myrank], ts->transfer_dst[myrank],
-                              node, PACK, ts->VarList1, ts->VarList2, ts->Symmetry);
-        MPI_Isend((void *)ts->send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD,
-                  ts->reqs + ts->req_no++);
-      }
-      // receive from cpu#node to this cpu
-      if ((length = Parallel::data_packer(0, ts->transfer_src[node], ts->transfer_dst[node],
-                                          node, UNPACK, ts->VarList1, ts->VarList2, ts->Symmetry)))
-      {
-        ts->rec_data[node] = new double[length];
-        if (!ts->rec_data[node])
-        {
-          cout << "out of memory in transfer_begin, recv" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        MPI_Irecv((void *)ts->rec_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD,
-                  ts->reqs + ts->req_no++);
-      }
-    }
-  }
-  // NOTE: MPI_Waitall is NOT called here - that happens in transfer_end
-}
-//
-static void transfer_end(Parallel::TransferState *ts)
-{
-  // Wait for all pending MPI operations
-  MPI_Waitall(ts->req_no, ts->reqs, ts->stats);
-
-  // Unpack received data from remote ranks
-  for (int node = 0; node < ts->cpusize; node++)
-    if (ts->rec_data[node])
-      Parallel::data_packer(ts->rec_data[node], ts->transfer_src[node], ts->transfer_dst[node],
-                            node, UNPACK, ts->VarList1, ts->VarList2, ts->Symmetry);
-
-  // Cleanup MPI buffers
-  for (int node = 0; node < ts->cpusize; node++)
-  {
-    if (ts->send_data[node])
-      delete[] ts->send_data[node];
-    if (ts->rec_data[node])
-      delete[] ts->rec_data[node];
-  }
-  delete[] ts->reqs;
-  delete[] ts->stats;
-  delete[] ts->send_data;
-  delete[] ts->rec_data;
-}
-//
-Parallel::SyncHandle *Parallel::SyncBegin(Patch *Pat, MyList<var> *VarList, int Symmetry)
-{
-  int cpusize;
-  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-
-  SyncHandle *handle = new SyncHandle;
-  handle->num_states = 1;
-  handle->states = new TransferState[1];
-
-  TransferState *ts = &handle->states[0];
-  ts->cpusize = cpusize;
-  ts->VarList1 = VarList;
-  ts->VarList2 = VarList;
-  ts->Symmetry = Symmetry;
-  ts->owns_gsl = true;
-
-  ts->dst = build_ghost_gsl(Pat);
-  ts->src = new MyList<Parallel::gridseg> *[cpusize];
-  ts->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
-  ts->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
-  for (int node = 0; node < cpusize; node++)
-  {
-    ts->src[node] = build_owned_gsl0(Pat, node);
-    build_gstl(ts->src[node], ts->dst, &ts->transfer_src[node], &ts->transfer_dst[node]);
-  }
-
-  transfer_begin(ts);
-
-  return handle;
-}
-//
-Parallel::SyncHandle *Parallel::SyncBegin(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry)
-{
-  int cpusize;
-  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-
-  // Count patches
-  int num_patches = 0;
-  MyList<Patch> *Pp = PatL;
-  while (Pp) { num_patches++; Pp = Pp->next; }
-
-  SyncHandle *handle = new SyncHandle;
-  handle->num_states = num_patches + 1; // intra-patch transfers + 1 inter-patch transfer
-  handle->states = new TransferState[handle->num_states];
-
-  // Intra-patch sync: for each patch, build ghost lists and initiate transfer
-  int idx = 0;
-  Pp = PatL;
-  while (Pp)
-  {
-    TransferState *ts = &handle->states[idx];
-    ts->cpusize = cpusize;
-    ts->VarList1 = VarList;
-    ts->VarList2 = VarList;
-    ts->Symmetry = Symmetry;
-    ts->owns_gsl = true;
-
-    ts->dst = build_ghost_gsl(Pp->data);
-    ts->src = new MyList<Parallel::gridseg> *[cpusize];
-    ts->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
-    ts->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
-    for (int node = 0; node < cpusize; node++)
-    {
-      ts->src[node] = build_owned_gsl0(Pp->data, node);
-      build_gstl(ts->src[node], ts->dst, &ts->transfer_src[node], &ts->transfer_dst[node]);
-    }
-
-    transfer_begin(ts);
-
-    idx++;
-    Pp = Pp->next;
-  }
-
-  // Inter-patch sync: buffer zone exchange between patches
-  {
-    TransferState *ts = &handle->states[idx];
-    ts->cpusize = cpusize;
-    ts->VarList1 = VarList;
-    ts->VarList2 = VarList;
-    ts->Symmetry = Symmetry;
-    ts->owns_gsl = true;
-
-    ts->dst = build_buffer_gsl(PatL);
-    ts->src = new MyList<Parallel::gridseg> *[cpusize];
-    ts->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
-    ts->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
-    for (int node = 0; node < cpusize; node++)
-    {
-      ts->src[node] = build_owned_gsl(PatL, node, 5, Symmetry);
-      build_gstl(ts->src[node], ts->dst, &ts->transfer_src[node], &ts->transfer_dst[node]);
-    }
-
-    transfer_begin(ts);
-  }
-
-  return handle;
-}
-//
-void Parallel::SyncEnd(SyncHandle *handle)
-{
-  if (!handle)
-    return;
-
-  // Wait for all pending transfers and unpack
-  for (int i = 0; i < handle->num_states; i++)
-  {
-    TransferState *ts = &handle->states[i];
-    transfer_end(ts);
-
-    // Cleanup grid segment lists only if this state owns them
-    if (ts->owns_gsl)
-    {
-      if (ts->dst)
-        ts->dst->destroyList();
-      for (int node = 0; node < ts->cpusize; node++)
-      {
-        if (ts->src[node])
-          ts->src[node]->destroyList();
-        if (ts->transfer_src[node])
-          ts->transfer_src[node]->destroyList();
-        if (ts->transfer_dst[node])
-          ts->transfer_dst[node]->destroyList();
-      }
-      delete[] ts->src;
-      delete[] ts->transfer_src;
-      delete[] ts->transfer_dst;
-    }
-  }
-
-  delete[] handle->states;
-  delete handle;
-}
-//
-// SyncPreparePlan: Pre-build grid segment lists for a patch list.
-// The plan can be reused across multiple SyncBeginWithPlan calls
-// as long as the mesh topology does not change (no regridding).
-//
