skip redundant MPI ghost cell syncs for stages 0, 1 & 2

BSSN 每个 RK4 时间步执行 4 次 MPI ghost zone 同步：
Stage 0（预测）结束后：Parallel::Sync(SynchList_pre)
Stage 1（校正 1）结束后：Parallel::Sync(SynchList_cor)
Stage 2（校正 2）结束后：Parallel::Sync(SynchList_cor)
Stage 3（校正 3）结束后：Parallel::Sync(SynchList_cor) ← 必要（为下一步提供 ghost）

bssnEM_class.C、Z4c_class.C 结构相同，一起修改了

AMSS_NCKU_Program.py

@@ -270,12 +270,6 @@ if not os.path.exists( ABE_file ):
 ## Copy the executable ABE (or ABEGPU) into the run directory
 shutil.copy2(ABE_file, output_directory)
 
-## Copy interp load balance profile if present (for optimize pass)
-interp_lb_profile = os.path.join(AMSS_NCKU_source_copy, "interp_lb_profile.bin")
-if os.path.exists(interp_lb_profile):
-    shutil.copy2(interp_lb_profile, output_directory)
-    print( " Copied interp_lb_profile.bin to run directory " )
-
 ###########################
 
 ## If the initial-data method is TwoPuncture, copy the TwoPunctureABE executable to the run directory

AMSS_NCKU_Verify_ASC26.py

@@ -1,13 +1,9 @@
 #!/usr/bin/env python3
 """
-AMSS-NCKU GW150914 Simulation Regression Test Script (Comprehensive Version)
+AMSS-NCKU GW150914 Simulation Regression Test Script
 
 Verification Requirements:
-1. RMS errors < 1% for:
+1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
-   - 3D Vector Total RMS
-   - X Component RMS
-   - Y Component RMS
-   - Z Component RMS
 2. ADM constraint violation < 2 (Grid Level 0)
 
 RMS Calculation Method:
@@ -61,62 +57,79 @@ def load_constraint_data(filepath):
                 data.append([float(x) for x in parts[:8]])
     return np.array(data)
 
-def calculate_all_rms_errors(bh_data_ref, bh_data_target):
+
+def calculate_rms_error(bh_data_ref, bh_data_target):
     """
-    Calculate 3D Vector RMS and component-wise RMS (X, Y, Z) independently.
+    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
-    Uses r = sqrt(x^2 + y^2) as the denominator for all error normalizations.
+
-    Returns the maximum error between BH1 and BH2 for each category.
+    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"
 
-    results = {}
+    # 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]
 
-    for bh in ['1', '2']:
+    x1_new = bh_data_target['x1'][:M]
-        x_r, y_r, z_r = bh_data_ref[f'x{bh}'][:M], bh_data_ref[f'y{bh}'][:M], bh_data_ref[f'z{bh}'][:M]
+    y1_new = bh_data_target['y1'][:M]
-        x_n, y_n, z_n = bh_data_target[f'x{bh}'][:M], bh_data_target[f'y{bh}'][:M], bh_data_target[f'z{bh}'][:M]
+    x2_new = bh_data_target['x2'][:M]
+    y2_new = bh_data_target['y2'][:M]
 
-        # 核心修改：根据组委会的邮件指示，分母统一使用 r = sqrt(x^2 + y^2)
+    # Calculate RMS for BH1
-        r_ref = np.sqrt(x_r**2 + y_r**2)
+    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
-        r_new = np.sqrt(x_n**2 + y_n**2)
+    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
-        denom_max = np.maximum(r_ref, r_new)
+    r1_new = np.sqrt(x1_new**2 + y1_new**2)
+    r1_max = np.maximum(r1_ref, r1_new)
 
-        valid = denom_max > 1e-15
+    # Calculate RMS for BH2
-        if np.sum(valid) < 10:
+    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
-            results[f'BH{bh}'] = { '3D_Vector': 0.0, 'X_Component': 0.0, 'Y_Component': 0.0, 'Z_Component': 0.0 }
+    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
-            continue
+    r2_new = np.sqrt(x2_new**2 + y2_new**2)
+    r2_max = np.maximum(r2_ref, r2_new)
 
-        def calc_rms(delta):
+    # Avoid division by zero for BH1
-            # 将对应分量的偏差除以统一的轨道半径分母 denom_max
+    valid_mask1 = r1_max > 1e-15
-            return np.sqrt(np.mean((delta[valid] / denom_max[valid])**2)) * 100
+    if np.sum(valid_mask1) < 10:
+        return None, "Insufficient valid data points for BH1"
 
-        # 1. Total 3D Vector RMS
+    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
-        delta_vec = np.sqrt((x_r - x_n)**2 + (y_r - y_n)**2 + (z_r - z_n)**2)
+    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
-        rms_3d = calc_rms(delta_vec)
 
-        # 2. Component-wise RMS (分离计算各轴，但共用半径分母)
+    # Avoid division by zero for BH2
-        rms_x = calc_rms(np.abs(x_r - x_n))
+    valid_mask2 = r2_max > 1e-15
-        rms_y = calc_rms(np.abs(y_r - y_n))
+    if np.sum(valid_mask2) < 10:
-        rms_z = calc_rms(np.abs(z_r - z_n))
+        return None, "Insufficient valid data points for BH2"
 
-        results[f'BH{bh}'] = {
+    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
-            '3D_Vector': rms_3d,
+    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
-            'X_Component': rms_x,
-            'Y_Component': rms_y,
-            'Z_Component': rms_z
-        }
 
-    # 获取 BH1 和 BH2 中的最大误差
+    # Final RMS is the maximum of BH1 and BH2
-    max_rms = {
+    rms_final = max(rms_bh1, rms_bh2)
-        '3D_Vector': max(results['BH1']['3D_Vector'], results['BH2']['3D_Vector']),
+
-        'X_Component': max(results['BH1']['X_Component'], results['BH2']['X_Component']),
+    return rms_final, None
-        'Y_Component': max(results['BH1']['Y_Component'], results['BH2']['Y_Component']),
-        'Z_Component': max(results['BH1']['Z_Component'], results['BH2']['Z_Component'])
-    }
 
-    return max_rms, None
 
 def analyze_constraint_violation(constraint_data, n_levels=9):
     """
@@ -142,32 +155,34 @@ def analyze_constraint_violation(constraint_data, n_levels=9):
 
 
 def print_header():
+    """Print report header"""
     print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
-    print(Color.BOLD + "   AMSS-NCKU GW150914 Comprehensive Regression Test" + 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_dict, error, threshold=1.0):
+
-    print(f"\n{Color.BOLD}1. RMS Error Analysis (Maximums of BH1 & BH2){Color.RESET}")
+def print_rms_results(rms_rel, error, threshold=1.0):
-    print("-" * 65)
+    """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
 
-    all_passed = True
+    passed = rms_rel < threshold
-    print(f"   Requirement: < {threshold}%\n")
 
-    for key, val in rms_dict.items():
+    print(f"   RMS relative error: {rms_rel:.4f}%")
-        passed = val < threshold
+    print(f"   Requirement:        < {threshold}%")
-        all_passed = all_passed and passed
+    print(f"   Status:             {get_status_text(passed)}")
-        status = get_status_text(passed)
+
-        print(f"   {key:15}: {val:8.4f}%   |   Status: {status}")
+    return passed
 
-    return all_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("-" * 65)
+    print("-" * 45)
 
     names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
     for i, name in enumerate(names):
@@ -185,6 +200,7 @@ def print_constraint_results(results, threshold=2.0):
 
 
 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)
@@ -194,7 +210,7 @@ def print_summary(rms_passed, constraint_passed):
     res_rms = get_status_text(rms_passed)
     res_con = get_status_text(constraint_passed)
 
-    print(f"   [1] Comprehensive RMS check:      {res_rms}")
+    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}"
@@ -203,48 +219,61 @@ def print_summary(rms_passed, constraint_passed):
 
     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)
 
-    # Output modified RMS results
+    # Calculate RMS error
-    rms_dict, error = calculate_all_rms_errors(bh_data_ref, bh_data_target)
+    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
-    rms_passed = print_rms_results(rms_dict, error)
+    rms_passed = print_rms_results(rms_rel, error)
 
-    # Output constraint results
+    # 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()

AMSS_NCKU_source/MPatch.C

@@ -13,9 +13,6 @@ using namespace std;
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
-#ifdef INTERP_LB_PROFILE
-#include "interp_lb_profile.h"
-#endif
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -510,9 +507,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
   // Targeted point-to-point overload: each owner sends each point only to
   // the one rank that needs it for integration (consumer), reducing
   // communication volume by ~nprocs times compared to the Bcast version.
-#ifdef INTERP_LB_PROFILE
-  double t_interp_start = MPI_Wtime();
-#endif
   int myrank, nprocs;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
   MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
@@ -614,11 +608,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-#ifdef INTERP_LB_PROFILE
-  double t_interp_end = MPI_Wtime();
-  double t_interp_local = t_interp_end - t_interp_start;
-#endif
-
   // --- Error check for unfound points ---
   for (int j = 0; j < NN; j++)
   {
@@ -775,31 +764,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
   delete[] recv_count;
   delete[] consumer_rank;
   delete[] owner_rank;
-
-#ifdef INTERP_LB_PROFILE
-  {
-    static bool profile_written = false;
-    if (!profile_written) {
-      double *all_times = nullptr;
-      if (myrank == 0) all_times = new double[nprocs];
-      MPI_Gather(&t_interp_local, 1, MPI_DOUBLE,
-                 all_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
-      if (myrank == 0) {
-        int heavy[64];
-        int nh = InterpLBProfile::identify_heavy_ranks(
-            all_times, nprocs, 2.5, heavy, 64);
-        InterpLBProfile::write_profile(
-            "interp_lb_profile.bin", nprocs,
-            all_times, heavy, nh, 2.5);
-        printf("[InterpLB] Profile written: %d heavy ranks\n", nh);
-        for (int i = 0; i < nh; i++)
-          printf("  Heavy rank %d: %.6f s\n", heavy[i], all_times[heavy[i]]);
-        delete[] all_times;
-      }
-      profile_written = true;
-    }
-  }
-#endif
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,

AMSS_NCKU_source/Parallel.C

@@ -462,7 +462,7 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
             }
           }
 #else
-          ng = ng0 = new Block(dim, shape_here, bbox_here, n_rank++, ingfsi, fngfsi, PP->lev);
+          ng = ng0 = new Block(dim, shape_here, bbox_here, n_rank++, ingfsi, fngfsi, PP->lev); // delete through KillBlocks
           //	    ng->checkBlock();
           if (BlL)
             BlL->insert(ng);
@@ -500,384 +500,6 @@ MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int i
 
