Cache GPU RHS symbols and zero vacuum sources once

.idea/vcs.xml

@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="VcsDirectoryMappings">
-    <mapping directory="" vcs="Git" />
-  </component>
-</project>

AMSS_NCKU_Program.py

@@ -126,6 +126,11 @@ setup.generate_AMSSNCKU_input()
 #inputvalue = input()  ## Wait for user input (press Enter) to proceed
 #print()
 
+setup.print_puncture_information()
+
+
+##################################################################
+
 ## Generate AMSS-NCKU program input files based on the configured parameters
 
 print(                                                                                   )
@@ -307,7 +312,7 @@ if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
     
     import generate_TwoPuncture_input
     
-    generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input(numerical_grid.puncture_data)
+    generate_TwoPuncture_input.generate_AMSSNCKU_TwoPuncture_input()
     
     print(                                                                                              )
     print( " The input parfile for the TwoPunctureABE executable has been generated. " )
@@ -349,7 +354,7 @@ if (input_data.Initial_Data_Method == "Ansorg-TwoPuncture" ):
 
 import renew_puncture_parameter
     
-renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory, numerical_grid.puncture_data)
+renew_puncture_parameter.append_AMSSNCKU_BSSN_input(File_directory, output_directory)
 
 
 ## Generated AMSS-NCKU input filename

AMSS_NCKU_Verify_ASC26.py

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

AMSS_NCKU_source/ABE.C

@@ -24,18 +24,16 @@ using namespace std;
 
 #include "misc.h"
 #include "macrodef.h"
+#ifdef USE_GPU
+extern void bssn_cuda_dump_stage_profile();
+#endif
 
 #ifndef ABEtype
 #error "not define ABEtype"
 #endif
 
 #if (ABEtype == 0)
-
-#ifdef USE_GPU
-#include "bssn_gpu_class.h"
-#else
 #include "bssn_class.h"
-#endif
 
 #elif (ABEtype == 1)
 #include "bssnEScalar_class.h"
@@ -474,10 +472,13 @@ int main(int argc, char *argv[])
             cout << endl;
       }
 
-      ADM->Evolve(Steps);
+	      ADM->Evolve(Steps);
+#ifdef USE_GPU
+	      bssn_cuda_dump_stage_profile();
+#endif
 	
-      if (myrank == 0)
+	      if (myrank == 0)
-      {
+	      {
             cout << endl;
             cout << " Total Evolve Time: "  << MPI_Wtime() - End_clock   << " seconds!" << endl;
             cout << " Total Running Time: " << MPI_Wtime() - Begin_clock << " seconds!" << endl;

AMSS_NCKU_source/Block.C

@@ -11,6 +11,10 @@ using namespace std;
 
 #include "Block.h"
 #include "misc.h"
+#ifdef USE_GPU
+#include "bssn_gpu.h"
+#include "bssn_cuda_ops.h"
+#endif
 
 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)
 {
@@ -101,6 +105,11 @@ Block::~Block()
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
   if (myrank == rank)
   {
+#ifdef USE_GPU
+    bssn_gpu_clear_cached_device_buffers();
+    bssn_cuda_release_rk4_caches();
+    bssn_cuda_release_interp_caches();
+#endif
     for (int i = 0; i < dim; i++)
       delete[] X[i];
     for (int i = 0; i < ingfs; i++)

AMSS_NCKU_source/MPatch.C

@@ -7,6 +7,7 @@
 #include <string>
 #include <cmath>
 #include <new>
+#include <map>
 #include <vector>
 using namespace std;
 
@@ -14,12 +15,82 @@ using namespace std;
 #include "MPatch.h"
 #include "Parallel.h"
 #include "fmisc.h"
+#include "bssn_cuda_ops.h"
 #ifdef INTERP_LB_PROFILE
 #include "interp_lb_profile.h"
 #endif
 
+#if defined(__GNUC__) || defined(__clang__)
+extern int bssn_cuda_interp_points_batch(const int *ex,
+                                         const double *X, const double *Y, const double *Z,
+                                         const double *const *fields,
+                                         const double *soa_flat,
+                                         int num_var,
+                                         const double *px, const double *py, const double *pz,
+                                         int num_points,
+                                         int ordn,
+                                         int symmetry,
+                                         double *out) __attribute__((weak));
+#endif
+
 namespace
 {
+struct InterpVarDesc
+{
+  int sgfn;
+  double soa[dim];
+};
+
+struct InterpPlanKey
+{
+  const Patch *patch;
+  const double *x;
+  const double *y;
+  const double *z;
+  int NN;
+  int Symmetry;
+  int myrank;
+};
+
+struct InterpPlanKeyLess
+{
+  bool operator()(const InterpPlanKey &lhs, const InterpPlanKey &rhs) const
+  {
+    if (lhs.patch != rhs.patch) return lhs.patch < rhs.patch;
+    if (lhs.x != rhs.x) return lhs.x < rhs.x;
+    if (lhs.y != rhs.y) return lhs.y < rhs.y;
+    if (lhs.z != rhs.z) return lhs.z < rhs.z;
+    if (lhs.NN != rhs.NN) return lhs.NN < rhs.NN;
+    if (lhs.Symmetry != rhs.Symmetry) return lhs.Symmetry < rhs.Symmetry;
+    return lhs.myrank < rhs.myrank;
+  }
+};
+
+struct CachedInterpPlan
+{
+  int nblocks;
+  vector<int> owner_rank;
+  vector<int> owner_block;
+  vector<vector<int> > block_points;
+  vector<vector<double> > block_px;
+  vector<vector<double> > block_py;
+  vector<vector<double> > block_pz;
+
+  CachedInterpPlan() : nblocks(0) {}
+};
+
+struct CachedInterpPlanEntry
+{
+  bool valid;
+  InterpPlanKey key;
+  vector<double> xvals;
+  vector<double> yvals;
+  vector<double> zvals;
+  CachedInterpPlan plan;
+
+  CachedInterpPlanEntry() : valid(false) {}
+};
+
 struct InterpBlockView
 {
   Block *bp;
@@ -178,8 +249,309 @@ int find_block_index_for_point(const BlockBinIndex &index, const double *pox, co
 
