prolong3: 减少Z-pass 冗余计算

.gitignore

@@ -1,6 +1,6 @@
 __pycache__
 GW150914
-GW150914*
+GW150914-origin
 docs
 *.tmp
-.codex
+

AMSS_NCKU_Input.py

@@ -16,9 +16,9 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 8                             ## number of mpi processes used in the simulation
+MPI_processes    = 64                             ## number of mpi processes used in the simulation
 
-GPU_Calculation  = "yes"                          ## Use GPU or not 
+GPU_Calculation  = "no"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
 CPU_Part         = 1.0
 GPU_Part         = 0.0

AMSS_NCKU_Program.py

@@ -258,7 +258,7 @@ print()
 if (input_data.GPU_Calculation == "no"):
     ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE")
 elif (input_data.GPU_Calculation == "yes"):
-    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE_CUDA")
+    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABEGPU")
 
 if not os.path.exists( ABE_file ):
     print(                                                                                                  )

AMSS_NCKU_Verify_ASC26.py

@@ -9,11 +9,6 @@ Verification Requirements:
    - Y Component RMS
    - Z Component RMS
 2. ADM constraint violation < 2 (Grid Level 0)
-3. The following figure PDFs must match GW150914-origin exactly after rasterization:
-   - ADM_Constraint_Grid_Level_0.pdf
-   - BH_Trajectory_21_XY.pdf
-   - BH_Trajectory_XY.pdf
-   The script also reports the percentage of differing pixels for each figure.
 
 RMS Calculation Method:
 - Computes trajectory deviation on the XY plane independently for BH1 and BH2
@@ -28,10 +23,6 @@ Reference: GW150914-origin (baseline simulation)
 import numpy as np
 import sys
 import os
-import shutil
-import subprocess
-import tempfile
-from PIL import Image
 
 # ANSI Color Codes
 class Color:
@@ -70,132 +61,6 @@ def load_constraint_data(filepath):
                 data.append([float(x) for x in parts[:8]])
     return np.array(data)
 
-
-def resolve_figure_dir(path):
-    """Resolve the sibling figure directory from an output or figure path."""
-    normalized = os.path.normpath(path)
-    if os.path.basename(normalized) == "figure":
-        return normalized
-    return os.path.join(os.path.dirname(normalized), "figure")
-
-
-def render_pdf_to_images(pdf_path, dpi=150):
-    """Render a PDF to RGB images using Ghostscript."""
-    gs_path = shutil.which("gs")
-    if gs_path is None:
-        raise RuntimeError("Ghostscript executable 'gs' was not found in PATH")
-
-    with tempfile.TemporaryDirectory(prefix="amss_verify_pdf_") as temp_dir:
-        output_pattern = os.path.join(temp_dir, "page-%03d.ppm")
-        cmd = [
-            gs_path,
-            "-q",
-            "-dSAFER",
-            "-dBATCH",
-            "-dNOPAUSE",
-            "-sDEVICE=ppmraw",
-            f"-r{dpi}",
-            f"-o{output_pattern}",
-            pdf_path
-        ]
-
-        try:
-            subprocess.run(cmd, check=True, stdout=subprocess.DEVNULL, stderr=subprocess.PIPE, text=True)
-        except subprocess.CalledProcessError as exc:
-            message = exc.stderr.strip() or str(exc)
-            raise RuntimeError(f"Failed to render PDF '{pdf_path}': {message}") from exc
-
-        ppm_files = sorted(
-            os.path.join(temp_dir, filename)
-            for filename in os.listdir(temp_dir)
-            if filename.endswith(".ppm")
-        )
-
-        if not ppm_files:
-            raise RuntimeError(f"No rendered pages were produced for '{pdf_path}'")
-
-        images = []
-        for ppm_file in ppm_files:
-            with Image.open(ppm_file) as img:
-                images.append(np.array(img.convert("RGB"), dtype=np.uint8))
-
-        return images
-
-
-def compare_rendered_pages(ref_img, target_img):
-    """Return (different_pixels, total_pixels) for two rendered RGB pages."""
-    ref_h, ref_w = ref_img.shape[:2]
-    tgt_h, tgt_w = target_img.shape[:2]
-    total_pixels = max(ref_h, tgt_h) * max(ref_w, tgt_w)
-
-    if ref_h == tgt_h and ref_w == tgt_w:
-        different_pixels = int(np.count_nonzero(np.any(ref_img != target_img, axis=2)))
-        return different_pixels, total_pixels
-
-    diff_mask = np.ones((max(ref_h, tgt_h), max(ref_w, tgt_w)), dtype=bool)
-    overlap_h = min(ref_h, tgt_h)
-    overlap_w = min(ref_w, tgt_w)
-    overlap_diff = np.any(ref_img[:overlap_h, :overlap_w] != target_img[:overlap_h, :overlap_w], axis=2)
-    diff_mask[:overlap_h, :overlap_w] = overlap_diff
-    different_pixels = int(np.count_nonzero(diff_mask))
-    return different_pixels, total_pixels
-
-
-def compare_pdf_images(ref_pdf, target_pdf, dpi=150, threshold_percent=0.001):
-    """Compare two PDFs by rasterizing them and counting differing pixels."""
-    ref_pages = render_pdf_to_images(ref_pdf, dpi=dpi)
-    target_pages = render_pdf_to_images(target_pdf, dpi=dpi)
-
-    total_pixels = 0
-    different_pixels = 0
-    max_pages = max(len(ref_pages), len(target_pages))
-
-    for page_idx in range(max_pages):
-        if page_idx < len(ref_pages) and page_idx < len(target_pages):
-            page_diff, page_total = compare_rendered_pages(ref_pages[page_idx], target_pages[page_idx])
-        else:
-            existing_page = ref_pages[page_idx] if page_idx < len(ref_pages) else target_pages[page_idx]
-            page_total = existing_page.shape[0] * existing_page.shape[1]
-            page_diff = page_total
-
-        total_pixels += page_total
-        different_pixels += page_diff
-
-    diff_percent = (different_pixels / total_pixels * 100.0) if total_pixels else 0.0
-    return {
-        "different_pixels": different_pixels,
-        "total_pixels": total_pixels,
-        "diff_percent": diff_percent,
-        "pages_ref": len(ref_pages),
-        "pages_target": len(target_pages),
-        "passed": diff_percent < threshold_percent
-    }
-
-
-def compare_required_figures(reference_figure_dir, target_figure_dir):
-    """Compare the required GW150914 figure PDFs."""
-    figure_names = [
-        "ADM_Constraint_Grid_Level_0.pdf",
-        "BH_Trajectory_21_XY.pdf",
-        "BH_Trajectory_XY.pdf"
-    ]
-
-    results = []
-    for figure_name in figure_names:
-        ref_pdf = os.path.join(reference_figure_dir, figure_name)
-        target_pdf = os.path.join(target_figure_dir, figure_name)
-
-        if not os.path.exists(ref_pdf):
-            raise FileNotFoundError(f"Reference figure not found: {ref_pdf}")
-        if not os.path.exists(target_pdf):
-            raise FileNotFoundError(f"Target figure not found: {target_pdf}")
-
-        comparison = compare_pdf_images(ref_pdf, target_pdf)
-        comparison["name"] = figure_name
-        results.append(comparison)
-
-    return results
-
 def calculate_all_rms_errors(bh_data_ref, bh_data_target):
     """
     Calculate 3D Vector RMS and component-wise RMS (X, Y, Z) independently.
@@ -319,45 +184,18 @@ def print_constraint_results(results, threshold=2.0):
     return passed
 
 
-def print_figure_results(results, threshold_percent=0.001):
+def print_summary(rms_passed, constraint_passed):
-    print(f"\n{Color.BOLD}3. Figure Pixel Comparison (PDF Rasterization){Color.RESET}")
-    print("-" * 65)
-    print(f"   Requirement: < {threshold_percent:.3f}% differing pixels\n")
-
-    all_passed = True
-    for result in results:
-        passed = result["passed"]
-        all_passed = all_passed and passed
-        status = get_status_text(passed)
-        print(f"   {result['name']:32}: {result['diff_percent']:10.6f}%   |   Status: {status}")
-
-        if result["pages_ref"] != result["pages_target"]:
-            print(f"   {'':32}  pages(ref/target): {result['pages_ref']}/{result['pages_target']}")
-
-    return all_passed
-
-
-def print_figure_error(error_message):
-    print(f"\n{Color.BOLD}3. Figure Pixel Comparison (PDF Rasterization){Color.RESET}")
-    print("-" * 65)
-    print(f"   {Color.RED}Error: {error_message}{Color.RESET}")
-    return False
-
-
-def print_summary(rms_passed, constraint_passed, figure_passed):
     print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
     print(Color.BOLD + "Verification Summary" + Color.RESET)
     print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
 
-    all_passed = rms_passed and constraint_passed and figure_passed
+    all_passed = rms_passed and constraint_passed
     
     res_rms = get_status_text(rms_passed)
     res_con = get_status_text(constraint_passed)
-    res_fig = get_status_text(figure_passed)
 
     print(f"   [1] Comprehensive RMS check:      {res_rms}")
     print(f"   [2] ADM constraint check:         {res_con}")
-    print(f"   [3] Figure pixel comparison:      {res_fig}")
     
     final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
     print(f"\n   Overall result: {final_status}")
@@ -374,8 +212,6 @@ def main():
 
     script_dir = os.path.dirname(os.path.abspath(__file__))
     reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
-    target_figure_dir = resolve_figure_dir(target_dir)
-    reference_figure_dir = os.path.join(script_dir, "GW150914-origin/figure")
 
     bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
     bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
@@ -394,8 +230,6 @@ def main():
     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}")
-    print(f"{Color.BOLD}Reference Figures:   {Color.RESET} {Color.BLUE}{reference_figure_dir}{Color.RESET}")
-    print(f"{Color.BOLD}Target Figures:      {Color.RESET} {Color.BLUE}{target_figure_dir}{Color.RESET}")
 
     bh_data_ref = load_bh_trajectory(bh_file_ref)
     bh_data_target = load_bh_trajectory(bh_file_target)
@@ -409,13 +243,7 @@ def main():
     constraint_results = analyze_constraint_violation(constraint_data)
     constraint_passed = print_constraint_results(constraint_results)
 
-    try:
+    all_passed = print_summary(rms_passed, constraint_passed)
-        figure_results = compare_required_figures(reference_figure_dir, target_figure_dir)
-        figure_passed = print_figure_results(figure_results)
-    except (FileNotFoundError, RuntimeError) as exc:
-        figure_passed = print_figure_error(str(exc))
-
-    all_passed = print_summary(rms_passed, constraint_passed, figure_passed)
     sys.exit(0 if all_passed else 1)
 
 if __name__ == "__main__":

AMSS_NCKU_source/MPatch.C

@@ -7,7 +7,6 @@
 #include <string>
 #include <cmath>
 #include <new>
-#include <vector>
 using namespace std;
 
 #include "misc.h"
@@ -18,168 +17,6 @@ using namespace std;
 #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)
 {
 
@@ -530,11 +367,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim];
+  double DH[dim], llb[dim], uub[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
   {
@@ -557,10 +392,39 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    MyList<Block> *Bp = blb;
-    if (block_i >= 0)
+    bool notfind = true;
+    while (notfind && Bp) // run along Blocks
     {
-      Block *BP = block_index.views[block_i].bp;
+      Block *BP = Bp->data;
+
+      bool flag = true;
+      for (int i = 0; i < dim; i++)
+      {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#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;
+          break;
+        }
+      }
+
+      if (flag)
+      {
+        notfind = false;
         owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
@@ -576,6 +440,10 @@ void Patch::Interp_Points(MyList<var> *VarList,
           }
         }
       }
+      if (Bp == ble)
+        break;
+      Bp = Bp->next;
+    }
   }
 
   // Replace MPI_Allreduce with per-owner MPI_Bcast:
@@ -667,11 +535,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim];
+  double DH[dim], llb[dim], uub[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++)
@@ -695,10 +561,39 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    MyList<Block> *Bp = blb;
-    if (block_i >= 0)
+    bool notfind = true;
+    while (notfind && Bp)
     {
-      Block *BP = block_index.views[block_i].bp;
+      Block *BP = Bp->data;
+
+      bool flag = true;
+      for (int i = 0; i < dim; i++)
+      {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#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;
+          break;
+        }
+      }
+
+      if (flag)
+      {
+        notfind = false;
         owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
@@ -713,6 +608,10 @@ void Patch::Interp_Points(MyList<var> *VarList,
           }
         }
       }
+      if (Bp == ble)
+        break;
+      Bp = Bp->next;
+    }
   }
 
 #ifdef INTERP_LB_PROFILE
@@ -934,11 +833,9 @@ 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];
+  double DH[dim], llb[dim], uub[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
   {
@@ -961,10 +858,39 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    MyList<Block> *Bp = blb;
-    if (block_i >= 0)
+    bool notfind = true;
+    while (notfind && Bp) // run along Blocks
     {
-      Block *BP = block_index.views[block_i].bp;
+      Block *BP = Bp->data;
+
+      bool flag = true;
+      for (int i = 0; i < dim; i++)
+      {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#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;
+          break;
+        }
+      }
+
+      if (flag)
+      {
+        notfind = false;
         owner_rank[j] = BP->rank;
         if (myrank == BP->rank)
         {
@@ -980,6 +906,10 @@ void Patch::Interp_Points(MyList<var> *VarList,
           }
         }
       }
+      if (Bp == ble)
+        break;
+      Bp = Bp->next;
+    }
   }
 
   // Collect unique global owner ranks and translate to local ranks in Comm_here

AMSS_NCKU_source/Parallel.h

@@ -104,22 +104,16 @@ namespace Parallel
     double **recv_bufs;
     int *send_buf_caps;
     int *recv_buf_caps;
-    unsigned char *send_buf_pinned;
-    unsigned char *recv_buf_pinned;
     MPI_Request *reqs;
     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();
   };
 
   void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
-  void Sync_ensure_cache(MyList<Patch> *PatL, int Symmetry, SyncCache &cache);
   void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
                        MyList<var> *VarList1, MyList<var> *VarList2,
                        int Symmetry, SyncCache &cache);
@@ -127,10 +121,7 @@ namespace Parallel
   struct AsyncSyncState {
     int req_no;
     bool active;
-    int *req_node;
+    AsyncSyncState() : req_no(0), active(false) {}
-    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,
@@ -186,7 +177,6 @@ namespace Parallel
                          MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
   void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
   double L2Norm(Patch *Pat, var *vf);
-  void L2Norm7(Patch *Pat, var **vf, double *norms);
   void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
   void checkvarl(MyList<var> *pp, bool first_only);
   MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
@@ -222,7 +212,6 @@ namespace Parallel
   void checkpatchlist(MyList<Patch> *PatL, bool buflog);
 
   double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
   bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
                              int NN, double **XX,
                              double *Shellf, int Symmetry, MPI_Comm Comm_here);

AMSS_NCKU_source/ShellPatch.C

@@ -3472,43 +3472,6 @@ double ShellPatch::L2Norm(var *vf)
 
   return tvf;
 }
-void ShellPatch::L2Norm7(var **vf, double *norms)
-{
-  double tvf[7], dtvf[7];
-  int BDW = overghost;
-  for (int i = 0; i < 7; i++)
-    dtvf[i] = 0;
-
-  MyList<ss_patch> *sPp = PatL;
-  while (sPp)
-  {
-    MyList<Block> *Bp = sPp->data->blb;
-    while (Bp)
-    {
-      Block *cg = Bp->data;
-      if (myrank == cg->rank)
-      {
-        f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2],
-                        sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
-                        cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
-                        cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
-                        cg->fgfs[vf[6]->sgfn], tvf, BDW);
-        for (int i = 0; i < 7; i++)
-          dtvf[i] += tvf[i];
-      }
-      if (Bp == sPp->data->ble)
-        break;
-      Bp = Bp->next;
-    }
-    sPp = sPp->next;
-  }
-
-  MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-
-  for (int i = 0; i < 7; i++)
-    norms[i] = sqrt(tvf[i]);
-}
 
 // find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
 void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,

AMSS_NCKU_source/ShellPatch.h

@@ -198,7 +198,6 @@ public:
    void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
                             char *filename, int sst);
    double L2Norm(var *vf);
-   void L2Norm7(var **vf, double *norms);
    void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
 };
 

AMSS_NCKU_source/Z4c_class.C

@@ -28,14 +28,6 @@ using namespace std;
 #include "kodiss.h"
 #include "parameters.h"
 
-#ifndef USE_CUDA_Z4C
-#define USE_CUDA_Z4C 0
-#endif
-
-#if USE_CUDA_Z4C && (ABEtype == 2)
-#include "z4c_rhs_cuda.h"
-#endif
-
 #ifdef With_AHF
 #include "derivatives.h"
 #include "myglobal.h"
@@ -178,550 +170,8 @@ Z4c_class::~Z4c_class()
 #ifndef CPBC
 // for sommerfeld boundary
 
