Cache GPU RHS symbols and zero vacuum sources once

Reviewed-on: #3

AMSS_NCKU_source/ABE.C

@@ -23,22 +23,20 @@ using namespace std;
 #include <mpi.h>
 
 #include "misc.h"
-#include "macrodef.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)
+#if (ABEtype == 0)
-
+#include "bssn_class.h"
-#ifdef USE_GPU
+
-#include "bssn_gpu_class.h"
+#elif (ABEtype == 1)
-#else
+#include "bssnEScalar_class.h"
-#include "bssn_class.h"
-#endif
-
-#elif (ABEtype == 1)
-#include "bssnEScalar_class.h"
 
 #elif (ABEtype == 2)
 #include "Z4c_class.h"
@@ -474,10 +472,13 @@ int main(int argc, char *argv[])
             cout << endl;
       }
 
-      ADM->Evolve(Steps);
+	      ADM->Evolve(Steps);
-
+#ifdef USE_GPU
-      if (myrank == 0)
+	      bssn_cuda_dump_stage_profile();
-      {
+#endif
+	
+	      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

@@ -9,8 +9,12 @@
 #include <new>
 using namespace std;
 
-#include "Block.h"
+#include "Block.h"
-#include "misc.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)
 {
@@ -95,14 +99,19 @@ Block::Block(int DIM, int *shapei, double *bboxi, int ranki, int ingfsi, int fng
   }
 #endif
 }
-Block::~Block()
+Block::~Block()
-{
+{
-  int myrank;
+  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
-  if (myrank == rank)
+  if (myrank == rank)
-  {
+  {
-    for (int i = 0; i < dim; i++)
+#ifdef USE_GPU
-      delete[] X[i];
+    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++)
       free(igfs[i]);
     delete[] igfs;

AMSS_NCKU_source/MPatch.C

@@ -2,29 +2,100 @@
 #include <iostream>
 #include <iomanip>
 #include <fstream>
-#include <cstdlib>
+#include <cstdlib>
-#include <cstdio>
+#include <cstdio>
-#include <string>
+#include <string>
-#include <cmath>
+#include <cmath>
-#include <new>
+#include <new>
-#include <vector>
+#include <map>
-using namespace std;
+#include <vector>
+using namespace std;
 
-#include "misc.h"
+#include "misc.h"
-#include "MPatch.h"
+#include "MPatch.h"
-#include "Parallel.h"
+#include "Parallel.h"
-#include "fmisc.h"
+#include "fmisc.h"
-#ifdef INTERP_LB_PROFILE
+#include "bssn_cuda_ops.h"
-#include "interp_lb_profile.h"
+#ifdef INTERP_LB_PROFILE
-#endif
+#include "interp_lb_profile.h"
-
+#endif
-namespace
+
-{
+#if defined(__GNUC__) || defined(__clang__)
-struct InterpBlockView
+extern int bssn_cuda_interp_points_batch(const int *ex,
-{
+                                         const double *X, const double *Y, const double *Z,
-  Block *bp;
+                                         const double *const *fields,
-  double llb[dim];
+                                         const double *soa_flat,
-  double uub[dim];
+                                         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;
+  double llb[dim];
+  double uub[dim];
 };
 
 struct BlockBinIndex
@@ -154,10 +225,10 @@ void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
   index.valid = true;
 }
 
-int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
+int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
-{
+{
-  if (!index.valid)
+  if (!index.valid)
-    return -1;
+    return -1;
 
   const int bx = coord_to_bin(pox[0], index.lo[0], index.inv[0], index.bins[0]);
   const int by = coord_to_bin(pox[1], index.lo[1], index.inv[1], index.bins[1]);
@@ -175,13 +246,314 @@ int find_block_index_for_point(const BlockBinIndex &index, const double *pox, co
   for (size_t bi = 0; bi < index.views.size(); bi++)
     if (point_in_block_view(index.views[bi], pox, DH))
       return int(bi);
-
+
-  return -1;
+  return -1;
-}
+}
-} // namespace
+
-
+void collect_interp_vars(MyList<var> *VarList, vector<InterpVarDesc> &vars)
-Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
+{
-{
+  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)
+{
 
   int hbuffer_width = buffer_width;
   if (lev == 0)
@@ -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
+  double DH[dim];
-  // All ranks traverse the same block list so they all agree on ownership
+  for (int i = 0; i < dim; i++)
-  int *owner_rank;
+    DH[i] = getdX(i);
-  owner_rank = new int[NN];
+  BlockBinIndex block_index;
-  for (int j = 0; j < NN; j++)
+  build_block_bin_index(this, DH, block_index);
-    owner_rank[j] = -1;
+  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();
-  double DH[dim];
+
-  for (int i = 0; i < dim; i++)
+  interpolate_owned_points(VarList, Shellf, Symmetry, ordn, block_index, plan);
-    DH[i] = getdX(i);
-  BlockBinIndex block_index;
-  build_block_bin_index(this, DH, block_index);
-
-  for (int j = 0; j < NN; j++) // run along points
-  {
-    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.
@@ -631,9 +958,8 @@ void Patch::Interp_Points(MyList<var> *VarList,
       MPI_Bcast(Shellf + jstart * num_var, count, MPI_DOUBLE, cur_owner, MPI_COMM_WORLD);
     }
   }
-
+
-  delete[] owner_rank;
+}
-}
 void Patch::Interp_Points(MyList<var> *VarList,
                           int NN, double **XX,
                           double *Shellf, int Symmetry,
@@ -661,102 +987,22 @@ 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
+  double DH[dim];
-  int *owner_rank;
+  for (int i = 0; i < dim; i++)
-  owner_rank = new int[NN];
+    DH[i] = getdX(i);
-  for (int j = 0; j < NN; j++)
+  BlockBinIndex block_index;
-    owner_rank[j] = -1;
+  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);
-  double DH[dim];
+  const int *owner_rank = plan.owner_rank.data();
-  for (int i = 0; i < dim; i++)
+
-    DH[i] = getdX(i);
+  interpolate_owned_points(VarList, Shellf, Symmetry, ordn, block_index, plan);
-  BlockBinIndex block_index;
-  build_block_bin_index(this, DH, block_index);
-
-  // --- Interpolation phase (identical to original) ---
-  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 ---
+  // --- Targeted point-to-point communication phase ---
-  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];
   {
@@ -873,9 +1119,8 @@ void Patch::Interp_Points(MyList<var> *VarList,
   delete[] send_offset;
   delete[] recv_offset;
   delete[] send_count;
-  delete[] recv_count;
+  delete[] recv_count;
-  delete[] consumer_rank;
+  delete[] consumer_rank;
-  delete[] owner_rank;
 
 #ifdef INTERP_LB_PROFILE
   {
@@ -923,64 +1168,20 @@ 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
+  // Build global-to-local rank translation for Comm_here
-  int *owner_rank;
+  MPI_Group world_group, local_group;
-  owner_rank = new int[NN];
+  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
-  for (int j = 0; j < NN; j++)
+  MPI_Comm_group(Comm_here, &local_group);
-    owner_rank[j] = -1;
 
-  // Build global-to-local rank translation for Comm_here
+  double DH[dim];
-  MPI_Group world_group, local_group;
+  for (int i = 0; i < dim; i++)
-  MPI_Comm_group(MPI_COMM_WORLD, &world_group);
+    DH[i] = getdX(i);
-  MPI_Comm_group(Comm_here, &local_group);
+  BlockBinIndex block_index;
-
+  build_block_bin_index(this, DH, block_index);
-  double DH[dim];
+  CachedInterpPlan &plan = get_cached_interp_plan(this, NN, XX, Symmetry, myrank, DH, block_index, lmyrank == 0, true);
-  for (int i = 0; i < dim; i++)
+  const int *owner_rank = plan.owner_rank.data();
-    DH[i] = getdX(i);
+
-  BlockBinIndex block_index;
+  interpolate_owned_points(VarList, Shellf, Symmetry, ordn, block_index, plan);
-  build_block_bin_index(this, DH, block_index);
-
-  for (int j = 0; j < NN; j++) // run along points
-  {
-    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
@@ -1008,10 +1209,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
     }
   }
 
-  MPI_Group_free(&world_group);
+  MPI_Group_free(&world_group);
-  MPI_Group_free(&local_group);
+  MPI_Group_free(&local_group);
-  delete[] owner_rank;
+}
-}
 void Patch::checkBlock()
 {
   int myrank;

AMSS_NCKU_source/MPatch.h

@@ -8,7 +8,7 @@
 #include "var.h"
 #include "macrodef.h" //need dim here; Vertex or Cell; ghost_width
 
-class Patch
+class Patch
 {
 
 public:
@@ -50,6 +50,8 @@ public:
                          double *Shellf, int Symmetry, MPI_Comm Comm_here);
    void Find_Maximum(MyList<var> *VarList, double *XX,
                      double *Shellf, MPI_Comm Comm_here);
-};
+};
-
+
-#endif /* PATCH_H */
+void patch_release_interp_plan_cache();
+
+#endif /* PATCH_H */

AMSS_NCKU_source/Parallel.h

@@ -89,9 +89,12 @@ namespace Parallel
   void transfermix(MyList<gridseg> **src, MyList<gridseg> **dst,
                    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);
-  void Sync(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  void Sync(Patch *Pat, MyList<var> *VarList, int Symmetry, const char *context);
-  void Sync_merged(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry);
+  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;
@@ -105,9 +108,13 @@ namespace Parallel
     int *send_buf_caps;
     int *recv_buf_caps;
     MPI_Request *reqs;
-    MPI_Status *stats;
+    MPI_Status *stats;
-    int max_reqs;
+    int max_reqs;
-    bool lengths_valid;
+    bool lengths_valid;
+    int lengths_var_count;
+    int *tc_req_node;
+    int *tc_req_is_recv;
+    int *tc_completed;
     SyncCache();
     void invalidate();
     void destroy();
@@ -118,16 +125,20 @@ namespace Parallel
                        MyList<var> *VarList1, MyList<var> *VarList2,
                        int Symmetry, SyncCache &cache);
 
-  struct AsyncSyncState {
+  struct AsyncSyncState {
-    int req_no;
+    int req_no;
-    bool active;
+    bool active;
-    AsyncSyncState() : req_no(0), active(false) {}
+    int mpi_tag;
-  };
+    int *req_node;
+    int *req_is_recv;
+    int pending_recv;
+    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,
+  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
-                  SyncCache &cache, AsyncSyncState &state);
+                  SyncCache &cache, AsyncSyncState &state);
-  void Sync_finish(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);

AMSS_NCKU_source/bssn_class.C

@@ -14,7 +14,8 @@ using namespace std;
 #include <string.h>
 #endif
 
-#include <time.h>
+#include <time.h>
+#include <unistd.h>
 
 #include "macrodef.h"
 #include "misc.h"
@@ -28,20 +29,30 @@ using namespace std;
 #include "rungekutta4_rout.h"
 #include "sommerfeld_rout.h"
 #include "getnp4.h"
-#include "shellfunctions.h"
+#include "shellfunctions.h"
-#include "parameters.h"
+#include "parameters.h"
+#ifdef USE_GPU
+#include "bssn_macro.h"
+#include "bssn_gpu.h"
+#endif
 
 #ifdef With_AHF
 #include "derivatives.h"
 #include "myglobal.h"
 #endif
 
-#include "perf.h"
+#include "perf.h"
-
+
-#include "derivatives.h"
+#include "derivatives.h"
-#include "ricci_gamma.h"
+#include "ricci_gamma.h"
-
+
-//================================================================================================
+// Compile-time switch for per-timestep memory usage collection/printing.
+// Default is OFF to reduce overhead in production runs.
+#ifndef BSSN_ENABLE_MEM_USAGE_LOG
+#define BSSN_ENABLE_MEM_USAGE_LOG 0
+#endif
+
+//================================================================================================
 
 // define bssn_class
 
@@ -734,9 +745,12 @@ void bssn_class::Initialize()
   // Initialize sync caches (per-level, for predictor and corrector)
   sync_cache_pre = new Parallel::SyncCache[GH->levels];
   sync_cache_cor = new Parallel::SyncCache[GH->levels];
-  sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
+  sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
-  sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
+  sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
-}
+  sync_cache_restrict = new Parallel::SyncCache[GH->levels];
+  sync_cache_outbd = new Parallel::SyncCache[GH->levels];
+  sync_cache_psi4 = new Parallel::SyncCache[GH->levels];
+}
 
 //================================================================================================
 
@@ -748,8 +762,8 @@ void bssn_class::Initialize()
 
 //================================================================================================
 
