Stabilize EScalar CUDA fallback path

Rewritten done by Codex.
This still has errors, do not pick this one now.

.gitignore

@@ -1,6 +1,6 @@
 __pycache__
 GW150914
-GW150914-origin
+GW150914*
 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    = 64                             ## number of mpi processes used in the simulation
+MPI_processes    = 2                             ## number of mpi processes used in the simulation
 
-GPU_Calculation  = "no"                          ## Use GPU or not 
+GPU_Calculation  = "yes"                          ## 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
@@ -31,7 +31,7 @@ GPU_Part         = 0.0
 ## Setting the physical system and numerical method
 
 Symmetry                 = "equatorial-symmetry"   ## Symmetry of System: choose equatorial-symmetry、no-symmetry、octant-symmetry
-Equation_Class           = "BSSN"                  ## Evolution Equation: choose "BSSN", "BSSN-EScalar", "BSSN-EM", "Z4C" 
+Equation_Class           = "BSSN-EScalar"                  ## Evolution Equation: choose "BSSN", "BSSN-EScalar", "BSSN-EM", "Z4C"
                                                    ## If "BSSN-EScalar" is chosen, it is necessary to set other parameters below
 Initial_Data_Method      = "Ansorg-TwoPuncture"    ## initial data method: choose "Ansorg-TwoPuncture", "Lousto-Analytical", "Cao-Analytical", "KerrSchild-Analytical"
 Time_Evolution_Method    = "runge-kutta-45"        ## time evolution method: choose "runge-kutta-45"

AMSS_NCKU_Program.py

@@ -58,31 +58,36 @@ File_directory = os.path.join(input_data.File_directory)
 
 ## If the specified output directory exists, ask the user whether to continue
 if os.path.exists(File_directory):
-    print( " Output dictionary has been existed !!!  "                                                              )
-    print( " If you want to overwrite the existing file directory, please input 'continue' in the terminal !! "     ) 
-    print( " If you want to retain the existing file directory, please input 'stop' in the terminal to stop the "   ) 
-    print( " simulation. Then you can reset the output dictionary in the input script file AMSS_NCKU_Input.py !!! " )
-    print(                                                                                                          )
-    ## Prompt whether to overwrite the existing directory
-    while True:
-        try:
-            inputvalue = input()
-            ## If the user agrees to overwrite, proceed and remove the existing directory
-            if ( inputvalue == "continue" ):
-                print( " Continue the calculation !!! " )
-                print(                                  )
-                break  
-            ## If the user chooses not to overwrite, exit and keep the existing directory
-            elif ( inputvalue == "stop" ):
-                print( " Stop the calculation !!! "    )
-                sys.exit() 
-            ## If the user input is invalid, prompt again
-            else:
+    auto_overwrite = str(getattr(input_data, "Auto_Overwrite_Output", "yes")).strip().lower()
+    if auto_overwrite in ("1", "yes", "y", "true", "on", "continue"):
+        print( " Output dictionary has been existed; Auto_Overwrite_Output=yes, continue the calculation. " )
+        print(                                                                                              )
+    else:
+        print( " Output dictionary has been existed !!!  "                                                              )
+        print( " If you want to overwrite the existing file directory, please input 'continue' in the terminal !! "     ) 
+        print( " If you want to retain the existing file directory, please input 'stop' in the terminal to stop the "   ) 
+        print( " simulation. Then you can reset the output dictionary in the input script file AMSS_NCKU_Input.py !!! " )
+        print(                                                                                                          )
+        ## Prompt whether to overwrite the existing directory
+        while True:
+            try:
+                inputvalue = input()
+                ## If the user agrees to overwrite, proceed and remove the existing directory
+                if ( inputvalue == "continue" ):
+                    print( " Continue the calculation !!! " )
+                    print(                                  )
+                    break  
+                ## If the user chooses not to overwrite, exit and keep the existing directory
+                elif ( inputvalue == "stop" ):
+                    print( " Stop the calculation !!! "    )
+                    sys.exit() 
+                ## If the user input is invalid, prompt again
+                else:
+                    print( " Please input your choice !!! "                   )
+                    print( " Input 'continue' or 'stop' in the terminal !!! " )
+            except ValueError:
                 print( " Please input your choice !!! "                   )
                 print( " Input 'continue' or 'stop' in the terminal !!! " )
-        except ValueError:
-            print( " Please input your choice !!! "                   )
-            print( " Input 'continue' or 'stop' in the terminal !!! " )
         
 ## Remove the existing output directory if present
 shutil.rmtree(File_directory, ignore_errors=True)
@@ -258,7 +263,7 @@ 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, "ABEGPU")
+    ABE_file = os.path.join(AMSS_NCKU_source_copy, "ABE_CUDA")
 
 if not os.path.exists( ABE_file ):
     print(                                                                                                  )

AMSS_NCKU_Verify_ASC26.py

@@ -2,13 +2,18 @@
 """
 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)
+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.
 
 RMS Calculation Method:
 - Computes trajectory deviation on the XY plane independently for BH1 and BH2
@@ -20,9 +25,13 @@ Default: output_dir = GW150914/AMSS_NCKU_output
 Reference: GW150914-origin (baseline simulation)
 """
 
-import numpy as np
-import sys
-import os
+import numpy as np
+import sys
+import os
+import shutil
+import subprocess
+import tempfile
+from PIL import Image
 
 # ANSI Color Codes
 class Color:
@@ -49,17 +58,143 @@ 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)
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
+
+
+def resolve_figure_dir(path):
+    """Resolve the sibling figure directory from an output or figure path."""
+    normalized = os.path.normpath(path)
+    if os.path.basename(normalized) == "figure":
+        return normalized
+    return os.path.join(os.path.dirname(normalized), "figure")
+
+
+def render_pdf_to_images(pdf_path, dpi=150):
+    """Render a PDF to RGB images using Ghostscript."""
+    gs_path = shutil.which("gs")
+    if gs_path is None:
+        raise RuntimeError("Ghostscript executable 'gs' was not found in PATH")
+
+    with tempfile.TemporaryDirectory(prefix="amss_verify_pdf_") as temp_dir:
+        output_pattern = os.path.join(temp_dir, "page-%03d.ppm")
+        cmd = [
+            gs_path,
+            "-q",
+            "-dSAFER",
+            "-dBATCH",
+            "-dNOPAUSE",
+            "-sDEVICE=ppmraw",
+            f"-r{dpi}",
+            f"-o{output_pattern}",
+            pdf_path
+        ]
+
+        try:
+            subprocess.run(cmd, check=True, stdout=subprocess.DEVNULL, stderr=subprocess.PIPE, text=True)
+        except subprocess.CalledProcessError as exc:
+            message = exc.stderr.strip() or str(exc)
+            raise RuntimeError(f"Failed to render PDF '{pdf_path}': {message}") from exc
+
+        ppm_files = sorted(
+            os.path.join(temp_dir, filename)
+            for filename in os.listdir(temp_dir)
+            if filename.endswith(".ppm")
+        )
+
+        if not ppm_files:
+            raise RuntimeError(f"No rendered pages were produced for '{pdf_path}'")
+
+        images = []
+        for ppm_file in ppm_files:
+            with Image.open(ppm_file) as img:
+                images.append(np.array(img.convert("RGB"), dtype=np.uint8))
+
+        return images
+
+
+def compare_rendered_pages(ref_img, target_img):
+    """Return (different_pixels, total_pixels) for two rendered RGB pages."""
+    ref_h, ref_w = ref_img.shape[:2]
+    tgt_h, tgt_w = target_img.shape[:2]
+    total_pixels = max(ref_h, tgt_h) * max(ref_w, tgt_w)
+
+    if ref_h == tgt_h and ref_w == tgt_w:
+        different_pixels = int(np.count_nonzero(np.any(ref_img != target_img, axis=2)))
+        return different_pixels, total_pixels
+
+    diff_mask = np.ones((max(ref_h, tgt_h), max(ref_w, tgt_w)), dtype=bool)
+    overlap_h = min(ref_h, tgt_h)
+    overlap_w = min(ref_w, tgt_w)
+    overlap_diff = np.any(ref_img[:overlap_h, :overlap_w] != target_img[:overlap_h, :overlap_w], axis=2)
+    diff_mask[:overlap_h, :overlap_w] = overlap_diff
+    different_pixels = int(np.count_nonzero(diff_mask))
+    return different_pixels, total_pixels
+
+
+def compare_pdf_images(ref_pdf, target_pdf, dpi=150, threshold_percent=0.001):
+    """Compare two PDFs by rasterizing them and counting differing pixels."""
+    ref_pages = render_pdf_to_images(ref_pdf, dpi=dpi)
+    target_pages = render_pdf_to_images(target_pdf, dpi=dpi)
+
+    total_pixels = 0
+    different_pixels = 0
+    max_pages = max(len(ref_pages), len(target_pages))
+
+    for page_idx in range(max_pages):
+        if page_idx < len(ref_pages) and page_idx < len(target_pages):
+            page_diff, page_total = compare_rendered_pages(ref_pages[page_idx], target_pages[page_idx])
+        else:
+            existing_page = ref_pages[page_idx] if page_idx < len(ref_pages) else target_pages[page_idx]
+            page_total = existing_page.shape[0] * existing_page.shape[1]
+            page_diff = page_total
+
+        total_pixels += page_total
+        different_pixels += page_diff
+
+    diff_percent = (different_pixels / total_pixels * 100.0) if total_pixels else 0.0
+    return {
+        "different_pixels": different_pixels,
+        "total_pixels": total_pixels,
+        "diff_percent": diff_percent,
+        "pages_ref": len(ref_pages),
+        "pages_target": len(target_pages),
+        "passed": diff_percent < threshold_percent
+    }
+
+
+def compare_required_figures(reference_figure_dir, target_figure_dir):
+    """Compare the required GW150914 figure PDFs."""
+    figure_names = [
+        "ADM_Constraint_Grid_Level_0.pdf",
+        "BH_Trajectory_21_XY.pdf",
+        "BH_Trajectory_XY.pdf"
+    ]
+
+    results = []
+    for figure_name in figure_names:
+        ref_pdf = os.path.join(reference_figure_dir, figure_name)
+        target_pdf = os.path.join(target_figure_dir, figure_name)
+
+        if not os.path.exists(ref_pdf):
+            raise FileNotFoundError(f"Reference figure not found: {ref_pdf}")
+        if not os.path.exists(target_pdf):
+            raise FileNotFoundError(f"Target figure not found: {target_pdf}")
+
+        comparison = compare_pdf_images(ref_pdf, target_pdf)
+        comparison["name"] = figure_name
+        results.append(comparison)
+
+    return results
 
 def calculate_all_rms_errors(bh_data_ref, bh_data_target):
     """
@@ -165,7 +300,7 @@ 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)
 
@@ -180,22 +315,49 @@ 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_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}")
+
+    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}")
     
     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}")
@@ -210,12 +372,14 @@ 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")
-
-    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")
+    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")
 
     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}")
@@ -227,9 +391,11 @@ 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_header()
+    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Reference Figures:   {Color.RESET} {Color.BLUE}{reference_figure_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target Figures:      {Color.RESET} {Color.BLUE}{target_figure_dir}{Color.RESET}")
 
     bh_data_ref = load_bh_trajectory(bh_file_ref)
     bh_data_target = load_bh_trajectory(bh_file_target)
@@ -239,12 +405,18 @@ 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)
-
-    all_passed = print_summary(rms_passed, constraint_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)
+
+    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)
 
 if __name__ == "__main__":
     main()

AMSS_NCKU_source/Block.C

@@ -6,14 +6,68 @@
 #include <cstdio>
 #include <string>
 #include <cmath>
-#include <new>
-using namespace std;
-
-#include "Block.h"
-#include "misc.h"
-
-Block::Block(int DIM, int *shapei, double *bboxi, int ranki, int ingfsi, int fngfsi, int levi, const int cgpui) : rank(ranki), ingfs(ingfsi), fngfs(fngfsi), lev(levi), cgpu(cgpui)
-{
+#include <new>
+using namespace std;
+
+#include "Block.h"
+#include "misc.h"
+
+#if USE_CUDA_BSSN || USE_CUDA_Z4C
+#include <cuda_runtime_api.h>
+#endif
+
+namespace {
+
+bool cuda_pin_gridfuncs_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_CUDA_PIN_GRIDFUNCS");
+    enabled = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+
+double *alloc_gridfunc(size_t count, unsigned char &pinned)
+{
+  pinned = 0;
+#if USE_CUDA_BSSN || USE_CUDA_Z4C
+  if (cuda_pin_gridfuncs_enabled())
+  {
+    double *ptr = 0;
+    cudaError_t err = cudaMallocHost((void **)&ptr, count * sizeof(double));
+    if (err == cudaSuccess)
+    {
+      pinned = 1;
+      return ptr;
+    }
+    cudaGetLastError();
+  }
+#endif
+  return (double *)malloc(sizeof(double) * count);
+}
+
+void free_gridfunc(double *ptr, unsigned char pinned)
+{
+  if (!ptr)
+    return;
+#if USE_CUDA_BSSN || USE_CUDA_Z4C
+  if (pinned)
+  {
+    cudaFreeHost(ptr);
+    return;
+  }
+#else
+  (void)pinned;
+#endif
+  free(ptr);
+}
+
+}
+
+Block::Block(int DIM, int *shapei, double *bboxi, int ranki, int ingfsi, int fngfsi, int levi, const int cgpui) : rank(ranki), lev(levi), cgpu(cgpui), ingfs(ingfsi), fngfs(fngfsi), igfs(0), fgfs(0), fgfs_pinned(0)
+{
   for (int i = 0; i < dim; i++)
     X[i] = 0;
 
@@ -68,14 +122,15 @@ Block::Block(int DIM, int *shapei, double *bboxi, int ranki, int ingfsi, int fng
 #endif
     }
 
-    int nn = shape[0] * shape[1] * shape[2];
-    fgfs = new double *[fngfs];
-    for (int i = 0; i < fngfs; i++)
-    {
-      fgfs[i] = (double *)malloc(sizeof(double) * nn);
-      if (!(fgfs[i]))
-      {
-        cout << "on node#" << rank << ", out of memory when constructing Block." << endl;
+    int nn = shape[0] * shape[1] * shape[2];
+    fgfs = new double *[fngfs];
+    fgfs_pinned = new unsigned char[fngfs];
+    for (int i = 0; i < fngfs; i++)
+    {
+      fgfs[i] = alloc_gridfunc((size_t)nn, fgfs_pinned[i]);
+      if (!(fgfs[i]))
+      {
+        cout << "on node#" << rank << ", out of memory when constructing Block." << endl;
         MPI_Abort(MPI_COMM_WORLD, 1);
       }
       memset(fgfs[i], 0, sizeof(double) * nn);
@@ -103,17 +158,19 @@ Block::~Block()
   {
     for (int i = 0; i < dim; i++)
       delete[] X[i];
-    for (int i = 0; i < ingfs; i++)
-      free(igfs[i]);
-    delete[] igfs;
-    for (int i = 0; i < fngfs; i++)
-      free(fgfs[i]);
-    delete[] fgfs;
-    X[0] = X[1] = X[2] = 0;
-    igfs = 0;
-    fgfs = 0;
-  }
-}
+    for (int i = 0; i < ingfs; i++)
+      free(igfs[i]);
+    delete[] igfs;
+    for (int i = 0; i < fngfs; i++)
+      free_gridfunc(fgfs[i], fgfs_pinned ? fgfs_pinned[i] : 0);
+    delete[] fgfs;
+    delete[] fgfs_pinned;
+    X[0] = X[1] = X[2] = 0;
+    igfs = 0;
+    fgfs = 0;
+    fgfs_pinned = 0;
+  }
+}
 void Block::checkBlock()
 {
   int myrank;
@@ -184,12 +241,14 @@ void Block::swapList(MyList<var> *VarList1, MyList<var> *VarList2, int myrank)
   if (rank == myrank)
   {
     MyList<var> *varl1 = VarList1, *varl2 = VarList2;
-    while (varl1 && varl2)
-    {
-      misc::swap<double *>(fgfs[varl1->data->sgfn], fgfs[varl2->data->sgfn]);
-      varl1 = varl1->next;
-      varl2 = varl2->next;
-    }
+    while (varl1 && varl2)
+    {
+      misc::swap<double *>(fgfs[varl1->data->sgfn], fgfs[varl2->data->sgfn]);
+      if (fgfs_pinned)
+        misc::swap<unsigned char>(fgfs_pinned[varl1->data->sgfn], fgfs_pinned[varl2->data->sgfn]);
+      varl1 = varl1->next;
+      varl2 = varl2->next;
+    }
     if (varl1 || varl2)
     {
       cout << "error in Block::swaplist, var lists does not match." << endl;