-#if USE_CUDA_Z4C && (ABEtype == 2)
-#ifdef WithShell
-#error "USE_CUDA_Z4C resident path currently supports Cartesian non-shell Z4C only"
-#endif
-#if (MRBD == 2)
-#error "USE_CUDA_Z4C resident path does not support MRBD == 2"
-#endif
-
-namespace {
-
-static const int k_z4c_cuda_bh_state_indices[3] = {18, 19, 20};
-
-bool fill_z4c_cuda_views(Block *cg, MyList<var> *vars,
-                         double **host_views,
-                         double *propspeeds = 0,
-                         double *soa_flat = 0)
-{
-  int idx = 0;
-  while (vars && idx < Z4C_CUDA_STATE_COUNT)
-  {
-    host_views[idx] = cg->fgfs[vars->data->sgfn];
-    if (propspeeds)
-      propspeeds[idx] = vars->data->propspeed;
-    if (soa_flat)
-    {
-      soa_flat[3 * idx + 0] = vars->data->SoA[0];
-      soa_flat[3 * idx + 1] = vars->data->SoA[1];
-      soa_flat[3 * idx + 2] = vars->data->SoA[2];
-    }
-    vars = vars->next;
-    ++idx;
-  }
-  return idx == Z4C_CUDA_STATE_COUNT && vars == 0;
-}
-
-void z4c_cuda_download_level_state(MyList<Patch> *PatL, MyList<var> *vars, int myrank, bool release_ctx)
-{
-  MyList<Patch> *Pp = PatL;
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank && z4c_cuda_has_resident_state(cg))
-      {
-        double *state_out[Z4C_CUDA_STATE_COUNT];
-        if (!fill_z4c_cuda_views(cg, vars, state_out))
-        {
-          cout << "CUDA Z4C state list mismatch on resident state download" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        if (z4c_cuda_download_resident_state(cg, cg->shape, state_out))
-        {
-          cout << "CUDA Z4C resident state download failed" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        if (release_ctx)
-          z4c_cuda_release_step_ctx(cg);
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-}
-
-bool z4c_cuda_patch_contains_point(Patch *patch, const double *point)
-{
-  if (!patch)
-    return false;
-  for (int d = 0; d < dim; d++)
-  {
-    const double h = patch->getdX(d);
-    const double lo = patch->bbox[d] + patch->lli[d] * h;
-    const double hi = patch->bbox[dim + d] - patch->uui[d] * h;
-    if (point[d] < lo || point[d] > hi)
-      return false;
-  }
-  return true;
-}
-
-bool z4c_cuda_point_in_block(Patch *patch, Block *block,
-                             const double *point, const double *DH)
-{
-  if (!patch || !block)
-    return false;
-  for (int d = 0; d < dim; d++)
-  {
-    double llb;
-    double uub;
-#ifdef Vertex
-#ifdef Cell
-#error Both Cell and Vertex are defined
-#endif
-    llb = (feq(block->bbox[d], patch->bbox[d], DH[d] / 2))
-              ? block->bbox[d] + patch->lli[d] * DH[d]
-              : block->bbox[d] + (ghost_width - 0.5) * DH[d];
-    uub = (feq(block->bbox[dim + d], patch->bbox[dim + d], DH[d] / 2))
-              ? block->bbox[dim + d] - patch->uui[d] * DH[d]
-              : block->bbox[dim + d] - (ghost_width - 0.5) * DH[d];
-#else
-#ifdef Cell
-    llb = (feq(block->bbox[d], patch->bbox[d], DH[d] / 2))
-              ? block->bbox[d] + patch->lli[d] * DH[d]
-              : block->bbox[d] + ghost_width * DH[d];
-    uub = (feq(block->bbox[dim + d], patch->bbox[dim + d], DH[d] / 2))
-              ? block->bbox[dim + d] - patch->uui[d] * DH[d]
-              : block->bbox[dim + d] - ghost_width * DH[d];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-    if (point[d] - llb < -DH[d] / 2 || point[d] - uub > DH[d] / 2)
-      return false;
-  }
-  return true;
-}
-
-int z4c_cuda_interp_tile_start(const double *coords, int n, double x, double dx, int ordn)
-{
-  if (!coords || n <= ordn)
-    return 0;
-  int cxi = int((x - coords[0]) / dx + 0.4) + 1;
-  int start = cxi - ordn / 2;
-  if (start < 0)
-    start = 0;
-  const int max_start = n - ordn;
-  if (start > max_start)
-    start = max_start;
-  return start;
-}
-
-bool z4c_cuda_interp_bh_point_resident(MyList<Patch> *PatL,
-                                       int myrank,
-                                       const double *point,
-                                       var *forx, var *fory, var *forz,
-                                       int Symmetry,
-                                       double *shellf)
-{
-  const int ordn = 2 * ghost_width;
-  int owner_rank = -1;
-
-  shellf[0] = shellf[1] = shellf[2] = 0.0;
-
-  MyList<Patch> *PL = PatL;
-  while (PL)
-  {
-    Patch *patch = PL->data;
-    if (!z4c_cuda_patch_contains_point(patch, point))
-    {
-      PL = PL->next;
-      continue;
-    }
-
-    double DH[dim];
-    for (int d = 0; d < dim; d++)
-      DH[d] = patch->getdX(d);
-
-    MyList<Block> *BP = patch->blb;
-    while (BP)
-    {
-      Block *block = BP->data;
-      if (z4c_cuda_point_in_block(patch, block, point, DH))
-      {
-        owner_rank = block->rank;
-        if (myrank == owner_rank)
-        {
-          int interp_ordn = ordn;
-          int interp_sym = Symmetry;
-          double x = point[0];
-          double y = point[1];
-          double z = point[2];
-
-          if (z4c_cuda_has_resident_state(block) &&
-              block->shape[0] >= ordn && block->shape[1] >= ordn && block->shape[2] >= ordn)
-          {
-            const int sx = ordn;
-            const int sy = ordn;
-            const int sz = ordn;
-            const int region_all = sx * sy * sz;
-            const int i0 = z4c_cuda_interp_tile_start(block->X[0], block->shape[0], x, DH[0], ordn);
-            const int j0 = z4c_cuda_interp_tile_start(block->X[1], block->shape[1], y, DH[1], ordn);
-            const int k0 = z4c_cuda_interp_tile_start(block->X[2], block->shape[2], z, DH[2], ordn);
-            double *packed_fields = new double[3 * region_all];
-            var *vars[3] = {forx, fory, forz};
-            for (int f = 0; f < 3; f++)
-            {
-              if (z4c_cuda_pack_state_region_to_host_buffer(block,
-                                                            k_z4c_cuda_bh_state_indices[f],
-                                                            packed_fields + f * region_all,
-                                                            block->shape,
-                                                            i0, j0, k0,
-                                                            sx, sy, sz) != 0)
-              {
-                delete[] packed_fields;
-                cout << "CUDA Z4C BH tile download failed" << endl;
-                MPI_Abort(MPI_COMM_WORLD, 1);
-              }
-              int tile_shape[3] = {sx, sy, sz};
-              f_global_interp(tile_shape,
-                              block->X[0] + i0,
-                              block->X[1] + j0,
-                              block->X[2] + k0,
-                              packed_fields + f * region_all,
-                              shellf[f],
-                              x, y, z,
-                              interp_ordn,
-                              vars[f]->SoA,
-                              interp_sym);
-            }
-            delete[] packed_fields;
-          }
-          else
-          {
-            f_global_interp(block->shape, block->X[0], block->X[1], block->X[2],
-                            block->fgfs[forx->sgfn], shellf[0],
-                            x, y, z, interp_ordn, forx->SoA, interp_sym);
-            f_global_interp(block->shape, block->X[0], block->X[1], block->X[2],
-                            block->fgfs[fory->sgfn], shellf[1],
-                            x, y, z, interp_ordn, fory->SoA, interp_sym);
-            f_global_interp(block->shape, block->X[0], block->X[1], block->X[2],
-                            block->fgfs[forz->sgfn], shellf[2],
-                            x, y, z, interp_ordn, forz->SoA, interp_sym);
-          }
-        }
-        break;
-      }
-      if (BP == patch->ble)
-        break;
-      BP = BP->next;
-    }
-
-    if (owner_rank >= 0)
-      break;
-    PL = PL->next;
-  }
-
-  if (owner_rank < 0)
-    return false;
-
-  MPI_Bcast(shellf, 3, MPI_DOUBLE, owner_rank, MPI_COMM_WORLD);
-  return true;
-}
-
-bool z4c_cuda_compute_porg_rhs_resident(cgh *GH,
-                                        int ilev,
-                                        int myrank,
-                                        int BH_num,
-                                        double **BH_PS,
-                                        double **BH_RHS,
-                                        var *forx, var *fory, var *forz,
-                                        int Symmetry)
-{
-  for (int n = 0; n < BH_num; n++)
-  {
-    double shellf[3] = {0.0, 0.0, 0.0};
-    int lev = ilev;
-    while (lev >= 0 &&
-           !z4c_cuda_interp_bh_point_resident(GH->PatL[lev], myrank, BH_PS[n],
-                                              forx, fory, forz, Symmetry, shellf))
-    {
-      --lev;
-    }
-    if (lev < 0)
-      return false;
-    BH_RHS[n][0] = -shellf[0];
-    BH_RHS[n][1] = -shellf[1];
-    BH_RHS[n][2] = -shellf[2];
-  }
-  return true;
-}
-
-} // namespace
-#endif
-
 void Z4c_class::Step(int lev, int YN)
 {
-#if USE_CUDA_Z4C && (ABEtype == 2)
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
-#ifdef With_AHF
-  AH_Step_Find(lev, dT_lev);
-#endif
-  bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
-  double ndeps = numepss;
-  if (lev < GH->movls)
-    ndeps = numepsb;
-  double TRK4 = PhysTime;
-  int iter_count = 0;
-  int pre = 0, cor = 1;
-  int ERROR = 0;
-
-  MyList<Patch> *Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      if (myrank == cg->rank)
-      {
-        double *state_in[Z4C_CUDA_STATE_COUNT];
-        double *state_out[Z4C_CUDA_STATE_COUNT];
-        double propspeed[Z4C_CUDA_STATE_COUNT];
-        double soa_flat[3 * Z4C_CUDA_STATE_COUNT];
-        if (!fill_z4c_cuda_views(cg, StateList, state_in, propspeed, soa_flat) ||
-            !fill_z4c_cuda_views(cg, SynchList_pre, state_out))
-        {
-          cout << "CUDA Z4C state list mismatch on predictor step" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        int apply_bam_bc = 0;
-#if (MRBD == 0)
-#if (SommerType == 0)
-        apply_bam_bc = (lev == 0) ? 1 : 0;
-#endif
-#elif (MRBD == 1)
-        apply_bam_bc = 1;
-#endif
-        int keep_resident_state = 1;
-        int apply_enforce_ga = 0;
-#if (AGM == 0)
-        apply_enforce_ga = 1;
-#endif
-        if (z4c_cuda_rk4_substep(cg,
-                                 cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                 state_in, state_out,
-                                 propspeed, soa_flat, Pp->data->bbox,
-                                 dT_lev, TRK4, iter_count, apply_bam_bc,
-                                 Symmetry, lev, ndeps, pre,
-                                 keep_resident_state, apply_enforce_ga, chitiny))
-        {
-          cout << "CUDA Z4C predictor substep failed in domain: ("
-               << cg->bbox[0] << ":" << cg->bbox[3] << ","
-               << cg->bbox[1] << ":" << cg->bbox[4] << ","
-               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-          ERROR = 1;
-        }
-      }
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-
-  {
-    int erh = ERROR;
-    MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-  }
-  if (ERROR)
-  {
-    if (myrank == 0 && ErrorMonitor->outfile)
-      ErrorMonitor->outfile << "CUDA Z4C failed in predictor at t = " << PhysTime
-                            << ", lev = " << lev << endl;
-    MPI_Abort(MPI_COMM_WORLD, 1);
-  }
-
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
-
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-      if (Symmetry > 0)
-        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
-      if (Symmetry == 2)
-      {
-        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
-        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
-      }
-    }
-  }
-
-  if ((lev == a_lev) && (LastAnas + dT_lev >= AnasTime))
-    z4c_cuda_download_level_state(GH->PatL[lev], SynchList_pre, myrank, false);
-  if (lev == a_lev)
-    AnalysisStuff(lev, dT_lev);
-
-  for (iter_count = 1; iter_count < 4; iter_count++)
-  {
-    if (iter_count == 1 || iter_count == 3)
-      TRK4 += dT_lev / 2;
-    Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-          double *state_in[Z4C_CUDA_STATE_COUNT];
-          double *state_out[Z4C_CUDA_STATE_COUNT];
-          double propspeed[Z4C_CUDA_STATE_COUNT];
-          double soa_flat[3 * Z4C_CUDA_STATE_COUNT];
-          if (!fill_z4c_cuda_views(cg, SynchList_pre, state_in, propspeed, soa_flat) ||
-              !fill_z4c_cuda_views(cg, SynchList_cor, state_out))
-          {
-            cout << "CUDA Z4C state list mismatch on corrector step" << endl;
-            MPI_Abort(MPI_COMM_WORLD, 1);
-          }
-          int apply_bam_bc = 0;
-#if (MRBD == 0)
-#if (SommerType == 0)
-          apply_bam_bc = (lev == 0) ? 1 : 0;
-#endif
-#elif (MRBD == 1)
-          apply_bam_bc = 1;
-#endif
-          int keep_resident_state = 1;
-          int apply_enforce_ga = 0;
-#if (AGM == 0)
-          apply_enforce_ga = 1;
-#elif (AGM == 1)
-          apply_enforce_ga = (iter_count == 3) ? 1 : 0;
-#endif
-          if (z4c_cuda_rk4_substep(cg,
-                                   cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                                   state_in, state_out,
-                                   propspeed, soa_flat, Pp->data->bbox,
-                                   dT_lev, TRK4, iter_count, apply_bam_bc,
-                                   Symmetry, lev, ndeps, cor,
-                                   keep_resident_state, apply_enforce_ga, chitiny))
-          {
-            cout << "CUDA Z4C corrector substep failed in domain: ("
-                 << cg->bbox[0] << ":" << cg->bbox[3] << ","
-                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
-                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
-            ERROR = 1;
-          }
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-
-    {
-      int erh = ERROR;
-      MPI_Allreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
-    }
-    if (ERROR)
-    {
-      if (myrank == 0 && ErrorMonitor->outfile)
-        ErrorMonitor->outfile << "CUDA Z4C failed in RK4 substep#" << iter_count
-                              << " at t = " << PhysTime
-                              << ", lev = " << lev << endl;
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
-
-    if (BH_num > 0 && lev == GH->levels - 1)
-    {
-      if (!z4c_cuda_compute_porg_rhs_resident(GH, lev, myrank, BH_num,
-                                              Porg, Porg1,
-                                              Sfx, Sfy, Sfz, Symmetry))
-      {
-        if (myrank == 0 && ErrorMonitor->outfile)
-          ErrorMonitor->outfile << "CUDA Z4C failed to interpolate black-hole shift at t = "
-                                << PhysTime << endl;
-        MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-      for (int ithBH = 0; ithBH < BH_num; ithBH++)
-      {
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg1[ithBH][0], Porg_rhs[ithBH][0], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg1[ithBH][1], Porg_rhs[ithBH][1], iter_count);
-        f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg1[ithBH][2], Porg_rhs[ithBH][2], iter_count);
-        if (Symmetry > 0)
-          Porg1[ithBH][2] = fabs(Porg1[ithBH][2]);
-        if (Symmetry == 2)
-        {
-          Porg1[ithBH][0] = fabs(Porg1[ithBH][0]);
-          Porg1[ithBH][1] = fabs(Porg1[ithBH][1]);
-        }
-      }
-    }
-
-    if (iter_count < 3)
-    {
-      Pp = GH->PatL[lev];
-      while (Pp)
-      {
-        MyList<Block> *BP = Pp->data->blb;
-        while (BP)
-        {
-          Block *cg = BP->data;
-          cg->swapList(SynchList_pre, SynchList_cor, myrank);
-          if (BP == Pp->data->ble)
-            break;
-          BP = BP->next;
-        }
-        Pp = Pp->next;
-      }
-      if (BH_num > 0 && lev == GH->levels - 1)
-      {
-        for (int ithBH = 0; ithBH < BH_num; ithBH++)
-        {
-          Porg[ithBH][0] = Porg1[ithBH][0];
-          Porg[ithBH][1] = Porg1[ithBH][1];
-          Porg[ithBH][2] = Porg1[ithBH][2];
-        }
-      }
-    }
-  }
-
-  z4c_cuda_download_level_state(GH->PatL[lev], SynchList_cor, myrank, true);
-
-#if (RPS == 0)
-  RestrictProlong(lev, YN, BB);
-#endif
-
-  Pp = GH->PatL[lev];
-  while (Pp)
-  {
-    MyList<Block> *BP = Pp->data->blb;
-    while (BP)
-    {
-      Block *cg = BP->data;
-      cg->swapList(StateList, SynchList_cor, myrank);
-      cg->swapList(OldStateList, SynchList_cor, myrank);
-      if (BP == Pp->data->ble)
-        break;
-      BP = BP->next;
-    }
-    Pp = Pp->next;
-  }
-  if (BH_num > 0 && lev == GH->levels - 1)
-  {
-    for (int ithBH = 0; ithBH < BH_num; ithBH++)
-    {
-      Porg0[ithBH][0] = Porg1[ithBH][0];
-      Porg0[ithBH][1] = Porg1[ithBH][1];
-      Porg0[ithBH][2] = Porg1[ithBH][2];
-    }
-  }
-#else
   double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
 #ifdef With_AHF
   AH_Step_Find(lev, dT_lev);
@@ -1592,13 +1042,9 @@ void Z4c_class::Step(int lev, int YN)
       Porg0[ithBH][2] = Porg1[ithBH][2];
     }
   }
-#endif
 }
 #else
 // for constraint preserving boundary (CPBC)
-#if USE_CUDA_Z4C && (ABEtype == 2)
-#error "USE_CUDA_Z4C resident path does not support CPBC"
-#endif
 #ifndef WithShell
 #error "CPBC only supports Shell"
 #endif

AMSS_NCKU_source/Z4c_rhs.f90

@@ -94,7 +94,6 @@
                Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon,                    &            
                Symmetry,Lev,eps,co)
 
-  if (co == 0) then
 #if (ABV == 0)  
   call ricci_gamma(ex, X, Y, Z,                                      &
                chi,                                                  &
@@ -118,7 +117,6 @@
                Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
                Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
                Symmetry)
-  endif
 
   return
 
@@ -229,7 +227,6 @@
   call get_Z4cparameters(kappa1,kappa2,kappa3,FF,eta)
 
 !!! sanity check
-#ifdef DEBUG
   dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
       +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
       +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -264,7 +261,6 @@
      gont = 1
      return
   endif
-#endif
 
   PI = dacos(-ONE)
 
@@ -1267,7 +1263,6 @@
 
   endif
 
-  if (co == 0) then
 #if (ABV == 0)  
   call ricci_gamma(ex, X, Y, Z,                                      &
                chi,                                                  &
@@ -1292,7 +1287,6 @@
                Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
                Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
                Symmetry)
-  endif
 
   gont = 0
 

AMSS_NCKU_source/Z4c_rhs_ss.f90

@@ -122,7 +122,6 @@
   call get_Z4cparameters(kappa1,kappa2,kappa3,FF,eta)
 
 !!! sanity check
-#ifdef DEBUG
   dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
       +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
       +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
@@ -157,7 +156,6 @@
      gont = 1
      return
   endif
-#endif
 
   PI = dacos(-ONE)
 
@@ -1390,7 +1388,6 @@
   call kodis_sh(ex,crho,sigma,R,TZ,TZ_rhs,SSS,Symmetry,eps,sst)
   endif
 
-  if (co == 0) then
 #if (ABV == 1)  
   call ricci_gamma_ss(ex,crho,sigma,R,X, Y, Z,                                 &
                drhodx, drhody, drhodz,                                         &
@@ -1407,7 +1404,6 @@
                Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
                Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
                Symmetry,Lev,sst)
-#endif
   call constraint_bssn_ss(ex,crho,sigma,R,X, Y, Z,  &
                drhodx, drhody, drhodz,                                         &
                dsigmadx,dsigmady,dsigmadz,                                     &
@@ -1426,7 +1422,7 @@
                Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
                Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon, &
                Symmetry,Lev,sst)
-  endif
+#endif
 
   gont = 0
 

AMSS_NCKU_source/bssn_class.h

@@ -48,8 +48,6 @@ public:
        double StartTime, TotalTime;
        double AnasTime, DumpTime, d2DumpTime, CheckTime;
        double LastAnas, LastConsOut;
-       bool cuda_level0_constraint_cache_valid;
-       int *ConstraintRefreshLevels;
        double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
@@ -132,11 +130,9 @@ 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, *TimingMonitor;
+       monitor *ConVMonitor;
        surface_integral *Waveshell;
        checkpoint *CheckPoint;
 

AMSS_NCKU_source/bssn_gpu.h

@@ -0,0 +1,73 @@
+
+#ifndef BSSN_GPU_H_
+#define BSSN_GPU_H_
+#include "bssn_macro.h"
+#include "macrodef.fh"
+
+#define DEVICE_ID 0
+// #define DEVICE_ID_BY_MPI_RANK
+#define GRID_DIM 256
+#define BLOCK_DIM 128
+
+#define _FH2_(i, j, k) fh[(i) + (j) * _1D_SIZE[2] + (k) * _2D_SIZE[2]]
+#define _FH3_(i, j, k) fh[(i) + (j) * _1D_SIZE[3] + (k) * _2D_SIZE[3]]
+#define pow2(x) ((x) * (x))
+#define TimeBetween(a, b) ((b.tv_sec - a.tv_sec) + (b.tv_usec - a.tv_usec) / 1000000.0f)
+#define M_ metac.
+#define Mh_ meta->
+#define Ms_ metassc.
+#define Msh_ metass->
+
+// #define TIMING
+
+#define RHS_SS_PARA int calledby, int mpi_rank, int *ex, double &T, double *crho, double *sigma, double *R, double *X, double *Y, double *Z, double *drhodx, double *drhody, double *drhodz, double *dsigmadx, double *dsigmady, double *dsigmadz, double *dRdx, double *dRdy, double *dRdz, double *drhodxx, double *drhodxy, double *drhodxz, double *drhodyy, double *drhodyz, double *drhodzz, double *dsigmadxx, double *dsigmadxy, double *dsigmadxz, double *dsigmadyy, double *dsigmadyz, double *dsigmadzz, double *dRdxx, double *dRdxy, double *dRdxz, double *dRdyy, double *dRdyz, double *dRdzz, double *chi, double *trK, double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz, double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz, double *Gamx, double *Gamy, double *Gamz, double *Lap, double *betax, double *betay, double *betaz, double *dtSfx, double *dtSfy, double *dtSfz, double *chi_rhs, double *trK_rhs, double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs, double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs, double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs, double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs, double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs, double *rho, double *Sx, double *Sy, double *Sz, double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz, double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz, double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz, double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz, double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz, double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res, double *Gmx_Res, double *Gmy_Res, double *Gmz_Res, int &Symmetry, int &Lev, double &eps, int &sst, int &co
+
+/**  main function */
+int gpu_rhs(int calledby, int mpi_rank, int *ex, double &T,
+            double *X, double *Y, double *Z,
+
+            double *chi, double *trK,
+
+            double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+
+            double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+
+            double *Gamx, double *Gamy, double *Gamz,
+
+            double *Lap, double *betax, double *betay, double *betaz,
+
+            double *dtSfx, double *dtSfy, double *dtSfz,
+
+            double *chi_rhs, double *trK_rhs,
+
+            double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+
+            double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+
+            double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+
+            double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+
+            double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+
+            double *rho, double *Sx, double *Sy, double *Sz, double *Sxx,
+            double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+
+            double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+
+            double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+
+            double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+
+            double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+
+            double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+            double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+            int &Symmetry, int &Lev, double &eps, int &co);
+
+int gpu_rhs_ss(RHS_SS_PARA);
+
+/** Init GPU side data in GPUMeta. */
+// void init_fluid_meta_gpu(GPUMeta *gpu_meta);
+
+#endif

AMSS_NCKU_source/bssn_gpu_class.h

@@ -0,0 +1,210 @@
+
+#ifndef BSSN_GPU_CLASS_H
+#define BSSN_GPU_CLASS_H
+
+#ifdef newc
+#include <iostream>
+#include <iomanip>
+#include <fstream>
+#include <cstdlib>
+#include <string>
+#include <cmath>
+using namespace std;
+#else
+#include <iostream.h>
+#include <iomanip.h>
+#include <fstream.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#endif
+
+#include <mpi.h>
+
+#include "macrodef.h"
+#include "cgh.h"
+#include "ShellPatch.h"
+#include "misc.h"
+#include "var.h"
+#include "MyList.h"
+#include "monitor.h"
+#include "surface_integral.h"
+#include "checkpoint.h"
+
+// added by yangquan
+#include "bssn_macro.h"
+
+extern void setpbh(int iBHN, double **iPBH, double *iMass, int rBHN);
+
+class bssn_class
+{
+public:
+       // added by yangquan
+       //----------------------
+       int gpu_num_mynode;
+       int cpu_core_num_mynode;
+       int mpi_process_num_mynode;
+       int my_sequence_mynode;
+       int mynode_id;
+       int use_gpu;
+
+       virtual void Step_GPU(int lev, int YN);
+       virtual void Get_runtime_envirment();
+       // virtual void Step_OPENMP(int lev,int YN);
+       //----------------------
+
+       int ngfs;
+       int nprocs, myrank;
+       cgh *GH;
+       ShellPatch *SH;
+       double PhysTime;
+
+       int checkrun;
+       char checkfilename[50];
+       int Steps;
+       double StartTime, TotalTime;
+       double AnasTime, DumpTime, d2DumpTime, CheckTime;
+       double LastAnas, LastConsOut;
+       double Courant;
+       double numepss, numepsb, numepsh;
+       int Symmetry;
+       int maxl, decn;
+       double maxrex, drex;
+       int trfls, a_lev;
+
+       double dT;
+       double chitiny;
+
+       double **Porg0, **Porgbr, **Porg, **Porg1, **Porg_rhs;
+       int BH_num, BH_num_input;
+       double *Mass, *Pmom, *Spin;
+       double ADMMass;
+
+       var *phio, *trKo;
+       var *gxxo, *gxyo, *gxzo, *gyyo, *gyzo, *gzzo;
+       var *Axxo, *Axyo, *Axzo, *Ayyo, *Ayzo, *Azzo;
+       var *Gmxo, *Gmyo, *Gmzo;
+       var *Lapo, *Sfxo, *Sfyo, *Sfzo;
+       var *dtSfxo, *dtSfyo, *dtSfzo;
+
+       var *phi0, *trK0;
+       var *gxx0, *gxy0, *gxz0, *gyy0, *gyz0, *gzz0;
+       var *Axx0, *Axy0, *Axz0, *Ayy0, *Ayz0, *Azz0;
+       var *Gmx0, *Gmy0, *Gmz0;
+       var *Lap0, *Sfx0, *Sfy0, *Sfz0;
+       var *dtSfx0, *dtSfy0, *dtSfz0;
+
+       var *phi, *trK;
+       var *gxx, *gxy, *gxz, *gyy, *gyz, *gzz;
+       var *Axx, *Axy, *Axz, *Ayy, *Ayz, *Azz;
+       var *Gmx, *Gmy, *Gmz;
+       var *Lap, *Sfx, *Sfy, *Sfz;
+       var *dtSfx, *dtSfy, *dtSfz;
+
+       var *phi1, *trK1;
+       var *gxx1, *gxy1, *gxz1, *gyy1, *gyz1, *gzz1;
+       var *Axx1, *Axy1, *Axz1, *Ayy1, *Ayz1, *Azz1;
+       var *Gmx1, *Gmy1, *Gmz1;
+       var *Lap1, *Sfx1, *Sfy1, *Sfz1;
+       var *dtSfx1, *dtSfy1, *dtSfz1;
+
+       var *phi_rhs, *trK_rhs;
+       var *gxx_rhs, *gxy_rhs, *gxz_rhs, *gyy_rhs, *gyz_rhs, *gzz_rhs;
+       var *Axx_rhs, *Axy_rhs, *Axz_rhs, *Ayy_rhs, *Ayz_rhs, *Azz_rhs;
+       var *Gmx_rhs, *Gmy_rhs, *Gmz_rhs;
+       var *Lap_rhs, *Sfx_rhs, *Sfy_rhs, *Sfz_rhs;
+       var *dtSfx_rhs, *dtSfy_rhs, *dtSfz_rhs;
+
+       var *rho, *Sx, *Sy, *Sz, *Sxx, *Sxy, *Sxz, *Syy, *Syz, *Szz;
+
+       var *Gamxxx, *Gamxxy, *Gamxxz, *Gamxyy, *Gamxyz, *Gamxzz;
+       var *Gamyxx, *Gamyxy, *Gamyxz, *Gamyyy, *Gamyyz, *Gamyzz;
+       var *Gamzxx, *Gamzxy, *Gamzxz, *Gamzyy, *Gamzyz, *Gamzzz;
+
+       var *Rxx, *Rxy, *Rxz, *Ryy, *Ryz, *Rzz;
+
+       var *Rpsi4, *Ipsi4;
+       var *t1Rpsi4, *t1Ipsi4, *t2Rpsi4, *t2Ipsi4;
+
+       var *Cons_Ham, *Cons_Px, *Cons_Py, *Cons_Pz, *Cons_Gx, *Cons_Gy, *Cons_Gz;
+
+#ifdef Point_Psi4
+       var *phix, *phiy, *phiz;
+       var *trKx, *trKy, *trKz;
+       var *Axxx, *Axxy, *Axxz;
+       var *Axyx, *Axyy, *Axyz;
+       var *Axzx, *Axzy, *Axzz;
+       var *Ayyx, *Ayyy, *Ayyz;
+       var *Ayzx, *Ayzy, *Ayzz;
+       var *Azzx, *Azzy, *Azzz;
+#endif
+       // FIXME: uc = StateList, up = OldStateList, upp = SynchList_cor; so never touch these three data
+       MyList<var> *StateList, *SynchList_pre, *SynchList_cor, *RHSList;
+       MyList<var> *OldStateList, *DumpList;
+       MyList<var> *ConstraintList;
+
+       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
+       monitor *ConVMonitor;
+       surface_integral *Waveshell;
+       checkpoint *CheckPoint;
+
+public:
+       bssn_class(double Couranti, double StartTimei, double TotalTimei, double DumpTimei, double d2DumpTimei, double CheckTimei, double AnasTimei,
+                  int Symmetryi, int checkruni, char *checkfilenamei, double numepssi, double numepsbi, double numepshi,
+                  int a_levi, int maxli, int decni, double maxrexi, double drexi);
+       ~bssn_class();
+
+       void Evolve(int Steps);
+       void RecursiveStep(int lev);
+#if (PSTR == 1)
+       void ParallelStep();
+       void SHStep();
+#endif
+       void RestrictProlong(int lev, int YN, bool BB, MyList<var> *SL, MyList<var> *OL, MyList<var> *corL);
+       void RestrictProlong_aux(int lev, int YN, bool BB, MyList<var> *SL, MyList<var> *OL, MyList<var> *corL);
+       void RestrictProlong(int lev, int YN, bool BB);
+       void ProlongRestrict(int lev, int YN, bool BB);
+       void Setup_Black_Hole_position();
+       void compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, var *fory, var *forz, int lev);
+       bool read_Pablo_file(int *ext, double *datain, char *filename);
+       void write_Pablo_file(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
+                             char *filename);
+       void AnalysisStuff(int lev, double dT_lev);
+       void Setup_KerrSchild();
+       void Enforce_algcon(int lev, int fg);
+
+       void testRestrict();
+       void testOutBd();
+
+       virtual void Setup_Initial_Data_Lousto();
+       virtual void Setup_Initial_Data_Cao();
+       virtual void Initialize();
+       virtual void Read_Ansorg();
+       virtual void Read_Pablo() {};
+       virtual void Compute_Psi4(int lev);
+       virtual void Step(int lev, int YN);
+       virtual void Interp_Constraint(bool infg);
+       virtual void Constraint_Out();
+       virtual void Compute_Constraint();
+
+#ifdef With_AHF
+protected:
+       MyList<var> *AHList, *AHDList, *GaugeList;
+       int AHfindevery;
+       double AHdumptime;
+       int *lastahdumpid, HN_num; // number of possible horizons
+       int *findeveryl;
+       double *xc, *yc, *zc, *xr, *yr, *zr;
+       bool *trigger;
+       double *dTT;
+       int *dumpid;
+
+public:
+       void AH_Prepare_derivatives();
+       bool AH_Interp_Points(MyList<var> *VarList,
+                             int NN, double **XX,
+                             double *Shellf, int Symmetryi);
+       void AH_Step_Find(int lev, double dT_lev);
+#endif
+};
+#endif /* BSSN_GPU_CLASS_H */

