Add optional BSSN kernel profiling switches

Remove dead chi derivative setup in BSSN RHS
Localize chi Ricci intermediates in RHS
2026-04-13 16:51:06 +08:00 · 2026-04-13 15:55:43 +08:00 · 2026-04-13 15:14:31 +08:00 · 2026-04-13 15:10:22 +08:00 · 2026-04-13 14:50:55 +08:00 · 2026-04-13 13:17:36 +08:00
24 changed files with 2698 additions and 1316 deletions
--- a/AMSS_NCKU_Input.py
+++ b/AMSS_NCKU_Input.py
@@ -16,10 +16,7 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                 ## The file directory name should not be too long
-MPI_processes    = 64                            ## number of mpi processes used in the simulation
-OMP_Threads      = 3                             ## number of OpenMP threads used by each MPI process
-MPI_hosts        = ["localhost", "192.168.20.102"] ## MPI hosts for multi-node runs
-MPI_processes_per_node = 32                      ## MPI ranks launched on each node in MPI_hosts
+MPI_processes    = 64                             ## number of mpi processes used in the simulation

 GPU_Calculation  = "no"                          ## Use GPU or not 
                                                 ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
--- a/AMSS_NCKU_source/Parallel.C
+++ b/AMSS_NCKU_source/Parallel.C
@@ -5284,6 +5284,41 @@ double Parallel::L2Norm(Patch *Pat, var *vf)

  return tvf;
 }
+void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms)
+{
+  int myrank;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+
+  double tvf[7], dtvf[7];
+  int BDW = ghost_width;
+  for (int i = 0; i < 7; i++)
+    dtvf[i] = 0;
+
+  MyList<Block> *BP = Pat->blb;
+  while (BP)
+  {
+    Block *cg = BP->data;
+    if (myrank == cg->rank)
+    {
+      f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                      Pat->bbox[0], Pat->bbox[1], Pat->bbox[2],
+                      Pat->bbox[3], Pat->bbox[4], Pat->bbox[5],
+                      cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
+                      cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
+                      cg->fgfs[vf[6]->sgfn], tvf, BDW);
+      for (int i = 0; i < 7; i++)
+        dtvf[i] += tvf[i];
+    }
+    if (BP == Pat->ble)
+      break;
+    BP = BP->next;
+  }
+
+  MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  for (int i = 0; i < 7; i++)
+    norms[i] = sqrt(tvf[i]);
+}
 double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
 {
  int myrank;
@@ -5315,6 +5350,41 @@ double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)

  return tvf;
 }
+void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here)
+{
+  int myrank;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+
+  double tvf[7], dtvf[7];
+  int BDW = ghost_width;
+  for (int i = 0; i < 7; i++)
+    dtvf[i] = 0;
+
+  MyList<Block> *BP = Pat->blb;
+  while (BP)
+  {
+    Block *cg = BP->data;
+    if (myrank == cg->rank)
+    {
+      f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                      Pat->bbox[0], Pat->bbox[1], Pat->bbox[2],
+                      Pat->bbox[3], Pat->bbox[4], Pat->bbox[5],
+                      cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
+                      cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
+                      cg->fgfs[vf[6]->sgfn], tvf, BDW);
+      for (int i = 0; i < 7; i++)
+        dtvf[i] += tvf[i];
+    }
+    if (BP == Pat->ble)
+      break;
+    BP = BP->next;
+  }
+
+  MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, Comm_here);
+
+  for (int i = 0; i < 7; i++)
+    norms[i] = sqrt(tvf[i]);
+}
 void Parallel::checkgsl(MyList<Parallel::gridseg> *pp, bool first_only)
 {
  int myrank = 0;
--- a/AMSS_NCKU_source/Parallel.h
+++ b/AMSS_NCKU_source/Parallel.h
@@ -183,6 +183,7 @@ namespace Parallel
                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
  double L2Norm(Patch *Pat, var *vf);
+  void L2Norm7(Patch *Pat, var **vf, double *norms);
  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
  void checkvarl(MyList<var> *pp, bool first_only);
  MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
@@ -218,6 +219,7 @@ namespace Parallel
  void checkpatchlist(MyList<Patch> *PatL, bool buflog);