AMSS_NCKU_source/Block.h

@@ -13,14 +13,15 @@ public:
    int shape[dim];
    double bbox[2 * dim];
    double *X[dim];
-   int rank; // where the real data locate in
-   int lev, cgpu;
-   int ingfs, fngfs;
-   int *(*igfs);
-   double *(*fgfs);
+   int rank; // where the real data locate in
+   int lev, cgpu;
+   int ingfs, fngfs;
+   int *(*igfs);
+   double *(*fgfs);
+   unsigned char *fgfs_pinned;
 
 public:
-   Block() {};
+   Block() : rank(0), lev(0), cgpu(0), ingfs(0), fngfs(0), igfs(0), fgfs(0), fgfs_pinned(0) {};
    Block(int DIM, int *shapei, double *bboxi, int ranki, int ingfsi, int fngfs, int levi, const int cgpui = 0);
 
    ~Block();

AMSS_NCKU_source/MPatch.C

@@ -11,12 +11,15 @@
 using namespace std;
 
 #include "misc.h"
-#include "MPatch.h"
-#include "Parallel.h"
-#include "fmisc.h"
-#ifdef INTERP_LB_PROFILE
-#include "interp_lb_profile.h"
-#endif
+#include "MPatch.h"
+#include "Parallel.h"
+#include "fmisc.h"
+#if USE_CUDA_BSSN
+#include "bssn_rhs_cuda.h"
+#endif
+#ifdef INTERP_LB_PROFILE
+#include "interp_lb_profile.h"
+#endif
 
 namespace
 {
@@ -154,8 +157,8 @@ void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
   index.valid = true;
 }
 
-int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
-{
+int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
+{
   if (!index.valid)
     return -1;
 
@@ -175,10 +178,448 @@ int find_block_index_for_point(const BlockBinIndex &index, const double *pox, co
   for (size_t bi = 0; bi < index.views.size(); bi++)
     if (point_in_block_view(index.views[bi], pox, DH))
       return int(bi);
-
-  return -1;
-}
-} // namespace
+
+  return -1;
+}
+
+inline int fortran_idint_local(double x)
+{
+  return int(x);
+}
+
+bool interp_fast_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST");
+    enabled = (!env || atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+
+bool interp_gpu_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_GPU");
+    enabled = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+
+bool interp_fast_compare_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST_COMPARE");
+    enabled = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+
+double interp_fast_compare_tol()
+{
+  static double tol = -1.0;
+  if (tol < 0.0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST_COMPARE_TOL");
+    tol = (env && atof(env) > 0.0) ? atof(env) : 1.0e-11;
+  }
+  return tol;
+}
+
+long long interp_fast_compare_limit()
+{
+  static long long limit = -1;
+  if (limit < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST_COMPARE_LIMIT");
+    limit = (env && atoll(env) > 0) ? atoll(env) : 4096;
+  }
+  return limit;
+}
+
+struct FastInterpStencil
+{
+  int cxB[dim];
+  double cx[dim];
+  double wx[8];
+  double wy[8];
+  double wz[8];
+  int nsamples;
+  int loc[512];
+  unsigned char sign_mask[512];
+  double weight[512];
+};
+
+inline void lagrange_unit_weights(double x, int ordn, double *w)
+{
+  for (int i = 0; i < ordn; i++)
+  {
+    double num = 1.0;
+    double den = 1.0;
+    for (int j = 0; j < ordn; j++)
+    {
+      if (j == i)
+        continue;
+      num *= (x - double(j));
+      den *= double(i - j);
+    }
+    w[i] = num / den;
+  }
+}
+
+inline void z_unit_weights(double x, int ordn, double *w)
+{
+  if (ordn == 6)
+  {
+    static const double c_uniform[6] = {-1.0, 5.0, -10.0, 10.0, -5.0, 1.0};
+    for (int i = 0; i < 6; i++)
+    {
+      if (x == double(i))
+      {
+        for (int j = 0; j < 6; j++)
+          w[j] = (j == i) ? 1.0 : 0.0;
+        return;
+      }
+    }
+    double den = 0.0;
+    for (int i = 0; i < 6; i++)
+    {
+      w[i] = c_uniform[i] / (x - double(i));
+      den += w[i];
+    }
+    for (int i = 0; i < 6; i++)
+      w[i] /= den;
+    return;
+  }
+  lagrange_unit_weights(x, ordn, w);
+}
+
+inline bool fast_interp_map_index(int idx, int extent, int d,
+                                  int &mapped, unsigned char &mask)
+{
+  if (idx > 0)
+    mapped = idx;
+  else
+  {
+    mask |= (unsigned char)(1u << d);
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+    mapped = 2 - idx;
+#else
+#ifdef Cell
+    mapped = 1 - idx;
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+  }
+  return mapped >= 1 && mapped <= extent;
+}
+
+bool prepare_fast_interp_stencil(Block *BP, const double *pox, int ordn,
+                                 int Symmetry, FastInterpStencil &st)
+{
+  if (!BP || ordn <= 0 || ordn > 8)
+    return false;
+
+  st.nsamples = 0;
+
+  const int NO_SYMM = 0;
+  const int OCTANT = 2;
+  int cmin[dim], cmax[dim], cxT[dim];
+  for (int d = 0; d < dim; d++)
+  {
+    const double *X = BP->X[d];
+    const double dX = X[1] - X[0];
+    const int cxI = fortran_idint_local((pox[d] - X[0]) / dX + 0.4) + 1;
+    st.cxB[d] = cxI - ordn / 2 + 1;
+    cxT[d] = st.cxB[d] + ordn - 1;
+    cmin[d] = 1;
+    cmax[d] = BP->shape[d];
+
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+    if (Symmetry == OCTANT && d < 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 2;
+    if (Symmetry != NO_SYMM && d == 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 2;
+#else
+#ifdef Cell
+    if (Symmetry == OCTANT && d < 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 1;
+    if (Symmetry != NO_SYMM && d == 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 1;
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+
+    if (st.cxB[d] < cmin[d])
+    {
+      st.cxB[d] = cmin[d];
+      cxT[d] = st.cxB[d] + ordn - 1;
+    }
+    if (cxT[d] > cmax[d])
+    {
+      cxT[d] = cmax[d];
+      st.cxB[d] = cxT[d] + 1 - ordn;
+    }
+
+    if (st.cxB[d] > 0)
+      st.cx[d] = (pox[d] - X[st.cxB[d] - 1]) / dX;
+    else
+    {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+      st.cx[d] = (pox[d] + X[1 - st.cxB[d]]) / dX;
+#else
+#ifdef Cell
+      st.cx[d] = (pox[d] + X[-st.cxB[d]]) / dX;
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+    }
+  }
+
+  lagrange_unit_weights(st.cx[0], ordn, st.wx);
+  lagrange_unit_weights(st.cx[1], ordn, st.wy);
+  z_unit_weights(st.cx[2], ordn, st.wz);
+
+  for (int kk = 0; kk < ordn; kk++)
+  {
+    for (int jj = 0; jj < ordn; jj++)
+    {
+      for (int ii = 0; ii < ordn; ii++)
+      {
+        unsigned char mask = 0;
+        int ix, iy, iz;
+        if (!fast_interp_map_index(st.cxB[0] + ii, BP->shape[0], 0, ix, mask) ||
+            !fast_interp_map_index(st.cxB[1] + jj, BP->shape[1], 1, iy, mask) ||
+            !fast_interp_map_index(st.cxB[2] + kk, BP->shape[2], 2, iz, mask))
+          return false;
+        const int s = st.nsamples++;
+        st.loc[s] = (ix - 1) + (iy - 1) * BP->shape[0] +
+                    (iz - 1) * BP->shape[0] * BP->shape[1];
+        st.sign_mask[s] = mask;
+        st.weight[s] = st.wx[ii] * st.wy[jj] * st.wz[kk];
+      }
+    }
+  }
+  return true;
+}
+
+bool interpolate_var_list_with_stencil(Block *BP, MyList<var> *VarList,
+                                       int num_var, const double *pox,
+                                       int ordn, int Symmetry,
+                                       const FastInterpStencil &st,
+                                       double *out)
+{
+  if (num_var <= 0 || num_var > 128)
+    return false;
+
+  double *data_ptrs[128];
+  double *soa_ptrs[128];
+  var *vars[128];
+  MyList<var> *varl = VarList;
+  int k = 0;
+  while (varl)
+  {
+    if (k >= num_var)
+      return false;
+    vars[k] = varl->data;
+    data_ptrs[k] = BP->fgfs[vars[k]->sgfn];
+    soa_ptrs[k] = vars[k]->SoA;
+    out[k] = 0.0;
+    varl = varl->next;
+    k++;
+  }
+
+  if (k != num_var)
+    return false;
+
+  for (int s = 0; s < st.nsamples; s++)
+  {
+    const int loc = st.loc[s];
+    const double w = st.weight[s];
+    const unsigned char mask = st.sign_mask[s];
+    if (mask == 0)
+    {
+      for (int v = 0; v < num_var; v++)
+        out[v] += w * data_ptrs[v][loc];
+    }
+    else
+    {
+      for (int v = 0; v < num_var; v++)
+      {
+        const double *SoA = soa_ptrs[v];
+        double sgn = 1.0;
+        if (mask & 1u)
+          sgn *= SoA[0];
+        if (mask & 2u)
+          sgn *= SoA[1];
+        if (mask & 4u)
+          sgn *= SoA[2];
+        out[v] += w * sgn * data_ptrs[v][loc];
+      }
+    }
+  }
+
+  if (interp_fast_compare_enabled())
+  {
+    static int report_count = 0;
+    static long long compare_calls = 0;
+    if (compare_calls++ >= interp_fast_compare_limit())
+      return true;
+    const double tol = interp_fast_compare_tol();
+    varl = VarList;
+    k = 0;
+    while (varl)
+    {
+      var *vp = vars[k];
+      double ref = 0.0;
+      double x = pox[0], y = pox[1], z = pox[2];
+      f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2],
+                      BP->fgfs[vp->sgfn], ref,
+                      x, y, z, ordn, vp->SoA, Symmetry);
+      const double diff = fabs(ref - out[k]);
+      const double scale = 1.0 + fabs(ref);
+      if (diff > tol * scale && report_count < 32)
+      {
+        int rank = 0;
+        MPI_Comm_rank(MPI_COMM_WORLD, &rank);
+        fprintf(stderr,
+                "[AMSS-INTERP-CMP][rank %d] var=%s diff=%.17e ref=%.17e fast=%.17e p=(%.17e,%.17e,%.17e)\n",
+                rank, vp->name, diff, ref, out[k], pox[0], pox[1], pox[2]);
+        report_count++;
+      }
+      varl = varl->next;
+      k++;
+    }
+  }
+
+  return true;
+}
+
+bool interpolate_var_list_fast(Block *BP, MyList<var> *VarList, int num_var,
+                               const double *pox, int ordn, int Symmetry,
+                               double *out)
+{
+  if (!interp_fast_enabled())
+    return false;
+
+  FastInterpStencil st;
+  if (!prepare_fast_interp_stencil(BP, pox, ordn, Symmetry, st))
+    return false;
+
+  return interpolate_var_list_with_stencil(BP, VarList, num_var, pox,
+                                           ordn, Symmetry, st, out);
+}
+
+struct CachedInterpPoint
+{
+  Block *bp;
+  int owner_rank;
+  FastInterpStencil stencil;
+};
+
+struct SurfaceInterpCache
+{
+  Patch *patch;
+  int NN;
+  int symmetry;
+  double key[9];
+  vector<CachedInterpPoint> points;
+
+  SurfaceInterpCache() : patch(0), NN(0), symmetry(-1) {}
+};
+
+bool surface_cache_key_matches(const SurfaceInterpCache &cache, Patch *patch,
+                               int NN, double **XX, int Symmetry)
+{
+  if (cache.patch != patch || cache.NN != NN || cache.symmetry != Symmetry ||
+      int(cache.points.size()) != NN || NN <= 0)
+    return false;
+  const int mid = NN / 2;
+  const int last = NN - 1;
+  const int ids[3] = {0, mid, last};
+  int p = 0;
+  for (int q = 0; q < 3; q++)
+    for (int d = 0; d < dim; d++)
+      if (cache.key[p++] != XX[d][ids[q]])
+        return false;
+  return true;
+}
+
+SurfaceInterpCache *find_surface_cache(Patch *patch, int NN, double **XX,
+                                       int Symmetry)
+{
+  static vector<SurfaceInterpCache> caches;
+  for (size_t i = 0; i < caches.size(); i++)
+    if (surface_cache_key_matches(caches[i], patch, NN, XX, Symmetry))
+      return &caches[i];
+  if (caches.size() >= 24)
+    caches.erase(caches.begin());
+  caches.push_back(SurfaceInterpCache());
+  return &caches.back();
+}
+
+bool build_surface_cache(SurfaceInterpCache &cache, Patch *patch, int NN,
+                         double **XX, int Symmetry, const double *DH,
+                         const BlockBinIndex &block_index, int ordn)
+{
+  int myrank = 0;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  cache.patch = patch;
+  cache.NN = NN;
+  cache.symmetry = Symmetry;
+  cache.points.clear();
+  cache.points.resize(NN);
+  const int mid = NN / 2;
+  const int last = NN - 1;
+  const int ids[3] = {0, mid, last};
+  int p = 0;
+  for (int q = 0; q < 3; q++)
+    for (int d = 0; d < dim; d++)
+      cache.key[p++] = XX[d][ids[q]];
+
+  for (int j = 0; j < NN; j++)
+  {
+    double pox[dim];
+    for (int d = 0; d < dim; d++)
+      pox[d] = XX[d][j];
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i < 0)
+    {
+      cache.points[j].bp = 0;
+      cache.points[j].owner_rank = -1;
+      continue;
+    }
+    Block *BP = block_index.views[block_i].bp;
+    cache.points[j].bp = BP;
+    cache.points[j].owner_rank = BP->rank;
+    cache.points[j].stencil.nsamples = 0;
+    if (BP->rank == myrank)
+    {
+      if (!prepare_fast_interp_stencil(BP, pox, ordn, Symmetry,
+                                       cache.points[j].stencil))
+        return false;
+    }
+  }
+  return true;
+}
+} // namespace
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
@@ -561,22 +1002,26 @@ void Patch::Interp_Points(MyList<var> *VarList,
     if (block_i >= 0)
     {
       Block *BP = block_index.views[block_i].bp;
-      owner_rank[j] = BP->rank;
-      if (myrank == BP->rank)
-      {
-        //---> interpolation
-        varl = VarList;
-        int k = 0;
-        while (varl) // run along variables
-        {
-          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-          varl = varl->next;
-          k++;
-        }
-      }
-    }
-  }
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
+      {
+        //---> interpolation
+        if (!interpolate_var_list_fast(BP, VarList, num_var, pox, ordn,
+                                       Symmetry, Shellf + j * num_var))
+        {
+          varl = VarList;
+          int k = 0;
+          while (varl) // run along variables
+          {
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+            varl = varl->next;
+            k++;
+          }
+        }
+      }
+    }
+  }
 