-bssn_class::~bssn_class()
+bssn_class::~bssn_class()
-{
+{
 #ifdef With_AHF
   AHList->clearList();
   AHDList->clearList();
@@ -1006,12 +1020,30 @@ bssn_class::~bssn_class()
       sync_cache_rp_coarse[i].destroy();
     delete[] sync_cache_rp_coarse;
   }
-  if (sync_cache_rp_fine)
+  if (sync_cache_rp_fine)
-  {
+  {
-    for (int i = 0; i < GH->levels; i++)
+    for (int i = 0; i < GH->levels; i++)
-      sync_cache_rp_fine[i].destroy();
+      sync_cache_rp_fine[i].destroy();
-    delete[] sync_cache_rp_fine;
+    delete[] sync_cache_rp_fine;
-  }
+  }
+  if (sync_cache_restrict)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_restrict[i].destroy();
+    delete[] sync_cache_restrict;
+  }
+  if (sync_cache_outbd)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_outbd[i].destroy();
+    delete[] sync_cache_outbd;
+  }
+  if (sync_cache_psi4)
+  {
+    for (int i = 0; i < GH->levels; i++)
+      sync_cache_psi4[i].destroy();
+    delete[] sync_cache_psi4;
+  }
 
   delete GH;
 #ifdef WithShell
@@ -1044,8 +1076,25 @@ bssn_class::~bssn_class()
   delete ConVMonitor;
   delete Waveshell;
 
-  delete CheckPoint;
+  delete CheckPoint;
-}
+}
+
+void bssn_class::InvalidateSyncCaches()
+{
+  if (!GH)
+    return;
+
+  for (int il = 0; il < GH->levels; il++)
+  {
+    sync_cache_pre[il].invalidate();
+    sync_cache_cor[il].invalidate();
+    sync_cache_rp_coarse[il].invalidate();
+    sync_cache_rp_fine[il].invalidate();
+    sync_cache_restrict[il].invalidate();
+    sync_cache_outbd[il].invalidate();
+    sync_cache_psi4[il].invalidate();
+  }
+}
 
 //================================================================================================
 
@@ -2028,9 +2077,10 @@ void bssn_class::Read_Ansorg()
 
 void bssn_class::Evolve(int Steps)
 {
-  clock_t prev_clock, curr_clock;
+  clock_t prev_clock, curr_clock;
-  double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
+  double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
-  LastAnas = 0;
+  LastAnas = 0;
+  LastConsOut = 0;
 #if 0
 //initial checkpoint for special uasge
      {
@@ -2127,8 +2177,10 @@ void bssn_class::Evolve(int Steps)
   #endif
   */
   
-  perf bssn_perf;
+#if BSSN_ENABLE_MEM_USAGE_LOG
-  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
+  perf bssn_perf;
+  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
+#endif
 
   for (int lev = 0; lev < GH->levels; lev++)
     GH->Lt[lev] = PhysTime;
@@ -2213,7 +2265,7 @@ void bssn_class::Evolve(int Steps)
     GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
                SynchList_cor, OldStateList, StateList, SynchList_pre,
                fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
-    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+    InvalidateSyncCaches();
 #endif
 
 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2222,21 +2274,23 @@ void bssn_class::Evolve(int Steps)
 //		fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
 #endif
 
-    // Retrieve memory usage information used during computation; master process prints it
+#if BSSN_ENABLE_MEM_USAGE_LOG
-    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
+    // Retrieve memory usage information used during computation; master process prints it
-                          &peak_min, &peak_avg, &peak_max, nprocs);
+    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
-    if (myrank == 0)
+                          &peak_min, &peak_avg, &peak_max, nprocs);
-    {
+    if (myrank == 0)
-      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
+    {
-             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
+      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
-             (double)current_min / (1024.0 * 1024.0),
+             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
-             (double)current_avg / (1024.0 * 1024.0),
+             (double)current_min / (1024.0 * 1024.0),
-             (double)current_max / (1024.0 * 1024.0),
+             (double)current_avg / (1024.0 * 1024.0),
-             (double)peak_min / (1024.0 * 1024.0),
+             (double)current_max / (1024.0 * 1024.0),
-             (double)peak_avg / (1024.0 * 1024.0),
+             (double)peak_min / (1024.0 * 1024.0),
-             (double)peak_max / (1024.0 * 1024.0));
+             (double)peak_avg / (1024.0 * 1024.0),
-      cout << endl;
+             (double)peak_max / (1024.0 * 1024.0));
-    }
+      cout << endl;
+    }
+#endif
     
     // Output puncture positions at each step
     if (myrank == 0)
@@ -2284,18 +2338,21 @@ void bssn_class::Evolve(int Steps)
     ////////////////////////////////////////////////////////////
 
     // When LastCheck >= CheckTime, perform runtime checks and output status data
-    if (LastCheck >= CheckTime)
+    if (LastCheck >= CheckTime)
-    {
+    {
-      LastCheck = 0;
+      LastCheck = 0;
-
+
-      CheckPoint->write_Black_Hole_position(BH_num_input, BH_num, Porg0, Porgbr, Mass);
+      CheckPoint->write_Black_Hole_position(BH_num_input, BH_num, Porg0, Porgbr, Mass);
       CheckPoint->writecheck_cgh(PhysTime, GH);
 #ifdef WithShell
       CheckPoint->writecheck_sh(PhysTime, SH);
-#endif
+#endif
-      CheckPoint->write_bssn(LastDump, Last2dDump, LastAnas);
+      CheckPoint->write_bssn(LastDump, Last2dDump, LastAnas);
-    }
+    }
-  }
+
+    // Keep output/analysis phases aligned across ranks before the next coarse step.
+    MPI_Barrier(MPI_COMM_WORLD);
+  }
   /*
   #ifdef With_AHF
   // final apparent horizon finding
@@ -2429,7 +2486,7 @@ void bssn_class::RecursiveStep(int lev)
   if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
                       fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+  InvalidateSyncCaches();
 #endif
 }
 
@@ -2608,7 +2665,7 @@ void bssn_class::ParallelStep()
   if (GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
                       SynchList_cor, OldStateList, StateList, SynchList_pre,
                       fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+  InvalidateSyncCaches();
 #endif
 }
 
@@ -2775,7 +2832,7 @@ void bssn_class::ParallelStep()
         if (GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
                             SynchList_cor, OldStateList, StateList, SynchList_pre,
                             fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor))
-        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+        InvalidateSyncCaches();
 
         //               a_stream.clear();
         //               a_stream.str("");
@@ -2790,7 +2847,7 @@ void bssn_class::ParallelStep()
       if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                           SynchList_cor, OldStateList, StateList, SynchList_pre,
                           fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+      InvalidateSyncCaches();
 
       //               a_stream.clear();
       //               a_stream.str("");
@@ -2809,7 +2866,7 @@ void bssn_class::ParallelStep()
           if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
                               fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+          InvalidateSyncCaches();
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -2825,7 +2882,7 @@ void bssn_class::ParallelStep()
           if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                               SynchList_cor, OldStateList, StateList, SynchList_pre,
                               fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
+          InvalidateSyncCaches();
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -3014,9 +3071,14 @@ void bssn_class::RecursiveStep(int lev, int num) // in all 2^(lev+1)-1 steps
 
 #if (PSTR == 0)
 #if 1
-void bssn_class::Step(int lev, int YN)
+void bssn_class::Step(int lev, int YN)
-{
+{
-  setpbh(BH_num, Porg0, Mass, BH_num_input);
+#ifdef USE_GPU
+  Step_MainPath_GPU(lev, YN);
+  return;
+#endif
+
+  setpbh(BH_num, Porg0, Mass, BH_num_input);
 
   double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
 
@@ -5796,7 +5858,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -5820,7 +5882,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5847,7 +5909,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
@@ -5871,7 +5933,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -5940,7 +6002,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       }
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -5950,7 +6012,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5962,7 +6024,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
     else // no time refinement levels and for all same time levels
     {
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
@@ -5972,7 +6034,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -6027,7 +6089,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       }
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,SynchList_pre,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -6037,7 +6099,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6051,7 +6113,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       if (myrank == 0)
         cout << "===: " << GH->Lt[lev - 1] << "," << GH->Lt[lev] + dT_lev << endl;
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry, sync_cache_restrict[lev]);
 #elif (RPB == 1)
       //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,Symmetry);
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
@@ -6061,7 +6123,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif
@@ -6102,7 +6164,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6115,7 +6177,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
     {
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif
@@ -6236,7 +6298,7 @@ for(int ilev = GH->levels-1;ilev>=lev;ilev--)
 for(int ilev=GH->levels-1;ilev>lev;ilev--)
     RestrictProlong(ilev,1,false,DG_List,DG_List,DG_List);
 #else
-  Parallel::Sync(GH->PatL[lev], DG_List, Symmetry);
+  Parallel::Sync_cached(GH->PatL[lev], DG_List, Symmetry, sync_cache_psi4[lev]);
 #endif
 
 #ifdef WithShell
@@ -6891,10 +6953,10 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
 {
   LastAnas += dT_lev;
 
-  if (LastAnas >= AnasTime)
+  if (LastAnas >= AnasTime)
-  {
+  {
-#ifdef Point_Psi4
+#ifdef Point_Psi4
-#error "not support parallel levels yet"
+#error "not support parallel levels yet"
     // Gam_ijk and R_ij have been calculated in Interp_Constraint()
     double SYM = 1, ANT = -1;
     for (int levh = lev; levh < GH->levels; levh++)
@@ -7238,9 +7300,9 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
 
 //================================================================================================
 
-void bssn_class::Constraint_Out()
+void bssn_class::Constraint_Out()
-{
+{
-  LastConsOut += dT * pow(0.5, Mymax(0, trfls));
+  LastConsOut += dT * pow(0.5, Mymax(0, trfls));
 
   if (LastConsOut >= AnasTime)
   // Constraint violation
@@ -7260,12 +7322,15 @@ void bssn_class::Constraint_Out()
           MyList<Block> *BP = Pp->data->blb;
           while (BP)
           {
-            Block *cg = BP->data;
+            Block *cg = BP->data;
-            if (myrank == cg->rank)
+            if (myrank == cg->rank)
-            {
+            {
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+#ifdef USE_GPU
-                                 cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+              gpu_rhs(CALLED_BY_CONSTRAINT_CONS_ONLY, myrank, RHS_PARA_CALLED_Constraint_Out);
-                                 cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
+#else
+              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                 cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+                                 cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
                                  cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                                  cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                  cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
@@ -7293,11 +7358,12 @@ void bssn_class::Constraint_Out()
                                  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_Ham->sgfn],
-                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->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],
+                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                 Symmetry, lev, ndeps, pre);
+                                 Symmetry, lev, ndeps, pre);
-            }
+#endif
+            }
             if (BP == Pp->data->ble)
               break;
             BP = BP->next;
@@ -7305,7 +7371,7 @@ void bssn_class::Constraint_Out()
           Pp = Pp->next;
         }
       }
-      Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry);
+      Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry, "bssn_class::Constraint_Out[level]");
     }
 #ifdef WithShell
     if (0) // if the constrait quantities can be reused from the step rhs calculation
@@ -7527,7 +7593,7 @@ void bssn_class::AH_Prepare_derivatives()
       }
       Pp = Pp->next;
     }
-    Parallel::Sync(GH->PatL[lev], AHDList, Symmetry);
+    Parallel::Sync(GH->PatL[lev], AHDList, Symmetry, "bssn_class::AH_Prepare_derivatives");
   }
 }
 