AMSS_NCKU_source/bssn_rhs.f90

@@ -62,7 +62,6 @@
   real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
 !  gont = 0: success; gont = 1: something wrong
   integer::gont
-  integer :: i,j,k
 
 !~~~~~~> Other variables:
 
@@ -86,13 +85,6 @@
 
   real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
   real*8            :: dX, dY, dZ, PI
-  real*8            :: divb_loc,det_loc
-  real*8            :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
-  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
@@ -105,7 +97,7 @@
 #endif
 
 #if (GAUGE == 6 || GAUGE == 7)
-  integer :: BHN
+  integer :: BHN,i,j,k
   real*8, dimension(9) :: Porg
   real*8, dimension(3) :: Mass
   real*8 :: r1,r2,M,A,w1,w2,C1,C2
@@ -153,24 +145,22 @@
   dY = Y(2) - Y(1)
   dZ = Z(2) - Z(1)
 
-  do k=1,ex(3)
+  alpn1 = Lap + ONE
-  do j=1,ex(2)
+  chin1 = chi + ONE
-  do i=1,ex(1)
+  gxx = dxx + ONE
-    alpn1(i,j,k) = Lap(i,j,k) + ONE
+  gyy = dyy + ONE
-    chin1(i,j,k) = chi(i,j,k) + ONE
+  gzz = dzz + 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)
 
+  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
+
   call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
   call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
   call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
@@ -178,179 +168,151 @@
   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)
+  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
-  do j=1,ex(2)
+              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)
-  do i=1,ex(1)
-    divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
-    div_beta(i,j,k) = divb_loc
 
-    chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
+  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
+              TWO *(  gxy * betaxy +   gyy * betayy +   gyz * betazy)
 
-    gxx_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axx(i,j,k) - F2o3 * gxx(i,j,k) * divb_loc + &
+  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
-         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) )
+              TWO *(  gxz * betaxz +   gyz * betayz +   gzz * betazz)
 
-    gyy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayy(i,j,k) - F2o3 * gyy(i,j,k) * divb_loc + &
+  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
-         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) )
+                      gxx * betaxy                  +   gxz * betazy + &
+                                       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 + &
+  gyz_rhs = - TWO * alpn1 * Ayz    +  F1o3 * gyz    * div_beta       + &
-         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) )
+                      gxy * betaxz +   gyy * betayz                  + &
+                      gxz * betaxy                  +   gzz * betazy   &
+                                                    -   gyz * betaxx
  
-    gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
+  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
-         gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
+                      gxx * betaxz +   gxy * betayz                  + &
-         gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
+                                       gyz * betayx +   gzz * betazx   &
+                                                    -   gxz * betayy     !rhs for gij
 
-    gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
+! invert tilted metric
-         gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
+  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-         gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
+           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
-
+  gupxx =   ( gyy * gzz - gyz * gyz ) / gupzz
-    gxz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axz(i,j,k) + F1o3 * gxz(i,j,k) * divb_loc + &
+  gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
-         gxx(i,j,k) * betaxz(i,j,k) + gxy(i,j,k) * betayz(i,j,k) + gyz(i,j,k) * betayx(i,j,k) + &
+  gupxz =   ( gxy * gyz - gyy * gxz ) / gupzz
-         gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
+  gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
-
+  gupyz = - ( gxx * gyz - gxy * gxz ) / 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) + &
+  gupzz =   ( gxx * gyy - gxy * gxy ) / 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) - &
-         gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
-    gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
-    gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
-    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
-    gupyz_loc = - ( gxx(i,j,k) * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / det_loc
-    gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
-    gupxx(i,j,k) = gupxx_loc
-    gupxy(i,j,k) = gupxy_loc
-    gupxz(i,j,k) = gupxz_loc
-    gupyy(i,j,k) = gupyy_loc
-    gupyz(i,j,k) = gupyz_loc
-    gupzz(i,j,k) = gupzz_loc
 
   if(co == 0)then
-      Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
+! Gam^i_Res = Gam^i + gup^ij_,j
-           gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
+  Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
-           gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
+                   +gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
-           gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
+                   +gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
-           gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
+                   +gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
-           gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
+                   +gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
-           gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
+                   +gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
-           gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
+                   +gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
-           gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
+                   +gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
-           gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
+                   +gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
-      Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
+  Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
-           gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
+                   +gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
-           gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
+                   +gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
-           gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
+                   +gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
-           gupxy_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)&
-           gupyy_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)&
-           gupyz_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)&
-           gupxy_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)&
-           gupyy_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))
-           gupyz_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)&
-      Gmz_Res(i,j,k) = Gamz(i,j,k) - ( &
+                   +gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
-           gupxx_loc*(gupxz_loc*gxxx(i,j,k)+gupyz_loc*gxyx(i,j,k)+gupzz_loc*gxzx(i,j,k)) + &
+                   +gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
-           gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
+                   +gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
-           gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
+                   +gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
-           gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
+                   +gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
-           gupyy_loc*(gupxz_loc*gxyy(i,j,k)+gupyz_loc*gyyy(i,j,k)+gupzz_loc*gyzy(i,j,k)) + &
+                   +gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
-           gupyz_loc*(gupxz_loc*gxzy(i,j,k)+gupyz_loc*gyzy(i,j,k)+gupzz_loc*gzzy(i,j,k)) + &
+                   +gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
-           gupxz_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))
-           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)))
   endif
 
-    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)))
+! second kind of connection
-    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)))
+  Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
-    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)))
+  Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
+  Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
  
-    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)))
+  Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
-    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)))
+  Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
-    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)))
+  Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
 
-    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))
+  Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
-    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))
+  Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
-    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))
+  Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
 
-    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)) )
+  Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
-    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)) )
+  Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
-    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)) )
+  Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
 
-    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) )
+  Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
-    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) )
+  Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
-    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) )
+  Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
 
-    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) )
+  Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
-    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) )
+  Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
-    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) )
+  Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
-  enddo
-  enddo
-  enddo
 ! Raise indices of \tilde A_{ij} and store in R_ij
 
+  Rxx =    gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
+      TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
+
+  Ryy =    gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
+      TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
+
+  Rzz =    gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
+      TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
+
+  Rxy =    gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
+          (gupxx * gupyy       + gupxy * gupxy)* Axy                       + &
+          (gupxx * gupyz       + gupxz * gupxy)* Axz                       + &
+          (gupxy * gupyz       + gupxz * gupyy)* Ayz
+
+  Rxz =    gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
+          (gupxx * gupyz       + gupxy * gupxz)* Axy                       + &
+          (gupxx * gupzz       + gupxz * gupxz)* Axz                       + &
+          (gupxy * gupzz       + gupxz * gupyz)* Ayz
+
+  Ryz =    gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
+          (gupxy * gupyz       + gupyy * gupxz)* Axy                       + &
+          (gupxy * gupzz       + gupyz * gupxz)* Axz                       + &
+          (gupyy * gupzz       + gupyz * gupyz)* Ayz
+
 ! Right hand side for Gam^i without shift terms...
   call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
   call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    gupxx_loc = gupxx(i,j,k)
-    gupxy_loc = gupxy(i,j,k)
-    gupxz_loc = gupxz(i,j,k)
-    gupyy_loc = gupyy(i,j,k)
-    gupyz_loc = gupyz(i,j,k)
-    gupzz_loc = gupzz(i,j,k)
 
-    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) + &
+   Gamx_rhs = - TWO * (   Lapx * Rxx +   Lapy * Rxy +   Lapz * Rxz ) + &
-         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))
+        TWO * alpn1 * (                                                &
-    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) + &
+        -F3o2/chin1 * (   chix * Rxx +   chiy * Rxy +   chiz * Rxz ) - &
-         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))
+              gupxx * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
-    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) + &
+              gupxy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
-         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))
+              gupxz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
-    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) + &
+                        Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz   + &
-         (gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
+                TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
-         (gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
-         (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) + &
-         (gupxx_loc * gupyz_loc + gupxy_loc * gupxz_loc) * Axy(i,j,k) + &
-         (gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
-         (gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
-    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) + &
-         (gupxy_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
-         (gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
-         (gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
-    Rxx(i,j,k) = Rxx_loc
-    Ryy(i,j,k) = Ryy_loc
-    Rzz(i,j,k) = Rzz_loc
-    Rxy(i,j,k) = Rxy_loc
-    Rxz(i,j,k) = Rxz_loc
-    Ryz(i,j,k) = Ryz_loc
 
-    Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
+   Gamy_rhs = - TWO * (   Lapx * Rxy +   Lapy * Ryy +   Lapz * Ryz ) + &
-         TWO * alpn1(i,j,k) * ( &
+        TWO * alpn1 * (                                                &
-         -F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
+        -F3o2/chin1 * (   chix * Rxy +  chiy * Ryy +    chiz * Ryz ) - &
-         gupxx_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
+              gupxy * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
-         gupxy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
+              gupyy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
-         gupxz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
+              gupyz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
-         Gamxxx(i,j,k) * Rxx_loc + Gamxyy(i,j,k) * Ryy_loc + Gamxzz(i,j,k) * Rzz_loc + &
+                        Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz   + &
-         TWO * (Gamxxy(i,j,k) * Rxy_loc + Gamxxz(i,j,k) * Rxz_loc + Gamxyz(i,j,k) * Ryz_loc))
+                TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
 
-    Gamy_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxy_loc + Lapy(i,j,k) * Ryy_loc + Lapz(i,j,k) * Ryz_loc) + &
+   Gamz_rhs = - TWO * (   Lapx * Rxz +   Lapy * Ryz +   Lapz * Rzz ) + &
-         TWO * alpn1(i,j,k) * ( &
+        TWO * alpn1 * (                                                &
-         -F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxy_loc + chiy(i,j,k) * Ryy_loc + chiz(i,j,k) * Ryz_loc) - &
+        -F3o2/chin1 * (   chix * Rxz +  chiy * Ryz +    chiz * Rzz ) - &
-         gupxy_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
+              gupxz * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
-         gupyy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
+              gupyz * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
-         gupyz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
+              gupzz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
-         Gamyxx(i,j,k) * Rxx_loc + Gamyyy(i,j,k) * Ryy_loc + Gamyzz(i,j,k) * Rzz_loc + &
+                        Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz   + &
-         TWO * (Gamyxy(i,j,k) * Rxy_loc + Gamyxz(i,j,k) * Rxz_loc + Gamyyz(i,j,k) * Ryz_loc))
+                TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
-
-    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)
@@ -359,54 +321,38 @@
   call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
                 X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
 
+  fxx = gxxx + gxyy + gxzz
+  fxy = gxyx + gyyy + gyzz
+  fxz = gxzx + gyzy + gzzz
+
+  Gamxa =       gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
+          TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
+  Gamya =       gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
+          TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
+  Gamza =       gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
+          TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
+
   call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
   call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
   call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    divb_loc = div_beta(i,j,k)
-    fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
-    fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
-    fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)
 
-    gupxx_loc = gupxx(i,j,k)
+  Gamx_rhs =               Gamx_rhs +  F2o3 *  Gamxa * div_beta        - &
-    gupxy_loc = gupxy(i,j,k)
+                     Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz  + &
-    gupxz_loc = gupxz(i,j,k)
+             F1o3 * (gupxx * fxx    + gupxy * fxy    + gupxz * fxz    ) + &
-    gupyy_loc = gupyy(i,j,k)
+                     gupxx * gxxx   + gupyy * gyyx   + gupzz * gzzx    + &
-    gupyz_loc = gupyz(i,j,k)
+              TWO * (gupxy * gxyx   + gupxz * gxzx   + gupyz * gyzx  )
-    gupzz_loc = gupzz(i,j,k)
 
-    Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
+  Gamy_rhs =               Gamy_rhs +  F2o3 *  Gamya * div_beta        - &
-         TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
+                     Gamxa * betayx - Gamya * betayy - Gamza * betayz  + &
-    Gamya_loc = gupxx_loc * Gamyxx(i,j,k) + gupyy_loc * Gamyyy(i,j,k) + gupzz_loc * Gamyzz(i,j,k) + &
+             F1o3 * (gupxy * fxx    + gupyy * fxy    + gupyz * fxz    ) + &
-         TWO * (gupxy_loc * Gamyxy(i,j,k) + gupxz_loc * Gamyxz(i,j,k) + gupyz_loc * Gamyyz(i,j,k))
+                     gupxx * gxxy   + gupyy * gyyy   + gupzz * gzzy    + &
-    Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
+              TWO * (gupxy * gxyy   + gupxz * gxzy   + gupyz * gyzy  )
-         TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
-    Gamxa(i,j,k) = Gamxa_loc
-    Gamya(i,j,k) = Gamya_loc
-    Gamza(i,j,k) = Gamza_loc
 
-    Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
+  Gamz_rhs =               Gamz_rhs +  F2o3 *  Gamza * div_beta        - &
-         Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
+                     Gamxa * betazx - Gamya * betazy - Gamza * betazz  + &
-         F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
+             F1o3 * (gupxz * fxx    + gupyz * fxy    + gupzz * fxz    ) + &
-         gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
+                     gupxx * gxxz   + gupyy * gyyz   + gupzz * gzzz    + &
-         TWO * (gupxy_loc * gxyx(i,j,k) + gupxz_loc * gxzx(i,j,k) + gupyz_loc * gyzx(i,j,k))
+              TWO * (gupxy * gxyz   + gupxz * gxzz   + gupyz * gyzz  )    !rhs for Gam^i
-
-    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
@@ -658,187 +604,189 @@
 !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)
 
-  do k=1,ex(3)
+  fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
-  do j=1,ex(2)
+  fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
-  do i=1,ex(1)
+  fxz = fxz - Gamxxz * chix - Gamyxz * chiy - Gamzxz * 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)
+  fyy = fyy - Gamxyy * chix - Gamyyy * chiy - Gamzyy * 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)
+  fyz = fyz - Gamxyz * chix - Gamyyz * chiy - Gamzyz * 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)
+  fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
-    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)
+! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f
-    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)
-    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)
 
-    chin_loc = chin1(i,j,k)
+  f =        gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
-    f_loc = gupxx(i,j,k) * (fxx(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chix(i,j,k)) + &
+             gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
-            gupyy(i,j,k) * (fyy(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiy(i,j,k)) + &
+             gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
-            gupzz(i,j,k) * (fzz(i,j,k) - F3o2/chin_loc * chiz(i,j,k) * chiz(i,j,k)) + &
+       TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
-            TWO * gupxy(i,j,k) * (fxy(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiy(i,j,k)) + &
+       TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
-            TWO * gupxz(i,j,k) * (fxz(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiz(i,j,k)) + &
+       TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz ) 
-            TWO * gupyz(i,j,k) * (fyz(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiz(i,j,k))
+! Add chi part to Ricci tensor:
-    f(i,j,k) = f_loc
 
-    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
+  Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * 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
+  Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * 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
+  Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/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
+  Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/TWO
-    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
+  Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/TWO
-    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
+  Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO
-  enddo
-  enddo
-  enddo
 
 ! covariant second derivatives of the lapse respect to physical metric
   call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
                 SYM,SYM,SYM,symmetry,Lev)
 
-  do k=1,ex(3)
+  gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
-  do j=1,ex(2)
+  gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
-  do i=1,ex(1)
+  gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
-    chin_loc = chin1(i,j,k)
+! now get physical second kind of connection
-    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
+  Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*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
+  Gamyxx = Gamyxx - (                     - gxx * gxxy )*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
+  Gamzxx = Gamzxx - (                     - gxx * gxxz )*HALF
+  Gamxyy = Gamxyy - (                     - gyy * gxxx )*HALF
+  Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
+  Gamzyy = Gamzyy - (                     - gyy * gxxz )*HALF
+  Gamxzz = Gamxzz - (                     - gzz * gxxx )*HALF
+  Gamyzz = Gamyzz - (                     - gzz * gxxy )*HALF
+  Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
+  Gamxxy = Gamxxy - (  chiy        /chin1 - gxy * gxxx )*HALF
+  Gamyxy = Gamyxy - (         chix /chin1 - gxy * gxxy )*HALF
+  Gamzxy = Gamzxy - (                     - gxy * gxxz )*HALF
+  Gamxxz = Gamxxz - (  chiz        /chin1 - gxz * gxxx )*HALF
+  Gamyxz = Gamyxz - (                     - gxz * gxxy )*HALF
+  Gamzxz = Gamzxz - (         chix /chin1 - gxz * gxxz )*HALF
+  Gamxyz = Gamxyz - (                     - gyz * gxxx )*HALF
+  Gamyyz = Gamyyz - (  chiz        /chin1 - gyz * gxxy )*HALF
+  Gamzyz = Gamzyz - (         chiy /chin1 - gyz * gxxz )*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
+  fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
-    Gamyxx(i,j,k) = Gamyxx(i,j,k) - (                                   - gxx(i,j,k) * gxxy(i,j,k) )*HALF
+  fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
-    Gamzxx(i,j,k) = Gamzxx(i,j,k) - (                                   - gxx(i,j,k) * gxxz(i,j,k) )*HALF
+  fzz = fzz - Gamxzz*Lapx - Gamyzz*Lapy - Gamzzz*Lapz
-    Gamxyy(i,j,k) = Gamxyy(i,j,k) - (                                   - gyy(i,j,k) * gxxx(i,j,k) )*HALF
+  fxy = fxy - Gamxxy*Lapx - Gamyxy*Lapy - Gamzxy*Lapz
-    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
+  fxz = fxz - Gamxxz*Lapx - Gamyxz*Lapy - Gamzxz*Lapz
-    Gamzyy(i,j,k) = Gamzyy(i,j,k) - (                                   - gyy(i,j,k) * gxxz(i,j,k) )*HALF
+  fyz = fyz - Gamxyz*Lapx - Gamyyz*Lapy - Gamzyz*Lapz
-    Gamxzz(i,j,k) = Gamxzz(i,j,k) - (                                   - gzz(i,j,k) * gxxx(i,j,k) )*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
-    Gamxxy(i,j,k) = Gamxxy(i,j,k) - ( chiy(i,j,k) /chin_loc - gxy(i,j,k) * gxxx(i,j,k) )*HALF
-    Gamyxy(i,j,k) = Gamyxy(i,j,k) - ( chix(i,j,k) /chin_loc - gxy(i,j,k) * gxxy(i,j,k) )*HALF
-    Gamzxy(i,j,k) = Gamzxy(i,j,k) - (                     - gxy(i,j,k) * gxxz(i,j,k) )*HALF
-    Gamxxz(i,j,k) = Gamxxz(i,j,k) - ( chiz(i,j,k) /chin_loc - gxz(i,j,k) * gxxx(i,j,k) )*HALF
-    Gamyxz(i,j,k) = Gamyxz(i,j,k) - (                     - gxz(i,j,k) * gxxy(i,j,k) )*HALF
-    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
-    Gamyyz(i,j,k) = Gamyyz(i,j,k) - ( chiz(i,j,k) /chin_loc - gyz(i,j,k) * gxxy(i,j,k) )*HALF
-    Gamzyz(i,j,k) = Gamzyz(i,j,k) - ( chiy(i,j,k) /chin_loc - gyz(i,j,k) * gxxz(i,j,k) )*HALF
 
-    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)
+! store D^i D_i Lap in trK_rhs upto chi
-    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)
+  trK_rhs =    gupxx * fxx + gupyy * fyy + gupzz * fzz + &
-    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 * fxy + gupxz * fxz + gupyz * fyz )
-    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)
+#if 1        
-    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)
+!! follow bam code
-    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)
+  S =  chin1 * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
+     TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
+  f = F2o3 * trK * trK -(&
+       gupxx * ( &
+       gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
+       TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz) ) + &
+       gupyy * ( &
+       gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
+       TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz) ) + &
+       gupzz * ( &
+       gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
+       TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz) ) + &
+       TWO * ( &
+       gupxy * ( &
+       gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
+       gupxy * (Axx * Ayy + Axy * Axy) + &
+       gupxz * (Axx * Ayz + Axz * Axy) + &
+       gupyz * (Axy * Ayz + Axz * Ayy) ) + &
+       gupxz * ( &
+       gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
+       gupxy * (Axx * Ayz + Axy * Axz) + &
+       gupxz * (Axx * Azz + Axz * Axz) + &
+       gupyz * (Axy * Azz + Axz * Ayz) ) + &
+       gupyz * ( &
+       gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
+       gupxy * (Axy * Ayz + Ayy * Axz) + &
+       gupxz * (Axy * Azz + Ayz * Axz) + &
+       gupyz * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
+  f = - F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
   
-    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) + &
+  fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
-                     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))
+  fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
-  enddo
+  fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
-  enddo
+  fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
-  enddo
+  fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
-  do k=1,ex(3)
+  fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
-  do j=1,ex(2)
+#else        
-  do i=1,ex(1)
+! Add lapse and S_ij parts to Ricci tensor:
-    divb_loc = div_beta(i,j,k)
-    chin_loc = chin1(i,j,k)
 
-    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) + &
+  fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
-           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)) )
+  fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
-    S(i,j,k) = S_loc
+  fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
+  fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
+  fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
+  fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
 
-    f_loc = F2o3 * trK(i,j,k) * trK(i,j,k) - ( &
+! Compute trace-free part (note: chi^-1 and chi cancel!):
-            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) + &
-                             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) + gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + &
-                                    gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k)) ) + &
-            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) + &
-                             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(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
-                                    gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k)) ) + &
-            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) + &
-                             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) + &
-                                    gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k)) ) + &
-            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) + &
-                                     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)) + &
-                                     gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k)) ) + &
-                    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) + &
-                                     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)) + &
-                                     gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k)) ) + &
-                    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) + &
-                                     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)) + &
-                                     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_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) + &
+  f = F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
-            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 * fxy + gupxz * fxz + gupyz * fyz ) )
-            alpn1(i,j,k)/chin_loc * f_loc )
+#endif
-    f(i,j,k) = f_loc
 
-    l_fxx = alpn1(i,j,k) * (Rxx(i,j,k) - EIGHT * PI * Sxx(i,j,k)) - fxx(i,j,k)
+  Axx_rhs = fxx - gxx * f
-    l_fxy = alpn1(i,j,k) * (Rxy(i,j,k) - EIGHT * PI * Sxy(i,j,k)) - fxy(i,j,k)
+  Ayy_rhs = fyy - gyy * f
-    l_fxz = alpn1(i,j,k) * (Rxz(i,j,k) - EIGHT * PI * Sxz(i,j,k)) - fxz(i,j,k)
+  Azz_rhs = fzz - gzz * f
-    l_fyy = alpn1(i,j,k) * (Ryy(i,j,k) - EIGHT * PI * Syy(i,j,k)) - fyy(i,j,k)
+  Axy_rhs = fxy - gxy * f
-    l_fyz = alpn1(i,j,k) * (Ryz(i,j,k) - EIGHT * PI * Syz(i,j,k)) - fyz(i,j,k)
+  Axz_rhs = fxz - gxz * f
-    l_fzz = alpn1(i,j,k) * (Rzz(i,j,k) - EIGHT * PI * Szz(i,j,k)) - fzz(i,j,k)
+  Ayz_rhs = fyz - gyz * f
 