-Parallel::SyncPlan *Parallel::SyncPreparePlan(MyList<Patch> *PatL, int Symmetry)
-{
-  int cpusize;
-  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
-
-  // Count patches
-  int num_patches = 0;
-  MyList<Patch> *Pp = PatL;
-  while (Pp) { num_patches++; Pp = Pp->next; }
-
-  SyncPlan *plan = new SyncPlan;
-  plan->num_entries = num_patches + 1; // intra-patch + 1 inter-patch
-  plan->Symmetry = Symmetry;
-  plan->entries = new SyncPlanEntry[plan->num_entries];
-
-  // Intra-patch entries: ghost zone exchange within each patch
-  int idx = 0;
-  Pp = PatL;
-  while (Pp)
-  {
-    SyncPlanEntry *pe = &plan->entries[idx];
-    pe->cpusize = cpusize;
-    pe->dst = build_ghost_gsl(Pp->data);
-    pe->src = new MyList<Parallel::gridseg> *[cpusize];
-    pe->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
-    pe->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
-    for (int node = 0; node < cpusize; node++)
-    {
-      pe->src[node] = build_owned_gsl0(Pp->data, node);
-      build_gstl(pe->src[node], pe->dst, &pe->transfer_src[node], &pe->transfer_dst[node]);
-    }
-    idx++;
-    Pp = Pp->next;
-  }
-
-  // Inter-patch entry: buffer zone exchange between patches
-  {
-    SyncPlanEntry *pe = &plan->entries[idx];
-    pe->cpusize = cpusize;
-    pe->dst = build_buffer_gsl(PatL);
-    pe->src = new MyList<Parallel::gridseg> *[cpusize];
-    pe->transfer_src = new MyList<Parallel::gridseg> *[cpusize];
-    pe->transfer_dst = new MyList<Parallel::gridseg> *[cpusize];
-    for (int node = 0; node < cpusize; node++)
-    {
-      pe->src[node] = build_owned_gsl(PatL, node, 5, Symmetry);
-      build_gstl(pe->src[node], pe->dst, &pe->transfer_src[node], &pe->transfer_dst[node]);
-    }
-  }
-
-  return plan;
-}
-//
-void Parallel::SyncFreePlan(SyncPlan *plan)
-{
-  if (!plan)
-    return;
-
-  for (int i = 0; i < plan->num_entries; i++)
-  {
-    SyncPlanEntry *pe = &plan->entries[i];
-    if (pe->dst)
-      pe->dst->destroyList();
-    for (int node = 0; node < pe->cpusize; node++)
-    {
-      if (pe->src[node])
-        pe->src[node]->destroyList();
-      if (pe->transfer_src[node])
-        pe->transfer_src[node]->destroyList();
-      if (pe->transfer_dst[node])
-        pe->transfer_dst[node]->destroyList();
-    }
-    delete[] pe->src;
-    delete[] pe->transfer_src;
-    delete[] pe->transfer_dst;
-  }
-  delete[] plan->entries;
-  delete plan;
-}
-//
-// SyncBeginWithPlan: Use pre-built GSLs from a SyncPlan to initiate async transfer.
-// This avoids the O(cpusize * blocks^2) cost of rebuilding GSLs on every call.
-//
-Parallel::SyncHandle *Parallel::SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList)
-{
-  return SyncBeginWithPlan(plan, VarList, VarList);
-}
-//
-Parallel::SyncHandle *Parallel::SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList1, MyList<var> *VarList2)
-{
-  SyncHandle *handle = new SyncHandle;
-  handle->num_states = plan->num_entries;
-  handle->states = new TransferState[handle->num_states];
-
-  for (int i = 0; i < plan->num_entries; i++)
-  {
-    SyncPlanEntry *pe = &plan->entries[i];
-    TransferState *ts = &handle->states[i];
-
-    ts->cpusize = pe->cpusize;
-    ts->VarList1 = VarList1;
-    ts->VarList2 = VarList2;
-    ts->Symmetry = plan->Symmetry;
-    ts->owns_gsl = false; // GSLs are owned by the plan, not this handle
-
-    // Borrow GSL pointers from the plan (do NOT free them in SyncEnd)
-    ts->transfer_src = pe->transfer_src;
-    ts->transfer_dst = pe->transfer_dst;
-    ts->src = pe->src;
-    ts->dst = pe->dst;
-
-    transfer_begin(ts);
-  }
-
-  return handle;
-}
 // collect buffer grid segments or blocks for the periodic boundary condition of given patch
 // ---------------------------------------------------
 // |con |                                       |con |
--- a/AMSS_NCKU_source/Parallel.h
+++ b/AMSS_NCKU_source/Parallel.h
@@ -81,53 +81,6 @@ namespace Parallel
                   int Symmetry);
  void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
  void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-
-  // Async Sync: overlap MPI communication with computation
-  struct TransferState
-  {
-    MPI_Request *reqs;
-    MPI_Status *stats;
-    int req_no;
-    double **send_data;
-    double **rec_data;
-    int cpusize;
-    MyList<gridseg> **transfer_src;
-    MyList<gridseg> **transfer_dst;
-    MyList<gridseg> **src;
-    MyList<gridseg> *dst;
-    MyList<var> *VarList1;
-    MyList<var> *VarList2;
-    int Symmetry;
-    bool owns_gsl; // true if this state owns and should free the GSLs
-  };
-  struct SyncHandle
-  {
-    TransferState *states;
-    int num_states;
-  };
-  SyncHandle *SyncBegin(Patch *Pat, MyList<var> *VarList, int Symmetry);
-  SyncHandle *SyncBegin(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
-  void SyncEnd(SyncHandle *handle);
-
-  // Cached GSL plan: pre-build grid segment lists once, reuse across multiple Sync calls
-  struct SyncPlanEntry
-  {
-    int cpusize;
-    MyList<gridseg> **transfer_src;
-    MyList<gridseg> **transfer_dst;
-    MyList<gridseg> **src;
-    MyList<gridseg> *dst;
-  };
-  struct SyncPlan
-  {
-    SyncPlanEntry *entries;
-    int num_entries;
-    int Symmetry;
-  };
-  SyncPlan *SyncPreparePlan(MyList<Patch> *PatL, int Symmetry);
-  void SyncFreePlan(SyncPlan *plan);
-  SyncHandle *SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList);
-  SyncHandle *SyncBeginWithPlan(SyncPlan *plan, MyList<var> *VarList1, MyList<var> *VarList2);
  void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                   MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                   int Symmetry);
--- a/AMSS_NCKU_source/Z4c_class.C
+++ b/AMSS_NCKU_source/Z4c_class.C
@@ -186,12 +186,6 @@ void Z4c_class::Step(int lev, int YN)
  int ERROR = 0;

