迁移C算子的循环融合和临时量消除

避免 transfer_cached 每次调用分配释放 3 个临时数组，减少堆操作开销。

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

AMSS_NCKU_Program.py

@@ -270,6 +270,12 @@ 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

@@ -1,9 +1,13 @@
 #!/usr/bin/env python3
 """
-AMSS-NCKU GW150914 Simulation Regression Test Script
+AMSS-NCKU GW150914 Simulation Regression Test Script (Comprehensive Version)
 
 Verification Requirements:
-1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
+1. RMS errors < 1% for:
+   - 3D Vector Total RMS
+   - X Component RMS
+   - Y Component RMS
+   - Z Component RMS
 2. ADM constraint violation < 2 (Grid Level 0)
 
 RMS Calculation Method:
@@ -57,79 +61,62 @@ 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 trajectory-based RMS error on the XY plane between baseline and optimized simulations.
+    Calculate 3D Vector RMS and component-wise RMS (X, Y, Z) independently.
-
+    Uses r = sqrt(x^2 + y^2) as the denominator for all error normalizations.
-    This function computes the RMS error independently for BH1 and BH2 trajectories,
+    Returns the maximum error between BH1 and BH2 for each category.
-    then returns the maximum of the two as the final RMS error metric.
-
-    For each black hole, the RMS is calculated as:
-        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
-
-    where:
-        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
-        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
-
-    Args:
-        bh_data_ref: Reference (baseline) trajectory data
-        bh_data_target: Target (optimized) trajectory data
-
-    Returns:
-        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
-        error: Error message if any
     """
-    # Align data: truncate to the length of the shorter dataset
     M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
 
     if M < 10:
         return None, "Insufficient data points for comparison"
 
-    # Extract XY coordinates for both black holes
+    results = {}
-    x1_ref = bh_data_ref['x1'][:M]
-    y1_ref = bh_data_ref['y1'][:M]
-    x2_ref = bh_data_ref['x2'][:M]
-    y2_ref = bh_data_ref['y2'][:M]
 
-    x1_new = bh_data_target['x1'][:M]
+    for bh in ['1', '2']:
-    y1_new = bh_data_target['y1'][: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]
-    x2_new = bh_data_target['x2'][: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]
-    y2_new = bh_data_target['y2'][:M]
 
-    # Calculate RMS for BH1
+        # 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)
-    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
+        r_ref = np.sqrt(x_r**2 + y_r**2)
-    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
+        r_new = np.sqrt(x_n**2 + y_n**2)
-    r1_new = np.sqrt(x1_new**2 + y1_new**2)
+        denom_max = np.maximum(r_ref, r_new)
-    r1_max = np.maximum(r1_ref, r1_new)
 
-    # Calculate RMS for BH2
+        valid = denom_max > 1e-15
-    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
+        if np.sum(valid) < 10:
-    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
+            results[f'BH{bh}'] = { '3D_Vector': 0.0, 'X_Component': 0.0, 'Y_Component': 0.0, 'Z_Component': 0.0 }
-    r2_new = np.sqrt(x2_new**2 + y2_new**2)
+            continue
-    r2_max = np.maximum(r2_ref, r2_new)
 
-    # Avoid division by zero for BH1
+        def calc_rms(delta):
-    valid_mask1 = r1_max > 1e-15
+            # 将对应分量的偏差除以统一的轨道半径分母 denom_max
-    if np.sum(valid_mask1) < 10:
+            return np.sqrt(np.mean((delta[valid] / denom_max[valid])**2)) * 100
-        return None, "Insufficient valid data points for BH1"
 
-    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
+        # 1. Total 3D Vector RMS
-    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+        delta_vec = np.sqrt((x_r - x_n)**2 + (y_r - y_n)**2 + (z_r - z_n)**2)
+        rms_3d = calc_rms(delta_vec)
 
-    # Avoid division by zero for BH2
+        # 2. Component-wise RMS (分离计算各轴，但共用半径分母)
-    valid_mask2 = r2_max > 1e-15
+        rms_x = calc_rms(np.abs(x_r - x_n))
-    if np.sum(valid_mask2) < 10:
+        rms_y = calc_rms(np.abs(y_r - y_n))
-        return None, "Insufficient valid data points for BH2"
+        rms_z = calc_rms(np.abs(z_r - z_n))
 
-    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
+        results[f'BH{bh}'] = {
-    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+            '3D_Vector': rms_3d,
+            'X_Component': rms_x,
+            'Y_Component': rms_y,
+            'Z_Component': rms_z
+        }
 
-    # Final RMS is the maximum of BH1 and BH2
+    # 获取 BH1 和 BH2 中的最大误差
-    rms_final = max(rms_bh1, rms_bh2)
+    max_rms = {
-
+        '3D_Vector': max(results['BH1']['3D_Vector'], results['BH2']['3D_Vector']),
-    return rms_final, None
+        'X_Component': max(results['BH1']['X_Component'], results['BH2']['X_Component']),
+        '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):
     """
@@ -155,34 +142,32 @@ 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 Simulation Regression Test Report" + Color.RESET)
+    print(Color.BOLD + "   AMSS-NCKU GW150914 Comprehensive Regression Test" + Color.RESET)
     print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
 
-
+def print_rms_results(rms_dict, error, threshold=1.0):
-def print_rms_results(rms_rel, error, threshold=1.0):
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Maximums of BH1 & BH2){Color.RESET}")
-    """Print RMS error results"""
+    print("-" * 65)
-    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
-    print("-" * 45)
 
     if error:
         print(f"   {Color.RED}Error: {error}{Color.RESET}")
         return False
 
-    passed = rms_rel < threshold
+    all_passed = True
+    print(f"   Requirement: < {threshold}%\n")
 
-    print(f"   RMS relative error: {rms_rel:.4f}%")
+    for key, val in rms_dict.items():
-    print(f"   Requirement:        < {threshold}%")
+        passed = val < threshold
-    print(f"   Status:             {get_status_text(passed)}")
+        all_passed = all_passed and passed
-
+        status = get_status_text(passed)
-    return passed
+        print(f"   {key:15}: {val:8.4f}%   |   Status: {status}")
 
+    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("-" * 45)
+    print("-" * 65)
 
     names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
     for i, name in enumerate(names):
@@ -200,7 +185,6 @@ 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)
@@ -210,7 +194,7 @@ def print_summary(rms_passed, constraint_passed):
     res_rms = get_status_text(rms_passed)
     res_con = get_status_text(constraint_passed)
 
-    print(f"   [1] RMS trajectory check:         {res_rms}")
+    print(f"   [1] Comprehensive RMS 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}"
@@ -219,61 +203,48 @@ 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)
 
-    # Calculate RMS error
+    # Output modified RMS results
-    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
+    rms_dict, error = calculate_all_rms_errors(bh_data_ref, bh_data_target)
-    rms_passed = print_rms_results(rms_rel, error)
+    rms_passed = print_rms_results(rms_dict, error)
 
-    # Analyze constraint violation
+    # Output constraint results
     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

@@ -7,12 +7,178 @@
 #include <string>
 #include <cmath>
 #include <new>
+#include <vector>
 using namespace std;
 
 #include "misc.h"
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
+#ifdef INTERP_LB_PROFILE
+#include "interp_lb_profile.h"
+#endif
+
+namespace
+{
+struct InterpBlockView
+{
+  Block *bp;
+  double llb[dim];
+  double uub[dim];
+};
+
+struct BlockBinIndex
+{
+  int bins[dim];
+  double lo[dim];
+  double inv[dim];
+  vector<InterpBlockView> views;
+  vector<vector<int>> bin_to_blocks;
+  bool valid;
+
+  BlockBinIndex() : valid(false)
+  {
+    for (int i = 0; i < dim; i++)
+    {
+      bins[i] = 1;
+      lo[i] = 0.0;
+      inv[i] = 0.0;
+    }
+  }
+};
+
+inline int clamp_int(int v, int lo, int hi)
+{
+  return (v < lo) ? lo : ((v > hi) ? hi : v);
+}
+
+inline int coord_to_bin(double x, double lo, double inv, int nb)
+{
+  if (nb <= 1 || inv <= 0.0)
+    return 0;
+  int b = int(floor((x - lo) * inv));
+  return clamp_int(b, 0, nb - 1);
+}
+
+inline int bin_loc(const BlockBinIndex &index, int b0, int b1, int b2)
+{
+  return b0 + index.bins[0] * (b1 + index.bins[1] * b2);
+}
+
+inline bool point_in_block_view(const InterpBlockView &view, const double *pox, const double *DH)
+{
+  for (int i = 0; i < dim; i++)
+  {
+    if (pox[i] - view.llb[i] < -DH[i] / 2 || pox[i] - view.uub[i] > DH[i] / 2)
+      return false;
+  }
+  return true;
+}
+
+void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
+{
+  index = BlockBinIndex();
+
+  MyList<Block> *Bp = patch->blb;
+  while (Bp)
+  {
+    Block *BP = Bp->data;
+    InterpBlockView view;
+    view.bp = BP;
+    for (int i = 0; i < dim; i++)
+    {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
+#else
+#ifdef Cell
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+    }
+    index.views.push_back(view);
+    if (Bp == patch->ble)
+      break;
+    Bp = Bp->next;
+  }
+
+  const int nblocks = int(index.views.size());
+  if (nblocks <= 0)
+    return;
+
+  int bins_1d = int(ceil(pow(double(nblocks), 1.0 / 3.0)));
+  bins_1d = clamp_int(bins_1d, 1, 32);
+  for (int i = 0; i < dim; i++)
+  {
+    index.bins[i] = bins_1d;
+    index.lo[i] = patch->bbox[i] + patch->lli[i] * DH[i];
+    const double hi = patch->bbox[dim + i] - patch->uui[i] * DH[i];
+    if (hi > index.lo[i] && bins_1d > 1)
+      index.inv[i] = bins_1d / (hi - index.lo[i]);
+    else
+      index.inv[i] = 0.0;
+  }
+
+  index.bin_to_blocks.resize(index.bins[0] * index.bins[1] * index.bins[2]);
+
+  for (int bi = 0; bi < nblocks; bi++)
+  {
+    const InterpBlockView &view = index.views[bi];
+    int bmin[dim], bmax[dim];
+    for (int d = 0; d < dim; d++)
+    {
+      const double low = view.llb[d] - DH[d] / 2;
+      const double up = view.uub[d] + DH[d] / 2;
+      bmin[d] = coord_to_bin(low, index.lo[d], index.inv[d], index.bins[d]);
+      bmax[d] = coord_to_bin(up, index.lo[d], index.inv[d], index.bins[d]);
+      if (bmax[d] < bmin[d])
+      {
+        int t = bmin[d];
+        bmin[d] = bmax[d];
+        bmax[d] = t;
+      }
+    }
+
+    for (int bz = bmin[2]; bz <= bmax[2]; bz++)
+      for (int by = bmin[1]; by <= bmax[1]; by++)
+        for (int bx = bmin[0]; bx <= bmax[0]; bx++)
+          index.bin_to_blocks[bin_loc(index, bx, by, bz)].push_back(bi);
+  }
+
+  index.valid = true;
+}
+
+int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
+{
+  if (!index.valid)
+    return -1;
+
+  const int bx = coord_to_bin(pox[0], index.lo[0], index.inv[0], index.bins[0]);
+  const int by = coord_to_bin(pox[1], index.lo[1], index.inv[1], index.bins[1]);
+  const int bz = coord_to_bin(pox[2], index.lo[2], index.inv[2], index.bins[2]);
+  const vector<int> &cand = index.bin_to_blocks[bin_loc(index, bx, by, bz)];
+
+  for (size_t ci = 0; ci < cand.size(); ci++)
+  {
+    const int bi = cand[ci];
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return bi;
+  }
+
+  // Fallback to full scan for numerical edge cases around bin boundaries.
+  for (size_t bi = 0; bi < index.views.size(); bi++)
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return int(bi);
+
+  return -1;
+}
+} // namespace
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -364,9 +530,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -389,57 +557,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
-    while (notfind && Bp) // run along Blocks
     {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
-      for (int i = 0; i < dim; i++)
       {
-#ifdef Vertex
+        //---> interpolation
-#ifdef Cell
+        varl = VarList;
-#error Both Cell and Vertex are defined
+        int k = 0;
-#endif
+        while (varl) // run along variables
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
         {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
@@ -507,6 +642,9 @@ 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);
@@ -529,9 +667,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   // --- Interpolation phase (identical to original) ---
   for (int j = 0; j < NN; j++)
@@ -555,59 +695,31 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
-    while (notfind && Bp)
     {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
-      for (int i = 0; i < dim; i++)
       {
-#ifdef Vertex
+        varl = VarList;
-#ifdef Cell
+        int k = 0;
-#error Both Cell and Vertex are defined
+        while (varl)
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
         {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          varl = VarList;
-          int k = 0;
-          while (varl)
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
+#ifdef INTERP_LB_PROFILE
+  double t_interp_end = MPI_Wtime();
+  double t_interp_local = t_interp_end - t_interp_start;
+#endif
+
   // --- Error check for unfound points ---
   for (int j = 0; j < NN; j++)
   {
@@ -764,6 +876,31 @@ 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,
@@ -797,9 +934,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   MPI_Comm_group(MPI_COMM_WORLD, &world_group);
   MPI_Comm_group(Comm_here, &local_group);
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -822,57 +961,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
-    while (notfind && Bp) // run along Blocks
     {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
-      for (int i = 0; i < dim; i++)
       {
-#ifdef Vertex
+        //---> interpolation
-#ifdef Cell
+        varl = VarList;
-#error Both Cell and Vertex are defined
+        int k = 0;
-#endif
+        while (varl) // run along variables
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
         {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 

