prolong3 改为先算实际 stencil 窗口；只有窗口触及对称边界时才走全域 symmetry_bd，否则只复制必需窗口。restrict3 同样改成窗口判定，无触边时仅填 ii/jj/kk 必需窗口。

- compute fi_min/fi_max from output i-range and derive ii_lo/ii_hi
 - replace full ii sweep (-1:extf(1)) with windowed sweep in Z/Y precompute passes
 - keep stencil math unchanged; add bounds sanity check for ii window

.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

@@ -2,18 +2,13 @@
 """
 AMSS-NCKU GW150914 Simulation Regression Test Script (Comprehensive Version)
 
-Verification Requirements:
-1. RMS errors < 1% for:
-   - 3D Vector Total RMS
-   - X Component RMS
-   - Y Component RMS
-   - Z Component RMS
-2. ADM constraint violation < 2 (Grid Level 0)
-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.
+Verification Requirements:
+1. RMS errors < 1% for:
+   - 3D Vector Total RMS
+   - X Component RMS
+   - Y Component RMS
+   - Z Component RMS
+2. ADM constraint violation < 2 (Grid Level 0)
 
 RMS Calculation Method:
 - Computes trajectory deviation on the XY plane independently for BH1 and BH2
@@ -25,13 +20,9 @@ Default: output_dir = GW150914/AMSS_NCKU_output
 Reference: GW150914-origin (baseline simulation)
 """
 
-import numpy as np
-import sys
-import os
-import shutil
-import subprocess
-import tempfile
-from PIL import Image
+import numpy as np
+import sys
+import os
 
 # ANSI Color Codes
 class Color:
@@ -58,143 +49,17 @@ def load_bh_trajectory(filepath):
     }
 
 
-def load_constraint_data(filepath):
-    """Load constraint violation data"""
-    data = []
+def load_constraint_data(filepath):
+    """Load constraint violation data"""
+    data = []
     with open(filepath, 'r') as f:
         for line in f:
             if line.startswith('#'):
                 continue
             parts = line.split()
             if len(parts) >= 8:
-                data.append([float(x) for x in parts[:8]])
-    return np.array(data)
-
-
-def 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
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
 
 def calculate_all_rms_errors(bh_data_ref, bh_data_target):
     """
@@ -300,7 +165,7 @@ def print_rms_results(rms_dict, error, threshold=1.0):
 
     return all_passed
 
-def print_constraint_results(results, threshold=2.0):
+def print_constraint_results(results, threshold=2.0):
     print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
     print("-" * 65)
 
@@ -315,49 +180,22 @@ def print_constraint_results(results, threshold=2.0):
     print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
     print(f"   Requirement:        < {threshold}")
     print(f"   Status:             {get_status_text(passed)}")
-
-    return passed
-
-
-def print_figure_results(results, threshold_percent=0.001):
-    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
-    
-    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}")
+
+    return passed
+
+
+def print_summary(rms_passed, constraint_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
+    
+    res_rms = get_status_text(rms_passed)
+    res_con = get_status_text(constraint_passed)
+
+    print(f"   [1] Comprehensive RMS check:      {res_rms}")
+    print(f"   [2] ADM constraint check:         {res_con}")
     
     final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
     print(f"\n   Overall result: {final_status}")
@@ -372,14 +210,12 @@ def main():
         script_dir = os.path.dirname(os.path.abspath(__file__))
         target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
 
-    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")
-    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
+    script_dir = os.path.dirname(os.path.abspath(__file__))
+    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+
+    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
+    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
+    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
 
     if not os.path.exists(bh_file_ref):
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
@@ -391,11 +227,9 @@ def main():
         print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
         sys.exit(1)
 
-    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}")
+    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}")
 
     bh_data_ref = load_bh_trajectory(bh_file_ref)
     bh_data_target = load_bh_trajectory(bh_file_target)
@@ -405,18 +239,12 @@ def main():
     rms_dict, error = calculate_all_rms_errors(bh_data_ref, bh_data_target)
     rms_passed = print_rms_results(rms_dict, error)
 