   // Replace MPI_Allreduce with per-owner MPI_Bcast:
   // Group consecutive points by owner rank and broadcast each group.
@@ -659,10 +1104,8 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
-
-  // owner_rank[j] records which MPI rank owns point j
-  int *owner_rank;
+  // owner_rank[j] records which MPI rank owns point j
+  int *owner_rank;
   owner_rank = new int[NN];
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
@@ -670,12 +1113,117 @@ void Patch::Interp_Points(MyList<var> *VarList,
   double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
-  BlockBinIndex block_index;
-  build_block_bin_index(this, DH, block_index);
-
-  // --- Interpolation phase (identical to original) ---
-  for (int j = 0; j < NN; j++)
-  {
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
+  SurfaceInterpCache *surface_cache = 0;
+  bool use_surface_cache = false;
+  if (interp_fast_enabled())
+  {
+    surface_cache = find_surface_cache(this, NN, XX, Symmetry);
+    use_surface_cache = surface_cache_key_matches(*surface_cache, this, NN, XX, Symmetry);
+    if (!use_surface_cache)
+      use_surface_cache = build_surface_cache(*surface_cache, this, NN, XX,
+                                              Symmetry, DH, block_index, ordn);
+  }
+
+  // --- Interpolation phase (identical to original) ---
+#if USE_CUDA_BSSN
+  const bool use_gpu_interp = interp_gpu_enabled() && use_surface_cache && num_var == 2 &&
+                              VarList && VarList->next && !VarList->next->next;
+#else
+  const bool use_gpu_interp = false;
+#endif
+  if (use_gpu_interp)
+  {
+#if USE_CUDA_BSSN
+    vector<vector<int> > local_points(block_index.views.size());
+    for (int j = 0; j < NN; j++)
+    {
+      for (int i = 0; i < dim; i++)
+      {
+        if (myrank == 0 && (XX[i][j] < bbox[i] + lli[i] * DH[i] || XX[i][j] > bbox[dim + i] - uui[i] * DH[i]))
+        {
+          cout << "Patch::Interp_Points: point (";
+          for (int k = 0; k < dim; k++)
+          {
+            cout << XX[k][j];
+            if (k < dim - 1)
+              cout << ",";
+            else
+              cout << ") is out of current Patch." << endl;
+          }
+          MPI_Abort(MPI_COMM_WORLD, 1);
+        }
+      }
+
+      CachedInterpPoint &cp = surface_cache->points[j];
+      Block *BP = cp.bp;
+      owner_rank[j] = cp.owner_rank;
+      if (BP && myrank == BP->rank)
+      {
+        for (size_t bi = 0; bi < block_index.views.size(); bi++)
+        {
+          if (block_index.views[bi].bp == BP)
+          {
+            local_points[bi].push_back(j);
+            break;
+          }
+        }
+      }
+    }
+
+    var *v0 = VarList->data;
+    var *v1 = VarList->next->data;
+    double soa6[6] = {
+        v0->SoA[0], v0->SoA[1], v0->SoA[2],
+        v1->SoA[0], v1->SoA[1], v1->SoA[2]};
+
+    for (size_t bi = 0; bi < local_points.size(); bi++)
+    {
+      const int count = int(local_points[bi].size());
+      if (count <= 0)
+        continue;
+
+      Block *BP = block_index.views[bi].bp;
+      vector<double> px(count), py(count), pz(count), out(2 * count);
+      for (int q = 0; q < count; q++)
+      {
+        const int j = local_points[bi][q];
+        px[q] = XX[0][j];
+        py[q] = XX[1][j];
+        pz[q] = XX[2][j];
+      }
+
+      const double dx = BP->X[0][1] - BP->X[0][0];
+      const double dy = BP->X[1][1] - BP->X[1][0];
+      const double dz = BP->X[2][1] - BP->X[2][0];
+      const int ok = bssn_cuda_interp_host_two_fields(
+          BP, BP->shape,
+          BP->fgfs[v0->sgfn], BP->fgfs[v1->sgfn],
+          BP->X[0][0], BP->X[1][0], BP->X[2][0],
+          dx, dy, dz,
+          &px[0], &py[0], &pz[0], count,
+          ordn, Symmetry, soa6, &out[0]);
+      if (ok != 0)
+      {
+        if (myrank == 0)
+          cout << "Patch::Interp_Points: CUDA two-field interpolation failed" << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+
+      for (int q = 0; q < count; q++)
+      {
+        const int j = local_points[bi][q];
+        Shellf[j * num_var] = out[2 * q];
+        Shellf[j * num_var + 1] = out[2 * q + 1];
+      }
+    }
+#endif
+  }
+  else
+  {
+  for (int j = 0; j < NN; j++)
+  {
     double pox[dim];
     for (int i = 0; i < dim; i++)
     {
@@ -692,28 +1240,59 @@ void Patch::Interp_Points(MyList<var> *VarList,
             cout << ") is out of current Patch." << endl;
         }
         MPI_Abort(MPI_COMM_WORLD, 1);
-      }
-    }
-
-    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    if (block_i >= 0)
-    {
-      Block *BP = block_index.views[block_i].bp;
-      owner_rank[j] = BP->rank;
-      if (myrank == BP->rank)
-      {
-        varl = VarList;
-        int k = 0;
-        while (varl)
-        {
-          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-          varl = varl->next;
-          k++;
-        }
-      }
-    }
-  }
+      }
+    }
+
+    if (use_surface_cache)
+    {
+      CachedInterpPoint &cp = surface_cache->points[j];
+      Block *BP = cp.bp;
+      owner_rank[j] = cp.owner_rank;
+      if (BP && myrank == BP->rank)
+      {
+        if (!interpolate_var_list_with_stencil(BP, VarList, num_var, pox,
+                                               ordn, Symmetry, cp.stencil,
+                                               Shellf + j * num_var))
+        {
+          MyList<var> *varl_fallback = VarList;
+          int k = 0;
+          while (varl_fallback)
+          {
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl_fallback->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl_fallback->data->SoA, Symmetry);
+            varl_fallback = varl_fallback->next;
+            k++;
+          }
+        }
+      }
+    }
+    else
+    {
+      const int block_i = find_block_index_for_point(block_index, pox, DH);
+      if (block_i >= 0)
+      {
+        Block *BP = block_index.views[block_i].bp;
+        owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
+      {
+        if (!interpolate_var_list_fast(BP, VarList, num_var, pox, ordn,
+                                       Symmetry, Shellf + j * num_var))
+        {
+          MyList<var> *varl_fallback = VarList;
+          int k = 0;
+          while (varl_fallback)
+          {
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl_fallback->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl_fallback->data->SoA, Symmetry);
+            varl_fallback = varl_fallback->next;
+            k++;
+          }
+        }
+      }
+      }
+    }
+  }
+  }
 
 #ifdef INTERP_LB_PROFILE
   double t_interp_end = MPI_Wtime();
@@ -965,22 +1544,26 @@ void Patch::Interp_Points(MyList<var> *VarList,
     if (block_i >= 0)
     {
       Block *BP = block_index.views[block_i].bp;
-      owner_rank[j] = BP->rank;
-      if (myrank == BP->rank)
-      {
-        //---> interpolation
-        varl = VarList;
-        int k = 0;
-        while (varl) // run along variables
-        {
-          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-          varl = varl->next;
-          k++;
-        }
-      }
-    }
-  }
+      owner_rank[j] = BP->rank;
+      if (myrank == BP->rank)
+      {
+        //---> interpolation
+        if (!interpolate_var_list_fast(BP, VarList, num_var, pox, ordn,
+                                       Symmetry, Shellf + j * num_var))
+        {
+          varl = VarList;
+          int k = 0;
+          while (varl) // run along variables
+          {
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+            varl = varl->next;
+            k++;
+          }
+        }
+      }
+    }
+  }
 
   // Collect unique global owner ranks and translate to local ranks in Comm_here
   // Then broadcast each owner's points via MPI_Bcast on Comm_here

AMSS_NCKU_source/Parallel.h

@@ -104,6 +104,14 @@ namespace Parallel
     double **recv_bufs;
     int *send_buf_caps;
     int *recv_buf_caps;
+    unsigned char *send_buf_pinned;
+    unsigned char *recv_buf_pinned;
+    unsigned char *send_buf_is_dev;
+    unsigned char *recv_buf_is_dev;
+    int *send_buf_caps_dev;
+    int *recv_buf_caps_dev;
+    double **send_bufs_dev;
+    double **recv_bufs_dev;
     MPI_Request *reqs;
     MPI_Status *stats;
     int max_reqs;
@@ -111,12 +119,14 @@ namespace Parallel
     int *tc_req_node;
     int *tc_req_is_recv;
     int *tc_completed;
+    bool cuda_aware_mode;
     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);
@@ -183,6 +193,7 @@ namespace Parallel
                          MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
   void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
   double L2Norm(Patch *Pat, var *vf);
+  void L2Norm7(Patch *Pat, var **vf, double *norms);
   void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
   void checkvarl(MyList<var> *pp, bool first_only);
   MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
@@ -218,6 +229,7 @@ namespace Parallel
   void checkpatchlist(MyList<Patch> *PatL, bool buflog);
 
   double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
+  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
   bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
                              int NN, double **XX,
                              double *Shellf, int Symmetry, MPI_Comm Comm_here);

AMSS_NCKU_source/ShellPatch.C

@@ -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)
@@ -3469,13 +3469,50 @@ double ShellPatch::L2Norm(var *vf)
   MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   tvf = sqrt(tvf);
-
-  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)
+
+  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)
 {
   MyList<var> *varl;
   int num_var = 0;

AMSS_NCKU_source/ShellPatch.h

@@ -195,10 +195,11 @@ 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 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 L2Norm7(var **vf, double *norms);
+   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
+};
 
 #endif /* SHELLPATCH_H */

AMSS_NCKU_source/Z4c_class.C

@@ -1,9 +1,10 @@
 
-#ifdef newc
-#include <sstream>
-#include <cstdio>
-#include <map>
-using namespace std;
+#ifdef newc
+#include <sstream>
+#include <cstdio>
+#include <cstdlib>
+#include <map>
+using namespace std;
 #else
 #include <stdio.h>
 #include <map.h>
@@ -26,12 +27,20 @@ using namespace std;
 #include "shellfunctions.h"
 #include "cpbc.h"
 #include "kodiss.h"
-#include "parameters.h"
-
-#ifdef With_AHF
-#include "derivatives.h"
-#include "myglobal.h"
-#endif
+#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
 
 //================================================================================================
 
@@ -105,20 +114,22 @@ void Z4c_class::Initialize()
   else
     GH->compose_cgh(nprocs);
 
-#ifdef WithShell
-  SH = new ShellPatch(0, ngfs, pname, Symmetry, myrank, ErrorMonitor);
-  if (!checkrun)
-    SH->matchcheck(GH->PatL[0]);
+#ifdef WithShell
+  SH = new ShellPatch(0, ngfs, pname, Symmetry, myrank, ErrorMonitor);
+  if (!checkrun)
+    SH->matchcheck(GH->PatL[0]);
   SH->compose_sh(nprocs);
   SH->setupcordtrans();
   SH->Dump_xyz(0, 0, 1);
   SH->setupintintstuff(nprocs, GH->PatL[0], Symmetry);
 
-  if (checkrun)
-    CheckPoint->readcheck_sh(SH, myrank);
-#endif
-
-  double h = GH->PatL[0]->data->blb->data->getdX(0);
+  if (checkrun)
+    CheckPoint->readcheck_sh(SH, myrank);
+#endif
+
+  Initialize_Level_Runtime();
+
+  double h = GH->PatL[0]->data->blb->data->getdX(0);
   for (int i = 1; i < dim; i++)
     h = Mymin(h, GH->PatL[0]->data->blb->data->getdX(i));
   dT = Courant * h;
@@ -167,12 +178,753 @@ 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
-
-void Z4c_class::Step(int lev, int YN)
-{
-  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
+#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;
+}
+
+bool z4c_cuda_keep_resident_after_step(int lev, int trfls_in, int analysis_lev)
+{
+  static int keep_all_levels = -1;
+  if (keep_all_levels < 0)
+  {
+    const char *env = getenv("AMSS_CUDA_KEEP_ALL_LEVELS");
+    keep_all_levels = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_CUDA_Z4C_KEEP_RESIDENT_AFTER_STEP");
+    if (env)
+      enabled = (atoi(env) != 0) ? 1 : 0;
+    else
+    {
+      env = getenv("AMSS_CUDA_KEEP_RESIDENT_AFTER_STEP");
+      enabled = (env && atoi(env) != 0) ? 1 : 0;
+    }
+  }
+  if (!enabled)
+    return false;
+  if (lev == analysis_lev)
+    return false;
+  if (keep_all_levels)
+    return true;
+  return lev < trfls_in;
+}
+
+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)
+          {
+            var *vars[3] = {forx, fory, forz};
+            static int use_device_bh_interp = -1;
+            if (use_device_bh_interp < 0)
+            {
+              const char *env = getenv("AMSS_CUDA_Z4C_BH_INTERP_DEVICE");
+              use_device_bh_interp = (env && atoi(env) != 0) ? 1 : 0;
+            }
+            bool used_device_interp = false;
+            if (use_device_bh_interp)
+            {
+              double soa3[9];
+              for (int f = 0; f < 3; f++)
+              {
+                soa3[3 * f + 0] = vars[f]->SoA[0];
+                soa3[3 * f + 1] = vars[f]->SoA[1];
+                soa3[3 * f + 2] = vars[f]->SoA[2];
+              }
+              used_device_interp =
+                  (z4c_cuda_interp_state_point3(block, block->shape,
+                                                k_z4c_cuda_bh_state_indices[0],
+                                                k_z4c_cuda_bh_state_indices[1],
+                                                k_z4c_cuda_bh_state_indices[2],
+                                                block->X[0][0], block->X[1][0], block->X[2][0],
+                                                DH[0], DH[1], DH[2],
+                                                x, y, z,
+                                                interp_ordn, interp_sym,
+                                                soa3, shellf) == 0);
+            }
+            if (!used_device_interp)
+            {
+              double *shift_views[3] = {
+                  block->fgfs[forx->sgfn],
+                  block->fgfs[fory->sgfn],
+                  block->fgfs[forz->sgfn]};
+              if (z4c_cuda_download_state_subset(block, block->shape, 3,
+                                                 k_z4c_cuda_bh_state_indices,
+                                                 shift_views) != 0)
+              {
+                cout << "CUDA Z4C BH shift download failed" << endl;
+                MPI_Abort(MPI_COMM_WORLD, 1);
+              }
+              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);
+            }
+          }
+          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;
+}
+
+bool z4c_cuda_download_bh_shift_level(MyList<Patch> *PatL,
+                                      int myrank,
+                                      var *forx, var *fory, var *forz)
+{
+  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 *fields[3] = {
+            cg->fgfs[forx->sgfn],
+            cg->fgfs[fory->sgfn],
+            cg->fgfs[forz->sgfn]};
+        if (z4c_cuda_download_state_subset(cg, cg->shape, 3,
+                                           k_z4c_cuda_bh_state_indices,
+                                           fields))
+          return false;
+      }
+      if (BP == Pp->data->ble)
+        break;
+      BP = BP->next;
+    }
+    Pp = Pp->next;
+  }
+  return true;
+}
+
+bool z4c_cuda_refresh_constraint_level(MyList<Patch> *PatL,
+                                       int myrank,
+                                       var *Cons_Ham, var *Cons_Px,
+                                       var *Cons_Py, var *Cons_Pz,
+                                       var *Cons_Gx, var *Cons_Gy,
+                                       var *Cons_Gz, var *TZ0,
+                                       int Symmetry, int lev, double eps)
+{
+  bool all_resident = true;
+  const int tz_index = 24;
+  MyList<Patch> *Pp = PatL;
+  while (Pp)
+  {
+    MyList<Block> *BP = Pp->data->blb;
+    while (BP)
+    {
+      Block *cg = BP->data;
+      if (myrank == cg->rank)
+      {
+        if (!z4c_cuda_has_resident_state(cg))
+        {
+          all_resident = false;
+        }
+        else
+        {
+          double *constraints[7] = {
+              cg->fgfs[Cons_Ham->sgfn], cg->fgfs[Cons_Px->sgfn],
+              cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
+              cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn],
+              cg->fgfs[Cons_Gz->sgfn]};
+          double *tz_out[1] = {cg->fgfs[TZ0->sgfn]};
+          int co = 0;
+          if (z4c_cuda_compute_constraints_resident(cg, cg->shape,
+                                                   cg->X[0], cg->X[1], cg->X[2],
+                                                   Symmetry, eps, co,
+                                                   constraints) ||
+              z4c_cuda_download_state_subset(cg, cg->shape, 1, &tz_index, tz_out))
+          {
+            cout << "CUDA Z4C resident constraint refresh failed" << endl;
+            MPI_Abort(MPI_COMM_WORLD, 1);
+          }
+        }
+      }
+      if (BP == Pp->data->ble)
+        break;
+      BP = BP->next;
+    }
+    Pp = Pp->next;
+  }
+  return all_resident;
+}
+
+long long &z4c_constraint_output_counter()
+{
+  static long long counter = 0;
+  return counter;
+}
+
+int z4c_constraint_output_every()
+{
+  static int every = -1;
+  if (every < 0)
+  {
+    const char *env = getenv("AMSS_CUDA_Z4C_CONSTRAINT_EVERY");
+    every = (env && atoi(env) > 0) ? atoi(env) : 1;
+  }
+  return every;
+}
+
+bool z4c_constraint_output_due_now()
+{
+  const int every = z4c_constraint_output_every();
+  return every <= 1 || (z4c_constraint_output_counter() % every) == 0;
+}
+
+void z4c_constraint_output_advance()
+{
+  z4c_constraint_output_counter()++;
+}
+
+} // 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;
+  const double dT_mon = dT * pow(0.5, Mymax(0, trfls));
+  const bool need_constraint_after_step =
+      (LastConsOut + dT_mon >= AnasTime) && z4c_constraint_output_due_now();
+
+  if (BH_num > 0 && lev == GH->levels - 1)
+  {
+    if (!z4c_cuda_download_bh_shift_level(GH->PatL[lev], myrank, Sfx0, Sfy0, Sfz0))
+    {
+      if (myrank == 0 && ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "CUDA Z4C failed to download predictor black-hole shift at t = "
+                              << PhysTime << endl;
+      MPI_Abort(MPI_COMM_WORLD, 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]);
+      }
+    }
+  }
+
+  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::AsyncSyncState async_pre;
+    Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+    Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry);
+  }
+
+  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 (!ERROR && iter_count == 3 && need_constraint_after_step)
+          {
+            double *constraints[7] = {
+                cg->fgfs[Cons_Ham->sgfn], cg->fgfs[Cons_Px->sgfn],
+                cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
+                cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn],
+                cg->fgfs[Cons_Gz->sgfn]};
+            double *tz_out[1] = {cg->fgfs[TZ0->sgfn]};
+            const int tz_index = 24;
+            if (z4c_cuda_download_constraint_outputs(cg->shape, constraints) ||
+                z4c_cuda_download_state_subset(cg, cg->shape, 1, &tz_index, tz_out))
+            {
+              cout << "CUDA Z4C constraint download 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::AsyncSyncState async_cor;
+      Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+      Parallel::Sync_finish(sync_cache_cor[lev], async_cor, 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];
+        }
+      }
+    }
+  }
+
+  {
+    const bool keep_resident = z4c_cuda_keep_resident_after_step(lev, trfls, a_lev);
+    const bool need_host_after_step =
+        ((lev == a_lev) && (LastAnas + dT_lev >= AnasTime));
+    if (!keep_resident || need_host_after_step)
+      z4c_cuda_download_level_state(GH->PatL[lev], SynchList_cor, myrank, !keep_resident);
+  }
+
+#if (RPS == 0)
+  RestrictProlong(lev, YN, BB);
+#endif
+
+  Pp = GH->PatL[lev];
+  while (Pp)
+  {
+    MyList<Block> *BP = Pp->data->blb;
+    while (BP)
+    {
+      Block *cg = BP->data;
+      cg->swapList(StateList, SynchList_cor, myrank);
+      cg->swapList(OldStateList, SynchList_cor, myrank);
+      if (BP == Pp->data->ble)
+        break;
+      BP = BP->next;
+    }
+    Pp = Pp->next;
+  }
+  if (BH_num > 0 && lev == GH->levels - 1)
+  {
+    for (int ithBH = 0; ithBH < BH_num; ithBH++)
+    {
+      Porg0[ithBH][0] = Porg1[ithBH][0];
+      Porg0[ithBH][1] = Porg1[ithBH][1];
+      Porg0[ithBH][2] = Porg1[ithBH][2];
+    }
+  }
+#else
+  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
 #ifdef With_AHF
   AH_Step_Find(lev, dT_lev);
 #endif
@@ -1039,15 +1791,19 @@ 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];
-    }
-  }
-}
-#else
-// for constraint preserving boundary (CPBC)
-#ifndef WithShell
-#error "CPBC only supports Shell"
-#endif
+      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
 