  MyList<ss_patch> *sPp;
-
-  // Pre-build grid segment lists once for this level's patches.
-  // These are reused across predictor + 3 corrector SyncBegin calls,
-  // avoiding O(cpusize * blocks^2) rebuild each time.
-  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
-
  // Predictor
  MyList<Patch> *Pp = GH->PatL[lev];
  while (Pp)
@@ -327,17 +321,13 @@ void Z4c_class::Step(int lev, int YN)
    }
    Pp = Pp->next;
  }
-  // Start async ghost zone exchange - overlaps with error check and Shell computation
-  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
-
-  // check error information (overlaps with MPI transfer)
+  // check error information
  {
    int erh = ERROR;
    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
  }
  if (ERROR)
  {
-    Parallel::SyncEnd(sync_pre); sync_pre = 0;
    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
    if (myrank == 0)
    {
@@ -485,7 +475,6 @@ void Z4c_class::Step(int lev, int YN)
  }
  if (ERROR)
  {
-    Parallel::SyncEnd(sync_pre); sync_pre = 0;
    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
    if (myrank == 0)
    {
@@ -496,8 +485,7 @@ void Z4c_class::Step(int lev, int YN)
  }
 #endif

-  // Complete async ghost zone exchange
-  if (sync_pre) Parallel::SyncEnd(sync_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);

 #ifdef WithShell
  if (lev == 0)
@@ -705,17 +693,13 @@ void Z4c_class::Step(int lev, int YN)
      Pp = Pp->next;
    }

-    // Start async ghost zone exchange - overlaps with error check and Shell computation
-    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
-
-    // check error information (overlaps with MPI transfer)
+    // check error information
    {
      int erh = ERROR;
      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
    }
    if (ERROR)
    {
-      Parallel::SyncEnd(sync_cor); sync_cor = 0;
      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
      if (myrank == 0)
      {
@@ -873,7 +857,6 @@ void Z4c_class::Step(int lev, int YN)
    }
    if (ERROR)
    {
-      Parallel::SyncEnd(sync_cor); sync_cor = 0;
      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
      if (myrank == 0)
      {
@@ -885,8 +868,7 @@ void Z4c_class::Step(int lev, int YN)
    }
 #endif

-    // Complete async ghost zone exchange
-    if (sync_cor) Parallel::SyncEnd(sync_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);

 #ifdef WithShell
    if (lev == 0)
@@ -1060,8 +1042,6 @@ void Z4c_class::Step(int lev, int YN)
      Porg0[ithBH][2] = Porg1[ithBH][2];
    }
  }
-
-  Parallel::SyncFreePlan(sync_plan);
 }
 #else
 // for constraint preserving boundary (CPBC)
@@ -1095,10 +1075,6 @@ void Z4c_class::Step(int lev, int YN)
  int ERROR = 0;