@@ -7763,12 +7829,15 @@ void bssn_class::Interp_Constraint(bool infg)
           MyList<Block> *BP = Pp->data->blb;
           while (BP)
           {
-            Block *cg = BP->data;
+            Block *cg = BP->data;
-            if (myrank == cg->rank)
+            if (myrank == cg->rank)
-            {
+            {
-              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+#ifdef USE_GPU
-                                 cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+              gpu_rhs(CALLED_BY_CONSTRAINT_CONS_ONLY, myrank, RHS_PARA_CALLED_Interp_Constraint);
-                                 cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
+#else
+              f_compute_rhs_bssn(cg->shape, TRK4, cg->X[0], cg->X[1], cg->X[2],
+                                 cg->fgfs[phi0->sgfn], cg->fgfs[trK0->sgfn],
+                                 cg->fgfs[gxx0->sgfn], cg->fgfs[gxy0->sgfn], cg->fgfs[gxz0->sgfn], 
                                  cg->fgfs[gyy0->sgfn], cg->fgfs[gyz0->sgfn], cg->fgfs[gzz0->sgfn],
                                  cg->fgfs[Axx0->sgfn], cg->fgfs[Axy0->sgfn], cg->fgfs[Axz0->sgfn], 
                                  cg->fgfs[Ayy0->sgfn], cg->fgfs[Ayz0->sgfn], cg->fgfs[Azz0->sgfn],
@@ -7796,11 +7865,12 @@ void bssn_class::Interp_Constraint(bool infg)
                                  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_Ham->sgfn],
-                                 cg->fgfs[Cons_Px->sgfn], cg->fgfs[Cons_Py->sgfn], cg->fgfs[Cons_Pz->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],
+                                 cg->fgfs[Cons_Gx->sgfn], cg->fgfs[Cons_Gy->sgfn], cg->fgfs[Cons_Gz->sgfn],
-                                 Symmetry, lev, ndeps, pre);
+                                 Symmetry, lev, ndeps, pre);
-            }
+#endif
+            }
             if (BP == Pp->data->ble)
               break;
             BP = BP->next;
@@ -7808,7 +7878,7 @@ void bssn_class::Interp_Constraint(bool infg)
           Pp = Pp->next;
         }
       }
-      Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry);
+      Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry, "bssn_class::Interp_Constraint[level]");
     }
 #ifdef WithShell
     if (0) // if the constrait quantities can be reused from the step rhs calculation
@@ -8066,7 +8136,7 @@ void bssn_class::Compute_Constraint()
         Pp = Pp->next;
       }
     }
-    Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry);
+    Parallel::Sync(GH->PatL[lev], ConstraintList, Symmetry, "bssn_class::Compute_Constraint[level]");
   }
   // prolong restrict constraint quantities
   for (lev = GH->levels - 1; lev > 0; lev--)
@@ -8379,12 +8449,18 @@ void bssn_class::Enforce_algcon(int lev, int fg)
 
 //================================================================================================
 
-bool bssn_class::check_Stdin_Abort() 
+bool bssn_class::check_Stdin_Abort() 
-{
+{
-
+    // Non-interactive launches (mpirun via Python/subprocess, batch jobs, redirected stdin)
-    fd_set readfds;
+    // should not probe stdin. Some MPI runtimes treat stdin as a managed channel and can
-
+    // fail when rank 0 polls/consumes it.
-    struct timeval timeout;
+    if (!isatty(STDIN_FILENO)) {
+        return false;
+    }
+
+    fd_set readfds;
+
+    struct timeval timeout;
 
     FD_ZERO(&readfds);
     FD_SET(STDIN_FILENO, &readfds);
@@ -8393,14 +8469,17 @@ bool bssn_class::check_Stdin_Abort()
     timeout.tv_sec = 0;
     timeout.tv_usec = 0;
 
-    int activity = select(STDIN_FILENO + 1, &readfds, nullptr, nullptr, &timeout);
+    int activity = select(STDIN_FILENO + 1, &readfds, nullptr, nullptr, &timeout);
-
+    if (activity <= 0) {
-    if (activity > 0 && FD_ISSET(STDIN_FILENO, &readfds)) {
+        return false;
-        string input_abort;
+    }
-        if (cin >> input_abort) {
+
-            if (input_abort == "stop") {
+    if (FD_ISSET(STDIN_FILENO, &readfds)) {
-                return true;
+        string input_abort;
-            }
+        if (cin >> input_abort) {
+            if (input_abort == "stop") {
+                return true;
+            }
         }
     }
 

AMSS_NCKU_source/bssn_class.h

@@ -128,8 +128,11 @@ public:
 
        Parallel::SyncCache *sync_cache_pre;  // per-level cache for predictor sync
        Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
-       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
+       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
-       Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
+       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;
@@ -169,16 +172,20 @@ public:
        
        bool check_Stdin_Abort(); 
 
-       virtual void Setup_Initial_Data_Cao();
+       virtual void Setup_Initial_Data_Cao();
-       virtual void Setup_Initial_Data_Lousto();
+       virtual void Setup_Initial_Data_Lousto();
-       virtual void Initialize();
+       virtual void Initialize();
-       virtual void Read_Ansorg();
+       virtual void Read_Ansorg();
-       virtual void Read_Pablo() {};
+       virtual void Read_Pablo() {};
-       virtual void Compute_Psi4(int lev);
+       void InvalidateSyncCaches();
-       virtual void Step(int lev, int YN);
+       virtual void Compute_Psi4(int lev);
-       virtual void Interp_Constraint(bool infg);
+       virtual void Step(int lev, int YN);
-       virtual void Constraint_Out();
+#ifdef USE_GPU
-       virtual void Compute_Constraint();
+       void Step_MainPath_GPU(int lev, int YN);
+#endif
+       virtual void Interp_Constraint(bool infg);
+       virtual void Constraint_Out();
+       virtual void Compute_Constraint();
 
 #ifdef With_AHF
 protected:

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

@@ -4,10 +4,8 @@
 #include "bssn_macro.h"
 #include "macrodef.fh"
 
-#define DEVICE_ID 0
+#define GRID_DIM 256
-// #define DEVICE_ID_BY_MPI_RANK
+#define BLOCK_DIM 128
-#define GRID_DIM 256
-#define BLOCK_DIM 128
 
 #define _FH2_(i, j, k) fh[(i) + (j) * _1D_SIZE[2] + (k) * _2D_SIZE[2]]
 #define _FH3_(i, j, k) fh[(i) + (j) * _1D_SIZE[3] + (k) * _2D_SIZE[3]]
@@ -65,9 +63,45 @@ int gpu_rhs(int calledby, int mpi_rank, int *ex, double &T,
             double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
             int &Symmetry, int &Lev, double &eps, int &co);
 
-int gpu_rhs_ss(RHS_SS_PARA);
+int gpu_rhs_ss(RHS_SS_PARA);
-
+
-/** Init GPU side data in GPUMeta. */
+int bssn_gpu_bind_process_device(int mpi_rank);
-// void init_fluid_meta_gpu(GPUMeta *gpu_meta);
+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);
 
 #endif

AMSS_NCKU_source/bssn_macro.h

@@ -65,9 +65,10 @@ if(TIME_COUNT_EACH_RANK == 1){\
      }\
 }
 
-//3---------------------GPU---------------------
+//3---------------------GPU---------------------
-#define CALLED_BY_STEP 0
+#define CALLED_BY_STEP 0
-#define CALLED_BY_CONSTRAINT 1
+#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.f90

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

AMSS_NCKU_source/bssn_rhs_c.C

@@ -39,7 +39,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
     // printf("nx=%d ny=%d nz=%d all=%d\n", nx, ny, nz, all);
 