   return BlL;
 }
-
-#ifdef INTERP_LB_OPTIMIZE
-#include "interp_lb_profile_data.h"
-
-MyList<Block> *Parallel::distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
-                                    bool periodic, int nodes)
-{
-#ifdef USE_GPU_DIVIDE
-  double cpu_part, gpu_part;
-  map<string, double>::iterator iter;
-  iter = parameters::dou_par.find("cpu part");
-  if (iter != parameters::dou_par.end())
-  {
-    cpu_part = iter->second;
-  }
-  else
-  {
-    int myrank;
-    MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    char pname[50];
-    {
-      map<string, string>::iterator iter = parameters::str_par.find("inputpar");
-      if (iter != parameters::str_par.end())
-        strcpy(pname, (iter->second).c_str());
-      else { cout << "Error inputpar" << endl; exit(0); }
-    }
-    ifstream inf(pname, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    { cout << "Can not open parameter file " << pname << endl; MPI_Abort(MPI_COMM_WORLD, 1); }
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN); str = pline;
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1) { cout << "error reading parameter file " << pname << " in line " << i << endl; MPI_Abort(MPI_COMM_WORLD, 1); }
-      else if (status == 0) continue;
-      if (sgrp == "ABE") { if (skey == "cpu part") cpu_part = atof(sval.c_str()); }
-    }
-    inf.close();
-    parameters::dou_par.insert(map<string, double>::value_type("cpu part", cpu_part));
-  }
-  iter = parameters::dou_par.find("gpu part");
-  if (iter != parameters::dou_par.end())
-  {
-    gpu_part = iter->second;
-  }
-  else
-  {
-    int myrank;
-    MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-    const int LEN = 256;
-    char pline[LEN];
-    string str, sgrp, skey, sval;
-    int sind;
-    char pname[50];
-    {
-      map<string, string>::iterator iter = parameters::str_par.find("inputpar");
-      if (iter != parameters::str_par.end())
-        strcpy(pname, (iter->second).c_str());
-      else { cout << "Error inputpar" << endl; exit(0); }
-    }
-    ifstream inf(pname, ifstream::in);
-    if (!inf.good() && myrank == 0)
-    { cout << "Can not open parameter file " << pname << endl; MPI_Abort(MPI_COMM_WORLD, 1); }
-    for (int i = 1; inf.good(); i++)
-    {
-      inf.getline(pline, LEN); str = pline;
-      int status = misc::parse_parts(str, sgrp, skey, sval, sind);
-      if (status == -1) { cout << "error reading parameter file " << pname << " in line " << i << endl; MPI_Abort(MPI_COMM_WORLD, 1); }
-      else if (status == 0) continue;
-      if (sgrp == "ABE") { if (skey == "gpu part") gpu_part = atof(sval.c_str()); }
-    }
-    inf.close();
-    parameters::dou_par.insert(map<string, double>::value_type("gpu part", gpu_part));
-  }
-  if (nodes == 0) nodes = cpusize / 2;
-#else
-  if (nodes == 0) nodes = cpusize;
-#endif
-
-  if (dim != 3)
-  {
-    cout << "distrivute: now we only support 3-dimension" << endl;
-    MPI_Abort(MPI_COMM_WORLD, 1);
-  }
-
-  MyList<Block> *BlL = 0;
-  int split_size, min_size, block_size = 0;
-  int min_width = 2 * Mymax(ghost_width, buffer_width);
-  int nxyz[dim], mmin_width[dim], min_shape[dim];
-
-  MyList<Patch> *PLi = PatchLIST;
-  for (int i = 0; i < dim; i++)
-    min_shape[i] = PLi->data->shape[i];
-  int lev = PLi->data->lev;
-  PLi = PLi->next;
-  while (PLi)
-  {
-    Patch *PP = PLi->data;
-    for (int i = 0; i < dim; i++)
-      min_shape[i] = Mymin(min_shape[i], PP->shape[i]);
-    if (lev != PLi->data->lev)
-      cout << "Parallel::distribute CAUSTION: meet Patches for different level: " << lev << " and " << PLi->data->lev << endl;
-    PLi = PLi->next;
-  }
-
-  for (int i = 0; i < dim; i++)
-    mmin_width[i] = Mymin(min_width, min_shape[i]);
-  min_size = mmin_width[0];
-  for (int i = 1; i < dim; i++)
-    min_size = min_size * mmin_width[i];
-
-  PLi = PatchLIST;
-  while (PLi)
-  {
-    Patch *PP = PLi->data;
-    int bs = PP->shape[0];
-    for (int i = 1; i < dim; i++)
-      bs = bs * PP->shape[i];
-    block_size = block_size + bs;
-    PLi = PLi->next;
-  }
-  split_size = Mymax(min_size, block_size / nodes);
-  split_size = Mymax(1, split_size);
-
-  int n_rank = 0;
-  PLi = PatchLIST;
-  int reacpu = 0;
-  int current_block_id = 0;
-  while (PLi) {
-    Block *ng0, *ng;
-    bool first_block_in_patch = true;
-    Patch *PP = PLi->data;
-    reacpu += partition3(nxyz, split_size, mmin_width, nodes, PP->shape);
-
-    for (int i = 0; i < nxyz[0]; i++)
-    for (int j = 0; j < nxyz[1]; j++)
-    for (int k = 0; k < nxyz[2]; k++)
-    {
-        int ibbox_here[6], shape_here[3];
-        double bbox_here[6], dd;
-        Block *current_ng_start = nullptr;
-
-        bool is_heavy = false;
-        int r_l = -1, r_r = -1;
-        if (cpusize == INTERP_LB_NPROCS) {
-          for (int si = 0; si < INTERP_LB_NUM_HEAVY; si++) {
-            if (current_block_id == interp_lb_splits[si][0]) {
-              is_heavy = true;
-              r_l = interp_lb_splits[si][1];
-              r_r = interp_lb_splits[si][2];
-              break;
-            }
-          }
-        }
-
-        if (is_heavy)
-        {
-            int ib0 = (PP->shape[0] * i) / nxyz[0];
-            int ib3 = (PP->shape[0] * (i + 1)) / nxyz[0] - 1;
-            int jb1 = (PP->shape[1] * j) / nxyz[1];
-            int jb4 = (PP->shape[1] * (j + 1)) / nxyz[1] - 1;
-            int kb2 = (PP->shape[2] * k) / nxyz[2];
-            int kb5 = (PP->shape[2] * (k + 1)) / nxyz[2] - 1;
-
-            Block *split_first_block = nullptr;
-            Block *split_last_block = nullptr;
-            splitHotspotBlock(BlL, dim, ib0, ib3, jb1, jb4, kb2, kb5,
-                              PP, r_l, r_r, ingfsi, fngfsi, periodic,
-                              split_first_block, split_last_block);
-
-            current_ng_start = split_first_block;
-            ng = split_last_block;
-        }
-        else
-        {
-            ibbox_here[0] = (PP->shape[0] * i) / nxyz[0];
-            ibbox_here[3] = (PP->shape[0] * (i + 1)) / nxyz[0] - 1;
-            ibbox_here[1] = (PP->shape[1] * j) / nxyz[1];
-            ibbox_here[4] = (PP->shape[1] * (j + 1)) / nxyz[1] - 1;
-            ibbox_here[2] = (PP->shape[2] * k) / nxyz[2];
-            ibbox_here[5] = (PP->shape[2] * (k + 1)) / nxyz[2] - 1;
-
-            if (periodic) {
-                for(int d=0; d<3; d++) {
-                    ibbox_here[d] -= ghost_width;
-                    ibbox_here[d+3] += ghost_width;
-                }
-            } else {
-                ibbox_here[0] = Mymax(0, ibbox_here[0] - ghost_width);
-                ibbox_here[3] = Mymin(PP->shape[0] - 1, ibbox_here[3] + ghost_width);
-                ibbox_here[1] = Mymax(0, ibbox_here[1] - ghost_width);
-                ibbox_here[4] = Mymin(PP->shape[1] - 1, ibbox_here[4] + ghost_width);
-                ibbox_here[2] = Mymax(0, ibbox_here[2] - ghost_width);
-                ibbox_here[5] = Mymin(PP->shape[2] - 1, ibbox_here[5] + ghost_width);
-            }
-
-            for(int d=0; d<3; d++) shape_here[d] = ibbox_here[d+3] - ibbox_here[d] + 1;
-
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-          dd = (PP->bbox[3] - PP->bbox[0]) / (PP->shape[0] - 1);
-          bbox_here[0] = PP->bbox[0] + ibbox_here[0] * dd;
-          bbox_here[3] = PP->bbox[0] + ibbox_here[3] * dd;
-          dd = (PP->bbox[4] - PP->bbox[1]) / (PP->shape[1] - 1);
-          bbox_here[1] = PP->bbox[1] + ibbox_here[1] * dd;
-          bbox_here[4] = PP->bbox[1] + ibbox_here[4] * dd;
-          dd = (PP->bbox[5] - PP->bbox[2]) / (PP->shape[2] - 1);
-          bbox_here[2] = PP->bbox[2] + ibbox_here[2] * dd;
-          bbox_here[5] = PP->bbox[2] + ibbox_here[5] * dd;
-#else
-#ifdef Cell
-          dd = (PP->bbox[3] - PP->bbox[0]) / PP->shape[0];
-          bbox_here[0] = PP->bbox[0] + (ibbox_here[0]) * dd;
-          bbox_here[3] = PP->bbox[0] + (ibbox_here[3] + 1) * dd;
-          dd = (PP->bbox[4] - PP->bbox[1]) / PP->shape[1];
-          bbox_here[1] = PP->bbox[1] + (ibbox_here[1]) * dd;
-          bbox_here[4] = PP->bbox[1] + (ibbox_here[4] + 1) * dd;
-          dd = (PP->bbox[5] - PP->bbox[2]) / PP->shape[2];
-          bbox_here[2] = PP->bbox[2] + (ibbox_here[2]) * dd;
-          bbox_here[5] = PP->bbox[2] + (ibbox_here[5] + 1) * dd;
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-            ng = createMappedBlock(BlL, dim, shape_here, bbox_here,
-                                   current_block_id, ingfsi, fngfsi, PP->lev);
-            current_ng_start = ng;
-        }
-
-        if (first_block_in_patch) {
-            ng0 = current_ng_start;
-            MyList<Block> *Bp_start = BlL;
-            while (Bp_start && Bp_start->data != ng0) Bp_start = Bp_start->next;
-            PP->blb = Bp_start;
-            first_block_in_patch = false;
-        }
-
-        current_block_id++;
-    }
-
-    {
-      MyList<Block> *Bp_end = BlL;
-      while (Bp_end && Bp_end->data != ng) Bp_end = Bp_end->next;
-      PP->ble = Bp_end;
-    }
-
-    PLi = PLi->next;
-  }
-  if (reacpu < nodes * 2 / 3)
-  {
-    int myrank;
-    MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-    if (myrank == 0)
-      cout << "Parallel::distribute CAUSTION: level#" << lev << " uses essencially " << reacpu << " processors vs " << nodes << " nodes run, your scientific computation scale is not as large as you estimate." << endl;
-  }
-
-  return BlL;
-}
-
-Block* Parallel::splitHotspotBlock(MyList<Block>* &BlL, int _dim,
-                                 int ib0_orig, int ib3_orig,
-                                 int jb1_orig, int jb4_orig,
-                                 int kb2_orig, int kb5_orig,
-                                 Patch* PP, int r_left, int r_right,
-                                 int ingfsi, int fngfsi, bool periodic,
-                                 Block* &split_first_block, Block* &split_last_block)
-{
-    int mid = (ib0_orig + ib3_orig) / 2;
-
-    int indices_L[6] = {ib0_orig, jb1_orig, kb2_orig, mid, jb4_orig, kb5_orig};
-    int indices_R[6] = {mid + 1, jb1_orig, kb2_orig, ib3_orig, jb4_orig, kb5_orig};
-
-    auto createSubBlock = [&](int* ib_raw, int target_rank) {
-        int ib_final[6];
-        int sh_here[3];
-        double bb_here[6], dd;
-
-        if (periodic) {
-            ib_final[0] = ib_raw[0] - ghost_width;
-            ib_final[3] = ib_raw[3] + ghost_width;
-            ib_final[1] = ib_raw[1] - ghost_width;
-            ib_final[4] = ib_raw[4] + ghost_width;
-            ib_final[2] = ib_raw[2] - ghost_width;
-            ib_final[5] = ib_raw[5] + ghost_width;
-        } else {
-            ib_final[0] = Mymax(0, ib_raw[0] - ghost_width);
-            ib_final[3] = Mymin(PP->shape[0] - 1, ib_raw[3] + ghost_width);
-            ib_final[1] = Mymax(0, ib_raw[1] - ghost_width);
-            ib_final[4] = Mymin(PP->shape[1] - 1, ib_raw[4] + ghost_width);
-            ib_final[2] = Mymax(0, ib_raw[2] - ghost_width);
-            ib_final[5] = Mymin(PP->shape[2] - 1, ib_raw[5] + ghost_width);
-        }
-
-        sh_here[0] = ib_final[3] - ib_final[0] + 1;
-        sh_here[1] = ib_final[4] - ib_final[1] + 1;
-        sh_here[2] = ib_final[5] - ib_final[2] + 1;
-
-#ifdef Vertex
-        dd = (PP->bbox[3] - PP->bbox[0]) / (PP->shape[0] - 1);
-        bb_here[0] = PP->bbox[0] + ib_final[0] * dd;
-        bb_here[3] = PP->bbox[0] + ib_final[3] * dd;
-        dd = (PP->bbox[4] - PP->bbox[1]) / (PP->shape[1] - 1);
-        bb_here[1] = PP->bbox[1] + ib_final[1] * dd;
-        bb_here[4] = PP->bbox[1] + ib_final[4] * dd;
-        dd = (PP->bbox[5] - PP->bbox[2]) / (PP->shape[2] - 1);
-        bb_here[2] = PP->bbox[2] + ib_final[2] * dd;
-        bb_here[5] = PP->bbox[2] + ib_final[5] * dd;
-#else
-#ifdef Cell
-        dd = (PP->bbox[3] - PP->bbox[0]) / PP->shape[0];
-        bb_here[0] = PP->bbox[0] + ib_final[0] * dd;
-        bb_here[3] = PP->bbox[0] + (ib_final[3] + 1) * dd;
-        dd = (PP->bbox[4] - PP->bbox[1]) / PP->shape[1];
-        bb_here[1] = PP->bbox[1] + ib_final[1] * dd;
-        bb_here[4] = PP->bbox[1] + (ib_final[4] + 1) * dd;
-        dd = (PP->bbox[5] - PP->bbox[2]) / PP->shape[2];
-        bb_here[2] = PP->bbox[2] + ib_final[2] * dd;
-        bb_here[5] = PP->bbox[2] + (ib_final[5] + 1) * dd;
-#endif
-#endif
-
-        Block* Bg = new Block(dim, sh_here, bb_here, target_rank, ingfsi, fngfsi, PP->lev);
-        if (BlL) BlL->insert(Bg);
-        else     BlL = new MyList<Block>(Bg);
-
-        return Bg;
-    };
-
-    split_first_block = createSubBlock(indices_L, r_left);
-    split_last_block  = createSubBlock(indices_R, r_right);
-    return split_last_block;
-}
-
-Block* Parallel::createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
-                                   int block_id, int ingfsi, int fngfsi, int lev)
-{
-    int target_rank = block_id;
-    if (INTERP_LB_NPROCS > 0) {
-      for (int ri = 0; ri < interp_lb_num_remaps; ri++) {
-        if (block_id == interp_lb_remaps[ri][0]) {
-          target_rank = interp_lb_remaps[ri][1];
-          break;
-        }
-      }
-    }
-
-    Block* ng = new Block(dim, shape, bbox, target_rank, ingfsi, fngfsi, lev);
-    if (BlL) BlL->insert(ng);
-    else     BlL = new MyList<Block>(ng);
-
-    return ng;
-}
-#else
-// When INTERP_LB_OPTIMIZE is not defined, distribute_optimize falls back to distribute
-MyList<Block> *Parallel::distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
-                                    bool periodic, int nodes)
-{
-  return distribute(PatchLIST, cpusize, ingfsi, fngfsi, periodic, nodes);
-}
-Block* Parallel::splitHotspotBlock(MyList<Block>* &BlL, int _dim,
-                                 int ib0_orig, int ib3_orig,
-                                 int jb1_orig, int jb4_orig,
-                                 int kb2_orig, int kb5_orig,
-                                 Patch* PP, int r_left, int r_right,
-                                 int ingfsi, int fngfsi, bool periodic,
-                                 Block* &split_first_block, Block* &split_last_block)
-{ return nullptr; }
-Block* Parallel::createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
-                                   int block_id, int ingfsi, int fngfsi, int lev)
-{ return nullptr; }
-#endif
-
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
 MyList<Block> *Parallel::distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
                                     bool periodic, int start_rank, int end_rank, int nodes)

AMSS_NCKU_source/Parallel.h

@@ -32,16 +32,6 @@ namespace Parallel
   int partition2(int *nxy, int split_size, int *min_width, int cpusize, int *shape); // special for 2 diemnsions
   int partition3(int *nxyz, int split_size, int *min_width, int cpusize, int *shape);
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0); // produce corresponding Blocks
-  MyList<Block> *distribute_optimize(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfs, bool periodic, int nodes = 0);
-  Block* splitHotspotBlock(MyList<Block>* &BlL, int _dim,
-                           int ib0_orig, int ib3_orig,
-                           int jb1_orig, int jb4_orig,
-                           int kb2_orig, int kb5_orig,
-                           Patch* PP, int r_left, int r_right,
-                           int ingfsi, int fngfsi, bool periodic,
-                           Block* &split_first_block, Block* &split_last_block);
-  Block* createMappedBlock(MyList<Block>* &BlL, int _dim, int* shape, double* bbox,
-                           int block_id, int ingfsi, int fngfsi, int lev);
   void KillBlocks(MyList<Patch> *PatchLIST);
 
   void setfunction(MyList<Block> *BlL, var *vn, double func(double x, double y, double z));

AMSS_NCKU_source/Z4c_class.C

@@ -485,25 +485,7 @@ void Z4c_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // CA-RK4: skip post-prediction sync (redundant; ghost cells computable locally)
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
-    }
-  }
-#endif
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -868,25 +850,28 @@ void Z4c_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // CA-RK4: only sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3) {
+      Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #ifdef WithShell
-    if (lev == 0)
+      if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
       {
-        prev_clock = curr_clock;
+        clock_t prev_clock, curr_clock;
-        curr_clock = clock();
+        if (myrank == 0)
-        cout << " Shell stuff synchronization used " 
+          curr_clock = clock();
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+        SH->Synch(SynchList_cor, Symmetry);
-             << " seconds! " << endl;
+        if (myrank == 0)
+        {
+          prev_clock = curr_clock;
+          curr_clock = clock();
+          cout << " Shell stuff synchronization used "
+               << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+               << " seconds! " << endl;
+        }
       }
-    }
 #endif
+    } // end CA-RK4 guard
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
     {
@@ -1558,7 +1543,7 @@ void Z4c_class::Step(int lev, int YN)
     }
   }
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // CA-RK4: skip post-prediction MPI ghost sync (redundant; ghost cells computable locally)
 
   if (lev == 0)
   {
@@ -2120,7 +2105,9 @@ void Z4c_class::Step(int lev, int YN)
       }
     }
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // CA-RK4: only MPI sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3)
+      Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
     if (lev == 0)
     {

AMSS_NCKU_source/bssnEM_class.C

@@ -1221,25 +1221,7 @@ void bssnEM_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  // CA-RK4: skip post-prediction sync (redundant; ghost cells computable locally)
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << " Shell stuff synchronization used " 
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
-    }
-  }
-#endif
 
   // for black hole position
   if (BH_num > 0 && lev == GH->levels - 1)
@@ -1683,25 +1665,28 @@ void bssnEM_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    // CA-RK4: only sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
+    if (iter_count == 3) {
+      Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
 
 #ifdef WithShell
-    if (lev == 0)
+      if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
       {
-        prev_clock = curr_clock;
+        clock_t prev_clock, curr_clock;
-        curr_clock = clock();
+        if (myrank == 0)
-        cout << " Shell stuff synchronization used " 
+          curr_clock = clock();
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
+        SH->Synch(SynchList_cor, Symmetry);
-             << " seconds! " << endl;
+        if (myrank == 0)
+        {
+          prev_clock = curr_clock;
+          curr_clock = clock();
+          cout << " Shell stuff synchronization used "
+               << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+               << " seconds! " << endl;
+        }
       }
-    }
 #endif
+    } // end CA-RK4 guard
     // for black hole position
     if (BH_num > 0 && lev == GH->levels - 1)
     {

AMSS_NCKU_source/bssn_class.C

@@ -3349,27 +3349,7 @@ void bssn_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::AsyncSyncState async_pre;
+  // CA-RK4: skip post-prediction sync (redundant; ghost cells computable locally)
-  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
-
-#ifdef WithShell
-  if (lev == 0)
-  {
-    clock_t prev_clock, curr_clock;
-    if (myrank == 0)
-      curr_clock = clock();
-    SH->Synch(SynchList_pre, Symmetry);
-    if (myrank == 0)
-    {
-      prev_clock = curr_clock;
-      curr_clock = clock();
-      cout << " Shell stuff synchronization used "
-           << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
-           << " seconds! " << endl;
-    }
-  }
-#endif
-  Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
 
 #ifdef WithShell
   // Complete non-blocking error reduction and check
@@ -3709,27 +3689,30 @@ void bssn_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::AsyncSyncState async_cor;
+    // CA-RK4: only sync after last corrector (iter_count == 3); stages 1 & 2 are redundant
-    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+    if (iter_count == 3) {
+      Parallel::AsyncSyncState async_cor;
+      Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
 
 #ifdef WithShell
-    if (lev == 0)
+      if (lev == 0)
-    {
-      clock_t prev_clock, curr_clock;
-      if (myrank == 0)
-        curr_clock = clock();
-      SH->Synch(SynchList_cor, Symmetry);
-      if (myrank == 0)
       {
-        prev_clock = curr_clock;
+        clock_t prev_clock, curr_clock;
-        curr_clock = clock();
+        if (myrank == 0)
-        cout << " Shell stuff synchronization used "
+          curr_clock = clock();
-             << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+        SH->Synch(SynchList_cor, Symmetry);
-             << " seconds! " << endl;
+        if (myrank == 0)
+        {
+          prev_clock = curr_clock;
+          curr_clock = clock();
+          cout << " Shell stuff synchronization used "
+               << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC)
+               << " seconds! " << endl;
+        }
       }
-    }
 #endif
-    Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
+      Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry);
+    } // end CA-RK4 guard
 