AMSS_NCKU_source/Parallel.h

@@ -32,6 +32,16 @@ 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));
@@ -98,6 +108,9 @@ namespace Parallel
     MPI_Status *stats;
     int max_reqs;
     bool lengths_valid;
+    int *tc_req_node;
+    int *tc_req_is_recv;
+    int *tc_completed;
     SyncCache();
     void invalidate();
     void destroy();
@@ -111,7 +124,10 @@ namespace Parallel
   struct AsyncSyncState {
     int req_no;
     bool active;
-    AsyncSyncState() : req_no(0), active(false) {}
+    int *req_node;
+    int *req_is_recv;
+    int pending_recv;
+    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
   };
 
   void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,

AMSS_NCKU_source/bssn_class.C

@@ -36,12 +36,18 @@ using namespace std;
 #include "myglobal.h"
 #endif
 
-#include "perf.h"
+#include "perf.h"
-
+
-#include "derivatives.h"
+#include "derivatives.h"
-#include "ricci_gamma.h"
+#include "ricci_gamma.h"
-
+
-//================================================================================================
+// Compile-time switch for per-timestep memory usage collection/printing.
+// Default is OFF to reduce overhead in production runs.
+#ifndef BSSN_ENABLE_MEM_USAGE_LOG
+#define BSSN_ENABLE_MEM_USAGE_LOG 0
+#endif
+
+//================================================================================================
 
 // define bssn_class
 
@@ -736,6 +742,8 @@ void bssn_class::Initialize()
   sync_cache_cor = new Parallel::SyncCache[GH->levels];
   sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
   sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
+  sync_cache_restrict = new Parallel::SyncCache[GH->levels];
+  sync_cache_outbd = new Parallel::SyncCache[GH->levels];
 }
 
 //================================================================================================
@@ -2127,8 +2135,10 @@ void bssn_class::Evolve(int Steps)
   #endif
   */
   
-  perf bssn_perf;
+#if BSSN_ENABLE_MEM_USAGE_LOG
-  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
+  perf bssn_perf;
+  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
+#endif
 
   for (int lev = 0; lev < GH->levels; lev++)
     GH->Lt[lev] = PhysTime;
@@ -2213,7 +2223,7 @@ void bssn_class::Evolve(int Steps)
     GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
                SynchList_cor, OldStateList, StateList, SynchList_pre,
                fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
-    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 #endif
 
 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2222,21 +2232,23 @@ void bssn_class::Evolve(int Steps)
 //		fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
 #endif
 
-    // Retrieve memory usage information used during computation; master process prints it
+#if BSSN_ENABLE_MEM_USAGE_LOG
-    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
+    // Retrieve memory usage information used during computation; master process prints it
-                          &peak_min, &peak_avg, &peak_max, nprocs);
+    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
-    if (myrank == 0)
+                          &peak_min, &peak_avg, &peak_max, nprocs);
-    {
+    if (myrank == 0)
-      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
+    {
-             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
+      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
-             (double)current_min / (1024.0 * 1024.0),
+             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
-             (double)current_avg / (1024.0 * 1024.0),
+             (double)current_min / (1024.0 * 1024.0),
-             (double)current_max / (1024.0 * 1024.0),
+             (double)current_avg / (1024.0 * 1024.0),
-             (double)peak_min / (1024.0 * 1024.0),
+             (double)current_max / (1024.0 * 1024.0),
-             (double)peak_avg / (1024.0 * 1024.0),
+             (double)peak_min / (1024.0 * 1024.0),
-             (double)peak_max / (1024.0 * 1024.0));
+             (double)peak_avg / (1024.0 * 1024.0),
-      cout << endl;
+             (double)peak_max / (1024.0 * 1024.0));
-    }
+      cout << endl;
+    }
+#endif
     
     // Output puncture positions at each step
     if (myrank == 0)
@@ -2426,10 +2438,10 @@ void bssn_class::RecursiveStep(int lev)
 #endif
 
 #if (REGLEV == 0)
-  GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
+  if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
-                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
+                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 #endif
 }
 
@@ -2605,10 +2617,10 @@ void bssn_class::ParallelStep()
   delete[] tporg;
   delete[] tporgo;
 #if (REGLEV == 0)
-  GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
+  if (GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
-                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
+                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 #endif
 }
 
@@ -2772,10 +2784,10 @@ void bssn_class::ParallelStep()
       if (lev + 1 >= GH->movls)
       {
         //	       GH->Regrid_Onelevel_aux(lev,Symmetry,BH_num,Porgbr,Porg0,
-        GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
+        if (GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
                             SynchList_cor, OldStateList, StateList, SynchList_pre,
-                            fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor);
+                            fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor))
-        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 
         //               a_stream.clear();
         //               a_stream.str("");
@@ -2787,10 +2799,10 @@ void bssn_class::ParallelStep()
     // for this level
     if (YN == 1)
     {
-      GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
+      if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                           SynchList_cor, OldStateList, StateList, SynchList_pre,
-                          fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor);
+                          fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 
       //               a_stream.clear();
       //               a_stream.str("");
@@ -2806,10 +2818,10 @@ void bssn_class::ParallelStep()
         if (YN == 1)
         {
           //	   GH->Regrid_Onelevel_aux(lev-2,Symmetry,BH_num,Porgbr,Porg0,
-          GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
+          if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
-                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
+                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -2822,10 +2834,10 @@ void bssn_class::ParallelStep()
         if (i % 4 == 3)
         {
           //	   GH->Regrid_Onelevel_aux(lev-2,Symmetry,BH_num,Porgbr,Porg0,
-          GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
+          if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
-                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor);
+                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -5796,7 +5808,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -5820,7 +5832,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5847,7 +5859,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
@@ -5871,7 +5883,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -5940,7 +5952,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       }
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -5950,7 +5962,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5962,7 +5974,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
     else // no time refinement levels and for all same time levels
     {
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
@@ -5972,7 +5984,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -6027,7 +6039,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       }
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,SynchList_pre,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -6037,7 +6049,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6051,7 +6063,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       if (myrank == 0)
         cout << "===: " << GH->Lt[lev - 1] << "," << GH->Lt[lev] + dT_lev << endl;
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
@@ -6061,7 +6073,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif
@@ -6102,7 +6114,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6115,7 +6127,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
     {
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif

AMSS_NCKU_source/bssn_class.h

@@ -130,6 +130,8 @@ public:
        Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
        Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
        Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
+       Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
+       Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong
 
        monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
        monitor *ConVMonitor;

AMSS_NCKU_source/bssn_rhs.f90

@@ -59,9 +59,10 @@
   real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Rxx,Rxy,Rxz,Ryy,Ryz,Rzz
   real*8,intent(in) :: eps
   real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: ham_Res, movx_Res, movy_Res, movz_Res
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
-!  gont = 0: success; gont = 1: something wrong
+!  gont = 0: success; gont = 1: something wrong
-  integer::gont
+  integer::gont
+  integer :: i,j,k
 
 !~~~~~~> Other variables:
 
@@ -83,11 +84,18 @@
   real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
   real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
 
-  real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
+  real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
-  real*8            :: dX, dY, dZ, PI
+  real*8            :: dX, dY, dZ, PI
-  real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
+  real*8            :: divb_loc,det_loc
-  real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
+  real*8            :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
-  real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
+  real*8            :: Rxx_loc,Rxy_loc,Rxz_loc,Ryy_loc,Ryz_loc,Rzz_loc
+  real*8            :: fxx_loc,fxy_loc,fxz_loc
+  real*8            :: Gamxa_loc,Gamya_loc,Gamza_loc
+  real*8            :: f_loc,chin_loc
+  real*8            :: l_fxx,l_fxy,l_fxz,l_fyy,l_fyz,l_fzz,S_loc
+  real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
+  real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
+  real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
   double precision,parameter::FF = 0.75d0,eta=2.d0
   real*8, parameter :: F1o3 = 1.D0/3.D0, F2o3 = 2.D0/3.D0,F3o2=1.5d0, F1o6 = 1.D0/6.D0
   real*8, parameter :: F16=1.6d1,F8=8.d0
@@ -96,11 +104,11 @@
   real*8, dimension(ex(1),ex(2),ex(3)) :: reta
 #endif
 
-#if (GAUGE == 6 || GAUGE == 7)
+#if (GAUGE == 6 || GAUGE == 7)
-  integer :: BHN,i,j,k
+  integer :: BHN
-  real*8, dimension(9) :: Porg
+  real*8, dimension(9) :: Porg
-  real*8, dimension(3) :: Mass
+  real*8, dimension(3) :: Mass
-  real*8 :: r1,r2,M,A,w1,w2,C1,C2
+  real*8 :: r1,r2,M,A,w1,w2,C1,C2
   real*8, dimension(ex(1),ex(2),ex(3)) :: reta
 
   call getpbh(BHN,Porg,Mass)
@@ -145,174 +153,204 @@
   dY = Y(2) - Y(1)
   dZ = Z(2) - Z(1)
 
-  alpn1 = Lap + ONE
+  do k=1,ex(3)
-  chin1 = chi + ONE
+  do j=1,ex(2)
-  gxx = dxx + ONE
+  do i=1,ex(1)
-  gyy = dyy + ONE
+    alpn1(i,j,k) = Lap(i,j,k) + ONE
-  gzz = dzz + ONE
+    chin1(i,j,k) = chi(i,j,k) + ONE
+    gxx(i,j,k) = dxx(i,j,k) + ONE
+    gyy(i,j,k) = dyy(i,j,k) + ONE
+    gzz(i,j,k) = dzz(i,j,k) + ONE
+  enddo
+  enddo
+  enddo
 
   call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
   call fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev)
   call fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev)
   
-  div_beta = betaxx + betayy + betazz
+  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
- 
-  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
 