     // temp variable
-    double gxx[all],gyy[all],gzz[all];
     double chix[all],chiy[all],chiz[all];
     double gxxx[all],gxyx[all],gxzx[all],gyyx[all],gyzx[all],gzzx[all];
     double gxxy[all],gxyy[all],gxzy[all],gyyy[all],gyzy[all],gzzy[all];
@@ -51,9 +50,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
     double Gamxx[all],Gamxy[all],Gamxz[all];
     double Gamyx[all],Gamyy[all],Gamyz[all];
     double Gamzx[all],Gamzy[all],Gamzz[all];
-    double Kx[all], Ky[all], Kz[all], div_beta[all], S[all];
+    double Kx[all], Ky[all], Kz[all], S[all];
     double f[all], fxx[all], fxy[all], fxz[all], fyy[all], fyz[all], fzz[all];
-    double Gamxa[all], Gamya[all], Gamza[all], alpn1[all], chin1[all];
+    double alpn1[all], chin1[all];
     double gupxx[all], gupxy[all], gupxz[all];
     double gupyy[all], gupyz[all], gupzz[all];
     double SSS[3] = { 1.0,  1.0,  1.0};
@@ -107,9 +106,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
             chin1[i] = chi[i] + 1.0;
-            gxx[i] = dxx[i] + 1.0;
-            gyy[i] = dyy[i] + 1.0;
-            gzz[i] = dzz[i] + 1.0;
         }
         // 9ms //
         fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev);
@@ -127,231 +123,196 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
         // 3ms //
         for(int i=0;i<all;i+=1){
-            div_beta[i] = betaxx[i] + betayy[i] + betazz[i];
+            const double divb = betaxx[i] + betayy[i] + betazz[i];
-            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - div_beta[i]); 
+            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - divb); 
-            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * gxx[i] * div_beta[i] + 
+            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * (dxx[i] + ONE) * divb + 
-                    TWO * (gxx[i] * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
+                    TWO * ((dxx[i] + ONE) * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
-            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * gyy[i] * div_beta[i] + 
+            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * (dyy[i] + ONE) * divb + 
-                    TWO * (gxy[i] * betaxy[i] + gyy[i] * betayy[i] + gyz[i] * betazy[i]);
+                    TWO * (gxy[i] * betaxy[i] + (dyy[i] + ONE) * betayy[i] + gyz[i] * betazy[i]);
-            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * gzz[i] * div_beta[i] + 
+            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * (dzz[i] + ONE) * divb + 
-                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + gzz[i] * betazz[i]);
+                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + (dzz[i] + ONE) * betazz[i]);
-            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * div_beta[i] + 
+            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * divb + 
-                        gxx[i] * betaxy[i] + gxz[i] * betazy[i] + gyy[i] * betayx[i] 
+                        (dxx[i] + ONE) * betaxy[i] + gxz[i] * betazy[i] + (dyy[i] + ONE) * betayx[i] 
                         + gyz[i] * betazx[i] - gxy[i] * betazz[i];        
-            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * div_beta[i] + 
+            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * divb + 
-                        gxy[i] * betaxz[i] + gyy[i] * betayz[i] + gxz[i] * betaxy[i] 
+                        gxy[i] * betaxz[i] + (dyy[i] + ONE) * betayz[i] + gxz[i] * betaxy[i] 
-                        + gzz[i] * betazy[i] - gyz[i] * betaxx[i];
+                        + (dzz[i] + ONE) * betazy[i] - gyz[i] * betaxx[i];
-            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * div_beta[i] + 
+            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * divb + 
-                        gxx[i] * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
+                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
-                        + gzz[i] * betazx[i] - gxz[i] * betayy[i];                  
+                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
         }
-        // 1ms //
+        // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
         for(int i=0;i<all;i+=1){
-            double det = gxx[i] * gyy[i] * gzz[i] + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] - 
+            double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
-                        gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];  
+                        gxz[i] * (dyy[i] + ONE) * gxz[i] - gxy[i] * gxy[i] * (dzz[i] + ONE) - (dxx[i] + ONE) * gyz[i] * gyz[i];
-            gupxx[i] = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
+            double lg_xx = ((dyy[i] + ONE) * (dzz[i] + ONE) - gyz[i] * gyz[i]) / det;
-            gupxy[i] = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
+            double lg_xy = -(gxy[i] * (dzz[i] + ONE) - gyz[i] * gxz[i]) / det;
-            gupxz[i] = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
+            double lg_xz = (gxy[i] * gyz[i] - (dyy[i] + ONE) * gxz[i]) / det;
-            gupyy[i] = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
+            double lg_yy = ((dxx[i] + ONE) * (dzz[i] + ONE) - gxz[i] * gxz[i]) / det;
-            gupyz[i] = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
+            double lg_yz = -((dxx[i] + ONE) * gyz[i] - gxy[i] * gxz[i]) / det;
-            gupzz[i] = (gxx[i] * gyy[i] - gxy[i] * gxy[i]) / det;   
+            double lg_zz = ((dxx[i] + ONE) * (dyy[i] + ONE) - gxy[i] * gxy[i]) / det;
-        }
+            gupxx[i] = lg_xx; gupxy[i] = lg_xy; gupxz[i] = lg_xz;
-        // 2.2ms //
+            gupyy[i] = lg_yy; gupyz[i] = lg_yz; gupzz[i] = lg_zz;
-        if(co==0){
+
-            for (int i=0;i<all;i+=1) {
+            if(co==0){
                 Gmx_Res[i] = Gamx[i] - (
-                    gupxx[i] * (gupxx[i]*gxxx[i] + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i]) +
+                    lg_xx * (lg_xx*gxxx[i] + lg_xy*gxyx[i] + lg_xz*gxzx[i]) +
-                    gupxy[i] * (gupxx[i]*gxyx[i] + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i]) +
+                    lg_xy * (lg_xx*gxyx[i] + lg_xy*gyyx[i] + lg_xz*gyzx[i]) +
-                    gupxz[i] * (gupxx[i]*gxzx[i] + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i]) +
+                    lg_xz * (lg_xx*gxzx[i] + lg_xy*gyzx[i] + lg_xz*gzzx[i]) +
-
+                    lg_xx * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
-                    gupxx[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
+                    lg_xy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
-                    gupxy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
+                    lg_xz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
-                    gupxz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
+                    lg_xx * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-
+                    lg_xy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    gupxx[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    lg_xz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                    gupxy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
-                    gupxz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
-
                 Gmy_Res[i] = Gamy[i] - (
-                    gupxx[i] * (gupxy[i]*gxxx[i] + gupyy[i]*gxyx[i] + gupyz[i]*gxzx[i]) +
+                    lg_xx * (lg_xy*gxxx[i] + lg_yy*gxyx[i] + lg_yz*gxzx[i]) +
-                    gupxy[i] * (gupxy[i]*gxyx[i] + gupyy[i]*gyyx[i] + gupyz[i]*gyzx[i]) +
+                    lg_xy * (lg_xy*gxyx[i] + lg_yy*gyyx[i] + lg_yz*gyzx[i]) +
-                    gupxz[i] * (gupxy[i]*gxzx[i] + gupyy[i]*gyzx[i] + gupyz[i]*gzzx[i]) +
+                    lg_xz * (lg_xy*gxzx[i] + lg_yy*gyzx[i] + lg_yz*gzzx[i]) +
-
+                    lg_xy * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
-                    gupxy[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
+                    lg_yy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
-                    gupyy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
+                    lg_yz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
-                    gupyz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
+                    lg_xy * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-
+                    lg_yy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    gupxy[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    lg_yz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                    gupyy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
-                    gupyz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
-
                 Gmz_Res[i] = Gamz[i] - (
-                    gupxx[i] * (gupxz[i]*gxxx[i] + gupyz[i]*gxyx[i] + gupzz[i]*gxzx[i]) +
+                    lg_xx * (lg_xz*gxxx[i] + lg_yz*gxyx[i] + lg_zz*gxzx[i]) +
-                    gupxy[i] * (gupxz[i]*gxyx[i] + gupyz[i]*gyyx[i] + gupzz[i]*gyzx[i]) +
+                    lg_xy * (lg_xz*gxyx[i] + lg_yz*gyyx[i] + lg_zz*gyzx[i]) +
-                    gupxz[i] * (gupxz[i]*gxzx[i] + gupyz[i]*gyzx[i] + gupzz[i]*gzzx[i]) +
+                    lg_xz * (lg_xz*gxzx[i] + lg_yz*gyzx[i] + lg_zz*gzzx[i]) +
-
+                    lg_xy * (lg_xz*gxxy[i] + lg_yz*gxyy[i] + lg_zz*gxzy[i]) +
-                    gupxy[i] * (gupxz[i]*gxxy[i] + gupyz[i]*gxyy[i] + gupzz[i]*gxzy[i]) +
+                    lg_yy * (lg_xz*gxyy[i] + lg_yz*gyyy[i] + lg_zz*gyzy[i]) +
-                    gupyy[i] * (gupxz[i]*gxyy[i] + gupyz[i]*gyyy[i] + gupzz[i]*gyzy[i]) +
+                    lg_yz * (lg_xz*gxzy[i] + lg_yz*gyzy[i] + lg_zz*gzzy[i]) +
-                    gupyz[i] * (gupxz[i]*gxzy[i] + gupyz[i]*gyzy[i] + gupzz[i]*gzzy[i]) +
+                    lg_xz * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-
+                    lg_yz * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    gupxz[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    lg_zz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                    gupyz[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
-                    gupzz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
             }
+
+            Gamxxx[i] = HALF * ( lg_xx*gxxx[i]
+                            + lg_xy*(TWO*gxyx[i] - gxxy[i])
+                            + lg_xz*(TWO*gxzx[i] - gxxz[i]) );
+            Gamyxx[i] = HALF * ( lg_xy*gxxx[i]
+                            + lg_yy*(TWO*gxyx[i] - gxxy[i])
+                            + lg_yz*(TWO*gxzx[i] - gxxz[i]) );
+            Gamzxx[i] = HALF * ( lg_xz*gxxx[i]
+                            + lg_yz*(TWO*gxyx[i] - gxxy[i])
+                            + lg_zz*(TWO*gxzx[i] - gxxz[i]) );
+            Gamxyy[i] = HALF * ( lg_xx*(TWO*gxyy[i] - gyyx[i])
+                            + lg_xy*gyyy[i]
+                            + lg_xz*(TWO*gyzy[i] - gyyz[i]) );
+            Gamyyy[i] = HALF * ( lg_xy*(TWO*gxyy[i] - gyyx[i])
+                            + lg_yy*gyyy[i]
+                            + lg_yz*(TWO*gyzy[i] - gyyz[i]) );
+            Gamzyy[i] = HALF * ( lg_xz*(TWO*gxyy[i] - gyyx[i])
+                            + lg_yz*gyyy[i]
+                            + lg_zz*(TWO*gyzy[i] - gyyz[i]) );
+            Gamxzz[i] = HALF * ( lg_xx*(TWO*gxzz[i] - gzzx[i])
+                            + lg_xy*(TWO*gyzz[i] - gzzy[i])
+                            + lg_xz*gzzz[i] );
+            Gamyzz[i] = HALF * ( lg_xy*(TWO*gxzz[i] - gzzx[i])
+                            + lg_yy*(TWO*gyzz[i] - gzzy[i])
+                            + lg_yz*gzzz[i] );
+            Gamzzz[i] = HALF * ( lg_xz*(TWO*gxzz[i] - gzzx[i])
+                            + lg_yz*(TWO*gyzz[i] - gzzy[i])
+                            + lg_zz*gzzz[i] );
+            Gamxxy[i] = HALF * ( lg_xx*gxxy[i]
+                            + lg_xy*gyyx[i]
+                            + lg_xz*(gxzy[i] + gyzx[i] - gxyz[i]) );
+            Gamyxy[i] = HALF * ( lg_xy*gxxy[i]
+                            + lg_yy*gyyx[i]
+                            + lg_yz*(gxzy[i] + gyzx[i] - gxyz[i]) );
+            Gamzxy[i] = HALF * ( lg_xz*gxxy[i]
+                            + lg_yz*gyyx[i]
+                            + lg_zz*(gxzy[i] + gyzx[i] - gxyz[i]) );
+            Gamxxz[i] = HALF * ( lg_xx*gxxz[i]
+                            + lg_xy*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + lg_xz*gzzx[i] );
+            Gamyxz[i] = HALF * ( lg_xy*gxxz[i]
+                            + lg_yy*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + lg_yz*gzzx[i] );
+            Gamzxz[i] = HALF * ( lg_xz*gxxz[i]
+                            + lg_yz*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + lg_zz*gzzx[i] );
+            Gamxyz[i] = HALF * ( lg_xx*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + lg_xy*gyyz[i]
+                            + lg_xz*gzzy[i] );
+            Gamyyz[i] = HALF * ( lg_xy*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + lg_yy*gyyz[i]
+                            + lg_yz*gzzy[i] );
+            Gamzyz[i] = HALF * ( lg_xz*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + lg_yz*gyyz[i]
+                            + lg_zz*gzzy[i] );
         }
-        // 5ms //
+        // Fused: A^{ij} raise-index + Gamma_rhs part 1 (2 loops -> 1)
         for (int i=0;i<all;i+=1) {
-
+            double axx = gupxx[i]*gupxx[i]*Axx[i]
-            Gamxxx[i] = HALF * ( gupxx[i]*gxxx[i]
-                            + gupxy[i]*(TWO*gxyx[i] - gxxy[i])
-                            + gupxz[i]*(TWO*gxzx[i] - gxxz[i]) );
-
-            Gamyxx[i] = HALF * ( gupxy[i]*gxxx[i]
-                            + gupyy[i]*(TWO*gxyx[i] - gxxy[i])
-                            + gupyz[i]*(TWO*gxzx[i] - gxxz[i]) );
-
-            Gamzxx[i] = HALF * ( gupxz[i]*gxxx[i]
-                            + gupyz[i]*(TWO*gxyx[i] - gxxy[i])
-                            + gupzz[i]*(TWO*gxzx[i] - gxxz[i]) );
-
-            Gamxyy[i] = HALF * ( gupxx[i]*(TWO*gxyy[i] - gyyx[i])
-                            + gupxy[i]*gyyy[i]
-                            + gupxz[i]*(TWO*gyzy[i] - gyyz[i]) );
-
-            Gamyyy[i] = HALF * ( gupxy[i]*(TWO*gxyy[i] - gyyx[i])
-                            + gupyy[i]*gyyy[i]
-                            + gupyz[i]*(TWO*gyzy[i] - gyyz[i]) );
-
-            Gamzyy[i] = HALF * ( gupxz[i]*(TWO*gxyy[i] - gyyx[i])
-                            + gupyz[i]*gyyy[i]
-                            + gupzz[i]*(TWO*gyzy[i] - gyyz[i]) );
-
-            Gamxzz[i] = HALF * ( gupxx[i]*(TWO*gxzz[i] - gzzx[i])
-                            + gupxy[i]*(TWO*gyzz[i] - gzzy[i])
-                            + gupxz[i]*gzzz[i] );
-
-            Gamyzz[i] = HALF * ( gupxy[i]*(TWO*gxzz[i] - gzzx[i])
-                            + gupyy[i]*(TWO*gyzz[i] - gzzy[i])
-                            + gupyz[i]*gzzz[i] );
-
-            Gamzzz[i] = HALF * ( gupxz[i]*(TWO*gxzz[i] - gzzx[i])
-                            + gupyz[i]*(TWO*gyzz[i] - gzzy[i])
-                            + gupzz[i]*gzzz[i] );
-
-            Gamxxy[i] = HALF * ( gupxx[i]*gxxy[i]
-                            + gupxy[i]*gyyx[i]
-                            + gupxz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
-
-            Gamyxy[i] = HALF * ( gupxy[i]*gxxy[i]
-                            + gupyy[i]*gyyx[i]
-                            + gupyz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
-
-            Gamzxy[i] = HALF * ( gupxz[i]*gxxy[i]
-                            + gupyz[i]*gyyx[i]
-                            + gupzz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
-
-            Gamxxz[i] = HALF * ( gupxx[i]*gxxz[i]
-                            + gupxy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + gupxz[i]*gzzx[i] );
-
-            Gamyxz[i] = HALF * ( gupxy[i]*gxxz[i]
-                            + gupyy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + gupyz[i]*gzzx[i] );
-
-            Gamzxz[i] = HALF * ( gupxz[i]*gxxz[i]
-                            + gupyz[i]*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + gupzz[i]*gzzx[i] );
-
-            Gamxyz[i] = HALF * ( gupxx[i]*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + gupxy[i]*gyyz[i]
-                            + gupxz[i]*gzzy[i] );
-
-            Gamyyz[i] = HALF * ( gupxy[i]*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + gupyy[i]*gyyz[i]
-                            + gupyz[i]*gzzy[i] );
-
-            Gamzyz[i] = HALF * ( gupxz[i]*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + gupyz[i]*gyyz[i]
-                            + gupzz[i]*gzzy[i] );
-
-        }
-        // 1.8ms //
-        for (int i=0;i<all;i+=1) {
-
-            Rxx[i] = gupxx[i]*gupxx[i]*Axx[i]
                 + gupxy[i]*gupxy[i]*Ayy[i]
                 + gupxz[i]*gupxz[i]*Azz[i]
                 + TWO * ( gupxx[i]*gupxy[i]*Axy[i]
                         + gupxx[i]*gupxz[i]*Axz[i]
                         + gupxy[i]*gupxz[i]*Ayz[i] );
-
+            double ayy = gupxy[i]*gupxy[i]*Axx[i]
-            Ryy[i] = gupxy[i]*gupxy[i]*Axx[i]
                 + gupyy[i]*gupyy[i]*Ayy[i]
                 + gupyz[i]*gupyz[i]*Azz[i]
                 + TWO * ( gupxy[i]*gupyy[i]*Axy[i]
                         + gupxy[i]*gupyz[i]*Axz[i]
                         + gupyy[i]*gupyz[i]*Ayz[i] );
-
+            double azz = gupxz[i]*gupxz[i]*Axx[i]
-            Rzz[i] = gupxz[i]*gupxz[i]*Axx[i]
                 + gupyz[i]*gupyz[i]*Ayy[i]
                 + gupzz[i]*gupzz[i]*Azz[i]
                 + TWO * ( gupxz[i]*gupyz[i]*Axy[i]
                         + gupxz[i]*gupzz[i]*Axz[i]
                         + gupyz[i]*gupzz[i]*Ayz[i] );
-
+            double axy = gupxx[i]*gupxy[i]*Axx[i]
-            Rxy[i] = gupxx[i]*gupxy[i]*Axx[i]
                 + gupxy[i]*gupyy[i]*Ayy[i]
                 + gupxz[i]*gupyz[i]*Azz[i]
                 + ( gupxx[i]*gupyy[i] + gupxy[i]*gupxy[i] ) * Axy[i]
                 + ( gupxx[i]*gupyz[i] + gupxz[i]*gupxy[i] ) * Axz[i]
                 + ( gupxy[i]*gupyz[i] + gupxz[i]*gupyy[i] ) * Ayz[i];
-
+            double axz = gupxx[i]*gupxz[i]*Axx[i]
-            Rxz[i] = gupxx[i]*gupxz[i]*Axx[i]
                 + gupxy[i]*gupyz[i]*Ayy[i]
                 + gupxz[i]*gupzz[i]*Azz[i]
                 + ( gupxx[i]*gupyz[i] + gupxy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxx[i]*gupzz[i] + gupxz[i]*gupxz[i] ) * Axz[i]
                 + ( gupxy[i]*gupzz[i] + gupxz[i]*gupyz[i] ) * Ayz[i];
-
+            double ayz = gupxy[i]*gupxz[i]*Axx[i]
-            Ryz[i] = gupxy[i]*gupxz[i]*Axx[i]
                 + gupyy[i]*gupyz[i]*Ayy[i]
                 + gupyz[i]*gupzz[i]*Azz[i]
                 + ( 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;
-        // 4ms //
+            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
-        for(int i=0;i<all;i+=1){
-            Gamx_rhs[i] = - TWO * (   Lapx[i] * Rxx[i] +   Lapy[i] * Rxy[i] +   Lapz[i] * Rxz[i] ) + 
-                TWO * alpn1[i] * (                                                
-                -F3o2/chin1[i] * (   chix[i] * Rxx[i] +   chiy[i] * Rxy[i] +   chiz[i] * Rxz[i] ) - 
-                    gupxx[i] * (   F2o3 * Kx[i]  +  EIGHT * PI * Sx[i]            ) - 
-                    gupxy[i] * (   F2o3 * Ky[i]  +  EIGHT * PI * Sy[i]            ) - 
-                    gupxz[i] * (   F2o3 * Kz[i]  +  EIGHT * PI * Sz[i]            ) + 
-                                Gamxxx[i] * Rxx[i] + Gamxyy[i] * Ryy[i] + Gamxzz[i] * Rzz[i]   + 
-                        TWO * ( Gamxxy[i] * Rxy[i] + Gamxxz[i] * Rxz[i] + Gamxyz[i] * Ryz[i] ) );
 