   return -1;
 }
+
+void collect_interp_vars(MyList<var> *VarList, vector<InterpVarDesc> &vars)
+{
+  vars.clear();
+  MyList<var> *varl = VarList;
+  while (varl)
+  {
+    InterpVarDesc desc;
+    desc.sgfn = varl->data->sgfn;
+    for (int d = 0; d < dim; ++d)
+      desc.soa[d] = varl->data->SoA[d];
+    vars.push_back(desc);
+    varl = varl->next;
+  }
+}
+
+bool should_try_cuda_interp(int ordn, int num_points, int num_var)
+{
+#if defined(__GNUC__) || defined(__clang__)
+  if (!bssn_cuda_interp_points_batch)
+    return false;
+#else
+  return false;
+#endif
+  if (ordn != 6)
+    return false;
+  if (num_points < 32)
+    return false;
+  return num_points * num_var >= 256;
+}
+
+CachedInterpPlanEntry &interp_plan_cache_entry()
+{
+  static CachedInterpPlanEntry cache;
+  return cache;
+}
+
+bool same_interp_plan_key(const InterpPlanKey &lhs, const InterpPlanKey &rhs)
+{
+  return lhs.patch == rhs.patch &&
+         lhs.NN == rhs.NN &&
+         lhs.Symmetry == rhs.Symmetry &&
+         lhs.myrank == rhs.myrank;
+}
+
+bool same_interp_plan_points(const CachedInterpPlanEntry &cache, int NN, double **XX)
+{
+  if (static_cast<int>(cache.xvals.size()) != NN ||
+      static_cast<int>(cache.yvals.size()) != NN ||
+      static_cast<int>(cache.zvals.size()) != NN)
+    return false;
+
+  for (int j = 0; j < NN; ++j)
+  {
+    if (cache.xvals[j] != XX[0][j] ||
+        cache.yvals[j] != XX[1][j] ||
+        cache.zvals[j] != XX[2][j])
+      return false;
+  }
+  return true;
+}
+
+CachedInterpPlan &get_cached_interp_plan(Patch *patch,
+                                         int NN, double **XX,
+                                         int Symmetry, int myrank,
+                                         const double *DH,
+                                         const BlockBinIndex &block_index,
+                                         bool report_bounds_here,
+                                         bool allow_missing_points)
+{
+  InterpPlanKey key;
+  key.patch = patch;
+  key.x = XX[0];
+  key.y = XX[1];
+  key.z = XX[2];
+  key.NN = NN;
+  key.Symmetry = Symmetry;
+  key.myrank = myrank;
+
+  CachedInterpPlanEntry &cache = interp_plan_cache_entry();
+  if (cache.valid &&
+      same_interp_plan_key(cache.key, key) &&
+      same_interp_plan_points(cache, NN, XX) &&
+      cache.plan.nblocks == static_cast<int>(block_index.views.size()))
+    return cache.plan;
+
+  cache.valid = true;
+  cache.key = key;
+  cache.xvals.assign(XX[0], XX[0] + NN);
+  cache.yvals.assign(XX[1], XX[1] + NN);
+  cache.zvals.assign(XX[2], XX[2] + NN);
+  cache.plan = CachedInterpPlan();
+  CachedInterpPlan &plan = cache.plan;
+  plan.nblocks = static_cast<int>(block_index.views.size());
+  plan.owner_rank.assign(NN, -1);
+  plan.owner_block.assign(NN, -1);
+  plan.block_points.resize(plan.nblocks);
+  plan.block_px.resize(plan.nblocks);
+  plan.block_py.resize(plan.nblocks);
+  plan.block_pz.resize(plan.nblocks);
+
+  for (int j = 0; j < NN; ++j)
+  {
+    double pox[dim];
+    for (int i = 0; i < dim; ++i)
+    {
+      pox[i] = XX[i][j];
+      if (report_bounds_here &&
+          (XX[i][j] < patch->bbox[i] + patch->lli[i] * DH[i] ||
+           XX[i][j] > patch->bbox[dim + i] - patch->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);
+      }
+    }
+
+    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;
+      plan.owner_rank[j] = BP->rank;
+      plan.owner_block[j] = block_i;
+      if (BP->rank == myrank)
+      {
+        plan.block_points[block_i].push_back(j);
+        plan.block_px[block_i].push_back(XX[0][j]);
+        plan.block_py[block_i].push_back(XX[1][j]);
+        plan.block_pz[block_i].push_back(XX[2][j]);
+      }
+    }
+  }
+
+  if (!allow_missing_points && report_bounds_here)
+  {
+    for (int j = 0; j < NN; ++j)
+    {
+      if (plan.owner_rank[j] >= 0)
+        continue;
+      cout << "ERROR: Patch::Interp_Points fails to find point (";
+      for (int d = 0; d < dim; ++d)
+      {
+        cout << XX[d][j];
+        if (d < dim - 1)
+          cout << ",";
+        else
+          cout << ")";
+      }
+      cout << " on Patch (";
+      for (int d = 0; d < dim; ++d)
+      {
+        cout << patch->bbox[d] << "+" << patch->lli[d] * DH[d];
+        if (d < dim - 1)
+          cout << ",";
+        else
+          cout << ")--";
+      }
+      cout << "(";
+      for (int d = 0; d < dim; ++d)
+      {
+        cout << patch->bbox[dim + d] << "-" << patch->uui[d] * DH[d];
+        if (d < dim - 1)
+          cout << ",";
+        else
+          cout << ")" << endl;
+      }
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
+
+  return plan;
+}
+
+void release_interp_plan_cache_internal()
+{
+  CachedInterpPlanEntry &cache = interp_plan_cache_entry();
+  cache.valid = false;
+  cache.xvals.clear();
+  cache.yvals.clear();
+  cache.zvals.clear();
+  cache.plan = CachedInterpPlan();
+}
+
+bool run_cuda_interp_for_block(Block *BP,
+                               const vector<InterpVarDesc> &vars,
+                               const vector<int> &point_ids,
+                               const vector<double> &px,
+                               const vector<double> &py,
+                               const vector<double> &pz,
+                               double *Shellf,
+                               int num_var,
+                               int ordn,
+                               int Symmetry)
+{
+  if (!should_try_cuda_interp(ordn, static_cast<int>(point_ids.size()), num_var))
+    return false;
+
+  vector<const double *> field_ptrs(num_var);
+  vector<double> soa_flat(3 * num_var);
+  for (int v = 0; v < num_var; ++v)
+  {
+    field_ptrs[v] = BP->fgfs[vars[v].sgfn];
+    for (int d = 0; d < dim; ++d)
+      soa_flat[3 * v + d] = vars[v].soa[d];
+  }
+
+  const int npts = static_cast<int>(point_ids.size());
+  vector<double> out(static_cast<size_t>(npts) * static_cast<size_t>(num_var));
+  if (bssn_cuda_interp_points_batch(BP->shape,
+                                    BP->X[0], BP->X[1], BP->X[2],
+                                    field_ptrs.data(),
+                                    soa_flat.data(),
+                                    num_var,
+                                    px.data(), py.data(), pz.data(),
+                                    npts,
+                                    ordn,
+                                    Symmetry,
+                                    out.data()) != 0)
+  {
+    return false;
+  }
+
+  for (int p = 0; p < npts; ++p)
+  {
+    const int j = point_ids[p];
+    memcpy(Shellf + j * num_var, out.data() + p * num_var, sizeof(double) * num_var);
+  }
+  return true;
+}
+
+void run_cpu_interp_for_block(Block *BP,
+                              const vector<InterpVarDesc> &vars,
+                              const vector<int> &point_ids,
+                              const vector<double> &px,
+                              const vector<double> &py,
+                              const vector<double> &pz,
+                              double *Shellf,
+                              int num_var,
+                              int ordn,
+                              int Symmetry)
+{
+  for (size_t p = 0; p < point_ids.size(); ++p)
+  {
+    const int j = point_ids[p];
+    double x = px[p];
+    double y = py[p];
+    double z = pz[p];
+    int ordn_local = ordn;
+    int symmetry_local = Symmetry;
+    for (int v = 0; v < num_var; ++v)
+    {
+      f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2],
+                      BP->fgfs[vars[v].sgfn], Shellf[j * num_var + v],
+                      x, y, z, ordn_local, const_cast<double *>(vars[v].soa), symmetry_local);
+    }
+  }
+}
+
+void interpolate_owned_points(MyList<var> *VarList,
+                              double *Shellf, int Symmetry,
+                              int ordn,
+                              const BlockBinIndex &block_index,
+                              const CachedInterpPlan &plan)
+{
+  vector<InterpVarDesc> vars;
+  collect_interp_vars(VarList, vars);
+  const int num_var = static_cast<int>(vars.size());
+
+  for (size_t bi = 0; bi < plan.block_points.size(); ++bi)
+  {
+    if (plan.block_points[bi].empty())
+      continue;
+
+    Block *BP = block_index.views[bi].bp;
+    bool done = run_cuda_interp_for_block(BP, vars,
+                                          plan.block_points[bi],
+                                          plan.block_px[bi],
+                                          plan.block_py[bi],
+                                          plan.block_pz[bi],
+                                          Shellf, num_var, ordn, Symmetry);
+    if (!done)
+      run_cpu_interp_for_block(BP, vars,
+                               plan.block_points[bi],
+                               plan.block_px[bi],
+                               plan.block_py[bi],
+                               plan.block_pz[bi],
+                               Shellf, num_var, ordn, Symmetry);
+  }
+}
 } // namespace
 
+void patch_release_interp_plan_cache()
+{
+  release_interp_plan_cache_internal();
+}
+
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
 
@@ -523,60 +895,15 @@ void Patch::Interp_Points(MyList<var> *VarList,
 
   memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // owner_rank[j] records which MPI rank owns point j
-  // All ranks traverse the same block list so they all agree on ownership
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
-
   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);
+  CachedInterpPlan &plan = get_cached_interp_plan(this, NN, XX, Symmetry, myrank, DH, block_index, myrank == 0, false);
+  const int *owner_rank = plan.owner_rank.data();
 
-  for (int j = 0; j < NN; j++) // run along points
+  interpolate_owned_points(VarList, Shellf, Symmetry, ordn, block_index, plan);
-  {
-    double pox[dim];
-    for (int i = 0; i < dim; i++)
-    {
-      pox[i] = XX[i][j];
-      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);
-      }
-    }
-
-    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)
-      {
-        //---> 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++;
-        }
-      }
-    }
-  }
 
   // Replace MPI_Allreduce with per-owner MPI_Bcast:
   // Group consecutive points by owner rank and broadcast each group.
@@ -632,7 +959,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  delete[] owner_rank;
 }
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
@@ -661,101 +987,21 @@ void Patch::Interp_Points(MyList<var> *VarList,
 
   memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // 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;
-
   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);
+  CachedInterpPlan &plan = get_cached_interp_plan(this, NN, XX, Symmetry, myrank, DH, block_index, myrank == 0, false);
+  const int *owner_rank = plan.owner_rank.data();
 
-  // --- Interpolation phase (identical to original) ---
+  interpolate_owned_points(VarList, Shellf, Symmetry, ordn, block_index, plan);
-  for (int j = 0; j < NN; j++)
-  {
-    double pox[dim];
-    for (int i = 0; i < dim; i++)
-    {
-      pox[i] = XX[i][j];
-      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);
-      }
-    }
-
-    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++;
-        }
-      }
-    }
-  }
 
 #ifdef INTERP_LB_PROFILE
   double t_interp_end = MPI_Wtime();
   double t_interp_local = t_interp_end - t_interp_start;
 #endif
 
-  // --- Error check for unfound points ---
-  for (int j = 0; j < NN; j++)
-  {
-    if (owner_rank[j] < 0 && myrank == 0)
-    {
-      cout << "ERROR: Patch::Interp_Points fails to find point (";
-      for (int d = 0; d < dim; d++)
-      {
-        cout << XX[d][j];
-        if (d < dim - 1)
-          cout << ",";
-        else
-          cout << ")";
-      }
-      cout << " on Patch (";
-      for (int d = 0; d < dim; d++)
-      {
-        cout << bbox[d] << "+" << lli[d] * DH[d];
-        if (d < dim - 1)
-          cout << ",";
-        else
-          cout << ")--";
-      }
-      cout << "(";
-      for (int d = 0; d < dim; d++)
-      {
-        cout << bbox[dim + d] << "-" << uui[d] * DH[d];
-        if (d < dim - 1)
-          cout << ",";
-        else
-          cout << ")" << endl;
-      }
-      MPI_Abort(MPI_COMM_WORLD, 1);
-    }
-  }
-
   // --- Targeted point-to-point communication phase ---
   // Compute consumer_rank[j] using the same deterministic formula as surface_integral
   int *consumer_rank = new int[NN];
@@ -875,7 +1121,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
   delete[] send_count;
   delete[] recv_count;
   delete[] consumer_rank;
-  delete[] owner_rank;
 