 // 0: extroplate rhs, 1: extroplate variable
 // 2: extroplate variable but before RHS calculation
@@ -2408,17 +3164,23 @@ void Z4c_class::Check_extrop()
 
 //================================================================================================
 
-void Z4c_class::Constraint_Out()
-{
-  // here we have to use the same variable name as in the parent class
-  LastConsOut += dT * pow(0.5, Mymax(0, trfls));
-  
-  if (LastConsOut >= AnasTime)
-  // Constraint violation
-  {
-    // recompute least the constraint data lost for moved new grid
-    for (int lev = 0; lev < GH->levels; lev++)
-    {
+void Z4c_class::Constraint_Out()
+{
+  // here we have to use the same variable name as in the parent class
+  LastConsOut += dT * pow(0.5, Mymax(0, trfls));
+  
+  if (LastConsOut >= AnasTime)
+  // Constraint violation
+  {
+#if USE_CUDA_Z4C && (ABEtype == 2)
+    bool cuda_constraints_ready = true;
+#else
+    const bool cuda_constraints_ready = false;
+#endif
+    // recompute least the constraint data lost for moved new grid
+    if (!cuda_constraints_ready)
+      for (int lev = 0; lev < GH->levels; lev++)
+    {
       // make sure the data consistent for higher levels
       if (lev > 0)
       {

AMSS_NCKU_source/Z4c_rhs.f90

@@ -94,29 +94,31 @@
                Hcon,Mxcon,Mycon,Mzcon,Gmxcon,Gmycon,Gmzcon,                    &            
                Symmetry,Lev,eps,co)
 
-#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)
+  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
 
   return
 
@@ -226,11 +228,12 @@
 
   call get_Z4cparameters(kappa1,kappa2,kappa3,FF,eta)
 
-!!! 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) &
+!!! 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) &
       +sum(TZ)
   if(dX.ne.dX) then
      if(sum(chi).ne.sum(chi))write(*,*)"Z4c_rhs.f90: find NaN in chi"
@@ -257,10 +260,11 @@
      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
+     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs.f90: find NaN in TZ"
+     gont = 1
+     return
+  endif
+#endif
 
   PI = dacos(-ONE)
 
@@ -1263,30 +1267,32 @@
 
   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)
+  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
 
   gont = 0
 

AMSS_NCKU_source/Z4c_rhs_ss.f90

@@ -121,11 +121,12 @@
 
   call get_Z4cparameters(kappa1,kappa2,kappa3,FF,eta)
 
-!!! 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) &
+!!! 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) &
       +sum(TZ)
   if(dX.ne.dX) then
      if(sum(chi).ne.sum(chi))write(*,*)"Z4c_rhs_ss.f90: find NaN in chi"
@@ -152,10 +153,11 @@
      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
+     if(sum(TZ).ne.sum(Tz))write(*,*)"Z4c_rhs_ss.f90: find NaN in TZ"
+     gont = 1
+     return
+  endif
+#endif
 
   PI = dacos(-ONE)
 
@@ -1388,41 +1390,43 @@
   call kodis_sh(ex,crho,sigma,R,TZ,TZ_rhs,SSS,Symmetry,eps,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
+  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
 
   gont = 0
 

AMSS_NCKU_source/bssnEM_class.C

@@ -15,10 +15,13 @@ using namespace std;
 #include "misc.h"
 #include "Ansorg.h"
 #include "fmisc.h"
-#include "Parallel.h"
-#include "bssnEM_class.h"
-#include "bssn_rhs.h"
-#include "empart.h"
+#include "Parallel.h"
+#include "bssnEM_class.h"
+#include "bssn_rhs.h"
+#if USE_CUDA_BSSN
+#include "bssn_rhs_cuda.h"
+#endif
+#include "empart.h"
 #include "initial_puncture.h"
 #include "initial_maxwell.h"
 #include "enforce_algebra.h"
@@ -32,11 +35,111 @@ using namespace std;
 #ifdef With_AHF
 #include "derivatives.h"
 #include "myglobal.h"
-#endif
-
-//================================================================================================
-
-// Define bssnEM_class
+#endif
+
+//================================================================================================
+
+#if USE_CUDA_BSSN
+namespace {
+
+bool fill_bssn_cuda_views_prefix(Block *cg, MyList<var> *vars,
+                                 double **host_views,
+                                 double *propspeeds = nullptr,
+                                 double *soa_flat = nullptr)
+{
+  int idx = 0;
+  while (vars && idx < BSSN_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 == BSSN_CUDA_STATE_COUNT;
+}
+
+void skip_bssn_cuda_prefix(MyList<var> *&a, MyList<var> *&b, MyList<var> *&c)
+{
+  for (int i = 0; i < BSSN_CUDA_STATE_COUNT && a && b && c; ++i)
+  {
+    a = a->next;
+    b = b->next;
+    c = c->next;
+  }
+}
+
+void skip_bssn_cuda_prefix(MyList<var> *&a, MyList<var> *&b,
+                           MyList<var> *&c, MyList<var> *&d)
+{
+  for (int i = 0; i < BSSN_CUDA_STATE_COUNT && a && b && c && d; ++i)
+  {
+    a = a->next;
+    b = b->next;
+    c = c->next;
+    d = d->next;
+  }
+}
+
+int run_bssn_em_cuda_substep(Block *cg,
+                             MyList<var> *state_in_list,
+                             MyList<var> *state_out_list,
+                             Patch *patch,
+                             double &dT_lev,
+                             double &TRK4,
+                             int &iter_count,
+                             int &Symmetry,
+                             int lev,
+                             double &ndeps,
+                             int &co,
+                             double &chitiny,
+                             var *rho, var *Sx, var *Sy, var *Sz,
+                             var *Sxx, var *Sxy, var *Sxz,
+                             var *Syy, var *Syz, var *Szz)
+{
+  double *state_in[BSSN_CUDA_STATE_COUNT];
+  double *state_out[BSSN_CUDA_STATE_COUNT];
+  double *matter[BSSN_CUDA_MATTER_COUNT] = {
+      cg->fgfs[rho->sgfn], cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
+      cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn],
+      cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn]};
+  double propspeed[BSSN_CUDA_STATE_COUNT];
+  double soa_flat[3 * BSSN_CUDA_STATE_COUNT];
+  if (!fill_bssn_cuda_views_prefix(cg, state_in_list, state_in, propspeed, soa_flat) ||
+      !fill_bssn_cuda_views_prefix(cg, state_out_list, state_out))
+    return 1;
+
+  int apply_bam_bc = 0;
+#if (SommerType == 0)
+#ifndef WithShell
+  apply_bam_bc = (lev == 0) ? 1 : 0;
+#endif
+#endif
+  int use_zero_matter = 0;
+  int keep_resident_state = 0;
+  int apply_enforce_ga = 0;
+  return bssn_cuda_rk4_substep(cg,
+                               cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                               state_in, state_out, matter,
+                               propspeed, soa_flat, patch->bbox,
+                               dT_lev, TRK4, iter_count, apply_bam_bc,
+                               Symmetry, lev, ndeps, co,
+                               use_zero_matter,
+                               keep_resident_state, apply_enforce_ga, chitiny);
+}
+
+}
+#endif
+
+//================================================================================================
+
+// Define bssnEM_class
 
 // It inherits some members and methods from the parent class bssn_class and modifies others.
 // The modified members and methods are defined below (and in the header bssnEM_class.h).
@@ -232,19 +335,21 @@ void bssnEM_class::Initialize()
   else
     GH->compose_cgh(nprocs);
 
-#ifdef WithShell
-  SH = new ShellPatch(0, ngfs, pname, Symmetry, myrank, ErrorMonitor);
-  SH->matchcheck(GH->PatL[0]);
+#ifdef WithShell
+  SH = new ShellPatch(0, ngfs, pname, Symmetry, myrank, ErrorMonitor);
+  SH->matchcheck(GH->PatL[0]);
   SH->compose_sh(nprocs);
   SH->setupcordtrans();
   SH->Dump_xyz(0, 0, 1);
   SH->setupintintstuff(nprocs, GH->PatL[0], Symmetry);
 
-  if (checkrun)
-    CheckPoint->readcheck_sh(SH, myrank);
-#endif
-
-  double h = GH->PatL[0]->data->blb->data->getdX(0);
+  if (checkrun)
+    CheckPoint->readcheck_sh(SH, myrank);
+#endif
+
+  Initialize_Level_Runtime();
+
+  double h = GH->PatL[0]->data->blb->data->getdX(0);
   for (int i = 1; i < dim; i++)
     h = Mymin(h, GH->PatL[0]->data->blb->data->getdX(i));
   dT = Courant * h;
@@ -851,10 +956,11 @@ void bssnEM_class::Step(int lev, int YN)
                      cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                      cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                      cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn]);
-#endif
-
-        if (
-            f_compute_rhs_empart(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+#endif
+
+        bool used_gpu_substep = false;
+        if (
+            f_compute_rhs_empart(cg->shape, cg->X[0], cg->X[1], cg->X[2],
                                  cg->fgfs[phi0->sgfn],
                                  cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
                                  cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
@@ -871,11 +977,20 @@ void bssnEM_class::Step(int lev, int YN)
                                  cg->fgfs[Kpsi_rhs->sgfn], cg->fgfs[Kphi_rhs->sgfn],
                                  cg->fgfs[rho->sgfn], 
                                  cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                 cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                 cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                 Symmetry, lev, ndeps) ||
-            f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+                                 cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn],
+                                 cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
+                                 Symmetry, lev, ndeps) ||
+#if USE_CUDA_BSSN
+            ((used_gpu_substep =
+                  (run_bssn_em_cuda_substep(cg, StateList, SynchList_pre, Pp->data,
+                                            dT_lev, TRK4, iter_count, Symmetry, lev,
+                                            ndeps, pre, chitiny,
+                                            rho, Sx, Sy, Sz, Sxx, Sxy, Sxz, Syy, Syz, Szz) == 0))
+                 ? 0
+                 : 1) ||
+#endif
+            (!used_gpu_substep && f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                               cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
                                cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
                                cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                                cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
@@ -904,10 +1019,10 @@ void bssnEM_class::Step(int lev, int YN)
                                cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
                                cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
                                cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                               cg->fgfs[Cons_Ham->sgfn],
-                               cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                               cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                               Symmetry, lev, ndeps, pre))
+                               cg->fgfs[Cons_Ham->sgfn],
+                               cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
+                               cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
+                               Symmetry, lev, ndeps, pre)))
         {
           cout << "find NaN in domain: (" 
                << cg->bbox[0] << ":" << cg->bbox[3] << "," 
@@ -917,11 +1032,15 @@ void bssnEM_class::Step(int lev, int YN)
         }
 
         // rk4 substep and boundary
-        {
-          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList; 
-          // we do not check the correspondence here
-          
-          while (varl0)
+        {
+          MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varlrhs = RHSList;
+          // we do not check the correspondence here
+#if USE_CUDA_BSSN
+          if (used_gpu_substep)
+            skip_bssn_cuda_prefix(varl0, varl, varlrhs);
+#endif
+
+          while (varl0)
           {
 #ifndef WithShell
             if (lev == 0) // sommerfeld indeed
@@ -1221,7 +1340,7 @@ void bssnEM_class::Step(int lev, int YN)
   }
 #endif
 
-  Parallel::Sync(GH->PatL[lev], SynchList_pre, Symmetry);
+  Parallel::Sync_cached(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev]);
 
 #ifdef WithShell
   if (lev == 0)
@@ -1307,10 +1426,11 @@ void bssnEM_class::Step(int lev, int YN)
                          cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
                          cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
                          cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn]);
-#endif
-
-          if (
-              f_compute_rhs_empart(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+#endif
+
+          bool used_gpu_substep = false;
+          if (
+              f_compute_rhs_empart(cg->shape, cg->X[0], cg->X[1], cg->X[2],
                                    cg->fgfs[phi->sgfn],
                                    cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
                                    cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
@@ -1327,11 +1447,20 @@ void bssnEM_class::Step(int lev, int YN)
                                    cg->fgfs[Kpsi1->sgfn], cg->fgfs[Kphi1->sgfn],
                                    cg->fgfs[rho->sgfn], 
                                    cg->fgfs[Sx->sgfn], cg->fgfs[Sy->sgfn], cg->fgfs[Sz->sgfn],
-                                   cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn], 
-                                   cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
-                                   Symmetry, lev, ndeps) ||
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
-                                 cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
+                                   cg->fgfs[Sxx->sgfn], cg->fgfs[Sxy->sgfn], cg->fgfs[Sxz->sgfn],
+                                   cg->fgfs[Syy->sgfn], cg->fgfs[Syz->sgfn], cg->fgfs[Szz->sgfn],
+                                   Symmetry, lev, ndeps) ||
+#if USE_CUDA_BSSN
+              ((used_gpu_substep =
+                    (run_bssn_em_cuda_substep(cg, SynchList_pre, SynchList_cor, Pp->data,
+                                              dT_lev, TRK4, iter_count, Symmetry, lev,
+                                              ndeps, cor, chitiny,
+                                              rho, Sx, Sy, Sz, Sxx, Sxy, Sxz, Syy, Syz, Szz) == 0))
+                   ? 0
+                   : 1) ||
+#endif
+              (!used_gpu_substep && f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                 cg->fgfs[phi->sgfn], cg->fgfs[trK->sgfn],
                                  cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], 
                                  cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
                                  cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], 
@@ -1359,10 +1488,10 @@ void bssnEM_class::Step(int lev, int YN)
                                  cg->fgfs[Gamzyy->sgfn], cg->fgfs[Gamzyz->sgfn], cg->fgfs[Gamzzz->sgfn],
                                  cg->fgfs[Rxx->sgfn], cg->fgfs[Rxy->sgfn], cg->fgfs[Rxz->sgfn], 
                                  cg->fgfs[Ryy->sgfn], cg->fgfs[Ryz->sgfn], cg->fgfs[Rzz->sgfn],
-                                 cg->fgfs[Cons_Ham->sgfn],
-                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
-                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                 Symmetry, lev, ndeps, cor))
+                                 cg->fgfs[Cons_Ham->sgfn],
+                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->sgfn],
+                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
+                                 Symmetry, lev, ndeps, cor)))
           {
             cout << "find NaN in domain: (" 
                  << cg->bbox[0] << ":" << cg->bbox[3] << "," 
@@ -1371,11 +1500,15 @@ void bssnEM_class::Step(int lev, int YN)
             ERROR = 1;
           }
           // rk4 substep and boundary
-          {
-            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList; 
-            // we do not check the correspondence here
-            
-            while (varl0)
+          {
+            MyList<var> *varl0 = StateList, *varl = SynchList_pre, *varl1 = SynchList_cor, *varlrhs = RHSList;
+            // we do not check the correspondence here
+#if USE_CUDA_BSSN
+            if (used_gpu_substep)
+              skip_bssn_cuda_prefix(varl0, varl, varl1, varlrhs);
+#endif
+
+            while (varl0)
             {
 #ifndef WithShell
               if (lev == 0) // sommerfeld indeed
@@ -1683,7 +1816,7 @@ void bssnEM_class::Step(int lev, int YN)
     }
 #endif
 