  MyList<ss_patch> *sPp;
-
-  // Pre-build grid segment lists once for this level's patches.
-  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
-
  // Predictor
  MyList<Patch> *Pp = GH->PatL[lev];
  while (Pp)
@@ -1566,17 +1542,13 @@ void Z4c_class::Step(int lev, int YN)
  }
 #endif
  }
-  // Start async ghost zone exchange - overlaps with error check
-  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
-
-  // check error information (overlaps with MPI transfer)
+  // check error information
  {
    int erh = ERROR;
    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
  }
  if (ERROR)
  {
-    Parallel::SyncEnd(sync_pre); sync_pre = 0;
    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
    if (myrank == 0)
    {
@@ -1586,8 +1558,7 @@ void Z4c_class::Step(int lev, int YN)
    }
  }

-  // Complete async ghost zone exchange
-  if (sync_pre) Parallel::SyncEnd(sync_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);

  if (lev == 0)
  {
@@ -2132,17 +2103,13 @@ void Z4c_class::Step(int lev, int YN)
        sPp = sPp->next;
      }
    }
-    // Start async ghost zone exchange - overlaps with error check
-    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
-
-    // check error information (overlaps with MPI transfer)
+    // check error information
    {
      int erh = ERROR;
      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
    }
    if (ERROR)
    {
-      Parallel::SyncEnd(sync_cor); sync_cor = 0;
      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
      if (myrank == 0)
      {
@@ -2153,8 +2120,7 @@ void Z4c_class::Step(int lev, int YN)
      }
    }

-    // Complete async ghost zone exchange
-    if (sync_cor) Parallel::SyncEnd(sync_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);

    if (lev == 0)
    {
@@ -2380,8 +2346,6 @@ void Z4c_class::Step(int lev, int YN)
 	  DG_List->clearList();
 	}
 #endif
-
-  Parallel::SyncFreePlan(sync_plan);
 }
 #endif
 #undef MRBD
--- a/AMSS_NCKU_source/bssn_class.C
+++ b/AMSS_NCKU_source/bssn_class.C
@@ -3035,12 +3035,6 @@ void bssn_class::Step(int lev, int YN)
  int ERROR = 0;

  MyList<ss_patch> *sPp;
-
-  // Pre-build grid segment lists once for this level's patches.
-  // These are reused across predictor + 3 corrector SyncBegin calls,
-  // avoiding O(cpusize * blocks^2) rebuild each time.
-  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
-
  // Predictor
  MyList<Patch> *Pp = GH->PatL[lev];
  while (Pp)
@@ -3164,18 +3158,13 @@ void bssn_class::Step(int lev, int YN)
    }
    Pp = Pp->next;
  }
-
-  // Start async ghost zone exchange - overlaps with error check and Shell computation
-  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
-
-  // check error information (overlaps with MPI transfer)
+  // check error information
  {
    int erh = ERROR;
    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
  }
  if (ERROR)
  {
-    Parallel::SyncEnd(sync_pre); sync_pre = 0;
    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
    if (myrank == 0)
    {
@@ -3335,7 +3324,6 @@ void bssn_class::Step(int lev, int YN)

  if (ERROR)
  {
-    Parallel::SyncEnd(sync_pre); sync_pre = 0;
    SH->Dump_Data(StateList, 0, PhysTime, dT_lev);
    if (myrank == 0)
    {
@@ -3346,8 +3334,7 @@ void bssn_class::Step(int lev, int YN)
  }
 #endif

-  // Complete async ghost zone exchange
-  if (sync_pre) Parallel::SyncEnd(sync_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);

 #ifdef WithShell
  if (lev == 0)
@@ -3541,10 +3528,7 @@ void bssn_class::Step(int lev, int YN)
      Pp = Pp->next;
    }

-    // Start async ghost zone exchange - overlaps with error check and Shell computation
-    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
-
-    // check error information (overlaps with MPI transfer)
+    // check error information
    {
      int erh = ERROR;
      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
@@ -3552,7 +3536,6 @@ void bssn_class::Step(int lev, int YN)

    if (ERROR)
    {
-      Parallel::SyncEnd(sync_cor); sync_cor = 0;
      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
      if (myrank == 0)
      {
@@ -3709,7 +3692,6 @@ void bssn_class::Step(int lev, int YN)
    }
    if (ERROR)
    {
-      Parallel::SyncEnd(sync_cor); sync_cor = 0;
      SH->Dump_Data(SynchList_pre, 0, PhysTime, dT_lev);
      if (myrank == 0)
      {
@@ -3722,8 +3704,7 @@ void bssn_class::Step(int lev, int YN)
    }
 #endif

-    // Complete async ghost zone exchange
-    if (sync_cor) Parallel::SyncEnd(sync_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);

 #ifdef WithShell
    if (lev == 0)
@@ -3914,8 +3895,6 @@ void bssn_class::Step(int lev, int YN)
      Porg0[ithBH][2] = Porg1[ithBH][2];
    }
  }
-
-  Parallel::SyncFreePlan(sync_plan);
 }

 //================================================================================================
@@ -4838,12 +4817,6 @@ void bssn_class::Step(int lev, int YN)
  int ERROR = 0;