-    Axx_rhs(i,j,k) = l_fxx - gxx(i,j,k) * f_loc
+! Now: store A_il A^l_j into fij:
-    Ayy_rhs(i,j,k) = l_fyy - gyy(i,j,k) * f_loc
-    Azz_rhs(i,j,k) = l_fzz - gzz(i,j,k) * f_loc
-    Axy_rhs(i,j,k) = l_fxy - gxy(i,j,k) * f_loc
-    Axz_rhs(i,j,k) = l_fxz - gxz(i,j,k) * f_loc
-    Ayz_rhs(i,j,k) = l_fyz - gyz(i,j,k) * f_loc
 
-    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) + &
+  fxx =       gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
-                 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) + &
+       TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
-                 gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k))
+  fyy =       gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
-    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) + &
+       TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
-                 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) + &
+  fzz =       gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
-                 gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k))
+       TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
-    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) + &
+  fxy =       gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
-                 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 *(Axx * Ayy + Axy * Axy)                            + &
-                 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 *(Axx * Ayz + Axz * Axy)                            + &
-    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 *(Axy * Ayz + Axz * Ayy)
-                 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)) + &
+  fxz =       gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
-                 gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
+              gupxy *(Axx * Ayz + Axy * Axz)                            + &
-                 gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k))
+              gupxz *(Axx * Azz + Axz * Axz)                            + &
-    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) + &
+              gupyz *(Axy * Azz + Axz * Ayz)
-                 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)) + &
+  fyz =       gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
-                 gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
+              gupxy *(Axy * Ayz + Ayy * Axz)                            + &
-                 gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k))
+              gupxz *(Axy * Azz + Ayz * Axz)                            + &
-    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) + &
+              gupyz *(Ayy * Azz + Ayz * Ayz)
-                 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)) + &
-                 gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k))
 
-    trK_rhs(i,j,k) = chin_loc * trK_rhs(i,j,k)
+  f = chin1
+! store D^i D_i Lap in trK_rhs
+  trK_rhs = f*trK_rhs
           
-    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)) + &
+  Axx_rhs =           f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx)  + &
-                     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)) - &
+           TWO * (  Axx * betaxx +   Axy * betayx +   Axz * betazx )- &
-                     F2o3 * Axx(i,j,k) * divb_loc
+             F2o3 * Axx * div_beta
-    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)) + &
-                     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)) - &
-                     F2o3 * Ayy(i,j,k) * divb_loc
-    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)) + &
-                     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
-    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)) + &
-                     Axx(i,j,k) * betaxy(i,j,k) + Axz(i,j,k) * betazy(i,j,k) + Ayy(i,j,k) * betayx(i,j,k) + &
-                     Ayz(i,j,k) * betazx(i,j,k) + F1o3 * Axy(i,j,k) * divb_loc - Axy(i,j,k) * betazz(i,j,k)
-    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) + &
-                     Azz(i,j,k) * betazy(i,j,k) + F1o3 * Ayz(i,j,k) * divb_loc - Ayz(i,j,k) * betaxx(i,j,k)
-    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)) + &
-                     Axx(i,j,k) * betaxz(i,j,k) + Axy(i,j,k) * betayz(i,j,k) + Ayz(i,j,k) * betayx(i,j,k) + &
-                     Azz(i,j,k) * betazx(i,j,k) + F1o3 * Axz(i,j,k) * divb_loc - Axz(i,j,k) * betayy(i,j,k)
 
-    trK_rhs(i,j,k) = - trK_rhs(i,j,k) + alpn1(i,j,k) * ( F1o3 * trK(i,j,k) * trK(i,j,k) + &
+  Ayy_rhs =           f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy)  + &
-                    gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
+           TWO * (  Axy * betaxy +   Ayy * betayy +   Ayz * betazy )- &
-                    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)) + &
+             F2o3 * Ayy * div_beta
-                    FOUR * PI * (rho(i,j,k) + S_loc) )
+
-  enddo
+  Azz_rhs =           f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz)  + &
-  enddo
+           TWO * (  Axz * betaxz +   Ayz * betayz +   Azz * betazz )- &
-  enddo
+             F2o3 * Azz * div_beta
+
+  Axy_rhs =           f * Axy_rhs+ alpn1 *( trK * Axy  - TWO * fxy )+ &
+                    Axx * betaxy                  +   Axz * betazy  + &
+                                     Ayy * betayx +   Ayz * betazx  + &
+             F1o3 * Axy * div_beta                -   Axy * betazz
+
+  Ayz_rhs =           f * Ayz_rhs+ alpn1 *( trK * Ayz  - TWO * fyz )+ &
+                    Axy * betaxz +   Ayy * betayz                   + &
+                    Axz * betaxy                  +   Azz * betazy  + &
+             F1o3 * Ayz * div_beta                -   Ayz * betaxx
+ 
+  Axz_rhs =           f * Axz_rhs+ alpn1 *( trK * Axz  - TWO * fxz )+ &
+                    Axx * betaxz +   Axy * betayz                   + &
+                                     Ayz * betayx +   Azz * betazx  + &
+             F1o3 * Axz * div_beta                -   Axz * betayy      !rhs for Aij
+
+! Compute trace of S_ij
+
+  S =  f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
+     TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
+
+  trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK         + &
+                gupxx * fxx + gupyy * fyy + gupzz * fzz   + &
+        TWO * ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + &
+       FOUR * PI * ( rho + S ))                                !rhs for trK
   
 !!!! gauge variable part
 
@@ -1000,15 +948,15 @@
 !!!!!!!!!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): stencil coefficients sum to zero,
+! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
 ! so the constant offset has no effect on dissipation.
 
-  call lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
   call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
   call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
-  call lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
   call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
-  call lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
+  call lopsided_kodis(ex,X,Y,Z,gzz,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/bssn_rhs.h

@@ -32,19 +32,6 @@
 #define f_compute_rhs_Z4c_ss compute_rhs_z4c_ss_
 #define f_compute_constraint_fr compute_constraint_fr_
 #endif
-
-#ifdef __cplusplus
-extern "C"
-{
-#endif
-        void f_bssn_rhs_kernel_timing_reset();
-        int f_bssn_rhs_kernel_timing_bucket_count();
-        const double *f_bssn_rhs_kernel_timing_local_seconds();
-        const char *f_bssn_rhs_kernel_timing_label(int);
-#ifdef __cplusplus
-}
-#endif
-
 extern "C"
 {
         int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z

AMSS_NCKU_source/bssn_rhs_c.C

@@ -2,88 +2,12 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
-#include <time.h>
 // 0-based i,j,k
 // #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
 // ex(1)=nx, ex(2)=ny, ex(3)=nz
 
 // 用法：a[ IDX_F(i,j,k,nx,ny) ]
 
-#ifndef BSSN_KERNEL_FINE_TIMING
-#define BSSN_KERNEL_FINE_TIMING 0
-#endif
-
-#if BSSN_KERNEL_FINE_TIMING
-namespace rhs_kernel_timing
-{
-    enum Bucket
-    {
-        KB_SETUP_DERIVS = 0,
-        KB_GEOM_GAMMA,
-        KB_RICCI_METRIC,
-        KB_CHI_LAPSE,
-        KB_AIJ_TRK_GAUGE,
-        KB_KO_CONSTRAINT,
-        KB_COUNT
-    };
-
-    static double local_bucket_seconds[KB_COUNT];
-
-    static const char *bucket_labels[KB_COUNT] =
-    {
-        "setup_derivs",
-        "geom_gamma",
-        "ricci_metric",
-        "chi_lapse",
-        "aij_trk_gauge",
-        "ko_constraint"
-    };
-
-    static inline double now_seconds()
-    {
-        struct timespec ts;
-        clock_gettime(CLOCK_MONOTONIC, &ts);
-        return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
-    }
-}
-
-extern "C" void f_bssn_rhs_kernel_timing_reset()
-{
-    for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
-        rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
-}
-
-extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
-{
-    return rhs_kernel_timing::KB_COUNT;
-}
-
-extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
-{
-    return rhs_kernel_timing::local_bucket_seconds;
-}
-
-extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
-{
-    if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
-        return "unknown";
-    return rhs_kernel_timing::bucket_labels[bucket_index];
-}
-
-#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
-#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
-    rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
-        rhs_kernel_timing::now_seconds() - (var_name)
-#else
-extern "C" void f_bssn_rhs_kernel_timing_reset() {}
-extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
-extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
-extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
-
-#define RHS_KERNEL_TIMER_DECL(var_name)
-#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
-#endif
-
 // C function that calculates the right-hand side for BSSN equations
 int f_compute_rhs_bssn(int *ex, double &T, 
                        double *X, double *Y, double *Z,
@@ -178,7 +102,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
     dY = Y[1] - Y[0];
     dZ = Z[1] - Z[0];
 
-        RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
         // 1ms //
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
@@ -218,8 +141,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
                         + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
         }
-        RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
-        RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
         // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
         for(int i=0;i<all;i+=1){
             double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
@@ -362,6 +283,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                 + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
+            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
+            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
+
             Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
                 TWO * alpn1[i] * (
                 -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
@@ -391,8 +315,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                             + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                         );
         }
-        RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
-        RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
         // 22.3ms //
         fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
         X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
@@ -410,6 +332,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
             double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
             double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
             double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
+            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
 
             double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                     + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
@@ -763,74 +686,69 @@ int f_compute_rhs_bssn(int *ex, double &T,
                     + Gamxyz[i] * gzzx[i] + Gamyyz[i] * gzzy[i] + Gamzyz[i] * gzzz[i]
                 );
         }
-        RHS_KERNEL_TIMER_ADD(KB_RICCI_METRIC, timer_ricci_metric);
 
-        RHS_KERNEL_TIMER_DECL(timer_chi_lapse);
         // 22.3ms //
             fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 7ms //
         for (int i=0;i<all;i+=1) {
-            const double inv_chin1 = ONE / chin1[i];
+            fxx[i] = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
-            const double half_inv_chin1 = HALF * inv_chin1;
+            fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
-            const double scaled_inv = F3o2 * inv_chin1;
+            fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
-            const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
+            fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
-            const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
+            fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
-            const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
+            fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
-            const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
+            f[i] =
-            const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
+                gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
-            const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
+                + gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
-            const double ricci_chi =
+                + gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
-                gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
+                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
-                + gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
+                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
-                + gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
+                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-                + TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-                + TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-                + TWO * gupyz[i] * (cyz - scaled_inv * chiy[i] * chiz[i]);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            f[i] = ricci_chi;
-            Rxx[i] = Rxx[i] + ( cxx - half_inv_chin1 * chix[i] * chix[i] + (dxx[i] + ONE) * ricci_chi ) * half_inv_chin1;
-            Ryy[i] = Ryy[i] + ( cyy - half_inv_chin1 * chiy[i] * chiy[i] + (dyy[i] + ONE) * ricci_chi ) * half_inv_chin1;
-            Rzz[i] = Rzz[i] + ( czz - half_inv_chin1 * chiz[i] * chiz[i] + (dzz[i] + ONE) * ricci_chi ) * half_inv_chin1;
 
-            Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
+            Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
-            Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
+            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
-            Ryz[i] = Ryz[i] + ( cyz - half_inv_chin1 * chiy[i] * chiz[i] + gyz[i] * ricci_chi ) * half_inv_chin1;
+            Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
         }
 
         // 24ms //
         fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
+        fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 6ms //
         for (int i=0;i<all;i+=1) {
-            const double inv_chin1 = ONE / chin1[i];
+            /* gxxx,gxxy,gxxz (这里是“升指标后的chi导数/chi”那类量，你沿用原变量名即可) */
-            const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
+            gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
-            const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
+            gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
-            const double gchi_z = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) * inv_chin1;
+            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
 
             /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) * inv_chin1) - (dxx[i] + ONE) * gchi_x ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_y ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_z ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_x ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) * inv_chin1) - (dyy[i] + ONE) * gchi_y ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_z ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_x ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_y ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) * inv_chin1) - (dzz[i] + ONE) * gchi_z ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1)      - gxy[i] * gchi_x ) * HALF;
+            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
-            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1)      - gxy[i] * gchi_y ) * HALF;
+            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
-            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gchi_z ) * HALF;
+            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gxxz[i] ) * HALF;
 
-            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1)      - gxz[i] * gchi_x ) * HALF;
+            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] / chin1[i])      - gxz[i] * gxxx[i] ) * HALF;
-            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gchi_y ) * HALF;
+            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gxxy[i] ) * HALF;
-            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] * inv_chin1)      - gxz[i] * gchi_z ) * HALF;
+            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i])      - gxz[i] * gxxz[i] ) * HALF;
 
-            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gchi_x ) * HALF;
+            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gxxx[i] ) * HALF;
-            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1)      - gyz[i] * gchi_y ) * HALF;
+            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i])      - gyz[i] * gxxy[i] ) * HALF;
-            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] * inv_chin1)      - gyz[i] * gchi_z ) * HALF;
+            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i])      - gyz[i] * gxxz[i] ) * HALF;
 
             /* fxx..fyz 修正：减去 Γ * ∂Lap */
             fxx[i] = fxx[i] - Gamxxx[i] * Lapx[i] - Gamyxx[i] * Lapy[i] - Gamzxx[i] * Lapz[i];
@@ -844,8 +762,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                     +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
         }
-        RHS_KERNEL_TIMER_ADD(KB_CHI_LAPSE, timer_chi_lapse);
-        RHS_KERNEL_TIMER_DECL(timer_aij_trk_gauge);
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
             const double divb = betaxx[i] + betayy[i] + betazz[i];
@@ -1098,12 +1014,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
             betaz_rhs[i] = FF * dtSfz[i];
 
             reta[i] =
-                gupxx[i] * chix[i] * chix[i]
+                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
-                + gupyy[i] * chiy[i] * chiy[i]
+                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
-                + gupzz[i] * chiz[i] * chiz[i]
+                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
-                + TWO * ( gupxy[i] * chix[i] * chiy[i]
+                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
-                        + gupxz[i] * chix[i] * chiz[i]
+                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
-                        + gupyz[i] * chiy[i] * chiz[i] );
+                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
 
             #if (GAUGE == 2)
             reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
@@ -1116,12 +1032,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #elif (GAUGE == 4 || GAUGE == 5)
             reta[i] =
-                gupxx[i] * chix[i] * chix[i]
+                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
-                + gupyy[i] * chiy[i] * chiy[i]
+                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
-                + gupzz[i] * chiz[i] * chiz[i]
+                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
-                + TWO * ( gupxy[i] * chix[i] * chiy[i]
+                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
-                        + gupxz[i] * chix[i] * chiz[i]
+                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
-                        + gupyz[i] * chiy[i] * chiz[i] );
+                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
 
             #if (GAUGE == 4)
             reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
@@ -1146,8 +1062,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #endif
         }
-        RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
-        RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
         // advection + KO dissipation with shared symmetry buffer
         lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
         lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
@@ -1225,6 +1139,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
             fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
             fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
+        }
         // 7ms //
         for (int i=0;i<all;i+=1) {
             gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
@@ -1278,8 +1193,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
             movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
         }
-        }
-        RHS_KERNEL_TIMER_ADD(KB_KO_CONSTRAINT, timer_ko_constraint);
 
 
             

AMSS_NCKU_source/bssn_rhs_cuda.h

@@ -1,127 +0,0 @@
-#ifndef BSSN_RHS_CUDA_H
-#define BSSN_RHS_CUDA_H
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-enum {
-    BSSN_CUDA_STATE_COUNT = 24,
-    BSSN_CUDA_MATTER_COUNT = 10
-};
-
-int f_compute_rhs_bssn(int *ex, double &T,
-                       double *X, double *Y, double *Z,
-                       double *chi, double *trK,
-                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
-                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
-                       double *Gamx, double *Gamy, double *Gamz,
-                       double *Lap, double *betax, double *betay, double *betaz,
-                       double *dtSfx, double *dtSfy, double *dtSfz,
-                       double *chi_rhs, double *trK_rhs,
-                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
-                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
-                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
-                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
-                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
-                       double *rho, double *Sx, double *Sy, double *Sz,
-                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
-                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
-                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
-                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
-                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
-                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
-                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
-                       int &Symmetry, int &Lev, double &eps, int &co);
-
-int bssn_cuda_rk4_substep(void *block_tag,
-                          int *ex, double *X, double *Y, double *Z,
-                          double **state_host_in,
-                          double **state_host_out,
-                          double **matter_host,
-                          const double *propspeed,
-                          const double *soa_flat,
-                          const double *bbox,
-                          double &dT,
-                          double &T,
-                          int &RK4,
-                          int &apply_bam_bc,
-                          int &Symmetry,
-                          int &Lev,
-                          double &eps,
-                          int &co,
-                          int &use_zero_matter,
-                          int &keep_resident_state,
-                          int &apply_enforce_ga,
-                          double &chitiny);
-
-int bssn_cuda_copy_state_region_to_host(void *block_tag,
-                                        int state_index,
-                                        double *host_state,
-                                        int *ex,
-                                        int i0, int j0, int k0,
-                                        int sx, int sy, int sz);
-
-int bssn_cuda_copy_state_region_from_host(void *block_tag,
-                                          int state_index,
-                                          double *host_state,
-                                          int *ex,
-                                          int i0, int j0, int k0,
-                                          int sx, int sy, int sz);
-
-int bssn_cuda_download_resident_state(void *block_tag,
-                                      int *ex,
-                                      double **state_host_out);
-
-int bssn_cuda_download_constraint_outputs(int *ex,
-                                          double **constraint_host_out);
-
-int bssn_cuda_pack_state_region_to_host_buffer(void *block_tag,
-                                               int state_index,
-                                               double *host_buffer,
-                                               int *ex,
-                                               int i0, int j0, int k0,
-                                               int sx, int sy, int sz);
-
-int bssn_cuda_unpack_state_region_from_host_buffer(void *block_tag,
-                                                   int state_index,
-                                                   double *host_buffer,
-                                                   int *ex,
-                                                   int i0, int j0, int k0,
-                                                   int sx, int sy, int sz);
-
-int bssn_cuda_pack_state_batch_to_host_buffer(void *block_tag,
-                                              int state_count,
-                                              double *host_buffer,
-                                              int *ex,
-                                              int i0, int j0, int k0,
-                                              int sx, int sy, int sz);
-
-int bssn_cuda_unpack_state_batch_from_host_buffer(void *block_tag,
-                                                  int state_count,
-                                                  double *host_buffer,
-                                                  int *ex,
-                                                  int i0, int j0, int k0,
-                                                  int sx, int sy, int sz);
-
-int bssn_cuda_download_state_subset(void *block_tag,
-                                    int *ex,
-                                    int subset_count,
-                                    const int *state_indices,
-                                    double **state_host_out);
-
-int bssn_cuda_upload_state_subset(void *block_tag,
-                                  int *ex,
-                                  int subset_count,
-                                  const int *state_indices,
-                                  double **state_host_in);
-
-int bssn_cuda_has_resident_state(void *block_tag);
-
-void bssn_cuda_release_step_ctx(void *block_tag);
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif

AMSS_NCKU_source/diff_newwb.f90

@@ -1513,7 +1513,6 @@
   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 :: 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
@@ -1566,47 +1565,9 @@
   fxz = ZEO
   fyz = ZEO
 
-  i_core_min = max(1, imin+2)
-  i_core_max = min(ex(1), imax-2)
-  j_core_min = max(1, jmin+2)
-  j_core_max = min(ex(2), jmax-2)
-  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
 !

AMSS_NCKU_source/fdderivs_c.C

@@ -141,26 +141,12 @@ void fdderivs(const int ex[3],
     const int j4_hi = ex2 - 3;
     const int k4_hi = ex3 - 3;
 
-    /*
-     * Strategy A:
-     * Avoid redundant work in overlap of 2nd/4th-order regions.
-     * Only compute 2nd-order on shell points that are NOT overwritten by
-     * the 4th-order pass.
-     */
-    const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
-
     if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
         for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
             const int kF = k0 + 1;
             for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
                 const int jF = j0 + 1;
                 for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
-                    if (has4 &&
-                        i0 >= i4_lo && i0 <= i4_hi &&
-                        j0 >= j4_lo && j0 <= j4_hi &&
-                        k0 >= k4_lo && k0 <= k4_hi) {
-                        continue;
-                    }
                     const int iF = i0 + 1;
                     const size_t p = idx_ex(i0, j0, k0, ex);
 
@@ -207,7 +193,7 @@ void fdderivs(const int ex[3],
         }
     }
 
-    if (has4) {
+    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
         for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
             const int kF = k0 + 1;
             for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {

AMSS_NCKU_source/fmisc.f90

@@ -1514,81 +1514,6 @@ f_out = f_out*dX*dY*dZ
   return
 
   end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
-  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
-
-  implicit none
-!~~~~~~> Input parameters:
-  integer,intent(in ):: ex(1:3)
-  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
-  integer,intent(in)::gw
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
-  real*8, intent(out) :: f_out(7)
-!~~~~~~> Other variables:
-
-  real*8            :: dX, dY, dZ
-  integer::imin,jmin,kmin
-  integer::imax,jmax,kmax
-  integer::i,j,k
-  real*8 :: s1,s2,s3,s4,s5,s6,s7
-
-  dX = X(2) - X(1)
-  dY = Y(2) - Y(1)
-  dZ = Z(2) - Z(1)
-
-! for ghost zone
-   imin = gw+1
-   jmin = gw+1
-   kmin = gw+1
-
-   imax = ex(1) - gw
-   jmax = ex(2) - gw
-   kmax = ex(3) - gw
-
-!for patch boundary (i.e., not ghost boundary)
-
-if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
-if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
-if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
-if(dabs(X(1)-xmin) < dX) imin = 1
-if(dabs(Y(1)-ymin) < dY) jmin = 1
-if(dabs(Z(1)-zmin) < dZ) kmin = 1
-
-  s1 = 0.d0
-  s2 = 0.d0
-  s3 = 0.d0
-  s4 = 0.d0
-  s5 = 0.d0
-  s6 = 0.d0
-  s7 = 0.d0
-
-  do k=kmin,kmax
-    do j=jmin,jmax
-!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
-      do i=imin,imax
-        s1 = s1 + f1(i,j,k)*f1(i,j,k)
-        s2 = s2 + f2(i,j,k)*f2(i,j,k)
-        s3 = s3 + f3(i,j,k)*f3(i,j,k)
-        s4 = s4 + f4(i,j,k)*f4(i,j,k)
-        s5 = s5 + f5(i,j,k)*f5(i,j,k)
-        s6 = s6 + f6(i,j,k)*f6(i,j,k)
-        s7 = s7 + f7(i,j,k)*f7(i,j,k)
-      enddo
-    enddo
-  enddo
-
-  f_out(1) = s1*dX*dY*dZ
-  f_out(2) = s2*dX*dY*dZ
-  f_out(3) = s3*dX*dY*dZ
-  f_out(4) = s4*dX*dY*dZ
-  f_out(5) = s5*dX*dY*dZ
-  f_out(6) = s6*dX*dY*dZ
-  f_out(7) = s7*dX*dY*dZ
-
-  return
-
-  end subroutine l2normhelper7
 !--------------------------------------------------------------------------------------
 ! calculate L2norm especially for shell Blocks
   subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&

AMSS_NCKU_source/fmisc.h

@@ -13,7 +13,6 @@
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
 #define f_l2normhelper l2normhelper
-#define f_l2normhelper7 l2normhelper7
 #define f_l2normhelper_sh l2normhelper_sh
 #define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
@@ -43,7 +42,6 @@
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
 #define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper7 L2NORMHELPER7
 #define f_l2normhelper_sh L2NORMHELPER_SH
 #define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
@@ -73,7 +71,6 @@
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
 #define f_l2normhelper l2normhelper_
-#define f_l2normhelper7 l2normhelper7_
 #define f_l2normhelper_sh l2normhelper_sh_
 #define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
@@ -167,15 +164,6 @@ extern "C"
 						double *, double &, int &);
 }
 