-  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
+  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-
+  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
-  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
+  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
+  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
-  call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
+
-  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
+  do k=1,ex(3)
-
+  do j=1,ex(2)
-  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
+  do i=1,ex(1)
-              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
+    divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
-
+    div_beta(i,j,k) = divb_loc
-  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
+
-              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
+    chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
-
+
-  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
+    gxx_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axx(i,j,k) - F2o3 * gxx(i,j,k) * divb_loc + &
-              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
+         TWO * ( gxx(i,j,k) * betaxx(i,j,k) + gxy(i,j,k) * betayx(i,j,k) + gxz(i,j,k) * betazx(i,j,k) )
-
+
-  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
+    gyy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayy(i,j,k) - F2o3 * gyy(i,j,k) * divb_loc + &
-                      gxx * betaxy                  +   gxz * betazy + &
+         TWO * ( gxy(i,j,k) * betaxy(i,j,k) + gyy(i,j,k) * betayy(i,j,k) + gyz(i,j,k) * betazy(i,j,k) )
-                                       gyy * betayx +   gyz * betazx   &
+
-                                                    -   gxy * betazz
+    gzz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Azz(i,j,k) - F2o3 * gzz(i,j,k) * divb_loc + &
-
+         TWO * ( gxz(i,j,k) * betaxz(i,j,k) + gyz(i,j,k) * betayz(i,j,k) + gzz(i,j,k) * betazz(i,j,k) )
-  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
+
-                      gxy * betaxz +   gyy * betayz                  + &
+    gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
-                      gxz * betaxy                  +   gzz * betazy   &
+         gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
-                                                    -   gyz * betaxx
+         gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
- 
+
-  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
+    gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
-                      gxx * betaxz +   gxy * betayz                  + &
+         gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
-                                       gyz * betayx +   gzz * betazx   &
+         gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
-                                                    -   gxz * betayy     !rhs for gij
+
-
+    gxz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axz(i,j,k) + F1o3 * gxz(i,j,k) * divb_loc + &
-! invert tilted metric
+         gxx(i,j,k) * betaxz(i,j,k) + gxy(i,j,k) * betayz(i,j,k) + gyz(i,j,k) * betayx(i,j,k) + &
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+         gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+
-  gupxx =   ( gyy * gzz - gyz * gyz ) / gupzz
+    det_loc = gxx(i,j,k) * gyy(i,j,k) * gzz(i,j,k) + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) + &
-  gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
+         gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) - gxz(i,j,k) * gyy(i,j,k) * gxz(i,j,k) - &
-  gupxz =   ( gxy * gyz - gyy * gxz ) / gupzz
+         gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
-  gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
+    gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
-  gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
+    gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
-  gupzz =   ( gxx * gyy - gxy * gxy ) / gupzz
+    gupxz_loc = ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) / det_loc
-
+    gupyy_loc = ( gxx(i,j,k) * gzz(i,j,k) - gxz(i,j,k) * gxz(i,j,k) ) / det_loc
-  if(co == 0)then
+    gupyz_loc = - ( gxx(i,j,k) * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / det_loc
-! Gam^i_Res = Gam^i + gup^ij_,j
+    gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
-  Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
+    gupxx(i,j,k) = gupxx_loc
-                   +gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
+    gupxy(i,j,k) = gupxy_loc
-                   +gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
+    gupxz(i,j,k) = gupxz_loc
-                   +gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+    gupyy(i,j,k) = gupyy_loc
-                   +gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+    gupyz(i,j,k) = gupyz_loc
-                   +gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+    gupzz(i,j,k) = gupzz_loc
-                   +gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+
-                   +gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+    if(co == 0)then
-                   +gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
+      Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
-  Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
+           gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
-                   +gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
+           gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
-                   +gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
+           gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
-                   +gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+           gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
-                   +gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+           gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
-                   +gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+           gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
-                   +gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+           gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
-                   +gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+           gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
-                   +gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
+           gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
-  Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
+      Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
-                   +gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
+           gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
-                   +gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
+           gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
-                   +gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
+           gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
-                   +gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
+           gupxy_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
-                   +gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
+           gupyy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
-                   +gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+           gupyz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
-                   +gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+           gupxy_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
-                   +gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
+           gupyy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
-  endif
+           gupyz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
-
+      Gmz_Res(i,j,k) = Gamz(i,j,k) - ( &
-! second kind of connection
+           gupxx_loc*(gupxz_loc*gxxx(i,j,k)+gupyz_loc*gxyx(i,j,k)+gupzz_loc*gxzx(i,j,k)) + &
-  Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
+           gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
-  Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
+           gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
-  Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
+           gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
- 
+           gupyy_loc*(gupxz_loc*gxyy(i,j,k)+gupyz_loc*gyyy(i,j,k)+gupzz_loc*gyzy(i,j,k)) + &
-  Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
+           gupyz_loc*(gupxz_loc*gxzy(i,j,k)+gupyz_loc*gyzy(i,j,k)+gupzz_loc*gzzy(i,j,k)) + &
-  Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
+           gupxz_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
-  Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
+           gupyz_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
-
+           gupzz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
-  Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
+    endif
-  Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
+
-  Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
+    Gamxxx(i,j,k)=HALF*( gupxx_loc*gxxx(i,j,k) + gupxy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupxz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
-
+    Gamyxx(i,j,k)=HALF*( gupxy_loc*gxxx(i,j,k) + gupyy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupyz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
-  Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
+    Gamzxx(i,j,k)=HALF*( gupxz_loc*gxxx(i,j,k) + gupyz_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupzz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
-  Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
+
-  Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
+    Gamxyy(i,j,k)=HALF*( gupxx_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupxy_loc*gyyy(i,j,k) + gupxz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
-
+    Gamyyy(i,j,k)=HALF*( gupxy_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyy_loc*gyyy(i,j,k) + gupyz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
-  Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
+    Gamzyy(i,j,k)=HALF*( gupxz_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyz_loc*gyyy(i,j,k) + gupzz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
-  Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
+
-  Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
+    Gamxzz(i,j,k)=HALF*( gupxx_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupxy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupxz_loc*gzzz(i,j,k))
-
+    Gamyzz(i,j,k)=HALF*( gupxy_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupyz_loc*gzzz(i,j,k))
-  Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
+    Gamzzz(i,j,k)=HALF*( gupxz_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyz_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupzz_loc*gzzz(i,j,k))
-  Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
+
-  Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
+    Gamxxy(i,j,k)=HALF*( gupxx_loc*gxxy(i,j,k) + gupxy_loc*gyyx(i,j,k) + gupxz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
-! Raise indices of \tilde A_{ij} and store in R_ij
+    Gamyxy(i,j,k)=HALF*( gupxy_loc*gxxy(i,j,k) + gupyy_loc*gyyx(i,j,k) + gupyz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
-
+    Gamzxy(i,j,k)=HALF*( gupxz_loc*gxxy(i,j,k) + gupyz_loc*gyyx(i,j,k) + gupzz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
-  Rxx =    gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
+
-      TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
+    Gamxxz(i,j,k)=HALF*( gupxx_loc*gxxz(i,j,k) + gupxy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupxz_loc*gzzx(i,j,k) )
-
+    Gamyxz(i,j,k)=HALF*( gupxy_loc*gxxz(i,j,k) + gupyy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupyz_loc*gzzx(i,j,k) )
-  Ryy =    gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
+    Gamzxz(i,j,k)=HALF*( gupxz_loc*gxxz(i,j,k) + gupyz_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupzz_loc*gzzx(i,j,k) )
-      TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
+
-
+    Gamxyz(i,j,k)=HALF*( gupxx_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupxy_loc*gyyz(i,j,k) + gupxz_loc*gzzy(i,j,k) )
-  Rzz =    gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
+    Gamyyz(i,j,k)=HALF*( gupxy_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyy_loc*gyyz(i,j,k) + gupyz_loc*gzzy(i,j,k) )
-      TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
+    Gamzyz(i,j,k)=HALF*( gupxz_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyz_loc*gyyz(i,j,k) + gupzz_loc*gzzy(i,j,k) )
-
+  enddo
-  Rxy =    gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
+  enddo
-          (gupxx * gupyy       + gupxy * gupxy)* Axy                       + &
+  enddo
-          (gupxx * gupyz       + gupxz * gupxy)* Axz                       + &
+! Raise indices of \tilde A_{ij} and store in R_ij
-          (gupxy * gupyz       + gupxz * gupyy)* Ayz
+
-
+! Right hand side for Gam^i without shift terms...
-  Rxz =    gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
+  call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
-          (gupxx * gupyz       + gupxy * gupxz)* Axy                       + &
+  call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
-          (gupxx * gupzz       + gupxz * gupxz)* Axz                       + &
+  do k=1,ex(3)
-          (gupxy * gupzz       + gupxz * gupyz)* Ayz
+  do j=1,ex(2)
-
+  do i=1,ex(1)
-  Ryz =    gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
+    gupxx_loc = gupxx(i,j,k)
-          (gupxy * gupyz       + gupyy * gupxz)* Axy                       + &
+    gupxy_loc = gupxy(i,j,k)
-          (gupxy * gupzz       + gupyz * gupxz)* Axz                       + &
+    gupxz_loc = gupxz(i,j,k)
-          (gupyy * gupzz       + gupyz * gupyz)* Ayz
+    gupyy_loc = gupyy(i,j,k)
-
+    gupyz_loc = gupyz(i,j,k)
-! Right hand side for Gam^i without shift terms...
+    gupzz_loc = gupzz(i,j,k)
-  call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+
-  call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
+    Rxx_loc = gupxx_loc * gupxx_loc * Axx(i,j,k) + gupxy_loc * gupxy_loc * Ayy(i,j,k) + gupxz_loc * gupxz_loc * Azz(i,j,k) + &
-
+         TWO * (gupxx_loc * gupxy_loc * Axy(i,j,k) + gupxx_loc * gupxz_loc * Axz(i,j,k) + gupxy_loc * gupxz_loc * Ayz(i,j,k))
-   Gamx_rhs = - TWO * (   Lapx * Rxx +   Lapy * Rxy +   Lapz * Rxz ) + &
+    Ryy_loc = gupxy_loc * gupxy_loc * Axx(i,j,k) + gupyy_loc * gupyy_loc * Ayy(i,j,k) + gupyz_loc * gupyz_loc * Azz(i,j,k) + &
-        TWO * alpn1 * (                                                &
+         TWO * (gupxy_loc * gupyy_loc * Axy(i,j,k) + gupxy_loc * gupyz_loc * Axz(i,j,k) + gupyy_loc * gupyz_loc * Ayz(i,j,k))
-        -F3o2/chin1 * (   chix * Rxx +   chiy * Rxy +   chiz * Rxz ) - &
+    Rzz_loc = gupxz_loc * gupxz_loc * Axx(i,j,k) + gupyz_loc * gupyz_loc * Ayy(i,j,k) + gupzz_loc * gupzz_loc * Azz(i,j,k) + &
-              gupxx * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
+         TWO * (gupxz_loc * gupyz_loc * Axy(i,j,k) + gupxz_loc * gupzz_loc * Axz(i,j,k) + gupyz_loc * gupzz_loc * Ayz(i,j,k))
-              gupxy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
+    Rxy_loc = gupxx_loc * gupxy_loc * Axx(i,j,k) + gupxy_loc * gupyy_loc * Ayy(i,j,k) + gupxz_loc * gupyz_loc * Azz(i,j,k) + &
-              gupxz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+         (gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
-                        Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz   + &
+         (gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
-                TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
+         (gupxy_loc * gupyz_loc + gupxz_loc * gupyy_loc) * Ayz(i,j,k)
-
+    Rxz_loc = gupxx_loc * gupxz_loc * Axx(i,j,k) + gupxy_loc * gupyz_loc * Ayy(i,j,k) + gupxz_loc * gupzz_loc * Azz(i,j,k) + &
-   Gamy_rhs = - TWO * (   Lapx * Rxy +   Lapy * Ryy +   Lapz * Ryz ) + &
+         (gupxx_loc * gupyz_loc + gupxy_loc * gupxz_loc) * Axy(i,j,k) + &
-        TWO * alpn1 * (                                                &
+         (gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
-        -F3o2/chin1 * (   chix * Rxy +  chiy * Ryy +    chiz * Ryz ) - &
+         (gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
-              gupxy * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
+    Ryz_loc = gupxy_loc * gupxz_loc * Axx(i,j,k) + gupyy_loc * gupyz_loc * Ayy(i,j,k) + gupyz_loc * gupzz_loc * Azz(i,j,k) + &
-              gupyy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
+         (gupxy_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
-              gupyz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+         (gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
-                        Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz   + &
+         (gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
-                TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
+    Rxx(i,j,k) = Rxx_loc
-
+    Ryy(i,j,k) = Ryy_loc
-   Gamz_rhs = - TWO * (   Lapx * Rxz +   Lapy * Ryz +   Lapz * Rzz ) + &
+    Rzz(i,j,k) = Rzz_loc
-        TWO * alpn1 * (                                                &
+    Rxy(i,j,k) = Rxy_loc
-        -F3o2/chin1 * (   chix * Rxz +  chiy * Ryz +    chiz * Rzz ) - &
+    Rxz(i,j,k) = Rxz_loc
-              gupxz * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
+    Ryz(i,j,k) = Ryz_loc
-              gupyz * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
+
-              gupzz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+    Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
-                        Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz   + &
+         TWO * alpn1(i,j,k) * ( &
-                TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
+         -F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
+         gupxx_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
+         gupxy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
+         gupxz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
+         Gamxxx(i,j,k) * Rxx_loc + Gamxyy(i,j,k) * Ryy_loc + Gamxzz(i,j,k) * Rzz_loc + &
+         TWO * (Gamxxy(i,j,k) * Rxy_loc + Gamxxz(i,j,k) * Rxz_loc + Gamxyz(i,j,k) * Ryz_loc))
+
+    Gamy_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxy_loc + Lapy(i,j,k) * Ryy_loc + Lapz(i,j,k) * Ryz_loc) + &
+         TWO * alpn1(i,j,k) * ( &
+         -F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxy_loc + chiy(i,j,k) * Ryy_loc + chiz(i,j,k) * Ryz_loc) - &
+         gupxy_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
+         gupyy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
+         gupyz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
+         Gamyxx(i,j,k) * Rxx_loc + Gamyyy(i,j,k) * Ryy_loc + Gamyzz(i,j,k) * Rzz_loc + &
+         TWO * (Gamyxy(i,j,k) * Rxy_loc + Gamyxz(i,j,k) * Rxz_loc + Gamyyz(i,j,k) * Ryz_loc))
+
+    Gamz_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxz_loc + Lapy(i,j,k) * Ryz_loc + Lapz(i,j,k) * Rzz_loc) + &
+         TWO * alpn1(i,j,k) * ( &
+         -F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxz_loc + chiy(i,j,k) * Ryz_loc + chiz(i,j,k) * Rzz_loc) - &
+         gupxz_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
+         gupyz_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
+         gupzz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
+         Gamzxx(i,j,k) * Rxx_loc + Gamzyy(i,j,k) * Ryy_loc + Gamzzz(i,j,k) * Rzz_loc + &
+         TWO * (Gamzxy(i,j,k) * Rxy_loc + Gamzxz(i,j,k) * Rxz_loc + Gamzyz(i,j,k) * Ryz_loc))
+  enddo
+  enddo
+  enddo
 
   call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
                 X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
@@ -321,38 +359,54 @@
   call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
                 X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
 