  MyList<ss_patch> *sPp;
-
-  // Pre-build grid segment lists once for this level's patches.
-  // These are reused across predictor + 3 corrector SyncBegin calls,
-  // avoiding O(cpusize * blocks^2) rebuild each time.
-  Parallel::SyncPlan *sync_plan = Parallel::SyncPreparePlan(GH->PatL[lev], Symmetry);
-
  // Predictor
  MyList<Patch> *Pp = GH->PatL[lev];
  while (Pp)
@@ -4970,17 +4943,13 @@ void bssn_class::Step(int lev, int YN)

  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Predictor rhs calculation");

-  // Start async ghost zone exchange - overlaps with error check and BH position
-  Parallel::SyncHandle *sync_pre = Parallel::SyncBeginWithPlan(sync_plan, SynchList_pre);
-
-  // check error information (overlaps with MPI transfer)
+  // check error information
  {
    int erh = ERROR;
    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
  }
  if (ERROR)
  {
-    Parallel::SyncEnd(sync_pre); sync_pre = 0;
    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
    if (myrank == 0)
    {
@@ -4992,8 +4961,7 @@ void bssn_class::Step(int lev, int YN)

  //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Predictor sync");

-  // Complete async ghost zone exchange
-  if (sync_pre) Parallel::SyncEnd(sync_pre);
+  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);

 #if (MAPBH == 0)
  // for black hole position
@@ -5172,17 +5140,13 @@ void bssn_class::Step(int lev, int YN)

    //   misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector error check");

-    // Start async ghost zone exchange - overlaps with error check and BH position
-    Parallel::SyncHandle *sync_cor = Parallel::SyncBeginWithPlan(sync_plan, SynchList_cor);
-
-    // check error information (overlaps with MPI transfer)
+    // check error information
    {
      int erh = ERROR;
      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, GH->Commlev[lev]);
    }
    if (ERROR)
    {
-      Parallel::SyncEnd(sync_cor); sync_cor = 0;
      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
      if (myrank == 0)
      {
@@ -5196,8 +5160,7 @@ void bssn_class::Step(int lev, int YN)

    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Corrector sync");

-    // Complete async ghost zone exchange
-    if (sync_cor) Parallel::SyncEnd(sync_cor);
+    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);

    //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after Corrector sync");

@@ -5313,8 +5276,6 @@ void bssn_class::Step(int lev, int YN)

  //     if(myrank==GH->start_rank[lev]) cout<<GH->mylev<<endl;
  //     misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"complet GH Step");
-
-  Parallel::SyncFreePlan(sync_plan);
 }

 //================================================================================================
--- a/AMSS_NCKU_source/bssn_rhs.f90
+++ b/AMSS_NCKU_source/bssn_rhs.f90
@@ -106,8 +106,7 @@
  call getpbh(BHN,Porg,Mass)
 #endif

-!!! sanity check (disabled in production builds for performance)
-#ifdef DEBUG
+!!! sanity check
  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -137,7 +136,6 @@
     gont = 1
     return
  endif
-#endif

  PI = dacos(-ONE)

@@ -945,60 +943,103 @@
  SSA(2)=SYM
  SSA(3)=ANTI

-!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
-! lopsided_kodis shares the symmetry_bd buffer between advection and
-! dissipation, eliminating redundant full-grid copies. For metric variables
-! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
-! so the constant offset has no effect on dissipation.
+!!!!!!!!!advection term part

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

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

-  call lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS)
+  call lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS)

-  call lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-
-#if 1 
-!! bam does not apply dissipation on gauge variables
-  call lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
-  call lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-#endif
-#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
-  call lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps)
-  call lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps)
-#endif
-#else
-! No dissipation on gauge variables (advection only)
+  call lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS)
+  call lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS)
+  call lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA)
+!!
  call lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS)
+
 #if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
  call lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS)
  call lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS)
  call lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA)
 #endif
+
 #if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
  call lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS)
  call lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS)
  call lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA)
 #endif
+
+  if(eps>0)then 
+! usual Kreiss-Oliger dissipation      
+  call kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "before",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
 #endif
+  call kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps)
+#if 0
+#define i 42
+#define j 40
+#define k 40
+if(Lev == 1)then
+write(*,*) X(i),Y(j),Z(k)
+write(*,*) "after",Axx_rhs(i,j,k)
+endif
+#undef i
+#undef j
+#undef k
+!!stop
+#endif
+  call kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps)
+
+#if 1 
+!! bam does not apply dissipation on gauge variables
+  call kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps)
+#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
+  call kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps)
+  call kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps)
+#endif
+#endif
+
+  endif

  if(co == 0)then
 ! ham_Res = trR + 2/3 * K^2 - A_ij * A^ij - 16 * PI * rho
--- a/AMSS_NCKU_source/fmisc.f90
+++ b/AMSS_NCKU_source/fmisc.f90
@@ -883,13 +883,17 @@ 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
@@ -1111,7 +1115,149 @@ end subroutine d2dump
 !------------------------------------------------------------------------------
 ! 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

@@ -1124,6 +1270,15 @@ end subroutine d2dump
  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
@@ -1173,6 +1328,41 @@ end subroutine d2dump
  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
 !
@@ -1243,19 +1433,26 @@ end subroutine d2dump
  end do
  call polint(x1a,ymtmp,x1,y,dy,ordn)
 #else
-  integer  :: j, k
-  real*8, dimension(ordn,ordn) :: yatmp
+  integer  :: i, j, k
+  real*8, dimension(ordn) :: w1, w2
  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
+  real*8 :: yx_sum, x_sum