 #ifdef WithShell
     // Complete non-blocking error reduction and check

AMSS_NCKU_source/bssn_rhs_c.C

@@ -39,6 +39,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
     // printf("nx=%d ny=%d nz=%d all=%d\n", nx, ny, nz, all);
 
     // temp variable
+    double gxx[all],gyy[all],gzz[all];
     double chix[all],chiy[all],chiz[all];
     double gxxx[all],gxyx[all],gxzx[all],gyyx[all],gyzx[all],gzzx[all];
     double gxxy[all],gxyy[all],gxzy[all],gyyy[all],gyzy[all],gzzy[all];
@@ -50,9 +51,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
     double Gamxx[all],Gamxy[all],Gamxz[all];
     double Gamyx[all],Gamyy[all],Gamyz[all];
     double Gamzx[all],Gamzy[all],Gamzz[all];
-    double Kx[all], Ky[all], Kz[all], S[all];
+    double Kx[all], Ky[all], Kz[all], div_beta[all], S[all];
     double f[all], fxx[all], fxy[all], fxz[all], fyy[all], fyz[all], fzz[all];
-    double alpn1[all], chin1[all];
+    double Gamxa[all], Gamya[all], Gamza[all], alpn1[all], chin1[all];
     double gupxx[all], gupxy[all], gupxz[all];
     double gupyy[all], gupyz[all], gupzz[all];
     double SSS[3] = { 1.0,  1.0,  1.0};
@@ -69,34 +70,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
     const double FF = 0.75, eta = 2.0;
     const double F1o3 = 1.0/3.0, F2o3 = 2.0/3.0, F3o2 = 1.5, F1o6 = 1.0/6.0;
     const double F16 = 16.0, F8 = 8.0;
-    #if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
+    #if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5)
     double reta[all];
     /* 使用时：reta[idx]，其中 idx = i + nx*(j + ny*k)  (Fortran列主序) */
     #endif
-
-    #if (GAUGE == 6 || GAUGE == 7)
-    int BHN = 0;
-    double Porg[9] = {0.0};
-    double Mass[3] = {0.0};
-
-    extern "C" {
-        #ifdef fortran1
-        void getpbh(int &, double *, double *);
-        #elif defined(fortran2)
-        void GETPBH(int &, double *, double *);
-        #else
-        void getpbh_(int &, double *, double *);
-        #endif
-    }
-
-    #ifdef fortran1
-    getpbh(BHN, Porg, Mass);
-    #elif defined(fortran2)
-    GETPBH(BHN, Porg, Mass);
-    #else
-    getpbh_(BHN, Porg, Mass);
-    #endif
-    #endif
     PI = acos(-1.0); 
     dX = X[1] - X[0];
     dY = Y[1] - Y[0];
@@ -106,6 +83,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
             chin1[i] = chi[i] + 1.0;
+            gxx[i] = dxx[i] + 1.0;
+            gyy[i] = dyy[i] + 1.0;
+            gzz[i] = dzz[i] + 1.0;
         }
         // 9ms //
         fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev);
@@ -123,196 +103,231 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
         // 3ms //
         for(int i=0;i<all;i+=1){
-            const double divb = betaxx[i] + betayy[i] + betazz[i];
+            div_beta[i] = betaxx[i] + betayy[i] + betazz[i];
-            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - divb); 
+            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - div_beta[i]); 
-            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * (dxx[i] + ONE) * divb + 
+            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * gxx[i] * div_beta[i] + 
-                    TWO * ((dxx[i] + ONE) * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
+                    TWO * (gxx[i] * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
-            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * (dyy[i] + ONE) * divb + 
+            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * gyy[i] * div_beta[i] + 
-                    TWO * (gxy[i] * betaxy[i] + (dyy[i] + ONE) * betayy[i] + gyz[i] * betazy[i]);
+                    TWO * (gxy[i] * betaxy[i] + gyy[i] * betayy[i] + gyz[i] * betazy[i]);
-            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * (dzz[i] + ONE) * divb + 
+            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * gzz[i] * div_beta[i] + 
-                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + (dzz[i] + ONE) * betazz[i]);
+                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + gzz[i] * betazz[i]);
-            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * divb + 
+            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * div_beta[i] + 
-                        (dxx[i] + ONE) * betaxy[i] + gxz[i] * betazy[i] + (dyy[i] + ONE) * betayx[i] 
+                        gxx[i] * betaxy[i] + gxz[i] * betazy[i] + gyy[i] * betayx[i] 
                         + gyz[i] * betazx[i] - gxy[i] * betazz[i];        
-            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * divb + 
+            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * div_beta[i] + 
-                        gxy[i] * betaxz[i] + (dyy[i] + ONE) * betayz[i] + gxz[i] * betaxy[i] 
+                        gxy[i] * betaxz[i] + gyy[i] * betayz[i] + gxz[i] * betaxy[i] 
-                        + (dzz[i] + ONE) * betazy[i] - gyz[i] * betaxx[i];
+                        + gzz[i] * betazy[i] - gyz[i] * betaxx[i];
-            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * divb + 
+            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * div_beta[i] + 
-                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
+                        gxx[i] * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
-                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
+                        + gzz[i] * betazx[i] - gxz[i] * betayy[i];                  
         }
-        // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
+        // 1ms //
         for(int i=0;i<all;i+=1){
-            double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
+            double det = gxx[i] * gyy[i] * gzz[i] + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] - 
-                        gxz[i] * (dyy[i] + ONE) * gxz[i] - gxy[i] * gxy[i] * (dzz[i] + ONE) - (dxx[i] + ONE) * gyz[i] * gyz[i];
+                        gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];  
-            double lg_xx = ((dyy[i] + ONE) * (dzz[i] + ONE) - gyz[i] * gyz[i]) / det;
+            gupxx[i] = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
-            double lg_xy = -(gxy[i] * (dzz[i] + ONE) - gyz[i] * gxz[i]) / det;
+            gupxy[i] = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
-            double lg_xz = (gxy[i] * gyz[i] - (dyy[i] + ONE) * gxz[i]) / det;
+            gupxz[i] = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
-            double lg_yy = ((dxx[i] + ONE) * (dzz[i] + ONE) - gxz[i] * gxz[i]) / det;
+            gupyy[i] = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
-            double lg_yz = -((dxx[i] + ONE) * gyz[i] - gxy[i] * gxz[i]) / det;
+            gupyz[i] = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
-            double lg_zz = ((dxx[i] + ONE) * (dyy[i] + ONE) - gxy[i] * gxy[i]) / det;
+            gupzz[i] = (gxx[i] * gyy[i] - gxy[i] * gxy[i]) / det;   
-            gupxx[i] = lg_xx; gupxy[i] = lg_xy; gupxz[i] = lg_xz;
+        }
-            gupyy[i] = lg_yy; gupyz[i] = lg_yz; gupzz[i] = lg_zz;
+        // 2.2ms //
-
+        if(co==0){
-            if(co==0){
+            for (int i=0;i<all;i+=1) {
                 Gmx_Res[i] = Gamx[i] - (
-                    lg_xx * (lg_xx*gxxx[i] + lg_xy*gxyx[i] + lg_xz*gxzx[i]) +
+                    gupxx[i] * (gupxx[i]*gxxx[i] + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i]) +
-                    lg_xy * (lg_xx*gxyx[i] + lg_xy*gyyx[i] + lg_xz*gyzx[i]) +
+                    gupxy[i] * (gupxx[i]*gxyx[i] + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i]) +
-                    lg_xz * (lg_xx*gxzx[i] + lg_xy*gyzx[i] + lg_xz*gzzx[i]) +
+                    gupxz[i] * (gupxx[i]*gxzx[i] + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i]) +
-                    lg_xx * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
+
-                    lg_xy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
+                    gupxx[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
-                    lg_xz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
+                    gupxy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
-                    lg_xx * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
+                    gupxz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
-                    lg_xy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
+
-                    lg_xz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
+                    gupxx[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    gupxy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
+                    gupxz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
+
                 Gmy_Res[i] = Gamy[i] - (
-                    lg_xx * (lg_xy*gxxx[i] + lg_yy*gxyx[i] + lg_yz*gxzx[i]) +
+                    gupxx[i] * (gupxy[i]*gxxx[i] + gupyy[i]*gxyx[i] + gupyz[i]*gxzx[i]) +
-                    lg_xy * (lg_xy*gxyx[i] + lg_yy*gyyx[i] + lg_yz*gyzx[i]) +
+                    gupxy[i] * (gupxy[i]*gxyx[i] + gupyy[i]*gyyx[i] + gupyz[i]*gyzx[i]) +
-                    lg_xz * (lg_xy*gxzx[i] + lg_yy*gyzx[i] + lg_yz*gzzx[i]) +
+                    gupxz[i] * (gupxy[i]*gxzx[i] + gupyy[i]*gyzx[i] + gupyz[i]*gzzx[i]) +
-                    lg_xy * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
+
-                    lg_yy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
+                    gupxy[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
-                    lg_yz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
+                    gupyy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
-                    lg_xy * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
+                    gupyz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
-                    lg_yy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
+
-                    lg_yz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
+                    gupxy[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    gupyy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
+                    gupyz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
+
                 Gmz_Res[i] = Gamz[i] - (
-                    lg_xx * (lg_xz*gxxx[i] + lg_yz*gxyx[i] + lg_zz*gxzx[i]) +
+                    gupxx[i] * (gupxz[i]*gxxx[i] + gupyz[i]*gxyx[i] + gupzz[i]*gxzx[i]) +
-                    lg_xy * (lg_xz*gxyx[i] + lg_yz*gyyx[i] + lg_zz*gyzx[i]) +
+                    gupxy[i] * (gupxz[i]*gxyx[i] + gupyz[i]*gyyx[i] + gupzz[i]*gyzx[i]) +
-                    lg_xz * (lg_xz*gxzx[i] + lg_yz*gyzx[i] + lg_zz*gzzx[i]) +
+                    gupxz[i] * (gupxz[i]*gxzx[i] + gupyz[i]*gyzx[i] + gupzz[i]*gzzx[i]) +
-                    lg_xy * (lg_xz*gxxy[i] + lg_yz*gxyy[i] + lg_zz*gxzy[i]) +
+
-                    lg_yy * (lg_xz*gxyy[i] + lg_yz*gyyy[i] + lg_zz*gyzy[i]) +
+                    gupxy[i] * (gupxz[i]*gxxy[i] + gupyz[i]*gxyy[i] + gupzz[i]*gxzy[i]) +
-                    lg_yz * (lg_xz*gxzy[i] + lg_yz*gyzy[i] + lg_zz*gzzy[i]) +
+                    gupyy[i] * (gupxz[i]*gxyy[i] + gupyz[i]*gyyy[i] + gupzz[i]*gyzy[i]) +
-                    lg_xz * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
+                    gupyz[i] * (gupxz[i]*gxzy[i] + gupyz[i]*gyzy[i] + gupzz[i]*gzzy[i]) +
-                    lg_yz * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
+
-                    lg_zz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
+                    gupxz[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    gupyz[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
+                    gupzz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
             }
-
-            Gamxxx[i] = HALF * ( lg_xx*gxxx[i]
-                            + lg_xy*(TWO*gxyx[i] - gxxy[i])
-                            + lg_xz*(TWO*gxzx[i] - gxxz[i]) );
-            Gamyxx[i] = HALF * ( lg_xy*gxxx[i]
-                            + lg_yy*(TWO*gxyx[i] - gxxy[i])
-                            + lg_yz*(TWO*gxzx[i] - gxxz[i]) );
-            Gamzxx[i] = HALF * ( lg_xz*gxxx[i]
-                            + lg_yz*(TWO*gxyx[i] - gxxy[i])
-                            + lg_zz*(TWO*gxzx[i] - gxxz[i]) );
-            Gamxyy[i] = HALF * ( lg_xx*(TWO*gxyy[i] - gyyx[i])
-                            + lg_xy*gyyy[i]
-                            + lg_xz*(TWO*gyzy[i] - gyyz[i]) );
-            Gamyyy[i] = HALF * ( lg_xy*(TWO*gxyy[i] - gyyx[i])
-                            + lg_yy*gyyy[i]
-                            + lg_yz*(TWO*gyzy[i] - gyyz[i]) );
-            Gamzyy[i] = HALF * ( lg_xz*(TWO*gxyy[i] - gyyx[i])
-                            + lg_yz*gyyy[i]
-                            + lg_zz*(TWO*gyzy[i] - gyyz[i]) );
-            Gamxzz[i] = HALF * ( lg_xx*(TWO*gxzz[i] - gzzx[i])
-                            + lg_xy*(TWO*gyzz[i] - gzzy[i])
-                            + lg_xz*gzzz[i] );
-            Gamyzz[i] = HALF * ( lg_xy*(TWO*gxzz[i] - gzzx[i])
-                            + lg_yy*(TWO*gyzz[i] - gzzy[i])
-                            + lg_yz*gzzz[i] );
-            Gamzzz[i] = HALF * ( lg_xz*(TWO*gxzz[i] - gzzx[i])
-                            + lg_yz*(TWO*gyzz[i] - gzzy[i])
-                            + lg_zz*gzzz[i] );
-            Gamxxy[i] = HALF * ( lg_xx*gxxy[i]
-                            + lg_xy*gyyx[i]
-                            + lg_xz*(gxzy[i] + gyzx[i] - gxyz[i]) );
-            Gamyxy[i] = HALF * ( lg_xy*gxxy[i]
-                            + lg_yy*gyyx[i]
-                            + lg_yz*(gxzy[i] + gyzx[i] - gxyz[i]) );
-            Gamzxy[i] = HALF * ( lg_xz*gxxy[i]
-                            + lg_yz*gyyx[i]
-                            + lg_zz*(gxzy[i] + gyzx[i] - gxyz[i]) );
-            Gamxxz[i] = HALF * ( lg_xx*gxxz[i]
-                            + lg_xy*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + lg_xz*gzzx[i] );
-            Gamyxz[i] = HALF * ( lg_xy*gxxz[i]
-                            + lg_yy*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + lg_yz*gzzx[i] );
-            Gamzxz[i] = HALF * ( lg_xz*gxxz[i]
-                            + lg_yz*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + lg_zz*gzzx[i] );
-            Gamxyz[i] = HALF * ( lg_xx*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + lg_xy*gyyz[i]
-                            + lg_xz*gzzy[i] );
-            Gamyyz[i] = HALF * ( lg_xy*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + lg_yy*gyyz[i]
-                            + lg_yz*gzzy[i] );
-            Gamzyz[i] = HALF * ( lg_xz*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + lg_yz*gyyz[i]
-                            + lg_zz*gzzy[i] );
         }
-        // Fused: A^{ij} raise-index + Gamma_rhs part 1 (2 loops -> 1)
+        // 5ms //
         for (int i=0;i<all;i+=1) {
-            double axx = gupxx[i]*gupxx[i]*Axx[i]
+
+            Gamxxx[i] = HALF * ( gupxx[i]*gxxx[i]
+                            + gupxy[i]*(TWO*gxyx[i] - gxxy[i])
+                            + gupxz[i]*(TWO*gxzx[i] - gxxz[i]) );
+
+            Gamyxx[i] = HALF * ( gupxy[i]*gxxx[i]
+                            + gupyy[i]*(TWO*gxyx[i] - gxxy[i])
+                            + gupyz[i]*(TWO*gxzx[i] - gxxz[i]) );
+
+            Gamzxx[i] = HALF * ( gupxz[i]*gxxx[i]
+                            + gupyz[i]*(TWO*gxyx[i] - gxxy[i])
+                            + gupzz[i]*(TWO*gxzx[i] - gxxz[i]) );
+
+            Gamxyy[i] = HALF * ( gupxx[i]*(TWO*gxyy[i] - gyyx[i])
+                            + gupxy[i]*gyyy[i]
+                            + gupxz[i]*(TWO*gyzy[i] - gyyz[i]) );
+
+            Gamyyy[i] = HALF * ( gupxy[i]*(TWO*gxyy[i] - gyyx[i])
+                            + gupyy[i]*gyyy[i]
+                            + gupyz[i]*(TWO*gyzy[i] - gyyz[i]) );
+
+            Gamzyy[i] = HALF * ( gupxz[i]*(TWO*gxyy[i] - gyyx[i])
+                            + gupyz[i]*gyyy[i]
+                            + gupzz[i]*(TWO*gyzy[i] - gyyz[i]) );
+
+            Gamxzz[i] = HALF * ( gupxx[i]*(TWO*gxzz[i] - gzzx[i])
+                            + gupxy[i]*(TWO*gyzz[i] - gzzy[i])
+                            + gupxz[i]*gzzz[i] );
+
+            Gamyzz[i] = HALF * ( gupxy[i]*(TWO*gxzz[i] - gzzx[i])
+                            + gupyy[i]*(TWO*gyzz[i] - gzzy[i])
+                            + gupyz[i]*gzzz[i] );
+
+            Gamzzz[i] = HALF * ( gupxz[i]*(TWO*gxzz[i] - gzzx[i])
+                            + gupyz[i]*(TWO*gyzz[i] - gzzy[i])
+                            + gupzz[i]*gzzz[i] );
+
+            Gamxxy[i] = HALF * ( gupxx[i]*gxxy[i]
+                            + gupxy[i]*gyyx[i]
+                            + gupxz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
+
+            Gamyxy[i] = HALF * ( gupxy[i]*gxxy[i]
+                            + gupyy[i]*gyyx[i]
+                            + gupyz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
+
+            Gamzxy[i] = HALF * ( gupxz[i]*gxxy[i]
+                            + gupyz[i]*gyyx[i]
+                            + gupzz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
+
+            Gamxxz[i] = HALF * ( gupxx[i]*gxxz[i]
+                            + gupxy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + gupxz[i]*gzzx[i] );
+
+            Gamyxz[i] = HALF * ( gupxy[i]*gxxz[i]
+                            + gupyy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + gupyz[i]*gzzx[i] );
+
+            Gamzxz[i] = HALF * ( gupxz[i]*gxxz[i]
+                            + gupyz[i]*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + gupzz[i]*gzzx[i] );
+
+            Gamxyz[i] = HALF * ( gupxx[i]*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + gupxy[i]*gyyz[i]
+                            + gupxz[i]*gzzy[i] );
+
+            Gamyyz[i] = HALF * ( gupxy[i]*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + gupyy[i]*gyyz[i]
+                            + gupyz[i]*gzzy[i] );
+
+            Gamzyz[i] = HALF * ( gupxz[i]*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + gupyz[i]*gyyz[i]
+                            + gupzz[i]*gzzy[i] );
+
+        }
+        // 1.8ms //
+        for (int i=0;i<all;i+=1) {
+
+            Rxx[i] = gupxx[i]*gupxx[i]*Axx[i]
                 + gupxy[i]*gupxy[i]*Ayy[i]
                 + gupxz[i]*gupxz[i]*Azz[i]
                 + TWO * ( gupxx[i]*gupxy[i]*Axy[i]
                         + gupxx[i]*gupxz[i]*Axz[i]
                         + gupxy[i]*gupxz[i]*Ayz[i] );
-            double ayy = gupxy[i]*gupxy[i]*Axx[i]
+
+            Ryy[i] = gupxy[i]*gupxy[i]*Axx[i]
                 + gupyy[i]*gupyy[i]*Ayy[i]
                 + gupyz[i]*gupyz[i]*Azz[i]
                 + TWO * ( gupxy[i]*gupyy[i]*Axy[i]
                         + gupxy[i]*gupyz[i]*Axz[i]
                         + gupyy[i]*gupyz[i]*Ayz[i] );
-            double azz = gupxz[i]*gupxz[i]*Axx[i]
+
+            Rzz[i] = gupxz[i]*gupxz[i]*Axx[i]
                 + gupyz[i]*gupyz[i]*Ayy[i]
                 + gupzz[i]*gupzz[i]*Azz[i]
                 + TWO * ( gupxz[i]*gupyz[i]*Axy[i]
                         + gupxz[i]*gupzz[i]*Axz[i]
                         + gupyz[i]*gupzz[i]*Ayz[i] );
-            double axy = gupxx[i]*gupxy[i]*Axx[i]
+
+            Rxy[i] = gupxx[i]*gupxy[i]*Axx[i]
                 + gupxy[i]*gupyy[i]*Ayy[i]
                 + gupxz[i]*gupyz[i]*Azz[i]
                 + ( gupxx[i]*gupyy[i] + gupxy[i]*gupxy[i] ) * Axy[i]
                 + ( gupxx[i]*gupyz[i] + gupxz[i]*gupxy[i] ) * Axz[i]
                 + ( gupxy[i]*gupyz[i] + gupxz[i]*gupyy[i] ) * Ayz[i];
-            double axz = gupxx[i]*gupxz[i]*Axx[i]
+
+            Rxz[i] = gupxx[i]*gupxz[i]*Axx[i]
                 + gupxy[i]*gupyz[i]*Ayy[i]
                 + gupxz[i]*gupzz[i]*Azz[i]
                 + ( gupxx[i]*gupyz[i] + gupxy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxx[i]*gupzz[i] + gupxz[i]*gupxz[i] ) * Axz[i]
                 + ( gupxy[i]*gupzz[i] + gupxz[i]*gupyz[i] ) * Ayz[i];
-            double ayz = gupxy[i]*gupxz[i]*Axx[i]
+
+            Ryz[i] = gupxy[i]*gupxz[i]*Axx[i]
                 + gupyy[i]*gupyz[i]*Ayy[i]
                 + gupyz[i]*gupzz[i]*Azz[i]
                 + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                 + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
-            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
+        }
-            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
+        // 4ms //
-
+        for(int i=0;i<all;i+=1){
-            Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
+            Gamx_rhs[i] = - TWO * (   Lapx[i] * Rxx[i] +   Lapy[i] * Rxy[i] +   Lapz[i] * Rxz[i] ) + 
                 TWO * alpn1[i] * (                                                
-                -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
+                -F3o2/chin1[i] * (   chix[i] * Rxx[i] +   chiy[i] * Rxy[i] +   chiz[i] * Rxz[i] ) - 
-                    gupxx[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] ) -
+                    gupxx[i] * (   F2o3 * Kx[i]  +  EIGHT * PI * Sx[i]            ) - 
-                    gupxy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] ) -
+                    gupxy[i] * (   F2o3 * Ky[i]  +  EIGHT * PI * Sy[i]            ) - 
-                    gupxz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] ) +
+                    gupxz[i] * (   F2o3 * Kz[i]  +  EIGHT * PI * Sz[i]            ) + 
-                                Gamxxx[i]*axx + Gamxyy[i]*ayy + Gamxzz[i]*azz +
+                                Gamxxx[i] * Rxx[i] + Gamxyy[i] * Ryy[i] + Gamxzz[i] * Rzz[i]   + 
-                        TWO * ( Gamxxy[i]*axy + Gamxxz[i]*axz + Gamxyz[i]*ayz ) );
+                        TWO * ( Gamxxy[i] * Rxy[i] + Gamxxz[i] * Rxz[i] + Gamxyz[i] * Ryz[i] ) );
 