-  fxx = gxxx + gxyy + gxzz
+  call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
-  fxy = gxyx + gyyy + gyzz
+  call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
-  fxz = gxzx + gyzy + gzzz
+  call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
-
+  do k=1,ex(3)
-  Gamxa =       gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
+  do j=1,ex(2)
-          TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
+  do i=1,ex(1)
-  Gamya =       gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
+    divb_loc = div_beta(i,j,k)
-          TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
+    fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
-  Gamza =       gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
+    fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
-          TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
+    fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)
-
+
-  call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
+    gupxx_loc = gupxx(i,j,k)
-  call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
+    gupxy_loc = gupxy(i,j,k)
-  call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
+    gupxz_loc = gupxz(i,j,k)
-
+    gupyy_loc = gupyy(i,j,k)
-  Gamx_rhs =               Gamx_rhs +  F2o3 *  Gamxa * div_beta        - &
+    gupyz_loc = gupyz(i,j,k)
-                     Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz  + &
+    gupzz_loc = gupzz(i,j,k)
-             F1o3 * (gupxx * fxx    + gupxy * fxy    + gupxz * fxz    ) + &
+
-                     gupxx * gxxx   + gupyy * gyyx   + gupzz * gzzx    + &
+    Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
-              TWO * (gupxy * gxyx   + gupxz * gxzx   + gupyz * gyzx  )
+         TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
-
+    Gamya_loc = gupxx_loc * Gamyxx(i,j,k) + gupyy_loc * Gamyyy(i,j,k) + gupzz_loc * Gamyzz(i,j,k) + &
-  Gamy_rhs =               Gamy_rhs +  F2o3 *  Gamya * div_beta        - &
+         TWO * (gupxy_loc * Gamyxy(i,j,k) + gupxz_loc * Gamyxz(i,j,k) + gupyz_loc * Gamyyz(i,j,k))
-                     Gamxa * betayx - Gamya * betayy - Gamza * betayz  + &
+    Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
-             F1o3 * (gupxy * fxx    + gupyy * fxy    + gupyz * fxz    ) + &
+         TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
-                     gupxx * gxxy   + gupyy * gyyy   + gupzz * gzzy    + &
+    Gamxa(i,j,k) = Gamxa_loc
-              TWO * (gupxy * gxyy   + gupxz * gxzy   + gupyz * gyzy  )
+    Gamya(i,j,k) = Gamya_loc
-
+    Gamza(i,j,k) = Gamza_loc
-  Gamz_rhs =               Gamz_rhs +  F2o3 *  Gamza * div_beta        - &
+
-                     Gamxa * betazx - Gamya * betazy - Gamza * betazz  + &
+    Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
-             F1o3 * (gupxz * fxx    + gupyz * fxy    + gupzz * fxz    ) + &
+         Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
-                     gupxx * gxxz   + gupyy * gyyz   + gupzz * gzzz    + &
+         F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
-              TWO * (gupxy * gxyz   + gupxz * gxzz   + gupyz * gyzz  )    !rhs for Gam^i
+         gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
+         TWO * (gupxy_loc * gxyx(i,j,k) + gupxz_loc * gxzx(i,j,k) + gupyz_loc * gyzx(i,j,k))
+
+    Gamy_rhs(i,j,k) = Gamy_rhs(i,j,k) + F2o3 * Gamya_loc * divb_loc - &
+         Gamxa_loc * betayx(i,j,k) - Gamya_loc * betayy(i,j,k) - Gamza_loc * betayz(i,j,k) + &
+         F1o3 * (gupxy_loc * fxx_loc + gupyy_loc * fxy_loc + gupyz_loc * fxz_loc) + &
+         gupxx_loc * gxxy(i,j,k) + gupyy_loc * gyyy(i,j,k) + gupzz_loc * gzzy(i,j,k) + &
+         TWO * (gupxy_loc * gxyy(i,j,k) + gupxz_loc * gxzy(i,j,k) + gupyz_loc * gyzy(i,j,k))
+
+    Gamz_rhs(i,j,k) = Gamz_rhs(i,j,k) + F2o3 * Gamza_loc * divb_loc - &
+         Gamxa_loc * betazx(i,j,k) - Gamya_loc * betazy(i,j,k) - Gamza_loc * betazz(i,j,k) + &
+         F1o3 * (gupxz_loc * fxx_loc + gupyz_loc * fxy_loc + gupzz_loc * fxz_loc) + &
+         gupxx_loc * gxxz(i,j,k) + gupyy_loc * gyyz(i,j,k) + gupzz_loc * gzzz(i,j,k) + &
+         TWO * (gupxy_loc * gxyz(i,j,k) + gupxz_loc * gxzz(i,j,k) + gupyz_loc * gyzz(i,j,k))
+  enddo
+  enddo
+  enddo
 