-extern "C"
-{
-	void f_l2normhelper7(int *, double *, double *, double *,
-						 double &, double &, double &,
-						 double &, double &, double &,
-						 double *, double *, double *, double *,
-						 double *, double *, double *, double *, int &);
-}
-
 extern "C"
 {
 	void f_l2normhelper_sh(int *, double *, double *, double *,

AMSS_NCKU_source/macrodef.h

@@ -29,16 +29,6 @@
 
 #define REGLEV 0
 
-#define BSSN_FINE_TIMING 0
-
-#define BSSN_FINE_TIMING_EVERY 1
-
-#define BSSN_FINE_TIMING_TOPN 8
-
-#define BSSN_KERNEL_FINE_TIMING 0
-
-#define BSSN_ENABLE_STDIN_ABORT_POLL 0
-
 //#define USE_GPU
 
 //#define CHECKDETAIL
@@ -98,21 +88,6 @@
 //     0: for every level;
 //     1: for all
 //
-// define BSSN_FINE_TIMING
-//     enable fine-grained per-timestep timing monitor
-//
-// define BSSN_FINE_TIMING_EVERY
-//     report timing every N coarse timesteps
-//
-// define BSSN_FINE_TIMING_TOPN
-//     number of hottest timing buckets shown in stdout
-//
-// define BSSN_KERNEL_FINE_TIMING
-//     enable split timing inside compute_rhs_bssn
-//
-// define BSSN_ENABLE_STDIN_ABORT_POLL
-//     poll stdin and broadcast abort flag every coarse step
-//
 // define USE_GPU
 //     use gpu or not
 //
@@ -167,3 +142,4 @@
 #define TINY 1e-10
 
 #endif   /* MICRODEF_H */
+

AMSS_NCKU_source/makefile

@@ -13,15 +13,12 @@ POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
 ##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
 PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 
-ifeq ($(TOOLCHAIN),intel)
-OMP_FLAG = -qopenmp
-
 ifeq ($(PGO_MODE),instrument)
-## Intel Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
+## 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 $(MKL_INC) $(INTERP_LB_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp $(MKL_INC) $(POLINT6_FLAG)
+              -align array64byte -fpp -I${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
@@ -29,24 +26,9 @@ else
 
 
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc $(MKL_INC) $(INTERP_LB_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp $(MKL_INC) $(POLINT6_FLAG)
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-endif
-
-TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(TP_PROFDATA) \
-              -Dfortran3 -Dnewc $(MKL_INC)
-else
-## NVHPC defaults: mpicc/mpicxx/mpifort wrappers
-## PGO_MODE is ignored in this branch.
-OMP_FLAG = -mp
-CXXAPPFLAGS = -O3 -tp=host -Mcache_align -Mfma \
-              -Dfortran3 -Dnewc $(MKL_INC) $(INTERP_LB_FLAGS)
-f90appflags = -O3 -tp=host -Mcache_align -Mfma -Mpreprocess \
-              $(MKL_INC) $(POLINT6_FLAG)
-TP_OPTFLAGS = -O3 -tp=host -Mcache_align -Mfma \
-              -Dfortran3 -Dnewc $(MKL_INC)
 endif
 
 .SUFFIXES: .o .f90 .C .for .cu
@@ -63,14 +45,6 @@ endif
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
-# CUDA rewrite of BSSN RHS (drop-in replacement for bssn_rhs_c + stencil helpers)
-bssn_rhs_cuda.o: bssn_rhs_cuda.cu bssn_rhs.h macrodef.h
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
-
-# CUDA rewrite of Z4C Cartesian RHS
-z4c_rhs_cuda.o: z4c_rhs_cuda.cu z4c_rhs_cuda.h bssn_rhs.h macrodef.h ricci_gamma.h
-	$(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 $@
@@ -90,78 +64,40 @@ lopsided_c.o: lopsided_c.C
 lopsided_kodis_c.o: lopsided_kodis_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-z4c_rhs_c.o: z4c_rhs_c.C
+interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
-#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
+TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(TP_PROFDATA) \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
 
 TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) $(OMP_FLAG) -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) $(OMP_FLAG) -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 # Input files
 
-## CUDA BSSN RHS switch
-##   1 : use the rewritten CUDA bssn_rhs backend
-##   0 : keep the normal CPU/Fortran selection below
-USE_CUDA_BSSN ?= 0
-USE_CUDA_Z4C ?= 0
-
-CXXAPPFLAGS += -DUSE_CUDA_BSSN=$(USE_CUDA_BSSN)
-CUDA_APP_FLAGS += -DUSE_CUDA_BSSN=$(USE_CUDA_BSSN)
-CXXAPPFLAGS += -DUSE_CUDA_Z4C=$(USE_CUDA_Z4C)
-CUDA_APP_FLAGS += -DUSE_CUDA_Z4C=$(USE_CUDA_Z4C)
-
 ## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
 ifeq ($(USE_CXX_KERNELS),0)
 # Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES_CPU =
+CFILES =
 else
 # C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES_CPU = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
-endif
-
-CFILES_CUDA_BSSN = bssn_rhs_cuda.o
-
-ifeq ($(USE_CUDA_BSSN),1)
-CFILES = $(CFILES_CUDA_BSSN)
-else
-CFILES = $(CFILES_CPU)
-endif
-
-ifeq ($(USE_CUDA_Z4C),1)
-CFILES += z4c_rhs_cuda.o
-Z4C_F90_OBJ =
-else ifeq ($(USE_CXX_Z4C_KERNELS),1)
-CFILES += z4c_rhs_c.o
-Z4C_F90_OBJ =
-else
-Z4C_F90_OBJ = Z4c_rhs.o
 endif
 
 ## RK4 kernel switch (independent from USE_CXX_KERNELS)
 ifeq ($(USE_CXX_RK4),1)
-RK4_C_OBJ = rungekutta4_rout_c.o
+CFILES += rungekutta4_rout_c.o
 RK4_F90_OBJ =
 else
-RK4_C_OBJ =
 RK4_F90_OBJ = rungekutta4_rout.o
 endif
 
-CFILES += $(RK4_C_OBJ)
-ABE_CUDA_CFILES = $(CFILES_CUDA_BSSN) z4c_rhs_cuda.o $(RK4_C_OBJ)
-
-ABE_LDLIBS = $(LDLIBS)
-ifeq ($(USE_CUDA_BSSN),1)
-ABE_LDLIBS += -lcudart $(CUDA_LIB_PATH)
-endif
-ifeq ($(USE_CUDA_Z4C),1)
-ABE_LDLIBS += -lcudart $(CUDA_LIB_PATH)
-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\
@@ -169,7 +105,7 @@ C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.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\
+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\
 	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
 	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
@@ -183,7 +119,7 @@ F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
 	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
 	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
            getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
-           fadmquantites_bssn.o $(Z4C_F90_OBJ) Z4c_rhs_ss.o point_diff_new_sh.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\
 	   bssn2adm.o adm_constraint.o adm_ricci_gamma.o\
@@ -207,10 +143,10 @@ initial_guess.o Newton.o Jacobian.o ilucg.o IntPnts0.o IntPnts.o
 
 TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o 
 
-#CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
+CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
 
 # file dependences
-$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(ABE_CUDA_CFILES) $(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\
@@ -221,7 +157,7 @@ $(C++FILES): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     empart.h NullNews.h kodiss.h Parallel_bam.h ricci_gamma.h\
              initial_null2.h NullShellPatch2.h 
              
-#$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
+$(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h\
 	     misc.h monitor.h MyList.h Parallel.h MPatch.h prolongrestrict.h\
 	     rungekutta4_rout.h var.h bssn_rhs.h sommerfeld_rout.h\
 	     cgh.h surface_integral.h ShellPatch.h shellfunctions.h perf.h\
@@ -233,7 +169,7 @@ $(C++FILES): 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) $(CFILES) $(ABE_CUDA_CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
 
 TwoPunctureFILES: TwoPunctures.h
 
@@ -243,18 +179,13 @@ misc.o : zbesh.o
 
 # projects
 ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(ABE_LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
 	
-ABE_CUDA: USE_CUDA_BSSN=1
+ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-ABE_CUDA: USE_CUDA_Z4C=1
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
-ABE_CUDA: $(C++FILES) $(ABE_CUDA_CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(ABE_CUDA_CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)
-	
-#ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
-#	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(TP_OPTFLAGS) $(OMP_FLAG) -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
-	rm *.o ABE ABE_CUDA ABEGPU TwoPunctureABE make.log -f
+	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,7 +1,28 @@
-## Toolchain selection
+## GCC version (commented out)
-##   nvhpc : NVIDIA HPC SDK + CUDA-aware MPI (default)
+## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-##   intel : Intel oneAPI toolchain (legacy path)
+## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-TOOLCHAIN ?= nvhpc
+## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
+
+## Intel oneAPI version with oneMKL (Optimized for performance)
+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 -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
@@ -22,70 +43,23 @@ else
 INTERP_LB_FLAGS =
 endif
 
-MKLROOT ?= /home/intel/oneapi/mkl/latest
-MKL_LIBDIR ?= $(MKLROOT)/lib/intel64
-MKL_INC ?= -I$(MKLROOT)/include
-
-NVHPC_ROOT ?= /home/nvidia/hpc_sdk/Linux_x86_64/25.11
-CUDA_HOME  ?= $(NVHPC_ROOT)/cuda
-CUDA_ARCH  ?= sm_80
-
 ## Kernel implementation switch
 ##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
 ##   0           : fall back to original Fortran kernels
 USE_CXX_KERNELS ?= 1
 
-## Z4C Cartesian RHS kernel switch
-##   1 (default) : use C++ rewrite of Z4c_rhs (main Cartesian path faster)
-##   0           : use original Fortran Z4c_rhs.o
-USE_CXX_Z4C_KERNELS ?= 1
-
 ## RK4 kernel implementation switch
 ##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
 ##   0           : use original Fortran rungekutta4_rout.o
 USE_CXX_RK4 ?= 1
 
-## 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 $(TBBMALLOC_SO) -Wl,--as-needed
-else
-TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
-endif
-
-ifeq ($(TOOLCHAIN),intel)
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
 CLINKER      = mpiicpx
-filein  = -I/usr/include/ $(MKL_INC) -I$(CUDA_HOME)/include
-LDLIBS       = -L$(MKL_LIBDIR) -Wl,-rpath,$(MKL_LIBDIR) \
-               -lmkl_intel_lp64 -lmkl_sequential -lmkl_core \
-               -lifcore -limf -liomp5 -lpthread -lm -ldl \
-               -L$(CUDA_HOME)/lib64 -Wl,-rpath,$(CUDA_HOME)/lib64 -lcuda -lcudart
-else ifeq ($(TOOLCHAIN),nvhpc)
-f90          = mpifort
-f77          = mpifort
-CXX          = mpicxx
-CC           = mpicc
-CLINKER      = mpicxx
 
-filein       = -I/usr/include/ $(MKL_INC) -I$(CUDA_HOME)/include
+Cu = nvcc
-LDLIBS       = -L$(MKL_LIBDIR) -Wl,-rpath,$(MKL_LIBDIR) \
+CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
-               -lmkl_intel_lp64 -lmkl_sequential -lmkl_core \
+#CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
-               -lpthread -lm -ldl \
+CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc
-               -L$(CUDA_HOME)/lib64 -Wl,-rpath,$(CUDA_HOME)/lib64 -lcuda -lcudart \
-               -fortranlibs
-endif
-
-ifeq ($(USE_TBBMALLOC),1)
-LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
-endif
-
-Cu = $(NVHPC_ROOT)/compilers/bin/nvcc
-CUDA_LIB_PATH = -L$(CUDA_HOME)/lib64 -I$(CUDA_HOME)/include
-CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc -arch=$(CUDA_ARCH)

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1956,13 +1956,11 @@
 
   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 :: tmp_xyz_line(extc(1))   ! 存储整条 X 线上完成 Y 向融合后的结果
   real*8 :: v1, v2, v3, v4, v5, v6
-  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max,ic_min,ic_max,kc_min,kc_max
+  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_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
+  real*8 :: tmp_z_slab(extc(1), extc(2))  ! 分配在 k 循环外
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2065,41 +2063,24 @@
      endif
   enddo
 
-  ic_min = minval(cix(imino:imaxo))
+  maxcx = maxval(cix(imino:imaxo))
-  ic_max = maxval(cix(imino:imaxo))
+  maxcy = maxval(ciy(jmino:jmaxo))
-  jc_min = minval(ciy(jmino:jmaxo))
+  maxcz = maxval(ciz(kmino:kmaxo))
-  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
+jc_min = minval(ciy(jmino:jmaxo))
+jc_max = maxval(ciy(jmino:jmaxo))
 
 do k = kmino, kmaxo
     pz = piz(k); kc = ciz(k)
     ! --- Pass 1: Z 方向，只算一次 ---
-    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
+    do iy = jc_min-3, jc_max+3   ! 仅需的 iy 范围
-        do ii = ic_min-2, ic_max+3  ! 仅需的 ii 范围（对应 cix-2:cix+3）
+        do ii = imini-3, imaxi+3  ! 仅需的 ii 范围
             tmp_z_slab(ii, iy) = sum(WC(:,pz) * funcc(ii, iy, kc-2:kc+3))
         end do
     end do
@@ -2107,7 +2088,7 @@ do k = kmino, kmaxo
     do j = jmino, jmaxo
         py = piy(j); jc = ciy(j)
         ! --- Pass 2: Y 方向 ---
-        do ii = ic_min-2, ic_max+3
+        do ii = imini-3, imaxi+3
             tmp_xyz_line(ii) = sum(WC(:,py) * tmp_z_slab(ii, jc-2:jc+3))
         end do
         ! --- Pass 3: X 方向 ---
@@ -2370,12 +2351,9 @@ end do
 
   real*8,dimension(3) :: CD,FD
 
-  real*8 :: tmp_xz_plane(-1:extf(1), 6)
+  real*8 :: tmp_xz_plane(extf(1), 6) 
-  real*8 :: tmp_x_line(-1:extf(1))
+  real*8 :: tmp_x_line(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"
@@ -2455,34 +2433,7 @@ end do
           stop
   endif
 
-  ! 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
@@ -2494,7 +2445,7 @@ do k = kmino, kmaxo
         ! 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
+        do ii = 1, extf(1)
             ! 预计算当前 j 对应的 6 行在 Z 方向的压缩结果
             ! 这里直接硬编码 jj 的偏移，彻底消除一层循环
             tmp_xz_plane(ii, 1) = C1*(funff(ii,fj-2,fk-2)+funff(ii,fj-2,fk+3)) + &
@@ -2519,7 +2470,7 @@ do k = kmino, kmaxo
 
         ! 优化点 2: 同样向量化 Y 方向压缩
         !DIR$ VECTOR ALWAYS
-        do ii = ii_lo, ii_hi
+        do ii = 1, extf(1)
             tmp_x_line(ii) = C1*(tmp_xz_plane(ii, 1) + tmp_xz_plane(ii, 6)) + &
                             C2*(tmp_xz_plane(ii, 2) + tmp_xz_plane(ii, 5)) + &
                             C3*(tmp_xz_plane(ii, 3) + tmp_xz_plane(ii, 4))

AMSS_NCKU_source/surface_integral.C

@@ -36,14 +36,7 @@ using namespace std;
 //| Constructor
 //|============================================================================
 
-surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry),
+surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry)
-                                                    wave_cache_spinw(-1),
-                                                    wave_cache_maxl(-1),
-                                                    wave_cache_modes(0),
-                                                    wave_theta_pos(0),
-                                                    wave_theta_neg(0),
-                                                    wave_phi_cos(0),
-                                                    wave_phi_sin(0)
 {
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
   MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
@@ -189,7 +182,6 @@ surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry),
 //|============================================================================
 surface_integral::~surface_integral()
 {
-  clear_wave_cache();
   delete[] nx_g;
   delete[] ny_g;
   delete[] nz_g;
@@ -198,65 +190,6 @@ surface_integral::~surface_integral()
   delete[] wtcostheta;
 #endif
 }
-void surface_integral::clear_wave_cache()
-{
-  delete[] wave_theta_pos;
-  delete[] wave_theta_neg;
-  delete[] wave_phi_cos;
-  delete[] wave_phi_sin;
-  wave_theta_pos = 0;
-  wave_theta_neg = 0;
-  wave_phi_cos = 0;
-  wave_phi_sin = 0;
-  wave_cache_spinw = -1;
-  wave_cache_maxl = -1;
-  wave_cache_modes = 0;
-}
-void surface_integral::build_wave_cache(int spinw, int maxl)
-{
-  if (wave_cache_spinw == spinw && wave_cache_maxl == maxl && wave_theta_pos && wave_theta_neg && wave_phi_cos && wave_phi_sin)
-    return;
-
-  clear_wave_cache();
-
-  int modes = 0;
-  for (int pl = spinw; pl < maxl + 1; pl++)
-    for (int pm = -pl; pm < pl + 1; pm++)
-      modes++;
-
-  wave_theta_pos = new double[modes * N_theta];
-  wave_theta_neg = new double[modes * N_theta];
-  wave_phi_cos = new double[modes * N_phi];
-  wave_phi_sin = new double[modes * N_phi];
-
-  int countlm = 0;
-  for (int pl = spinw; pl < maxl + 1; pl++)
-    for (int pm = -pl; pm < pl + 1; pm++)
-    {
-      const double prefactor = sqrt((2 * pl + 1.0) / 4.0 / PI);
-      for (int i = 0; i < N_theta; i++)
-      {
-#ifdef GaussInt
-        const double weight = wtcostheta[i];
-#else
-        const double weight = 1.0;
-#endif
-        wave_theta_pos[countlm * N_theta + i] = prefactor * misc::Wigner_d_function(pl, pm, spinw, arcostheta[i]) * weight;
-        wave_theta_neg[countlm * N_theta + i] = prefactor * misc::Wigner_d_function(pl, pm, spinw, -arcostheta[i]) * weight;
-      }
-      for (int j = 0; j < N_phi; j++)
-      {
-        const double phase = pm * (j + 0.5) * dphi;
-        wave_phi_cos[countlm * N_phi + j] = cos(phase);
-        wave_phi_sin[countlm * N_phi + j] = sin(phase);
-      }
-      countlm++;
-    }
-
-  wave_cache_spinw = spinw;
-  wave_cache_maxl = maxl;
-  wave_cache_modes = modes;
-}
 //|----------------------------------------------------------------
 //  spin weighted spinw component of psi4, general routine
 //  l takes from spinw to maxl; m takes from -l to l
@@ -331,39 +264,6 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     lpsy = 8;
 
   double psi4RR, psi4II;
-  if (Symmetry == 0 || Symmetry == 1)
-  {
-    build_wave_cache(spinw, maxl);
-    for (n = Nmin; n <= Nmax; n++)
-    {
-      i = int(n / N_phi);
-      j = n - i * N_phi;
-
-      const double psi4RR0 = shellf[InList * n];
-      const double psi4II0 = shellf[InList * n + 1];
-      const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
-      const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
-      for (int countlm = 0; countlm < wave_cache_modes; countlm++)
-      {
-        const int theta_idx = countlm * N_theta + i;
-        const int phi_idx = countlm * N_phi + j;
-        const double theta_pos = wave_theta_pos[theta_idx];
-        const double cosmphi_here = wave_phi_cos[phi_idx];
-        const double sinmphi_here = wave_phi_sin[phi_idx];
-
-        RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
-        IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
-        if (Symmetry == 1)
-        {
-          const double theta_neg = wave_theta_neg[theta_idx];
-          RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
-          IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
-        }
-      }
-    }
-  }
-  else
-  {
   for (n = Nmin; n <= Nmax; n++)
   {
     //       need round off always
@@ -448,7 +348,6 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
         countlm++; // no sanity check for countlm and NN which should be noted in the input parameters
       }
   }
-  }
 
   for (int ii = 0; ii < NN; ii++)
   {
@@ -567,39 +466,6 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     lpsy = 8;
 
   double psi4RR, psi4II;
-  if (Symmetry == 0 || Symmetry == 1)
-  {
-    build_wave_cache(spinw, maxl);
-    for (n = Nmin; n <= Nmax; n++)
-    {
-      i = int(n / N_phi);
-      j = n - i * N_phi;
-
-      const double psi4RR0 = shellf[InList * n];
-      const double psi4II0 = shellf[InList * n + 1];
-      const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
-      const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
-      for (int countlm = 0; countlm < wave_cache_modes; countlm++)
-      {
-        const int theta_idx = countlm * N_theta + i;
-        const int phi_idx = countlm * N_phi + j;
-        const double theta_pos = wave_theta_pos[theta_idx];
-        const double cosmphi_here = wave_phi_cos[phi_idx];
-        const double sinmphi_here = wave_phi_sin[phi_idx];
-
-        RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
-        IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
-        if (Symmetry == 1)
-        {
-          const double theta_neg = wave_theta_neg[theta_idx];
-          RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
-          IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
-        }
-      }
-    }
-  }
-  else
-  {
   for (n = Nmin; n <= Nmax; n++)
   {
     //       need round off always
@@ -684,7 +550,6 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
         countlm++; // no sanity check for countlm and NN which should be noted in the input parameters
       }
   }
-  }
 
   for (int ii = 0; ii < NN; ii++)
   {
@@ -2454,7 +2319,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
                                      var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
                                      var *Gmx, var *Gmy, var *Gmz,
                                      var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-                                     double *Rout, monitor *Monitor, bool refresh_mass_fields)
+                                     double *Rout, monitor *Monitor)
 {
   if (myrank == 0 && GH->grids[lev] != 1)
     if (Monitor && Monitor->outfile)
@@ -2464,8 +2329,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
 
   double mass, px, py, pz, sx, sy, sz;
 
-  if (refresh_mass_fields)
-  {
   MyList<Patch> *Pp = GH->PatL[lev];
   while (Pp)
   {
@@ -2489,7 +2352,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
     Pp = Pp->next;
   }
-  }
 
   const int InList = 17;
 
@@ -2719,7 +2581,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
                                      var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
                                      var *Gmx, var *Gmy, var *Gmz,
                                      var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-                                     double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields)
+                                     double *Rout, monitor *Monitor, MPI_Comm Comm_here)
 {
   int lmyrank;
   MPI_Comm_rank(Comm_here, &lmyrank);
@@ -2731,8 +2593,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
 
   double mass, px, py, pz, sx, sy, sz;
 
-  if (refresh_mass_fields)
-  {
   MyList<Patch> *Pp = GH->PatL[lev];
   while (Pp)
   {
@@ -2756,7 +2616,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
     }
     Pp = Pp->next;
   }
-  }
 
   const int InList = 17;
 
@@ -2994,7 +2853,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
                                      var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
                                      var *Gmx, var *Gmy, var *Gmz,
                                      var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-                                     double *Rout, monitor *Monitor, bool refresh_mass_fields)
+                                     double *Rout, monitor *Monitor)
 {
   if (lev != 0)
   {
@@ -3010,8 +2869,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
 
   double mass, px, py, pz, sx, sy, sz;
 
-  if (refresh_mass_fields)
-  {
   MyList<ss_patch> *Pp = GH->PatL;
   while (Pp)
   {
@@ -3046,7 +2903,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
     }
     Pp = Pp->next;
   }
-  }
 
   const int InList = 17;
 