-            Gamy_rhs[i] = -TWO * ( Lapx[i]*axy + Lapy[i]*ayy + Lapz[i]*ayz )
+            Gamy_rhs[i] = -TWO * ( Lapx[i]*Rxy[i] + Lapy[i]*Ryy[i] + Lapz[i]*Ryz[i] )
                         +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*axy + chiy[i]*ayy + chiz[i]*ayz )
+                            -F3o2/chin1[i] * ( chix[i]*Rxy[i] + chiy[i]*Ryy[i] + chiz[i]*Ryz[i] )
                             - gupxy[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                             - gupyy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                             - gupyz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamyxx[i]*axx + Gamyyy[i]*ayy + Gamyzz[i]*azz
+                            + Gamyxx[i]*Rxx[i] + Gamyyy[i]*Ryy[i] + Gamyzz[i]*Rzz[i]
-                            + TWO * ( Gamyxy[i]*axy + Gamyxz[i]*axz + Gamyyz[i]*ayz )
+                            + TWO * ( Gamyxy[i]*Rxy[i] + Gamyxz[i]*Rxz[i] + Gamyyz[i]*Ryz[i] )
                         );
 
-            Gamz_rhs[i] = -TWO * ( Lapx[i]*axz + Lapy[i]*ayz + Lapz[i]*azz )
+            Gamz_rhs[i] = -TWO * ( Lapx[i]*Rxz[i] + Lapy[i]*Ryz[i] + Lapz[i]*Rzz[i] )
                         +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*axz + chiy[i]*ayz + chiz[i]*azz )
+                            -F3o2/chin1[i] * ( chix[i]*Rxz[i] + chiy[i]*Ryz[i] + chiz[i]*Rzz[i] )
                             - gupxz[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                             - gupyz[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                             - gupzz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamzxx[i]*axx + Gamzyy[i]*ayy + Gamzzz[i]*azz
+                            + Gamzxx[i]*Rxx[i] + Gamzyy[i]*Ryy[i] + Gamzzz[i]*Rzz[i]
-                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
+                            + TWO * ( Gamzxy[i]*Rxy[i] + Gamzxz[i]*Rxz[i] + Gamzyz[i]*Ryz[i] )
                         );
         }
         // 22.3ms //
@@ -326,63 +341,65 @@ int f_compute_rhs_bssn(int *ex, double &T,
         fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev);
         fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev);
 
-        // Fused: fxx/Gamxa + Gamma_rhs part 2 (2 loops -> 1)
+        // 3.5ms //
         for(int i=0;i<all;i+=1){
-            const double divb = betaxx[i] + betayy[i] + betazz[i];
+            fxx[i] = gxxx[i] + gxyy[i] + gxzz[i];
-            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
+            fxy[i] = gxyx[i] + gyyy[i] + gyzz[i];
-            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
+            fxz[i] = gxzx[i] + gyzy[i] + gzzz[i];
-            double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
+            Gamxa[i] = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
-            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
-
-            double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                     + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
-            double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
+
+            Gamya[i] = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
                     + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
-            double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
+
+            Gamza[i] = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
                     + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
+        }
+        // 3.9ms //
+        for(int i=0;i<all;i+=1){
             Gamx_rhs[i] = Gamx_rhs[i]
-                        + F2o3 * gxa * divb
+                        + F2o3 * Gamxa[i] * div_beta[i]
-                        - gxa * betaxx[i] - gya * betaxy[i] - gza * betaxz[i]
+                        - Gamxa[i] * betaxx[i] - Gamya[i] * betaxy[i] - Gamza[i] * betaxz[i]
-                        + F1o3 * ( gupxx[i] * lfxx + gupxy[i] * lfxy + gupxz[i] * lfxz )
+                        + F1o3 * ( gupxx[i] * fxx[i] + gupxy[i] * fxy[i] + gupxz[i] * fxz[i] )
                         + gupxx[i] * gxxx[i] + gupyy[i] * gyyx[i] + gupzz[i] * gzzx[i]
                         + TWO * ( gupxy[i] * gxyx[i] + gupxz[i] * gxzx[i] + gupyz[i] * gyzx[i] );
 
             Gamy_rhs[i] = Gamy_rhs[i]
-                        + F2o3 * gya * divb
+                        + F2o3 * Gamya[i] * div_beta[i]
-                        - gxa * betayx[i] - gya * betayy[i] - gza * betayz[i]
+                        - Gamxa[i] * betayx[i] - Gamya[i] * betayy[i] - Gamza[i] * betayz[i]
-                        + F1o3 * ( gupxy[i] * lfxx + gupyy[i] * lfxy + gupyz[i] * lfxz )
+                        + F1o3 * ( gupxy[i] * fxx[i] + gupyy[i] * fxy[i] + gupyz[i] * fxz[i] )
                         + gupxx[i] * gxxy[i] + gupyy[i] * gyyy[i] + gupzz[i] * gzzy[i]
                         + TWO * ( gupxy[i] * gxyy[i] + gupxz[i] * gxzy[i] + gupyz[i] * gyzy[i] );
 
             Gamz_rhs[i] = Gamz_rhs[i]
-                        + F2o3 * gza * divb
+                        + F2o3 * Gamza[i] * div_beta[i]
-                        - gxa * betazx[i] - gya * betazy[i] - gza * betazz[i]
+                        - Gamxa[i] * betazx[i] - Gamya[i] * betazy[i] - Gamza[i] * betazz[i]
-                        + F1o3 * ( gupxz[i] * lfxx + gupyz[i] * lfxy + gupzz[i] * lfxz )
+                        + F1o3 * ( gupxz[i] * fxx[i] + gupyz[i] * fxy[i] + gupzz[i] * fxz[i] )
                         + gupxx[i] * gxxz[i] + gupyy[i] * gyyz[i] + gupzz[i] * gzzz[i]
                         + TWO * ( gupxy[i] * gxyz[i] + gupxz[i] * gxzz[i] + gupyz[i] * gyzz[i] );
         }
         // 4.4ms //
         for (int i=0;i<all;i+=1) {
-            gxxx[i] = (dxx[i] + ONE)*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
+            gxxx[i] = gxx[i]*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
-            gxyx[i] = (dxx[i] + ONE)*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
+            gxyx[i] = gxx[i]*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
-            gxzx[i] = (dxx[i] + ONE)*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
+            gxzx[i] = gxx[i]*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
-            gyyx[i] = (dxx[i] + ONE)*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
+            gyyx[i] = gxx[i]*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
-            gyzx[i] = (dxx[i] + ONE)*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
+            gyzx[i] = gxx[i]*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
-            gzzx[i] = (dxx[i] + ONE)*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
+            gzzx[i] = gxx[i]*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
 
-            gxxy[i] = gxy[i]*Gamxxx[i] + (dyy[i] + ONE)*Gamyxx[i] + gyz[i]*Gamzxx[i];
+            gxxy[i] = gxy[i]*Gamxxx[i] + gyy[i]*Gamyxx[i] + gyz[i]*Gamzxx[i];
-            gxyy[i] = gxy[i]*Gamxxy[i] + (dyy[i] + ONE)*Gamyxy[i] + gyz[i]*Gamzxy[i];
+            gxyy[i] = gxy[i]*Gamxxy[i] + gyy[i]*Gamyxy[i] + gyz[i]*Gamzxy[i];
-            gxzy[i] = gxy[i]*Gamxxz[i] + (dyy[i] + ONE)*Gamyxz[i] + gyz[i]*Gamzxz[i];
+            gxzy[i] = gxy[i]*Gamxxz[i] + gyy[i]*Gamyxz[i] + gyz[i]*Gamzxz[i];
-            gyyy[i] = gxy[i]*Gamxyy[i] + (dyy[i] + ONE)*Gamyyy[i] + gyz[i]*Gamzyy[i];
+            gyyy[i] = gxy[i]*Gamxyy[i] + gyy[i]*Gamyyy[i] + gyz[i]*Gamzyy[i];
-            gyzy[i] = gxy[i]*Gamxyz[i] + (dyy[i] + ONE)*Gamyyz[i] + gyz[i]*Gamzyz[i];
+            gyzy[i] = gxy[i]*Gamxyz[i] + gyy[i]*Gamyyz[i] + gyz[i]*Gamzyz[i];
-            gzzy[i] = gxy[i]*Gamxzz[i] + (dyy[i] + ONE)*Gamyzz[i] + gyz[i]*Gamzzz[i];
+            gzzy[i] = gxy[i]*Gamxzz[i] + gyy[i]*Gamyzz[i] + gyz[i]*Gamzzz[i];
 