 #ifdef INTERP_LB_PROFILE
   {
@@ -923,12 +1168,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
 
   memset(Shellf, 0, sizeof(double) * NN * num_var);
 
-  // owner_rank[j] stores the global rank that owns point j
-  int *owner_rank;
-  owner_rank = new int[NN];
-  for (int j = 0; j < NN; j++)
-    owner_rank[j] = -1;
-
   // Build global-to-local rank translation for Comm_here
   MPI_Group world_group, local_group;
   MPI_Comm_group(MPI_COMM_WORLD, &world_group);
@@ -939,48 +1178,10 @@ void Patch::Interp_Points(MyList<var> *VarList,
     DH[i] = getdX(i);
   BlockBinIndex block_index;
   build_block_bin_index(this, DH, block_index);
+  CachedInterpPlan &plan = get_cached_interp_plan(this, NN, XX, Symmetry, myrank, DH, block_index, lmyrank == 0, true);
+  const int *owner_rank = plan.owner_rank.data();
 
-  for (int j = 0; j < NN; j++) // run along points
+  interpolate_owned_points(VarList, Shellf, Symmetry, ordn, block_index, plan);
-  {
-    double pox[dim];
-    for (int i = 0; i < dim; i++)
-    {
-      pox[i] = XX[i][j];
-      if (lmyrank == 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);
-      }
-    }
-
-    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)
-      {
-        //---> 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++;
-        }
-      }
-    }
-  }
 
   // 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
@@ -1010,7 +1211,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
 
   MPI_Group_free(&world_group);
   MPI_Group_free(&local_group);
-  delete[] owner_rank;
 }
 void Patch::checkBlock()
 {

AMSS_NCKU_source/MPatch.h

@@ -52,4 +52,6 @@ public:
                      double *Shellf, MPI_Comm Comm_here);
 };
 
+void patch_release_interp_plan_cache();
+
 #endif /* PATCH_H */

AMSS_NCKU_source/Parallel.h

@@ -90,8 +90,11 @@ namespace Parallel
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /*target */,
                    int Symmetry);
   void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry);
+  void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry, const char *context);
   void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, const char *context);
   void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, const char *context);
 
   struct SyncCache {
     bool valid;
@@ -108,6 +111,7 @@ namespace Parallel
     MPI_Status *stats;
     int max_reqs;
     bool lengths_valid;
+    int lengths_var_count;
     int *tc_req_node;
     int *tc_req_is_recv;
     int *tc_completed;
@@ -124,16 +128,17 @@ namespace Parallel
   struct AsyncSyncState {
     int req_no;
     bool active;
+    int mpi_tag;
     int *req_node;
     int *req_is_recv;
     int pending_recv;
-    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
+    AsyncSyncState() : req_no(0), active(false), mpi_tag(0), req_node(0), req_is_recv(0), pending_recv(0) {}
   };
 
   void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
                   SyncCache &cache, AsyncSyncState &state);
   void Sync_finish(SyncCache &cache, AsyncSyncState &state,
-                   MyList<var> *VarList, int Symmetry);
+                   MyList<var> *VarList, int Symmetry, bool unpack_to_host = true);
   void OutBdLow2Hi(Patch *Patc, Patch *Patf,
                    MyList<var> *VarList1 /* source */, MyList<var> *VarList2 /* target */,
                    int Symmetry);
@@ -183,7 +188,6 @@ namespace Parallel
                          MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
   void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
   double L2Norm(Patch *Pat, var *vf);
-  void L2Norm7(Patch *Pat, var **vf, double *norms);
   void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
   void checkvarl(MyList<var> *pp, bool first_only);
   MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
@@ -219,7 +223,6 @@ namespace Parallel
   void checkpatchlist(MyList<Patch> *PatL, bool buflog);
 
   double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
   bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
                              int NN, double **XX,
                              double *Shellf, int Symmetry, MPI_Comm Comm_here);

AMSS_NCKU_source/ShellPatch.C

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

AMSS_NCKU_source/ShellPatch.h

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

AMSS_NCKU_source/bssn_class.h

@@ -48,7 +48,6 @@ public:
        double StartTime, TotalTime;
        double AnasTime, DumpTime, d2DumpTime, CheckTime;
        double LastAnas, LastConsOut;
-       int *ConstraintRefreshLevels;
        double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
@@ -133,9 +132,10 @@ public:
        Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
        Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
        Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong
+       Parallel::SyncCache *sync_cache_psi4;       // cached Psi4 sync on PatL[lev]
 
        monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
-       monitor *ConVMonitor, *TimingMonitor;
+       monitor *ConVMonitor;
        surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
@@ -177,8 +177,12 @@ public:
        virtual void Initialize();
        virtual void Read_Ansorg();
        virtual void Read_Pablo() {};
+       void InvalidateSyncCaches();
        virtual void Compute_Psi4(int lev);
        virtual void Step(int lev, int YN);
+#ifdef USE_GPU
+       void Step_MainPath_GPU(int lev, int YN);
+#endif
        virtual void Interp_Constraint(bool infg);
        virtual void Constraint_Out();
        virtual void Compute_Constraint();

AMSS_NCKU_source/bssn_cuda_ops.h

@@ -0,0 +1,68 @@
+#ifndef BSSN_CUDA_OPS_H
+#define BSSN_CUDA_OPS_H
+
+int bssn_cuda_enforce_ga(int *ex,
+                         double *dxx, double *gxy, double *gxz,
+                         double *dyy, double *gyz, double *dzz,
+                         double *Axx, double *Axy, double *Axz,
+                         double *Ayy, double *Ayz, double *Azz);
+
+int bssn_cuda_rk4_boundary_var(int *ex, double dT,
+                               const double *X, const double *Y, const double *Z,
+                               double xmin, double ymin, double zmin,
+                               double xmax, double ymax, double zmax,
+                               const double *state0,
+                               const double *phi_field,
+                               const double *lap_field,
+                               const double *boundary_src,
+                               double *stage_data,
+                               double *rhs_accum,
+                               double propspeed,
+                               const double SoA[3],
+                               int symmetry,
+                               int lev,
+                               int rk_stage,
+                               bool force_host_boundary_fix,
+                               bool download_to_host = true);
+
+int bssn_cuda_rk4_boundary_batch(int *ex, double dT,
+                                 const double *X, const double *Y, const double *Z,
+                                 double xmin, double ymin, double zmin,
+                                 double xmax, double ymax, double zmax,
+                                 int symmetry,
+                                 const double *const *state0_list,
+                                 double *const *stage_data_list,
+                                 double *const *rhs_accum_list,
+                                 int num_var,
+                                 int rk_stage,
+                                 bool download_to_host = false);
+
+int bssn_cuda_lowerbound(int *ex, double *chi, double tinny, bool download_to_host = true);
+int bssn_cuda_download_buffer(int *ex, double *host_ptr);
+void bssn_cuda_release_rk4_caches();
+void bssn_cuda_release_interp_caches();
+
+int bssn_cuda_prolong3_pack(int wei,
+                            const double *llbc, const double *uubc, const int *extc, const double *func,
+                            const double *llbf, const double *uubf, const int *extf, double *funf,
+                            const double *llbp, const double *uubp,
+                            const double *SoA, int symmetry);
+
+int bssn_cuda_restrict3_pack(int wei,
+                             const double *llbc, const double *uubc, const int *extc, double *func,
+                             const double *llbf, const double *uubf, const int *extf, const double *funf,
+                             const double *llbr, const double *uubr,
+                             const double *SoA, int symmetry);
+
+int bssn_cuda_interp_points_batch(const int *ex,
+                                  const double *X, const double *Y, const double *Z,
+                                  const double *const *fields,
+                                  const double *soa_flat,
+                                  int num_var,
+                                  const double *px, const double *py, const double *pz,
+                                  int num_points,
+                                  int ordn,
+                                  int symmetry,
+                                  double *out);
+
+#endif