@@ -3272,626 +3128,6 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
   delete[] shellf;
   DG_List->clearList();
 }
-void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
-                                         var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
-                                         var *chi, var *trK,
-                                         var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-                                         var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-                                         var *Gmx, var *Gmy, var *Gmz,
-                                         var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-                                         double *Rout, monitor *Monitor, bool refresh_mass_fields)
-{
-  if (Symmetry != 0 && Symmetry != 1)
-  {
-    surf_Wave(rex, lev, GH, Rpsi4, Ipsi4, spinw, maxl, NN, RP, IP, Monitor);
-    surf_MassPAng(rex, lev, GH, chi, trK,
-                  gxx, gxy, gxz, gyy, gyz, gzz,
-                  Axx, Axy, Axz, Ayy, Ayz, Azz,
-                  Gmx, Gmy, Gmz,
-                  Sfx_rhs, Sfy_rhs, Sfz_rhs,
-                  Rout, Monitor, refresh_mass_fields);
-    return;
-  }
-
-  if (myrank == 0 && GH->grids[lev] != 1)
-    if (Monitor && Monitor->outfile)
-      Monitor->outfile << "WARNING: surface integral on multipatches" << endl;
-    else
-      cout << "WARNING: surface integral on multipatches" << endl;
-
-  if (refresh_mass_fields)
-  {
-    MyList<Patch> *Pp = GH->PatL[lev];
-    while (Pp)
-    {
-      MyList<Block> *BP = Pp->data->blb;
-      while (BP)
-      {
-        Block *cg = BP->data;
-        if (myrank == cg->rank)
-        {
-          f_admmass_bssn(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                         cg->fgfs[chi->sgfn], cg->fgfs[trK->sgfn],
-                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                         cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                         cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                         Symmetry);
-        }
-        if (BP == Pp->data->ble)
-          break;
-        BP = BP->next;
-      }
-      Pp = Pp->next;
-    }
-  }
-
-  const int InList = 19;
-  const int idx_rpsi4 = 0, idx_ipsi4 = 1;
-  const int idx_sfx = 2, idx_sfy = 3, idx_sfz = 4;
-  const int idx_chi = 5, idx_trk = 6;
-  const int idx_gxx = 7, idx_gxy = 8, idx_gxz = 9, idx_gyy = 10, idx_gyz = 11, idx_gzz = 12;
-  const int idx_axx = 13, idx_axy = 14, idx_axz = 15, idx_ayy = 16, idx_ayz = 17, idx_azz = 18;
-
-  MyList<var> *DG_List = new MyList<var>(Rpsi4);
-  DG_List->insert(Ipsi4);
-  DG_List->insert(Sfx_rhs);
-  DG_List->insert(Sfy_rhs);
-  DG_List->insert(Sfz_rhs);
-  DG_List->insert(chi);
-  DG_List->insert(trK);
-  DG_List->insert(gxx);
-  DG_List->insert(gxy);
-  DG_List->insert(gxz);
-  DG_List->insert(gyy);
-  DG_List->insert(gyz);
-  DG_List->insert(gzz);
-  DG_List->insert(Axx);
-  DG_List->insert(Axy);
-  DG_List->insert(Axz);
-  DG_List->insert(Ayy);
-  DG_List->insert(Ayz);
-  DG_List->insert(Azz);
-
-  int n;
-  double *pox[3];
-  for (int ia = 0; ia < 3; ia++)
-    pox[ia] = new double[n_tot];
-  for (n = 0; n < n_tot; n++)
-  {
-    pox[0][n] = rex * nx_g[n];
-    pox[1][n] = rex * ny_g[n];
-    pox[2][n] = rex * nz_g[n];
-  }
-
-  int mp, Lp, Nmin, Nmax;
-  mp = n_tot / cpusize;
-  Lp = n_tot - cpusize * mp;
-  if (Lp > myrank)
-  {
-    Nmin = myrank * mp + myrank;
-    Nmax = Nmin + mp;
-  }
-  else
-  {
-    Nmin = myrank * mp + Lp;
-    Nmax = Nmin + mp - 1;
-  }
-
-  double *shellf = new double[n_tot * InList];
-  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
-
-  double *RP_out = new double[NN];
-  double *IP_out = new double[NN];
-  for (int ii = 0; ii < NN; ii++)
-  {
-    RP_out[ii] = 0.0;
-    IP_out[ii] = 0.0;
-  }
-
-  double Mass_out = 0.0;
-  double ang_outx = 0.0, ang_outy = 0.0, ang_outz = 0.0;
-  double p_outx = 0.0, p_outy = 0.0, p_outz = 0.0;
-  const double f1o8 = 0.125;
-
-  build_wave_cache(spinw, maxl);
-
-  for (n = Nmin; n <= Nmax; n++)
-  {
-    const int base = InList * n;
-    const int i = int(n / N_phi);
-    const int j = n - i * N_phi;
-
-    const double psi4RR0 = shellf[base + idx_rpsi4];
-    const double psi4II0 = shellf[base + idx_ipsi4];
-    const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
-    const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
-    for (int countlm = 0; countlm < wave_cache_modes; countlm++)
-    {
-      const int theta_idx = countlm * N_theta + i;
-      const int phi_idx = countlm * N_phi + j;
-      const double theta_pos = wave_theta_pos[theta_idx];
-      const double cosmphi_here = wave_phi_cos[phi_idx];
-      const double sinmphi_here = wave_phi_sin[phi_idx];
-
-      RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
-      IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
-      if (Symmetry == 1)
-      {
-        const double theta_neg = wave_theta_neg[theta_idx];
-        RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
-        IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
-      }
-    }
-
-    double Chi = shellf[base + idx_chi];
-    double TRK = shellf[base + idx_trk];
-    double Gxx = shellf[base + idx_gxx] + 1.0;
-    double Gxy = shellf[base + idx_gxy];
-    double Gxz = shellf[base + idx_gxz];
-    double Gyy = shellf[base + idx_gyy] + 1.0;
-    double Gyz = shellf[base + idx_gyz];
-    double Gzz = shellf[base + idx_gzz] + 1.0;
-    double axx = shellf[base + idx_axx];
-    double axy = shellf[base + idx_axy];
-    double axz = shellf[base + idx_axz];
-    double ayy = shellf[base + idx_ayy];
-    double ayz = shellf[base + idx_ayz];
-    double azz = shellf[base + idx_azz];
-
-    Chi = 1.0 / (1.0 + Chi);
-    const double Psi = Chi * sqrt(Chi);
-
-#ifdef GaussInt
-    const double theta_weight = wtcostheta[i];
-    Mass_out += (shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n]) * theta_weight;
-#else
-    const double theta_weight = 1.0;
-    Mass_out += shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n];
-#endif
-
-    double detg = Gxx * Gyy * Gzz + Gxy * Gyz * Gxz + Gxz * Gxy * Gyz -
-                  Gxz * Gyy * Gxz - Gxy * Gxy * Gzz - Gxx * Gyz * Gyz;
-    const double gupxx = (Gyy * Gzz - Gyz * Gyz) / detg;
-    const double gupxy = -(Gxy * Gzz - Gyz * Gxz) / detg;
-    const double gupxz = (Gxy * Gyz - Gyy * Gxz) / detg;
-    const double gupyy = (Gxx * Gzz - Gxz * Gxz) / detg;
-    const double gupyz = -(Gxx * Gyz - Gxy * Gxz) / detg;
-    const double gupzz = (Gxx * Gyy - Gxy * Gxy) / detg;
-
-    const double aupxx = gupxx * axx + gupxy * axy + gupxz * axz;
-    const double aupxy = gupxx * axy + gupxy * ayy + gupxz * ayz;
-    const double aupxz = gupxx * axz + gupxy * ayz + gupxz * azz;
-    const double aupyx = gupxy * axx + gupyy * axy + gupyz * axz;
-    const double aupyy = gupxy * axy + gupyy * ayy + gupyz * ayz;
-    const double aupyz = gupxy * axz + gupyy * ayz + gupyz * azz;
-    const double aupzx = gupxz * axx + gupyz * axy + gupzz * axz;
-    const double aupzy = gupxz * axy + gupyz * ayy + gupzz * ayz;
-    const double aupzz = gupxz * axz + gupyz * ayz + gupzz * azz;
-
-    if (Symmetry == 0)
-    {
-      ang_outx += f1o8 * Psi * (nx_g[n] * (pox[1][n] * aupxz - pox[2][n] * aupxy) + ny_g[n] * (pox[1][n] * aupyz - pox[2][n] * aupyy) + nz_g[n] * (pox[1][n] * aupzz - pox[2][n] * aupzy)) * theta_weight;
-      ang_outy += f1o8 * Psi * (nx_g[n] * (pox[2][n] * aupxx - pox[0][n] * aupxz) + ny_g[n] * (pox[2][n] * aupyx - pox[0][n] * aupyz) + nz_g[n] * (pox[2][n] * aupzx - pox[0][n] * aupzz)) * theta_weight;
-      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
-    }
-    else
-    {
-      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
-    }
-
-    axx = Chi * (axx + Gxx * TRK / 3.0);
-    axy = Chi * (axy + Gxy * TRK / 3.0);
-    axz = Chi * (axz + Gxz * TRK / 3.0);
-    ayy = Chi * (ayy + Gyy * TRK / 3.0);
-    ayz = Chi * (ayz + Gyz * TRK / 3.0);
-    azz = Chi * (azz + Gzz * TRK / 3.0);
-
-    axx -= TRK;
-    ayy -= TRK;
-    azz -= TRK;
-
-    p_outx += f1o8 * Psi * (nx_g[n] * axx + ny_g[n] * axy + nz_g[n] * axz) * theta_weight;
-    p_outy += f1o8 * Psi * (nx_g[n] * axy + ny_g[n] * ayy + nz_g[n] * ayz) * theta_weight;
-    if (Symmetry == 0)
-      p_outz += f1o8 * Psi * (nx_g[n] * axz + ny_g[n] * ayz + nz_g[n] * azz) * theta_weight;
-  }
-
-  for (int ii = 0; ii < NN; ii++)
-  {
-#ifdef GaussInt
-    RP_out[ii] = RP_out[ii] * rex * dphi;
-    IP_out[ii] = IP_out[ii] * rex * dphi;
-#else
-    RP_out[ii] = RP_out[ii] * rex * dphi * dcostheta;
-    IP_out[ii] = IP_out[ii] * rex * dphi * dcostheta;
-#endif
-  }
-
-  double mass, px, py, pz, sx, sy, sz;
-  {
-    double *reduce_out = new double[2 * NN + 7];
-    double *reduce_in = new double[2 * NN + 7];
-    memcpy(reduce_out, RP_out, NN * sizeof(double));
-    memcpy(reduce_out + NN, IP_out, NN * sizeof(double));
-    reduce_out[2 * NN + 0] = Mass_out;
-    reduce_out[2 * NN + 1] = ang_outx;
-    reduce_out[2 * NN + 2] = ang_outy;
-    reduce_out[2 * NN + 3] = ang_outz;
-    reduce_out[2 * NN + 4] = p_outx;
-    reduce_out[2 * NN + 5] = p_outy;
-    reduce_out[2 * NN + 6] = p_outz;
-    MPI_Allreduce(reduce_out, reduce_in, 2 * NN + 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, reduce_in, NN * sizeof(double));
-    memcpy(IP, reduce_in + NN, NN * sizeof(double));
-    mass = reduce_in[2 * NN + 0];
-    sx = reduce_in[2 * NN + 1];
-    sy = reduce_in[2 * NN + 2];
-    sz = reduce_in[2 * NN + 3];
-    px = reduce_in[2 * NN + 4];
-    py = reduce_in[2 * NN + 5];
-    pz = reduce_in[2 * NN + 6];
-    delete[] reduce_out;
-    delete[] reduce_in;
-  }
-
-#ifdef GaussInt
-  mass = mass * rex * rex * dphi * factor;
-
-  sx = sx * rex * rex * dphi * (1.0 / PI) * factor;
-  sy = sy * rex * rex * dphi * (1.0 / PI) * factor;
-  sz = sz * rex * rex * dphi * (1.0 / PI) * factor;
-
-  px = px * rex * rex * dphi * (1.0 / PI) * factor;
-  py = py * rex * rex * dphi * (1.0 / PI) * factor;
-  pz = pz * rex * rex * dphi * (1.0 / PI) * factor;
-#else
-  mass = mass * rex * rex * dphi * dcostheta * factor;
-
-  sx = sx * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  sy = sy * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  sz = sz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-
-  px = px * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  py = py * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  pz = pz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-#endif
-
-  Rout[0] = mass;
-  Rout[1] = px;
-  Rout[2] = py;
-  Rout[3] = pz;
-  Rout[4] = sx;
-  Rout[5] = sy;
-  Rout[6] = sz;
-
-  delete[] pox[0];
-  delete[] pox[1];
-  delete[] pox[2];
-  delete[] shellf;
-  delete[] RP_out;
-  delete[] IP_out;
-  DG_List->clearList();
-}
-void surface_integral::surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
-                                         var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
-                                         var *chi, var *trK,
-                                         var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-                                         var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-                                         var *Gmx, var *Gmy, var *Gmz,
-                                         var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-                                         double *Rout, monitor *Monitor, bool refresh_mass_fields)
-{
-  if (Symmetry != 0 && Symmetry != 1)
-  {
-    surf_Wave(rex, lev, GH, Rpsi4, Ipsi4, spinw, maxl, NN, RP, IP, Monitor);
-    surf_MassPAng(rex, lev, GH, chi, trK,
-                  gxx, gxy, gxz, gyy, gyz, gzz,
-                  Axx, Axy, Axz, Ayy, Ayz, Azz,
-                  Gmx, Gmy, Gmz,
-                  Sfx_rhs, Sfy_rhs, Sfz_rhs,
-                  Rout, Monitor, refresh_mass_fields);
-    return;
-  }
-
-  if (lev != 0)
-  {
-    if (myrank == 0)
-    {
-      if (Monitor && Monitor->outfile)
-        Monitor->outfile << "WARNING: shell surface integral not on level 0" << endl;
-      else
-        cout << "WARNING: shell surface integral not on level 0" << endl;
-    }
-    return;
-  }
-
-  if (refresh_mass_fields)
-  {
-    MyList<ss_patch> *Pp = GH->PatL;
-    while (Pp)
-    {
-      MyList<Block> *BL = Pp->data->blb;
-      int fngfs = Pp->data->fngfs;
-      while (BL)
-      {
-        Block *cg = BL->data;
-        if (myrank == cg->rank)
-        {
-          f_admmass_bssn_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
-                            cg->fgfs[fngfs + ShellPatch::gx], cg->fgfs[fngfs + ShellPatch::gy], cg->fgfs[fngfs + ShellPatch::gz],
-                            cg->fgfs[fngfs + ShellPatch::drhodx], cg->fgfs[fngfs + ShellPatch::drhody], cg->fgfs[fngfs + ShellPatch::drhodz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadx], cg->fgfs[fngfs + ShellPatch::dsigmady], cg->fgfs[fngfs + ShellPatch::dsigmadz],
-                            cg->fgfs[fngfs + ShellPatch::dRdx], cg->fgfs[fngfs + ShellPatch::dRdy], cg->fgfs[fngfs + ShellPatch::dRdz],
-                            cg->fgfs[fngfs + ShellPatch::drhodxx], cg->fgfs[fngfs + ShellPatch::drhodxy], cg->fgfs[fngfs + ShellPatch::drhodxz],
-                            cg->fgfs[fngfs + ShellPatch::drhodyy], cg->fgfs[fngfs + ShellPatch::drhodyz], cg->fgfs[fngfs + ShellPatch::drhodzz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadxx], cg->fgfs[fngfs + ShellPatch::dsigmadxy], cg->fgfs[fngfs + ShellPatch::dsigmadxz],
-                            cg->fgfs[fngfs + ShellPatch::dsigmadyy], cg->fgfs[fngfs + ShellPatch::dsigmadyz], cg->fgfs[fngfs + ShellPatch::dsigmadzz],
-                            cg->fgfs[fngfs + ShellPatch::dRdxx], cg->fgfs[fngfs + ShellPatch::dRdxy], cg->fgfs[fngfs + ShellPatch::dRdxz],
-                            cg->fgfs[fngfs + ShellPatch::dRdyy], cg->fgfs[fngfs + ShellPatch::dRdyz], cg->fgfs[fngfs + ShellPatch::dRdzz],
-                            cg->fgfs[chi->sgfn], cg->fgfs[trK->sgfn],
-                            cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
-                            cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
-                            cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
-                            cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
-                            Symmetry, Pp->data->sst);
-        }
-        if (BL == Pp->data->ble)
-          break;
-        BL = BL->next;
-      }
-      Pp = Pp->next;
-    }
-  }
-
-  const int InList = 19;
-  const int idx_rpsi4 = 0, idx_ipsi4 = 1;
-  const int idx_sfx = 2, idx_sfy = 3, idx_sfz = 4;
-  const int idx_chi = 5, idx_trk = 6;
-  const int idx_gxx = 7, idx_gxy = 8, idx_gxz = 9, idx_gyy = 10, idx_gyz = 11, idx_gzz = 12;
-  const int idx_axx = 13, idx_axy = 14, idx_axz = 15, idx_ayy = 16, idx_ayz = 17, idx_azz = 18;
-
-  MyList<var> *DG_List = new MyList<var>(Rpsi4);
-  DG_List->insert(Ipsi4);
-  DG_List->insert(Sfx_rhs);
-  DG_List->insert(Sfy_rhs);
-  DG_List->insert(Sfz_rhs);
-  DG_List->insert(chi);
-  DG_List->insert(trK);
-  DG_List->insert(gxx);
-  DG_List->insert(gxy);
-  DG_List->insert(gxz);
-  DG_List->insert(gyy);
-  DG_List->insert(gyz);
-  DG_List->insert(gzz);
-  DG_List->insert(Axx);
-  DG_List->insert(Axy);
-  DG_List->insert(Axz);
-  DG_List->insert(Ayy);
-  DG_List->insert(Ayz);
-  DG_List->insert(Azz);
-
-  int n;
-  double *pox[3];
-  for (int ia = 0; ia < 3; ia++)
-    pox[ia] = new double[n_tot];
-  for (n = 0; n < n_tot; n++)
-  {
-    pox[0][n] = rex * nx_g[n];
-    pox[1][n] = rex * ny_g[n];
-    pox[2][n] = rex * nz_g[n];
-  }
-
-  double *shellf = new double[n_tot * InList];
-  GH->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
-
-  int mp, Lp, Nmin, Nmax;
-  mp = n_tot / cpusize;
-  Lp = n_tot - cpusize * mp;
-
-  if (Lp > myrank)
-  {
-    Nmin = myrank * mp + myrank;
-    Nmax = Nmin + mp;
-  }
-  else
-  {
-    Nmin = myrank * mp + Lp;
-    Nmax = Nmin + mp - 1;
-  }
-
-  double *RP_out = new double[NN];
-  double *IP_out = new double[NN];
-  for (int ii = 0; ii < NN; ii++)
-  {
-    RP_out[ii] = 0.0;
-    IP_out[ii] = 0.0;
-  }
-
-  double Mass_out = 0.0;
-  double ang_outx = 0.0, ang_outy = 0.0, ang_outz = 0.0;
-  double p_outx = 0.0, p_outy = 0.0, p_outz = 0.0;
-  const double f1o8 = 0.125;
-
-  build_wave_cache(spinw, maxl);
-
-  for (n = Nmin; n <= Nmax; n++)
-  {
-    const int base = InList * n;
-    const int i = int(n / N_phi);
-    const int j = n - i * N_phi;
-
-    const double psi4RR0 = shellf[base + idx_rpsi4];
-    const double psi4II0 = shellf[base + idx_ipsi4];
-    const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
-    const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
-    for (int countlm = 0; countlm < wave_cache_modes; countlm++)
-    {
-      const int theta_idx = countlm * N_theta + i;
-      const int phi_idx = countlm * N_phi + j;
-      const double theta_pos = wave_theta_pos[theta_idx];
-      const double cosmphi_here = wave_phi_cos[phi_idx];
-      const double sinmphi_here = wave_phi_sin[phi_idx];
-
-      RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
-      IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
-      if (Symmetry == 1)
-      {
-        const double theta_neg = wave_theta_neg[theta_idx];
-        RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
-        IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
-      }
-    }
-
-    double Chi = shellf[base + idx_chi];
-    double TRK = shellf[base + idx_trk];
-    double Gxx = shellf[base + idx_gxx] + 1.0;
-    double Gxy = shellf[base + idx_gxy];
-    double Gxz = shellf[base + idx_gxz];
-    double Gyy = shellf[base + idx_gyy] + 1.0;
-    double Gyz = shellf[base + idx_gyz];
-    double Gzz = shellf[base + idx_gzz] + 1.0;
-    double axx = shellf[base + idx_axx];
-    double axy = shellf[base + idx_axy];
-    double axz = shellf[base + idx_axz];
-    double ayy = shellf[base + idx_ayy];
-    double ayz = shellf[base + idx_ayz];
-    double azz = shellf[base + idx_azz];
-
-    Chi = 1.0 / (1.0 + Chi);
-    const double Psi = Chi * sqrt(Chi);
-
-#ifdef GaussInt
-    const double theta_weight = wtcostheta[i];
-    Mass_out += (shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n]) * theta_weight;
-#else
-    const double theta_weight = 1.0;
-    Mass_out += shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n];
-#endif
-
-    double detg = Gxx * Gyy * Gzz + Gxy * Gyz * Gxz + Gxz * Gxy * Gyz -
-                  Gxz * Gyy * Gxz - Gxy * Gxy * Gzz - Gxx * Gyz * Gyz;
-    const double gupxx = (Gyy * Gzz - Gyz * Gyz) / detg;
-    const double gupxy = -(Gxy * Gzz - Gyz * Gxz) / detg;
-    const double gupxz = (Gxy * Gyz - Gyy * Gxz) / detg;
-    const double gupyy = (Gxx * Gzz - Gxz * Gxz) / detg;
-    const double gupyz = -(Gxx * Gyz - Gxy * Gxz) / detg;
-    const double gupzz = (Gxx * Gyy - Gxy * Gxy) / detg;
-
-    const double aupxx = gupxx * axx + gupxy * axy + gupxz * axz;
-    const double aupxy = gupxx * axy + gupxy * ayy + gupxz * ayz;
-    const double aupxz = gupxx * axz + gupxy * ayz + gupxz * azz;
-    const double aupyx = gupxy * axx + gupyy * axy + gupyz * axz;
-    const double aupyy = gupxy * axy + gupyy * ayy + gupyz * ayz;
-    const double aupyz = gupxy * axz + gupyy * ayz + gupyz * azz;
-    const double aupzx = gupxz * axx + gupyz * axy + gupzz * axz;
-    const double aupzy = gupxz * axy + gupyz * ayy + gupzz * ayz;
-    const double aupzz = gupxz * axz + gupyz * ayz + gupzz * azz;
-
-    if (Symmetry == 0)
-    {
-      ang_outx += f1o8 * Psi * (nx_g[n] * (pox[1][n] * aupxz - pox[2][n] * aupxy) + ny_g[n] * (pox[1][n] * aupyz - pox[2][n] * aupyy) + nz_g[n] * (pox[1][n] * aupzz - pox[2][n] * aupzy)) * theta_weight;
-      ang_outy += f1o8 * Psi * (nx_g[n] * (pox[2][n] * aupxx - pox[0][n] * aupxz) + ny_g[n] * (pox[2][n] * aupyx - pox[0][n] * aupyz) + nz_g[n] * (pox[2][n] * aupzx - pox[0][n] * aupzz)) * theta_weight;
-      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
-    }
-    else
-    {
-      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
-    }
-
-    axx = Chi * (axx + Gxx * TRK / 3.0);
-    axy = Chi * (axy + Gxy * TRK / 3.0);
-    axz = Chi * (axz + Gxz * TRK / 3.0);
-    ayy = Chi * (ayy + Gyy * TRK / 3.0);
-    ayz = Chi * (ayz + Gyz * TRK / 3.0);
-    azz = Chi * (azz + Gzz * TRK / 3.0);
-
-    axx -= TRK;
-    ayy -= TRK;
-    azz -= TRK;
-
-    p_outx += f1o8 * Psi * (nx_g[n] * axx + ny_g[n] * axy + nz_g[n] * axz) * theta_weight;
-    p_outy += f1o8 * Psi * (nx_g[n] * axy + ny_g[n] * ayy + nz_g[n] * ayz) * theta_weight;
-    if (Symmetry == 0)
-      p_outz += f1o8 * Psi * (nx_g[n] * axz + ny_g[n] * ayz + nz_g[n] * azz) * theta_weight;
-  }
-
-  for (int ii = 0; ii < NN; ii++)
-  {
-#ifdef GaussInt
-    RP_out[ii] = RP_out[ii] * rex * dphi;
-    IP_out[ii] = IP_out[ii] * rex * dphi;
-#else
-    RP_out[ii] = RP_out[ii] * rex * dphi * dcostheta;
-    IP_out[ii] = IP_out[ii] * rex * dphi * dcostheta;
-#endif
-  }
-
-  double mass, px, py, pz, sx, sy, sz;
-  {
-    double *reduce_out = new double[2 * NN + 7];
-    double *reduce_in = new double[2 * NN + 7];
-    memcpy(reduce_out, RP_out, NN * sizeof(double));
-    memcpy(reduce_out + NN, IP_out, NN * sizeof(double));
-    reduce_out[2 * NN + 0] = Mass_out;
-    reduce_out[2 * NN + 1] = ang_outx;
-    reduce_out[2 * NN + 2] = ang_outy;
-    reduce_out[2 * NN + 3] = ang_outz;
-    reduce_out[2 * NN + 4] = p_outx;
-    reduce_out[2 * NN + 5] = p_outy;
-    reduce_out[2 * NN + 6] = p_outz;
-    MPI_Allreduce(reduce_out, reduce_in, 2 * NN + 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
-    memcpy(RP, reduce_in, NN * sizeof(double));
-    memcpy(IP, reduce_in + NN, NN * sizeof(double));
-    mass = reduce_in[2 * NN + 0];
-    sx = reduce_in[2 * NN + 1];
-    sy = reduce_in[2 * NN + 2];
-    sz = reduce_in[2 * NN + 3];
-    px = reduce_in[2 * NN + 4];
-    py = reduce_in[2 * NN + 5];
-    pz = reduce_in[2 * NN + 6];
-    delete[] reduce_out;
-    delete[] reduce_in;
-  }
-
-#ifdef GaussInt
-  mass = mass * rex * rex * dphi * factor;
-
-  sx = sx * rex * rex * dphi * (1.0 / PI) * factor;
-  sy = sy * rex * rex * dphi * (1.0 / PI) * factor;
-  sz = sz * rex * rex * dphi * (1.0 / PI) * factor;
-
-  px = px * rex * rex * dphi * (1.0 / PI) * factor;
-  py = py * rex * rex * dphi * (1.0 / PI) * factor;
-  pz = pz * rex * rex * dphi * (1.0 / PI) * factor;
-#else
-  mass = mass * rex * rex * dphi * dcostheta * factor;
-
-  sx = sx * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  sy = sy * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  sz = sz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-
-  px = px * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  py = py * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-  pz = pz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
-#endif
-
-  Rout[0] = mass;
-  Rout[1] = px;
-  Rout[2] = py;
-  Rout[3] = pz;
-  Rout[4] = sx;
-  Rout[5] = sy;
-  Rout[6] = sz;
-
-  delete[] pox[0];
-  delete[] pox[1];
-  delete[] pox[2];
-  delete[] shellf;
-  delete[] RP_out;
-  delete[] IP_out;
-  DG_List->clearList();
-}
 //|----------------------------------------------------------------
 //  do not discriminate box and shell
 //  for Gravitational wave specially symmetric case