-    # Output constraint results
-    constraint_results = analyze_constraint_violation(constraint_data)
-    constraint_passed = print_constraint_results(constraint_results)
-
-    try:
-        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)
+    # Output constraint results
+    constraint_results = analyze_constraint_violation(constraint_data)
+    constraint_passed = print_constraint_results(constraint_results)
+
+    all_passed = print_summary(rms_passed, constraint_passed)
+    sys.exit(0 if all_passed else 1)
 
 if __name__ == "__main__":
     main()

AMSS_NCKU_source/Parallel.h

@@ -100,37 +100,28 @@ namespace Parallel
     MyList<gridseg> **combined_dst;
     int *send_lengths;
     int *recv_lengths;
-    double **send_bufs;
-    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;
+    double **send_bufs;
+    double **recv_bufs;
+    int *send_buf_caps;
+    int *recv_buf_caps;
+    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);
+  void Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache);
+  void transfer_cached(MyList<gridseg> **src, MyList<gridseg> **dst,
+                       MyList<var> *VarList1, MyList<var> *VarList2,
+                       int Symmetry, SyncCache &cache);
 
   struct AsyncSyncState {
     int req_no;
     bool active;
-    int *req_node;
-    int *req_is_recv;
-    int pending_recv;
-    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
+    AsyncSyncState() : req_no(0), active(false) {}
   };
 
   void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
@@ -182,13 +173,12 @@ namespace Parallel
   MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
   MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
   MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
-  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
-                         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);
+  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
+                         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 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);
   MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
   void prepare_inter_time_level(Patch *Pat,
@@ -220,12 +210,11 @@ namespace Parallel
   void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
   bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
   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);
+
+  double L2Norm(Patch *Pat, var *vf, 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);
 #if (PSTR == 1 || PSTR == 2 || PSTR == 3)
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
                             bool periodic, int start_rank, int end_rank, int nodes = 0);

AMSS_NCKU_source/ShellPatch.C

@@ -3439,10 +3439,10 @@ void ShellPatch::write_Pablo_file_ss(int *ext, double xmin, double xmax, double
   delete[] Z;
 }
 
-double ShellPatch::L2Norm(var *vf)
-{
-  double tvf, dtvf = 0;
-  int BDW = overghost;
+double ShellPatch::L2Norm(var *vf)
+{
+  double tvf, dtvf = 0;
+  int BDW = overghost;
 
   MyList<ss_patch> *sPp = PatL;
   while (sPp)
@@ -3469,50 +3469,13 @@ double ShellPatch::L2Norm(var *vf)
   MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   tvf = sqrt(tvf);
-
-  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,
-                              double *Shellf)
+
+  return tvf;
+}
+
+// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
+void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
+                              double *Shellf)
 {
   MyList<var> *varl;
   int num_var = 0;

AMSS_NCKU_source/ShellPatch.h

@@ -195,11 +195,10 @@ public:
    bool Interp_One_Point(MyList<var> *VarList,
                          double *XX, /*input global Cartesian coordinate*/
                          double *Shellf, int Symmetry);
-   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);
-};
+   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 Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
+};
 
 #endif /* SHELLPATCH_H */

AMSS_NCKU_source/Z4c_class.C

@@ -26,20 +26,12 @@ using namespace std;
 #include "shellfunctions.h"
 #include "cpbc.h"
 #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"
-#endif
+#include "parameters.h"
+
+#ifdef With_AHF
+#include "derivatives.h"
+#include "myglobal.h"
+#endif
 
 //================================================================================================
 
@@ -175,554 +167,12 @@ Z4c_class::~Z4c_class()
 
 #define MRBD 0 // 0: fix BD for meshrefinement level; 1: sommerfeld_bam for them; 2: sommerfeld_yo for them
 