-  do k=1,ordn
-    do j=1,ordn
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+  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
-  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

@@ -1305,18 +1502,89 @@ if(dabs(X(1)-xmin) < dX) imin = 1
 if(dabs(Y(1)-ymin) < dY) jmin = 1
 if(dabs(Z(1)-zmin) < dZ) kmin = 1

-! 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)
+  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
  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1400,12 +1668,11 @@ if(Symmetry==2)then
  if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif

-! 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)
+  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

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

-! 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)
+  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

@@ -1604,8 +1870,11 @@ deallocate(f_flat)
 ! 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

-  fout = C1*f1+C2*f2+C3*f3
+  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

  return

@@ -1736,20 +2005,16 @@ deallocate(f_flat)
     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

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

  return
@@ -1810,13 +2075,11 @@ deallocate(f_flat)
     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

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

  return
@@ -1909,7 +2172,6 @@ deallocate(f_flat)
          write(*,*)"error in global_interpind1d, not recognized dumyd = ",dumyd
  endif

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

  return
@@ -2142,16 +2404,13 @@ deallocate(f_flat)

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

  real*8 :: gont
-  integer :: i

-  ! Lookup table for factorials 0! to 20! (precomputed)
+  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, &
@@ -2166,12 +2425,9 @@ deallocate(f_flat)
     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

--- a/AMSS_NCKU_source/fmisc.h
+++ b/AMSS_NCKU_source/fmisc.h
@@ -13,6 +13,7 @@
 #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_average average
@@ -42,6 +43,7 @@
 #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_average AVERAGE
@@ -71,6 +73,7 @@
 #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_average average_
@@ -164,6 +167,15 @@ extern "C"
 						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 *,
--- a/AMSS_NCKU_source/gaussj.C
+++ b/AMSS_NCKU_source/gaussj.C
@@ -16,66 +16,115 @@ using namespace std;
 #include <string.h>
 #include <math.h>
 #endif
-
-// Intel oneMKL LAPACK interface
-#include <mkl_lapacke.h>
-/* Linear equation solution using Intel oneMKL LAPACK.
+/* Linear equation solution by Gauss-Jordan elimination.
 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.
-
-Mathematical equivalence:
-  Solves: A * x = b  =>  x = A^(-1) * b
-  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
-  within numerical precision. */
+corresponding set of solution vectors */

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

-  // 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];
+  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;
+      }
  }

-  // 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;
+  for (l = n - 1; l >= 0; l--)
+  {
+    if (indxr[l] != indxc[l])
+      for (k = 0; k < n; k++)
+      {
+        swap = a[k * n + indxr[l]];
+        a[k * n + indxr[l]] = a[k * n + indxc[l]];
+        a[k * n + indxc[l]] = swap;
+      }
  }

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

  return 0;
 }
--- a/AMSS_NCKU_source/ilucg.f90
+++ b/AMSS_NCKU_source/ilucg.f90
@@ -512,10 +512,11 @@
      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)

-      DOUBLE PRECISION, EXTERNAL :: DDOT
-      DGVV = DDOT(N, V, 1, W, 1)
+      SUM = 0.0D0
+            DO 10 I = 1,N
+            SUM = SUM + V(I)*W(I)
+10          CONTINUE
+      DGVV = SUM
      RETURN
      END
--- a/AMSS_NCKU_source/lopsidediff.f90
+++ b/AMSS_NCKU_source/lopsidediff.f90
@@ -487,201 +487,6 @@ subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)