-            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + (dzz[i] + ONE)*Gamzxx[i];
+            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + gzz[i]*Gamzxx[i];
-            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + (dzz[i] + ONE)*Gamzxy[i];
+            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + gzz[i]*Gamzxy[i];
-            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + (dzz[i] + ONE)*Gamzxz[i];
+            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + gzz[i]*Gamzxz[i];
-            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + (dzz[i] + ONE)*Gamzyy[i];
+            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + gzz[i]*Gamzyy[i];
-            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + (dzz[i] + ONE)*Gamzyz[i];
+            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + gzz[i]*Gamzyz[i];
-            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + (dzz[i] + ONE)*Gamzzz[i];
+            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + gzz[i]*Gamzzz[i];
         }
         // 22.2ms //
             fdderivs(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
@@ -430,17 +447,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
         // 14ms //
         /* 假设 all = ex1*ex2*ex3，所有量都是 length=all 的 double 数组（已按同一扁平化规则排布） */
         for (int i = 0; i < all; i += 1) {
-            const double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
-                            + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
-            const double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
-                            + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
-            const double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
-                            + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
-
             Rxx[i] =
                 -HALF * Rxx[i]
-                + (dxx[i] + ONE) * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
+                + gxx[i] * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
-                + gxa * gxxx[i] + gya * gxyx[i] + gza * gxzx[i]
+                + Gamxa[i] * gxxx[i] + Gamya[i] * gxyx[i] + Gamza[i] * gxzx[i]
                 + gupxx[i] * (
                     TWO * (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxyx[i] + Gamzxx[i] * gxzx[i]) +
                         (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxxy[i] + Gamzxx[i] * gxxz[i])
@@ -474,8 +484,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
             Ryy[i] =
                 -HALF * Ryy[i]
-                + gxy[i] * Gamxy[i] + (dyy[i] + ONE) * Gamyy[i] + gyz[i] * Gamzy[i]
+                + gxy[i] * Gamxy[i] + gyy[i] * Gamyy[i] + gyz[i] * Gamzy[i]
-                + gxa * gxyy[i] + gya * gyyy[i] + gza * gyzy[i]
+                + Gamxa[i] * gxyy[i] + Gamya[i] * gyyy[i] + Gamza[i] * gyzy[i]
                 + gupxx[i] * (
                     TWO * (Gamxxy[i] * gxxy[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxzy[i]) +
                         (Gamxxy[i] * gxyx[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxyz[i])
@@ -509,8 +519,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
             Rzz[i] =
                 -HALF * Rzz[i]
-                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + (dzz[i] + ONE) * Gamzz[i]
+                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + gzz[i] * Gamzz[i]
-                + gxa * gxzz[i] + gya * gyzz[i] + gza * gzzz[i]
+                + Gamxa[i] * gxzz[i] + Gamya[i] * gyzz[i] + Gamza[i] * gzzz[i]
                 + gupxx[i] * (
                     TWO * (Gamxxz[i] * gxxz[i] + Gamyxz[i] * gxyz[i] + Gamzxz[i] * gxzz[i]) +
                         (Gamxxz[i] * gxzx[i] + Gamyxz[i] * gxzy[i] + Gamzxz[i] * gxzz[i])
@@ -545,10 +555,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Rxy[i] =
                 HALF * (
                     -Rxy[i]
-                    + (dxx[i] + ONE) * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
+                    + gxx[i] * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
-                    + gxy[i] * Gamxx[i] + (dyy[i] + ONE) * Gamyx[i] + gyz[i] * Gamzx[i]
+                    + gxy[i] * Gamxx[i] + gyy[i] * Gamyx[i] + gyz[i] * Gamzx[i]
-                    + gxa * gxyx[i] + gya * gyyx[i] + gza * gyzx[i]
+                    + Gamxa[i] * gxyx[i] + Gamya[i] * gyyx[i] + Gamza[i] * gyzx[i]
-                    + gxa * gxxy[i] + gya * gxyy[i] + gza * gxzy[i]
+                    + Gamxa[i] * gxxy[i] + Gamya[i] * gxyy[i] + Gamza[i] * gxzy[i]
                 )
                 + gupxx[i] * (
                     Gamxxx[i] * gxxy[i] + Gamyxx[i] * gxyy[i] + Gamzxx[i] * gxzy[i]
@@ -593,10 +603,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Rxz[i] =
                 HALF * (
                     -Rxz[i]
-                    + (dxx[i] + ONE) * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
+                    + gxx[i] * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
-                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + (dzz[i] + ONE) * Gamzx[i]
+                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + gzz[i] * Gamzx[i]
-                    + gxa * gxzx[i] + gya * gyzx[i] + gza * gzzx[i]
+                    + Gamxa[i] * gxzx[i] + Gamya[i] * gyzx[i] + Gamza[i] * gzzx[i]
-                    + gxa * gxxz[i] + gya * gxyz[i] + gza * gxzz[i]
+                    + Gamxa[i] * gxxz[i] + Gamya[i] * gxyz[i] + Gamza[i] * gxzz[i]
                 )
                 + gupxx[i] * (
                     Gamxxx[i] * gxxz[i] + Gamyxx[i] * gxyz[i] + Gamzxx[i] * gxzz[i]
@@ -641,10 +651,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Ryz[i] =
                 HALF * (
                     -Ryz[i]
-                    + gxy[i] * Gamxz[i] + (dyy[i] + ONE) * Gamyz[i] + gyz[i] * Gamzz[i]
+                    + gxy[i] * Gamxz[i] + gyy[i] * Gamyz[i] + gyz[i] * Gamzz[i]
-                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + (dzz[i] + ONE) * Gamzy[i]
+                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + gzz[i] * Gamzy[i]
-                    + gxa * gxzy[i] + gya * gyzy[i] + gza * gzzy[i]
+                    + Gamxa[i] * gxzy[i] + Gamya[i] * gyzy[i] + Gamza[i] * gzzy[i]
-                    + gxa * gxyz[i] + gya * gyyz[i] + gza * gyzz[i]
+                    + Gamxa[i] * gxyz[i] + Gamya[i] * gyyz[i] + Gamza[i] * gyzz[i]
                 )
                 + gupxx[i] * (
                     Gamxxy[i] * gxxz[i] + Gamyxy[i] * gxyz[i] + Gamzxy[i] * gxzz[i]
@@ -705,9 +715,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
                 + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
                 + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + gxx[i] * f[i] ) / (chin1[i] * TWO);
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + gyy[i] * f[i] ) / (chin1[i] * TWO);
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + gzz[i] * f[i] ) / (chin1[i] * TWO);
 
             Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
             Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
@@ -726,17 +736,17 @@ int f_compute_rhs_bssn(int *ex, double &T,
             gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
 
             /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - gxx[i] * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - gxx[i] * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - gxx[i] * gxxz[i] ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - gyy[i] * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - gyy[i] * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - gyy[i] * gxxz[i] ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - gzz[i] * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - gzz[i] * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - gzz[i] * gxxz[i] ) * HALF;
 
             Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
             Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
@@ -758,13 +768,14 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fxy[i] = fxy[i] - Gamxxy[i] * Lapx[i] - Gamyxy[i] * Lapy[i] - Gamzxy[i] * Lapz[i];
             fxz[i] = fxz[i] - Gamxxz[i] * Lapx[i] - Gamyxz[i] * Lapy[i] - Gamzxz[i] * Lapz[i];
             fyz[i] = fyz[i] - Gamxyz[i] * Lapx[i] - Gamyyz[i] * Lapy[i] - Gamzyz[i] * Lapz[i];
-
+        }
+        // 1ms //
+        for (int i=0;i<all;i+=1) {
             trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                     +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
         }
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
-            const double divb = betaxx[i] + betayy[i] + betazz[i];
 
             S[i] = chin1[i] * (
                     gupxx[i] * Sxx[i] + gupyy[i] * Syy[i] + gupzz[i] * Szz[i]
@@ -815,20 +826,23 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + (alpn1[i] / chin1[i]) * f[i]
             );
 
-            double l_fxx = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
+            fxx[i] = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
-            double l_fxy = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
+            fxy[i] = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
-            double l_fxz = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
+            fxz[i] = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
-            double l_fyy = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
+            fyy[i] = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
-            double l_fyz = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
+            fyz[i] = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
-            double l_fzz = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
+            fzz[i] = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
+        }
+        // 8ms //
+        for (int i=0;i<all;i+=1) {
 
             /* Aij_rhs = fij - gij * f */
-            Axx_rhs[i] = l_fxx - (dxx[i] + ONE) * f[i];
+            Axx_rhs[i] = fxx[i] - gxx[i] * f[i];
-            Ayy_rhs[i] = l_fyy - (dyy[i] + ONE) * f[i];
+            Ayy_rhs[i] = fyy[i] - gyy[i] * f[i];
-            Azz_rhs[i] = l_fzz - (dzz[i] + ONE) * f[i];
+            Azz_rhs[i] = fzz[i] - gzz[i] * f[i];
-            Axy_rhs[i] = l_fxy - gxy[i] * f[i];
+            Axy_rhs[i] = fxy[i] - gxy[i] * f[i];
-            Axz_rhs[i] = l_fxz - gxz[i] * f[i];
+            Axz_rhs[i] = fxz[i] - gxz[i] * f[i];
-            Ayz_rhs[i] = l_fyz - gyz[i] * f[i];
+            Ayz_rhs[i] = fyz[i] - gyz[i] * f[i];
 
             /* Now: store A_il A^l_j into fij: */
             fxx[i] =
@@ -890,19 +904,19 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 f[i] * Axx_rhs[i]
                 + alpn1[i] * ( trK[i] * Axx[i] - TWO * fxx[i] )
                 + TWO * ( Axx[i] * betaxx[i] + Axy[i] * betayx[i] + Axz[i] * betazx[i] )
-                - F2o3 * Axx[i] * divb;
+                - F2o3 * Axx[i] * div_beta[i];
 
             Ayy_rhs[i] =
                 f[i] * Ayy_rhs[i]
                 + alpn1[i] * ( trK[i] * Ayy[i] - TWO * fyy[i] )
                 + TWO * ( Axy[i] * betaxy[i] + Ayy[i] * betayy[i] + Ayz[i] * betazy[i] )
-                - F2o3 * Ayy[i] * divb;
+                - F2o3 * Ayy[i] * div_beta[i];
 
             Azz_rhs[i] =
                 f[i] * Azz_rhs[i]
                 + alpn1[i] * ( trK[i] * Azz[i] - TWO * fzz[i] )
                 + TWO * ( Axz[i] * betaxz[i] + Ayz[i] * betayz[i] + Azz[i] * betazz[i] )
-                - F2o3 * Azz[i] * divb;
+                - F2o3 * Azz[i] * div_beta[i];
 
             Axy_rhs[i] =
                 f[i] * Axy_rhs[i]
@@ -911,7 +925,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Axz[i] * betazy[i]
                 + Ayy[i] * betayx[i]
                 + Ayz[i] * betazx[i]
-                + F1o3 * Axy[i] * divb
+                + F1o3 * Axy[i] * div_beta[i]
                 - Axy[i] * betazz[i];
 
             Ayz_rhs[i] =
@@ -921,7 +935,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Ayy[i] * betayz[i]
                 + Axz[i] * betaxy[i]
                 + Azz[i] * betazy[i]
-                + F1o3 * Ayz[i] * divb
+                + F1o3 * Ayz[i] * div_beta[i]
                 - Ayz[i] * betaxx[i];
 
             Axz_rhs[i] =
@@ -931,7 +945,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Axy[i] * betayz[i]
                 + Ayz[i] * betayx[i]
                 + Azz[i] * betazx[i]
-                + F1o3 * Axz[i] * divb
+                + F1o3 * Axz[i] * div_beta[i]
                 - Axz[i] * betayy[i];
 
             /* Compute trace of S_ij */
@@ -952,141 +966,82 @@ int f_compute_rhs_bssn(int *ex, double &T,
         }
 
         // 1ms //
-        #if (GAUGE == 6 || GAUGE == 7)
+        for(int i=0;i<all;i+=1){
-        if (BHN == 2) {
-            const double M = Mass[0] + Mass[1];
-            const double A = TWO / M;
-            const double w1 = 1.2e1;
-            const double w2 = w1;
-            const double C1 = ONE / Mass[0] - A;
-            const double C2 = ONE / Mass[1] - A;
-            const double denom =
-                (Porg[0] - Porg[3]) * (Porg[0] - Porg[3]) +
-                (Porg[1] - Porg[4]) * (Porg[1] - Porg[4]) +
-                (Porg[2] - Porg[5]) * (Porg[2] - Porg[5]);
-
-            for (int k0 = 0; k0 < nz; ++k0) {
-                for (int j0 = 0; j0 < ny; ++j0) {
-                    for (int i0 = 0; i0 < nx; ++i0) {
-                        const size_t p = idx_ex(i0, j0, k0, ex);
-                        const double dx1 = Porg[0] - X[i0];
-                        const double dy1 = Porg[1] - Y[j0];
-                        const double dz1 = Porg[2] - Z[k0];
-                        const double dx2 = Porg[3] - X[i0];
-                        const double dy2 = Porg[4] - Y[j0];
-                        const double dz2 = Porg[5] - Z[k0];
-                        const double r1 = (dx1 * dx1 + dy1 * dy1 + dz1 * dz1) / denom;
-                        const double r2 = (dx2 * dx2 + dy2 * dy2 + dz2 * dz2) / denom;
-                        #if (GAUGE == 6)
-                        reta[p] = A + C1 / (ONE + w1 * r1) + C2 / (ONE + w2 * r2);
-                        #else
-                        reta[p] = A + C1 * exp(-w1 * r1) + C2 * exp(-w2 * r2);
-                        #endif
-                    }
-                }
-            }
-        } else {
-            printf("not support BH_num in Jason's form %d %d\n", (GAUGE == 6) ? 1 : 2, BHN);
-            for (int i = 0; i < all; ++i) reta[i] = ZEO;
-        }
-        #endif
-
-        for (int i = 0; i < all; i += 1) {
-            #if (GAUGE == 0)
             betax_rhs[i] = FF * dtSfx[i];
             betay_rhs[i] = FF * dtSfy[i];
             betaz_rhs[i] = FF * dtSfz[i];
+#if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5)
+            reta[i] =
+                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
+                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
+                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
+                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
+                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
+                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
 
+            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (1.0 - sqrt(chin1[i])), 2.0 );
+
+            dtSfx_rhs[i] = Gamx_rhs[i] - reta[i] * dtSfx[i];
+            dtSfy_rhs[i] = Gamy_rhs[i] - reta[i] * dtSfy[i];
+            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
+#else
             dtSfx_rhs[i] = Gamx_rhs[i] - eta * dtSfx[i];
             dtSfy_rhs[i] = Gamy_rhs[i] - eta * dtSfy[i];
             dtSfz_rhs[i] = Gamz_rhs[i] - eta * dtSfz[i];
-            #elif (GAUGE == 1)
+#endif
-            betax_rhs[i] = Gamx[i] - eta * betax[i];
+        }
-            betay_rhs[i] = Gamy[i] - eta * betay[i];
+        // 26ms //
-            betaz_rhs[i] = Gamz[i] - eta * betaz[i];
+        lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS);
-
+        lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA);
-            dtSfx_rhs[i] = ZEO;
+        lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS);
-            dtSfy_rhs[i] = ZEO;
+        lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS);
-            dtSfz_rhs[i] = ZEO;
+        lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA);
-            #elif (GAUGE == 2 || GAUGE == 3)
+        lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS);
-            betax_rhs[i] = FF * dtSfx[i];
+        lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS);
-            betay_rhs[i] = FF * dtSfy[i];
+        lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS);
-            betaz_rhs[i] = FF * dtSfz[i];
+        lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA);
-
+        lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA);
-            reta[i] =
+        lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS);
-                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
+        lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS);
-                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
+        lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS);
-                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
+        lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS);
-                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
+        lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS);
-                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
+        lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA);
-                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
+        lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA);
-
+        lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS);
-            #if (GAUGE == 2)
+        lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA);
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
+        lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS);
-            #else
+        lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS);
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - chin1[i]), 2.0 );
+        lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS);
-            #endif
+        lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS);
-
+        lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS);
-            dtSfx_rhs[i] = Gamx_rhs[i] - reta[i] * dtSfx[i];
+        // 20ms //
-            dtSfy_rhs[i] = Gamy_rhs[i] - reta[i] * dtSfy[i];
+        if(eps>0){
-            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
+            kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps);
-            #elif (GAUGE == 4 || GAUGE == 5)
+            kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps);
-            reta[i] =
+            kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps);
-                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
+            kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps);
-                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
+            kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps);
-                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
+            kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps);
-                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
+            kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps);
-                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
+            kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps);
-                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
+            kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps);
-
+            kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps);
-            #if (GAUGE == 4)
+            kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps);
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
+            kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps);
-            #else
+            kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps);
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - chin1[i]), 2.0 );
+            kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps);
-            #endif
+            kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps);
-
+            kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps);
-            betax_rhs[i] = FF * Gamx[i] - reta[i] * betax[i];
+            kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps);
-            betay_rhs[i] = FF * Gamy[i] - reta[i] * betay[i];
+            kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps);
-            betaz_rhs[i] = FF * Gamz[i] - reta[i] * betaz[i];
+            kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps);
-
+            kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps);
-            dtSfx_rhs[i] = ZEO;
+            kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps);
-            dtSfy_rhs[i] = ZEO;
+            kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps);
-            dtSfz_rhs[i] = ZEO;
+            kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps);
-            #elif (GAUGE == 6 || GAUGE == 7)
+            kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps);
-            betax_rhs[i] = FF * dtSfx[i];
-            betay_rhs[i] = FF * dtSfy[i];
-            betaz_rhs[i] = FF * dtSfz[i];
-
-            dtSfx_rhs[i] = Gamx_rhs[i] - reta[i] * dtSfx[i];
-            dtSfy_rhs[i] = Gamy_rhs[i] - reta[i] * dtSfy[i];
-            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
-            #endif
         }
-        // advection + KO dissipation with shared symmetry buffer
-        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
         // 2ms //
         if(co==0){
             for (int i=0;i<all;i+=1) {

AMSS_NCKU_source/cgh.C

@@ -130,11 +130,7 @@ void cgh::compose_cgh(int nprocs)
   for (int lev = 0; lev < levels; lev++)
   {
     checkPatchList(PatL[lev], false);
-#ifdef INTERP_LB_OPTIMIZE
-    Parallel::distribute_optimize(PatL[lev], nprocs, ingfs, fngfs, false);
-#else
     Parallel::distribute(PatL[lev], nprocs, ingfs, fngfs, false);
-#endif
 #if (RPB == 1)
     // we need distributed box of PatL[lev] and PatL[lev-1]
     if (lev > 0)