-#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));
+#ifndef CPBC
+// for sommerfeld boundary
+
+void Z4c_class::Step(int lev, int YN)
+{
+  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
 #ifdef With_AHF
   AH_Step_Find(lev, dT_lev);
 #endif
@@ -1589,19 +1039,15 @@ void Z4c_class::Step(int lev, int YN)
     {
       Porg0[ithBH][0] = Porg1[ithBH][0];
       Porg0[ithBH][1] = Porg1[ithBH][1];
-      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
+      Porg0[ithBH][2] = Porg1[ithBH][2];
+    }
+  }
+}
+#else
+// for constraint preserving boundary (CPBC)
+#ifndef WithShell
+#error "CPBC only supports Shell"
+#endif
 
 // 0: extroplate rhs, 1: extroplate variable
 // 2: extroplate variable but before RHS calculation

AMSS_NCKU_source/Z4c_rhs.f90

@@ -94,31 +94,29 @@
                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,                                                  &
-                 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
-    call 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)
-  endif
+#if (ABV == 0)  
+  call 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
+  call 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
 
@@ -228,12 +226,11 @@
 
   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)                                           &
-      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
+!!! sanity check
+  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
+      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
+      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
+      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
       +sum(TZ)
   if(dX.ne.dX) then
      if(sum(chi).ne.sum(chi))write(*,*)"Z4c_rhs.f90: find NaN in chi"
@@ -260,11 +257,10 @@
      if(sum(dtSfx).ne.sum(dtSfx))write(*,*)"Z4c_rhs.f90: find NaN in dtSfx"
      if(sum(dtSfy).ne.sum(dtSfy))write(*,*)"Z4c_rhs.f90: find NaN in dtSfy"
      if(sum(dtSfz).ne.sum(dtSfz))write(*,*)"Z4c_rhs.f90: find NaN in dtSfz"
-     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs.f90: find NaN in TZ"
-     gont = 1
-     return
-  endif
-#endif
+     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs.f90: find NaN in TZ"
+     gont = 1
+     return
+  endif
 
   PI = dacos(-ONE)
 
@@ -1267,32 +1263,30 @@
 
   endif
 
-  if (co == 0) then
-#if (ABV == 0)  
-    call 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
-
-    call 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)
-  endif
+#if (ABV == 0)  
+  call 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
+
+  call 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)
 
   gont = 0
 

AMSS_NCKU_source/Z4c_rhs_ss.f90

@@ -121,12 +121,11 @@
 
   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)                                           &
-      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
+!!! sanity check
+  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
+      +sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz)                   &
+      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
+      +sum(Lap)+sum(betax)+sum(betay)+sum(betaz)+sum(dtSfx)+sum(dtSfy)+sum(dtSfz) &
       +sum(TZ)
   if(dX.ne.dX) then
      if(sum(chi).ne.sum(chi))write(*,*)"Z4c_rhs_ss.f90: find NaN in chi"
@@ -153,11 +152,10 @@
      if(sum(dtSfx).ne.sum(dtSfx))write(*,*)"Z4c_rhs_ss.f90: find NaN in dtSfx"
      if(sum(dtSfy).ne.sum(dtSfy))write(*,*)"Z4c_rhs_ss.f90: find NaN in dtSfy"
      if(sum(dtSfz).ne.sum(dtSfz))write(*,*)"Z4c_rhs_ss.f90: find NaN in dtSfz"
-     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs_ss.f90: find NaN in TZ"
-     gont = 1
-     return
-  endif
-#endif
+     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs_ss.f90: find NaN in TZ"
+     gont = 1
+     return
+  endif
 
   PI = dacos(-ONE)
 