 !first kind of connection stored in gij,k
   gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
@@ -601,192 +655,190 @@
             Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz  + &
             Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy  + &
             Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
-!covariant second derivative of chi respect to tilted metric
+!covariant second derivative of chi respect to tilted metric
-  call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
-
+
-  fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
+  do k=1,ex(3)
-  fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
+  do j=1,ex(2)
-  fxz = fxz - Gamxxz * chix - Gamyxz * chiy - Gamzxz * chiz
+  do i=1,ex(1)
-  fyy = fyy - Gamxyy * chix - Gamyyy * chiy - Gamzyy * chiz
+    fxx(i,j,k) = fxx(i,j,k) - Gamxxx(i,j,k) * chix(i,j,k) - Gamyxx(i,j,k) * chiy(i,j,k) - Gamzxx(i,j,k) * chiz(i,j,k)
-  fyz = fyz - Gamxyz * chix - Gamyyz * chiy - Gamzyz * chiz
+    fxy(i,j,k) = fxy(i,j,k) - Gamxxy(i,j,k) * chix(i,j,k) - Gamyxy(i,j,k) * chiy(i,j,k) - Gamzxy(i,j,k) * chiz(i,j,k)
-  fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
+    fxz(i,j,k) = fxz(i,j,k) - Gamxxz(i,j,k) * chix(i,j,k) - Gamyxz(i,j,k) * chiy(i,j,k) - Gamzxz(i,j,k) * chiz(i,j,k)
-! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f
+    fyy(i,j,k) = fyy(i,j,k) - Gamxyy(i,j,k) * chix(i,j,k) - Gamyyy(i,j,k) * chiy(i,j,k) - Gamzyy(i,j,k) * chiz(i,j,k)
-
+    fyz(i,j,k) = fyz(i,j,k) - Gamxyz(i,j,k) * chix(i,j,k) - Gamyyz(i,j,k) * chiy(i,j,k) - Gamzyz(i,j,k) * chiz(i,j,k)
-  f =        gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
+    fzz(i,j,k) = fzz(i,j,k) - Gamxzz(i,j,k) * chix(i,j,k) - Gamyzz(i,j,k) * chiy(i,j,k) - Gamzzz(i,j,k) * chiz(i,j,k)
-             gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
+
-             gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
+    chin_loc = chin1(i,j,k)
-       TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
+    f_loc = gupxx(i,j,k) * (fxx(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chix(i,j,k)) + &
-       TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
+            gupyy(i,j,k) * (fyy(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiy(i,j,k)) + &
-       TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz ) 
+            gupzz(i,j,k) * (fzz(i,j,k) - F3o2/chin_loc * chiz(i,j,k) * chiz(i,j,k)) + &
-! Add chi part to Ricci tensor:
+            TWO * gupxy(i,j,k) * (fxy(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiy(i,j,k)) + &
-
+            TWO * gupxz(i,j,k) * (fxz(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiz(i,j,k)) + &
-  Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * f)/chin1/TWO
+            TWO * gupyz(i,j,k) * (fyz(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiz(i,j,k))
-  Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * f)/chin1/TWO
+    f(i,j,k) = f_loc
-  Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/TWO
+
-  Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/TWO
+    Rxx(i,j,k) = Rxx(i,j,k) + (fxx(i,j,k) - chix(i,j,k)*chix(i,j,k)/chin_loc/TWO + gxx(i,j,k) * f_loc)/chin_loc/TWO
-  Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/TWO
+    Ryy(i,j,k) = Ryy(i,j,k) + (fyy(i,j,k) - chiy(i,j,k)*chiy(i,j,k)/chin_loc/TWO + gyy(i,j,k) * f_loc)/chin_loc/TWO
-  Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO
+    Rzz(i,j,k) = Rzz(i,j,k) + (fzz(i,j,k) - chiz(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gzz(i,j,k) * f_loc)/chin_loc/TWO
-
+    Rxy(i,j,k) = Rxy(i,j,k) + (fxy(i,j,k) - chix(i,j,k)*chiy(i,j,k)/chin_loc/TWO + gxy(i,j,k) * f_loc)/chin_loc/TWO
-! covariant second derivatives of the lapse respect to physical metric
+    Rxz(i,j,k) = Rxz(i,j,k) + (fxz(i,j,k) - chix(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gxz(i,j,k) * f_loc)/chin_loc/TWO
-  call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
+    Ryz(i,j,k) = Ryz(i,j,k) + (fyz(i,j,k) - chiy(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gyz(i,j,k) * f_loc)/chin_loc/TWO
-                SYM,SYM,SYM,symmetry,Lev)
+  enddo
-
+  enddo
-  gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
+  enddo
-  gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
+
-  gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
+! covariant second derivatives of the lapse respect to physical metric
-! now get physical second kind of connection
+  call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
-  Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
+                SYM,SYM,SYM,symmetry,Lev)
-  Gamyxx = Gamyxx - (                     - gxx * gxxy )*HALF
+
-  Gamzxx = Gamzxx - (                     - gxx * gxxz )*HALF
+  do k=1,ex(3)
-  Gamxyy = Gamxyy - (                     - gyy * gxxx )*HALF
+  do j=1,ex(2)
-  Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
+  do i=1,ex(1)
-  Gamzyy = Gamzyy - (                     - gyy * gxxz )*HALF
+    chin_loc = chin1(i,j,k)
-  Gamxzz = Gamxzz - (                     - gzz * gxxx )*HALF
+    gxxx(i,j,k) = (gupxx(i,j,k) * chix(i,j,k) + gupxy(i,j,k) * chiy(i,j,k) + gupxz(i,j,k) * chiz(i,j,k)) / chin_loc
-  Gamyzz = Gamyzz - (                     - gzz * gxxy )*HALF
+    gxxy(i,j,k) = (gupxy(i,j,k) * chix(i,j,k) + gupyy(i,j,k) * chiy(i,j,k) + gupyz(i,j,k) * chiz(i,j,k)) / chin_loc
-  Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
+    gxxz(i,j,k) = (gupxz(i,j,k) * chix(i,j,k) + gupyz(i,j,k) * chiy(i,j,k) + gupzz(i,j,k) * chiz(i,j,k)) / chin_loc
-  Gamxxy = Gamxxy - (  chiy        /chin1 - gxy * gxxx )*HALF
+
-  Gamyxy = Gamyxy - (         chix /chin1 - gxy * gxxy )*HALF
+    Gamxxx(i,j,k) = Gamxxx(i,j,k) - ( (chix(i,j,k) + chix(i,j,k))/chin_loc - gxx(i,j,k) * gxxx(i,j,k) )*HALF
-  Gamzxy = Gamzxy - (                     - gxy * gxxz )*HALF
+    Gamyxx(i,j,k) = Gamyxx(i,j,k) - (                                   - gxx(i,j,k) * gxxy(i,j,k) )*HALF
-  Gamxxz = Gamxxz - (  chiz        /chin1 - gxz * gxxx )*HALF
+    Gamzxx(i,j,k) = Gamzxx(i,j,k) - (                                   - gxx(i,j,k) * gxxz(i,j,k) )*HALF
-  Gamyxz = Gamyxz - (                     - gxz * gxxy )*HALF
+    Gamxyy(i,j,k) = Gamxyy(i,j,k) - (                                   - gyy(i,j,k) * gxxx(i,j,k) )*HALF
-  Gamzxz = Gamzxz - (         chix /chin1 - gxz * gxxz )*HALF
+    Gamyyy(i,j,k) = Gamyyy(i,j,k) - ( (chiy(i,j,k) + chiy(i,j,k))/chin_loc - gyy(i,j,k) * gxxy(i,j,k) )*HALF
-  Gamxyz = Gamxyz - (                     - gyz * gxxx )*HALF
+    Gamzyy(i,j,k) = Gamzyy(i,j,k) - (                                   - gyy(i,j,k) * gxxz(i,j,k) )*HALF
-  Gamyyz = Gamyyz - (  chiz        /chin1 - gyz * gxxy )*HALF
+    Gamxzz(i,j,k) = Gamxzz(i,j,k) - (                                   - gzz(i,j,k) * gxxx(i,j,k) )*HALF
-  Gamzyz = Gamzyz - (         chiy /chin1 - gyz * gxxz )*HALF
+    Gamyzz(i,j,k) = Gamyzz(i,j,k) - (                                   - gzz(i,j,k) * gxxy(i,j,k) )*HALF
-
+    Gamzzz(i,j,k) = Gamzzz(i,j,k) - ( (chiz(i,j,k) + chiz(i,j,k))/chin_loc - gzz(i,j,k) * gxxz(i,j,k) )*HALF
-  fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
+    Gamxxy(i,j,k) = Gamxxy(i,j,k) - ( chiy(i,j,k) /chin_loc - gxy(i,j,k) * gxxx(i,j,k) )*HALF
-  fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
+    Gamyxy(i,j,k) = Gamyxy(i,j,k) - ( chix(i,j,k) /chin_loc - gxy(i,j,k) * gxxy(i,j,k) )*HALF
-  fzz = fzz - Gamxzz*Lapx - Gamyzz*Lapy - Gamzzz*Lapz
+    Gamzxy(i,j,k) = Gamzxy(i,j,k) - (                     - gxy(i,j,k) * gxxz(i,j,k) )*HALF
-  fxy = fxy - Gamxxy*Lapx - Gamyxy*Lapy - Gamzxy*Lapz
+    Gamxxz(i,j,k) = Gamxxz(i,j,k) - ( chiz(i,j,k) /chin_loc - gxz(i,j,k) * gxxx(i,j,k) )*HALF
-  fxz = fxz - Gamxxz*Lapx - Gamyxz*Lapy - Gamzxz*Lapz
+    Gamyxz(i,j,k) = Gamyxz(i,j,k) - (                     - gxz(i,j,k) * gxxy(i,j,k) )*HALF
-  fyz = fyz - Gamxyz*Lapx - Gamyyz*Lapy - Gamzyz*Lapz
+    Gamzxz(i,j,k) = Gamzxz(i,j,k) - ( chix(i,j,k) /chin_loc - gxz(i,j,k) * gxxz(i,j,k) )*HALF
-
+    Gamxyz(i,j,k) = Gamxyz(i,j,k) - (                     - gyz(i,j,k) * gxxx(i,j,k) )*HALF
-! store D^i D_i Lap in trK_rhs upto chi
+    Gamyyz(i,j,k) = Gamyyz(i,j,k) - ( chiz(i,j,k) /chin_loc - gyz(i,j,k) * gxxy(i,j,k) )*HALF
-  trK_rhs =    gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+    Gamzyz(i,j,k) = Gamzyz(i,j,k) - ( chiy(i,j,k) /chin_loc - gyz(i,j,k) * gxxz(i,j,k) )*HALF
-        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz )
+
-#if 1        
+    fxx(i,j,k) = fxx(i,j,k) - Gamxxx(i,j,k)*Lapx(i,j,k) - Gamyxx(i,j,k)*Lapy(i,j,k) - Gamzxx(i,j,k)*Lapz(i,j,k)
-!! follow bam code
+    fyy(i,j,k) = fyy(i,j,k) - Gamxyy(i,j,k)*Lapx(i,j,k) - Gamyyy(i,j,k)*Lapy(i,j,k) - Gamzyy(i,j,k)*Lapz(i,j,k)
-  S =  chin1 * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
+    fzz(i,j,k) = fzz(i,j,k) - Gamxzz(i,j,k)*Lapx(i,j,k) - Gamyzz(i,j,k)*Lapy(i,j,k) - Gamzzz(i,j,k)*Lapz(i,j,k)
-     TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
+    fxy(i,j,k) = fxy(i,j,k) - Gamxxy(i,j,k)*Lapx(i,j,k) - Gamyxy(i,j,k)*Lapy(i,j,k) - Gamzxy(i,j,k)*Lapz(i,j,k)
-  f = F2o3 * trK * trK -(&
+    fxz(i,j,k) = fxz(i,j,k) - Gamxxz(i,j,k)*Lapx(i,j,k) - Gamyxz(i,j,k)*Lapy(i,j,k) - Gamzxz(i,j,k)*Lapz(i,j,k)
-       gupxx * ( &
+    fyz(i,j,k) = fyz(i,j,k) - Gamxyz(i,j,k)*Lapx(i,j,k) - Gamyyz(i,j,k)*Lapy(i,j,k) - Gamzyz(i,j,k)*Lapz(i,j,k)
-       gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
+
-       TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz) ) + &
+    trK_rhs(i,j,k) = gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
-       gupyy * ( &
+                     TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k))
-       gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
+  enddo
-       TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz) ) + &
+  enddo
-       gupzz * ( &
+  enddo
-       gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
+  do k=1,ex(3)
-       TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz) ) + &
+  do j=1,ex(2)
-       TWO * ( &
+  do i=1,ex(1)
-       gupxy * ( &
+    divb_loc = div_beta(i,j,k)
-       gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
+    chin_loc = chin1(i,j,k)
-       gupxy * (Axx * Ayy + Axy * Axy) + &
+
-       gupxz * (Axx * Ayz + Axz * Axy) + &
+    S_loc = chin_loc * ( gupxx(i,j,k) * Sxx(i,j,k) + gupyy(i,j,k) * Syy(i,j,k) + gupzz(i,j,k) * Szz(i,j,k) + &
-       gupyz * (Axy * Ayz + Axz * Ayy) ) + &
+           TWO * (gupxy(i,j,k) * Sxy(i,j,k) + gupxz(i,j,k) * Sxz(i,j,k) + gupyz(i,j,k) * Syz(i,j,k)) )
-       gupxz * ( &
+    S(i,j,k) = S_loc
-       gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
+
-       gupxy * (Axx * Ayz + Axy * Axz) + &
+    f_loc = F2o3 * trK(i,j,k) * trK(i,j,k) - ( &
-       gupxz * (Axx * Azz + Axz * Axz) + &
+            gupxx(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axx(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + &
-       gupyz * (Axy * Azz + Axz * Ayz) ) + &
+                             gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + &
-       gupyz * ( &
+                             TWO * (gupxy(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + &
-       gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
+                                    gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k)) ) + &
-       gupxy * (Axy * Ayz + Ayy * Axz) + &
+            gupyy(i,j,k) * ( gupxx(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayy(i,j,k) + &
-       gupxz * (Axy * Azz + Ayz * Axz) + &
+                             gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
-       gupyz * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
+                             TWO * (gupxy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
-  f = - F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+                                    gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k)) ) + &
-        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
+            gupzz(i,j,k) * ( gupxx(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
-  
+                             gupzz(i,j,k) * Azz(i,j,k) * Azz(i,j,k) + &
-  fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
+                             TWO * (gupxy(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + &
-  fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
+                                    gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k)) ) + &
-  fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
+            TWO * ( gupxy(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
-  fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
+                                     gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
-  fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
+                                     gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
-  fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
+                                     gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
-#else        
+                                     gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k)) ) + &
-! Add lapse and S_ij parts to Ricci tensor:
+                    gupxz(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
-
+                                     gupzz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + &
-  fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
+                                     gupxy(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axy(i,j,k) * Axz(i,j,k)) + &
-  fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
+                                     gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
-  fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
+                                     gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k)) ) + &
-  fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
+                    gupyz(i,j,k) * ( gupxx(i,j,k) * Axy(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k) + &
-  fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
+                                     gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + &
-  fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
+                                     gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
-
+                                     gupxz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Axz(i,j,k)) + &
-! Compute trace-free part (note: chi^-1 and chi cancel!):
+                                     gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k)) ) ) ) - &
-
+            F16 * PI * rho(i,j,k) + EIGHT * PI * S_loc
-  f = F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+
-        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) )
+    f_loc = -F1o3 * ( gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
-#endif
+            TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
-
+            alpn1(i,j,k)/chin_loc * f_loc )
-  Axx_rhs = fxx - gxx * f
+    f(i,j,k) = f_loc
-  Ayy_rhs = fyy - gyy * f
+
-  Azz_rhs = fzz - gzz * f
+    l_fxx = alpn1(i,j,k) * (Rxx(i,j,k) - EIGHT * PI * Sxx(i,j,k)) - fxx(i,j,k)
-  Axy_rhs = fxy - gxy * f
+    l_fxy = alpn1(i,j,k) * (Rxy(i,j,k) - EIGHT * PI * Sxy(i,j,k)) - fxy(i,j,k)
-  Axz_rhs = fxz - gxz * f
+    l_fxz = alpn1(i,j,k) * (Rxz(i,j,k) - EIGHT * PI * Sxz(i,j,k)) - fxz(i,j,k)
-  Ayz_rhs = fyz - gyz * f
+    l_fyy = alpn1(i,j,k) * (Ryy(i,j,k) - EIGHT * PI * Syy(i,j,k)) - fyy(i,j,k)
-
+    l_fyz = alpn1(i,j,k) * (Ryz(i,j,k) - EIGHT * PI * Syz(i,j,k)) - fyz(i,j,k)
-! Now: store A_il A^l_j into fij:
+    l_fzz = alpn1(i,j,k) * (Rzz(i,j,k) - EIGHT * PI * Szz(i,j,k)) - fzz(i,j,k)
-
+
-  fxx =       gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
+    Axx_rhs(i,j,k) = l_fxx - gxx(i,j,k) * f_loc
-       TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
+    Ayy_rhs(i,j,k) = l_fyy - gyy(i,j,k) * f_loc
-  fyy =       gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
+    Azz_rhs(i,j,k) = l_fzz - gzz(i,j,k) * f_loc
-       TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
+    Axy_rhs(i,j,k) = l_fxy - gxy(i,j,k) * f_loc
-  fzz =       gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
+    Axz_rhs(i,j,k) = l_fxz - gxz(i,j,k) * f_loc
-       TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
+    Ayz_rhs(i,j,k) = l_fyz - gyz(i,j,k) * f_loc
-  fxy =       gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
+
-              gupxy *(Axx * Ayy + Axy * Axy)                            + &
+    fxx(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axx(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + &
-              gupxz *(Axx * Ayz + Axz * Axy)                            + &
+                 gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + TWO * (gupxy(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + &
-              gupyz *(Axy * Ayz + Axz * Ayy)
+                 gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k))
-  fxz =       gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
+    fyy(i,j,k) = gupxx(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayy(i,j,k) + &
-              gupxy *(Axx * Ayz + Axy * Axz)                            + &
+                 gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + TWO * (gupxy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
-              gupxz *(Axx * Azz + Axz * Axz)                            + &
+                 gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k))
-              gupyz *(Axy * Azz + Axz * Ayz)
+    fzz(i,j,k) = gupxx(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
-  fyz =       gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
+                 gupzz(i,j,k) * Azz(i,j,k) * Azz(i,j,k) + TWO * (gupxy(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
-              gupxy *(Axy * Ayz + Ayy * Axz)                            + &
+                 gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k))
-              gupxz *(Axy * Azz + Ayz * Axz)                            + &
+    fxy(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
-              gupyz *(Ayy * Azz + Ayz * Ayz)
+                 gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
-
+                 gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
-  f = chin1
+                 gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k))
-! store D^i D_i Lap in trK_rhs
+    fxz(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
-  trK_rhs = f*trK_rhs
+                 gupzz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupxy(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axy(i,j,k) * Axz(i,j,k)) + &
-          
+                 gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
-  Axx_rhs =           f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx)  + &
+                 gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k))
-           TWO * (  Axx * betaxx +   Axy * betayx +   Axz * betazx )- &
+    fyz(i,j,k) = gupxx(i,j,k) * Axy(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k) + &
-             F2o3 * Axx * div_beta
+                 gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
-
+                 gupxz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Axz(i,j,k)) + &
-  Ayy_rhs =           f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy)  + &
+                 gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k))
-           TWO * (  Axy * betaxy +   Ayy * betayy +   Ayz * betazy )- &
+
-             F2o3 * Ayy * div_beta
+    trK_rhs(i,j,k) = chin_loc * trK_rhs(i,j,k)
-
+
-  Azz_rhs =           f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz)  + &
+    Axx_rhs(i,j,k) = chin_loc * Axx_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axx(i,j,k) - TWO * fxx(i,j,k)) + &
-           TWO * (  Axz * betaxz +   Ayz * betayz +   Azz * betazz )- &
+                     TWO * (Axx(i,j,k) * betaxx(i,j,k) + Axy(i,j,k) * betayx(i,j,k) + Axz(i,j,k) * betazx(i,j,k)) - &
-             F2o3 * Azz * div_beta
+                     F2o3 * Axx(i,j,k) * divb_loc
-
+    Ayy_rhs(i,j,k) = chin_loc * Ayy_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Ayy(i,j,k) - TWO * fyy(i,j,k)) + &
-  Axy_rhs =           f * Axy_rhs+ alpn1 *( trK * Axy  - TWO * fxy )+ &
+                     TWO * (Axy(i,j,k) * betaxy(i,j,k) + Ayy(i,j,k) * betayy(i,j,k) + Ayz(i,j,k) * betazy(i,j,k)) - &
-                    Axx * betaxy                  +   Axz * betazy  + &
+                     F2o3 * Ayy(i,j,k) * divb_loc
-                                     Ayy * betayx +   Ayz * betazx  + &
+    Azz_rhs(i,j,k) = chin_loc * Azz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Azz(i,j,k) - TWO * fzz(i,j,k)) + &
-             F1o3 * Axy * div_beta                -   Axy * betazz
+                     TWO * (Axz(i,j,k) * betaxz(i,j,k) + Ayz(i,j,k) * betayz(i,j,k) + Azz(i,j,k) * betazz(i,j,k)) - &
-
+                     F2o3 * Azz(i,j,k) * divb_loc
-  Ayz_rhs =           f * Ayz_rhs+ alpn1 *( trK * Ayz  - TWO * fyz )+ &
+    Axy_rhs(i,j,k) = chin_loc * Axy_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axy(i,j,k) - TWO * fxy(i,j,k)) + &
-                    Axy * betaxz +   Ayy * betayz                   + &
+                     Axx(i,j,k) * betaxy(i,j,k) + Axz(i,j,k) * betazy(i,j,k) + Ayy(i,j,k) * betayx(i,j,k) + &
-                    Axz * betaxy                  +   Azz * betazy  + &
+                     Ayz(i,j,k) * betazx(i,j,k) + F1o3 * Axy(i,j,k) * divb_loc - Axy(i,j,k) * betazz(i,j,k)
-             F1o3 * Ayz * div_beta                -   Ayz * betaxx
+    Ayz_rhs(i,j,k) = chin_loc * Ayz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Ayz(i,j,k) - TWO * fyz(i,j,k)) + &
- 
+                     Axy(i,j,k) * betaxz(i,j,k) + Ayy(i,j,k) * betayz(i,j,k) + Axz(i,j,k) * betaxy(i,j,k) + &
-  Axz_rhs =           f * Axz_rhs+ alpn1 *( trK * Axz  - TWO * fxz )+ &
+                     Azz(i,j,k) * betazy(i,j,k) + F1o3 * Ayz(i,j,k) * divb_loc - Ayz(i,j,k) * betaxx(i,j,k)
-                    Axx * betaxz +   Axy * betayz                   + &
+    Axz_rhs(i,j,k) = chin_loc * Axz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axz(i,j,k) - TWO * fxz(i,j,k)) + &
-                                     Ayz * betayx +   Azz * betazx  + &
+                     Axx(i,j,k) * betaxz(i,j,k) + Axy(i,j,k) * betayz(i,j,k) + Ayz(i,j,k) * betayx(i,j,k) + &
-             F1o3 * Axz * div_beta                -   Axz * betayy      !rhs for Aij
+                     Azz(i,j,k) * betazx(i,j,k) + F1o3 * Axz(i,j,k) * divb_loc - Axz(i,j,k) * betayy(i,j,k)
-
+
-! Compute trace of S_ij
+    trK_rhs(i,j,k) = - trK_rhs(i,j,k) + alpn1(i,j,k) * ( F1o3 * trK(i,j,k) * trK(i,j,k) + &
-
+                    gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
-  S =  f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
+                    TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
-     TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
+                    FOUR * PI * (rho(i,j,k) + S_loc) )
-
+  enddo
-  trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK         + &
+  enddo
-                gupxx * fxx + gupyy * fyy + gupzz * fzz   + &
+  enddo
-        TWO * ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + &
-       FOUR * PI * ( rho + S ))                                !rhs for trK
   
 !!!! gauge variable part
 
@@ -948,15 +1000,15 @@
 !!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
 ! lopsided_kodis shares the symmetry_bd buffer between advection and
 ! dissipation, eliminating redundant full-grid copies. For metric variables
-! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
+! gxx/gyy/gzz (=dxx/dyy/dzz+1): stencil coefficients sum to zero,
-! so the constant offset has no effect on dissipation.
+! so the constant offset has no effect on dissipation.
-
+
-  call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
+  call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
-  call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
+  call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
-  call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
+  call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
 
   call lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
   call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)