-    Parallel::Sync(GH->PatL[lev], SynchList_cor, Symmetry);
+    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev]);
 
 #ifdef WithShell
     if (lev == 0)

AMSS_NCKU_source/bssnEScalar_class.h

@@ -54,17 +54,21 @@ public:
      void Interp_Constraint();
      void Constraint_Out(); 
 
-protected:
-     var *Sphio, *Spio;
-     var *Sphi0, *Spi0;
+protected:
+     var *Sphio, *Spio;
+     var *Sphi0, *Spi0;
      var *Sphi,  *Spi;
      var *Sphi1, *Spi1;
      var *Sphi_rhs, *Spi_rhs;
-
-     var *Cons_fR;
-
-     monitor *MaxScalar_Monitor;
-};
+
+     var *Cons_fR;
+
+     MyList<var> *BSSNStateList, *BSSNSynchList_pre, *BSSNSynchList_cor;
+     MyList<var> *ScalarSynchList_pre, *ScalarSynchList_cor;
+     Parallel::SyncCache *sync_cache_scalar_pre, *sync_cache_scalar_cor;
+
+     monitor *MaxScalar_Monitor;
+};
 
 #endif /* BSSNESCALAR_CLASS_H */
 

AMSS_NCKU_source/bssnEScalar_rhs.f90

@@ -3,11 +3,143 @@
 !! note that the potential for scalar field in F(R) gravity
 !!       is defined in the file Set_Rho_ADM.f90
 
-#include "macrodef.fh"
-
-! rhs for scalar and GR variables
-! here we consider vacuum spacetime only
-  function compute_rhs_bssn_escalar(ex, T,X, Y, Z,                             &
+#include "macrodef.fh"
+
+! scalar RHS and stress-energy only; BSSN RHS can be supplied by CUDA.
+  function compute_rhs_bssn_escalar_matter(ex, T, X, Y, Z,                    &
+               chi    ,   trK    ,                                            &
+               dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,    &
+               Axx    ,   Axy    ,   Axz    ,   Ayy    ,   Ayz    ,   Azz,    &
+               Gamx   ,  Gamy    ,  Gamz    ,                                 &
+               Lap    ,  betax   ,  betay   ,  betaz   ,                      &
+               dtSfx  ,  dtSfy   ,  dtSfz   ,                                 &
+               Sphi   ,   Spi    ,                                            &
+               Sphi_rhs ,   Spi_rhs ,                                         &
+               rho,Sx,Sy,Sz,Sxx,Sxy,Sxz,Syy,Syz,Szz,                          &
+               Symmetry,Lev,eps) result(gont)
+  implicit none
+
+  integer,intent(in ):: ex(1:3), Symmetry,Lev
+  real*8, intent(in ):: T
+  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: chi,dxx,dyy,dzz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: trK
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: gxy,gxz,gyz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: Axx,Axy,Axz,Ayy,Ayz,Azz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: Gamx,Gamy,Gamz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Lap, betax, betay, betaz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: dtSfx,  dtSfy,  dtSfz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: Sphi,Spi
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Sphi_rhs,Spi_rhs
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: rho,Sx,Sy,Sz
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Sxx,Sxy,Sxz,Syy,Syz,Szz
+  real*8,intent(in) :: eps
+  integer::gont
+
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz
+  real*8, dimension(ex(1),ex(2),ex(3)) :: chix,chiy,chiz
+  real*8, dimension(ex(1),ex(2),ex(3)) :: Lapx,Lapy,Lapz
+  real*8, dimension(ex(1),ex(2),ex(3)) :: Kx,Ky,Kz,S
+  real*8, dimension(ex(1),ex(2),ex(3)) :: f,fxx,fxy,fxz,fyy,fyz,fzz
+  real*8, dimension(ex(1),ex(2),ex(3)) :: alpn1,chin1
+  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            :: dX
+  real*8, parameter :: ZEO=0.d0, ONE = 1.D0, TWO = 2.D0, HALF = 0.5D0
+  real*8, parameter :: SYM = 1.D0
+
+  dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
+      +sum(Gamx)+sum(Gamy)+sum(Gamz)                                           &
+      +sum(Lap)+sum(Sphi)+sum(Spi)
+  if(dX.ne.dX) then
+     if(sum(chi).ne.sum(chi))write(*,*)"bssn_escalar_matter: find NaN in chi"
+     if(sum(trK).ne.sum(trK))write(*,*)"bssn_escalar_matter: find NaN in trk"
+     if(sum(dxx).ne.sum(dxx))write(*,*)"bssn_escalar_matter: find NaN in dxx"
+     if(sum(gxy).ne.sum(gxy))write(*,*)"bssn_escalar_matter: find NaN in gxy"
+     if(sum(gxz).ne.sum(gxz))write(*,*)"bssn_escalar_matter: find NaN in gxz"
+     if(sum(dyy).ne.sum(dyy))write(*,*)"bssn_escalar_matter: find NaN in dyy"
+     if(sum(gyz).ne.sum(gyz))write(*,*)"bssn_escalar_matter: find NaN in gyz"
+     if(sum(dzz).ne.sum(dzz))write(*,*)"bssn_escalar_matter: find NaN in dzz"
+     if(sum(Gamx).ne.sum(Gamx))write(*,*)"bssn_escalar_matter: find NaN in Gamx"
+     if(sum(Gamy).ne.sum(Gamy))write(*,*)"bssn_escalar_matter: find NaN in Gamy"
+     if(sum(Gamz).ne.sum(Gamz))write(*,*)"bssn_escalar_matter: find NaN in Gamz"
+     if(sum(Lap).ne.sum(Lap))write(*,*)"bssn_escalar_matter: find NaN in Lap"
+     if(sum(Sphi).ne.sum(Sphi))write(*,*)"bssn_escalar_matter: find NaN in Sphi"
+     if(sum(Spi).ne.sum(Spi))write(*,*)"bssn_escalar_matter: find NaN in Spi"
+     gont = 1
+     return
+  endif
+
+  alpn1 = Lap + ONE
+  chin1 = chi + ONE
+  gxx = dxx + ONE
+  gyy = dyy + ONE
+  gzz = dzz + ONE
+
+  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+
+  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 1
+  Sphi_rhs = alpn1 * Spi
+  call fderivs(ex,Sphi,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  call fdderivs(ex,Sphi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
+  Spi_rhs =   gupxx * fxx + gupyy * fyy + gupzz * fzz +           &
+             ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO -  &
+             ((Gamx+(gupxx*chix+gupxy*chiy+gupxz*chiz)/TWO/chin1)*Kx  &
+            + (Gamy+(gupxy*chix+gupyy*chiy+gupyz*chiz)/TWO/chin1)*Ky  &
+            + (Gamz+(gupxz*chix+gupyz*chiy+gupzz*chiz)/TWO/chin1)*Kz)
+  Spi_rhs = Spi_rhs*alpn1 +                                      &
+            (gupxx*Lapx*Kx + gupxy*Lapx*Ky + gupxz*Lapx*Kz       &
+            +gupxy*Lapy*Kx + gupyy*Lapy*Ky + gupyz*Lapy*Kz       &
+            +gupxz*Lapz*Kx + gupyz*Lapz*Ky + gupzz*Lapz*Kz)
+
+  call frpotential(ex,Sphi,f,S)
+  Spi_rhs = Spi_rhs*chin1 + alpn1*(trK*Spi - S)
+  rho = chin1*((gupxx * Kx * Kx + gupyy * Ky * Ky + gupzz * Kz * Kz)/TWO + &
+                gupxy * Kx * Ky + gupxz * Kx * Kz + gupyz * Ky * Kz )      &
+        + Spi*Spi/TWO+f
+  Sx = -Spi*Kx
+  Sy = -Spi*Ky
+  Sz = -Spi*Kz
+  f = (rho - Spi*Spi)/chin1
+  Sxx = Kx*Kx-f*gxx
+  Sxy = Kx*Ky-f*gxy
+  Sxz = Kx*Kz-f*gxz
+  Syy = Ky*Ky-f*gyy
+  Syz = Ky*Kz-f*gyz
+  Szz = Kz*Kz-f*gzz
+#else
+  Sphi_rhs = ZEO
+  Spi_rhs = ZEO
+  rho = ZEO
+  Sx = ZEO
+  Sy = ZEO
+  Sz = ZEO
+  Sxx = ZEO
+  Sxy = ZEO
+  Sxz = ZEO
+  Syy = ZEO
+  Syz = ZEO
+  Szz = ZEO
+#endif
+
+  gont = 0
+  return
+end function compute_rhs_bssn_escalar_matter
+
+! rhs for scalar and GR variables
+! here we consider vacuum spacetime only
+  function compute_rhs_bssn_escalar(ex, T,X, Y, Z,                             &
                chi    ,   trK    ,                                             &
                dxx    ,   gxy    ,   gxz    ,   dyy    ,   gyz    ,   dzz,     &
                Axx    ,   Axy    ,   Axz    ,   Ayy    ,   Ayz    ,   Azz,     &

AMSS_NCKU_source/bssn_class.h

@@ -45,10 +45,12 @@ public:
        int checkrun;
        char checkfilename[50];
        int Steps;
-       double StartTime, TotalTime;
-       double AnasTime, DumpTime, d2DumpTime, CheckTime;
-       double LastAnas, LastConsOut;
-       double Courant;
+       double StartTime, TotalTime;
+       double AnasTime, DumpTime, d2DumpTime, CheckTime;
+       double LastAnas, LastConsOut;
+       bool cuda_level0_constraint_cache_valid;
+       int *ConstraintRefreshLevels;
+       double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
        int maxl, decn;
@@ -133,9 +135,9 @@ public:
        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;
-       surface_integral *Waveshell;
+       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
+       monitor *ConVMonitor, *TimingMonitor;
+       surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
 public:
@@ -176,14 +178,17 @@ public:
        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:
+       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();
+
+protected:
+       void Initialize_Level_Runtime();
+
+#ifdef With_AHF
+protected:
        MyList<var> *AHList, *AHDList, *GaugeList;
        int AHfindevery;
        double AHdumptime;

AMSS_NCKU_source/bssn_gpu.h

@@ -1,73 +0,0 @@
-
-#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

@@ -1,210 +0,0 @@
-
-#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

@@ -59,9 +59,10 @@
   real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Rxx,Rxy,Rxz,Ryy,Ryz,Rzz
   real*8,intent(in) :: eps
   real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: ham_Res, movx_Res, movy_Res, movz_Res
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
-!  gont = 0: success; gont = 1: something wrong
-  integer::gont
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
+!  gont = 0: success; gont = 1: something wrong
+  integer::gont
+  integer :: i,j,k
 
 !~~~~~~> Other variables:
 
@@ -83,11 +84,18 @@
   real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
   real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
 
-  real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
-  real*8            :: 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
+  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
   double precision,parameter::FF = 0.75d0,eta=2.d0
   real*8, parameter :: F1o3 = 1.D0/3.D0, F2o3 = 2.D0/3.D0,F3o2=1.5d0, F1o6 = 1.D0/6.D0
   real*8, parameter :: F16=1.6d1,F8=8.d0
@@ -96,11 +104,11 @@
   real*8, dimension(ex(1),ex(2),ex(3)) :: reta
 #endif
 
-#if (GAUGE == 6 || GAUGE == 7)
-  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
+#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
   real*8, dimension(ex(1),ex(2),ex(3)) :: reta
 
   call getpbh(BHN,Porg,Mass)
@@ -145,174 +153,204 @@
   dY = Y(2) - Y(1)
   dZ = Z(2) - Z(1)
 
-  alpn1 = Lap + ONE
-  chin1 = chi + ONE
-  gxx = dxx + ONE
-  gyy = dyy + ONE
-  gzz = dzz + ONE
+  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
 
   call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
   call fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev)
   call fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev)
   
-  div_beta = betaxx + betayy + betazz
- 
-  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
+  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
 
-  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
-
-  call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
-  call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
-  call fderivs(ex,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 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
 
   call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
                 X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
@@ -321,38 +359,54 @@
   call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
                 X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
 
-  fxx = gxxx + gxyy + gxzz
-  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
+  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
 
 !first kind of connection stored in gij,k
   gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
@@ -601,192 +655,190 @@
             Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz  + &
             Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy  + &
             Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
-!covariant second derivative of chi respect to tilted metric
-  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
+!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
   
 !!!! gauge variable part
 
@@ -948,15 +1000,15 @@
 !!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
 ! lopsided_kodis shares the symmetry_bd buffer between advection and
 ! dissipation, eliminating redundant full-grid copies. For metric variables
-! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
-! 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)
+! 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)
 
   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

@@ -5,8 +5,9 @@
 #ifdef fortran1
 #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_bssn_escalar compute_rhs_bssn_escalar
+#define f_compute_rhs_bssn_escalar_matter compute_rhs_bssn_escalar_matter
+#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
@@ -15,26 +16,41 @@
 #ifdef fortran2
 #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_bssn_escalar COMPUTE_RHS_BSSN_ESCALAR
+#define f_compute_rhs_bssn_escalar_matter COMPUTE_RHS_BSSN_ESCALAR_MATTER
+#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 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_bssn_escalar compute_rhs_bssn_escalar_
+#define f_compute_rhs_bssn_escalar_matter compute_rhs_bssn_escalar_matter_
+#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
-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
+
+#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
                                double *, double *,                                                                                 // chi, trK
                                double *, double *, double *, double *, double *, double *,                                         // gij
                                double *, double *, double *, double *, double *, double *,                                         // Aij
@@ -83,10 +99,24 @@ extern "C"
                                   int &, int &, double &, int &, int &);
 }
 
-extern "C"
-{
-        int f_compute_rhs_bssn_escalar(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
-                                       double *, double *,                                                                                 // chi, trK
+extern "C"
+{
+        int f_compute_rhs_bssn_escalar_matter(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
+                                              double *, double *, double *,                                                              // Gam
+                                              double *, double *, double *, double *, double *, double *, double *,                      // Gauge
+                                              double *, double *,                                                                        // Sphi, Spi
+                                              double *, double *,                                                                        // Sphi, Spi rhs
+                                              double *, double *, double *, double *, double *, double *, double *, double *, double *, double *, // stress-energy
+                                              int &, int &, double &);
+}
+
+extern "C"
+{
+        int f_compute_rhs_bssn_escalar(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
                                        double *, double *, double *,                                                                       // Gam

AMSS_NCKU_source/bssn_rhs_c.C

@@ -2,12 +2,88 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
+#include <time.h>
 // 0-based i,j,k
 // #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
 // ex(1)=nx, ex(2)=ny, ex(3)=nz
 
 // 用法：a[ IDX_F(i,j,k,nx,ny) ]
 