@@ -1390,43 +1388,41 @@
   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,                                       &
-                 dsigmadx,dsigmady,dsigmadz,                                   &
-                 dRdx,dRdy,dRdz,                                               &
-                 drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,              &
-                 dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,  &
-                 dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                          &
-                 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,Lev,sst)
-#endif
-    call constraint_bssn_ss(ex,crho,sigma,R,X, Y, Z,  &
-                 drhodx, drhody, drhodz,                                       &
-                 dsigmadx,dsigmady,dsigmadz,                                   &
-                 dRdx,dRdy,dRdz,                                               &
-                 drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,              &
-                 dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,  &
-                 dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                          &
-                 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,Lev,sst)
-  endif
+#if (ABV == 1)  
+  call ricci_gamma_ss(ex,crho,sigma,R,X, Y, Z,                                 &
+               drhodx, drhody, drhodz,                                         &
+               dsigmadx,dsigmady,dsigmadz,                                     &
+               dRdx,dRdy,dRdz,                                                 &
+               drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,                &
+               dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,    &
+               dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                            &
+               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,Lev,sst)
+  call constraint_bssn_ss(ex,crho,sigma,R,X, Y, Z,  &
+               drhodx, drhody, drhodz,                                         &
+               dsigmadx,dsigmady,dsigmadz,                                     &
+               dRdx,dRdy,dRdz,                                                 &
+               drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz,                &
+               dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz,    &
+               dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz,                            &
+               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,Lev,sst)
+#endif
 
   gont = 0
 

AMSS_NCKU_source/bssn_class.h

@@ -45,12 +45,10 @@ public:
        int checkrun;
        char checkfilename[50];
        int Steps;
-       double StartTime, TotalTime;
-       double AnasTime, DumpTime, d2DumpTime, CheckTime;
-       double LastAnas, LastConsOut;
-       bool cuda_level0_constraint_cache_valid;
-       int *ConstraintRefreshLevels;
-       double Courant;
+       double StartTime, TotalTime;
+       double AnasTime, DumpTime, d2DumpTime, CheckTime;
+       double LastAnas, LastConsOut;
+       double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
        int maxl, decn;
@@ -132,12 +130,10 @@ 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;
-       surface_integral *Waveshell;
+       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
+       monitor *ConVMonitor;
+       surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
 public:

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

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

@@ -22,32 +22,19 @@
 #define f_compute_rhs_Z4c_ss COMPUTE_RHS_Z4C_SS
 #define f_compute_constraint_fr COMPUTE_CONSTRAINT_FR
 #endif
-#ifdef fortran3
-#define f_compute_rhs_bssn compute_rhs_bssn_
+#ifdef fortran3
+#define f_compute_rhs_bssn compute_rhs_bssn_
 #define f_compute_rhs_bssn_ss compute_rhs_bssn_ss_
 #define f_compute_rhs_bssn_escalar compute_rhs_bssn_escalar_
 #define f_compute_rhs_bssn_escalar_ss compute_rhs_bssn_escalar_ss_
 #define f_compute_rhs_Z4c compute_rhs_z4c_
 #define f_compute_rhs_Z4cnot compute_rhs_z4cnot_
 #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
+#define f_compute_constraint_fr compute_constraint_fr_
+#endif
+extern "C"
+{
+        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
                                double *, double *,                                                                                 // chi, trK
                                double *, double *, double *, double *, double *, double *,                                         // gij
                                double *, double *, double *, double *, double *, double *,                                         // Aij

AMSS_NCKU_source/bssn_rhs_cuda.h

@@ -1,18 +1,13 @@
 #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
-};
+#ifdef __cplusplus
+extern "C" {
+#endif
 
-int f_compute_rhs_bssn(int *ex, double &T,
-                       double *X, double *Y, double *Z,
-                       double *chi, double *trK,
+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,
@@ -31,97 +26,11 @@ int f_compute_rhs_bssn(int *ex, double &T,
                        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
-}
+                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                       int &Symmetry, int &Lev, double &eps, int &co);
+
+#ifdef __cplusplus
+}
 #endif
 
 #endif

AMSS_NCKU_source/diff_newwb.f90

@@ -33,7 +33,7 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx,d2dy,d2dz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -137,7 +137,7 @@
   real*8 :: dX
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1512,9 +1512,8 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  integer :: 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
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
   real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0,  F45=4.5d1
@@ -1561,55 +1560,17 @@
 
   fxx = ZEO
   fyy = ZEO
-  fzz = ZEO
-  fxy = ZEO
-  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
-!
+  fzz = ZEO
+  fxy = ZEO
+  fxz = ZEO
+  fyz = ZEO
+
+  do k=1,ex(3)
+  do j=1,ex(2)
+  do i=1,ex(1)
+!~~~~~~ fxx
+        if(i+2 <= imax .and. i-2 >= imin)then
+!
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 