AMSS_NCKU_source/cgh.C

@@ -130,7 +130,11 @@ 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)
@@ -1301,13 +1305,13 @@ bool cgh::Interp_One_Point(MyList<var> *VarList,
 }
 
 
-void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
+bool cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, double **Porg0,
                           MyList<var> *OldList, MyList<var> *StateList,
                           MyList<var> *FutureList, MyList<var> *tmList, bool BB,
                           monitor *ErrorMonitor)
 {
   if (lev < movls)
-    return;
+    return false;
 
 #if (0)
   // #if (PSTR == 1 || PSTR == 2)
@@ -1396,7 +1400,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
       for (bhi = 0; bhi < BH_num; bhi++)
         delete[] tmpPorg[bhi];
       delete[] tmpPorg;
-      return;
+      return false;
     }
     // x direction
     rr = (Porg0[bhi][0] - handle[lev][grd][0]) / dX;
@@ -1500,6 +1504,7 @@ void cgh::Regrid_Onelevel(int lev, int Symmetry, int BH_num, double **Porgbr, do
   for (int bhi = 0; bhi < BH_num; bhi++)
     delete[] tmpPorg[bhi];
   delete[] tmpPorg;
+  return tot_flag;
 }
 
 

AMSS_NCKU_source/cgh.h

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

AMSS_NCKU_source/diff_newwb.f90

@@ -33,7 +33,7 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx,d2dy,d2dz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -137,7 +137,7 @@
   real*8 :: dX
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1512,8 +1512,9 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
+  integer :: i_core_min,i_core_max,j_core_min,j_core_max,k_core_min,k_core_max
+  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
   real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0,  F45=4.5d1
@@ -1560,17 +1561,55 @@
 
   fxx = ZEO
   fyy = ZEO
-  fzz = ZEO
+  fzz = ZEO
-  fxy = ZEO
+  fxy = ZEO
-  fxz = ZEO
+  fxz = ZEO
-  fyz = ZEO
+  fyz = ZEO
-
+
-  do k=1,ex(3)
+  i_core_min = max(1, imin+2)
-  do j=1,ex(2)
+  i_core_max = min(ex(1), imax-2)
-  do i=1,ex(1)
+  j_core_min = max(1, jmin+2)
-!~~~~~~ fxx
+  j_core_max = min(ex(2), jmax-2)
-        if(i+2 <= imax .and. i-2 >= imin)then
+  k_core_min = max(1, kmin+2)
-!
+  k_core_max = min(ex(3), kmax-2)
+
+  if(i_core_min <= i_core_max .and. j_core_min <= j_core_max .and. k_core_min <= k_core_max)then
+   do k=k_core_min,k_core_max
+   do j=j_core_min,j_core_max
+   do i=i_core_min,i_core_max
+! interior points always use 4th-order stencils without branch checks
+      fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
+                          -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
+      fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
+                          -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
+      fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
+                          -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
+      fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
+                          -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
+                          +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
+                          -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
+      fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
+                          -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
+                          +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
+                          -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
+      fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
+                          -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
+                          +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
+                          -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
+   enddo
+   enddo
+   enddo
+  endif
+
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+      if(i>=i_core_min .and. i<=i_core_max .and. &
+         j>=j_core_min .and. j<=j_core_max .and. &
+         k>=k_core_min .and. k<=k_core_max) cycle
+!~~~~~~ fxx
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 

AMSS_NCKU_source/fdderivs_c.C

@@ -0,0 +1,186 @@
+#include "tool.h"
+void fdderivs(const int ex[3],
+              const double *f,
+              double *fxx, double *fxy, double *fxz,
+              double *fyy, double *fyz, double *fzz,
+              const double *X, const double *Y, const double *Z,
+              double SYM1, double SYM2, double SYM3,
+              int Symmetry, int onoff)
+{
+    (void)onoff;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+    const double ZEO = 0.0, ONE = 1.0, TWO = 2.0;
+    const double F1o4   = 2.5e-1;          // 1/4
+    const double F8     = 8.0;
+    const double F16    = 16.0;
+    const double F30    = 30.0;
+    const double F1o12  = ONE / 12.0;
+    const double F1o144 = ONE / 144.0;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    /* fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2 */
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+
+    static double *fh = NULL;
+    static size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    symmetry_bd(2, ex, f, fh, SoA);
+
+    /* 系数：按 Fortran 原式 */
+    const double Sdxdx = ONE / (dX * dX);
+    const double Sdydy = ONE / (dY * dY);
+    const double Sdzdz = ONE / (dZ * dZ);
+
+    const double Fdxdx = F1o12 / (dX * dX);
+    const double Fdydy = F1o12 / (dY * dY);
+    const double Fdzdz = F1o12 / (dZ * dZ);
+
+    const double Sdxdy = F1o4 / (dX * dY);
+    const double Sdxdz = F1o4 / (dX * dZ);
+    const double Sdydz = F1o4 / (dY * dZ);
+
+    const double Fdxdy = F1o144 / (dX * dY);
+    const double Fdxdz = F1o144 / (dX * dZ);
+    const double Fdydz = F1o144 / (dY * dZ);
+
+    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+    for (size_t p = 0; p < all; ++p) {
+        fxx[p] = ZEO; fxy[p] = ZEO; fxz[p] = ZEO;
+        fyy[p] = ZEO; fyz[p] = ZEO; fzz[p] = ZEO;
+    }
+
+    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
+    // only compute when x/y/z all satisfy the same-order stencil at this point.
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                const int iF = i0 + 1;
+                const size_t p = idx_ex(i0, j0, k0, ex);
+
+                if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
+                    (jF + 2 <= jmaxF && jF - 2 >= jminF) &&
+                    (kF + 2 <= kmaxF && kF - 2 >= kminF)) {
+                    fxx[p] = Fdxdx * (
+                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+                    fyy[p] = Fdydy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+                    fzz[p] = Fdzdz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                    fxy[p] = Fdxdy * (
+                           (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)])
+                        - F8 * (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)])
+                        + F8 * (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)])
+                           - (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)])
+                    );
+                    fxz[p] = Fdxdz * (
+                           (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)])
+                        - F8 * (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)])
+                        + F8 * (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)])
+                           - (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)])
+                    );
+                    fyz[p] = Fdydz * (
+                           (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)])
+                        - F8 * (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)])
+                        + F8 * (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)])
+                           - (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)])
+                    );
+                } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
+                           (jF + 1 <= jmaxF && jF - 1 >= jminF) &&
+                           (kF + 1 <= kmaxF && kF - 1 >= kminF)) {
+                    fxx[p] = Sdxdx * (
+                        fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                        fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+                    fyy[p] = Sdydy * (
+                        fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                        fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+                    fzz[p] = Sdzdz * (
+                        fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                    fxy[p] = Sdxdy * (
+                        fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
+                        fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
+                        fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
+                        fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
+                    );
+                    fxz[p] = Sdxdz * (
+                        fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
+                        fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
+                    );
+                    fyz[p] = Sdydz * (
+                        fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
+                        fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
+                        fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/fderivs_c.C

@@ -0,0 +1,135 @@
+#include "tool.h"
+
+/*
+ * C 版 fderivs
+ *
+ * Fortran:
+ * subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
+ *
+ * 约定：
+ *   f, fx, fy, fz: ex1*ex2*ex3，按 idx_ex 布局
+ *   X: ex1, Y: ex2, Z: ex3
+ */
+void fderivs(const int ex[3],
+             const double *f,
+             double *fx, double *fy, double *fz,
+             const double *X, const double *Y, const double *Z,
+             double SYM1, double SYM2, double SYM3,
+             int Symmetry, int onoff)
+{
+    (void)onoff; // Fortran 里没用到
+
+    const double ZEO = 0.0, ONE = 1.0;
+    const double TWO = 2.0, EIT = 8.0;
+    const double F12 = 12.0;
+
+    const int NO_SYMM = 0, EQ_SYMM = 1; // OCTANT=2 在本子程序里不直接用
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    // Fortran 1-based bounds
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1;
+
+    // SoA(1:3) = SYM1,SYM2,SYM3
+    const double SoA[3] = { SYM1, SYM2, SYM3 };
+
+    // fh: (ex1+2)*(ex2+2)*(ex3+2) because ord=2
+    const size_t nx = (size_t)ex1 + 2;
+    const size_t ny = (size_t)ex2 + 2;
+    const size_t nz = (size_t)ex3 + 2;
+    const size_t fh_size = nx * ny * nz;
+    static double *fh = NULL;
+    static size_t cap = 0;
+
+    if (fh_size > cap) {
+        free(fh);
+        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
+        cap = fh_size;
+    }
+    // double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // call symmetry_bd(2,ex,f,fh,SoA)
+    symmetry_bd(2, ex, f, fh, SoA);
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    const double d2dx  = ONE / TWO / dX;
+    const double d2dy  = ONE / TWO / dY;
+    const double d2dz  = ONE / TWO / dZ;
+
+    // fx = fy = fz = 0
+    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+    for (size_t p = 0; p < all; ++p) {
+        fx[p] = ZEO;
+        fy[p] = ZEO;
+        fz[p] = ZEO;
+    }
+
+    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
+    // only compute when x/y/z all satisfy the same-order stencil at this point.
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                const int iF = i0 + 1;
+                const size_t p = idx_ex(i0, j0, k0, ex);
+
+                if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
+                    (jF + 2 <= jmaxF && jF - 2 >= jminF) &&
+                    (kF + 2 <= kmaxF && kF - 2 >= kminF)) {
+                    fx[p] = d12dx * (
+                        fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)]
+                    );
+                    fy[p] = d12dy * (
+                        fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)]
+                    );
+                    fz[p] = d12dz * (
+                        fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
+                    );
+                } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
+                           (jF + 1 <= jmaxF && jF - 1 >= jminF) &&
+                           (kF + 1 <= kmaxF && kF - 1 >= kminF)) {
+                    fx[p] = d2dx * (
+                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+                    fy[p] = d2dy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+                    fz[p] = d2dz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                }
+            }
+        }
+    }
+
+    // free(fh);
+}

AMSS_NCKU_source/fmisc.f90

@@ -1111,27 +1111,177 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
+! common code for cell and vertex
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
+! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-
+#ifndef POLINT6_USE_BARYCENTRIC
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
+#define POLINT6_USE_BARYCENTRIC 1
-  subroutine polint(xa, ya, x, y, dy, ordn)
+#endif
-  implicit none
+
-
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
-  integer, intent(in) :: ordn
+  subroutine polint6_neville(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, m, ns, n_m
+  real*8, dimension(6) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, 6
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, 5
+    n_m = 6 - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint6_neville
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
+  subroutine polint6_barycentric(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, j
+  logical :: is_uniform
+  real*8, dimension(6) :: lambda
+  real*8 :: dx, den_i, term, num, den, step, tol
+  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
+
+  do i = 1, 6
+    if (x == xa(i)) then
+      y = ya(i)
+      dy = 0.d0
+      return
+    end if
+  end do
+
+  step = xa(2) - xa(1)
+  is_uniform = (step /= 0.d0)
+  if (is_uniform) then
+    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
+    do i = 3, 6
+      if (abs((xa(i) - xa(i-1)) - step) > tol) then
+        is_uniform = .false.
+        exit
+      end if
+    end do
+  end if
+
+  if (is_uniform) then
+    num = 0.d0
+    den = 0.d0
+    do i = 1, 6
+      term = c_uniform(i) / (x - xa(i))
+      num = num + term * ya(i)
+      den = den + term
+    end do
+    y = num / den
+    dy = 0.d0
+    return
+  end if
+
+  do i = 1, 6
+    den_i = 1.d0
+    do j = 1, 6
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        den_i = den_i * dx
+      end if
+    end do
+    lambda(i) = 1.d0 / den_i
+  end do
+
+  num = 0.d0
+  den = 0.d0
+  do i = 1, 6
+    term = lambda(i) / (x - xa(i))
+    num = num + term * ya(i)
+    den = den + term
+  end do
+
+  y = num / den
+  dy = 0.d0
+
+  return
+  end subroutine polint6_barycentric
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
   real*8, dimension(ordn), intent(in) :: xa, ya
   real*8, intent(in) :: x
   real*8, intent(out) :: y, dy
 
-  integer :: i, m, ns, n_m
+  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
+  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
+  real*8 :: dif, dift, hp, h, den_val
-
+
-  c = ya
+  if (ordn == 6) then
-  d = ya
+#if POLINT6_USE_BARYCENTRIC
-  ho = xa - x
+    call polint6_barycentric(xa, ya, x, y, dy)
+#else
+    call polint6_neville(xa, ya, x, y, dy)
+#endif
+    return
+  end if
+
+  c = ya
+  d = ya
+  ho = xa - x
 
   ns = 1
   dif = abs(x - xa(1))
@@ -1175,13 +1325,48 @@ end subroutine d2dump
     y = y + dy
   end do
 
-  return
+  return
-  end subroutine polint
+  end subroutine polint
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-!
+! Compute Lagrange interpolation basis weights for one target point.
-! interpolation in 2 dimensions, follow yx order
+!------------------------------------------------------------------------------
-!
+!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
-!------------------------------------------------------------------------------
+  subroutine polint_lagrange_weights(xa, x, w, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(1:ordn), intent(in) :: xa
+  real*8, intent(in) :: x
+  real*8, dimension(1:ordn), intent(out) :: w
+
+  integer :: i, j
+  real*8 :: num, den, dx
+
+  do i = 1, ordn
+    num = 1.d0
+    den = 1.d0
+    do j = 1, ordn
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        num = num * (x - xa(j))
+        den = den * dx
+      end if
+    end do
+    w(i) = num / den
+  end do
+
+  return
+  end subroutine polint_lagrange_weights
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
   implicit none
 