AMSS_NCKU_source/bssn_cuda_step.C

@@ -0,0 +1,936 @@
+#include "macrodef.h"
+
+#ifdef USE_GPU
+
+#include <algorithm>
+#include <cmath>
+#include <cstring>
+#include <cstdlib>
+#include <iomanip>
+#include <vector>
+
+#include "bssn_class.h"
+#include "bssn_cuda_ops.h"
+#include "bssn_gpu.h"
+#include "bssn_macro.h"
+
+namespace
+{
+enum StageProfileMetric
+{
+  STAGE_PROFILE_TOTAL = 0,
+  STAGE_PROFILE_RHS,
+  STAGE_PROFILE_RUN_STAGE,
+  STAGE_PROFILE_RUN_STAGE_DEVICE,
+  STAGE_PROFILE_RUN_STAGE_HOST_FIX,
+  STAGE_PROFILE_LOWERBOUND,
+  STAGE_PROFILE_ENSURE,
+  STAGE_PROFILE_DOWNLOAD,
+  STAGE_PROFILE_CLEAR_CACHE,
+  STAGE_PROFILE_SYNC_START,
+  STAGE_PROFILE_SYNC_FINISH,
+  STAGE_PROFILE_REFRESH,
+  STAGE_PROFILE_COUNT
+};
+
+static const int kStageProfileMaxLevels = 32;
+
+struct StageProfileStore
+{
+  bool env_checked;
+  bool enabled;
+  int calls[kStageProfileMaxLevels];
+  double metric[kStageProfileMaxLevels][STAGE_PROFILE_COUNT];
+};
+
+StageProfileStore &stage_profile_store()
+{
+  static StageProfileStore store = {};
+  return store;
+}
+
+bool stage_profile_enabled()
+{
+  StageProfileStore &store = stage_profile_store();
+  if (!store.env_checked)
+  {
+    const char *env = getenv("AMSS_GPU_STAGE_TIMING");
+    store.enabled = (env && env[0] && strcmp(env, "0") != 0);
+    store.env_checked = true;
+  }
+  return store.enabled;
+}
+
+void stage_profile_note_call(int lev)
+{
+  if (lev >= 0 && lev < kStageProfileMaxLevels)
+    stage_profile_store().calls[lev]++;
+}
+
+void stage_profile_add(int lev, StageProfileMetric metric, double seconds)
+{
+  if (lev >= 0 && lev < kStageProfileMaxLevels)
+    stage_profile_store().metric[lev][metric] += seconds;
+}
+
+const char *stage_profile_metric_name(StageProfileMetric metric)
+{
+  switch (metric)
+  {
+  case STAGE_PROFILE_TOTAL:
+    return "total";
+  case STAGE_PROFILE_RHS:
+    return "rhs";
+  case STAGE_PROFILE_RUN_STAGE:
+    return "run_stage";
+  case STAGE_PROFILE_RUN_STAGE_DEVICE:
+    return "run_stage_dev";
+  case STAGE_PROFILE_RUN_STAGE_HOST_FIX:
+    return "run_stage_host";
+  case STAGE_PROFILE_LOWERBOUND:
+    return "lower";
+  case STAGE_PROFILE_ENSURE:
+    return "ensure";
+  case STAGE_PROFILE_DOWNLOAD:
+    return "download";
+  case STAGE_PROFILE_CLEAR_CACHE:
+    return "clear_cache";
+  case STAGE_PROFILE_SYNC_START:
+    return "sync_start";
+  case STAGE_PROFILE_SYNC_FINISH:
+    return "sync_finish";
+  case STAGE_PROFILE_REFRESH:
+    return "refresh";
+  default:
+    return "unknown";
+  }
+}
+} // namespace
+
+void bssn_cuda_dump_stage_profile()
+{
+  if (!stage_profile_enabled())
+    return;
+
+  int myrank = 0;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+
+  StageProfileStore &store = stage_profile_store();
+  int global_calls_sum[kStageProfileMaxLevels] = {};
+  double global_metric_sum[kStageProfileMaxLevels][STAGE_PROFILE_COUNT] = {};
+  double global_metric_max[kStageProfileMaxLevels][STAGE_PROFILE_COUNT] = {};
+
+  MPI_Reduce(store.calls, global_calls_sum, kStageProfileMaxLevels, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);
+  MPI_Reduce(store.metric[0], global_metric_sum[0],
+             kStageProfileMaxLevels * STAGE_PROFILE_COUNT,
+             MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
+  MPI_Reduce(store.metric[0], global_metric_max[0],
+             kStageProfileMaxLevels * STAGE_PROFILE_COUNT,
+             MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
+
+  if (myrank != 0)
+    return;
+
+  cout << endl;
+  cout << " GPU stage timing summary (sum/max over MPI ranks) " << endl;
+  cout << " lev  calls";
+  for (int metric = 0; metric < STAGE_PROFILE_COUNT; ++metric)
+    cout << "  " << setw(22) << stage_profile_metric_name(static_cast<StageProfileMetric>(metric));
+  cout << endl;
+
+  for (int lev = 0; lev < kStageProfileMaxLevels; ++lev)
+  {
+    if (global_calls_sum[lev] == 0)
+      continue;
+
+    cout << setw(4) << lev << "  " << setw(5) << global_calls_sum[lev];
+    for (int metric = 0; metric < STAGE_PROFILE_COUNT; ++metric)
+    {
+      cout << "  "
+           << setw(10) << setprecision(6) << fixed << global_metric_sum[lev][metric]
+           << "/"
+           << setw(10) << setprecision(6) << fixed << global_metric_max[lev][metric];
+    }
+    cout << endl;
+  }
+  cout << endl;
+}
+
+void bssn_class::Step_MainPath_GPU(int lev, int YN)
+{
+#ifdef WithShell
+#error "Step_MainPath_GPU currently supports Patch grids only."
+#endif
+
+  const bool profile_enabled = stage_profile_enabled();
+  const double step_total_begin = profile_enabled ? MPI_Wtime() : 0.0;
+  if (profile_enabled)
+    stage_profile_note_call(lev);
+
+  if (bssn_gpu_bind_process_device(myrank))
+  {
+    cerr << "GPU device bind failure on MPI rank " << myrank << endl;
+    MPI_Abort(MPI_COMM_WORLD, 1);
+  }
+  if (profile_enabled)
+  {
+    const double t0 = MPI_Wtime();
+    bssn_gpu_clear_cached_device_buffers();
+    stage_profile_add(lev, STAGE_PROFILE_CLEAR_CACHE, MPI_Wtime() - t0);
+  }
+  else
+    bssn_gpu_clear_cached_device_buffers();
+
+  setpbh(BH_num, Porg0, Mass, BH_num_input);
+
+  const double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
+
+#if (MAPBH == 1)
+  if (BH_num > 0 && lev == GH->levels - 1)
+  {
+    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
+    for (int ithBH = 0; ithBH < BH_num; ithBH++)
+    {
+      for (int ith = 0; ith < 3; ith++)
+        Porg1[ithBH][ith] = Porg0[ithBH][ith] + Porg_rhs[ithBH][ith] * dT_lev;
+      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 (lev == a_lev)
+    AnalysisStuff(lev, dT_lev);
+#endif
+
+#ifdef With_AHF
+  AH_Step_Find(lev, dT_lev);
+#endif
+
+  const bool BB = fgt(PhysTime, StartTime, dT_lev / 2);
+  (void)BB;
+  double ndeps = (lev < GH->movls) ? numepsb : numepss;
+  double TRK4 = PhysTime;
+  int iter_count = 0;
+  int pre = 0, cor = 1;
+  int ERROR = 0;
+  const bool keep_stage_sync_on_device = (RPS == 1) && (MAPBH == 1) && (REGLEV == 0);
+
+  auto run_stage_on_block =
+      [&](Block *cg, Patch *patch, MyList<var> *state0_list,
+          MyList<var> *boundary_src_list, MyList<var> *stage_data_list,
+          MyList<var> *rhs_list, int rk_stage) {
+        MyList<var> *varl0 = state0_list;
+        MyList<var> *varlb = boundary_src_list;
+        MyList<var> *varls = stage_data_list;
+        MyList<var> *varlr = rhs_list;
+        std::vector<const double *> batch_state0;
+        std::vector<double *> batch_stage;
+        std::vector<double *> batch_rhs;
+
+        while (varl0)
+        {
+          const bool force_host_boundary_fix = false;
+          const bool can_batch_device_path = (lev > 0) && !force_host_boundary_fix;
+          if (can_batch_device_path)
+          {
+            batch_state0.push_back(cg->fgfs[varl0->data->sgfn]);
+            batch_stage.push_back(cg->fgfs[varls->data->sgfn]);
+            batch_rhs.push_back(cg->fgfs[varlr->data->sgfn]);
+            varl0 = varl0->next;
+            varlb = varlb->next;
+            varls = varls->next;
+            varlr = varlr->next;
+            continue;
+          }
+
+          const double var_begin = profile_enabled ? MPI_Wtime() : 0.0;
+          if (bssn_cuda_rk4_boundary_var(cg->shape, dT_lev,
+                                         cg->X[0], cg->X[1], cg->X[2],
+                                         patch->bbox[0], patch->bbox[1], patch->bbox[2],
+                                         patch->bbox[3], patch->bbox[4], patch->bbox[5],
+                                         cg->fgfs[varl0->data->sgfn],
+                                         cg->fgfs[phi0->sgfn],
+                                         cg->fgfs[Lap0->sgfn],
+                                         cg->fgfs[varlb->data->sgfn],
+                                         cg->fgfs[varls->data->sgfn],
+                                         cg->fgfs[varlr->data->sgfn],
+                                         varl0->data->propspeed,
+                                         varl0->data->SoA,
+                                         Symmetry, lev, rk_stage,
+                                         force_host_boundary_fix, false))
+          {
+            cerr << "GPU rk4/boundary failure: lev=" << lev
+                 << " rk_stage=" << rk_stage
+                 << " var=" << varl0->data->name
+                 << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+            ERROR = 1;
+            break;
+          }
+          if (profile_enabled)
+          {
+            stage_profile_add(lev,
+                              force_host_boundary_fix ? STAGE_PROFILE_RUN_STAGE_HOST_FIX
+                                                      : STAGE_PROFILE_RUN_STAGE_DEVICE,
+                              MPI_Wtime() - var_begin);
+          }
+          varl0 = varl0->next;
+          varlb = varlb->next;
+          varls = varls->next;
+          varlr = varlr->next;
+        }
+
+        if (!ERROR && !batch_state0.empty())
+        {
+          const double batch_begin = profile_enabled ? MPI_Wtime() : 0.0;
+          if (bssn_cuda_rk4_boundary_batch(cg->shape, dT_lev,
+                                           cg->X[0], cg->X[1], cg->X[2],
+                                           patch->bbox[0], patch->bbox[1], patch->bbox[2],
+                                           patch->bbox[3], patch->bbox[4], patch->bbox[5],
+                                           Symmetry,
+                                           &batch_state0[0],
+                                           &batch_stage[0],
+                                           &batch_rhs[0],
+                                           static_cast<int>(batch_state0.size()),
+                                           rk_stage, false))
+          {