  end subroutine lopsided

-!-----------------------------------------------------------------------------
-! Combined advection (lopsided) + Kreiss-Oliger dissipation (kodis)
-! Shares the symmetry_bd buffer fh, eliminating one full-grid copy per call.
-! Mathematically identical to calling lopsided then kodis separately.
-!-----------------------------------------------------------------------------
-subroutine lopsided_kodis(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA,eps)
-  implicit none
-
-!~~~~~~> Input parameters:
-
-  integer, intent(in)  :: ex(1:3),Symmetry
-  real*8,  intent(in)  :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
-  real*8,dimension(ex(1),ex(2),ex(3)),intent(in)   :: f,Sfx,Sfy,Sfz
-
-  real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
-  real*8,dimension(3),intent(in) ::SoA
-  real*8,intent(in) :: eps
-
-!~~~~~~> local variables:
-! note index -2,-1,0, so we have 3 extra points
-  real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3))   :: fh
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8 :: dX,dY,dZ
-  real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
-  real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
-  real*8,  parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
-  real*8,  parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
-  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
-! kodis parameters
-  real*8, parameter :: SIX=6.d0,FIT=1.5d1,TWT=2.d1
-  real*8, parameter :: cof=6.4d1   ! 2^6
-
-  dX = X(2)-X(1)
-  dY = Y(2)-Y(1)
-  dZ = Z(2)-Z(1)
-
-  d12dx = ONE/F12/dX
-  d12dy = ONE/F12/dY
-  d12dz = ONE/F12/dZ
-
-  d2dx = ONE/TWO/dX
-  d2dy = ONE/TWO/dY
-  d2dz = ONE/TWO/dZ
-
-  imax = ex(1)
-  jmax = ex(2)
-  kmax = ex(3)
-
-  imin = 1
-  jmin = 1
-  kmin = 1
-  if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
-  if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
-  if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
-
-! Single symmetry_bd call shared by both advection and dissipation
-  call symmetry_bd(3,ex,f,fh,SoA)
-
-! ---- Advection (lopsided) loop ----
-! upper bound set ex-1 only for efficiency, 
-! the loop body will set ex 0 also
-  do k=1,ex(3)-1
-  do j=1,ex(2)-1
-  do i=1,ex(1)-1
-! x direction   
-    if(Sfx(i,j,k) > ZEO)then
-      if(i+3 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
-                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
-                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
-     elseif(i+2 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-
-     elseif(i+1 <= imax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
-                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
-                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
-     endif
-   elseif(Sfx(i,j,k) < ZEO)then
-      if(i-3 >= imin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
-                  Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
-                                    -F6*fh(i-2,j,k)+    fh(i-3,j,k))
-     elseif(i-2 >= imin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-
-     elseif(i-1 >= imin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
-                  Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
-                                    -F6*fh(i+2,j,k)+    fh(i+3,j,k))
-     endif
-   endif
-
-! y direction   
-    if(Sfy(i,j,k) > ZEO)then
-      if(j+3 <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
-                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
-                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
-     elseif(j+2 <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-
-     elseif(j+1 <= jmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
-                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
-                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
-     endif
-   elseif(Sfy(i,j,k) < ZEO)then
-      if(j-3 >= jmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
-                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
-                                    -F6*fh(i,j-2,k)+    fh(i,j-3,k))
-     elseif(j-2 >= jmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-
-     elseif(j-1 >= jmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
-                  Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
-                                    -F6*fh(i,j+2,k)+    fh(i,j+3,k))
-     endif
-   endif
-
-! z direction   
-    if(Sfz(i,j,k) > ZEO)then
-      if(k+3 <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
-                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
-                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
-     elseif(k+2 <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-
-     elseif(k+1 <= kmax)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
-                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
-                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
-     endif
-   elseif(Sfz(i,j,k) < ZEO)then
-      if(k-3 >= kmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)-                                                   &
-                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
-                                    -F6*fh(i,j,k-2)+    fh(i,j,k-3))
-     elseif(k-2 >= kmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                           &
-                  Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-
-     elseif(k-1 >= kmin)then
-     f_rhs(i,j,k)=f_rhs(i,j,k)+                                                   &
-                  Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
-                                    -F6*fh(i,j,k+2)+    fh(i,j,k+3))
-     endif
-   endif
-  enddo
-  enddo
-  enddo
-
-! ---- Dissipation (kodis) loop ----
-  if(eps > ZEO) then
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-
-  if(i-3 >= imin .and. i+3 <= imax .and. &
-     j-3 >= jmin .and. j+3 <= jmax .and. &
-     k-3 >= kmin .and. k+3 <= kmax) then
-   f_rhs(i,j,k)       = f_rhs(i,j,k) + eps/cof *( (     &
-                              (fh(i-3,j,k)+fh(i+3,j,k)) - &
-                          SIX*(fh(i-2,j,k)+fh(i+2,j,k)) + &
-                          FIT*(fh(i-1,j,k)+fh(i+1,j,k)) - &
-                          TWT* fh(i,j,k)            )/dX + &
-                                                  (     &
-                              (fh(i,j-3,k)+fh(i,j+3,k)) - &
-                          SIX*(fh(i,j-2,k)+fh(i,j+2,k)) + &
-                          FIT*(fh(i,j-1,k)+fh(i,j+1,k)) - &
-                          TWT* fh(i,j,k)            )/dY + &
-                                                  (     &
-                              (fh(i,j,k-3)+fh(i,j,k+3)) - &
-                          SIX*(fh(i,j,k-2)+fh(i,j,k+2)) + &
-                          FIT*(fh(i,j,k-1)+fh(i,j,k+1)) - &
-                          TWT* fh(i,j,k)            )/dZ )
-  endif
-
-  enddo
-  enddo
-  enddo
-  endif
-
-  return
-
-  end subroutine lopsided_kodis
-
 #elif (ghost_width == 4)
 ! sixth order code
 ! Compute advection terms in right hand sides of field equations
--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -2,6 +2,20 @@

 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:
@@ -17,10 +31,10 @@ include makefile.inc
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)

 TwoPunctures.o: TwoPunctures.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@

 TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@

 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
@@ -102,7 +116,7 @@ ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)

 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)

 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -1,24 +1,27 @@
+
 ## 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 (Optimized for performance)
+## Intel oneAPI version with oneMKL
 filein  = -I/usr/include/ -I${MKLROOT}/include

-## Using sequential MKL (OpenMP disabled for better single-threaded performance)
-## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+## Use sequential oneMKL to avoid introducing extra OpenMP behavior into ABE.
+LDLIBS  = -L${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

-## 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
-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
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -10,17 +10,6 @@

 import AMSS_NCKU_Input as input_data
 import subprocess
-import time
-## CPU core binding configuration using taskset
-## taskset ensures all child processes inherit the CPU affinity mask
-## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
-## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
-NUMACTL_CPU_BIND = "taskset -c 0-111"
-
-## Build parallelism configuration
-## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
-## Set make -j to utilize available cores for faster builds
-BUILD_JOBS = 104


 ##################################################################
@@ -37,11 +26,11 @@ def makefile_ABE():
    print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
    print(                                                        )