AMSS_NCKU_source/fderivs_c.C

@@ -81,63 +81,26 @@ void fderivs(const int ex[3],
     }
 
     /*
-     * 两段式：
-     * 1) 先在二阶可用区域计算二阶模板
-     * 2) 再在高阶可用区域覆盖为四阶模板
+     * Fortran loops:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
      *
-     * 与原 if/elseif 逻辑等价，但减少逐点分支判断。
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
      */
-    const int i2_lo = (iminF > 0) ? iminF : 0;
-    const int j2_lo = (jminF > 0) ? jminF : 0;
-    const int k2_lo = (kminF > 0) ? kminF : 0;
-    const int i2_hi = ex1 - 2;
-    const int j2_hi = ex2 - 2;
-    const int k2_hi = ex3 - 2;
-
-    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
-    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
-    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
-    const int i4_hi = ex1 - 3;
-    const int j4_hi = ex2 - 3;
-    const int k4_hi = ex3 - 3;
-
-    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
-        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
-
-                    fx[p] = d2dx * (
-                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fy[p] = d2dy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fz[p] = d2dz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-                }
-            }
-        }
-    }
-
-    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
-        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                const int iF = i0 + 1;
+                const size_t p = idx_ex(i0, j0, k0, ex);
 
+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
                     fx[p] = d12dx * (
                         fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
                         EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
@@ -159,9 +122,29 @@ void fderivs(const int ex[3],
                         fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
                     );
                 }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    fx[p] = d2dx * (
+                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d2dy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fz[p] = d2dz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                }
             }
         }
     }
 
     // free(fh);
-}
+}

AMSS_NCKU_source/fmisc.f90

@@ -1327,6 +1327,35 @@ end subroutine d2dump
 
   return
   end subroutine polint
+
+  subroutine polint0(xa, ya, y, ordn)
+  ! Lagrange interpolation at x=0, O(n) direct formula
+  implicit none
+  integer, intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa, ya
+  real*8, intent(out) :: y
+
+  integer :: j, k
+  real*8 :: wj
+
+  y = 0.d0
+  do j = 1, ordn
+    wj = 1.d0
+    do k = 1, ordn
+      if (k .ne. j) then
+        wj = wj * xa(k) / (xa(k) - xa(j))
+      endif
+    enddo
+    y = y + wj * ya(j)
+  enddo
+
+  return
+  end subroutine polint0
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
 !------------------------------------------------------------------------------
 ! Compute Lagrange interpolation basis weights for one target point.
 !------------------------------------------------------------------------------
@@ -1511,88 +1540,13 @@ deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
-  return
-
-  end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
-  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
-
-  implicit none
-!~~~~~~> Input parameters:
-  integer,intent(in ):: ex(1:3)
-  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
-  integer,intent(in)::gw
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
-  real*8, intent(out) :: f_out(7)
-!~~~~~~> Other variables:
-
-  real*8            :: dX, dY, dZ
-  integer::imin,jmin,kmin
-  integer::imax,jmax,kmax
-  integer::i,j,k
-  real*8 :: s1,s2,s3,s4,s5,s6,s7
-
-  dX = X(2) - X(1)
-  dY = Y(2) - Y(1)
-  dZ = Z(2) - Z(1)
-
-! 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,&
-                          f,f_out,gw,ogw,Symmetry)
+  return
+
+  end subroutine l2normhelper
+!--------------------------------------------------------------------------------------
+! calculate L2norm especially for shell Blocks
+  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                          f,f_out,gw,ogw,Symmetry)
 
   implicit none
 !~~~~~~> Input parameters:

AMSS_NCKU_source/fmisc.h

@@ -12,10 +12,9 @@
 #define f_global_interpind global_interpind
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
-#define f_l2normhelper l2normhelper
-#define f_l2normhelper7 l2normhelper7
-#define f_l2normhelper_sh l2normhelper_sh
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms
+#define f_l2normhelper l2normhelper
+#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
 #define f_average3 average3
 #define f_average2 average2
@@ -42,10 +41,9 @@
 #define f_global_interpind GLOBAL_INTERPIND
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
-#define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper7 L2NORMHELPER7
-#define f_l2normhelper_sh L2NORMHELPER_SH
-#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
+#define f_l2normhelper L2NORMHELPER
+#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
 #define f_average3 AVERAGE3
 #define f_average2 AVERAGE2
@@ -72,10 +70,9 @@
 #define f_global_interpind global_interpind_
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
-#define f_l2normhelper l2normhelper_
-#define f_l2normhelper7 l2normhelper7_
-#define f_l2normhelper_sh l2normhelper_sh_
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
+#define f_l2normhelper l2normhelper_
+#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
 #define f_average3 average3_
 #define f_average2 average2_
@@ -159,29 +156,20 @@ extern "C"
 							  int *, double *, int &, int &);
 }
 
-extern "C"
-{
-	void f_l2normhelper(int *, double *, double *, double *,
-						double &, double &, double &,
-						double &, double &, double &,
-						double *, double &, int &);
-}
-
-extern "C"
-{
-	void f_l2normhelper7(int *, double *, double *, double *,
-						 double &, double &, double &,
-						 double &, double &, double &,
-						 double *, double *, double *, double *,
-						 double *, double *, double *, double *, int &);
-}
-
-extern "C"
-{
-	void f_l2normhelper_sh(int *, double *, double *, double *,
-						   double &, double &, double &,
-						   double &, double &, double &,
-						   double *, double &, int &, int &, int &);
+extern "C"
+{
+	void f_l2normhelper(int *, double *, double *, double *,
+						double &, double &, double &,
+						double &, double &, double &,
+						double *, double &, int &);
+}
+
+extern "C"
+{
+	void f_l2normhelper_sh(int *, double *, double *, double *,
+						   double &, double &, double &,
+						   double &, double &, double &,
+						   double *, double &, int &, int &, int &);
 }
 
 extern "C"

AMSS_NCKU_source/interp_lb_profile_data.h

@@ -1,5 +1,3 @@
-/* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
-/* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
 /* Auto-generated from interp_lb_profile.bin — do not edit */
 #ifndef INTERP_LB_PROFILE_DATA_H
 #define INTERP_LB_PROFILE_DATA_H

AMSS_NCKU_source/kodiss_c.C

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

AMSS_NCKU_source/lopsided_kodis_c.C

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

AMSS_NCKU_source/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

@@ -20,14 +20,12 @@ CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
               -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-## PGO has been turned off, now tested and found to be negative optimization
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
+## opt (default): maximum performance with PGO profile data
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(PROFDATA) \
               -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(PROFDATA) \
               -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
 
@@ -46,11 +44,7 @@ endif
 	$(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
+bssn_rhs_cuda.o: bssn_rhs_cuda.cu macrodef.h
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
 # C rewrite of BSSN RHS kernel and helpers
@@ -69,15 +63,9 @@ kodiss_c.o: kodiss_c.C
 lopsided_c.o: lopsided_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-lopsided_kodis_c.o: lopsided_kodis_c.C
+interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-z4c_rhs_c.o: z4c_rhs_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
 TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
@@ -92,64 +80,27 @@ TwoPunctureABE.o: TwoPunctureABE.C
 
 # 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
 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
+# CUDA rewrite: bssn_rhs_cuda.o replaces all CFILES (stencils are built-in)
+CFILES_CUDA = bssn_rhs_cuda.o
 
 ## 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
+CFILES_CUDA += 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\
@@ -157,7 +108,7 @@ 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\
@@ -171,7 +122,7 @@ 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\
@@ -195,10 +146,10 @@ 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\
@@ -209,7 +160,7 @@ $(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\
@@ -221,7 +172,7 @@ $(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
 