-            Gamy_rhs[i] = -TWO * ( Lapx[i]*Rxy[i] + Lapy[i]*Ryy[i] + Lapz[i]*Ryz[i] )
+            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 ) -
+                    gupxx[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] ) -
+                    gupxy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] ) -
+                    gupxz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] ) +
+                                Gamxxx[i]*axx + Gamxyy[i]*ayy + Gamxzz[i]*azz +
+                        TWO * ( Gamxxy[i]*axy + Gamxxz[i]*axz + Gamxyz[i]*ayz ) );
+
+            Gamy_rhs[i] = -TWO * ( Lapx[i]*axy + Lapy[i]*ayy + Lapz[i]*ayz )
                         +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*Rxy[i] + chiy[i]*Ryy[i] + chiz[i]*Ryz[i] )
+                            -F3o2/chin1[i] * ( chix[i]*axy + chiy[i]*ayy + chiz[i]*ayz )
                             - gupxy[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                             - gupyy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                             - gupyz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamyxx[i]*Rxx[i] + Gamyyy[i]*Ryy[i] + Gamyzz[i]*Rzz[i]
+                            + Gamyxx[i]*axx + Gamyyy[i]*ayy + Gamyzz[i]*azz
-                            + TWO * ( Gamyxy[i]*Rxy[i] + Gamyxz[i]*Rxz[i] + Gamyyz[i]*Ryz[i] )
+                            + TWO * ( Gamyxy[i]*axy + Gamyxz[i]*axz + Gamyyz[i]*ayz )
                         );
 
-            Gamz_rhs[i] = -TWO * ( Lapx[i]*Rxz[i] + Lapy[i]*Ryz[i] + Lapz[i]*Rzz[i] )
+            Gamz_rhs[i] = -TWO * ( Lapx[i]*axz + Lapy[i]*ayz + Lapz[i]*azz )
                         +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*Rxz[i] + chiy[i]*Ryz[i] + chiz[i]*Rzz[i] )
+                            -F3o2/chin1[i] * ( chix[i]*axz + chiy[i]*ayz + chiz[i]*azz )
                             - gupxz[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                             - gupyz[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                             - gupzz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamzxx[i]*Rxx[i] + Gamzyy[i]*Ryy[i] + Gamzzz[i]*Rzz[i]
+                            + Gamzxx[i]*axx + Gamzyy[i]*ayy + Gamzzz[i]*azz
-                            + TWO * ( Gamzxy[i]*Rxy[i] + Gamzxz[i]*Rxz[i] + Gamzyz[i]*Ryz[i] )
+                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                         );
         }
         // 22.3ms //
@@ -365,65 +326,63 @@ int f_compute_rhs_bssn(int *ex, double &T,
         fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev);
         fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev);
 
-        // 3.5ms //
+        // Fused: fxx/Gamxa + Gamma_rhs part 2 (2 loops -> 1)
         for(int i=0;i<all;i+=1){
-            fxx[i] = gxxx[i] + gxyy[i] + gxzz[i];
+            const double divb = betaxx[i] + betayy[i] + betazz[i];
-            fxy[i] = gxyx[i] + gyyy[i] + gyzz[i];
+            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
-            fxz[i] = gxzx[i] + gyzy[i] + gzzz[i];
+            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
-            Gamxa[i] = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[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] );
-
+            double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
-            Gamya[i] = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
                     + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
-
+            double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
-            Gamza[i] = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
                     + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
-        }
-        // 3.9ms //
-        for(int i=0;i<all;i+=1){
             Gamx_rhs[i] = Gamx_rhs[i]
-                        + F2o3 * Gamxa[i] * div_beta[i]
+                        + F2o3 * gxa * divb
-                        - Gamxa[i] * betaxx[i] - Gamya[i] * betaxy[i] - Gamza[i] * betaxz[i]
+                        - gxa * betaxx[i] - gya * betaxy[i] - gza * betaxz[i]
-                        + F1o3 * ( gupxx[i] * fxx[i] + gupxy[i] * fxy[i] + gupxz[i] * fxz[i] )
+                        + F1o3 * ( gupxx[i] * lfxx + gupxy[i] * lfxy + gupxz[i] * lfxz )
                         + gupxx[i] * gxxx[i] + gupyy[i] * gyyx[i] + gupzz[i] * gzzx[i]
                         + TWO * ( gupxy[i] * gxyx[i] + gupxz[i] * gxzx[i] + gupyz[i] * gyzx[i] );
 
             Gamy_rhs[i] = Gamy_rhs[i]
-                        + F2o3 * Gamya[i] * div_beta[i]
+                        + F2o3 * gya * divb
-                        - Gamxa[i] * betayx[i] - Gamya[i] * betayy[i] - Gamza[i] * betayz[i]
+                        - gxa * betayx[i] - gya * betayy[i] - gza * betayz[i]
-                        + F1o3 * ( gupxy[i] * fxx[i] + gupyy[i] * fxy[i] + gupyz[i] * fxz[i] )
+                        + F1o3 * ( gupxy[i] * lfxx + gupyy[i] * lfxy + gupyz[i] * lfxz )
                         + gupxx[i] * gxxy[i] + gupyy[i] * gyyy[i] + gupzz[i] * gzzy[i]
                         + TWO * ( gupxy[i] * gxyy[i] + gupxz[i] * gxzy[i] + gupyz[i] * gyzy[i] );
 
             Gamz_rhs[i] = Gamz_rhs[i]
-                        + F2o3 * Gamza[i] * div_beta[i]
+                        + F2o3 * gza * divb
-                        - Gamxa[i] * betazx[i] - Gamya[i] * betazy[i] - Gamza[i] * betazz[i]
+                        - gxa * betazx[i] - gya * betazy[i] - gza * betazz[i]
-                        + F1o3 * ( gupxz[i] * fxx[i] + gupyz[i] * fxy[i] + gupzz[i] * fxz[i] )
+                        + F1o3 * ( gupxz[i] * lfxx + gupyz[i] * lfxy + gupzz[i] * lfxz )
                         + gupxx[i] * gxxz[i] + gupyy[i] * gyyz[i] + gupzz[i] * gzzz[i]
                         + TWO * ( gupxy[i] * gxyz[i] + gupxz[i] * gxzz[i] + gupyz[i] * gyzz[i] );
         }
         // 4.4ms //
         for (int i=0;i<all;i+=1) {
-            gxxx[i] = gxx[i]*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
+            gxxx[i] = (dxx[i] + ONE)*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
-            gxyx[i] = gxx[i]*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
+            gxyx[i] = (dxx[i] + ONE)*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
-            gxzx[i] = gxx[i]*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
+            gxzx[i] = (dxx[i] + ONE)*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
-            gyyx[i] = gxx[i]*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
+            gyyx[i] = (dxx[i] + ONE)*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
-            gyzx[i] = gxx[i]*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
+            gyzx[i] = (dxx[i] + ONE)*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
-            gzzx[i] = gxx[i]*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
+            gzzx[i] = (dxx[i] + ONE)*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
 
-            gxxy[i] = gxy[i]*Gamxxx[i] + gyy[i]*Gamyxx[i] + gyz[i]*Gamzxx[i];
+            gxxy[i] = gxy[i]*Gamxxx[i] + (dyy[i] + ONE)*Gamyxx[i] + gyz[i]*Gamzxx[i];
-            gxyy[i] = gxy[i]*Gamxxy[i] + gyy[i]*Gamyxy[i] + gyz[i]*Gamzxy[i];
+            gxyy[i] = gxy[i]*Gamxxy[i] + (dyy[i] + ONE)*Gamyxy[i] + gyz[i]*Gamzxy[i];
-            gxzy[i] = gxy[i]*Gamxxz[i] + gyy[i]*Gamyxz[i] + gyz[i]*Gamzxz[i];
+            gxzy[i] = gxy[i]*Gamxxz[i] + (dyy[i] + ONE)*Gamyxz[i] + gyz[i]*Gamzxz[i];
-            gyyy[i] = gxy[i]*Gamxyy[i] + gyy[i]*Gamyyy[i] + gyz[i]*Gamzyy[i];
+            gyyy[i] = gxy[i]*Gamxyy[i] + (dyy[i] + ONE)*Gamyyy[i] + gyz[i]*Gamzyy[i];
-            gyzy[i] = gxy[i]*Gamxyz[i] + gyy[i]*Gamyyz[i] + gyz[i]*Gamzyz[i];
+            gyzy[i] = gxy[i]*Gamxyz[i] + (dyy[i] + ONE)*Gamyyz[i] + gyz[i]*Gamzyz[i];
-            gzzy[i] = gxy[i]*Gamxzz[i] + gyy[i]*Gamyzz[i] + gyz[i]*Gamzzz[i];
+            gzzy[i] = gxy[i]*Gamxzz[i] + (dyy[i] + ONE)*Gamyzz[i] + gyz[i]*Gamzzz[i];
 