AMSS_NCKU_source/surface_integral.h

@@ -36,11 +36,6 @@ private:
 
 	double *nx_g, *ny_g, *nz_g; // global list of unit normals
 	int myrank, cpusize;
-	int wave_cache_spinw, wave_cache_maxl, wave_cache_modes;
-	double *wave_theta_pos, *wave_theta_neg;
-	double *wave_phi_cos, *wave_phi_sin;
-	void clear_wave_cache();
-	void build_wave_cache(int spinw, int maxl);
 
 public:
 	surface_integral(int iSymmetry);
@@ -87,29 +82,13 @@ public:
 					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 					   var *Gmx, var *Gmy, var *Gmz,
 					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+					   double *Rout, monitor *Monitor);
 	void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
 					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
 					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 					   var *Gmx, var *Gmy, var *Gmz,
 					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+					   double *Rout, monitor *Monitor);
-	void surf_WaveMassPAng(double rex, int lev, cgh *GH,
-					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
-					   var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
-	void surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
-					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
-					   var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
 	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
 				   var *chi, var *trK,
 				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
@@ -136,7 +115,7 @@ public:
 					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 					   var *Gmx, var *Gmy, var *Gmz,
 					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-					   double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields = true);
+					   double *Rout, monitor *Monitor, MPI_Comm Comm_here);
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
 				   monitor *Monitor, MPI_Comm Comm_here);

AMSS_NCKU_source/z4c_rhs_c.C

@@ -1,725 +0,0 @@
-#include "macrodef.h"
-#include "bssn_rhs.h"
-#include "fmisc.h"
-#include "ricci_gamma.h"
-#include "share_func.h"
-#include "tool.h"
-#include <vector>
-
-#ifdef fortran1
-#define f_constraint_bssn constraint_bssn
-#define f_z4c_rhs_point z4c_rhs_point
-#endif
-#ifdef fortran2
-#define f_constraint_bssn CONSTRAINT_BSSN
-#define f_z4c_rhs_point Z4C_RHS_POINT
-#endif
-#ifdef fortran3
-#define f_constraint_bssn constraint_bssn_
-#define f_z4c_rhs_point z4c_rhs_point_
-#endif
-
-extern "C" void f_constraint_bssn(int *, double *, double *, double *,
-                                  double *, double *,
-                                  double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *,
-                                  double *, double *, double *, double *, double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *, double *, double *, double *, double *, double *,
-                                  double *, double *, double *,
-                                  int &);
-
-extern "C" void f_z4c_rhs_point(
-    double &A11,
-    double &A12,
-    double &A13,
-    double &A22,
-    double &A23,
-    double &A33,
-    double &alpha,
-    double &B1,
-    double &B2,
-    double &B3,
-    double &beta1,
-    double &beta2,
-    double &beta3,
-    double &chi,
-    double &chiDivFloor,
-    double &da1,
-    double &dA111,
-    double &dA112,
-    double &dA113,
-    double &dA122,
-    double &dA123,
-    double &dA133,
-    double &da2,
-    double &dA211,
-    double &dA212,
-    double &dA213,
-    double &dA222,
-    double &dA223,
-    double &dA233,
-    double &da3,
-    double &dA311,
-    double &dA312,
-    double &dA313,
-    double &dA322,
-    double &dA323,
-    double &dA333,
-    double &db11,
-    double &dB11,
-    double &db12,
-    double &dB12,
-    double &db13,
-    double &dB13,
-    double &db21,
-    double &dB21,
-    double &db22,
-    double &dB22,
-    double &db23,
-    double &dB23,
-    double &db31,
-    double &dB31,
-    double &db32,
-    double &dB32,
-    double &db33,
-    double &dB33,
-    double &dchi1,
-    double &dchi2,
-    double &dchi3,
-    double &dda11,
-    double &dda12,
-    double &dda13,
-    double &dda22,
-    double &dda23,
-    double &dda33,
-    double &ddb111,
-    double &ddb112,
-    double &ddb113,
-    double &ddb121,
-    double &ddb122,
-    double &ddb123,
-    double &ddb131,
-    double &ddb132,
-    double &ddb133,
-    double &ddb221,
-    double &ddb222,
-    double &ddb223,
-    double &ddb231,
-    double &ddb232,
-    double &ddb233,
-    double &ddb331,
-    double &ddb332,
-    double &ddb333,
-    double &ddchi11,
-    double &ddchi12,
-    double &ddchi13,
-    double &ddchi22,
-    double &ddchi23,
-    double &ddchi33,
-    double &deldelg1111,
-    double &deldelg1112,
-    double &deldelg1113,
-    double &deldelg1122,
-    double &deldelg1123,
-    double &deldelg1133,
-    double &deldelg1211,
-    double &deldelg1212,
-    double &deldelg1213,
-    double &deldelg1222,
-    double &deldelg1223,
-    double &deldelg1233,
-    double &deldelg1311,
-    double &deldelg1312,
-    double &deldelg1313,
-    double &deldelg1322,
-    double &deldelg1323,
-    double &deldelg1333,
-    double &deldelg2211,
-    double &deldelg2212,
-    double &deldelg2213,
-    double &deldelg2222,
-    double &deldelg2223,
-    double &deldelg2233,
-    double &deldelg2311,
-    double &deldelg2312,
-    double &deldelg2313,
-    double &deldelg2322,
-    double &deldelg2323,
-    double &deldelg2333,
-    double &deldelg3311,
-    double &deldelg3312,
-    double &deldelg3313,
-    double &deldelg3322,
-    double &deldelg3323,
-    double &deldelg3333,
-    double &delG11,
-    double &delg111,
-    double &delg112,
-    double &delg113,
-    double &delG12,
-    double &delg122,
-    double &delg123,
-    double &delG13,
-    double &delg133,
-    double &delG21,
-    double &delg211,
-    double &delg212,
-    double &delg213,
-    double &delG22,
-    double &delg222,
-    double &delg223,
-    double &delG23,
-    double &delg233,
-    double &delG31,
-    double &delg311,
-    double &delg312,
-    double &delg313,
-    double &delG32,
-    double &delg322,
-    double &delg323,
-    double &delG33,
-    double &delg333,
-    double &dKhat1,
-    double &dKhat2,
-    double &dKhat3,
-    double &dTheta1,
-    double &dTheta2,
-    double &dTheta3,
-    double &G1,
-    double &g11,
-    double &g12,
-    double &g13,
-    double &G2,
-    double &g22,
-    double &g23,
-    double &G3,
-    double &g33,
-    double &kappa1,
-    double &kappa2,
-    double &Khat,
-    double &rA11,
-    double &rA12,
-    double &rA13,
-    double &rA22,
-    double &rA23,
-    double &rA33,
-    double &rchi,
-    double &rG1,
-    double &rg11,
-    double &rg12,
-    double &rg13,
-    double &rG2,
-    double &rg22,
-    double &rg23,
-    double &rG3,
-    double &rg33,
-    double &rKhat,
-    double &rTheta,
-    double &Theta);
-
-static inline void z4c_contract_gamma(
-    const double gxx, const double gxy, const double gxz,
-    const double gyy, const double gyz, const double gzz,
-    const double gxxx, const double gxyx, const double gxzx,
-    const double gyyx, const double gyzx, const double gzzx,
-    const double gxxy, const double gxyy, const double gxzy,
-    const double gyyy, const double gyzy, const double gzzy,
-    const double gxxz, const double gxyz, const double gxzz,
-    const double gyyz, const double gyzz, const double gzzz,
-    double &Gamxa, double &Gamya, double &Gamza)
-{
-    double det = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz -
-                 gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz;
-    const double gupxx = (gyy * gzz - gyz * gyz) / det;
-    const double gupxy = -(gxy * gzz - gyz * gxz) / det;
-    const double gupxz = (gxy * gyz - gyy * gxz) / det;
-    const double gupyy = (gxx * gzz - gxz * gxz) / det;
-    const double gupyz = -(gxx * gyz - gxy * gxz) / det;
-    const double gupzz = (gxx * gyy - gxy * gxy) / det;
-
-    const double Gamxxx = 0.5 * (gupxx * gxxx + gupxy * (2.0 * gxyx - gxxy) + gupxz * (2.0 * gxzx - gxxz));
-    const double Gamyxx = 0.5 * (gupxy * gxxx + gupyy * (2.0 * gxyx - gxxy) + gupyz * (2.0 * gxzx - gxxz));
-    const double Gamzxx = 0.5 * (gupxz * gxxx + gupyz * (2.0 * gxyx - gxxy) + gupzz * (2.0 * gxzx - gxxz));
-
-    const double Gamxyy = 0.5 * (gupxx * (2.0 * gxyy - gyyx) + gupxy * gyyy + gupxz * (2.0 * gyzy - gyyz));
-    const double Gamyyy = 0.5 * (gupxy * (2.0 * gxyy - gyyx) + gupyy * gyyy + gupyz * (2.0 * gyzy - gyyz));
-    const double Gamzyy = 0.5 * (gupxz * (2.0 * gxyy - gyyx) + gupyz * gyyy + gupzz * (2.0 * gyzy - gyyz));
-
-    const double Gamxzz = 0.5 * (gupxx * (2.0 * gxzz - gzzx) + gupxy * (2.0 * gyzz - gzzy) + gupxz * gzzz);
-    const double Gamyzz = 0.5 * (gupxy * (2.0 * gxzz - gzzx) + gupyy * (2.0 * gyzz - gzzy) + gupyz * gzzz);
-    const double Gamzzz = 0.5 * (gupxz * (2.0 * gxzz - gzzx) + gupyz * (2.0 * gyzz - gzzy) + gupzz * gzzz);
-
-    const double Gamxxy = 0.5 * (gupxx * gxxy + gupxy * gyyx + gupxz * (gxzy + gyzx - gxyz));
-    const double Gamyxy = 0.5 * (gupxy * gxxy + gupyy * gyyx + gupyz * (gxzy + gyzx - gxyz));
-    const double Gamzxy = 0.5 * (gupxz * gxxy + gupyz * gyyx + gupzz * (gxzy + gyzx - gxyz));
-
-    const double Gamxxz = 0.5 * (gupxx * gxxz + gupxy * (gxyz + gyzx - gxzy) + gupxz * gzzx);
-    const double Gamyxz = 0.5 * (gupxy * gxxz + gupyy * (gxyz + gyzx - gxzy) + gupyz * gzzx);
-    const double Gamzxz = 0.5 * (gupxz * gxxz + gupyz * (gxyz + gyzx - gxzy) + gupzz * gzzx);
-
-    const double Gamxyz = 0.5 * (gupxx * (gxyz + gxzy - gyzx) + gupxy * gyyz + gupxz * gzzy);
-    const double Gamyyz = 0.5 * (gupxy * (gxyz + gxzy - gyzx) + gupyy * gyyz + gupyz * gzzy);
-    const double Gamzyz = 0.5 * (gupxz * (gxyz + gxzy - gyzx) + gupyz * gyyz + gupzz * gzzy);
-
-    Gamxa = gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz +
-            2.0 * (gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz);
-    Gamya = gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz +
-            2.0 * (gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz);
-    Gamza = gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz +
-            2.0 * (gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz);
-}
-
-static int compute_rhs_z4c_cartesian(
-    int *ex, double &T, double *X, double *Y, double *Z,
-    double *chi_state, double *chi_constraints, double *trK,
-    double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
-    double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
-    double *Gamx, double *Gamy, double *Gamz,
-    double *Lap, double *betax, double *betay, double *betaz,
-    double *dtSfx, double *dtSfy, double *dtSfz,
-    double *TZ,
-    double *chi_rhs, double *trK_rhs,
-    double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
-    double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
-    double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
-    double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
-    double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
-    double *TZ_rhs,
-    double *rho, double *Sx, double *Sy, double *Sz,
-    double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
-    double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
-    double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
-    double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
-    double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
-    double *Hcon, double *Mxcon, double *Mycon, double *Mzcon, double *Gmxcon, double *Gmycon, double *Gmzcon,
-    int &Symmetry, int &Lev, double &eps, int &co)
-{
-    (void)T;
-
-    const int nx = ex[0];
-    const int ny = ex[1];
-    const int nz = ex[2];
-    const int all = nx * ny * nz;
-
-    double alpn1[all], chin1[all], gxx[all], gyy[all], gzz[all];
-    double chix[all], chiy[all], chiz[all], chixx[all], chixy[all], chixz[all], chiyy[all], chiyz[all], chizz[all];
-    double gxxx[all], gxyx[all], gxzx[all], gyyx[all], gyzx[all], gzzx[all];
-    double gxxy[all], gxyy[all], gxzy[all], gyyy[all], gyzy[all], gzzy[all];
-    double gxxz[all], gxyz[all], gxzz[all], gyyz[all], gyzz[all], gzzz[all];
-    double gxxxx[all], gxxxy[all], gxxxz[all], gxxyy[all], gxxyz[all], gxxzz[all];
-    double gxyxx[all], gxyxy[all], gxyxz[all], gxyyy[all], gxyyz[all], gxyzz[all];
-    double gxzxx[all], gxzxy[all], gxzxz[all], gxzyy[all], gxzyz[all], gxzzz[all];
-    double gyyxx[all], gyyxy[all], gyyxz[all], gyyyy[all], gyyyz[all], gyyzz[all];
-    double gyzxx[all], gyzxy[all], gyzxz[all], gyzyy[all], gyzyz[all], gyzzz[all];
-    double gzzxx[all], gzzxy[all], gzzxz[all], gzzyy[all], gzzyz[all], gzzzz[all];
-    double Lapx[all], Lapy[all], Lapz[all], Lapxx[all], Lapxy[all], Lapxz[all], Lapyy[all], Lapyz[all], Lapzz[all];
-    double betaxx[all], betaxy[all], betaxz[all], betayx[all], betayy[all], betayz[all], betazx[all], betazy[all], betazz[all];
-    double dBxx[all], dBxy[all], dBxz[all], dByx[all], dByy[all], dByz[all], dBzx[all], dBzy[all], dBzz[all];
-    double sfxxx[all], sfxxy[all], sfxxz[all], sfxyy[all], sfxyz[all], sfxzz[all];
-    double sfyxx[all], sfyxy[all], sfyxz[all], sfyyy[all], sfyyz[all], sfyzz[all];
-    double sfzxx[all], sfzxy[all], sfzxz[all], sfzyy[all], sfzyz[all], sfzzz[all];
-    double Gamxx[all], Gamxy[all], Gamxz[all], Gamyx[all], Gamyy[all], Gamyz[all], Gamzx[all], Gamzy[all], Gamzz[all];
-    double Kx[all], Ky[all], Kz[all], TZx[all], TZy[all], TZz[all];
-    double Axxx[all], Axxy[all], Axxz[all], Axyx[all], Axyy[all], Axyz[all];
-    double Axzx[all], Axzy[all], Axzz[all], Ayyx[all], Ayyy[all], Ayyz[all];
-    double Ayzx[all], Ayzy[all], Ayzz[all], Azzx[all], Azzy[all], Azzz[all];
-
-    const double SSS[3] = {1.0, 1.0, 1.0};
-    const double AAS[3] = {-1.0, -1.0, 1.0};
-    const double ASA[3] = {-1.0, 1.0, -1.0};
-    const double SAA[3] = {1.0, -1.0, -1.0};
-    const double ASS[3] = {-1.0, 1.0, 1.0};
-    const double SAS[3] = {1.0, -1.0, 1.0};
-    const double SSA[3] = {1.0, 1.0, -1.0};
-
-    const double ONE = 1.0;
-    const double TWO = 2.0;
-    const double ZEO = 0.0;
-    double chiDivfloor = 1.0e-5;
-
-    double kappa1 = 2.0e-2;
-    double kappa2 = 0.0;
-    double FF = 0.75;
-    double eta = 2.0;
-
-    for (int idx = 0; idx < all; ++idx)
-    {
-        alpn1[idx] = Lap[idx] + ONE;
-        chin1[idx] = chi_state[idx] + ONE;
-        gxx[idx] = dxx[idx] + ONE;
-        gyy[idx] = dyy[idx] + ONE;
-        gzz[idx] = dzz[idx] + ONE;
-    }
-
-    fderivs(ex, betax, betaxx, betaxy, betaxz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, betay, betayx, betayy, betayz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, betaz, betazx, betazy, betazz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
-    fderivs(ex, dtSfx, dBxx, dBxy, dBxz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, dtSfy, dByx, dByy, dByz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, dtSfz, dBzx, dBzy, dBzz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
-    fderivs(ex, chi_state, chix, chiy, chiz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, dxx, gxxx, gxxy, gxxz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, gxy, gxyx, gxyy, gxyz, X, Y, Z, -1.0, -1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, gxz, gxzx, gxzy, gxzz, X, Y, Z, -1.0, 1.0, -1.0, Symmetry, Lev);
-    fderivs(ex, dyy, gyyx, gyyy, gyyz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, gyz, gyzx, gyzy, gyzz, X, Y, Z, 1.0, -1.0, -1.0, Symmetry, Lev);
-    fderivs(ex, dzz, gzzx, gzzy, gzzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-
-    fdderivs(ex, dxx, gxxxx, gxxxy, gxxxz, gxxyy, gxxyz, gxxzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, dyy, gyyxx, gyyxy, gyyxz, gyyyy, gyyyz, gyyzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, dzz, gzzxx, gzzxy, gzzxz, gzzyy, gzzyz, gzzzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, gxy, gxyxx, gxyxy, gxyxz, gxyyy, gxyyz, gxyzz, X, Y, Z, -1.0, -1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, gxz, gxzxx, gxzxy, gxzxz, gxzyy, gxzyz, gxzzz, X, Y, Z, -1.0, 1.0, -1.0, Symmetry, Lev);
-    fdderivs(ex, gyz, gyzxx, gyzxy, gyzxz, gyzyy, gyzyz, gyzzz, X, Y, Z, 1.0, -1.0, -1.0, Symmetry, Lev);
-
-    fderivs(ex, Gamx, Gamxx, Gamxy, Gamxz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, Gamy, Gamyx, Gamyy, Gamyz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, Gamz, Gamzx, Gamzy, Gamzz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
-
-    fderivs(ex, Lap, Lapx, Lapy, Lapz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, trK, Kx, Ky, Kz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, TZ, TZx, TZy, TZz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-
-    fdderivs(ex, betax, sfxxx, sfxxy, sfxxz, sfxyy, sfxyz, sfxzz, X, Y, Z, -1.0, 1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, betay, sfyxx, sfyxy, sfyxz, sfyyy, sfyyz, sfyzz, X, Y, Z, 1.0, -1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, betaz, sfzxx, sfzxy, sfzxz, sfzyy, sfzyz, sfzzz, X, Y, Z, 1.0, 1.0, -1.0, Symmetry, Lev);
-
-    fdderivs(ex, chi_state, chixx, chixy, chixz, chiyy, chiyz, chizz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fdderivs(ex, Lap, Lapxx, Lapxy, Lapxz, Lapyy, Lapyz, Lapzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-
-    fderivs(ex, Axx, Axxx, Axxy, Axxz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, Axy, Axyx, Axyy, Axyz, X, Y, Z, -1.0, -1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, Axz, Axzx, Axzy, Axzz, X, Y, Z, -1.0, 1.0, -1.0, Symmetry, Lev);
-    fderivs(ex, Ayy, Ayyx, Ayyy, Ayyz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-    fderivs(ex, Ayz, Ayzx, Ayzy, Ayzz, X, Y, Z, 1.0, -1.0, -1.0, Symmetry, Lev);
-    fderivs(ex, Azz, Azzx, Azzy, Azzz, X, Y, Z, 1.0, 1.0, 1.0, Symmetry, Lev);
-
-    for (int idx = 0; idx < all; ++idx)
-    {
-        double point_kappa1 = 0.0;
-        f_z4c_rhs_point(
-            Axx[idx], Axy[idx], Axz[idx], Ayy[idx], Ayz[idx], Azz[idx],
-            alpn1[idx], dtSfx[idx], dtSfy[idx], dtSfz[idx],
-            betax[idx], betay[idx], betaz[idx],
-            chin1[idx], chiDivfloor,
-            Lapx[idx],
-            Axxx[idx], Axyx[idx], Axzx[idx], Ayyx[idx], Ayzx[idx], Azzx[idx],
-            Lapy[idx],
-            Axxy[idx], Axyy[idx], Axzy[idx], Ayyy[idx], Ayzy[idx], Azzy[idx],
-            Lapz[idx],
-            Axxz[idx], Axyz[idx], Axzz[idx], Ayyz[idx], Ayzz[idx], Azzz[idx],
-            betaxx[idx], dBxx[idx], betayx[idx], dByx[idx], betazx[idx], dBzx[idx],
-            betaxy[idx], dBxy[idx], betayy[idx], dByy[idx], betazy[idx], dBzy[idx],
-            betaxz[idx], dBxz[idx], betayz[idx], dByz[idx], betazz[idx], dBzz[idx],
-            chix[idx], chiy[idx], chiz[idx],
-            Lapxx[idx], Lapxy[idx], Lapxz[idx], Lapyy[idx], Lapyz[idx], Lapzz[idx],
-            sfxxx[idx], sfyxx[idx], sfzxx[idx],
-            sfxxy[idx], sfyxy[idx], sfzxy[idx],
-            sfxxz[idx], sfyxz[idx], sfzxz[idx],
-            sfxyy[idx], sfyyy[idx], sfzyy[idx],
-            sfxyz[idx], sfyyz[idx], sfzyz[idx],
-            sfxzz[idx], sfyzz[idx], sfzzz[idx],
-            chixx[idx], chixy[idx], chixz[idx], chiyy[idx], chiyz[idx], chizz[idx],
-            gxxxx[idx], gxyxx[idx], gxzxx[idx], gyyxx[idx], gyzxx[idx], gzzxx[idx],
-            gxxxy[idx], gxyxy[idx], gxzxy[idx], gyyxy[idx], gyzxy[idx], gzzxy[idx],
-            gxxxz[idx], gxyxz[idx], gxzxz[idx], gyyxz[idx], gyzxz[idx], gzzxz[idx],
-            gxxyy[idx], gxyyy[idx], gxzyy[idx], gyyyy[idx], gyzyy[idx], gzzyy[idx],
-            gxxyz[idx], gxyyz[idx], gxzyz[idx], gyyyz[idx], gyzyz[idx], gzzyz[idx],
-            gxxzz[idx], gxyzz[idx], gxzzz[idx], gyyzz[idx], gyzzz[idx], gzzzz[idx],
-            Gamxx[idx], gxxx[idx], gxyx[idx], gxzx[idx],
-            Gamyx[idx], gyyx[idx], gyzx[idx],
-            Gamzx[idx], gzzx[idx],
-            Gamxy[idx], gxxy[idx], gxyy[idx], gxzy[idx],
-            Gamyy[idx], gyyy[idx], gyzy[idx],
-            Gamzy[idx], gzzy[idx],
-            Gamxz[idx], gxxz[idx], gxyz[idx], gxzz[idx],
-            Gamyz[idx], gyyz[idx], gyzz[idx],
-            Gamzz[idx], gzzz[idx],
-            Kx[idx], Ky[idx], Kz[idx],
-            TZx[idx], TZy[idx], TZz[idx],
-            Gamx[idx], gxx[idx], gxy[idx], gxz[idx],
-            Gamy[idx], gyy[idx], gyz[idx],
-            Gamz[idx], gzz[idx],
-            point_kappa1, kappa2,
-            trK[idx],
-            Axx_rhs[idx], Axy_rhs[idx], Axz_rhs[idx], Ayy_rhs[idx], Ayz_rhs[idx], Azz_rhs[idx],
-            chi_rhs[idx],
-            Gamx_rhs[idx], gxx_rhs[idx], gxy_rhs[idx], gxz_rhs[idx],
-            Gamy_rhs[idx], gyy_rhs[idx], gyz_rhs[idx],
-            Gamz_rhs[idx], gzz_rhs[idx], trK_rhs[idx], TZ_rhs[idx], TZ[idx]);
-    }
-
-    for (int idx = 0; idx < all; ++idx)
-        Lap_rhs[idx] = -TWO * alpn1[idx] * trK[idx];
-
-#if (GAUGE == 0)
-    for (int idx = 0; idx < all; ++idx)
-    {
-        betax_rhs[idx] = FF * dtSfx[idx];
-        betay_rhs[idx] = FF * dtSfy[idx];
-        betaz_rhs[idx] = FF * dtSfz[idx];
-        dtSfx_rhs[idx] = Gamx_rhs[idx] - eta * dtSfx[idx];
-        dtSfy_rhs[idx] = Gamy_rhs[idx] - eta * dtSfy[idx];
-        dtSfz_rhs[idx] = Gamz_rhs[idx] - eta * dtSfz[idx];
-    }
-#elif (GAUGE == 1)
-    for (int idx = 0; idx < all; ++idx)
-    {
-        betax_rhs[idx] = Gamx[idx] - eta * betax[idx];
-        betay_rhs[idx] = Gamy[idx] - eta * betay[idx];
-        betaz_rhs[idx] = Gamz[idx] - eta * betaz[idx];
-        dtSfx_rhs[idx] = ZEO;
-        dtSfy_rhs[idx] = ZEO;
-        dtSfz_rhs[idx] = ZEO;
-    }
-#else
-#error "z4c_rhs_c.C currently supports GAUGE == 0 or GAUGE == 1 for Z4C"
-#endif
-
-    lopsided(ex, X, Y, Z, gxx, gxx_rhs, betax, betay, betaz, Symmetry, SSS);
-    lopsided(ex, X, Y, Z, gxy, gxy_rhs, betax, betay, betaz, Symmetry, AAS);
-    lopsided(ex, X, Y, Z, gxz, gxz_rhs, betax, betay, betaz, Symmetry, ASA);
-    lopsided(ex, X, Y, Z, gyy, gyy_rhs, betax, betay, betaz, Symmetry, SSS);
-    lopsided(ex, X, Y, Z, gyz, gyz_rhs, betax, betay, betaz, Symmetry, SAA);
-    lopsided(ex, X, Y, Z, gzz, gzz_rhs, betax, betay, betaz, Symmetry, SSS);
-
-    lopsided(ex, X, Y, Z, Axx, Axx_rhs, betax, betay, betaz, Symmetry, SSS);
-    lopsided(ex, X, Y, Z, Axy, Axy_rhs, betax, betay, betaz, Symmetry, AAS);
-    lopsided(ex, X, Y, Z, Axz, Axz_rhs, betax, betay, betaz, Symmetry, ASA);
-    lopsided(ex, X, Y, Z, Ayy, Ayy_rhs, betax, betay, betaz, Symmetry, SSS);
-    lopsided(ex, X, Y, Z, Ayz, Ayz_rhs, betax, betay, betaz, Symmetry, SAA);
-    lopsided(ex, X, Y, Z, Azz, Azz_rhs, betax, betay, betaz, Symmetry, SSS);
-
-    lopsided(ex, X, Y, Z, chi_state, chi_rhs, betax, betay, betaz, Symmetry, SSS);
-    lopsided(ex, X, Y, Z, trK, trK_rhs, betax, betay, betaz, Symmetry, SSS);
-
-    lopsided(ex, X, Y, Z, Gamx, Gamx_rhs, betax, betay, betaz, Symmetry, ASS);
-    lopsided(ex, X, Y, Z, Gamy, Gamy_rhs, betax, betay, betaz, Symmetry, SAS);
-    lopsided(ex, X, Y, Z, Gamz, Gamz_rhs, betax, betay, betaz, Symmetry, SSA);
-
-    lopsided(ex, X, Y, Z, Lap, Lap_rhs, betax, betay, betaz, Symmetry, SSS);
-    lopsided(ex, X, Y, Z, betax, betax_rhs, betax, betay, betaz, Symmetry, ASS);
-    lopsided(ex, X, Y, Z, betay, betay_rhs, betax, betay, betaz, Symmetry, SAS);
-    lopsided(ex, X, Y, Z, betaz, betaz_rhs, betax, betay, betaz, Symmetry, SSA);
-#if (GAUGE == 0)
-    lopsided(ex, X, Y, Z, dtSfx, dtSfx_rhs, betax, betay, betaz, Symmetry, ASS);
-    lopsided(ex, X, Y, Z, dtSfy, dtSfy_rhs, betax, betay, betaz, Symmetry, SAS);
-    lopsided(ex, X, Y, Z, dtSfz, dtSfz_rhs, betax, betay, betaz, Symmetry, SSA);
-#endif
-    lopsided(ex, X, Y, Z, TZ, TZ_rhs, betax, betay, betaz, Symmetry, SSS);
-
-    for (int idx = 0; idx < all; ++idx)
-    {
-        double Gamxa = 0.0, Gamya = 0.0, Gamza = 0.0;
-        z4c_contract_gamma(
-            gxx[idx], gxy[idx], gxz[idx], gyy[idx], gyz[idx], gzz[idx],
-            gxxx[idx], gxyx[idx], gxzx[idx], gyyx[idx], gyzx[idx], gzzx[idx],
-            gxxy[idx], gxyy[idx], gxzy[idx], gyyy[idx], gyzy[idx], gzzy[idx],
-            gxxz[idx], gxyz[idx], gxzz[idx], gyyz[idx], gyzz[idx], gzzz[idx],
-            Gamxa, Gamya, Gamza);
-
-        TZ_rhs[idx] -= alpn1[idx] * (TWO + kappa2) * kappa1 * TZ[idx];
-        trK_rhs[idx] += alpn1[idx] * kappa1 * (ONE - kappa2) * TZ[idx];
-        Gamx_rhs[idx] -= TWO * alpn1[idx] * kappa1 * (Gamx[idx] - Gamxa);
-        Gamy_rhs[idx] -= TWO * alpn1[idx] * kappa1 * (Gamy[idx] - Gamya);
-        Gamz_rhs[idx] -= TWO * alpn1[idx] * kappa1 * (Gamz[idx] - Gamza);
-    }
-
-    if (eps > 0.0)
-    {
-        kodis(ex, X, Y, Z, chi_state, chi_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, trK, trK_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, gxx, gxx_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, gxy, gxy_rhs, AAS, Symmetry, eps);
-        kodis(ex, X, Y, Z, gxz, gxz_rhs, ASA, Symmetry, eps);
-        kodis(ex, X, Y, Z, gyy, gyy_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, gyz, gyz_rhs, SAA, Symmetry, eps);
-        kodis(ex, X, Y, Z, gzz, gzz_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Axx, Axx_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Axy, Axy_rhs, AAS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Axz, Axz_rhs, ASA, Symmetry, eps);
-        kodis(ex, X, Y, Z, Ayy, Ayy_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Ayz, Ayz_rhs, SAA, Symmetry, eps);
-        kodis(ex, X, Y, Z, Azz, Azz_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Gamx, Gamx_rhs, ASS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Gamy, Gamy_rhs, SAS, Symmetry, eps);
-        kodis(ex, X, Y, Z, Gamz, Gamz_rhs, SSA, Symmetry, eps);
-        kodis(ex, X, Y, Z, Lap, Lap_rhs, SSS, Symmetry, eps);
-        kodis(ex, X, Y, Z, betax, betax_rhs, ASS, Symmetry, eps);
-        kodis(ex, X, Y, Z, betay, betay_rhs, SAS, Symmetry, eps);
-        kodis(ex, X, Y, Z, betaz, betaz_rhs, SSA, Symmetry, eps);
-#if (GAUGE == 0)
-        kodis(ex, X, Y, Z, dtSfx, dtSfx_rhs, ASS, Symmetry, eps);
-        kodis(ex, X, Y, Z, dtSfy, dtSfy_rhs, SAS, Symmetry, eps);
-        kodis(ex, X, Y, Z, dtSfz, dtSfz_rhs, SSA, Symmetry, eps);
-#endif
-        kodis(ex, X, Y, Z, TZ, TZ_rhs, SSS, Symmetry, eps);
-    }
-
-    if (co == 0)
-    {
-#if (ABV == 0)
-        f_ricci_gamma(ex, X, Y, Z,
-                      chi_constraints,
-                      dxx, gxy, gxz, dyy, gyz, dzz,
-                      Gamx, Gamy, Gamz,
-                      Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-                      Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-                      Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-                      Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-                      Symmetry);
-#endif
-        f_constraint_bssn(ex, X, Y, Z,
-                          chi_constraints, trK,
-                          dxx, gxy, gxz, dyy, gyz, dzz,
-                          Axx, Axy, Axz, Ayy, Ayz, Azz,
-                          Gamx, Gamy, Gamz,
-                          Lap, betax, betay, betaz, rho, Sx, Sy, Sz,
-                          Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-                          Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-                          Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-                          Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-                          Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
-                          Symmetry);
-    }
-
-    return 0;
-}
-
-extern "C" int f_compute_rhs_Z4c(int *ex, double &T,
-                                 double *X, double *Y, double *Z,
-                                 double *chi, double *trK,
-                                 double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
-                                 double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
-                                 double *Gamx, double *Gamy, double *Gamz,
-                                 double *Lap, double *betax, double *betay, double *betaz,
-                                 double *dtSfx, double *dtSfy, double *dtSfz,
-                                 double *TZ,
-                                 double *chi_rhs, double *trK_rhs,
-                                 double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
-                                 double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
-                                 double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
-                                 double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
-                                 double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
-                                 double *TZ_rhs,
-                                 double *rho, double *Sx, double *Sy, double *Sz,
-                                 double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
-                                 double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
-                                 double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
-                                 double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
-                                 double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
-                                 double *Hcon, double *Mxcon, double *Mycon, double *Mzcon, double *Gmxcon, double *Gmycon, double *Gmzcon,
-                                 int &Symmetry, int &Lev, double &eps, int &co)
-{
-    return compute_rhs_z4c_cartesian(
-        ex, T, X, Y, Z,
-        chi, chi, trK,
-        dxx, gxy, gxz, dyy, gyz, dzz,
-        Axx, Axy, Axz, Ayy, Ayz, Azz,
-        Gamx, Gamy, Gamz,
-        Lap, betax, betay, betaz,
-        dtSfx, dtSfy, dtSfz,
-        TZ,
-        chi_rhs, trK_rhs,
-        gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
-        Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
-        Gamx_rhs, Gamy_rhs, Gamz_rhs,
-        Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
-        dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
-        TZ_rhs,
-        rho, Sx, Sy, Sz,
-        Sxx, Sxy, Sxz, Syy, Syz, Szz,
-        Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-        Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-        Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-        Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-        Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
-        Symmetry, Lev, eps, co);
-}
-
-extern "C" int f_compute_rhs_Z4cnot(int *ex, double &T,
-                                    double *X, double *Y, double *Z,
-                                    double *chi, double *trK,
-                                    double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
-                                    double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
-                                    double *Gamx, double *Gamy, double *Gamz,
-                                    double *Lap, double *betax, double *betay, double *betaz,
-                                    double *dtSfx, double *dtSfy, double *dtSfz,
-                                    double *TZ,
-                                    double *chi_rhs, double *trK_rhs,
-                                    double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
-                                    double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
-                                    double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
-                                    double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
-                                    double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
-                                    double *TZ_rhs,
-                                    double *rho, double *Sx, double *Sy, double *Sz,
-                                    double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
-                                    double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
-                                    double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
-                                    double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
-                                    double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
-                                    double *Hcon, double *Mxcon, double *Mycon, double *Mzcon, double *Gmxcon, double *Gmycon, double *Gmzcon,
-                                    int &Symmetry, int &Lev, double &eps, int &co, double &chitiny)
-{
-    const int all = ex[0] * ex[1] * ex[2];
-    std::vector<double> chi_clamped(chi, chi + all);
-    f_lowerboundset(ex, chi_clamped.data(), chitiny);
-
-    const int ret = compute_rhs_z4c_cartesian(
-        ex, T, X, Y, Z,
-        chi_clamped.data(), chi, trK,
-        dxx, gxy, gxz, dyy, gyz, dzz,
-        Axx, Axy, Axz, Ayy, Ayz, Azz,
-        Gamx, Gamy, Gamz,
-        Lap, betax, betay, betaz,
-        dtSfx, dtSfy, dtSfz,
-        TZ,
-        chi_rhs, trK_rhs,
-        gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs,
-        Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs,
-        Gamx_rhs, Gamy_rhs, Gamz_rhs,
-        Lap_rhs, betax_rhs, betay_rhs, betaz_rhs,
-        dtSfx_rhs, dtSfy_rhs, dtSfz_rhs,
-        TZ_rhs,
-        rho, Sx, Sy, Sz,
-        Sxx, Sxy, Sxz, Syy, Syz, Szz,
-        Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-        Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-        Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-        Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-        Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
-        Symmetry, Lev, eps, co);
-
-    if (ret != 0 || co != 0)
-        return ret;
-
-#if (ABV == 0)
-    f_ricci_gamma(ex, X, Y, Z,
-                  chi,
-                  dxx, gxy, gxz, dyy, gyz, dzz,
-                  Gamx, Gamy, Gamz,
-                  Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-                  Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-                  Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-                  Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-                  Symmetry);
-#endif
-    f_constraint_bssn(ex, X, Y, Z,
-                      chi, trK,
-                      dxx, gxy, gxz, dyy, gyz, dzz,
-                      Axx, Axy, Axz, Ayy, Ayz, Azz,
-                      Gamx, Gamy, Gamz,
-                      Lap, betax, betay, betaz, rho, Sx, Sy, Sz,
-                      Gamxxx, Gamxxy, Gamxxz, Gamxyy, Gamxyz, Gamxzz,
-                      Gamyxx, Gamyxy, Gamyxz, Gamyyy, Gamyyz, Gamyzz,
-                      Gamzxx, Gamzxy, Gamzxz, Gamzyy, Gamzyz, Gamzzz,
-                      Rxx, Rxy, Rxz, Ryy, Ryz, Rzz,
-                      Hcon, Mxcon, Mycon, Mzcon, Gmxcon, Gmycon, Gmzcon,
-                      Symmetry);
-    return ret;
-}