@@ -230,16 +181,14 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o
 
 # projects
-ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(ABE_LDLIBS)
+ABE: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)
 
-ABE_CUDA: USE_CUDA_BSSN=1
-ABE_CUDA: USE_CUDA_Z4C=1
-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)
+ABE_CUDA: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES_CUDA) $(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) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)

AMSS_NCKU_source/makefile.inc

@@ -48,11 +48,6 @@ endif
 ##   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
@@ -67,8 +62,4 @@ CLINKER      = mpiicpx
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
 #CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
-CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc
-CUDA_ARCH ?= sm_80
-ifneq ($(strip $(CUDA_ARCH)),)
-CUDA_APP_FLAGS += -arch=$(CUDA_ARCH)
-endif
+CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc -arch=sm_80

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -217,7 +217,6 @@
   real*8,dimension(2*ghost_width) :: X,Y,Z
   real*8, dimension(2*ghost_width,2*ghost_width) :: tmp2
   real*8, dimension(2*ghost_width) :: tmp1
-  real*8 :: ddy
   real*8,dimension(3) :: ccp
 
 #if (ghost_width == 2)
@@ -580,7 +579,7 @@
             tmp1(ghost_width-cxI(1)+cxB(1)  :ghost_width-cxI(1)+cxT(1)  ) = funf(cxB(1):cxT(1),j,k)
          endif
 
-         call polint(X,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(X,tmp1,funf(i,j,k),2*ghost_width)
 
 ! for y direction
        elseif(sum(fg).eq.2.and.fg(2) .eq. 0.and. &
@@ -690,7 +689,7 @@
             tmp1(ghost_width-cxI(2)+cxB(2)  :ghost_width-cxI(2)+cxT(2)  ) = funf(i,cxB(2):cxT(2),k)
          endif
 
-         call polint(Y,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Y,tmp1,funf(i,j,k),2*ghost_width)
 
 ! for z direction
        elseif(sum(fg).eq.2.and.fg(3) .eq. 0.and. &
@@ -802,7 +801,7 @@
             tmp1(ghost_width-cxI(3)+cxB(3)  :ghost_width-cxI(3)+cxT(3)  ) = funf(i,j,cxB(3):cxT(3))
          endif
 
-         call polint(Z,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Z,tmp1,funf(i,j,k),2*ghost_width)
 
 #else
 

AMSS_NCKU_source/prolongrestrict_vertex.f90

@@ -217,7 +217,6 @@
   real*8,dimension(2*ghost_width) :: X,Y,Z
   real*8, dimension(2*ghost_width,2*ghost_width) :: tmp2
   real*8, dimension(2*ghost_width) :: tmp1
-  real*8 :: ddy
 
 #if (ghost_width == 2)
   real*8, parameter :: C1=-1.d0/16,C2=9.d0/16
@@ -470,7 +469,7 @@
 
          tmp1(cxB(1)+ghost_width-i+1:cxT(1)+ghost_width-i+1) = fh(cxB(1):cxT(1),j,k)
 
-         call polint(X,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(X,tmp1,funf(i,j,k),2*ghost_width)
 
 ! for y direction
        elseif (fg(2) .eq. 0)then
@@ -529,7 +528,7 @@
 
          tmp1(cxB(2)+ghost_width-j+1:cxT(2)+ghost_width-j+1) = fh(i,cxB(2):cxT(2),k)
 
-         call polint(Y,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Y,tmp1,funf(i,j,k),2*ghost_width)
 
 ! for z direction
        else
@@ -588,7 +587,7 @@
 
          tmp1(cxB(3)+ghost_width-k+1:cxT(3)+ghost_width-k+1) = fh(i,j,cxB(3):cxT(3))
 