+#ifndef BSSN_KERNEL_FINE_TIMING
+#define BSSN_KERNEL_FINE_TIMING 0
+#endif
+
+#if BSSN_KERNEL_FINE_TIMING
+namespace rhs_kernel_timing
+{
+    enum Bucket
+    {
+        KB_SETUP_DERIVS = 0,
+        KB_GEOM_GAMMA,
+        KB_RICCI_METRIC,
+        KB_CHI_LAPSE,
+        KB_AIJ_TRK_GAUGE,
+        KB_KO_CONSTRAINT,
+        KB_COUNT
+    };
+
+    static double local_bucket_seconds[KB_COUNT];
+
+    static const char *bucket_labels[KB_COUNT] =
+    {
+        "setup_derivs",
+        "geom_gamma",
+        "ricci_metric",
+        "chi_lapse",
+        "aij_trk_gauge",
+        "ko_constraint"
+    };
+
+    static inline double now_seconds()
+    {
+        struct timespec ts;
+        clock_gettime(CLOCK_MONOTONIC, &ts);
+        return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
+    }
+}
+
+extern "C" void f_bssn_rhs_kernel_timing_reset()
+{
+    for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
+        rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
+}
+
+extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
+{
+    return rhs_kernel_timing::KB_COUNT;
+}
+
+extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
+{
+    return rhs_kernel_timing::local_bucket_seconds;
+}
+
+extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
+{
+    if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
+        return "unknown";
+    return rhs_kernel_timing::bucket_labels[bucket_index];
+}
+
+#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
+#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
+    rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
+        rhs_kernel_timing::now_seconds() - (var_name)
+#else
+extern "C" void f_bssn_rhs_kernel_timing_reset() {}
+extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
+extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
+extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
+
+#define RHS_KERNEL_TIMER_DECL(var_name)
+#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
+#endif
+
 // C function that calculates the right-hand side for BSSN equations
 int f_compute_rhs_bssn(int *ex, double &T, 
                        double *X, double *Y, double *Z,
@@ -102,6 +178,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
     dY = Y[1] - Y[0];
     dZ = Z[1] - Z[0];
 
+        RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
         // 1ms //
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
@@ -141,6 +218,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
                         + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
         }
+        RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
+        RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
         // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
         for(int i=0;i<all;i+=1){
             double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
@@ -283,9 +362,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                 + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
-            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
-            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
-
             Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
                 TWO * alpn1[i] * (
                 -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
@@ -315,6 +391,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
                             + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                         );
         }
+        RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
+        RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
         // 22.3ms //
         fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
         X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
@@ -332,7 +410,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
             double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
             double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
-            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
 
             double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                     + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
@@ -686,32 +763,38 @@ int f_compute_rhs_bssn(int *ex, double &T,
                     + Gamxyz[i] * gzzx[i] + Gamyyz[i] * gzzy[i] + Gamzyz[i] * gzzz[i]
                 );
         }
+        RHS_KERNEL_TIMER_ADD(KB_RICCI_METRIC, timer_ricci_metric);
 
+        RHS_KERNEL_TIMER_DECL(timer_chi_lapse);
         // 22.3ms //
             fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 7ms //
         for (int i=0;i<all;i+=1) {
-            fxx[i] = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
-            fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
-            fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
-            fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
-            fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
-            fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
-            f[i] =
-                gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
-                + gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
-                + gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
-                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
-                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
-                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+            const double inv_chin1 = ONE / chin1[i];
+            const double half_inv_chin1 = HALF * inv_chin1;
+            const double scaled_inv = F3o2 * inv_chin1;
+            const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
+            const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
+            const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
+            const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
+            const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
+            const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
+            const double ricci_chi =
+                gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
+                + gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
+                + gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
+                + TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
+                + TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
+                + TWO * gupyz[i] * (cyz - scaled_inv * chiy[i] * chiz[i]);
+            f[i] = ricci_chi;
+            Rxx[i] = Rxx[i] + ( cxx - half_inv_chin1 * chix[i] * chix[i] + (dxx[i] + ONE) * ricci_chi ) * half_inv_chin1;
+            Ryy[i] = Ryy[i] + ( cyy - half_inv_chin1 * chiy[i] * chiy[i] + (dyy[i] + ONE) * ricci_chi ) * half_inv_chin1;
+            Rzz[i] = Rzz[i] + ( czz - half_inv_chin1 * chiz[i] * chiz[i] + (dzz[i] + ONE) * ricci_chi ) * half_inv_chin1;
 
-            Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
-            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
-            Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
+            Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
+            Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
+            Ryz[i] = Ryz[i] + ( cyz - half_inv_chin1 * chiy[i] * chiz[i] + gyz[i] * ricci_chi ) * half_inv_chin1;
         }
 
         // 24ms //
@@ -719,35 +802,35 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
         // 6ms //
         for (int i=0;i<all;i+=1) {
-            /* gxxx,gxxy,gxxz (这里是“升指标后的chi导数/chi”那类量，你沿用原变量名即可) */
-            gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
-            gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
-            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
+            const double inv_chin1 = ONE / chin1[i];
+            const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
+            const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
+            const double gchi_z = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) * inv_chin1;
 
             /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) * inv_chin1) - (dxx[i] + ONE) * gchi_x ) * HALF;
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_y ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_z ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_x ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) * inv_chin1) - (dyy[i] + ONE) * gchi_y ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_z ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_x ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_y ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) * inv_chin1) - (dzz[i] + ONE) * gchi_z ) * HALF;
 
-            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
-            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
-            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gxxz[i] ) * HALF;
+            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1)      - gxy[i] * gchi_x ) * HALF;
+            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1)      - gxy[i] * gchi_y ) * HALF;
+            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gchi_z ) * HALF;
 
-            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] / chin1[i])      - gxz[i] * gxxx[i] ) * HALF;
-            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gxxy[i] ) * HALF;
-            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i])      - gxz[i] * gxxz[i] ) * HALF;
+            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1)      - gxz[i] * gchi_x ) * HALF;
+            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gchi_y ) * HALF;
+            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] * inv_chin1)      - gxz[i] * gchi_z ) * HALF;
 
-            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gxxx[i] ) * HALF;
-            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i])      - gyz[i] * gxxy[i] ) * HALF;
-            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i])      - gyz[i] * gxxz[i] ) * HALF;
+            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gchi_x ) * HALF;
+            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1)      - gyz[i] * gchi_y ) * HALF;
+            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] * inv_chin1)      - gyz[i] * gchi_z ) * HALF;
 
             /* fxx..fyz 修正：减去 Γ * ∂Lap */
             fxx[i] = fxx[i] - Gamxxx[i] * Lapx[i] - Gamyxx[i] * Lapy[i] - Gamzxx[i] * Lapz[i];
@@ -761,6 +844,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
             trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                     +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
         }
+        RHS_KERNEL_TIMER_ADD(KB_CHI_LAPSE, timer_chi_lapse);
+        RHS_KERNEL_TIMER_DECL(timer_aij_trk_gauge);
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
             const double divb = betaxx[i] + betayy[i] + betazz[i];
@@ -1061,6 +1146,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #endif
         }
+        RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
+        RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
         // advection + KO dissipation with shared symmetry buffer
         lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
         lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
@@ -1192,6 +1279,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
             }
         }
+        RHS_KERNEL_TIMER_ADD(KB_KO_CONSTRAINT, timer_ko_constraint);
 
 
             

AMSS_NCKU_source/bssn_rhs_cuda.h

@@ -0,0 +1,470 @@
+#ifndef BSSN_RHS_CUDA_H
+#define BSSN_RHS_CUDA_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+enum {
+    BSSN_CUDA_STATE_COUNT = 24,
+    BSSN_CUDA_MATTER_COUNT = 10
+};
+
+int f_compute_rhs_bssn(int *ex, double &T,
+                       double *X, double *Y, double *Z,
+                       double *chi, double *trK,
+                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                       double *Gamx, double *Gamy, double *Gamz,
+                       double *Lap, double *betax, double *betay, double *betaz,
+                       double *dtSfx, double *dtSfy, double *dtSfz,
+                       double *chi_rhs, double *trK_rhs,
+                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                       double *rho, double *Sx, double *Sy, double *Sz,
+                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                       int &Symmetry, int &Lev, double &eps, int &co);
+
+int bssn_cuda_rk4_substep(void *block_tag,
+                          int *ex, double *X, double *Y, double *Z,
+                          double **state_host_in,
+                          double **state_host_out,
+                          double **matter_host,
+                          const double *propspeed,
+                          const double *soa_flat,
+                          const double *bbox,
+                          double &dT,
+                          double &T,
+                          int &RK4,
+                          int &apply_bam_bc,
+                          int &Symmetry,
+                          int &Lev,
+                          double &eps,
+                          int &co,
+                          int &use_zero_matter,
+                          int &keep_resident_state,
+                          int &apply_enforce_ga,
+                          double &chitiny);
+
+int bssn_cuda_compute_escalar_matter(void *block_tag,
+                                     int *ex, double *X, double *Y, double *Z,
+                                     double **state_host_in,
+                                     double *Sphi_host,
+                                     double *Spi_host,
+                                     double *Sphi_rhs_host,
+                                     double *Spi_rhs_host,
+                                     double a2,
+                                     int &Symmetry,
+                                     int &Lev,
+                                     double &eps,
+                                     int &co,
+                                     int &apply_enforce_ga);
+
+int bssn_cuda_escalar_finalize_scalar_fields(void *block_tag,
+                                             int *ex, double *X, double *Y, double *Z,
+                                             double *Sphi_out_host,
+                                             double *Spi_out_host,
+                                             const double *propspeed,
+                                             const double *soa_flat,
+                                             const double *bbox,
+                                             double &dT,
+                                             int &RK4,
+                                             int &apply_bam_bc,
+                                             int &Symmetry,
+                                             int &Lev,
+                                             double &eps,
+                                             int &precor);
+
+int bssn_cuda_escalar_has_resident_fields(void *block_tag,
+                                          double *Sphi_host,
+                                          double *Spi_host);
+
+int bssn_cuda_escalar_has_any_resident_fields(void *block_tag);
+
+int bssn_cuda_escalar_download_fields_if_present(void *block_tag,
+                                                 int *ex,
+                                                 double *Sphi_host,
+                                                 double *Spi_host);
+
+int bssn_cuda_pack_escalar_batch_to_host_buffer(void *block_tag,
+                                                double **scalar_host_key,
+                                                double *host_buffer,
+                                                int *ex,
+                                                int i0, int j0, int k0,
+                                                int sx, int sy, int sz);
+
+int bssn_cuda_unpack_escalar_batch_from_host_buffer(void *block_tag,
+                                                    double **scalar_host_key,
+                                                    double *host_buffer,
+                                                    int *ex,
+                                                    int i0, int j0, int k0,
+                                                    int sx, int sy, int sz);
+
+int bssn_cuda_pack_escalar_batch_to_device_buffer(void *block_tag,
+                                                  double **scalar_host_key,
+                                                  double *device_buffer,
+                                                  int *ex,
+                                                  int i0, int j0, int k0,
+                                                  int sx, int sy, int sz);
+
+int bssn_cuda_unpack_escalar_batch_from_device_buffer(void *block_tag,
+                                                      double **scalar_host_key,
+                                                      double *device_buffer,
+                                                      int *ex,
+                                                      int i0, int j0, int k0,
+                                                      int sx, int sy, int sz);
+
+int bssn_cuda_restrict_escalar_batch_to_host_buffer(void *block_tag,
+                                                    double **scalar_host_key,
+                                                    double *host_buffer,
+                                                    int *ex,
+                                                    int sx, int sy, int sz,
+                                                    int fi0, int fj0, int fk0,
+                                                    const double *scalar_soa);
+
+int bssn_cuda_prolong_escalar_batch_to_host_buffer(void *block_tag,
+                                                   double **scalar_host_key,
+                                                   double *host_buffer,
+                                                   int *ex,
+                                                   int sx, int sy, int sz,
+                                                   int ii0, int jj0, int kk0,
+                                                   int lbc_i, int lbc_j, int lbc_k,
+                                                   const double *scalar_soa);
+
+int bssn_cuda_restrict_escalar_batch_to_device_buffer(void *block_tag,
+                                                      double **scalar_host_key,
+                                                      double *device_buffer,
+                                                      int *ex,
+                                                      int sx, int sy, int sz,
+                                                      int fi0, int fj0, int fk0,
+                                                      const double *scalar_soa);
+
+int bssn_cuda_prolong_escalar_batch_to_device_buffer(void *block_tag,
+                                                     double **scalar_host_key,
+                                                     double *device_buffer,
+                                                     int *ex,
+                                                     int sx, int sy, int sz,
+                                                     int ii0, int jj0, int kk0,
+                                                     int lbc_i, int lbc_j, int lbc_k,
+                                                     const double *scalar_soa);
+
+int bssn_cuda_prepare_escalar_inter_time_level(void *block_tag,
+                                               int *ex,
+                                               double **src1_host_key,
+                                               double **src2_host_key,
+                                               double **src3_host_key,
+                                               double **dst_host_key,
+                                               int source_count,
+                                               int tindex);
+
+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_resident_state_if_present(void *block_tag,
+                                                int *ex,
+                                                double **state_host_out);
+
+int bssn_cuda_resident_state_matches(void *block_tag,
+                                     double **state_host_key);
+
+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_interp_state_point3(void *block_tag,
+                                  int *ex,
+                                  int state0,
+                                  int state1,
+                                  int state2,
+                                  double x0,
+                                  double y0,
+                                  double z0,
+                                  double dx,
+                                  double dy,
+                                  double dz,
+                                  double px,
+                                  double py,
+                                  double pz,
+                                  int ordn,
+                                  int symmetry,
+                                  const double *soa3,
+                                  double *out3);
+
+int bssn_cuda_interp_host_two_fields(void *block_tag,
+                                     int *ex,
+                                     double *field0,
+                                     double *field1,
+                                     double x0,
+                                     double y0,
+                                     double z0,
+                                     double dx,
+                                     double dy,
+                                     double dz,
+                                     const double *px,
+                                     const double *py,
+                                     const double *pz,
+                                     int npoints,
+                                     int ordn,
+                                     int symmetry,
+                                     const double *soa6,
+                                     double *out_interleaved);
+
+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_pack_state_batch_to_host_buffer_for_host_views(void *block_tag,
+                                                             double **state_host_key,
+                                                             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_unpack_state_batch_from_host_buffer_for_host_views(void *block_tag,
+                                                                 double **state_host_key,
+                                                                 int state_count,
+                                                                 double *host_buffer,
+                                                                 int *ex,
+                                                                 int i0, int j0, int k0,
+                                                                 int sx, int sy, int sz);
+
+int bssn_cuda_restrict_state_batch_to_host_buffer_for_host_views(void *block_tag,
+                                                                 double **state_host_key,
+                                                                 int state_count,
+                                                                 double *host_buffer,
+                                                                 int *ex,
+                                                                 int sx, int sy, int sz,
+                                                                 int fi0, int fj0, int fk0,
+                                                                 const double *state_soa);
+
+int bssn_cuda_restrict_state_batch_to_host_buffer(void *block_tag,
+                                                  int state_count,
+                                                  double *host_buffer,
+                                                  int *ex,
+                                                  int sx, int sy, int sz,
+                                                  int fi0, int fj0, int fk0,
+                                                  const double *state_soa);
+
+int bssn_cuda_prolong_state_batch_to_host_buffer_for_host_views(void *block_tag,
+                                                                double **state_host_key,
+                                                                int state_count,
+                                                                double *host_buffer,
+                                                                int *ex,
+                                                                int sx, int sy, int sz,
+                                                                int ii0, int jj0, int kk0,
+                                                                int lbc_i, int lbc_j, int lbc_k,
+                                                                const double *state_soa);
+
+int bssn_cuda_prolong_state_batch_to_host_buffer(void *block_tag,
+                                                 int state_count,
+                                                 double *host_buffer,
+                                                 int *ex,
+                                                 int sx, int sy, int sz,
+                                                 int ii0, int jj0, int kk0,
+                                                 int lbc_i, int lbc_j, int lbc_k,
+                                                 const double *state_soa);
+
+int bssn_cuda_pack_state_batch_to_device_buffer(void *block_tag,
+                                                 int state_count,
+                                                double *device_buffer,
+                                                int *ex,
+                                                int i0, int j0, int k0,
+                                                int sx, int sy, int sz);
+
+int bssn_cuda_pack_state_batch_to_device_buffer_for_host_views(void *block_tag,
+                                                               double **state_host_key,
+                                                               int state_count,
+                                                               double *device_buffer,
+                                                               int *ex,
+                                                               int i0, int j0, int k0,
+                                                               int sx, int sy, int sz);
+
+int bssn_cuda_unpack_state_batch_from_device_buffer(void *block_tag,
+                                                    int state_count,
+                                                    double *device_buffer,
+                                                    int *ex,
+                                                    int i0, int j0, int k0,
+                                                    int sx, int sy, int sz);
+
+int bssn_cuda_unpack_state_batch_from_device_buffer_for_host_views(void *block_tag,
+                                                                   double **state_host_key,
+                                                                   int state_count,
+                                                                   double *device_buffer,
+                                                                   int *ex,
+                                                                   int i0, int j0, int k0,
+                                                                   int sx, int sy, int sz);
+
+int bssn_cuda_pack_state_segments_to_device_buffer(void *block_tag,
+                                                   int state_count,
+                                                   double *device_buffer,
+                                                   int *ex,
+                                                   int segment_count,
+                                                   const int *segment_meta);
+
+int bssn_cuda_pack_state_segments_to_device_buffer_for_host_views(void *block_tag,
+                                                                  double **state_host_key,
+                                                                  int state_count,
+                                                                  double *device_buffer,
+                                                                  int *ex,
+                                                                  int segment_count,
+                                                                  const int *segment_meta);
+
+int bssn_cuda_unpack_state_segments_from_device_buffer(void *block_tag,
+                                                       int state_count,
+                                                       double *device_buffer,
+                                                       int *ex,
+                                                       int segment_count,
+                                                       const int *segment_meta);
+
+int bssn_cuda_unpack_state_segments_from_device_buffer_for_host_views(void *block_tag,
+                                                                      double **state_host_key,
+                                                                      int state_count,
+                                                                      double *device_buffer,
+                                                                      int *ex,
+                                                                      int segment_count,
+                                                                      const int *segment_meta);
+
+int bssn_cuda_restrict_state_segments_to_device_buffer(void *block_tag,
+                                                       int state_count,
+                                                       double *device_buffer,
+                                                       int *ex,
+                                                       int segment_count,
+                                                       const int *segment_meta);
+
+int bssn_cuda_restrict_state_segments_to_device_buffer_for_host_views(void *block_tag,
+                                                                      double **state_host_key,
+                                                                      int state_count,
+                                                                      double *device_buffer,
+                                                                      int *ex,
+                                                                      int segment_count,
+                                                                      const int *segment_meta,
+                                                                      const double *state_soa);
+
+int bssn_cuda_prolong_state_segments_to_device_buffer(void *block_tag,
+                                                      int state_count,
+                                                      double *device_buffer,
+                                                      int *ex,
+                                                      int segment_count,
+                                                      const int *segment_meta);
+
+int bssn_cuda_prolong_state_segments_to_device_buffer_for_host_views(void *block_tag,
+                                                                     double **state_host_key,
+                                                                     int state_count,
+                                                                     double *device_buffer,
+                                                                     int *ex,
+                                                                     int segment_count,
+                                                                     const int *segment_meta,
+                                                                     const double *state_soa);
+
+int bssn_cuda_restrict_state_batch_to_device_buffer(void *block_tag,
+                                                    int state_count,
+                                                    double *device_buffer,
+                                                    int *ex,
+                                                    int sx, int sy, int sz,
+                                                    int fi0, int fj0, int fk0);
+
+int bssn_cuda_restrict_state_batch_to_device_buffer_for_host_views(void *block_tag,
+                                                                   double **state_host_key,
+                                                                   int state_count,
+                                                                   double *device_buffer,
+                                                                   int *ex,
+                                                                   int sx, int sy, int sz,
+                                                                   int fi0, int fj0, int fk0,
+                                                                   const double *state_soa);
+
+int bssn_cuda_prolong_state_batch_to_device_buffer(void *block_tag,
+                                                   int state_count,
+                                                   double *device_buffer,
+                                                   int *ex,
+                                                   int sx, int sy, int sz,
+                                                   int ii0, int jj0, int kk0,
+                                                   int lbc_i, int lbc_j, int lbc_k);
+
+int bssn_cuda_prolong_state_batch_to_device_buffer_for_host_views(void *block_tag,
+                                                                  double **state_host_key,
+                                                                  int state_count,
+                                                                  double *device_buffer,
+                                                                  int *ex,
+                                                                  int sx, int sy, int sz,
+                                                                  int ii0, int jj0, int kk0,
+                                                                  int lbc_i, int lbc_j, int lbc_k,
+                                                                  const double *state_soa);
+
+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_prepare_inter_time_level(void *block_tag,
+                                       int *ex,
+                                       double **src1_host_key,
+                                       double **src2_host_key,
+                                       double **src3_host_key,
+                                       double **dst_host_key,
+                                       int source_count,
+                                       int tindex);
+
+int bssn_cuda_has_resident_state(void *block_tag);
+
+void bssn_cuda_release_step_ctx(void *block_tag);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