AMSS_NCKU_source/z4c_rhs_cuda.h

@@ -1,83 +0,0 @@
-#ifndef Z4C_RHS_CUDA_H
-#define Z4C_RHS_CUDA_H
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-enum {
-    Z4C_CUDA_STATE_COUNT = 25
-};
-
-int z4c_cuda_rk4_substep(void *block_tag,
-                         int *ex, double *X, double *Y, double *Z,
-                         double **state_host_in,
-                         double **state_host_out,
-                         const double *propspeed,
-                         const double *soa_flat,
-                         const double *bbox,
-                         double &dT,
-                         double &T,
-                         int &RK4,
-                         int &apply_bam_bc,
-                         int &Symmetry,
-                         int &Lev,
-                         double &eps,
-                         int &co,
-                         int &keep_resident_state,
-                         int &apply_enforce_ga,
-                         double &chitiny);
-
-int z4c_cuda_download_resident_state(void *block_tag,
-                                     int *ex,
-                                     double **state_host_out);
-
-int z4c_cuda_pack_state_region_to_host_buffer(void *block_tag,
-                                              int state_index,
-                                              double *host_buffer,
-                                              int *ex,
-                                              int i0, int j0, int k0,
-                                              int sx, int sy, int sz);
-
-int z4c_cuda_unpack_state_region_from_host_buffer(void *block_tag,
-                                                  int state_index,
-                                                  double *host_buffer,
-                                                  int *ex,
-                                                  int i0, int j0, int k0,
-                                                  int sx, int sy, int sz);
-
-int z4c_cuda_pack_state_batch_to_host_buffer(void *block_tag,
-                                             int state_count,
-                                             double *host_buffer,
-                                             int *ex,
-                                             int i0, int j0, int k0,
-                                             int sx, int sy, int sz);
-
-int z4c_cuda_unpack_state_batch_from_host_buffer(void *block_tag,
-                                                 int state_count,
-                                                 double *host_buffer,
-                                                 int *ex,
-                                                 int i0, int j0, int k0,
-                                                 int sx, int sy, int sz);
-
-int z4c_cuda_download_state_subset(void *block_tag,
-                                   int *ex,
-                                   int subset_count,
-                                   const int *state_indices,
-                                   double **state_host_out);
-
-int z4c_cuda_upload_state_subset(void *block_tag,
-                                 int *ex,
-                                 int subset_count,
-                                 const int *state_indices,
-                                 double **state_host_in);
-
-int z4c_cuda_has_resident_state(void *block_tag);
-
-void z4c_cuda_release_step_ctx(void *block_tag);
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif

generate_macrodef.py

@@ -144,67 +144,11 @@ def generate_macrodef_h():
     print( "#define REGLEV 0",      file=file1 )
     print(                          file=file1 )
 
-    # Define fine-grained timing/debug macros.
-    # All of them default to OFF so production builds do not pay profiling overhead.
-
-    fine_timing = getattr(input_data, "Fine_Timing",
-                  getattr(input_data, "Finegrained_Timing", "no"))
-    kernel_fine_timing = getattr(input_data, "Kernel_Fine_Timing",
-                          getattr(input_data, "BSSN_Kernel_Fine_Timing", "no"))
-    stdin_abort_poll = getattr(input_data, "Enable_Stdin_Abort_Poll",
-                       getattr(input_data, "Stdin_Abort_Poll", "no"))
-    timing_report_every = max(1, int(getattr(
-        input_data, "Timing_Every_Steps",
-        getattr(input_data, "Timing_Report_Every", 1))))
-    timing_top_hotspots = max(1, int(getattr(
-        input_data, "Timing_Top_Hotspots", 8)))
-
-    if ( fine_timing == "yes" ):
-        print( "#define BSSN_FINE_TIMING 1", file=file1 )
-        print(                               file=file1 )
-    elif ( fine_timing == "no" ):
-        print( "#define BSSN_FINE_TIMING 0", file=file1 )
-        print(                               file=file1 )
-    else:
-        print( "Fine_Timing setting error!!!" )
-        print()
-        print( "# Fine_Timing setting error!!!", file=file1 )
-        print(                                   file=file1 )
-
-    print( f"#define BSSN_FINE_TIMING_EVERY {timing_report_every}", file=file1 )
-    print(                                                          file=file1 )
-    print( f"#define BSSN_FINE_TIMING_TOPN {timing_top_hotspots}",  file=file1 )
-    print(                                                          file=file1 )
-
-    if ( kernel_fine_timing == "yes" ):
-        print( "#define BSSN_KERNEL_FINE_TIMING 1", file=file1 )
-        print(                                      file=file1 )
-    elif ( kernel_fine_timing == "no" ):
-        print( "#define BSSN_KERNEL_FINE_TIMING 0", file=file1 )
-        print(                                      file=file1 )
-    else:
-        print( "Kernel_Fine_Timing setting error!!!" )
-        print()
-        print( "# Kernel_Fine_Timing setting error!!!", file=file1 )
-        print(                                          file=file1 )
-
-    if ( stdin_abort_poll == "yes" ):
-        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 1", file=file1 )
-        print(                                           file=file1 )
-    elif ( stdin_abort_poll == "no" ):
-        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 0", file=file1 )
-        print(                                           file=file1 )
-    else:
-        print( "Enable_Stdin_Abort_Poll setting error!!!" )
-        print()
-        print( "# Enable_Stdin_Abort_Poll setting error!!!", file=file1 )
-        print(                                               file=file1 )
-
     # Define macro USE_GPU
     # use GPU or not
     
     if ( input_data.GPU_Calculation == "yes"):
-        print( "//#define USE_GPU",   file=file1 )
+        print( "#define USE_GPU",   file=file1 )
         print(                      file=file1 )
     elif ( input_data.GPU_Calculation == "no"):
         print( "//#define USE_GPU", file=file1 )
@@ -280,21 +224,6 @@ def generate_macrodef_h():
     print( "//     0: for every level;",                                                 file=file1 ) 
     print( "//     1: for all",                                                          file=file1 )
     print( "//",                                                                         file=file1 )
-    print( "// define BSSN_FINE_TIMING",                                                 file=file1 )
-    print( "//     enable fine-grained per-timestep timing monitor",                     file=file1 )
-    print( "//",                                                                         file=file1 )
-    print( "// define BSSN_FINE_TIMING_EVERY",                                           file=file1 )
-    print( "//     report timing every N coarse timesteps",                              file=file1 )
-    print( "//",                                                                         file=file1 )
-    print( "// define BSSN_FINE_TIMING_TOPN",                                            file=file1 )
-    print( "//     number of hottest timing buckets shown in stdout",                    file=file1 )
-    print( "//",                                                                         file=file1 )
-    print( "// define BSSN_KERNEL_FINE_TIMING",                                          file=file1 )
-    print( "//     enable split timing inside compute_rhs_bssn",                         file=file1 )
-    print( "//",                                                                         file=file1 )
-    print( "// define BSSN_ENABLE_STDIN_ABORT_POLL",                                     file=file1 )
-    print( "//     poll stdin and broadcast abort flag every coarse step",               file=file1 )
-    print( "//",                                                                         file=file1 )
     print( "// define USE_GPU",                                                          file=file1 )
     print( "//     use gpu or not",                                                      file=file1 )
     print( "//",                                                                         file=file1 )

makefile_and_run.py

@@ -70,9 +70,9 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off USE_CUDA_BSSN=0 USE_CUDA_Z4C=0 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} INTERP_LB_MODE=off USE_CUDA_BSSN=1 USE_CUDA_Z4C=1 ABE_CUDA"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:
         print( " CPU/GPU numerical calculation setting is wrong " )
         print(                                                    )
@@ -151,7 +151,7 @@ def run_ABE():
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE_CUDA"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output