@@ -1229,11 +1414,11 @@ end subroutine d2dump
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+#ifdef POLINT_LEGACY_ORDER
-  integer  :: i,j,m,n
+  integer  :: i,j,m,n
-  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
+  real*8, dimension(ordn) :: yntmp
   real*8, dimension(ordn) :: yqtmp
 
   m=size(x1a)
@@ -1243,29 +1428,36 @@ end subroutine d2dump
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
    end do
-    yntmp=yatmp(i,:)
+    yntmp=yatmp(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
+  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
+#else
-  integer  :: j, k
+  integer  :: i, j, k
-  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: w1, w2
-  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
+  real*8 :: yx_sum, x_sum
-
+
-  do k=1,ordn
+  call polint_lagrange_weights(x1a, x1, w1, ordn)
-    do j=1,ordn
+  call polint_lagrange_weights(x2a, x2, w2, ordn)
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+
-    end do
+  do k = 1, ordn
-  end do
+    yx_sum = 0.d0
-  do k=1,ordn
+    do j = 1, ordn
-    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+      x_sum = 0.d0
-  end do
+      do i = 1, ordn
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
+        x_sum = x_sum + w1(i) * ya(i,j,k)
-#endif
+      end do
-
+      yx_sum = yx_sum + w2(j) * x_sum
-  return
+    end do
-  end subroutine polin3
+    ymtmp(k) = yx_sum
+  end do
+
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
   subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1608,11 +1800,14 @@ 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
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-
+  integer :: i,j,k
-  fout = C1*f1+C2*f2+C3*f3
+
-
+  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
-  return
+    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
+  end do
+
+  return
 
   end subroutine average2
 !-----------------------------------------------------------------------------  

AMSS_NCKU_source/interp_lb_profile.C

@@ -0,0 +1,107 @@
+#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

@@ -0,0 +1,38 @@
+#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

@@ -0,0 +1,29 @@
+/* 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

@@ -0,0 +1,117 @@
+#include "tool.h"
+
+/*
+ * C 版 kodis
+ *
+ * Fortran signature:
+ * subroutine kodis(ex,X,Y,Z,f,f_rhs,SoA,Symmetry,eps)
+ *
+ * 约定：
+ *   X: ex1, Y: ex2, Z: ex3
+ *   f, f_rhs: ex1*ex2*ex3 按 idx_ex 布局
+ *   SoA[3]
+ *   eps: double
+ */
+void kodis(const int ex[3],
+           const double *X, const double *Y, const double *Z,
+           const double *f, double *f_rhs,
+           const double SoA[3],
+           int Symmetry, double eps)
+{
+    const double ONE = 1.0, SIX = 6.0, FIT = 15.0, TWT = 20.0;
+    const double cof = 64.0;             // 2^6
+    const int NO_SYMM = 0, OCTANT = 2;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    // Fortran: dX = X(2)-X(1) -> C: X[1]-X[0]
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+    (void)ONE; // ONE 在原 Fortran 里只是参数，这里不一定用得上
+
+    // Fortran: imax=ex(1) 等是 1-based 上界
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    // Fortran: imin=jmin=kmin=1，某些对称情况变 -2
+    int iminF = 1, jminF = 1, kminF = 1;
+
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+    if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = -2;
+    if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = -2;
+
+    // 分配 fh：大小 (ex1+3)*(ex2+3)*(ex3+3)，对应 ord=3
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    // Fortran: call symmetry_bd(3,ex,f,fh,SoA)
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    /*
+     * Fortran loops:
+     * do k=1,ex3
+     * do j=1,ex2
+     * do i=1,ex1
+     *
+     * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
+     * 并定义 Fortran index: iF=i0+1, ...
+     */
+    // 收紧循环范围：只遍历满足 iF±3/jF±3/kF±3 条件的内部点
+    // 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) {
+            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);
+
+                    // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
+                    const double Dx_term =
+                        ( (fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
+                          SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
+                          FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
+                          TWT *  fh[idx_fh_F(iF    , jF, kF, ex)] ) / dX;
+
+                    const double Dy_term =
+                        ( (fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
+                          SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
+                          FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
+                          TWT *  fh[idx_fh_F(iF, jF    , kF, ex)] ) / dY;
+
+                    const double Dz_term =
+                        ( (fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
+                          SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
+                          FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
+                          TWT *  fh[idx_fh_F(iF, jF, kF    , ex)] ) / dZ;
+
+                    // Fortran:
+                    // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
+                    f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+            }
+        }
+    }
+
+    free(fh);
+}

AMSS_NCKU_source/lopsided_c.C

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

AMSS_NCKU_source/lopsided_kodis_c.C

@@ -0,0 +1,248 @@
+#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/macrodef.fh

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

AMSS_NCKU_source/macrodef.h

@@ -1,112 +1,145 @@
-
+
-#ifndef MICRODEF_H
+#ifndef MICRODEF_H
-#define MICRODEF_H
+#define MICRODEF_H
-
+
-#include "macrodef.fh"
+#include "macrodef.fh"  
-
+
-// application parameters
+// application parameters
-
+
-/// ****
+#define SommerType 0
-// sommerfeld boundary type
+
-// 0: bam, 1: shibata
+#define GaussInt
-#define SommerType 0
+
-
+#define ABEtype 0
-/// ****
+
-// for Using Gauss-Legendre quadrature in theta direction
+//#define With_AHF
-#define GaussInt
+#define Psi4type 0
-
+
-/// ****
+//#define Point_Psi4
-// 0: BSSN vacuum
+
-// 1: coupled to scalar field
+#define RPS 1
-// 2: Z4c vacuum
+
-// 3: coupled to Maxwell field
+#define AGM 0
-//
+
-#define ABEtype 2
+#define RPB 0
-
+
-/// ****
+#define MAPBH 1
-// using Apparent Horizon Finder
+
-//#define With_AHF
+#define PSTR 0
-
+
-/// ****
+#define REGLEV 0
-// Psi4 calculation method
+
-// 0: EB method
+//#define USE_GPU
-// 1: 4-D method
+
-//
+//#define CHECKDETAIL
-#define Psi4type 0
+
-
+//#define FAKECHECK
-/// ****
+
-// for Using point psi4 or not
+//
-//#define Point_Psi4
+// define SommerType
-
+//     sommerfeld boundary type
-/// ****
+//     0: bam
-// RestrictProlong in Step (0) or after Step (1)
+//     1: shibata
-#define RPS 1
+//
-
+// define GaussInt
-/// ****
+//     for Using Gauss-Legendre quadrature in theta direction
-// Enforce algebra constraint
+//
-// for every RK4 sub step: 0
+// define ABEtype
-// only when iter_count == 3: 1
+//     0: BSSN vacuum
-// after routine Step: 2
+//     1: coupled to scalar field
-#define AGM 0
+//     2: Z4c vacuum
-
+//     3: coupled to Maxwell field
-/// ****
+//
-// Restrict Prolong using BAM style 1 or old style 0
+// define With_AHF
-#define RPB 0
+//     using Apparent Horizon Finder
-
+//
-/// ****
+// define Psi4type
-// 1: move Analysis out ot 4 sub steps and treat PBH with Euler method
+//     Psi4 calculation method
-#define MAPBH 1
+//     0: EB method
-
+//     1: 4-D method
-/// ****
+//
-// parallel structure, 0: level by level, 1: considering all levels, 2: as 1 but reverse the CPU order, 3: Frank's scheme
+// define Point_Psi4
-#define PSTR 0
+//     for Using point psi4 or not
-
+//
-/// ****
+// define RPS
-// regrid for every level or for all levels at a time
+//     RestrictProlong in Step (0) or after Step (1)
-// 0: for every level; 1: for all
+//
-#define REGLEV 0
+// define AGM
-
+//     Enforce algebra constraint
-/// ****
+//     for every RK4 sub step: 0
-// use gpu or not
+//     only when iter_count == 3: 1
-//#define USE_GPU
+//     after routine Step: 2
-
+//
-/// ****
+// define RPB
-// use checkpoint for every process
+//     Restrict Prolong using BAM style 1 or old style 0
-//#define CHECKDETAIL
+//
-
+// define MAPBH
-/// ****
+//     1: move Analysis out ot 4 sub steps and treat PBH with Euler method
-// use FakeCheckPrepare to write CheckPoint
+//
-//#define FAKECHECK
+// define PSTR
-////================================================================
+//     parallel structure
-//  some basic parameters for numerical calculation
+//     0: level by level
-#define dim 3
+//     1: considering all levels
-
+//     2: as 1 but reverse the CPU order
-//#define Cell or Vertex in "microdef.fh"
+//     3: Frank's scheme
-
+//
-// ******
+// define REGLEV
-// buffer point number for mesh refinement interface
+//     regrid for every level or for all levels at a time
-#define buffer_width 6
+//     0: for every level;
-
+//     1: for all
-// ******
+//
-// buffer point number shell-box interface, on shell
+// define USE_GPU
-#define SC_width buffer_width
+//     use gpu or not
-// buffer point number shell-box interface, on box
+//
-#define CS_width (2*buffer_width)
+// define CHECKDETAIL
-
+//     use checkpoint for every process
-#if(buffer_width < ghost_width)
+//
-#error we always assume buffer_width>ghost_width
+// define FAKECHECK
-#endif
+//     use FakeCheckPrepare to write CheckPoint
-
+//
-#define PACK 1
+
-#define UNPACK 2
+////================================================================
-
+//  some basic parameters for numerical calculation
-#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
+////================================================================
-#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
+
-
+#define dim 3
-#define feq(a,b,d) (fabs(a-b)<d)
+
-#define flt(a,b,d) ((a-b)<d)
+//#define Cell or Vertex in "macrodef.fh" 
-#define fgt(a,b,d) ((a-b)>d)
+
-
+#define buffer_width 6
-#define TINY 1e-10
+
-
+#define SC_width buffer_width
-#endif   /* MICRODEF_H */
+
+#define CS_width (2*buffer_width)
+
+//
+// define Cell or Vertex in "macrodef.fh" 
+//
+// define buffer_width
+//     buffer point number for mesh refinement interface
+//
+// define SC_width buffer_width
+//     buffer point number shell-box interface, on shell
+//
+// define CS_width
+//     buffer point number shell-box interface, on box
+//
+
+#if(buffer_width < ghost_width)
+#   error we always assume buffer_width>ghost_width
+#endif
+
+#define PACK 1
+#define UNPACK 2
+
+#define Mymax(a,b) (((a) > (b)) ? (a) : (b))
+#define Mymin(a,b) (((a) < (b)) ? (a) : (b))
+
+#define feq(a,b,d) (fabs(a-b)<d)
+#define flt(a,b,d) ((a-b)<d)
+#define fgt(a,b,d) ((a-b)>d)
+
+#define TINY 1e-10
+
+#endif   /* MICRODEF_H */
+

AMSS_NCKU_source/makefile

@@ -1,6 +1,35 @@
 
 
-include makefile.inc
+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=$(POLINT6_USE_BARY)
+
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+##   make                        -> opt  (PGO-guided, maximum performance)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+
+ifeq ($(PGO_MODE),instrument)
+## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+else
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
+## 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 $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+endif
 
 .SUFFIXES: .o .f90 .C .for .cu
 
@@ -16,19 +45,65 @@ include makefile.inc
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
+# C rewrite of BSSN RHS kernel and helpers
+bssn_rhs_c.o: bssn_rhs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fderivs_c.o: fderivs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+fdderivs_c.o: fdderivs_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+kodiss_c.o: kodiss_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+lopsided_c.o: lopsided_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+lopsided_kodis_c.o: lopsided_kodis_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
+TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
+TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(TP_PROFDATA) \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
+
 TwoPunctures.o: TwoPunctures.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(CXXAPPFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 # Input files
+
+## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
+ifeq ($(USE_CXX_KERNELS),0)
+# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
+CFILES =
+else
+# C++ mode (default): C rewrite of bssn_rhs and helper kernels
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+endif
+
+## RK4 kernel switch (independent from USE_CXX_KERNELS)
+ifeq ($(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
+	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.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\
@@ -38,12 +113,12 @@ 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 = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   rungekutta4_rout.o bssn_rhs.o diff_new.o kodiss.o kodiss_sh.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
            fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
 	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
 	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
@@ -51,6 +126,14 @@ F90FILES = 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 \
@@ -63,7 +146,7 @@ TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o
 CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
 
 # file dependences
-$(C++FILES) $(C++FILESGPU) $(F90FILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
+$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
 
 $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
@@ -86,7 +169,7 @@ $(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h
              
 $(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
 
-$(C++FILES) $(C++FILES_GPU) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
 
 TwoPunctureFILES: TwoPunctures.h
 
@@ -95,14 +178,14 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o
 
 # projects
-ABE: $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) 
+ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
 	
-ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
+ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(CXXAPPFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -8,23 +8,56 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 
 ## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl
+LDLIBS  = -L${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 ?= 0
+
+## 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 ?= 0
 