-    ## Build command with CPU binding to nohz_full cores
+    ## Build command
    if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
+        makefile_command  = "make -j96" + " ABE"
    elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
+        makefile_command  = "make -j4" + " ABEGPU"
    else:
        print( " CPU/GPU numerical calculation setting is wrong " )
        print(                                                    )
@@ -78,8 +67,8 @@ def makefile_TwoPunctureABE():
    print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
    print(                                                            )
    
-    ## Build command with CPU binding to nohz_full cores
-    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
+    ## Build command
+    makefile_command = "make" + " 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) 
@@ -116,10 +105,10 @@ def run_ABE():
    ## Define the command to run; cast other values to strings as needed
    
    if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
        mpi_command_outfile = "ABE_out.log"
    elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
        mpi_command_outfile = "ABEGPU_out.log"
 
    ## Execute the MPI command and stream output
@@ -152,13 +141,13 @@ def run_ABE():
 ## Run the AMSS-NCKU TwoPuncture program TwoPunctureABE

 def run_TwoPunctureABE():
-    tp_time1=time.time()
+
    print(                                                          )
    print( " Running the AMSS-NCKU executable file TwoPunctureABE " ) 
    print(                                                          )
    
    ## Define the command to run
-    TwoPuncture_command         = NUMACTL_CPU_BIND + " ./TwoPunctureABE"
+    TwoPuncture_command         = "./TwoPunctureABE"
    TwoPuncture_command_outfile = "TwoPunctureABE_out.log"

    ## Execute the command with subprocess.Popen and stream output
@@ -179,9 +168,7 @@ def run_TwoPunctureABE():
    print(                                               )
    print( " The TwoPunctureABE simulation is finished " ) 
    print(                                               )
-    tp_time2=time.time()
-    et=tp_time2-tp_time1
-    print(f"Used time: {et}")
+    
    return

 ##################################################################
--- a/parallel_plot_helper.py
+++ b/parallel_plot_helper.py
@@ -1,29 +1,12 @@
 import multiprocessing

-def run_plot_task(task):
-    """Execute a single plotting task.

-    Parameters
-    ----------
-    task : tuple
-        A tuple of (function, args_tuple) where function is a callable
-        plotting function and args_tuple contains its arguments.
-    """
+def run_plot_task(task):
    func, args = task
    return func(*args)


 def run_plot_tasks_parallel(plot_tasks):
-    """Execute a list of independent plotting tasks in parallel.
-
-    Uses the 'fork' context to create worker processes so that the main
-    script is NOT re-imported/re-executed in child processes.
-
-    Parameters
-    ----------
-    plot_tasks : list of tuples
-        Each element is (function, args_tuple).
-    """
    ctx = multiprocessing.get_context('fork')
    with ctx.Pool() as pool:
        pool.map(run_plot_task, plot_tasks)
--- a/plot_binary_data.py
+++ b/plot_binary_data.py
@@ -8,12 +8,10 @@
 ##
 #################################################

-## Restrict OpenMP to one thread per process so that running
-## many workers in parallel does not create an O(workers * BLAS_threads)
-## thread explosion.  The variable MUST be set before numpy/scipy
-## are imported, because the BLAS library reads them only at load time.
+## 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")
+os.environ.setdefault("OMP_NUM_THREADS", "1")

 import numpy
 import scipy
@@ -199,15 +197,7 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):

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

-
-####################################################################################
-## Allow this module to be run as a standalone script so that each
-## binary-data plot can be executed in a fresh subprocess whose BLAS
-## environment variables (set above) take effect before numpy loads.
-##
-## Usage:  python3 plot_binary_data.py <filename> <binary_outdir> <figure_outdir>
-####################################################################################
-
+## Allow standalone subprocess execution for parallel binary-data plotting.
 if __name__ == '__main__':
    import sys
    if len(sys.argv) != 4:
--- a/plot_xiaoqu.py
+++ b/plot_xiaoqu.py
@@ -56,11 +56,7 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
        print(x)

    ## Plot each file in parallel using subprocesses.
-    ## Each subprocess is a fresh Python process where the BLAS thread-count
-    ## environment variables (set at the top of plot_binary_data.py) take
-    ## effect before numpy is imported.  This avoids the thread explosion
-    ## that occurs when multiprocessing.Pool with 'fork' context inherits
-    ## already-initialized multi-threaded BLAS from the parent.
+    ## 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

@@ -72,14 +68,12 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
            [sys.executable, script, filename, binary_outdir, figure_outdir],
        )
        running.append( (proc, filename) )
-        ## Keep at most max_workers subprocesses active at a time
        if len(running) >= max_workers:
            p, fn = running.pop(0)
            p.wait()
            if p.returncode != 0:
                failed.append(fn)

-    ## Wait for all remaining subprocesses to finish
    for p, fn in running:
        p.wait()
        if p.returncode != 0:
Author	SHA1	Message	Date
CGH0S7	45e3c725f9	Trigger-Discipline: parallelize result plotting	2026-04-24 10:04:57 +08:00
CGH0S7	7f603f189b	Trigger-Discipline: port TwoPuncture OpenMP optimizations	2026-04-24 09:25:13 +08:00
CGH0S7	a821f21a23	.gitignore updated	2026-04-24 09:10:12 +08:00
CGH0S7	34fe3e6aa5	Trigger-Discipline: port conservative build and fmisc optimizations	2026-04-24 09:09:50 +08:00
CGH0S7	79af79d471	baseline updated	2026-02-05 19:53:55 +08:00