+            cerr << "GPU rk4/boundary batch failure: lev=" << lev
+                 << " rk_stage=" << rk_stage
+                 << " vars=" << batch_state0.size()
+                 << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+            ERROR = 1;
+          }
+          else if (profile_enabled)
+          {
+            stage_profile_add(lev, STAGE_PROFILE_RUN_STAGE_DEVICE, MPI_Wtime() - batch_begin);
+          }
+        }
+      };
+
+  auto stage_download_var_list =
+      [&](Block *cg, MyList<var> *var_list, bool skip_unmapped) {
+        std::vector<double *> batch_host_ptrs;
+        std::vector<MyList<var> *> batch_vars;
+        while (var_list)
+        {
+          double *host_ptr = cg->fgfs[var_list->data->sgfn];
+          if (skip_unmapped && !bssn_gpu_find_device_buffer(host_ptr))
+          {
+            var_list = var_list->next;
+            continue;
+          }
+          batch_host_ptrs.push_back(host_ptr);
+          batch_vars.push_back(var_list);
+          var_list = var_list->next;
+        }
+        if (!batch_host_ptrs.empty() &&
+            bssn_gpu_download_buffer_batch(cg->shape, &batch_host_ptrs[0],
+                                           static_cast<int>(batch_host_ptrs.size())))
+        {
+          for (size_t i = 0; i < batch_host_ptrs.size(); ++i)
+          {
+            if (bssn_cuda_download_buffer(cg->shape, batch_host_ptrs[i]))
+            {
+              cerr << "GPU stage download failure: lev=" << lev
+                   << " var=" << batch_vars[i]->data->name
+                   << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                   << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                   << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+              ERROR = 1;
+              break;
+            }
+          }
+        }
+      };
+
+  auto stage_download_patch_list =
+      [&](MyList<var> *var_list, bool skip_unmapped) {
+        MyList<Patch> *patch_it = GH->PatL[lev];
+        while (patch_it)
+        {
+          MyList<Block> *block_it = patch_it->data->blb;
+          while (block_it)
+          {
+            Block *cg = block_it->data;
+            if (myrank == cg->rank)
+              stage_download_var_list(cg, var_list, skip_unmapped);
+
+            if (block_it == patch_it->data->ble)
+              break;
+            block_it = block_it->next;
+          }
+          if (ERROR)
+            break;
+          patch_it = patch_it->next;
+        }
+      };
+
+  auto ensure_stage_device_var_list =
+      [&](Block *cg, MyList<var> *var_list) {
+        const int n = cg->shape[0] * cg->shape[1] * cg->shape[2];
+        while (var_list)
+        {
+          double *host_ptr = cg->fgfs[var_list->data->sgfn];
+          if (!bssn_gpu_find_device_buffer(host_ptr) &&
+              bssn_gpu_stage_upload_buffer(host_ptr, n))
+          {
+            cerr << "GPU state ensure failure: lev=" << lev
+                 << " var=" << var_list->data->name
+                 << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+            ERROR = 1;
+            break;
+          }
+          var_list = var_list->next;
+        }
+      };
+
+  auto refresh_synced_device_regions =
+      [&](Block *cg, MyList<var> *var_list, Parallel::SyncCache &cache) {
+        std::vector<Parallel::gridseg *> local_segments;
+        for (int node = 0; node < cache.cpusize; ++node)
+        {
+          MyList<Parallel::gridseg> *seg = cache.combined_dst[node];
+          while (seg)
+          {
+            if (seg->data && seg->data->Bg == cg)
+              local_segments.push_back(seg->data);
+            seg = seg->next;
+          }
+        }
+
+        if (local_segments.empty())
+          return;
+
+        const int n = cg->shape[0] * cg->shape[1] * cg->shape[2];
+        while (var_list)
+        {
+          double *host_ptr = cg->fgfs[var_list->data->sgfn];
+          if (!bssn_gpu_find_device_buffer(host_ptr))
+          {
+            if (bssn_gpu_stage_upload_buffer(host_ptr, n))
+            {
+              cerr << "GPU sync refresh upload failure: lev=" << lev
+                   << " var=" << var_list->data->name
+                   << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                   << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                   << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+              ERROR = 1;
+              break;
+            }
+          }
+          else
+          {
+            for (size_t i = 0; i < local_segments.size(); ++i)
+            {
+              Parallel::gridseg *seg = local_segments[i];
+              if (bssn_gpu_stage_upload_region(host_ptr,
+                                               cg->shape,
+                                               cg->bbox,
+                                               cg->bbox + dim,
+                                               seg->shape,
+                                               seg->llb))
+              {
+                cerr << "GPU sync region refresh failure: lev=" << lev
+                     << " var=" << var_list->data->name
+                     << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                     << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                     << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+                ERROR = 1;
+                break;
+              }
+            }
+            if (ERROR)
+              break;
+          }
+          var_list = var_list->next;
+        }
+      };
+
+  auto refresh_stage_device_after_sync =
+      [&](MyList<var> *var_list, Parallel::SyncCache &cache) {
+        MyList<Patch> *patch_it = GH->PatL[lev];
+        while (patch_it)
+        {
+          MyList<Block> *block_it = patch_it->data->blb;
+          while (block_it)
+          {
+            Block *cg = block_it->data;
+            if (myrank == cg->rank)
+              refresh_synced_device_regions(cg, var_list, cache);
+
+            if (block_it == patch_it->data->ble)
+              break;
+            block_it = block_it->next;
+          }
+          if (ERROR)
+            break;
+          patch_it = patch_it->next;
+        }
+      };
+
+  auto refresh_stage_host_before_sync =
+      [&](MyList<var> *var_list, Parallel::SyncCache &cache) -> bool {
+        if (!cache.valid || !cache.combined_src || myrank < 0 || myrank >= cache.cpusize)
+          return false;
+
+        MyList<Patch> *patch_it = GH->PatL[lev];
+        while (patch_it)
+        {
+          MyList<Block> *block_it = patch_it->data->blb;
+          while (block_it)
+          {
+            Block *cg = block_it->data;
+            if (myrank == cg->rank)
+            {
+              std::vector<Parallel::gridseg *> local_segments;
+              MyList<Parallel::gridseg> *seg = cache.combined_src[myrank];
+              while (seg)
+              {
+                if (seg->data && seg->data->Bg == cg)
+                  local_segments.push_back(seg->data);
+                seg = seg->next;
+              }
+
+              if (!local_segments.empty())
+              {
+                MyList<var> *var_it = var_list;
+                while (var_it)
+                {
+                  double *host_ptr = cg->fgfs[var_it->data->sgfn];
+                  for (size_t i = 0; i < local_segments.size(); ++i)
+                  {
+                    Parallel::gridseg *src_seg = local_segments[i];
+                    if (bssn_gpu_stage_download_region(host_ptr,
+                                                       cg->shape,
+                                                       cg->bbox,
+                                                       cg->bbox + dim,
+                                                       src_seg->shape,
+                                                       src_seg->llb))
+                    {
+                      cerr << "GPU sync region download failure: lev=" << lev
+                           << " var=" << var_it->data->name
+                           << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                           << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                           << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+                      ERROR = 1;
+                      return true;
+                    }
+                  }
+                  var_it = var_it->next;
+                }
+              }
+            }
+
+            if (block_it == patch_it->data->ble)
+              break;
+            block_it = block_it->next;
+          }
+          patch_it = patch_it->next;
+        }
+
+        return true;
+      };
+
+  auto can_pack_sync_from_device =
+      [&](MyList<var> *var_list, Parallel::SyncCache &cache) -> bool {
+        if (!cache.valid || !cache.combined_src || myrank < 0 || myrank >= cache.cpusize)
+          return false;
+
+        MyList<Parallel::gridseg> *seg = cache.combined_src[myrank];
+        while (seg)
+        {
+          MyList<var> *var_it = var_list;
+          while (var_it)
+          {
+            if (!bssn_gpu_find_device_buffer(seg->data->Bg->fgfs[var_it->data->sgfn]))
+              return false;
+            var_it = var_it->next;
+          }
+          seg = seg->next;
+        }
+        return true;
+      };
+
+  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 t0 = 0.0;
+        if (profile_enabled)
+          t0 = MPI_Wtime();
+        if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_FIRST_TIME))
+          ERROR = 1;
+        if (profile_enabled)
+          stage_profile_add(lev, STAGE_PROFILE_RHS, MPI_Wtime() - t0);
+
+        if (profile_enabled)