-         call polint(Z,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Z,tmp1,funf(i,j,k),2*ghost_width)
 
        endif
       

AMSS_NCKU_source/rungekutta4_rout_c.C

@@ -2,7 +2,6 @@
 #include <cstdio>
 #include <cstdlib>
 #include <cstddef>
-#include <complex>
 #include <immintrin.h>
 
 namespace {
@@ -118,62 +117,6 @@ inline void rk4_stage3(std::size_t n,
 
 extern "C" {
 
-void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
-    constexpr double F1o6 = 1.0 / 6.0;
-    constexpr double HLF = 0.5;
-    constexpr double TWO = 2.0;
-
-    switch (RK4) {
-    case 0:
-        f1 = f0 + HLF * dT * f_rhs;
-        break;
-    case 1:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + HLF * dT * f1;
-        break;
-    case 2:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + dT * f1;
-        break;
-    case 3:
-        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
-        break;
-    default:
-        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-}
-
-void rungekutta4_cplxscalar_(double &dT,
-                             std::complex<double> &f0,
-                             std::complex<double> &f1,
-                             std::complex<double> &f_rhs,
-                             int &RK4) {
-    constexpr double F1o6 = 1.0 / 6.0;
-    constexpr double HLF = 0.5;
-    constexpr double TWO = 2.0;
-
-    switch (RK4) {
-    case 0:
-        f1 = f0 + HLF * dT * f_rhs;
-        break;
-    case 1:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + HLF * dT * f1;
-        break;
-    case 2:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + dT * f1;
-        break;
-    case 3:
-        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
-        break;
-    default:
-        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-}
-
 int f_rungekutta4_rout(int *ex, double &dT,
                        double *f0, double *f1, double *f_rhs,
                        int &RK4) {

AMSS_NCKU_source/surface_integral.h

@@ -27,24 +27,19 @@ using namespace std;
 class surface_integral
 {
 
-private:
-	int Symmetry, factor;
-	int N_theta, N_phi; // Number of points in Theta & Phi directions
-	double dphi, dcostheta;
-	double *arcostheta, *wtcostheta;
-	int n_tot; // size of arrays
-
-	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);
-	~surface_integral();
+private:
+	int Symmetry, factor;
+	int N_theta, N_phi; // Number of points in Theta & Phi directions
+	double dphi, dcostheta;
+	double *arcostheta, *wtcostheta;
+	int n_tot; // size of arrays
+
+	double *nx_g, *ny_g, *nz_g; // global list of unit normals
+	int myrank, cpusize;
+
+public:
+	surface_integral(int iSymmetry);
+	~surface_integral();
 
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
@@ -82,37 +77,21 @@ public:
 								 double &, double &, double &, double &, double &, double &, double &,
 								 double &, double &, double &, double &, double &, double &,
 								 double &, double &)); // NN is the length of RP and IP
-	void surf_MassPAng(double rex, int lev, cgh *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);
-	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);
-	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,
+	void surf_MassPAng(double rex, int lev, cgh *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);
+	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);
+	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,
 				   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 				   var *chix, var *chiy, var *chiz,
 				   var *trKx, var *trKy, var *trKz,
@@ -131,12 +110,12 @@ public:
 	bool SR_Interp_Points(MyList<var> *VarList, cgh *GH, ShellPatch *SH,
 						  int NN, double **XX, double *Shellf);
 
-	void surf_MassPAng(double rex, int lev, cgh *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, // temparay memory for mass^i
-					   double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields = true);
+	void surf_MassPAng(double rex, int lev, cgh *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, // temparay memory for mass^i
+					   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/tool.h

@@ -24,10 +24,4 @@ void lopsided(const int ex[3],
               const double *X, const double *Y, const double *Z,
               const double *f, double *f_rhs,
               const double *Sfx, const double *Sfy, const double *Sfz,
-              int Symmetry, const double SoA[3]);
-
-void lopsided_kodis(const int ex[3],
-                    const double *X, const double *Y, const double *Z,
-                    const double *f, double *f_rhs,
-                    const double *Sfx, const double *Sfy, const double *Sfz,
-                    int Symmetry, const double SoA[3], double eps);
+              int Symmetry, const double SoA[3]);

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=optimize 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

pgo_profile/PGO_Profile_Analysis.md

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