-            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + gzz[i]*Gamzxx[i];
+            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + (dzz[i] + ONE)*Gamzxx[i];
-            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + gzz[i]*Gamzxy[i];
+            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + (dzz[i] + ONE)*Gamzxy[i];
-            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + gzz[i]*Gamzxz[i];
+            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + (dzz[i] + ONE)*Gamzxz[i];
-            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + gzz[i]*Gamzyy[i];
+            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + (dzz[i] + ONE)*Gamzyy[i];
-            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + gzz[i]*Gamzyz[i];
+            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + (dzz[i] + ONE)*Gamzyz[i];
-            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + gzz[i]*Gamzzz[i];
+            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + (dzz[i] + ONE)*Gamzzz[i];
         }
         // 22.2ms //
             fdderivs(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
@@ -471,10 +430,17 @@ int f_compute_rhs_bssn(int *ex, double &T,
         // 14ms //
         /* 假设 all = ex1*ex2*ex3，所有量都是 length=all 的 double 数组（已按同一扁平化规则排布） */
         for (int i = 0; i < all; i += 1) {
+            const 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] );
+            const double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
+                            + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
+            const double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
+                            + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
+
             Rxx[i] =
                 -HALF * Rxx[i]
-                + gxx[i] * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
+                + (dxx[i] + ONE) * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
-                + Gamxa[i] * gxxx[i] + Gamya[i] * gxyx[i] + Gamza[i] * gxzx[i]
+                + gxa * gxxx[i] + gya * gxyx[i] + gza * gxzx[i]
                 + gupxx[i] * (
                     TWO * (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxyx[i] + Gamzxx[i] * gxzx[i]) +
                         (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxxy[i] + Gamzxx[i] * gxxz[i])
@@ -508,8 +474,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
             Ryy[i] =
                 -HALF * Ryy[i]
-                + gxy[i] * Gamxy[i] + gyy[i] * Gamyy[i] + gyz[i] * Gamzy[i]
+                + gxy[i] * Gamxy[i] + (dyy[i] + ONE) * Gamyy[i] + gyz[i] * Gamzy[i]
-                + Gamxa[i] * gxyy[i] + Gamya[i] * gyyy[i] + Gamza[i] * gyzy[i]
+                + gxa * gxyy[i] + gya * gyyy[i] + gza * gyzy[i]
                 + gupxx[i] * (
                     TWO * (Gamxxy[i] * gxxy[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxzy[i]) +
                         (Gamxxy[i] * gxyx[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxyz[i])
@@ -543,8 +509,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
             Rzz[i] =
                 -HALF * Rzz[i]
-                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + gzz[i] * Gamzz[i]
+                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + (dzz[i] + ONE) * Gamzz[i]
-                + Gamxa[i] * gxzz[i] + Gamya[i] * gyzz[i] + Gamza[i] * gzzz[i]
+                + gxa * gxzz[i] + gya * gyzz[i] + gza * gzzz[i]
                 + gupxx[i] * (
                     TWO * (Gamxxz[i] * gxxz[i] + Gamyxz[i] * gxyz[i] + Gamzxz[i] * gxzz[i]) +
                         (Gamxxz[i] * gxzx[i] + Gamyxz[i] * gxzy[i] + Gamzxz[i] * gxzz[i])
@@ -579,10 +545,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Rxy[i] =
                 HALF * (
                     -Rxy[i]
-                    + gxx[i] * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
+                    + (dxx[i] + ONE) * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
-                    + gxy[i] * Gamxx[i] + gyy[i] * Gamyx[i] + gyz[i] * Gamzx[i]
+                    + gxy[i] * Gamxx[i] + (dyy[i] + ONE) * Gamyx[i] + gyz[i] * Gamzx[i]
-                    + Gamxa[i] * gxyx[i] + Gamya[i] * gyyx[i] + Gamza[i] * gyzx[i]
+                    + gxa * gxyx[i] + gya * gyyx[i] + gza * gyzx[i]
-                    + Gamxa[i] * gxxy[i] + Gamya[i] * gxyy[i] + Gamza[i] * gxzy[i]
+                    + gxa * gxxy[i] + gya * gxyy[i] + gza * gxzy[i]
                 )
                 + gupxx[i] * (
                     Gamxxx[i] * gxxy[i] + Gamyxx[i] * gxyy[i] + Gamzxx[i] * gxzy[i]
@@ -627,10 +593,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Rxz[i] =
                 HALF * (
                     -Rxz[i]
-                    + gxx[i] * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
+                    + (dxx[i] + ONE) * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
-                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + gzz[i] * Gamzx[i]
+                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + (dzz[i] + ONE) * Gamzx[i]
-                    + Gamxa[i] * gxzx[i] + Gamya[i] * gyzx[i] + Gamza[i] * gzzx[i]
+                    + gxa * gxzx[i] + gya * gyzx[i] + gza * gzzx[i]
-                    + Gamxa[i] * gxxz[i] + Gamya[i] * gxyz[i] + Gamza[i] * gxzz[i]
+                    + gxa * gxxz[i] + gya * gxyz[i] + gza * gxzz[i]
                 )
                 + gupxx[i] * (
                     Gamxxx[i] * gxxz[i] + Gamyxx[i] * gxyz[i] + Gamzxx[i] * gxzz[i]
@@ -675,10 +641,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Ryz[i] =
                 HALF * (
                     -Ryz[i]
-                    + gxy[i] * Gamxz[i] + gyy[i] * Gamyz[i] + gyz[i] * Gamzz[i]
+                    + gxy[i] * Gamxz[i] + (dyy[i] + ONE) * Gamyz[i] + gyz[i] * Gamzz[i]
-                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + gzz[i] * Gamzy[i]
+                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + (dzz[i] + ONE) * Gamzy[i]
-                    + Gamxa[i] * gxzy[i] + Gamya[i] * gyzy[i] + Gamza[i] * gzzy[i]
+                    + gxa * gxzy[i] + gya * gyzy[i] + gza * gzzy[i]
-                    + Gamxa[i] * gxyz[i] + Gamya[i] * gyyz[i] + Gamza[i] * gyzz[i]
+                    + gxa * gxyz[i] + gya * gyyz[i] + gza * gyzz[i]
                 )
                 + gupxx[i] * (
                     Gamxxy[i] * gxxz[i] + Gamyxy[i] * gxyz[i] + Gamzxy[i] * gxzz[i]
@@ -739,9 +705,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
                 + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
                 + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + gxx[i] * f[i] ) / (chin1[i] * TWO);
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + gyy[i] * f[i] ) / (chin1[i] * TWO);
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + gzz[i] * f[i] ) / (chin1[i] * TWO);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
 
             Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
             Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
@@ -760,17 +726,17 @@ int f_compute_rhs_bssn(int *ex, double &T,
             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]) / chin1[i]) - gxx[i] * gxxx[i] ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - gxx[i] * gxxy[i] ) * 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           - gxx[i] * gxxz[i] ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - gyy[i] * gxxx[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - gyy[i] * gxxy[i] ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - gyy[i] * gxxz[i] ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - gzz[i] * gxxx[i] ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - gzz[i] * gxxy[i] ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - gzz[i] * gxxz[i] ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
 
             Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
             Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
@@ -792,14 +758,13 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fxy[i] = fxy[i] - Gamxxy[i] * Lapx[i] - Gamyxy[i] * Lapy[i] - Gamzxy[i] * Lapz[i];
             fxz[i] = fxz[i] - Gamxxz[i] * Lapx[i] - Gamyxz[i] * Lapy[i] - Gamzxz[i] * Lapz[i];
             fyz[i] = fyz[i] - Gamxyz[i] * Lapx[i] - Gamyyz[i] * Lapy[i] - Gamzyz[i] * Lapz[i];
-        }
+
-        // 1ms //
-        for (int i=0;i<all;i+=1) {
             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] );
         }
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
+            const double divb = betaxx[i] + betayy[i] + betazz[i];
 
             S[i] = chin1[i] * (
                     gupxx[i] * Sxx[i] + gupyy[i] * Syy[i] + gupzz[i] * Szz[i]
@@ -850,23 +815,20 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + (alpn1[i] / chin1[i]) * f[i]
             );
 
-            fxx[i] = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
+            double l_fxx = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
-            fxy[i] = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
+            double l_fxy = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
-            fxz[i] = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
+            double l_fxz = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
-            fyy[i] = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
+            double l_fyy = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
-            fyz[i] = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
+            double l_fyz = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
-            fzz[i] = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
+            double l_fzz = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
-        }
-        // 8ms //
-        for (int i=0;i<all;i+=1) {
 
             /* Aij_rhs = fij - gij * f */
-            Axx_rhs[i] = fxx[i] - gxx[i] * f[i];
+            Axx_rhs[i] = l_fxx - (dxx[i] + ONE) * f[i];
-            Ayy_rhs[i] = fyy[i] - gyy[i] * f[i];
+            Ayy_rhs[i] = l_fyy - (dyy[i] + ONE) * f[i];
-            Azz_rhs[i] = fzz[i] - gzz[i] * f[i];
+            Azz_rhs[i] = l_fzz - (dzz[i] + ONE) * f[i];
-            Axy_rhs[i] = fxy[i] - gxy[i] * f[i];
+            Axy_rhs[i] = l_fxy - gxy[i] * f[i];
-            Axz_rhs[i] = fxz[i] - gxz[i] * f[i];
+            Axz_rhs[i] = l_fxz - gxz[i] * f[i];
-            Ayz_rhs[i] = fyz[i] - gyz[i] * f[i];
+            Ayz_rhs[i] = l_fyz - gyz[i] * f[i];
 
             /* Now: store A_il A^l_j into fij: */
             fxx[i] =
@@ -928,19 +890,19 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 f[i] * Axx_rhs[i]
                 + alpn1[i] * ( trK[i] * Axx[i] - TWO * fxx[i] )
                 + TWO * ( Axx[i] * betaxx[i] + Axy[i] * betayx[i] + Axz[i] * betazx[i] )
-                - F2o3 * Axx[i] * div_beta[i];
+                - F2o3 * Axx[i] * divb;
 
             Ayy_rhs[i] =
                 f[i] * Ayy_rhs[i]
                 + alpn1[i] * ( trK[i] * Ayy[i] - TWO * fyy[i] )
                 + TWO * ( Axy[i] * betaxy[i] + Ayy[i] * betayy[i] + Ayz[i] * betazy[i] )
-                - F2o3 * Ayy[i] * div_beta[i];
+                - F2o3 * Ayy[i] * divb;
 
             Azz_rhs[i] =
                 f[i] * Azz_rhs[i]
                 + alpn1[i] * ( trK[i] * Azz[i] - TWO * fzz[i] )
                 + TWO * ( Axz[i] * betaxz[i] + Ayz[i] * betayz[i] + Azz[i] * betazz[i] )
-                - F2o3 * Azz[i] * div_beta[i];
+                - F2o3 * Azz[i] * divb;
 
             Axy_rhs[i] =
                 f[i] * Axy_rhs[i]
@@ -949,7 +911,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Axz[i] * betazy[i]
                 + Ayy[i] * betayx[i]
                 + Ayz[i] * betazx[i]
-                + F1o3 * Axy[i] * div_beta[i]
+                + F1o3 * Axy[i] * divb
                 - Axy[i] * betazz[i];
 
             Ayz_rhs[i] =
@@ -959,7 +921,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Ayy[i] * betayz[i]
                 + Axz[i] * betaxy[i]
                 + Azz[i] * betazy[i]
-                + F1o3 * Ayz[i] * div_beta[i]
+                + F1o3 * Ayz[i] * divb
                 - Ayz[i] * betaxx[i];
 
             Axz_rhs[i] =
@@ -969,7 +931,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Axy[i] * betayz[i]
                 + Ayz[i] * betayx[i]
                 + Azz[i] * betazx[i]
-                + F1o3 * Axz[i] * div_beta[i]
+                + F1o3 * Axz[i] * divb
                 - Axz[i] * betayy[i];
 
             /* Compute trace of S_ij */
@@ -1060,9 +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];
@@ -1078,9 +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];
@@ -1100,58 +1076,31 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #endif
         }
-        // 26ms //
+        // advection + KO dissipation with shared symmetry buffer
-        lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS);
+        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA);
+        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA);
+        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS);
+        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA);
+        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA);
+        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        // 20ms //
-        if(eps>0){
-            kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps);
-            kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps);
-            kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps);
-            kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps);
-            kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps);
-            kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps);
-            kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps);
-        }
         // 2ms //
         if(co==0){
             for (int i=0;i<all;i+=1) {
@@ -1204,59 +1153,59 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
             fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
             fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
-        }
+            // 7ms //
-        // 7ms //
+            for (int i=0;i<all;i+=1) {
-        for (int i=0;i<all;i+=1) {
+                gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
-            gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
+                                      + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
-                                  + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
+                gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-            gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                      + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
-                                  + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
+                gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-            gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                      + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
-                                  + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
+                gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
-            gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
+                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
-                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
+                gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
-            gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
+                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
-                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
+                gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
-            gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
+                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
-                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
+                gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-            gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                      + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
-                                  + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
+                gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
-            gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
+                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
-                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
+                gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-            gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
-                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
+                gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
-            gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
+                                      + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
-                                  + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
+                gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-            gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                      + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
-                                  + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
+                gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
-            gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
+                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
-                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
+                gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-            gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                      + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
-                                  + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
+                gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-            gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                      + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
-                                  + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
+                gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
-            gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
+                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
-                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
+                gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-            gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                      + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
-                                  + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
+                gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
-            gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
+                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
-                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
+                gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
-            gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
+                                      + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
-                                  + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
 