+          t0 = MPI_Wtime();
+        run_stage_on_block(cg, Pp->data, StateList, StateList, SynchList_pre, RHSList, iter_count);
+        if (profile_enabled)
+          stage_profile_add(lev, STAGE_PROFILE_RUN_STAGE, MPI_Wtime() - t0);
+
+        if (profile_enabled)
+          t0 = MPI_Wtime();
+        if (bssn_cuda_lowerbound(cg->shape, cg->fgfs[phi->sgfn], chitiny, false))
+        {
+          cerr << "GPU lowerbound failure: lev=" << lev
+               << " rk_stage=" << iter_count
+               << " var=" << phi->name
+               << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+               << cg->bbox[1] << ":" << cg->bbox[4] << ","
+               << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+          ERROR = 1;
+        }
+        if (profile_enabled)
+          stage_profile_add(lev, STAGE_PROFILE_LOWERBOUND, MPI_Wtime() - t0);
+      }
+      if (BP == Pp->data->ble)
+        break;
+      BP = BP->next;
+    }
+    Pp = Pp->next;
+  }
+
+  if (!ERROR)
+  {
+    if (!keep_stage_sync_on_device)
+    {
+      double t0 = 0.0;
+      if (profile_enabled)
+        t0 = MPI_Wtime();
+      stage_download_patch_list(SynchList_pre, false);
+      if (profile_enabled)
+        stage_profile_add(lev, STAGE_PROFILE_DOWNLOAD, MPI_Wtime() - t0);
+      if (!ERROR)
+      {
+        if (profile_enabled)
+          t0 = MPI_Wtime();
+        bssn_gpu_clear_cached_device_buffers();
+        if (profile_enabled)
+          stage_profile_add(lev, STAGE_PROFILE_CLEAR_CACHE, MPI_Wtime() - t0);
+      }
+    }
+  }
+
+  MPI_Request err_req_pre;
+  {
+    int erh = ERROR;
+    MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_pre);
+  }
+
+  Parallel::AsyncSyncState async_pre;
+  if (profile_enabled)
+  {
+    const double t0 = MPI_Wtime();
+    Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+    stage_profile_add(lev, STAGE_PROFILE_SYNC_START, MPI_Wtime() - t0);
+  }
+  else
+    Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);
+  if (profile_enabled)
+  {
+    const double t0 = MPI_Wtime();
+    Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry,
+                          !keep_stage_sync_on_device);
+    stage_profile_add(lev, STAGE_PROFILE_SYNC_FINISH, MPI_Wtime() - t0);
+  }
+  else
+    Parallel::Sync_finish(sync_cache_pre[lev], async_pre, SynchList_pre, Symmetry,
+                          !keep_stage_sync_on_device);
+  if (!ERROR && !keep_stage_sync_on_device)
+  {
+    if (profile_enabled)
+    {
+      const double t0 = MPI_Wtime();
+      refresh_stage_device_after_sync(SynchList_pre, sync_cache_pre[lev]);
+      stage_profile_add(lev, STAGE_PROFILE_REFRESH, MPI_Wtime() - t0);
+    }
+    else
+      refresh_stage_device_after_sync(SynchList_pre, sync_cache_pre[lev]);
+  }
+
+  MPI_Wait(&err_req_pre, MPI_STATUS_IGNORE);
+  if (ERROR)
+  {
+    Parallel::Dump_Data(GH->PatL[lev], StateList, 0, PhysTime, dT_lev);
+    if (myrank == 0)
+    {
+      if (ErrorMonitor->outfile)
+        ErrorMonitor->outfile << "find NaN in state variables at t = " << PhysTime
+                              << ", lev = " << lev << endl;
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+  }
+
+#if (MAPBH == 0)
+  if (BH_num > 0 && lev == GH->levels - 1)
+  {
+    compute_Porg_rhs(Porg0, Porg_rhs, Sfx0, Sfy0, Sfz0, lev);
+    for (int ithBH = 0; ithBH < BH_num; ithBH++)
+    {
+      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][0], Porg[ithBH][0], Porg_rhs[ithBH][0], iter_count);
+      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][1], Porg[ithBH][1], Porg_rhs[ithBH][1], iter_count);
+      f_rungekutta4_scalar(dT_lev, Porg0[ithBH][2], Porg[ithBH][2], Porg_rhs[ithBH][2], iter_count);
+      if (Symmetry > 0)
+        Porg[ithBH][2] = fabs(Porg[ithBH][2]);
+      if (Symmetry == 2)
+      {
+        Porg[ithBH][0] = fabs(Porg[ithBH][0]);
+        Porg[ithBH][1] = fabs(Porg[ithBH][1]);
+      }
+    }
+  }
+
+  if (lev == a_lev)
+    AnalysisStuff(lev, dT_lev);
+#endif
+
+  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 t0 = 0.0;
+          if (profile_enabled)
+            t0 = MPI_Wtime();
+          ensure_stage_device_var_list(cg, SynchList_pre);
+          if (profile_enabled)
+            stage_profile_add(lev, STAGE_PROFILE_ENSURE, MPI_Wtime() - t0);
+
+          if (profile_enabled)
+            t0 = MPI_Wtime();
+          if (gpu_rhs(CALLED_BY_STEP, myrank, RHS_PARA_CALLED_THEN))
+            ERROR = 1;
+          if (profile_enabled)
+            stage_profile_add(lev, STAGE_PROFILE_RHS, MPI_Wtime() - t0);
+
+          if (profile_enabled)
+            t0 = MPI_Wtime();
+          run_stage_on_block(cg, Pp->data, StateList, SynchList_pre, SynchList_cor, RHSList, iter_count);
+          if (profile_enabled)
+            stage_profile_add(lev, STAGE_PROFILE_RUN_STAGE, MPI_Wtime() - t0);
+
+          if (profile_enabled)
+            t0 = MPI_Wtime();
+          if (bssn_cuda_lowerbound(cg->shape, cg->fgfs[phi1->sgfn], chitiny, false))
+          {
+          cerr << "GPU lowerbound failure: lev=" << lev
+               << " rk_stage=" << iter_count
+               << " var=" << phi1->name
+                 << " bbox=(" << cg->bbox[0] << ":" << cg->bbox[3] << ","
+                 << cg->bbox[1] << ":" << cg->bbox[4] << ","
+                 << cg->bbox[2] << ":" << cg->bbox[5] << ")" << endl;
+            ERROR = 1;
+          }
+          if (profile_enabled)
+            stage_profile_add(lev, STAGE_PROFILE_LOWERBOUND, MPI_Wtime() - t0);
+        }
+
+        if (BP == Pp->data->ble)
+          break;
+        BP = BP->next;
+      }
+      Pp = Pp->next;
+    }
+
+    if (!ERROR)
+    {
+      if (!keep_stage_sync_on_device)
+      {
+        double t0 = 0.0;
+        if (profile_enabled)
+          t0 = MPI_Wtime();
+        stage_download_patch_list(SynchList_cor, false);
+        if (profile_enabled)
+          stage_profile_add(lev, STAGE_PROFILE_DOWNLOAD, MPI_Wtime() - t0);
+        if (!ERROR)
+        {
+          if (profile_enabled)
+            t0 = MPI_Wtime();
+          bssn_gpu_clear_cached_device_buffers();
+          if (profile_enabled)
+            stage_profile_add(lev, STAGE_PROFILE_CLEAR_CACHE, MPI_Wtime() - t0);
+        }
+      }
+    }
+
+    MPI_Request err_req_cor;
+    {
+      int erh = ERROR;
+      MPI_Iallreduce(&erh, &ERROR, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD, &err_req_cor);
+    }
+
+    Parallel::AsyncSyncState async_cor;
+    if (profile_enabled)
+    {
+      const double t0 = MPI_Wtime();
+      Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+      stage_profile_add(lev, STAGE_PROFILE_SYNC_START, MPI_Wtime() - t0);
+    }
+    else
+      Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);
+    if (profile_enabled)
+    {
+      const double t0 = MPI_Wtime();
+      Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry,
+                            !keep_stage_sync_on_device);
+      stage_profile_add(lev, STAGE_PROFILE_SYNC_FINISH, MPI_Wtime() - t0);
+    }
+    else
+      Parallel::Sync_finish(sync_cache_cor[lev], async_cor, SynchList_cor, Symmetry,
+                            !keep_stage_sync_on_device);
+    if (!ERROR && !keep_stage_sync_on_device && iter_count < 3)
+    {
+      if (profile_enabled)
+      {
+        const double t0 = MPI_Wtime();
+        refresh_stage_device_after_sync(SynchList_cor, sync_cache_cor[lev]);
+        stage_profile_add(lev, STAGE_PROFILE_REFRESH, MPI_Wtime() - t0);
+      }
+      else
+        refresh_stage_device_after_sync(SynchList_cor, sync_cache_cor[lev]);
+    }
+
+    MPI_Wait(&err_req_cor, MPI_STATUS_IGNORE);
+    if (ERROR)
+    {
+      Parallel::Dump_Data(GH->PatL[lev], SynchList_pre, 0, PhysTime, dT_lev);
+      if (myrank == 0)
+      {
+        if (ErrorMonitor->outfile)
+          ErrorMonitor->outfile << "find NaN in RK4 substep#" << iter_count
+                                << " variables at t = " << PhysTime
+                                << ", lev = " << lev << endl;
+        MPI_Abort(MPI_COMM_WORLD, 1);
+      }
+    }
+
+#if (MAPBH == 0)
+    if (BH_num > 0 && lev == GH->levels - 1)
+    {
+      compute_Porg_rhs(Porg, Porg1, Sfx, Sfy, Sfz, lev);
+      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]);
+        }
+      }
+    }
+#endif
+
+    if (iter_count < 3)
+    {
+      Pp = GH->PatL[lev];
+      while (Pp)
+      {
+        MyList<Block> *BP = Pp->data->blb;
+        while (BP)
+        {
+          BP->data->swapList(SynchList_pre, SynchList_cor, myrank);
+          if (BP == Pp->data->ble)
+            break;
+          BP = BP->next;
+        }
+        Pp = Pp->next;
+      }
+
+#if (MAPBH == 0)
+      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];
+        }
+      }
+#endif
+    }
+  }
+
+#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 (!ERROR && keep_stage_sync_on_device)
+  {
+    // After the swaps above, only StateList points at arrays updated during this step.
+    // OldStateList/SynchList_cor remain valid on host because their backing arrays were
+    // read-only during the RK step, and SynchList_pre is reused only as scratch later.
+    const double t0 = profile_enabled ? MPI_Wtime() : 0.0;
+    stage_download_patch_list(StateList, true);
+    if (profile_enabled)
+      stage_profile_add(lev, STAGE_PROFILE_DOWNLOAD, MPI_Wtime() - t0);
+  }
+
+  if (profile_enabled)
+  {
+    const double t0 = MPI_Wtime();
+    bssn_gpu_clear_cached_device_buffers();
+    stage_profile_add(lev, STAGE_PROFILE_CLEAR_CACHE, MPI_Wtime() - t0);
+  }
+  else
+    bssn_gpu_clear_cached_device_buffers();
+
+  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];
+    }
+  }
+
+  if (profile_enabled)
+    stage_profile_add(lev, STAGE_PROFILE_TOTAL, MPI_Wtime() - step_total_begin);
+}
+
+#endif