  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
+  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
                             int NN, double **XX,
                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
--- a/AMSS_NCKU_source/ShellPatch.C
+++ b/AMSS_NCKU_source/ShellPatch.C
@@ -3472,6 +3472,43 @@ double ShellPatch::L2Norm(var *vf)

  return tvf;
 }
+void ShellPatch::L2Norm7(var **vf, double *norms)
+{
+  double tvf[7], dtvf[7];
+  int BDW = overghost;
+  for (int i = 0; i < 7; i++)
+    dtvf[i] = 0;
+
+  MyList<ss_patch> *sPp = PatL;
+  while (sPp)
+  {
+    MyList<Block> *Bp = sPp->data->blb;
+    while (Bp)
+    {
+      Block *cg = Bp->data;
+      if (myrank == cg->rank)
+      {
+        f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2],
+                        sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
+                        cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
+                        cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
+                        cg->fgfs[vf[6]->sgfn], tvf, BDW);
+        for (int i = 0; i < 7; i++)
+          dtvf[i] += tvf[i];
+      }
+      if (Bp == sPp->data->ble)
+        break;
+      Bp = Bp->next;
+    }
+    sPp = sPp->next;
+  }
+
+  MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  for (int i = 0; i < 7; i++)
+    norms[i] = sqrt(tvf[i]);
+}

 // find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
 void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
--- a/AMSS_NCKU_source/ShellPatch.h
+++ b/AMSS_NCKU_source/ShellPatch.h
@@ -198,6 +198,7 @@ public:
   void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
                            char *filename, int sst);
   double L2Norm(var *vf);
+   void L2Norm7(var **vf, double *norms);
   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
 };

--- a/AMSS_NCKU_source/bssn_class.C
+++ b/AMSS_NCKU_source/bssn_class.C
@@ -47,6 +47,233 @@ using namespace std;
 #define BSSN_ENABLE_MEM_USAGE_LOG 0
 #endif