AMSS_NCKU_source/fdderivs_c.C

@@ -71,85 +71,149 @@ void fdderivs(const int ex[3],
     const double Fdxdz = F1o144 / (dX * dZ);
     const double Fdydz = F1o144 / (dY * dZ);
 
-    /* 只清零不被主循环覆盖的边界面 */
+    /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
-    {
+    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
-        /* 高边界：k0=ex3-1 */
+    for (size_t p = 0; p < all; ++p) {
-        for (int j0 = 0; j0 < ex2; ++j0)
+        fxx[p] = ZEO; fyy[p] = ZEO; fzz[p] = ZEO;
-            for (int i0 = 0; i0 < ex1; ++i0) {
+        fxy[p] = ZEO; fxz[p] = ZEO; fyz[p] = ZEO;
-                const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
-                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-            }
-        /* 高边界：j0=ex2-1 */
-        for (int k0 = 0; k0 < ex3 - 1; ++k0)
-            for (int i0 = 0; i0 < ex1; ++i0) {
-                const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
-                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-            }
-        /* 高边界：i0=ex1-1 */
-        for (int k0 = 0; k0 < ex3 - 1; ++k0)
-            for (int j0 = 0; j0 < ex2 - 1; ++j0) {
-                const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
-                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-            }
-
-        /* 低边界：当二阶模板也不可用时，对应 i0/j0/k0=0 面 */
-        if (kminF == 1) {
-            for (int j0 = 0; j0 < ex2; ++j0)
-                for (int i0 = 0; i0 < ex1; ++i0) {
-                    const size_t p = idx_ex(i0, j0, 0, ex);
-                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-                }
-        }
-        if (jminF == 1) {
-            for (int k0 = 0; k0 < ex3; ++k0)
-                for (int i0 = 0; i0 < ex1; ++i0) {
-                    const size_t p = idx_ex(i0, 0, k0, ex);
-                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-                }
-        }
-        if (iminF == 1) {
-            for (int k0 = 0; k0 < ex3; ++k0)
-                for (int j0 = 0; j0 < ex2; ++j0) {
-                    const size_t p = idx_ex(0, j0, k0, ex);
-                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-                }
-        }
     }
 
     /*
-     * 两段式：
+     * Fortran:
-     * 1) 二阶可用区域先计算二阶模板
+     * do k=1,ex3-1
-     * 2) 高阶可用区域再覆盖四阶模板
+     * do j=1,ex2-1
+     * do i=1,ex1-1
      */
-    const int i2_lo = (iminF > 0) ? iminF : 0;
-    const int j2_lo = (jminF > 0) ? jminF : 0;
-    const int k2_lo = (kminF > 0) ? kminF : 0;
-    const int i2_hi = ex1 - 2;
-    const int j2_hi = ex2 - 2;
-    const int k2_hi = ex3 - 2;
     
-    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+        const int kF = k0 + 1;
-    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-    const int i4_hi = ex1 - 3;
+            const int jF = j0 + 1;
-    const int j4_hi = ex2 - 3;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-    const int k4_hi = ex3 - 3;
+                const int iF = i0 + 1;
+                const size_t p = idx_ex(i0, j0, k0, ex);
 
-    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
-        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
-            const int kF = k0 + 1;
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
-            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
-                const int jF = j0 + 1;
+                {
-                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                    fxx[p] = Fdxdx * (
-                    const int iF = i0 + 1;
+                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
-                    const size_t p = idx_ex(i0, j0, k0, ex);
+                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
 
+                    fyy[p] = Fdydy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fzz[p] = Fdzdz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+
+                    /* fxy 高阶：完全照搬 Fortran 的括号结构 */
+                    {
+                        const double t_jm2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
+
+                        const double t_jm1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
+
+                        const double t_jp1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
+
+                        const double t_jp2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
+
+                        fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
+                    }
+
+                    /* fxz 高阶 */
+                    {
+                        const double t_km2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
+
+                        const double t_km1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
+
+                        const double t_kp1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
+
+                        const double t_kp2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
+
+                        fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                    }
+
+                    /* fyz 高阶 */
+                    {
+                        const double t_km2 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
+
+                        const double t_km1 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
+
+                        const double t_kp1 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
+
+                        const double t_kp2 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
+
+                        fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                    }
+                }
+                /* 二阶分支：i±1,j±1,k±1 在范围内 */
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
                     fxx[p] = Sdxdx * (
                         fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
@@ -188,127 +252,13 @@ void fdderivs(const int ex[3],
                         fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
                         fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
                     );
-                }
+                }else{
-            }
+                    fxx[p] = 0.0;
-        }
+                    fyy[p] = 0.0;
-    }
+                    fzz[p] = 0.0;
-
+                    fxy[p] = 0.0;
-    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+                    fxz[p] = 0.0;
-        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+                    fyz[p] = 0.0;
-            const int kF = k0 + 1;
-            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
-
-                    fxx[p] = Fdxdx * (
-                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fyy[p] = Fdydy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fzz[p] = Fdzdz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-
-                    {
-                        const double t_jm2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
-
-                        const double t_jm1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
-
-                        const double t_jp1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
-
-                        const double t_jp2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
-
-                        fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
-                    }
-
-                    {
-                        const double t_km2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
-
-                        const double t_km1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
-
-                        const double t_kp1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
-
-                        const double t_kp2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
-
-                        fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
-                    }
-
-                    {
-                        const double t_km2 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
-
-                        const double t_km1 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
-
-                        const double t_kp1 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
-
-                        const double t_kp2 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
-
-                        fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
-                    }
                 }
             }
         }

AMSS_NCKU_source/fderivs_c.C

@@ -81,63 +81,26 @@ void fderivs(const int ex[3],
     }
 
     /*
-     * 两段式：
+     * Fortran loops:
-     * 1) 先在二阶可用区域计算二阶模板
+     * do k=1,ex3-1
-     * 2) 再在高阶可用区域覆盖为四阶模板
+     * do j=1,ex2-1
+     * do i=1,ex1-1
      *
-     * 与原 if/elseif 逻辑等价，但减少逐点分支判断。
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
      */
-    const int i2_lo = (iminF > 0) ? iminF : 0;
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-    const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int kF = k0 + 1;
-    const int k2_lo = (kminF > 0) ? kminF : 0;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-    const int i2_hi = ex1 - 2;
+            const int jF = j0 + 1;
-    const int j2_hi = ex2 - 2;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-    const int k2_hi = ex3 - 2;
+                const int iF = i0 + 1;
-
+                const size_t p = idx_ex(i0, j0, k0, ex);
-    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
-    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
-    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
-    const int i4_hi = ex1 - 3;
-    const int j4_hi = ex2 - 3;
-    const int k4_hi = ex3 - 3;
-
-    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
-        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
-
-                    fx[p] = d2dx * (
-                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fy[p] = d2dy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fz[p] = d2dz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-                }
-            }
-        }
-    }
-
-    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
-        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
 
+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
                     fx[p] = d12dx * (
                         fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
                         EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
@@ -159,6 +122,26 @@ void fderivs(const int ex[3],
                         fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
                     );
                 }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    fx[p] = d2dx * (
+                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d2dy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fz[p] = d2dz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                }
             }
         }
     }

AMSS_NCKU_source/fmisc.f90

@@ -1115,147 +1115,6 @@ 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)
@@ -1270,15 +1129,6 @@ 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
@@ -1328,41 +1178,6 @@ 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
 !
@@ -1433,26 +1248,19 @@ end subroutine d2dump
   end do
   call polint(x1a,ymtmp,x1,y,dy,ordn)
 #else
-  integer  :: i, j, k
+  integer  :: j, k
-  real*8, dimension(ordn) :: w1, w2
+  real*8, dimension(ordn,ordn) :: yatmp
   real*8, dimension(ordn) :: ymtmp
-  real*8 :: yx_sum, x_sum
+  real*8 :: dy_temp
 
-  call polint_lagrange_weights(x1a, x1, w1, ordn)
+  do k=1,ordn
-  call polint_lagrange_weights(x2a, x2, w2, ordn)
+    do j=1,ordn
-
+      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, 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
 
@@ -1801,11 +1609,8 @@ 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
 
-  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
+  fout = C1*f1+C2*f2+C3*f3
-    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
-  end do
 
   return
 

AMSS_NCKU_source/interp_lb_profile.C

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

AMSS_NCKU_source/interp_lb_profile.h

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

AMSS_NCKU_source/interp_lb_profile_data.h

@@ -1,29 +0,0 @@
-/* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
-/* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
-/* Auto-generated from interp_lb_profile.bin — do not edit */
-#ifndef INTERP_LB_PROFILE_DATA_H
-#define INTERP_LB_PROFILE_DATA_H
-
-#define INTERP_LB_NPROCS 64
-#define INTERP_LB_NUM_HEAVY 4
-
-static const int interp_lb_heavy_blocks[4] = {27, 35, 28, 36};
-
-/* Split table: {block_id, r_left, r_right} */
-static const int interp_lb_splits[4][3] = {
-    {27, 26, 27},
-    {35, 34, 35},
-    {28, 28, 29},
-    {36, 36, 37},
-};
-
-/* Rank remap for displaced neighbor blocks */
-static const int interp_lb_num_remaps = 4;
-static const int interp_lb_remaps[][2] = {
-    {26, 25},
-    {29, 30},
-    {34, 33},
-    {37, 38},
-};
-
-#endif /* INTERP_LB_PROFILE_DATA_H */

AMSS_NCKU_source/kodiss_c.C

@@ -63,28 +63,19 @@ void kodis(const int ex[3],
      * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
      * 并定义 Fortran index: iF=i0+1, ...
      */
-    // 收紧循环范围：只遍历满足 iF±3/jF±3/kF±3 条件的内部点
+    for (int k0 = 0; k0 < ex3; ++k0) {
-    // iF-3 >= iminF => iF >= iminF+3 => i0 >= iminF+2 (因为 iF=i0+1)
-    // iF+3 <= imaxF => iF <= imaxF-3 => i0 <= imaxF-4
-    const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
-    const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
-    const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
-    const int i0_hi = imaxF - 4;  // inclusive
-    const int j0_hi = jmaxF - 4;
-    const int k0_hi = kmaxF - 4;
-
-    if (i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi) {
-        free(fh);
-        return;
-    }
-
-    for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
         const int kF = k0 + 1;
-        for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+        for (int j0 = 0; j0 < ex2; ++j0) {
             const int jF = j0 + 1;
-            for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+            for (int i0 = 0; i0 < ex1; ++i0) {
                 const int iF = i0 + 1;
 
+                // Fortran if 条件：
+                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
+                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
+                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
+                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
+                {
                     const size_t p = idx_ex(i0, j0, k0, ex);
 
                     // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
@@ -109,6 +100,7 @@ void kodis(const int ex[3],
                     // Fortran:
                     // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
                     f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+                }
             }
         }
     }

AMSS_NCKU_source/lopsided_kodis_c.C

@@ -1,248 +0,0 @@
-#include "tool.h"
-
-/*
- * Combined advection (lopsided) + KO dissipation (kodis).
- * Uses one shared symmetry_bd buffer per call.
- */
-void lopsided_kodis(const int ex[3],
-                    const double *X, const double *Y, const double *Z,
-                    const double *f, double *f_rhs,
-                    const double *Sfx, const double *Sfy, const double *Sfz,
-                    int Symmetry, const double SoA[3], double eps)
-{
-    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
-    const double F6 = 6.0, F18 = 18.0;
-    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
-    const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
-    const double cof = 64.0; // 2^6
-
-    const int NO_SYMM = 0, EQ_SYMM = 1;
-
-    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
-
-    const double dX = X[1] - X[0];
-    const double dY = Y[1] - Y[0];
-    const double dZ = Z[1] - Z[0];
-
-    const double d12dx = ONE / F12 / dX;
-    const double d12dy = ONE / F12 / dY;
-    const double d12dz = ONE / F12 / dZ;
-
-    const int imaxF = ex1;
-    const int jmaxF = ex2;
-    const int kmaxF = ex3;
-
-    int iminF = 1, jminF = 1, kminF = 1;
-    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
-    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
-    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
-
-    // fh for Fortran-style domain (-2:ex1,-2:ex2,-2:ex3)
-    const size_t nx = (size_t)ex1 + 3;
-    const size_t ny = (size_t)ex2 + 3;
-    const size_t nz = (size_t)ex3 + 3;
-    const size_t fh_size = nx * ny * nz;
-
-    double *fh = (double*)malloc(fh_size * sizeof(double));
-    if (!fh) return;
-
-    symmetry_bd(3, ex, f, fh, SoA);
-
-    // Advection (same stencil logic as lopsided_c.C)
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-        const int kF = k0 + 1;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-            const int jF = j0 + 1;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-                const int iF = i0 + 1;
-                const size_t p = idx_ex(i0, j0, k0, ex);
-
-                const double sfx = Sfx[p];
-                if (sfx > ZEO) {
-                    if (i0 <= ex1 - 4) {
-                        f_rhs[p] += sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
-                    } else if (i0 <= ex1 - 3) {
-                        f_rhs[p] += sfx * d12dx *
-                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
-                    } else if (i0 <= ex1 - 2) {
-                        f_rhs[p] -= sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
-                    }
-                } else if (sfx < ZEO) {
-                    if ((i0 - 2) >= iminF) {
-                        f_rhs[p] -= sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
-                    } else if ((i0 - 1) >= iminF) {
-                        f_rhs[p] += sfx * d12dx *
-                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
-                    } else if (i0 >= iminF) {
-                        f_rhs[p] += sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
-                    }
-                }
-
-                const double sfy = Sfy[p];
-                if (sfy > ZEO) {
-                    if (j0 <= ex2 - 4) {
-                        f_rhs[p] += sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
-                    } else if (j0 <= ex2 - 3) {
-                        f_rhs[p] += sfy * d12dy *
-                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
-                    } else if (j0 <= ex2 - 2) {
-                        f_rhs[p] -= sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
-                    }
-                } else if (sfy < ZEO) {
-                    if ((j0 - 2) >= jminF) {
-                        f_rhs[p] -= sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
-                    } else if ((j0 - 1) >= jminF) {
-                        f_rhs[p] += sfy * d12dy *
-                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
-                    } else if (j0 >= jminF) {
-                        f_rhs[p] += sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
-                    }
-                }
-
-                const double sfz = Sfz[p];
-                if (sfz > ZEO) {
-                    if (k0 <= ex3 - 4) {
-                        f_rhs[p] += sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
-                    } else if (k0 <= ex3 - 3) {
-                        f_rhs[p] += sfz * d12dz *
-                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
-                    } else if (k0 <= ex3 - 2) {
-                        f_rhs[p] -= sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
-                    }
-                } else if (sfz < ZEO) {
-                    if ((k0 - 2) >= kminF) {
-                        f_rhs[p] -= sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
-                    } else if ((k0 - 1) >= kminF) {
-                        f_rhs[p] += sfz * d12dz *
-                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
-                    } else if (k0 >= kminF) {
-                        f_rhs[p] += sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
-                    }
-                }
-            }
-        }
-    }
-
-    // KO dissipation (same domain restriction as kodiss_c.C)
-    if (eps > ZEO) {
-        const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
-        const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
-        const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
-        const int i0_hi = imaxF - 4; // inclusive
-        const int j0_hi = jmaxF - 4;
-        const int k0_hi = kmaxF - 4;
-
-        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
-            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
-                const int kF = k0 + 1;
-                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
-                    const int jF = j0 + 1;
-                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
-                        const int iF = i0 + 1;
-                        const size_t p = idx_ex(i0, j0, k0, ex);
-
-                        const double Dx_term =
-                            ((fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
-                             SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
-                             FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
-                             TWT *  fh[idx_fh_F(iF,     jF, kF, ex)]) / dX;
-
-                        const double Dy_term =
-                            ((fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
-                             SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
-                             FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
-                             TWT *  fh[idx_fh_F(iF, jF,     kF, ex)]) / dY;
-
-                        const double Dz_term =
-                            ((fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
-                             SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
-                             FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
-                             TWT *  fh[idx_fh_F(iF, jF, kF,     ex)]) / dZ;
-
-                        f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
-                    }
-                }
-            }
-        }
-    }
-
-    free(fh);
-}

AMSS_NCKU_source/makefile

@@ -2,12 +2,6 @@
 
 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=$(POLINT6_USE_BARY)
-
 ## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
 ##   make                        -> opt  (PGO-guided, maximum performance)
 ##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
@@ -16,19 +10,17 @@ PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 ifeq ($(PGO_MODE),instrument)
 ## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
 CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+              -align array64byte -fpp -I${MKLROOT}/include
 else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
+## opt (default): maximum performance with PGO profile data
-## PGO has been turned off, now tested and found to be negative optimization
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+              -fprofile-instr-use=$(PROFDATA) \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+              -fprofile-instr-use=$(PROFDATA) \
+              -align array64byte -fpp -I${MKLROOT}/include
 endif
 