AMSS_NCKU_source/fmisc.f90

@@ -1511,13 +1511,88 @@ deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
-  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)
+  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)
 
   implicit none
 !~~~~~~> Input parameters:

AMSS_NCKU_source/fmisc.h

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

AMSS_NCKU_source/macrodef.fh

@@ -13,7 +13,7 @@
 
 #define ABV 0
 
-#define EScalar_CC 2
+#define EScalar_CC  2
 
 #if 0
 

AMSS_NCKU_source/macrodef.h

@@ -10,7 +10,7 @@
 
 #define GaussInt
 
-#define ABEtype 0
+#define ABEtype 1
 
 //#define With_AHF
 #define Psi4type 0
@@ -29,6 +29,16 @@
 
 #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
@@ -88,6 +98,21 @@
 //     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
 //

AMSS_NCKU_source/makefile

@@ -1,35 +1,53 @@
 
 
-include makefile.inc
-
-## polint(ordn=6) kernel selector:
-##   1 (default): barycentric fast path
-##   0          : fallback to Neville path
-POLINT6_USE_BARY ?= 1
-POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
-
-## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
-##   make                        -> opt  (PGO-guided, maximum performance)
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+include makefile.inc
+
+## polint(ordn=6) kernel selector:
+##   1 (default): barycentric fast path
+##   0          : fallback to Neville path
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+##   make                        -> opt  (PGO-guided, maximum performance)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+
+ifeq ($(TOOLCHAIN),intel)
+OMP_FLAG = -qopenmp
 
 ifeq ($(PGO_MODE),instrument)
-## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-## PGO has been turned off, now tested and found to be negative optimization
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-endif
+## Intel Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -Dfortran3 -Dnewc $(MKL_INC) $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -align array64byte -fpp $(MKL_INC) $(POLINT6_FLAG)
+else
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
+## PGO has been turned off, now tested and found to be negative optimization
+## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
+
+
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -Dfortran3 -Dnewc $(MKL_INC) $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp $(MKL_INC) $(POLINT6_FLAG)
+endif
+
+TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(TP_PROFDATA) \
+              -Dfortran3 -Dnewc $(MKL_INC)
+else
+## NVHPC defaults: mpicc/mpicxx/mpifort wrappers
+## PGO_MODE is ignored in this branch.
+OMP_FLAG = -mp
+CXXAPPFLAGS = -O3 -tp=host -Mcache_align -Mfma \
+              -Dfortran3 -Dnewc $(MKL_INC) $(INTERP_LB_FLAGS)
+f90appflags = -O3 -tp=host -Mcache_align -Mfma -Mpreprocess \
+              $(MKL_INC) $(POLINT6_FLAG)
+TP_OPTFLAGS = -O3 -tp=host -Mcache_align -Mfma \
+              -Dfortran3 -Dnewc $(MKL_INC)
+endif
 
 .SUFFIXES: .o .f90 .C .for .cu
 
@@ -42,7 +60,15 @@ endif
 .for.o:
 	$(f77) -c $< -o $@
 
-.cu.o:
+.cu.o:
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
+# CUDA rewrite of BSSN RHS (drop-in replacement for bssn_rhs_c + stencil helpers)
+bssn_rhs_cuda.o: bssn_rhs_cuda.cu bssn_rhs.h macrodef.h
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
+# CUDA rewrite of Z4C Cartesian RHS
+z4c_rhs_cuda.o: z4c_rhs_cuda.cu z4c_rhs_cuda.h bssn_rhs.h macrodef.h ricci_gamma.h
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
 # C rewrite of BSSN RHS kernel and helpers
@@ -58,45 +84,83 @@ fdderivs_c.o: fdderivs_c.C
 kodiss_c.o: kodiss_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-lopsided_c.o: lopsided_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-lopsided_kodis_c.o: lopsided_kodis_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
-interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+lopsided_c.o: lopsided_c.C
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
-TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
-TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(TP_PROFDATA) \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
+lopsided_kodis_c.o: lopsided_kodis_c.C
+	${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 $@
 
 TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) $(OMP_FLAG) -c $< -o $@
 
 TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) $(OMP_FLAG) -c $< -o $@
 
 # Input files
 
+## CUDA BSSN RHS switch
+##   1 : use the rewritten CUDA bssn_rhs backend
+##   0 : keep the normal CPU/Fortran selection below
+USE_CUDA_BSSN ?= 0
+USE_CUDA_Z4C ?= 0
+
+CXXAPPFLAGS += -DUSE_CUDA_BSSN=$(USE_CUDA_BSSN)
+CUDA_APP_FLAGS += -DUSE_CUDA_BSSN=$(USE_CUDA_BSSN)
+CXXAPPFLAGS += -DUSE_CUDA_Z4C=$(USE_CUDA_Z4C)
+CUDA_APP_FLAGS += -DUSE_CUDA_Z4C=$(USE_CUDA_Z4C)
+
 ## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
-ifeq ($(USE_CXX_KERNELS),0)
-# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES =
-else
-# C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
-endif
-
-## RK4 kernel switch (independent from USE_CXX_KERNELS)
-ifeq ($(USE_CXX_RK4),1)
-CFILES += rungekutta4_rout_c.o
-RK4_F90_OBJ =
-else
-RK4_F90_OBJ = rungekutta4_rout.o
-endif
+ifeq ($(USE_CXX_KERNELS),0)
+# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
+CFILES_CPU =
+else
+# C++ mode (default): C rewrite of bssn_rhs and helper kernels
+CFILES_CPU = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+endif
+
+CFILES_CUDA_BSSN = bssn_rhs_cuda.o
+
+ifeq ($(USE_CUDA_BSSN),1)
+CFILES = $(CFILES_CUDA_BSSN)
+else
+CFILES = $(CFILES_CPU)
+endif
+
+ifeq ($(USE_CUDA_Z4C),1)
+CFILES += z4c_rhs_cuda.o
+Z4C_F90_OBJ =
+else ifeq ($(USE_CXX_Z4C_KERNELS),1)
+CFILES += z4c_rhs_c.o
+Z4C_F90_OBJ =
+else
+Z4C_F90_OBJ = Z4c_rhs.o
+endif
+
+## RK4 kernel switch (independent from USE_CXX_KERNELS)
+ifeq ($(USE_CXX_RK4),1)
+RK4_C_OBJ = rungekutta4_rout_c.o
+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\
@@ -105,7 +169,7 @@ 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\
@@ -113,13 +177,13 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
 	   NullShellPatch2_Evo.o \
 	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
 
-F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
-           fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
+	   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\
 	   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\
@@ -143,10 +207,10 @@ 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) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
+$(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(ABE_CUDA_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\
@@ -157,7 +221,7 @@ $(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\
@@ -169,7 +233,7 @@ $(C++FILES_GPU): Block.h enforce_algebra.h fmisc.h initial_puncture.h macrodef.h
              
 $(AHFDOBJS): cctk.h cctk_Config.h cctk_Types.h cctk_Constants.h myglobal.h
 
-$(C++FILES) $(C++FILES_GPU) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
+$(C++FILES) $(C++FILES_GPU) $(CFILES) $(ABE_CUDA_CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.h
 
 TwoPunctureFILES: TwoPunctures.h
 
@@ -179,13 +243,18 @@ misc.o : zbesh.o
 
 # projects
 ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(ABE_LDLIBS)
+
+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)
+#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)
+	$(CLINKER) $(TP_OPTFLAGS) $(OMP_FLAG) -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
-	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
+	rm *.o ABE ABE_CUDA ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,28 +1,7 @@
-## GCC version (commented out)
-## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
-
-## Intel oneAPI version with oneMKL (Optimized for performance)
-filein  = -I/usr/include/ -I${MKLROOT}/include
-
-## Using sequential MKL (OpenMP disabled for better single-threaded performance)
-## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
-
-## Memory allocator switch
-##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
-##   0           : use system default allocator (ptmalloc)
-USE_TBBMALLOC ?= 1
-TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
-ifneq ($(wildcard $(TBBMALLOC_SO)),)
-TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
-else
-TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
-endif
-ifeq ($(USE_TBBMALLOC),1)
-LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
-endif
+## Toolchain selection
+##   nvhpc : NVIDIA HPC SDK + CUDA-aware MPI (default)
+##   intel : Intel oneAPI toolchain (legacy path)
+TOOLCHAIN ?= nvhpc
 
 ## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
 ##   opt        : (default) maximum performance with PGO profile-guided optimization
@@ -43,23 +22,70 @@ else
 INTERP_LB_FLAGS =
 endif
 
+MKLROOT ?= /home/intel/oneapi/mkl/latest
+MKL_LIBDIR ?= $(MKLROOT)/lib/intel64
+MKL_INC ?= -I$(MKLROOT)/include
+
+NVHPC_ROOT ?= /home/nvidia/hpc_sdk/Linux_x86_64/25.11
+CUDA_HOME  ?= $(NVHPC_ROOT)/cuda
+CUDA_ARCH  ?= sm_80
+
 ## Kernel implementation switch
 ##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
 ##   0           : fall back to original Fortran kernels
 USE_CXX_KERNELS ?= 1
 
+## Z4C Cartesian RHS kernel switch
+##   1 (default) : use C++ rewrite of Z4c_rhs (main Cartesian path faster)
+##   0           : use original Fortran Z4c_rhs.o
+USE_CXX_Z4C_KERNELS ?= 1
+
 ## RK4 kernel implementation switch
 ##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
 ##   0           : use original Fortran rungekutta4_rout.o
 USE_CXX_RK4 ?= 1
 
+## Memory allocator switch
+##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
+##   0           : use system default allocator (ptmalloc)
+USE_TBBMALLOC ?= 1
+TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
+ifneq ($(wildcard $(TBBMALLOC_SO)),)
+TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
+else
+TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
+endif
+
+ifeq ($(TOOLCHAIN),intel)
 f90          = ifx
 f77          = ifx
 CXX          = icpx
 CC           = icx
 CLINKER      = mpiicpx
+filein  = -I/usr/include/ $(MKL_INC) -I$(CUDA_HOME)/include
+LDLIBS       = -L$(MKL_LIBDIR) -Wl,-rpath,$(MKL_LIBDIR) \
+               -lmkl_intel_lp64 -lmkl_sequential -lmkl_core \
+               -lifcore -limf -liomp5 -lpthread -lm -ldl \
+               -L$(CUDA_HOME)/lib64 -Wl,-rpath,$(CUDA_HOME)/lib64 -lcuda -lcudart
+else ifeq ($(TOOLCHAIN),nvhpc)
+f90          = mpifort
+f77          = mpifort
+CXX          = mpicxx
+CC           = mpicc
+CLINKER      = mpicxx
 
-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
+filein       = -I/usr/include/ $(MKL_INC) -I$(CUDA_HOME)/include
+LDLIBS       = -L$(MKL_LIBDIR) -Wl,-rpath,$(MKL_LIBDIR) \
+               -lmkl_intel_lp64 -lmkl_sequential -lmkl_core \
+               -lpthread -lm -ldl \
+               -L$(CUDA_HOME)/lib64 -Wl,-rpath,$(CUDA_HOME)/lib64 -lcuda -lcudart \
+               -fortranlibs
+endif
+
+ifeq ($(USE_TBBMALLOC),1)
+LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
+endif
+
+Cu = $(NVHPC_ROOT)/compilers/bin/nvcc
+CUDA_LIB_PATH = -L$(CUDA_HOME)/lib64 -I$(CUDA_HOME)/include
+CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc -arch=$(CUDA_ARCH)

AMSS_NCKU_source/surface_integral.h

@@ -27,24 +27,29 @@ 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
+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();
 
-	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,
-				   monitor *Monitor); // NN is the length of RP and IP
-									  // this routine can only deal with the symmetry of Psi4
+	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); // NN is the length of RP and IP
+									  // this routine can only deal with the symmetry of Psi4
 	void surf_Wave(double rex, int lev, ShellPatch *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
 				   monitor *Monitor);
@@ -77,21 +82,37 @@ 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);
-	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,
+	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,
 				   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 				   var *chix, var *chiy, var *chiz,
 				   var *trKx, var *trKy, var *trKz,
@@ -110,12 +131,12 @@ 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);
+	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_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
 				   monitor *Monitor, MPI_Comm Comm_here);