+#ifndef BSSN_FINE_TIMING
+#define BSSN_FINE_TIMING 0
+#endif
+
+#ifndef BSSN_FINE_TIMING_EVERY
+#define BSSN_FINE_TIMING_EVERY 1
+#endif
+
+#ifndef BSSN_FINE_TIMING_TOPN
+#define BSSN_FINE_TIMING_TOPN 8
+#endif
+
+#ifndef BSSN_KERNEL_FINE_TIMING
+#define BSSN_KERNEL_FINE_TIMING 0
+#endif
+
+#ifndef BSSN_ENABLE_STDIN_ABORT_POLL
+#define BSSN_ENABLE_STDIN_ABORT_POLL 0
+#endif
+
+#if BSSN_FINE_TIMING
+namespace step_timing
+{
+  enum Bucket
+  {
+    TB_ANALYSIS_PSI4 = 0,
+    TB_ANALYSIS_SURFACE,
+    TB_ANALYSIS_IO,
+    TB_BH_PREDICTOR,
+    TB_PREDICTOR_RHS,
+    TB_PREDICTOR_SYNC,
+    TB_BH_CORRECTOR,
+    TB_CORRECTOR_RHS,
+    TB_CORRECTOR_SYNC,
+    TB_STATE_SWAP,
+    TB_RESTRICT_PROLONG,
+    TB_CONSTRAINT_OUT,
+    TB_DUMP_3D,
+    TB_DUMP_2D,
+    TB_CHECKPOINT,
+    TB_REGRID,
+    TB_COUNT
+  };
+
+  static double local_bucket_seconds[TB_COUNT];
+
+  static const char *bucket_labels[TB_COUNT] =
+  {
+    "analysis_psi4",
+    "analysis_surface",
+    "analysis_io",
+    "bh_predictor",
+    "predictor_rhs",
+    "predictor_sync",
+    "bh_corrector",
+    "corrector_rhs",
+    "corrector_sync",
+    "state_swap",
+    "restrict_prolong",
+    "constraint_out",
+    "dump_3d",
+    "dump_2d",
+    "checkpoint",
+    "regrid"
+  };
+
+  void reset()
+  {
+    for (int i = 0; i < TB_COUNT; i++)
+      local_bucket_seconds[i] = 0.0;
+  }
+
+  void add(Bucket bucket, double seconds)
+  {
+    local_bucket_seconds[int(bucket)] += seconds;
+  }
+
+  void report(int myrank, int nprocs, monitor *TimingMonitor,
+              int step_index, double phys_time, double step_wall_seconds)
+  {
+    double max_bucket_seconds[TB_COUNT];
+    double avg_bucket_seconds[TB_COUNT];
+
+    MPI_Reduce(local_bucket_seconds, max_bucket_seconds, TB_COUNT, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
+    MPI_Reduce(local_bucket_seconds, avg_bucket_seconds, TB_COUNT, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
+
+    if (myrank != 0)
+      return;
+
+    for (int i = 0; i < TB_COUNT; i++)
+      avg_bucket_seconds[i] /= Mymax(1, nprocs);
+
+    if (TimingMonitor)
+    {
+      double row[2 + 2 * TB_COUNT];
+      row[0] = double(step_index);
+      row[1] = step_wall_seconds;
+      for (int i = 0; i < TB_COUNT; i++)
+      {
+        row[2 + i] = max_bucket_seconds[i];
+        row[2 + TB_COUNT + i] = avg_bucket_seconds[i];
+      }
+      TimingMonitor->writefile(phys_time, 2 + 2 * TB_COUNT, row);
+    }
+
+    double residual = step_wall_seconds;
+    for (int i = 0; i < TB_COUNT; i++)
+      residual -= max_bucket_seconds[i];
+    if (residual < 0.0)
+      residual = 0.0;
+
+    int order[TB_COUNT];
+    for (int i = 0; i < TB_COUNT; i++)
+      order[i] = i;
+
+    for (int i = 0; i < TB_COUNT - 1; i++)
+      for (int j = i + 1; j < TB_COUNT; j++)
+        if (max_bucket_seconds[order[j]] > max_bucket_seconds[order[i]])
+        {
+          int tmp = order[i];
+          order[i] = order[j];
+          order[j] = tmp;
+        }
+
+    ios::fmtflags old_flags = cout.flags();
+    streamsize old_precision = cout.precision();
+
+    cout << " Fine timing hot spots (max rank wall estimate):" << endl;
+    const int topn = Mymin(BSSN_FINE_TIMING_TOPN, TB_COUNT);
+    for (int i = 0; i < topn; i++)
+    {
+      const int ib = order[i];
+      const double frac = (step_wall_seconds > 0.0) ? (100.0 * max_bucket_seconds[ib] / step_wall_seconds) : 0.0;
+      cout << "  "
+           << setw(20) << left << bucket_labels[ib]
+           << " = " << setw(10) << right << setprecision(6) << max_bucket_seconds[ib]
+           << " s  (" << setw(6) << setprecision(4) << frac << "%)" << endl;
+    }
+    if (residual > 1.0e-6)
+    {
+      const double frac = (step_wall_seconds > 0.0) ? (100.0 * residual / step_wall_seconds) : 0.0;
+      cout << "  "
+           << setw(20) << left << "unprofiled_residual"
+           << " = " << setw(10) << right << setprecision(6) << residual
+           << " s  (" << setw(6) << setprecision(4) << frac << "%)" << endl;
+    }
+    cout << endl;
+    cout.flags(old_flags);
+    cout.precision(old_precision);
+  }
+}
+
+#define STEP_TIMER_DECL(var_name) const double var_name = MPI_Wtime()
+#define STEP_TIMER_ADD(bucket_name, var_name) step_timing::add(step_timing::bucket_name, MPI_Wtime() - (var_name))
+#else
+#define STEP_TIMER_DECL(var_name)
+#define STEP_TIMER_ADD(bucket_name, var_name)
+#endif
+
+#if BSSN_KERNEL_FINE_TIMING
+namespace rhs_kernel_timing_report
+{
+  void report(int myrank, int nprocs, int step_index, double step_wall_seconds)
+  {
+    const int bucket_count = f_bssn_rhs_kernel_timing_bucket_count();
+    const double *local_bucket_seconds = f_bssn_rhs_kernel_timing_local_seconds();
+
+    if (bucket_count <= 0 || !local_bucket_seconds)
+      return;
+
+    double *max_bucket_seconds = new double[bucket_count];
+    double *avg_bucket_seconds = new double[bucket_count];
+    int *order = new int[bucket_count];
+
+    MPI_Reduce((void *)local_bucket_seconds, max_bucket_seconds, bucket_count, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
+    MPI_Reduce((void *)local_bucket_seconds, avg_bucket_seconds, bucket_count, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
+
+    if (myrank == 0)
+    {
+      double kernel_total = 0.0;
+      for (int i = 0; i < bucket_count; ++i)
+      {
+        avg_bucket_seconds[i] /= Mymax(1, nprocs);
+        order[i] = i;
+        kernel_total += max_bucket_seconds[i];
+      }
+
+      for (int i = 0; i < bucket_count - 1; ++i)
+        for (int j = i + 1; j < bucket_count; ++j)
+          if (max_bucket_seconds[order[j]] > max_bucket_seconds[order[i]])
+          {
+            int tmp = order[i];
+            order[i] = order[j];
+            order[j] = tmp;
+          }
+
+      ios::fmtflags old_flags = cout.flags();
+      streamsize old_precision = cout.precision();
+
+      const double kernel_frac = (step_wall_seconds > 0.0) ? (100.0 * kernel_total / step_wall_seconds) : 0.0;
+      cout << " RHS kernel split (max-rank accumulated over step " << step_index << "): total "
+           << setprecision(6) << kernel_total << " s  (" << setprecision(4)
+           << kernel_frac << "% of coarse step)" << endl;
+
+      const int topn = Mymin(BSSN_FINE_TIMING_TOPN, bucket_count);
+      for (int i = 0; i < topn; ++i)
+      {
+        const int ib = order[i];
+        const double frac = (kernel_total > 0.0) ? (100.0 * max_bucket_seconds[ib] / kernel_total) : 0.0;
+        cout << "  "
+             << setw(20) << left << f_bssn_rhs_kernel_timing_label(ib)
+             << " = " << setw(10) << right << setprecision(6) << max_bucket_seconds[ib]
+             << " s  (" << setw(6) << setprecision(4) << frac << "% of kernel)" << endl;
+      }
+      cout << endl;
+
+      cout.flags(old_flags);
+      cout.precision(old_precision);
+    }
+
+    delete[] max_bucket_seconds;
+    delete[] avg_bucket_seconds;
+    delete[] order;
+  }
+}
+#endif
+
 //================================================================================================