-            movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
+                movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
-                        + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
+                            + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
-                        + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
+                            + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
-            movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
+                movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
-                        + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
+                            + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
-                        + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
+                            + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
-            movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
+                movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
-                        + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
+                            + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
-                        + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
+                            + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
 
-            movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
+                movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
-            movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
+                movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
-            movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+                movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+            }
         }
 
 

AMSS_NCKU_source/bssn_rhs_cuda.h

@@ -1,36 +0,0 @@
-#ifndef BSSN_RHS_CUDA_H
-#define BSSN_RHS_CUDA_H
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-int f_compute_rhs_bssn(int *ex, double &T,
-                       double *X, double *Y, double *Z,
-                       double *chi, double *trK,
-                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
-                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
-                       double *Gamx, double *Gamy, double *Gamz,
-                       double *Lap, double *betax, double *betay, double *betaz,
-                       double *dtSfx, double *dtSfy, double *dtSfz,
-                       double *chi_rhs, double *trK_rhs,
-                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
-                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
-                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
-                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
-                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
-                       double *rho, double *Sx, double *Sy, double *Sz,
-                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
-                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
-                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
-                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
-                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
-                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
-                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
-                       int &Symmetry, int &Lev, double &eps, int &co);
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif

AMSS_NCKU_source/cgh.C

@@ -23,10 +23,14 @@ using namespace std;
 #include <mpi.h>
 
 #include "macrodef.h"
-#include "misc.h"
+#include "misc.h"
-#include "cgh.h"
+#include "cgh.h"
-#include "Parallel.h"
+#include "Parallel.h"
-#include "parameters.h"
+#include "parameters.h"
+#ifdef USE_GPU
+#include "bssn_gpu.h"
+#include "bssn_cuda_ops.h"
+#endif
 
 //================================================================================================
 
@@ -881,13 +885,20 @@ void cgh::recompose_cgh(int nprocs, bool *lev_flag,
       tmPat = construct_patchlist(lev, Symmetry);
       // tmPat construction completes
       Parallel::distribute(tmPat, nprocs, ingfs, fngfs, false);
-      //    checkPatchList(tmPat,true);
+      //    checkPatchList(tmPat,true);
-      bool CC = (lev > trfls);
+      bool CC = (lev > trfls);
-      Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
+      Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
-
+
-      Parallel::KillBlocks(PatL[lev]);
+#ifdef USE_GPU
-      PatL[lev]->destroyList();
+      bssn_gpu_clear_cached_device_buffers();
-      PatL[lev] = tmPat;
+      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;
 #if (RPB == 1)
       Parallel::destroypsuList_bam(bdsul[lev]);
       Parallel::destroypsuList_bam(rsul[lev]);
@@ -910,13 +921,20 @@ void cgh::recompose_cgh(int nprocs, bool *lev_flag,
       tmPat = construct_patchlist(lev, Symmetry);
       // tmPat construction completes
       Parallel::distribute(tmPat, end_rank[lev] - start_rank[lev] + 1, ingfs, fngfs, false, start_rank[lev], end_rank[lev]);
-      //    checkPatchList(tmPat,true);
+      //    checkPatchList(tmPat,true);
-      bool CC = (lev > trfls);
+      bool CC = (lev > trfls);
-      Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
+      Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
-
+
-      Parallel::KillBlocks(PatL[lev]);
+#ifdef USE_GPU
-      PatL[lev]->destroyList();
+      bssn_gpu_clear_cached_device_buffers();
-      PatL[lev] = tmPat;
+      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;
 #if (RPB == 1)
 #error "not support yet"
 #endif
@@ -1518,13 +1536,20 @@ void cgh::recompose_cgh_Onelevel(int nprocs, int lev,
   tmPat = construct_patchlist(lev, Symmetry);
   // tmPat construction completes
   Parallel::distribute(tmPat, nprocs, ingfs, fngfs, false);
-  //    checkPatchList(tmPat,true);
+  //    checkPatchList(tmPat,true);
-  bool CC = (lev > trfls);
+  bool CC = (lev > trfls);
-  Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
+  Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
-
+
-  Parallel::KillBlocks(PatL[lev]);
+#ifdef USE_GPU
-  PatL[lev]->destroyList();
+  bssn_gpu_clear_cached_device_buffers();
-  PatL[lev] = tmPat;
+  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;
 }
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
 #warning "recompose_cgh_Onelevel is not implimented yet"
@@ -1540,14 +1565,21 @@ void cgh::recompose_cgh_Onelevel(int nprocs, int lev,
   // tmPat construction completes
   Parallel::distribute(tmPat, end_rank[lev] - start_rank[lev] + 1, ingfs, fngfs, false, start_rank[lev], end_rank[lev]);
   misc::tillherecheck(Commlev[lev], start_rank[lev], "after distribute");
-  //    checkPatchList(tmPat,true);
+  //    checkPatchList(tmPat,true);
-  bool CC = (lev > trfls);
+  bool CC = (lev > trfls);
-  Parallel::fill_level_data(tmPat, PatL[lev], PatL[lev - 1], OldList, StateList, FutureList, tmList, Symmetry, BB, CC);
+  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");
+  misc::tillherecheck(Commlev[lev], start_rank[lev], "after fill_level_data");
-
+
-  Parallel::KillBlocks(PatL[lev]);
+#ifdef USE_GPU
-  PatL[lev]->destroyList();
+  bssn_gpu_clear_cached_device_buffers();
-  PatL[lev] = tmPat;
+  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;
 }
 
 

AMSS_NCKU_source/diff_newwb.f90

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

AMSS_NCKU_source/fderivs_c.C

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

AMSS_NCKU_source/fmisc.f90

@@ -1327,35 +1327,6 @@ end subroutine d2dump
 
   return
   end subroutine polint
-
-  subroutine polint0(xa, ya, y, ordn)
-  ! Lagrange interpolation at x=0, O(n) direct formula
-  implicit none
-  integer, intent(in) :: ordn
-  real*8, dimension(ordn), intent(in) :: xa, ya
-  real*8, intent(out) :: y
-
-  integer :: j, k
-  real*8 :: wj
-
-  y = 0.d0
-  do j = 1, ordn
-    wj = 1.d0
-    do k = 1, ordn
-      if (k .ne. j) then
-        wj = wj * xa(k) / (xa(k) - xa(j))
-      endif
-    enddo
-    y = y + wj * ya(j)
-  enddo
-
-  return
-  end subroutine polint0
-!------------------------------------------------------------------------------
-!
-! interpolation in 2 dimensions, follow yx order
-!
-!------------------------------------------------------------------------------
 !------------------------------------------------------------------------------
 ! Compute Lagrange interpolation basis weights for one target point.
 !------------------------------------------------------------------------------

AMSS_NCKU_source/interp_lb_profile_data.h

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

AMSS_NCKU_source/kodiss_c.C

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

AMSS_NCKU_source/lopsided_kodis_c.C

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

AMSS_NCKU_source/makefile

@@ -1,35 +1,37 @@
 
 
-include makefile.inc
+include makefile.inc
-
+
-## polint(ordn=6) kernel selector:
+## polint(ordn=6) kernel selector:
-##   1 (default): barycentric fast path
+##   1 (default): barycentric fast path
-##   0          : fallback to Neville path
+##   0          : fallback to Neville path
-POLINT6_USE_BARY ?= 1
+POLINT6_USE_BARY ?= 1
-POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
-
+
-## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
-##   make                        -> opt  (PGO-guided, maximum performance)
+##   make                        -> opt  (PGO-guided, maximum performance)
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 
 ifeq ($(PGO_MODE),instrument)
 ## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-else
+else
-## opt (default): maximum performance with PGO profile data
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+## PGO has been turned off, now tested and found to be negative optimization
-              -fprofile-instr-use=$(PROFDATA) \
+## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+
-              -fprofile-instr-use=$(PROFDATA) \
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-endif
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-.SUFFIXES: .o .f90 .C .for .cu
+endif
+
+.SUFFIXES: .o .f90 .C .for .cu
 
 .f90.o:
 	$(f90) $(f90appflags) -c $< -o $@
@@ -43,10 +45,6 @@ endif
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
-# CUDA rewrite of BSSN RHS (drop-in replacement for bssn_rhs_c + stencil helpers)
-bssn_rhs_cuda.o: bssn_rhs_cuda.cu macrodef.h
-	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
-
 # C rewrite of BSSN RHS kernel and helpers
 bssn_rhs_c.o: bssn_rhs_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
@@ -60,11 +58,14 @@ fdderivs_c.o: fdderivs_c.C
 kodiss_c.o: kodiss_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-lopsided_c.o: lopsided_c.C
+lopsided_c.o: lopsided_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
+
-interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+lopsided_kodis_c.o: lopsided_kodis_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
@@ -81,25 +82,21 @@ TwoPunctureABE.o: TwoPunctureABE.C
 # Input files
 
 ## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
-ifeq ($(USE_CXX_KERNELS),0)
+ifeq ($(USE_CXX_KERNELS),0)
-# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
+# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES =
+CFILES =
-else
+else
-# C++ mode (default): C rewrite of bssn_rhs and helper kernels
+# C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
-endif
+endif
-
+
-# CUDA rewrite: bssn_rhs_cuda.o replaces all CFILES (stencils are built-in)
+## RK4 kernel switch (independent from USE_CXX_KERNELS)
-CFILES_CUDA = bssn_rhs_cuda.o
+ifeq ($(USE_CXX_RK4),1)
-
+CFILES += rungekutta4_rout_c.o
-## RK4 kernel switch (independent from USE_CXX_KERNELS)
+RK4_F90_OBJ =
-ifeq ($(USE_CXX_RK4),1)
+else
-CFILES += rungekutta4_rout_c.o
+RK4_F90_OBJ = rungekutta4_rout.o
-CFILES_CUDA += rungekutta4_rout_c.o
+endif
-RK4_F90_OBJ =
-else
-RK4_F90_OBJ = rungekutta4_rout.o
-endif
 
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -108,20 +105,19 @@ C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
 	   NullShellPatch2_Evo.o writefile_f.o interp_lb_profile.o
 	   
-C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
+C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
-           cgh.o surface_integral.o ShellPatch.o\
+           cgh.o bssn_class.o surface_integral.o ShellPatch.o\
-	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
+	   bssnEScalar_class.o perf.o Z4c_class.o NullShellPatch.o\
-	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
+	   bssnEM_class.o cpbc_util.o z4c_rhs_point.o checkpoint.o\
-           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
+           Parallel_bam.o scalar_class.o transpbh.o NullShellPatch2.o\
-	   NullShellPatch2_Evo.o \
+	   NullShellPatch2_Evo.o bssn_cuda_step.o writefile_f.o
-	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
 
-F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
            fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
 	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
 	   getnpem2.o empart.o NullNews.o fourdcurvature.o\
@@ -146,7 +142,7 @@ initial_guess.o Newton.o Jacobian.o ilucg.o IntPnts0.o IntPnts.o
 
 TwoPunctureFILES = TwoPunctureABE.o TwoPunctures.o 
 
-CUDAFILES = bssn_gpu.o bssn_gpu_rhs_ss.o
+CUDAFILES = bssn_gpu.o bssn_cuda_ops.o
 
 # file dependences
 $(C++FILES) $(C++FILES_GPU) $(F90FILES) $(CFILES) $(AHFDOBJS) $(CUDAFILES): macrodef.fh
@@ -181,12 +177,9 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o
 
 # projects
-ABE: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
-
+	
-ABE_CUDA: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)
-
 ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
@@ -194,4 +187,4 @@ TwoPunctureABE: $(TwoPunctureFILES)
 	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
-	rm *.o ABE ABE_CUDA ABEGPU TwoPunctureABE make.log -f
+	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -9,6 +9,7 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 ## Using sequential MKL (OpenMP disabled for better single-threaded performance)
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
 LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
+CUDA_LDLIBS = -L/usr/local/cuda-12.9/targets/x86_64-linux/lib -lcudart
 
 ## Memory allocator switch
 ##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
@@ -24,6 +25,8 @@ ifeq ($(USE_TBBMALLOC),1)
 LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
 endif
 
+LDLIBS := $(CUDA_LDLIBS) $(LDLIBS)
+
 ## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
 ##   opt        : (default) maximum performance with PGO profile-guided optimization
 ##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
@@ -62,4 +65,4 @@ CLINKER      = mpiicpx
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
 #CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
-CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc -arch=sm_80
+CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc

AMSS_NCKU_source/prolongrestrict_cell.f90

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

AMSS_NCKU_source/prolongrestrict_vertex.f90

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

AMSS_NCKU_source/rungekutta4_rout_c.C

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

AMSS_NCKU_source/surface_integral.C

@@ -180,19 +180,64 @@ surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry)
 //|============================================================================
 //| Destructor
 //|============================================================================
-surface_integral::~surface_integral()
+surface_integral::~surface_integral()
-{
+{
-  delete[] nx_g;
+  release_cached_buffers();
-  delete[] ny_g;
+  delete[] nx_g;
-  delete[] nz_g;
+  delete[] ny_g;
-  delete[] arcostheta;
+  delete[] nz_g;
-#ifdef GaussInt
+  delete[] arcostheta;
-  delete[] wtcostheta;
+#ifdef GaussInt
-#endif
+  delete[] wtcostheta;
-}
+#endif
-//|----------------------------------------------------------------
+}
-//  spin weighted spinw component of psi4, general routine
+
-//  l takes from spinw to maxl; m takes from -l to l
+void surface_integral::get_surface_points(double rex, double **pox)
+{
+  SpherePointCache &cache = sphere_point_cache[rex];
+  if (!cache.pox[0])
+  {
+    for (int i = 0; i < 3; ++i)
+      cache.pox[i] = new double[n_tot];
+    for (int n = 0; n < n_tot; ++n)
+    {
+      cache.pox[0][n] = rex * nx_g[n];
+      cache.pox[1][n] = rex * ny_g[n];
+      cache.pox[2][n] = rex * nz_g[n];
+    }
+  }
+
+  pox[0] = cache.pox[0];
+  pox[1] = cache.pox[1];
+  pox[2] = cache.pox[2];
+}
+
+double *surface_integral::get_shellf_buffer(int num_var)
+{
+  double *&buffer = shellf_cache[num_var];
+  if (!buffer)
+    buffer = new double[n_tot * num_var];
+  return buffer;
+}
+
+void surface_integral::release_cached_buffers()
+{
+  for (map<double, SpherePointCache>::iterator it = sphere_point_cache.begin(); it != sphere_point_cache.end(); ++it)
+  {
+    delete[] it->second.pox[0];
+    delete[] it->second.pox[1];
+    delete[] it->second.pox[2];
+    it->second.pox[0] = it->second.pox[1] = it->second.pox[2] = 0;
+  }
+  sphere_point_cache.clear();
+
+  for (map<int, double *>::iterator it = shellf_cache.begin(); it != shellf_cache.end(); ++it)
+    delete[] it->second;
+  shellf_cache.clear();
+}
+//|----------------------------------------------------------------
+//  spin weighted spinw component of psi4, general routine
+//  l takes from spinw to maxl; m takes from -l to l
 //|----------------------------------------------------------------
 void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
                                  int spinw, int maxl, int NN, double *RP, double *IP,
@@ -209,16 +254,9 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   MyList<var> *DG_List = new MyList<var>(Rpsi4);
   DG_List->insert(Ipsi4);
 
-  int n;
+  int n;
-  double *pox[3];
+  double *pox[3];
-  for (int i = 0; i < 3; i++)
+  get_surface_points(rex, pox);
-    pox[i] = new double[n_tot];
-  for (n = 0; n < n_tot; n++)
-  {
-    pox[0][n] = rex * nx_g[n];
-    pox[1][n] = rex * ny_g[n];
-    pox[2][n] = rex * nz_g[n];
-  }
 
   int mp, Lp, Nmin, Nmax;
   mp = n_tot / cpusize;
@@ -234,8 +272,7 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
     Nmax = Nmin + mp - 1;
   }
 
-  double *shellf;
+  double *shellf = get_shellf_buffer(InList);
-  shellf = new double[n_tot * InList];
 
   GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
 
@@ -375,14 +412,10 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
 
   //|------= Free memory.
 
-  delete[] pox[0];
+  delete[] RP_out;
-  delete[] pox[1];
+  delete[] IP_out;
-  delete[] pox[2];
+  DG_List->clearList();
-  delete[] shellf;
+}
-  delete[] RP_out;
-  delete[] IP_out;
-  DG_List->clearList();
-}
 void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
                                  int spinw, int maxl, int NN, double *RP, double *IP,
                                  monitor *Monitor, MPI_Comm Comm_here) // NN is the length of RP and IP
@@ -402,19 +435,11 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
   MyList<var> *DG_List = new MyList<var>(Rpsi4);
   DG_List->insert(Ipsi4);
 
-  int n;
+  int n;
-  double *pox[3];
+  double *pox[3];
-  for (int i = 0; i < 3; i++)
+  get_surface_points(rex, pox);
-    pox[i] = new double[n_tot];
+
-  for (n = 0; n < n_tot; n++)
+  double *shellf = get_shellf_buffer(InList);
-  {
-    pox[0][n] = rex * nx_g[n];
-    pox[1][n] = rex * ny_g[n];
-    pox[2][n] = rex * nz_g[n];
-  }
-
-  double *shellf;
-  shellf = new double[n_tot * InList];
 
   //    misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before Interp_Points");
 
@@ -577,14 +602,10 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
 
   //|------= Free memory.
 
-  delete[] pox[0];
+  delete[] RP_out;
-  delete[] pox[1];
+  delete[] IP_out;
-  delete[] pox[2];
+  DG_List->clearList();
-  delete[] shellf;
+}
-  delete[] RP_out;
-  delete[] IP_out;
-  DG_List->clearList();
-}
 //|----------------------------------------------------------------
 //  for shell patch
 //|----------------------------------------------------------------
@@ -597,19 +618,11 @@ void surface_integral::surf_Wave(double rex, int lev, ShellPatch *GH, var *Rpsi4
   MyList<var> *DG_List = new MyList<var>(Rpsi4);
   DG_List->insert(Ipsi4);
 
-  int n;
+  int n;
-  double *pox[3];
+  double *pox[3];
-  for (int i = 0; i < 3; i++)
+  get_surface_points(rex, pox);
-    pox[i] = new double[n_tot];
-  for (n = 0; n < n_tot; n++)
-  {
-    pox[0][n] = rex * nx_g[n];
-    pox[1][n] = rex * ny_g[n];
-    pox[2][n] = rex * nz_g[n];
-  }
 
-  double *shellf;
+  double *shellf = get_shellf_buffer(InList);
-  shellf = new double[n_tot * InList];
 
   GH->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
 
@@ -2570,12 +2583,8 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
   Rout[5] = sy;
   Rout[6] = sz;
 
-  delete[] pox[0];
+  DG_List->clearList();
-  delete[] pox[1];
+}
-  delete[] pox[2];
-  delete[] shellf;
-  DG_List->clearList();
-}
 void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
                                      var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
                                      var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
@@ -2637,19 +2646,11 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
   DG_List->insert(Ayz);
   DG_List->insert(Azz);
 
-  int n;
+  int n;
-  double *pox[3];
+  double *pox[3];
-  for (int i = 0; i < 3; i++)
+  get_surface_points(rex, pox);
-    pox[i] = new double[n_tot];
+
-  for (n = 0; n < n_tot; n++)
+  double *shellf = get_shellf_buffer(InList);
-  {
-    pox[0][n] = rex * nx_g[n];
-    pox[1][n] = rex * ny_g[n];
-    pox[2][n] = rex * nz_g[n];
-  }
-
-  double *shellf;
-  shellf = new double[n_tot * InList];
 
   // we have assumed there is only one box on this level,
   // so we do not need loop boxes
@@ -2839,12 +2840,8 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
   Rout[5] = sy;
   Rout[6] = sz;
 
-  delete[] pox[0];
+  DG_List->clearList();
-  delete[] pox[1];
+}
-  delete[] pox[2];
-  delete[] shellf;
-  DG_List->clearList();
-}
 //|----------------------------------------------------------------
 //  for shell patch
 //|----------------------------------------------------------------

AMSS_NCKU_source/surface_integral.h

@@ -20,25 +20,41 @@ using namespace std;
 #include "cgh.h"
 #include "ShellPatch.h"
 #include "NullShellPatch.h"
-#include "NullShellPatch2.h"
+#include "NullShellPatch2.h"
-#include "var.h"
+#include "var.h"
-#include "monitor.h"
+#include "monitor.h"
+#include <map>
 
 class surface_integral
 {
 
-private:
+private:
-	int Symmetry, factor;
+	struct SpherePointCache
-	int N_theta, N_phi; // Number of points in Theta & Phi directions
+	{
-	double dphi, dcostheta;
+		double *pox[3];
-	double *arcostheta, *wtcostheta;
+		SpherePointCache()
-	int n_tot; // size of arrays
+		{
-
+			pox[0] = pox[1] = pox[2] = 0;
-	double *nx_g, *ny_g, *nz_g; // global list of unit normals
+		}
-	int myrank, cpusize;
+	};
-
+
-public:
+	int Symmetry, factor;
-	surface_integral(int iSymmetry);
+	int N_theta, N_phi; // Number of points in Theta & Phi directions
+	double dphi, dcostheta;
+	double *arcostheta, *wtcostheta;
+	int n_tot; // size of arrays
+
+	double *nx_g, *ny_g, *nz_g; // global list of unit normals
+	int myrank, cpusize;
+	map<double, SpherePointCache> sphere_point_cache;
+	map<int, double *> shellf_cache;
+
+	void get_surface_points(double rex, double **pox);
+	double *get_shellf_buffer(int num_var);
+	void release_cached_buffers();
+
+public:
+	surface_integral(int iSymmetry);
 	~surface_integral();
 
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,

AMSS_NCKU_source/tool.h

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

makefile_and_run.py

@@ -9,6 +9,7 @@
 
 
 import AMSS_NCKU_Input as input_data
+import os
 import subprocess
 import time
 
@@ -57,6 +58,48 @@ BUILD_JOBS = 64
 ##################################################################
 
 
+##################################################################
+
+def prepare_gpu_runtime_env():
+    """
+    Create a user-private CUDA MPS environment for GPU runs.
+
+    On shared machines another user's daemon may already occupy the default
+    /tmp/nvidia-mps pipe directory, which makes plain cudaSetDevice/cudaMalloc
+    fail with cudaErrorMpsConnectionFailed.  Binding AMSS-NCKU to a private
+    pipe directory avoids cross-user interference.
+    """
+    env = os.environ.copy()
+
+    pipe_dir = env.get("CUDA_MPS_PIPE_DIRECTORY", f"/tmp/amss-ncku-mps-{os.getuid()}")
+    log_dir  = env.get("CUDA_MPS_LOG_DIRECTORY",  f"/tmp/amss-ncku-mps-log-{os.getuid()}")
+
+    os.makedirs(pipe_dir, exist_ok=True)
+    os.makedirs(log_dir, exist_ok=True)
+
+    env["CUDA_MPS_PIPE_DIRECTORY"] = pipe_dir
+    env["CUDA_MPS_LOG_DIRECTORY"] = log_dir
+
+    control_socket = os.path.join(pipe_dir, "control")
+    if not os.path.exists(control_socket):
+        start = subprocess.run(
+            ["nvidia-cuda-mps-control", "-d"],
+            env=env,
+            stdout=subprocess.DEVNULL,
+            stderr=subprocess.DEVNULL,
+        )
+        if start.returncode != 0:
+            print(f" Warning: failed to start private CUDA MPS daemon in {pipe_dir}")
+        else:
+            print(f" Using private CUDA MPS pipe directory: {pipe_dir}")
+    else:
+        print(f" Using existing private CUDA MPS pipe directory: {pipe_dir}")
+
+    return env
+
+##################################################################
+
+
 
 ##################################################################
 
@@ -70,7 +113,7 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=optimize ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
     elif (input_data.GPU_Calculation == "yes"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:
@@ -146,16 +189,29 @@ def run_ABE():
 
     ## Define the command to run; cast other values to strings as needed
     
+    run_env = None
+
     if (input_data.GPU_Calculation == "no"):
         mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        run_env = prepare_gpu_runtime_env()
+        if int(input_data.MPI_processes) == 1:
+            mpi_command = "./ABEGPU"
+        else:
+            mpi_command = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output
-    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
+    mpi_process = subprocess.Popen(
+        mpi_command,
+        shell=True,
+        stdout=subprocess.PIPE,
+        stderr=subprocess.STDOUT,
+        text=True,
+        env=run_env,
+    )
 
     ## Write ABE run output to file while printing to stdout
     with open(mpi_command_outfile, 'w') as file0:  

pgo_profile/PGO_Profile_Analysis.md

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