AMSS_NCKU_source/bssn_gpu.h

@@ -4,8 +4,6 @@
 #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
 
@@ -67,6 +65,42 @@ int gpu_rhs(int calledby, int mpi_rank, int *ex, double &T,
 
 int gpu_rhs_ss(RHS_SS_PARA);
 
+int bssn_gpu_bind_process_device(int mpi_rank);
+void bssn_gpu_clear_cached_device_buffers();
+void bssn_gpu_release_pinned_host_buffers();
+const double *bssn_gpu_find_device_buffer(const double *host_ptr);
+void bssn_gpu_register_device_buffer(const double *host_ptr, const double *device_ptr);
+void bssn_gpu_prepare_host_buffer(const double *host_ptr, int count);
+int bssn_gpu_stage_upload_buffer(const double *host_ptr, int count);
+int bssn_gpu_stage_zero_buffer(const double *host_ptr, int count);
+int bssn_gpu_stage_upload_region(const double *host_ptr,
+                                 const int *full_shape,
+                                 const double *full_llb,
+                                 const double *full_uub,
+                                 const int *region_shape,
+                                 const double *region_llb);
+int bssn_gpu_stage_download_region(double *host_ptr,
+                                   const int *full_shape,
+                                   const double *full_llb,
+                                   const double *full_uub,
+                                   const int *region_shape,
+                                   const double *region_llb);
+int bssn_gpu_stage_download_region_to_buffer(const double *host_src_ptr,
+                                             const int *full_shape,
+                                             const double *full_llb,
+                                             const double *full_uub,
+                                             const int *region_shape,
+                                             const double *region_llb,
+                                             double *host_dst_ptr);
+int bssn_gpu_stage_upload_buffer_to_region(const double *host_src_ptr,
+                                           double *host_dst_ptr,
+                                           const int *full_shape,
+                                           const double *full_llb,
+                                           const double *full_uub,
+                                           const int *region_shape,
+                                           const double *region_llb);
+int bssn_gpu_download_buffer_batch(const int *ex, double **host_ptrs, int num_buffers);
+
 /** Init GPU side data in GPUMeta. */
 // void init_fluid_meta_gpu(GPUMeta *gpu_meta);
 

AMSS_NCKU_source/bssn_macro.h

@@ -68,6 +68,7 @@ if(TIME_COUNT_EACH_RANK == 1){\
 //3---------------------GPU---------------------
 #define CALLED_BY_STEP 0
 #define CALLED_BY_CONSTRAINT 1
+#define CALLED_BY_CONSTRAINT_CONS_ONLY 2
 
 #define RHS_PARA_CALLED_FIRST_TIME 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],cg->fgfs[Ayy0->sgfn],cg->fgfs[Ayz0->sgfn],cg->fgfs[Azz0->sgfn],cg->fgfs[Gmx0->sgfn],cg->fgfs[Gmy0->sgfn],cg->fgfs[Gmz0->sgfn],cg->fgfs[Lap0->sgfn],cg->fgfs[Sfx0->sgfn],cg->fgfs[Sfy0->sgfn],cg->fgfs[Sfz0->sgfn],cg->fgfs[dtSfx0->sgfn],cg->fgfs[dtSfy0->sgfn],cg->fgfs[dtSfz0->sgfn],cg->fgfs[phi_rhs->sgfn],cg->fgfs[trK_rhs->sgfn],cg->fgfs[gxx_rhs->sgfn],cg->fgfs[gxy_rhs->sgfn],cg->fgfs[gxz_rhs->sgfn],cg->fgfs[gyy_rhs->sgfn],cg->fgfs[gyz_rhs->sgfn],cg->fgfs[gzz_rhs->sgfn],cg->fgfs[Axx_rhs->sgfn],cg->fgfs[Axy_rhs->sgfn],cg->fgfs[Axz_rhs->sgfn],cg->fgfs[Ayy_rhs->sgfn],cg->fgfs[Ayz_rhs->sgfn],cg->fgfs[Azz_rhs->sgfn],cg->fgfs[Gmx_rhs->sgfn],cg->fgfs[Gmy_rhs->sgfn],cg->fgfs[Gmz_rhs->sgfn],cg->fgfs[Lap_rhs->sgfn],cg->fgfs[Sfx_rhs->sgfn],cg->fgfs[Sfy_rhs->sgfn],cg->fgfs[Sfz_rhs->sgfn],cg->fgfs[dtSfx_rhs->sgfn],cg->fgfs[dtSfy_rhs->sgfn],cg->fgfs[dtSfz_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],cg->fgfs[Gamxxx->sgfn],cg->fgfs[Gamxxy->sgfn],cg->fgfs[Gamxxz->sgfn],cg->fgfs[Gamxyy->sgfn],cg->fgfs[Gamxyz->sgfn],cg->fgfs[Gamxzz->sgfn],cg->fgfs[Gamyxx->sgfn],cg->fgfs[Gamyxy->sgfn],cg->fgfs[Gamyxz->sgfn],cg->fgfs[Gamyyy->sgfn],cg->fgfs[Gamyyz->sgfn],cg->fgfs[Gamyzz->sgfn],cg->fgfs[Gamzxx->sgfn],cg->fgfs[Gamzxy->sgfn],cg->fgfs[Gamzxz->sgfn],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
 

AMSS_NCKU_source/bssn_rhs.h

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

AMSS_NCKU_source/bssn_rhs_c.C

@@ -2,88 +2,12 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
-#include <time.h>
 // 0-based i,j,k
 // #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
 // ex(1)=nx, ex(2)=ny, ex(3)=nz
 
 // 用法：a[ IDX_F(i,j,k,nx,ny) ]
 
-#ifndef BSSN_KERNEL_FINE_TIMING
-#define BSSN_KERNEL_FINE_TIMING 0
-#endif
-
-#if BSSN_KERNEL_FINE_TIMING
-namespace rhs_kernel_timing
-{
-    enum Bucket
-    {
-        KB_SETUP_DERIVS = 0,
-        KB_GEOM_GAMMA,
-        KB_RICCI_METRIC,
-        KB_CHI_LAPSE,
-        KB_AIJ_TRK_GAUGE,
-        KB_KO_CONSTRAINT,
-        KB_COUNT
-    };
-
-    static double local_bucket_seconds[KB_COUNT];
-
-    static const char *bucket_labels[KB_COUNT] =
-    {
-        "setup_derivs",
-        "geom_gamma",
-        "ricci_metric",
-        "chi_lapse",
-        "aij_trk_gauge",
-        "ko_constraint"
-    };
-
-    static inline double now_seconds()
-    {
-        struct timespec ts;
-        clock_gettime(CLOCK_MONOTONIC, &ts);
-        return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
-    }
-}
-
-extern "C" void f_bssn_rhs_kernel_timing_reset()
-{
-    for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
-        rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
-}
-
-extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
-{
-    return rhs_kernel_timing::KB_COUNT;
-}
-
-extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
-{
-    return rhs_kernel_timing::local_bucket_seconds;
-}
-
-extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
-{
-    if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
-        return "unknown";
-    return rhs_kernel_timing::bucket_labels[bucket_index];
-}
-
-#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
-#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
-    rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
-        rhs_kernel_timing::now_seconds() - (var_name)
-#else
-extern "C" void f_bssn_rhs_kernel_timing_reset() {}
-extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
-extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
-extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
-
-#define RHS_KERNEL_TIMER_DECL(var_name)
-#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
-#endif
-
 // C function that calculates the right-hand side for BSSN equations
 int f_compute_rhs_bssn(int *ex, double &T, 
                        double *X, double *Y, double *Z,
@@ -178,7 +102,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
     dY = Y[1] - Y[0];
     dZ = Z[1] - Z[0];
 