AMSS_NCKU_source/z4c_rhs_c.C

@@ -0,0 +1,725 @@
+#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

@@ -0,0 +1,258 @@
+#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_pack_state_batch_to_host_buffer_for_host_views(void *block_tag,
+                                                            double **state_host_key,
+                                                            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_unpack_state_batch_from_host_buffer_for_host_views(void *block_tag,
+                                                                double **state_host_key,
+                                                                int state_count,
+                                                                double *host_buffer,
+                                                                int *ex,
+                                                                int i0, int j0, int k0,
+                                                                int sx, int sy, int sz);
+
+int z4c_cuda_pack_state_batch_to_device_buffer(void *block_tag,
+                                               int state_count,
+                                               double *device_buffer,
+                                               int *ex,
+                                               int i0, int j0, int k0,
+                                               int sx, int sy, int sz);
+
+int z4c_cuda_pack_state_batch_to_device_buffer_for_host_views(void *block_tag,
+                                                              double **state_host_key,
+                                                              int state_count,
+                                                              double *device_buffer,
+                                                              int *ex,
+                                                              int i0, int j0, int k0,
+                                                              int sx, int sy, int sz);
+
+int z4c_cuda_unpack_state_batch_from_device_buffer(void *block_tag,
+                                                   int state_count,
+                                                   double *device_buffer,
+                                                   int *ex,
+                                                   int i0, int j0, int k0,
+                                                   int sx, int sy, int sz);
+
+int z4c_cuda_unpack_state_batch_from_device_buffer_for_host_views(void *block_tag,
+                                                                  double **state_host_key,
+                                                                  int state_count,
+                                                                  double *device_buffer,
+                                                                  int *ex,
+                                                                  int i0, int j0, int k0,
+                                                                  int sx, int sy, int sz);
+
+int z4c_cuda_pack_state_segments_to_device_buffer(void *block_tag,
+                                                  int state_count,
+                                                  double *device_buffer,
+                                                  int *ex,
+                                                  int segment_count,
+                                                  const int *segment_meta);
+
+int z4c_cuda_pack_state_segments_to_device_buffer_for_host_views(void *block_tag,
+                                                                 double **state_host_key,
+                                                                 int state_count,
+                                                                 double *device_buffer,
+                                                                 int *ex,
+                                                                 int segment_count,
+                                                                 const int *segment_meta);
+
+int z4c_cuda_unpack_state_segments_from_device_buffer(void *block_tag,
+                                                      int state_count,
+                                                      double *device_buffer,
+                                                      int *ex,
+                                                      int segment_count,
+                                                      const int *segment_meta);
+
+int z4c_cuda_unpack_state_segments_from_device_buffer_for_host_views(void *block_tag,
+                                                                     double **state_host_key,
+                                                                     int state_count,
+                                                                     double *device_buffer,
+                                                                     int *ex,
+                                                                     int segment_count,
+                                                                     const int *segment_meta);
+
+int z4c_cuda_restrict_state_segments_to_device_buffer(void *block_tag,
+                                                      int state_count,
+                                                      double *device_buffer,
+                                                      int *ex,
+                                                      int segment_count,
+                                                      const int *segment_meta,
+                                                      const double *state_soa);
+
+int z4c_cuda_restrict_state_segments_to_device_buffer_for_host_views(void *block_tag,
+                                                                     double **state_host_key,
+                                                                     int state_count,
+                                                                     double *device_buffer,
+                                                                     int *ex,
+                                                                     int segment_count,
+                                                                     const int *segment_meta,
+                                                                     const double *state_soa);
+
+int z4c_cuda_prolong_state_segments_to_device_buffer(void *block_tag,
+                                                     int state_count,
+                                                     double *device_buffer,
+                                                     int *ex,
+                                                     int segment_count,
+                                                     const int *segment_meta,
+                                                     const double *state_soa);
+
+int z4c_cuda_prolong_state_segments_to_device_buffer_for_host_views(void *block_tag,
+                                                                    double **state_host_key,
+                                                                    int state_count,
+                                                                    double *device_buffer,
+                                                                    int *ex,
+                                                                    int segment_count,
+                                                                    const int *segment_meta,
+                                                                    const double *state_soa);
+
+int z4c_cuda_restrict_state_batch_to_device_buffer(void *block_tag,
+                                                   int state_count,
+                                                   double *device_buffer,
+                                                   int *ex,
+                                                   int sx, int sy, int sz,
+                                                   int fi0, int fj0, int fk0,
+                                                   const double *state_soa);
+
+int z4c_cuda_restrict_state_batch_to_device_buffer_for_host_views(void *block_tag,
+                                                                  double **state_host_key,
+                                                                  int state_count,
+                                                                  double *device_buffer,
+                                                                  int *ex,
+                                                                  int sx, int sy, int sz,
+                                                                  int fi0, int fj0, int fk0,
+                                                                  const double *state_soa);
+
+int z4c_cuda_prolong_state_batch_to_device_buffer(void *block_tag,
+                                                  int state_count,
+                                                  double *device_buffer,
+                                                  int *ex,
+                                                  int sx, int sy, int sz,
+                                                  int ii0, int jj0, int kk0,
+                                                  int lbc_i, int lbc_j, int lbc_k,
+                                                  const double *state_soa);
+
+int z4c_cuda_prolong_state_batch_to_device_buffer_for_host_views(void *block_tag,
+                                                                 double **state_host_key,
+                                                                 int state_count,
+                                                                 double *device_buffer,
+                                                                 int *ex,
+                                                                 int sx, int sy, int sz,
+                                                                 int ii0, int jj0, int kk0,
+                                                                 int lbc_i, int lbc_j, int lbc_k,
+                                                                 const double *state_soa);
+
+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_compute_constraints_resident(void *block_tag,
+                                          int *ex, double *X, double *Y, double *Z,
+                                          int Symmetry, double eps, int co,
+                                          double **constraint_host_out);
+
+int z4c_cuda_interp_state_point3(void *block_tag,
+                                 int *ex,
+                                 int state0,
+                                 int state1,
+                                 int state2,
+                                 double x0,
+                                 double y0,
+                                 double z0,
+                                 double dx,
+                                 double dy,
+                                 double dz,
+                                 double px,
+                                 double py,
+                                 double pz,
+                                 int ordn,
+                                 int symmetry,
+                                 const double *soa3,
+                                 double *out3);
+
+int z4c_cuda_download_constraint_outputs(int *ex,
+                                         double **constraint_host_out);
+
+int z4c_cuda_has_resident_state(void *block_tag);
+int z4c_cuda_resident_state_matches(void *block_tag,
+                                    double **state_host_key);
+
+void z4c_cuda_release_step_ctx(void *block_tag);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

generate_macrodef.py

@@ -144,11 +144,67 @@ 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 )
@@ -224,6 +280,21 @@ 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

@@ -9,6 +9,8 @@
 
 
 import AMSS_NCKU_Input as input_data
+import os
+import shutil
 import subprocess
 import time
 
@@ -56,6 +58,124 @@ BUILD_JOBS = 64
 
 ##################################################################
 
+def _truthy(value, default=False):
+    if value is None:
+        return default
+    if isinstance(value, bool):
+        return value
+    text = str(value).strip().lower()
+    if text == "":
+        return default
+    return text in ("1", "yes", "y", "true", "on", "enable", "enabled")
+
+
+def _input_or_env(input_name, env_name, default=None):
+    if env_name in os.environ:
+        return os.environ[env_name]
+    return getattr(input_data, input_name, default)
+
+
+def _start_cuda_mps_if_requested(runtime_env):
+    if input_data.GPU_Calculation != "yes":
+        return False
+
+    default_auto_mps = int(getattr(input_data, "MPI_processes", 1)) > 1
+    auto_mps = _truthy(
+        _input_or_env("CUDA_Auto_MPS", "AMSS_CUDA_AUTO_MPS", default_auto_mps),
+        default=default_auto_mps,
+    )
+    if not auto_mps:
+        return False
+
+    mps_control = shutil.which("nvidia-cuda-mps-control")
+    if not mps_control:
+        print(" CUDA MPS control command was not found; running without MPS.")
+        return False
+
+    uid = os.getuid()
+    pipe_dir = str(_input_or_env("CUDA_MPS_PIPE_DIRECTORY", "CUDA_MPS_PIPE_DIRECTORY",
+                                 f"/tmp/amss-ncku-mps-{uid}"))
+    log_dir = str(_input_or_env("CUDA_MPS_LOG_DIRECTORY", "CUDA_MPS_LOG_DIRECTORY",
+                                f"/tmp/amss-ncku-mps-log-{uid}"))
+    os.makedirs(pipe_dir, exist_ok=True)
+    os.makedirs(log_dir, exist_ok=True)
+
+    mps_env = runtime_env.copy()
+    mps_env["CUDA_MPS_PIPE_DIRECTORY"] = pipe_dir
+    mps_env["CUDA_MPS_LOG_DIRECTORY"] = log_dir
+
+    if os.path.exists(os.path.join(pipe_dir, "control")):
+        runtime_env.update({
+            "CUDA_MPS_PIPE_DIRECTORY": pipe_dir,
+            "CUDA_MPS_LOG_DIRECTORY": log_dir,
+        })
+        print(f" Reusing CUDA MPS daemon: {pipe_dir}")
+        return False
+
+    print(f" Starting CUDA MPS daemon for this run: {pipe_dir}")
+    result = subprocess.run([mps_control, "-d"], env=mps_env, text=True,
+                            stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
+    if result.returncode != 0:
+        print(" CUDA MPS daemon did not start; running without MPS.")
+        if result.stdout:
+            print(result.stdout, end="")
+        return False
+
+    runtime_env.update({
+        "CUDA_MPS_PIPE_DIRECTORY": pipe_dir,
+        "CUDA_MPS_LOG_DIRECTORY": log_dir,
+    })
+    return True
+
+
+def _stop_cuda_mps(runtime_env):
+    mps_control = shutil.which("nvidia-cuda-mps-control")
+    if not mps_control:
+        return
+    subprocess.run([mps_control], input="quit\n", env=runtime_env, text=True,
+                   stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
+
+
+def _gpu_runtime_env():
+    runtime_env = os.environ.copy()
+
+    defaults = {
+        "AMSS_INTERP_FAST": "1",
+        "AMSS_INTERP_GPU": "1",
+        "AMSS_ANALYSIS_MAP_EVERY": "1000000",
+        "AMSS_CUDA_AWARE_MPI": "1",
+        "AMSS_CUDA_KEEP_RESIDENT_AFTER_STEP": "1",
+        "AMSS_CUDA_Z4C_KEEP_RESIDENT_AFTER_STEP": "1",
+        "AMSS_CUDA_KEEP_ALL_LEVELS": "1",
+        "AMSS_CUDA_Z4C_AMR_DEVICE": "0",
+        "AMSS_CUDA_AMR_RESTRICT_DEVICE": "1",
+        "AMSS_CUDA_AMR_RESTRICT_BATCH": "0",
+        "AMSS_CUDA_DEVICE_SEGMENT_BATCH": "0",
+        "AMSS_CUDA_PIN_ESCALAR_TRANSFERS": "0",
+        "AMSS_ESCALAR_GPU_RK": "0",
+    }
+    if getattr(input_data, "Equation_Class", "") == "Z4C":
+        defaults["AMSS_CUDA_Z4C_KEEP_RESIDENT_AFTER_STEP"] = "0"
+        defaults["AMSS_CUDA_KEEP_ALL_LEVELS"] = "0"
+    for key, value in defaults.items():
+        runtime_env.setdefault(key, value)
+
+    optional_overrides = {
+        "AMSS_INTERP_FAST_COMPARE": "AMSS_Interp_Fast_Compare",
+        "AMSS_INTERP_FAST_COMPARE_LIMIT": "AMSS_Interp_Fast_Compare_Limit",
+        "AMSS_INTERP_FAST_COMPARE_TOL": "AMSS_Interp_Fast_Compare_Tol",
+        "AMSS_GPU_STAGE_TIMING": "AMSS_GPU_Stage_Timing",
+        "AMSS_GPU_STAGE_TIMING_EVERY": "AMSS_GPU_Stage_Timing_Every",
+    }
+    for env_name, input_name in optional_overrides.items():
+        if env_name not in runtime_env and hasattr(input_data, input_name):
+            runtime_env[env_name] = str(getattr(input_data, input_name))
+
+    return runtime_env
+
+
+##################################################################
+
 
 
 ##################################################################
@@ -70,9 +190,9 @@ 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 ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off USE_CUDA_BSSN=0 USE_CUDA_Z4C=0 ABE"
     elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off USE_CUDA_BSSN=1 USE_CUDA_Z4C=1 ABE_CUDA"
     else:
         print( " CPU/GPU numerical calculation setting is wrong " )
         print(                                                    )
@@ -145,29 +265,55 @@ def run_ABE():
     print(                                                      )
 
     ## Define the command to run; cast other values to strings as needed
+    mpi_env = None
+    started_mps = False
     
     if (input_data.GPU_Calculation == "no"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE_CUDA"
         mpi_command_outfile = "ABEGPU_out.log"
+        mpi_env = _gpu_runtime_env()
+        started_mps = _start_cuda_mps_if_requested(mpi_env)
+        print(" GPU optimized runtime switches:")
+        print(f"   AMSS_INTERP_FAST={mpi_env.get('AMSS_INTERP_FAST', '')}")
+        print(f"   AMSS_INTERP_GPU={mpi_env.get('AMSS_INTERP_GPU', '')}")
+        print(f"   AMSS_ANALYSIS_MAP_EVERY={mpi_env.get('AMSS_ANALYSIS_MAP_EVERY', '')}")
+        print(f"   AMSS_CUDA_AWARE_MPI={mpi_env.get('AMSS_CUDA_AWARE_MPI', '')}")
+        print(f"   AMSS_CUDA_KEEP_RESIDENT_AFTER_STEP={mpi_env.get('AMSS_CUDA_KEEP_RESIDENT_AFTER_STEP', '')}")
+        print(f"   AMSS_CUDA_Z4C_KEEP_RESIDENT_AFTER_STEP={mpi_env.get('AMSS_CUDA_Z4C_KEEP_RESIDENT_AFTER_STEP', '')}")
+        print(f"   AMSS_CUDA_KEEP_ALL_LEVELS={mpi_env.get('AMSS_CUDA_KEEP_ALL_LEVELS', '')}")
+        print(f"   AMSS_CUDA_Z4C_AMR_DEVICE={mpi_env.get('AMSS_CUDA_Z4C_AMR_DEVICE', '')}")
+        print(f"   AMSS_CUDA_AMR_RESTRICT_DEVICE={mpi_env.get('AMSS_CUDA_AMR_RESTRICT_DEVICE', '')}")
+        print(f"   AMSS_CUDA_AMR_RESTRICT_BATCH={mpi_env.get('AMSS_CUDA_AMR_RESTRICT_BATCH', '')}")
+        print(f"   AMSS_CUDA_DEVICE_SEGMENT_BATCH={mpi_env.get('AMSS_CUDA_DEVICE_SEGMENT_BATCH', '')}")
+        print(f"   AMSS_CUDA_PIN_ESCALAR_TRANSFERS={mpi_env.get('AMSS_CUDA_PIN_ESCALAR_TRANSFERS', '')}")
+        print(f"   AMSS_ESCALAR_GPU_RK={mpi_env.get('AMSS_ESCALAR_GPU_RK', '')}")
+        if "CUDA_MPS_PIPE_DIRECTORY" in mpi_env:
+            print(f"   CUDA_MPS_PIPE_DIRECTORY={mpi_env['CUDA_MPS_PIPE_DIRECTORY']}")
  
-    ## Execute the MPI command and stream output
-    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
+    try:
+        ## Execute the MPI command and stream output
+        mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE,
+                                       stderr=subprocess.STDOUT, text=True, env=mpi_env)
 
-    ## Write ABE run output to file while printing to stdout
-    with open(mpi_command_outfile, 'w') as file0:  
-        ## Read and print output lines; also write each line to file
-        for line in mpi_process.stdout:
-            print(line, end='')  # stream output in real time
-            file0.write(line)    # write the line to file
-            file0.flush()        # flush to ensure each line is written immediately (optional)            
-    file0.close()
+        ## Write ABE run output to file while printing to stdout
+        with open(mpi_command_outfile, 'w') as file0:
+            ## Read and print output lines; also write each line to file
+            for line in mpi_process.stdout:
+                print(line, end='')  # stream output in real time
+                file0.write(line)    # write the line to file
+                file0.flush()        # flush to ensure each line is written immediately (optional)
 
-    ## Wait for the process to finish
-    mpi_return_code = mpi_process.wait()
+        ## Wait for the process to finish
+        mpi_return_code = mpi_process.wait()
+        if mpi_return_code != 0:
+            raise subprocess.CalledProcessError(mpi_return_code, mpi_command)
+    finally:
+        if started_mps:
+            _stop_cuda_mps(mpi_env)
     
     print(                                           )
     print( " The ABE/ABEGPU simulation is finished " )