-## Aggressive optimization flags + PGO Phase 2 (profile-guided optimization)
-## -fprofile-instr-use: use collected profile data to guide optimization decisions
-##   (branch prediction, basic block layout, inlining, loop unrolling)
-PROFDATA     = ../../pgo_profile/default.profdata
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -fprofile-instr-use=$(PROFDATA) \
-               -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -fprofile-instr-use=$(PROFDATA) \
-               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
-CLINKER      = mpiicpx 
+CLINKER      = mpiicpx
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1934,18 +1934,35 @@
 ! 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
+  integer :: i,j,k,ii,jj,kk,px,py,pz
   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(-2:extc(1))   ! 包含 X 向 6 点模板访问所需下界
+  real*8 :: v1, v2, v3, v4, v5, v6
+  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max,ic_min,ic_max,kc_min,kc_max
+  integer :: i_lo, i_hi, j_lo, j_hi, k_lo, k_hi
+  logical :: need_full_symmetry
+  real*8 :: res_line
+  real*8 :: tmp_z_slab(-2:extc(1), -2:extc(2))  ! 包含 Y/X 向模板访问所需下界
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2020,145 +2037,140 @@
           return
   endif
 
-  call symmetry_bd(3,extc,func,funcc,SoA)
+  do i = imino,imaxo
-     
+     ii = i + lbf(1) - 1
-!~~~~~~> prolongation start...
+     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
-   do j = jmino,jmaxo
+     kk = k + lbf(3) - 1
-    do i = imino,imaxo
+     ciz(k) = kk/2 - lbc(3) + 1
-       cxI(1) = i
+     if(kk/2*2 == kk)then
-       cxI(2) = j
+        piz(k) = 1
-       cxI(3) = k
+     else
-! change to coarse level reference
+        piz(k) = 2
-!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---| 
+     endif
-!|=======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
-       if(ii/2*2==ii)then
-         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)= 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
-
-       if(jj/2*2==jj)then
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-       else
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-       endif
-
-       if(ii/2*2==ii)then
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-       else
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-       endif
-#endif
-    enddo
-   enddo
   enddo
 
+  ic_min = minval(cix(imino:imaxo))
+  ic_max = maxval(cix(imino:imaxo))
+  jc_min = minval(ciy(jmino:jmaxo))
+  jc_max = maxval(ciy(jmino:jmaxo))
+  kc_min = minval(ciz(kmino:kmaxo))
+  kc_max = maxval(ciz(kmino:kmaxo))
+
+  maxcx = ic_max
+  maxcy = jc_max
+  maxcz = kc_max
+  if(maxcx+3 > extc(1) .or. maxcy+3 > extc(2) .or. maxcz+3 > extc(3))then
+     write(*,*)"error in prolong"
+     return
+  endif
+
+  i_lo = ic_min - 2
+  i_hi = ic_max + 3
+  j_lo = jc_min - 2
+  j_hi = jc_max + 3
+  k_lo = kc_min - 2
+  k_hi = kc_max + 3
+  need_full_symmetry = (i_lo < 1) .or. (j_lo < 1) .or. (k_lo < 1)
+  if(need_full_symmetry)then
+     call symmetry_bd(3,extc,func,funcc,SoA)
+  else
+     funcc(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi) = func(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi)
+  endif
+
+     ! 对每个 k（pz, kc 固定）预计算 Z 向插值的 2D 切片
+
+do k = kmino, kmaxo
+    pz = piz(k); kc = ciz(k)
+    ! --- Pass 1: Z 方向，只算一次 ---
+    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
+        do ii = ic_min-2, ic_max+3  ! 仅需的 ii 范围（对应 cix-2:cix+3）
+            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 = ic_min-2, ic_max+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...
+#if 0
+ do k = kmino, kmaxo
+     pz = piz(k)
+     kc = ciz(k)
+
+     do j = jmino, jmaxo
+        py = piy(j)
+        jc = ciy(j)
+
+! --- 步骤 1 & 2 融合：分段处理 X 轴，提升 Cache 命中率 ---
+        ! 我们将 ii 循环逻辑重组，减少对 funcc 的跨行重复访问
+        do ii = 1, extc(1)
+           ! 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）
+           ! 我们直接在这里把 Y 方向的加权也做了，省去 tmp_yz 数组
+           ! 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
   return
 
   end subroutine prolong3
@@ -2357,7 +2369,14 @@
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
 
   real*8,dimension(3) :: CD,FD
-  
+
+  real*8 :: tmp_xz_plane(-1:extf(1), 6)
+  real*8 :: tmp_x_line(-1:extf(1))
+  integer :: fi, fj, fk, ii, jj, kk
+  integer :: fi_min, fi_max, ii_lo, ii_hi
+  integer :: fj_min, fj_max, fk_min, fk_max, jj_lo, jj_hi, kk_lo, kk_hi
+  logical :: need_full_symmetry
+
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2436,9 +2455,86 @@
           stop
   endif
 
-  call symmetry_bd(2,extf,funf,funff,SoA)
+  ! 仅计算 X 向最终写回所需的窗口：
+  ! func(i,j,k) 只访问 tmp_x_line(fi-2:fi+3)
+  fi_min = 2*(imino + lbc(1) - 1) - 1 - lbf(1) + 1
+  fi_max = 2*(imaxo + lbc(1) - 1) - 1 - lbf(1) + 1
+  fj_min = 2*(jmino + lbc(2) - 1) - 1 - lbf(2) + 1
+  fj_max = 2*(jmaxo + lbc(2) - 1) - 1 - lbf(2) + 1
+  fk_min = 2*(kmino + lbc(3) - 1) - 1 - lbf(3) + 1
+  fk_max = 2*(kmaxo + lbc(3) - 1) - 1 - lbf(3) + 1
+  ii_lo = fi_min - 2
+  ii_hi = fi_max + 3
+  jj_lo = fj_min - 2
+  jj_hi = fj_max + 3
+  kk_lo = fk_min - 2
+  kk_hi = fk_max + 3
+  if(ii_lo < -1 .or. ii_hi > extf(1) .or. &
+     jj_lo < -1 .or. jj_hi > extf(2) .or. &
+     kk_lo < -1 .or. kk_hi > extf(3))then
+      write(*,*)"restrict3: invalid stencil window"
+      write(*,*)"ii=",ii_lo,ii_hi," jj=",jj_lo,jj_hi," kk=",kk_lo,kk_hi
+      write(*,*)"extf=",extf
+      stop
+  endif
+  need_full_symmetry = (ii_lo < 1) .or. (jj_lo < 1) .or. (kk_lo < 1)
+  if(need_full_symmetry)then
+      call symmetry_bd(2,extf,funf,funff,SoA)
+  else
+      funff(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi) = funf(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi)
+  endif
 
 !~~~~~~> 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 = ii_lo, ii_hi
+            ! 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 = ii_lo, ii_hi
+            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
@@ -2462,7 +2558,7 @@
     enddo
    enddo
   enddo
-  
+#endif
   return
 
   end subroutine restrict3

AMSS_NCKU_source/rungekutta4_rout_c.C

@@ -0,0 +1,212 @@
+#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

@@ -0,0 +1,246 @@
+#ifndef SHARE_FUNC_H
+#define SHARE_FUNC_H
+
+#include <stdlib.h>
+#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];
+    return (size_t)i0 + (size_t)j0 * (size_t)ex1 + (size_t)k0 * (size_t)ex1 * (size_t)ex2;
+}
+
+/*
+ * fh 对应 Fortran: fh(-1:ex1, -1:ex2, -1:ex3)
+ * ord=2 => shift=1
+ * iF/jF/kF 为 Fortran 索引（可为 -1,0,1..ex）
+ */
+static inline size_t idx_fh_F_ord2(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 1;
+    const int nx = ex[0] + 2;      // ex1 + ord
+    const int ny = ex[1] + 2;
+
+    const int ii = iF + shift;     // 0..ex1+1
+    const int jj = jF + shift;     // 0..ex2+1
+    const int kk = kF + shift;     // 0..ex3+1
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * fh 对应 Fortran: fh(-2:ex1, -2:ex2, -2:ex3)
+ * ord=3 => shift=2
+ * iF/jF/kF 是 Fortran 索引（可为负）
+ */
+static inline size_t idx_fh_F(int iF, int jF, int kF, const int ex[3]) {
+    const int shift = 2;                 // ord=3 -> -2..ex
+    const int nx = ex[0] + 3;            // ex1 + ord
+    const int ny = ex[1] + 3;
+
+    const int ii = iF + shift;           // 0..ex1+2
+    const int jj = jF + shift;           // 0..ex2+2
+    const int kk = kF + shift;           // 0..ex3+2
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * func:  (1..extc1, 1..extc2, 1..extc3)   1-based in Fortran
+ * funcc: (-ord+1..extc1, -ord+1..extc2, -ord+1..extc3) in Fortran
+ *
+ * C 里我们把：
+ *   func  视为 0-based: i0=0..extc1-1, j0=0..extc2-1, k0=0..extc3-1
+ *   funcc 用“平移下标”存为一维数组：
+ *     iF in [-ord+1..extc1]  -> ii = iF + (ord-1)  in [0..extc1+ord-1]
+ *     总长度 nx = extc1 + ord
+ *     同理 ny = extc2 + ord, nz = extc3 + ord
+ */
+
+static inline size_t idx_func0(int i0, int j0, int k0, const int extc[3]) {
+    const int nx = extc[0], ny = extc[1];
+    return (size_t)i0 + (size_t)j0 * (size_t)nx + (size_t)k0 * (size_t)nx * (size_t)ny;
+}
+
+static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc[3]) {
+    const int shift = ord - 1;          // iF = -shift .. extc1
+    const int nx = extc[0] + ord;       // [-shift..extc1] 共 extc1+ord 个
+    const int ny = extc[1] + ord;
+
+    const int ii = iF + shift;          // 0..extc1+shift
+    const int jj = jF + shift;          // 0..extc2+shift
+    const int kk = kF + shift;          // 0..extc3+shift
+
+    return (size_t)ii + (size_t)jj * (size_t)nx + (size_t)kk * (size_t)nx * (size_t)ny;
+}
+
+/*
+ * 等价于 Fortran:
+ * funcc(1:extc1,1:extc2,1:extc3)=func
+ * do i=0,ord-1
+ *   funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1)
+ * enddo
+ * do i=0,ord-1
+ *   funcc(:,-i,1:extc3) = funcc(:,i+1,1:extc3)*SoA(2)
+ * enddo
+ * do i=0,ord-1
+ *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
+ * enddo
+ */
+static inline void symmetry_bd_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;
+
+    /* Fast paths used by current C kernels: ord=2 (derivs), ord=3 (lopsided/KO). */
+    if (ord == 2) {
+        symmetry_bd_impl(2, 1, extc, func, funcc, SoA);
+        return;
+    }
+    if (ord == 3) {
+        symmetry_bd_impl(3, 2, extc, func, funcc, SoA);
+        return;
+    }
+
+    symmetry_bd_impl(ord, ord - 1, extc, func, funcc, SoA);
+}
+#endif

AMSS_NCKU_source/tool.h

@@ -0,0 +1,33 @@
+#include "share_func.h"
+void fdderivs(const int ex[3],
+              const double *f,
+              double *fxx, double *fxy, double *fxz,
+              double *fyy, double *fyz, double *fzz,
+              const double *X, const double *Y, const double *Z,
+              double SYM1, double SYM2, double SYM3,
+              int Symmetry, int onoff);
+
+void fderivs(const int ex[3],
+             const double *f,
+             double *fx, double *fy, double *fz,
+             const double *X, const double *Y, const double *Z,
+             double SYM1, double SYM2, double SYM3,
+             int Symmetry, int onoff);
+
+void kodis(const int ex[3],
+           const double *X, const double *Y, const double *Z,
+           const double *f, double *f_rhs,
+           const double SoA[3],
+           int Symmetry, double eps);
+
+void lopsided(const int ex[3],
+              const double *X, const double *Y, const double *Z,
+              const double *f, double *f_rhs,
+              const double *Sfx, const double *Sfy, const double *Sfz,
+              int Symmetry, const double SoA[3]);
+
+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

@@ -0,0 +1,72 @@
+#!/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

@@ -11,17 +11,47 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 import time
-## CPU core binding configuration using taskset
-## taskset ensures all child processes inherit the CPU affinity mask
-## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
-## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
-#NUMACTL_CPU_BIND = "taskset -c 0-111"
-NUMACTL_CPU_BIND = "taskset -c 16-47,64-95"
 
-## Build parallelism configuration
+
-## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
+def get_last_n_cores_per_socket(n=32):
-## Set make -j to utilize available cores for faster builds
+    """
-BUILD_JOBS = 96
+    Read CPU topology via lscpu and return a taskset -c string
+    selecting the last `n` cores of each NUMA node (socket).
+
+    Example: 2 sockets x 56 cores each, n=32 -> node0: 24-55, node1: 80-111
+    -> "taskset -c 24-55,80-111"
+    """
+    result = subprocess.run(["lscpu", "--parse=NODE,CPU"], capture_output=True, text=True)
+
+    # Build a dict: node_id -> sorted list of CPU ids
+    node_cpus = {}
+    for line in result.stdout.splitlines():
+        if line.startswith("#") or not line.strip():
+            continue
+        parts = line.split(",")
+        if len(parts) < 2:
+            continue
+        node_id, cpu_id = int(parts[0]), int(parts[1])
+        node_cpus.setdefault(node_id, []).append(cpu_id)
+
+    segments = []
+    for node_id in sorted(node_cpus):
+        cpus = sorted(node_cpus[node_id])
+        selected = cpus[-n:]          # last n cores of this socket
+        segments.append(f"{selected[0]}-{selected[-1]}")
+
+    cpu_str = ",".join(segments)
+    total = len(segments) * n
+    print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
+    #return f"taskset -c {cpu_str}"
+    return f""
+
+
+## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
+NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
+
+## Build parallelism: match the number of bound cores
+BUILD_JOBS = 64
 
 
 ##################################################################
@@ -40,7 +70,7 @@ 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} ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off 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

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