-        RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
         // 1ms //
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
@@ -218,8 +141,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
                         + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
         }
-        RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
-        RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
         // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
         for(int i=0;i<all;i+=1){
             double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
@@ -362,6 +283,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                 + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
+            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
+            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
+
             Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
                 TWO * alpn1[i] * (
                 -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
@@ -391,8 +315,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                             + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                         );
         }
-        RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
-        RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
         // 22.3ms //
         fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
         X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
@@ -410,6 +332,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
             double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
             double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
             double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
+            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
 
             double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                     + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
@@ -763,74 +686,69 @@ int f_compute_rhs_bssn(int *ex, double &T,
                     + Gamxyz[i] * gzzx[i] + Gamyyz[i] * gzzy[i] + Gamzyz[i] * gzzz[i]
                 );
         }
-        RHS_KERNEL_TIMER_ADD(KB_RICCI_METRIC, timer_ricci_metric);
 
-        RHS_KERNEL_TIMER_DECL(timer_chi_lapse);
         // 22.3ms //
             fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 7ms //
         for (int i=0;i<all;i+=1) {
-            const double inv_chin1 = ONE / chin1[i];
+            fxx[i] = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
-            const double half_inv_chin1 = HALF * inv_chin1;
+            fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
-            const double scaled_inv = F3o2 * inv_chin1;
+            fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
-            const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
+            fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
-            const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
+            fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
-            const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
+            fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
-            const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
+            f[i] =
-            const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
+                gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
-            const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
+                + gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
-            const double ricci_chi =
+                + gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
-                gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
+                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
-                + gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
+                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
-                + gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
+                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-                + TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-                + TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-                + TWO * gupyz[i] * (cyz - scaled_inv * chiy[i] * chiz[i]);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            f[i] = ricci_chi;
-            Rxx[i] = Rxx[i] + ( cxx - half_inv_chin1 * chix[i] * chix[i] + (dxx[i] + ONE) * ricci_chi ) * half_inv_chin1;
-            Ryy[i] = Ryy[i] + ( cyy - half_inv_chin1 * chiy[i] * chiy[i] + (dyy[i] + ONE) * ricci_chi ) * half_inv_chin1;
-            Rzz[i] = Rzz[i] + ( czz - half_inv_chin1 * chiz[i] * chiz[i] + (dzz[i] + ONE) * ricci_chi ) * half_inv_chin1;
 
-            Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
+            Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
-            Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
+            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
-            Ryz[i] = Ryz[i] + ( cyz - half_inv_chin1 * chiy[i] * chiz[i] + gyz[i] * ricci_chi ) * half_inv_chin1;
+            Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
         }
 
         // 24ms //
         fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
+        fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 6ms //
         for (int i=0;i<all;i+=1) {
-            const double inv_chin1 = ONE / chin1[i];
+            /* gxxx,gxxy,gxxz (这里是“升指标后的chi导数/chi”那类量，你沿用原变量名即可) */
-            const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
+            gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
-            const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
+            gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
-            const double gchi_z = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) * inv_chin1;
+            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
 
             /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) * inv_chin1) - (dxx[i] + ONE) * gchi_x ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_y ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_z ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_x ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) * inv_chin1) - (dyy[i] + ONE) * gchi_y ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_z ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_x ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_y ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) * inv_chin1) - (dzz[i] + ONE) * gchi_z ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1)      - gxy[i] * gchi_x ) * HALF;
+            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
-            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1)      - gxy[i] * gchi_y ) * HALF;
+            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
-            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gchi_z ) * HALF;
+            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gxxz[i] ) * HALF;
 
-            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1)      - gxz[i] * gchi_x ) * HALF;
+            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] / chin1[i])      - gxz[i] * gxxx[i] ) * HALF;
-            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gchi_y ) * HALF;
+            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gxxy[i] ) * HALF;
-            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] * inv_chin1)      - gxz[i] * gchi_z ) * HALF;
+            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i])      - gxz[i] * gxxz[i] ) * HALF;
 
-            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gchi_x ) * HALF;
+            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gxxx[i] ) * HALF;
-            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1)      - gyz[i] * gchi_y ) * HALF;
+            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i])      - gyz[i] * gxxy[i] ) * HALF;
-            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] * inv_chin1)      - gyz[i] * gchi_z ) * HALF;
+            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i])      - gyz[i] * gxxz[i] ) * HALF;
 
             /* fxx..fyz 修正：减去 Γ * ∂Lap */
             fxx[i] = fxx[i] - Gamxxx[i] * Lapx[i] - Gamyxx[i] * Lapy[i] - Gamzxx[i] * Lapz[i];
@@ -844,8 +762,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                     +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
         }
-        RHS_KERNEL_TIMER_ADD(KB_CHI_LAPSE, timer_chi_lapse);
-        RHS_KERNEL_TIMER_DECL(timer_aij_trk_gauge);
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
             const double divb = betaxx[i] + betayy[i] + betazz[i];
@@ -1106,9 +1022,16 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
 
             #if (GAUGE == 2)
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
+            {
+                const double chi_sqrt = sqrt(chin1[i]);
+                const double damping = ONE - chi_sqrt;
+                reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / (damping * damping);
+            }
             #else
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - chin1[i]), 2.0 );
+            {
+                const double damping = ONE - chin1[i];
+                reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / (damping * damping);
+            }
             #endif
 
             dtSfx_rhs[i] = Gamx_rhs[i] - reta[i] * dtSfx[i];
@@ -1124,9 +1047,16 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
 
             #if (GAUGE == 4)
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
+            {
+                const double chi_sqrt = sqrt(chin1[i]);
+                const double damping = ONE - chi_sqrt;
+                reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / (damping * damping);
+            }
             #else
-            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - chin1[i]), 2.0 );
+            {
+                const double damping = ONE - chin1[i];
+                reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / (damping * damping);
+            }
             #endif
 
             betax_rhs[i] = FF * Gamx[i] - reta[i] * betax[i];
@@ -1146,8 +1076,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #endif
         }
-        RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
-        RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
         // advection + KO dissipation with shared symmetry buffer
         lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
         lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
@@ -1279,7 +1207,6 @@ 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/cgh.C

@@ -27,6 +27,10 @@ using namespace std;
 #include "cgh.h"
 #include "Parallel.h"
 #include "parameters.h"
+#ifdef USE_GPU
+#include "bssn_gpu.h"
+#include "bssn_cuda_ops.h"
+#endif
 
 //================================================================================================
 
@@ -885,6 +889,13 @@ void cgh::recompose_cgh(int nprocs, bool *lev_flag,
       bool CC = (lev > trfls);
       Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
 
+#ifdef USE_GPU
+      bssn_gpu_clear_cached_device_buffers();
+      bssn_gpu_release_pinned_host_buffers();
+      bssn_cuda_release_rk4_caches();
+      bssn_cuda_release_interp_caches();
+      patch_release_interp_plan_cache();
+#endif
       Parallel::KillBlocks(PatL[lev]);
       PatL[lev]->destroyList();
       PatL[lev] = tmPat;
@@ -914,6 +925,13 @@ void cgh::recompose_cgh(int nprocs, bool *lev_flag,
       bool CC = (lev > trfls);
       Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
 
+#ifdef USE_GPU
+      bssn_gpu_clear_cached_device_buffers();
+      bssn_gpu_release_pinned_host_buffers();
+      bssn_cuda_release_rk4_caches();
+      bssn_cuda_release_interp_caches();
+      patch_release_interp_plan_cache();
+#endif
       Parallel::KillBlocks(PatL[lev]);
       PatL[lev]->destroyList();
       PatL[lev] = tmPat;
@@ -1522,6 +1540,13 @@ void cgh::recompose_cgh_Onelevel(int nprocs, int lev,
   bool CC = (lev > trfls);
   Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
 
+#ifdef USE_GPU
+  bssn_gpu_clear_cached_device_buffers();
+  bssn_gpu_release_pinned_host_buffers();
+  bssn_cuda_release_rk4_caches();
+  bssn_cuda_release_interp_caches();
+  patch_release_interp_plan_cache();
+#endif
   Parallel::KillBlocks(PatL[lev]);
   PatL[lev]->destroyList();
   PatL[lev] = tmPat;
@@ -1545,6 +1570,13 @@ void cgh::recompose_cgh_Onelevel(int nprocs, int lev,
   Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
   misc::tillherecheck(Commlev[lev], start_rank[lev], "after fill_level_data");
 
+#ifdef USE_GPU
+  bssn_gpu_clear_cached_device_buffers();
+  bssn_gpu_release_pinned_host_buffers();
+  bssn_cuda_release_rk4_caches();
+  bssn_cuda_release_interp_caches();
+  patch_release_interp_plan_cache();
+#endif
   Parallel::KillBlocks(PatL[lev]);
   PatL[lev]->destroyList();
   PatL[lev] = tmPat;