 .SUFFIXES: .o .f90 .C .for .cu
@@ -61,17 +53,8 @@ kodiss_c.o: kodiss_c.C
 lopsided_c.o: lopsided_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-lopsided_kodis_c.o: lopsided_kodis_c.C
+## TwoPunctureABE uses fixed optimal flags, independent of CXXAPPFLAGS (which may be PGO-instrumented)
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo -Dfortran3 -Dnewc -I${MKLROOT}/include
-
-interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
-TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
-TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(TP_PROFDATA) \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
 
 TwoPunctures.o: TwoPunctures.C
 	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
@@ -81,29 +64,15 @@ TwoPunctureABE.o: TwoPunctureABE.C
 
 # Input files
 
-## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
+# C rewrite files
-ifeq ($(USE_CXX_KERNELS),0)
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o
-# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES =
-else
-# C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
-endif
-
-## RK4 kernel switch (independent from USE_CXX_KERNELS)
-ifeq ($(USE_CXX_RK4),1)
-CFILES += rungekutta4_rout_c.o
-RK4_F90_OBJ =
-else
-RK4_F90_OBJ = rungekutta4_rout.o
-endif
 
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
 	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
 	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
            Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.o
+	   NullShellPatch2_Evo.o writefile_f.o
 	   
 C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o surface_integral.o ShellPatch.o\
@@ -113,9 +82,9 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
 	   NullShellPatch2_Evo.o \
 	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
 
-F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+F90FILES = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
 	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
+	   rungekutta4_rout.o diff_new.o kodiss.o kodiss_sh.o\
 	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
 	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
            getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
@@ -126,14 +95,6 @@ F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
 	   scalar_rhs.o initial_scalar.o NullEvol2.o initial_null2.o\
 	   NullNews2.o tool_f.o
 
-ifeq ($(USE_CXX_KERNELS),0)
-# Fortran mode: include original bssn_rhs.o
-F90FILES = $(F90FILES_BASE) bssn_rhs.o
-else
-# C++ mode (default): bssn_rhs.o replaced by C++ kernel
-F90FILES = $(F90FILES_BASE)
-endif
-
 F77FILES = zbesh.o
 
 AHFDOBJS = expansion.o expansion_Jacobian.o patch.o coords.o patch_info.o patch_interp.o patch_system.o \

AMSS_NCKU_source/makefile.inc

@@ -10,49 +10,10 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
 LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
 
-## Memory allocator switch
-##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
-##   0           : use system default allocator (ptmalloc)
-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) $(LDLIBS)
-endif
-
 ## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
 ##   opt        : (default) maximum performance with PGO profile-guided optimization
 ##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
 PGO_MODE ?= opt
-
-## Interp_Points load balance profiling mode
-##   off        : (default) no load balance instrumentation
-##   profile    : Pass 1 — instrument Interp_Points to collect timing profile
-##   optimize   : Pass 2 — read profile and apply block rebalancing
-INTERP_LB_MODE ?= off
-
-ifeq ($(INTERP_LB_MODE),profile)
-INTERP_LB_FLAGS = -DINTERP_LB_PROFILE
-else ifeq ($(INTERP_LB_MODE),optimize)
-INTERP_LB_FLAGS = -DINTERP_LB_OPTIMIZE
-else
-INTERP_LB_FLAGS =
-endif
-
-## Kernel implementation switch
-##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
-##   0           : fall back to original Fortran kernels
-USE_CXX_KERNELS ?= 1
-
-## RK4 kernel implementation switch
-##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
-##   0           : use original Fortran rungekutta4_rout.o
-USE_CXX_RK4 ?= 1
-
 f90          = ifx
 f77          = ifx
 CXX          = icpx

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1934,33 +1934,18 @@
 ! when if=1 -> ic=0, this is different to vertex center grid 
   real*8, dimension(-2:extc(1),-2:extc(2),-2:extc(3))   :: funcc
   integer,dimension(3) :: cxI
-  integer :: i,j,k,ii,jj,kk,px,py,pz
+  integer :: i,j,k,ii,jj,kk
   real*8, dimension(6,6) :: tmp2
   real*8, dimension(6) :: tmp1
-  integer, dimension(extf(1)) :: cix
-  integer, dimension(extf(2)) :: ciy
-  integer, dimension(extf(3)) :: ciz
-  integer, dimension(extf(1)) :: pix
-  integer, dimension(extf(2)) :: piy
-  integer, dimension(extf(3)) :: piz
 
   real*8, parameter :: C1=7.7d1/8.192d3,C2=-6.93d2/8.192d3,C3=3.465d3/4.096d3
   real*8, parameter :: C6=6.3d1/8.192d3,C5=-4.95d2/8.192d3,C4=1.155d3/4.096d3
-  real*8, dimension(6,2), parameter :: WC = reshape((/&
-      C1,C2,C3,C4,C5,C6,&
-      C6,C5,C4,C3,C2,C1/), (/6,2/))
 
   integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
-  integer::maxcx,maxcy,maxcz
 
   real*8,dimension(3) :: CD,FD
-  real*8 :: tmp_yz(extc(1), 6)      ! 存储整条 X 线上 6 个 Y 轴偏置的 Z 向插值结果
+  
-  real*8 :: tmp_xyz_line(extc(1))   ! 存储整条 X 线上完成 Y 向融合后的结果
-  real*8 :: v1, v2, v3, v4, v5, v6
-  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max
-  real*8 :: res_line
-  real*8 :: tmp_z_slab(extc(1), extc(2))  ! 分配在 k 循环外
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2035,123 +2020,145 @@
           return
   endif
 
-  do i = imino,imaxo
-     ii = i + lbf(1) - 1
-     cix(i) = ii/2 - lbc(1) + 1
-     if(ii/2*2 == ii)then
-        pix(i) = 1
-     else
-        pix(i) = 2
-     endif
-  enddo
-  do j = jmino,jmaxo
-     jj = j + lbf(2) - 1
-     ciy(j) = jj/2 - lbc(2) + 1
-     if(jj/2*2 == jj)then
-        piy(j) = 1
-     else
-        piy(j) = 2
-     endif
-  enddo
-  do k = kmino,kmaxo
-     kk = k + lbf(3) - 1
-     ciz(k) = kk/2 - lbc(3) + 1
-     if(kk/2*2 == kk)then
-        piz(k) = 1
-     else
-        piz(k) = 2
-     endif
-  enddo
-
-  maxcx = maxval(cix(imino:imaxo))
-  maxcy = maxval(ciy(jmino:jmaxo))
-  maxcz = maxval(ciz(kmino:kmaxo))
-  if(maxcx+3 > extc(1) .or. maxcy+3 > extc(2) .or. maxcz+3 > extc(3))then
-     write(*,*)"error in prolong"
-     return
-  endif
-
   call symmetry_bd(3,extc,func,funcc,SoA)
-     ! 对每个 k（pz, kc 固定）预计算 Z 向插值的 2D 切片
-jc_min = minval(ciy(jmino:jmaxo))
-jc_max = maxval(ciy(jmino:jmaxo))
-
-do k = kmino, kmaxo
-    pz = piz(k); kc = ciz(k)
-    ! --- Pass 1: Z 方向，只算一次 ---
-    do iy = jc_min-3, jc_max+3   ! 仅需的 iy 范围
-        do ii = imini-3, imaxi+3  ! 仅需的 ii 范围
-            tmp_z_slab(ii, iy) = sum(WC(:,pz) * funcc(ii, iy, kc-2:kc+3))
-        end do
-    end do
-
-    do j = jmino, jmaxo
-        py = piy(j); jc = ciy(j)
-        ! --- Pass 2: Y 方向 ---
-        do ii = imini-3, imaxi+3
-            tmp_xyz_line(ii) = sum(WC(:,py) * tmp_z_slab(ii, jc-2:jc+3))
-        end do
-        ! --- Pass 3: X 方向 ---
-        do i = imino, imaxo
-            funf(i,j,k) = sum(WC(:,pix(i)) * tmp_xyz_line(cix(i)-2:cix(i)+3))
-        end do
-    end do
-end do
      
 !~~~~~~> prolongation start...
+  do k = kmino,kmaxo
+   do j = jmino,jmaxo
+    do i = imino,imaxo
+       cxI(1) = i
+       cxI(2) = j
+       cxI(3) = k
+! change to coarse level reference
+!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---| 
+!|=======x===============x===============x===============x=======|
+       cxI = (cxI+lbf-1)/2
+! change to array index      
+       cxI = cxI - lbc + 1
+
+       if(any(cxI+3 > extc)) write(*,*)"error in prolong"
+       ii=i+lbf(1)-1
+       jj=j+lbf(2)-1
+       kk=k+lbf(3)-1
 #if 0
- do k = kmino, kmaxo
+       if(ii/2*2==ii)then
-     pz = piz(k)
+         if(jj/2*2==jj)then
-     kc = ciz(k)
+           if(kk/2*2==kk)then
+             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
+             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
+           else
+             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
+             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
+           endif
+         else
+           if(kk/2*2==kk)then
+             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
+             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
+           else
+             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
+             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
+           endif
+         endif
+       else
+         if(jj/2*2==jj)then
+           if(kk/2*2==kk)then               
+             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
+             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
+           else
+             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
+             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
+           endif
+         else
+           if(kk/2*2==kk)then
+             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
+             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
+           else
+             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
+             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
+           endif
+         endif
+       endif
+#else 
+       if(kk/2*2==kk)then
+             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+       else
+             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
+                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
+                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
+                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
+                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
+                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
+       endif
 
-     do j = jmino, jmaxo
+       if(jj/2*2==jj)then
-        py = piy(j)
+             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-        jc = ciy(j)
+       else
+             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
+       endif
 
-! --- 步骤 1 & 2 融合：分段处理 X 轴，提升 Cache 命中率 ---
+       if(ii/2*2==ii)then
-        ! 我们将 ii 循环逻辑重组，减少对 funcc 的跨行重复访问
+             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-        do ii = 1, extc(1)
+       else
-           ! 1. 先做 Z 方向的 6 条线插值（针对当前的 ii 和当前的 6 个 iy）
+             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           ! 我们直接在这里把 Y 方向的加权也做了，省去 tmp_yz 数组
+       endif
-           ! 这样 funcc 的数据读进来后立即完成所有维度的贡献，不再写回内存
-           
-           res_line = 0.0d0
-           do jj = 1, 6
-              iy = jc - 3 + jj
-              ! 这一行代码是核心：一次性完成 Z 插值并加上 Y 的权重
-              ! 编译器会把 WC(jj, py) 存在寄存器里
-              res_line = res_line + WC(jj, py) * ( &
-                         WC(1, pz) * funcc(ii, iy, kc-2) + &
-                         WC(2, pz) * funcc(ii, iy, kc-1) + &
-                         WC(3, pz) * funcc(ii, iy, kc  ) + &
-                         WC(4, pz) * funcc(ii, iy, kc+1) + &
-                         WC(5, pz) * funcc(ii, iy, kc+2) + &
-                         WC(6, pz) * funcc(ii, iy, kc+3) )
-           end do
-           tmp_xyz_line(ii) = res_line
-        end do
-
-
-
-
-        ! 3. 【降维：X 向】最后在最内层只处理 X 方向的 6 点加权
-        ! 此时每个点的计算量从原来的 200+ 次乘法降到了仅 6 次
-        do i = imino, imaxo
-           px = pix(i)
-           ic = cix(i)
-           
-           ! 直接从预计算好的 line 中读取连续的 6 个点
-           ! ic-2 到 ic+3 对应原始 6 点算子
-           funf(i,j,k) = WC(1,px)*tmp_xyz_line(ic-2) + &
-                         WC(2,px)*tmp_xyz_line(ic-1) + &
-                         WC(3,px)*tmp_xyz_line(ic  ) + &
-                         WC(4,px)*tmp_xyz_line(ic+1) + &
-                         WC(5,px)*tmp_xyz_line(ic+2) + &
-                         WC(6,px)*tmp_xyz_line(ic+3)
-        end do
-     end do
-  end do
 #endif
+    enddo
+   enddo
+  enddo
+
   return
 
   end subroutine prolong3
@@ -2351,10 +2358,6 @@ end do
 
   real*8,dimension(3) :: CD,FD
   
-  real*8 :: tmp_xz_plane(extf(1), 6) 
-  real*8 :: tmp_x_line(extf(1))
-  integer :: fi, fj, fk, ii, jj, kk
-
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2436,56 +2439,6 @@ end do
   call symmetry_bd(2,extf,funf,funff,SoA)
 
 !~~~~~~> restriction start...
-do k = kmino, kmaxo
-    fk = 2*(k + lbc(3) - 1) - 1 - lbf(3) + 1
-
-    do j = jmino, jmaxo
-        fj = 2*(j + lbc(2) - 1) - 1 - lbf(2) + 1
-        
-        ! 优化点 1: 显式展开 Z 方向计算，减少循环开销
-        ! 确保 ii 循环是最内层且连续访问
-        !DIR$ VECTOR ALWAYS
-        do ii = 1, extf(1)
-            ! 预计算当前 j 对应的 6 行在 Z 方向的压缩结果
-            ! 这里直接硬编码 jj 的偏移，彻底消除一层循环
-            tmp_xz_plane(ii, 1) = C1*(funff(ii,fj-2,fk-2)+funff(ii,fj-2,fk+3)) + &
-                                  C2*(funff(ii,fj-2,fk-1)+funff(ii,fj-2,fk+2)) + &
-                                  C3*(funff(ii,fj-2,fk  )+funff(ii,fj-2,fk+1))
-            tmp_xz_plane(ii, 2) = C1*(funff(ii,fj-1,fk-2)+funff(ii,fj-1,fk+3)) + &
-                                  C2*(funff(ii,fj-1,fk-1)+funff(ii,fj-1,fk+2)) + &
-                                  C3*(funff(ii,fj-1,fk  )+funff(ii,fj-1,fk+1))
-            tmp_xz_plane(ii, 3) = C1*(funff(ii,fj  ,fk-2)+funff(ii,fj  ,fk+3)) + &
-                                  C2*(funff(ii,fj  ,fk-1)+funff(ii,fj  ,fk+2)) + &
-                                  C3*(funff(ii,fj  ,fk  )+funff(ii,fj  ,fk+1))
-            tmp_xz_plane(ii, 4) = C1*(funff(ii,fj+1,fk-2)+funff(ii,fj+1,fk+3)) + &
-                                  C2*(funff(ii,fj+1,fk-1)+funff(ii,fj+1,fk+2)) + &
-                                  C3*(funff(ii,fj+1,fk  )+funff(ii,fj+1,fk+1))
-            tmp_xz_plane(ii, 5) = C1*(funff(ii,fj+2,fk-2)+funff(ii,fj+2,fk+3)) + &
-                                  C2*(funff(ii,fj+2,fk-1)+funff(ii,fj+2,fk+2)) + &
-                                  C3*(funff(ii,fj+2,fk  )+funff(ii,fj+2,fk+1))
-            tmp_xz_plane(ii, 6) = C1*(funff(ii,fj+3,fk-2)+funff(ii,fj+3,fk+3)) + &
-                                  C2*(funff(ii,fj+3,fk-1)+funff(ii,fj+3,fk+2)) + &
-                                  C3*(funff(ii,fj+3,fk  )+funff(ii,fj+3,fk+1))
-        end do
-
-        ! 优化点 2: 同样向量化 Y 方向压缩
-        !DIR$ VECTOR ALWAYS
-        do ii = 1, extf(1)
-            tmp_x_line(ii) = C1*(tmp_xz_plane(ii, 1) + tmp_xz_plane(ii, 6)) + &
-                            C2*(tmp_xz_plane(ii, 2) + tmp_xz_plane(ii, 5)) + &
-                            C3*(tmp_xz_plane(ii, 3) + tmp_xz_plane(ii, 4))
-        end do
-
-        ! 优化点 3: 最终写入，利用已经缓存在 tmp_x_line 的数据
-        do i = imino, imaxo
-            fi = 2*(i + lbc(1) - 1) - 1 - lbf(1) + 1
-            func(i, j, k) = C1*(tmp_x_line(fi-2) + tmp_x_line(fi+3)) + &
-                            C2*(tmp_x_line(fi-1) + tmp_x_line(fi+2)) + &
-                            C3*(tmp_x_line(fi  ) + tmp_x_line(fi+1))
-        end do
-    end do
-end do
-#if 0
   do k = kmino,kmaxo
    do j = jmino,jmaxo
     do i = imino,imaxo
@@ -2509,7 +2462,7 @@ end do
     enddo
    enddo
   enddo
-#endif
+  
   return
 
   end subroutine restrict3

AMSS_NCKU_source/rungekutta4_rout_c.C

@@ -1,212 +0,0 @@
-#include "rungekutta4_rout.h"
-#include <cstdio>
-#include <cstdlib>
-#include <cstddef>
-#include <complex>
-#include <immintrin.h>
-
-namespace {
-
-inline void rk4_stage0(std::size_t n,
-                       const double *__restrict f0,
-                       const double *__restrict frhs,
-                       double *__restrict f1,
-                       double c) {
-    std::size_t i = 0;
-#if defined(__AVX512F__)
-    const __m512d vc = _mm512_set1_pd(c);
-    for (; i + 7 < n; i += 8) {
-        const __m512d v0 = _mm512_loadu_pd(f0 + i);
-        const __m512d vr = _mm512_loadu_pd(frhs + i);
-        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, vr, v0));
-    }
-#elif defined(__AVX2__)
-    const __m256d vc = _mm256_set1_pd(c);
-    for (; i + 3 < n; i += 4) {
-        const __m256d v0 = _mm256_loadu_pd(f0 + i);
-        const __m256d vr = _mm256_loadu_pd(frhs + i);
-        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, vr, v0));
-    }
-#endif
-#pragma ivdep
-    for (; i < n; ++i) {
-        f1[i] = f0[i] + c * frhs[i];
-    }
-}
-
-inline void rk4_rhs_accum(std::size_t n,
-                          const double *__restrict f1,
-                          double *__restrict frhs) {
-    std::size_t i = 0;
-#if defined(__AVX512F__)
-    const __m512d v2 = _mm512_set1_pd(2.0);
-    for (; i + 7 < n; i += 8) {
-        const __m512d v1 = _mm512_loadu_pd(f1 + i);
-        const __m512d vrhs = _mm512_loadu_pd(frhs + i);
-        _mm512_storeu_pd(frhs + i, _mm512_fmadd_pd(v2, v1, vrhs));
-    }
-#elif defined(__AVX2__)
-    const __m256d v2 = _mm256_set1_pd(2.0);
-    for (; i + 3 < n; i += 4) {
-        const __m256d v1 = _mm256_loadu_pd(f1 + i);
-        const __m256d vrhs = _mm256_loadu_pd(frhs + i);
-        _mm256_storeu_pd(frhs + i, _mm256_fmadd_pd(v2, v1, vrhs));
-    }
-#endif
-#pragma ivdep
-    for (; i < n; ++i) {
-        frhs[i] = frhs[i] + 2.0 * f1[i];
-    }
-}
-
-inline void rk4_f1_from_f0_f1(std::size_t n,
-                              const double *__restrict f0,
-                              double *__restrict f1,
-                              double c) {
-    std::size_t i = 0;
-#if defined(__AVX512F__)
-    const __m512d vc = _mm512_set1_pd(c);
-    for (; i + 7 < n; i += 8) {
-        const __m512d v0 = _mm512_loadu_pd(f0 + i);
-        const __m512d v1 = _mm512_loadu_pd(f1 + i);
-        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, v1, v0));
-    }
-#elif defined(__AVX2__)
-    const __m256d vc = _mm256_set1_pd(c);
-    for (; i + 3 < n; i += 4) {
-        const __m256d v0 = _mm256_loadu_pd(f0 + i);
-        const __m256d v1 = _mm256_loadu_pd(f1 + i);
-        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, v1, v0));
-    }
-#endif
-#pragma ivdep
-    for (; i < n; ++i) {
-        f1[i] = f0[i] + c * f1[i];
-    }
-}
-
-inline void rk4_stage3(std::size_t n,
-                       const double *__restrict f0,
-                       double *__restrict f1,
-                       const double *__restrict frhs,
-                       double c) {
-    std::size_t i = 0;
-#if defined(__AVX512F__)
-    const __m512d vc = _mm512_set1_pd(c);
-    for (; i + 7 < n; i += 8) {
-        const __m512d v0 = _mm512_loadu_pd(f0 + i);
-        const __m512d v1 = _mm512_loadu_pd(f1 + i);
-        const __m512d vr = _mm512_loadu_pd(frhs + i);
-        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, _mm512_add_pd(v1, vr), v0));
-    }
-#elif defined(__AVX2__)
-    const __m256d vc = _mm256_set1_pd(c);
-    for (; i + 3 < n; i += 4) {
-        const __m256d v0 = _mm256_loadu_pd(f0 + i);
-        const __m256d v1 = _mm256_loadu_pd(f1 + i);
-        const __m256d vr = _mm256_loadu_pd(frhs + i);
-        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, _mm256_add_pd(v1, vr), v0));
-    }
-#endif
-#pragma ivdep
-    for (; i < n; ++i) {
-        f1[i] = f0[i] + c * (f1[i] + frhs[i]);
-    }
-}
-
-} // namespace
-
-extern "C" {
-
-void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
-    constexpr double F1o6 = 1.0 / 6.0;
-    constexpr double HLF = 0.5;
-    constexpr double TWO = 2.0;
-
-    switch (RK4) {
-    case 0:
-        f1 = f0 + HLF * dT * f_rhs;
-        break;
-    case 1:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + HLF * dT * f1;
-        break;
-    case 2:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + dT * f1;
-        break;
-    case 3:
-        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
-        break;
-    default:
-        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-}
-
-void rungekutta4_cplxscalar_(double &dT,
-                             std::complex<double> &f0,
-                             std::complex<double> &f1,
-                             std::complex<double> &f_rhs,
-                             int &RK4) {
-    constexpr double F1o6 = 1.0 / 6.0;
-    constexpr double HLF = 0.5;
-    constexpr double TWO = 2.0;
-
-    switch (RK4) {
-    case 0:
-        f1 = f0 + HLF * dT * f_rhs;
-        break;
-    case 1:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + HLF * dT * f1;
-        break;
-    case 2:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + dT * f1;
-        break;
-    case 3:
-        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
-        break;
-    default:
-        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-}
-
-int f_rungekutta4_rout(int *ex, double &dT,
-                       double *f0, double *f1, double *f_rhs,
-                       int &RK4) {
-    const std::size_t n = static_cast<std::size_t>(ex[0]) *
-                          static_cast<std::size_t>(ex[1]) *
-                          static_cast<std::size_t>(ex[2]);
-    const double *const __restrict f0r = f0;
-    double *const __restrict f1r = f1;
-    double *const __restrict frhs = f_rhs;
-
-    if (__builtin_expect(static_cast<unsigned>(RK4) > 3u, 0)) {
-        std::fprintf(stderr, "rungekutta4_rout_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-
-    switch (RK4) {
-    case 0:
-        rk4_stage0(n, f0r, frhs, f1r, 0.5 * dT);
-        break;
-    case 1:
-        rk4_rhs_accum(n, f1r, frhs);
-        rk4_f1_from_f0_f1(n, f0r, f1r, 0.5 * dT);
-        break;
-    case 2:
-        rk4_rhs_accum(n, f1r, frhs);
-        rk4_f1_from_f0_f1(n, f0r, f1r, dT);
-        break;
-    default:
-        rk4_stage3(n, f0r, f1r, frhs, (1.0 / 6.0) * dT);
-        break;
-    }
-
-    return 0;
-}
-
-} // extern "C"

AMSS_NCKU_source/share_func.h

@@ -5,7 +5,6 @@
 #include <stddef.h>
 #include <math.h>
 #include <stdio.h>
-#include <string.h>
 /* 主网格：0-based -> 1D */
 static inline size_t idx_ex(int i0, int j0, int k0, const int ex[3]) {
     const int ex1 = ex[0], ex2 = ex[1];
@@ -88,159 +87,60 @@ static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc
  *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
  * enddo
  */
-static inline void symmetry_bd_impl(int ord,
-                 int shift,
-                 const int extc[3],
-                 const double *__restrict func,
-                 double *__restrict funcc,
-                 const double SoA[3])
-{
-    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
-    const int nx = extc1 + ord;
-    const int ny = extc2 + ord;
-
-    const size_t snx = (size_t)nx;
-    const size_t splane = (size_t)nx * (size_t)ny;
-    const size_t interior_i = (size_t)shift + 1u;          /* iF = 1 */
-    const size_t interior_j = ((size_t)shift + 1u) * snx;  /* jF = 1 */
-    const size_t interior_k = ((size_t)shift + 1u) * splane; /* kF = 1 */
-    const size_t interior0 = interior_k + interior_j + interior_i;
-
-    /* 1) funcc(1:extc1,1:extc2,1:extc3) = func */
-    for (int k0 = 0; k0 < extc3; ++k0) {
-        const double *src_k = func + (size_t)k0 * (size_t)extc2 * (size_t)extc1;
-        const size_t dst_k0 = interior0 + (size_t)k0 * splane;
-        for (int j0 = 0; j0 < extc2; ++j0) {
-            const double *src = src_k + (size_t)j0 * (size_t)extc1;
-            double *dst = funcc + dst_k0 + (size_t)j0 * snx;
-            memcpy(dst, src, (size_t)extc1 * sizeof(double));
-        }
-    }
-
-    /* 2) funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1) */
-    const double s1 = SoA[0];
-    if (s1 == 1.0) {
-        for (int ii = 0; ii < ord; ++ii) {
-            const size_t dst_i = (size_t)(shift - ii);
-            const size_t src_i = (size_t)(shift + ii + 1);
-            for (int k0 = 0; k0 < extc3; ++k0) {
-                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
-                for (int j0 = 0; j0 < extc2; ++j0) {
-                    const size_t off = kbase + (size_t)j0 * snx;
-                    funcc[off + dst_i] = funcc[off + src_i];
-                }
-            }
-        }
-    } else if (s1 == -1.0) {
-        for (int ii = 0; ii < ord; ++ii) {
-            const size_t dst_i = (size_t)(shift - ii);
-            const size_t src_i = (size_t)(shift + ii + 1);
-            for (int k0 = 0; k0 < extc3; ++k0) {
-                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
-                for (int j0 = 0; j0 < extc2; ++j0) {
-                    const size_t off = kbase + (size_t)j0 * snx;
-                    funcc[off + dst_i] = -funcc[off + src_i];
-                }
-            }
-        }
-    } else {
-        for (int ii = 0; ii < ord; ++ii) {
-            const size_t dst_i = (size_t)(shift - ii);
-            const size_t src_i = (size_t)(shift + ii + 1);
-            for (int k0 = 0; k0 < extc3; ++k0) {
-                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
-                for (int j0 = 0; j0 < extc2; ++j0) {
-                    const size_t off = kbase + (size_t)j0 * snx;
-                    funcc[off + dst_i] = funcc[off + src_i] * s1;
-                }
-            }
-        }
-    }
-
-    /* 3) funcc(:,-j,1:extc3) = funcc(:,j+1,1:extc3)*SoA(2) */
-    const double s2 = SoA[1];
-    if (s2 == 1.0) {
-        for (int jj = 0; jj < ord; ++jj) {
-            const size_t dst_j = (size_t)(shift - jj) * snx;
-            const size_t src_j = (size_t)(shift + jj + 1) * snx;
-            for (int k0 = 0; k0 < extc3; ++k0) {
-                const size_t kbase = interior_k + (size_t)k0 * splane;
-                double *dst = funcc + kbase + dst_j;
-                const double *src = funcc + kbase + src_j;
-                for (int i = 0; i < nx; ++i) dst[i] = src[i];
-            }
-        }
-    } else if (s2 == -1.0) {
-        for (int jj = 0; jj < ord; ++jj) {
-            const size_t dst_j = (size_t)(shift - jj) * snx;
-            const size_t src_j = (size_t)(shift + jj + 1) * snx;
-            for (int k0 = 0; k0 < extc3; ++k0) {
-                const size_t kbase = interior_k + (size_t)k0 * splane;
-                double *dst = funcc + kbase + dst_j;
-                const double *src = funcc + kbase + src_j;
-                for (int i = 0; i < nx; ++i) dst[i] = -src[i];
-            }
-        }
-    } else {
-        for (int jj = 0; jj < ord; ++jj) {
-            const size_t dst_j = (size_t)(shift - jj) * snx;
-            const size_t src_j = (size_t)(shift + jj + 1) * snx;
-            for (int k0 = 0; k0 < extc3; ++k0) {
-                const size_t kbase = interior_k + (size_t)k0 * splane;
-                double *dst = funcc + kbase + dst_j;
-                const double *src = funcc + kbase + src_j;
-                for (int i = 0; i < nx; ++i) dst[i] = src[i] * s2;
-            }
-        }
-    }
-
-    /* 4) funcc(:,:,-k) = funcc(:,:,k+1)*SoA(3) */
-    const double s3 = SoA[2];
-    if (s3 == 1.0) {
-        for (int kk = 0; kk < ord; ++kk) {
-            const size_t dst_k = (size_t)(shift - kk) * splane;
-            const size_t src_k = (size_t)(shift + kk + 1) * splane;
-            double *dst = funcc + dst_k;
-            const double *src = funcc + src_k;
-            for (size_t p = 0; p < splane; ++p) dst[p] = src[p];
-        }
-    } else if (s3 == -1.0) {
-        for (int kk = 0; kk < ord; ++kk) {
-            const size_t dst_k = (size_t)(shift - kk) * splane;
-            const size_t src_k = (size_t)(shift + kk + 1) * splane;
-            double *dst = funcc + dst_k;
-            const double *src = funcc + src_k;
-            for (size_t p = 0; p < splane; ++p) dst[p] = -src[p];
-        }
-    } else {
-        for (int kk = 0; kk < ord; ++kk) {
-            const size_t dst_k = (size_t)(shift - kk) * splane;
-            const size_t src_k = (size_t)(shift + kk + 1) * splane;
-            double *dst = funcc + dst_k;
-            const double *src = funcc + src_k;
-            for (size_t p = 0; p < splane; ++p) dst[p] = src[p] * s3;
-        }
-    }
-}
-
 static inline void symmetry_bd(int ord,
                  const int extc[3],
                  const double *func,
                  double *funcc,
                  const double SoA[3])
 {
-    if (ord <= 0) return;
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
 
-    /* Fast paths used by current C kernels: ord=2 (derivs), ord=3 (lopsided/KO). */
+    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
-    if (ord == 2) {
+    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
-        symmetry_bd_impl(2, 1, extc, func, funcc, SoA);
+    for (int k0 = 0; k0 < extc3; ++k0) {
-        return;
+        for (int j0 = 0; j0 < extc2; ++j0) {
-    }
+            for (int i0 = 0; i0 < extc1; ++i0) {
-    if (ord == 3) {
+                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
-        symmetry_bd_impl(3, 2, extc, func, funcc, SoA);
+                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
-        return;
+            }
+        }
     }
 
-    symmetry_bd_impl(ord, ord - 1, extc, func, funcc, SoA);
+    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    for (int ii = 0; ii <= ord - 1; ++ii) {
+        const int iF_dst = -ii;       // 0, -1, -2, ...
+        const int iF_src = ii + 1;    // 1, 2, 3, ...
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int jF = 1; jF <= extc2; ++jF) {
+                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
+            }
+        }
+    }
+
+    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
+    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
+    for (int jj = 0; jj <= ord - 1; ++jj) {
+        const int jF_dst = -jj;
+        const int jF_src = jj + 1;
+        for (int kF = 1; kF <= extc3; ++kF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
+            }
+        }
+    }
+
+    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
+    for (int kk = 0; kk <= ord - 1; ++kk) {
+        const int kF_dst = -kk;
+        const int kF_src = kk + 1;
+        for (int jF = -ord + 1; jF <= extc2; ++jF) {
+            for (int iF = -ord + 1; iF <= extc1; ++iF) {
+                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
+                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
+            }
+        }
+    }
 }
 #endif

AMSS_NCKU_source/tool.h

@@ -25,9 +25,3 @@ void lopsided(const int ex[3],
               const double *f, double *f_rhs,
               const double *Sfx, const double *Sfy, const double *Sfz,
               int Symmetry, const double SoA[3]);
-
-void lopsided_kodis(const int ex[3],
-                    const double *X, const double *Y, const double *Z,
-                    const double *f, double *f_rhs,
-                    const double *Sfx, const double *Sfy, const double *Sfz,
-                    int Symmetry, const double SoA[3], double eps);

generate_interp_lb_header.py

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

makefile_and_run.py

@@ -43,8 +43,7 @@ def get_last_n_cores_per_socket(n=32):
     cpu_str = ",".join(segments)
     total = len(segments) * n
     print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
-    #return f"taskset -c {cpu_str}"
+    return f"taskset -c {cpu_str}"
-    return f""
 
 
 ## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
@@ -70,7 +69,7 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
     elif (input_data.GPU_Calculation == "yes"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:

pgo_profile/PGO_Profile_Analysis.md

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