 // define bssn_class
@@ -65,6 +292,7 @@ bssn_class::bssn_class(double Couranti, double StartTimei, double TotalTimei,
                         xc(0), yc(0), zc(0), xr(0), yr(0), zr(0), trigger(0), dTT(0), dumpid(0),
 #endif
                         a_lev(a_levi), maxl(maxli), decn(decni), maxrex(maxrexi), drex(drexi),
+                         ConstraintRefreshLevels(0),
                         CheckPoint(0)
                         // CheckPoint(0)
 {
@@ -107,6 +335,24 @@ bssn_class::bssn_class(double Couranti, double StartTimei, double TotalTimei,
    a_stream.str("");
    a_stream << setw(15) << "# time Ham Px Py Pz Gx Gy Gz";
    ConVMonitor = new monitor("bssn_constraint.dat", myrank, a_stream.str());
+
+#if BSSN_FINE_TIMING
+    a_stream.clear();
+    a_stream.str("");
+    a_stream << setw(8) << "# step";
+    a_stream << setw(14) << "wall";
+    for (int ib = 0; ib < step_timing::TB_COUNT; ib++)
+      a_stream << setw(18) << step_timing::bucket_labels[ib];
+    for (int ib = 0; ib < step_timing::TB_COUNT; ib++)
+    {
+      char str_avg[64];
+      sprintf(str_avg, "avg_%s", step_timing::bucket_labels[ib]);
+      a_stream << setw(18) << str_avg;
+    }
+    TimingMonitor = new monitor("bssn_step_timing.dat", myrank, a_stream.str());
+#else
+    TimingMonitor = 0;
+#endif
  }
  // setup sphere integration engine
  Waveshell = new surface_integral(Symmetry);
@@ -702,6 +948,9 @@ void bssn_class::Initialize()
    }
  }
  GH = new cgh(0, ngfs, Symmetry, pname, checkrun, ErrorMonitor);
+  ConstraintRefreshLevels = new int[GH->levels];
+  for (int il = 0; il < GH->levels; il++)
+    ConstraintRefreshLevels[il] = 0;
  if (checkrun)
    CheckPoint->readcheck_cgh(PhysTime, GH, myrank, nprocs, Symmetry);
  else
@@ -791,6 +1040,8 @@ bssn_class::~bssn_class()
  DumpList->clearList();
  ConstraintList->clearList();

+  delete[] ConstraintRefreshLevels;
+
  delete phio;
  delete trKo;
  delete gxxo;
@@ -1050,6 +1301,7 @@ bssn_class::~bssn_class()
  delete BHMonitor;
  delete MAPMonitor;
  delete ConVMonitor;
+  delete TimingMonitor;
  delete Waveshell;

  delete CheckPoint;
@@ -2036,7 +2288,7 @@ void bssn_class::Read_Ansorg()

 void bssn_class::Evolve(int Steps)
 {
-  double prev_clock = 0.0, curr_clock = 0.0;
+  clock_t prev_clock, curr_clock;
  double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
  LastAnas = 0;
 #if 0
@@ -2147,12 +2399,21 @@ void bssn_class::Evolve(int Steps)

  for (int ncount = 1; ncount < Steps + 1; ncount++)
  {
+#if BSSN_FINE_TIMING
+    step_timing::reset();
+#endif
+#if BSSN_KERNEL_FINE_TIMING
+    f_bssn_rhs_kernel_timing_reset();
+#endif
+#if (BSSN_FINE_TIMING || BSSN_KERNEL_FINE_TIMING)
+    const double step_wall_start = MPI_Wtime();
+#endif
    // special for large mass ratio consideration
    //     if(fabs(Porg0[0][0]-Porg0[1][0])+fabs(Porg0[0][1]-Porg0[1][1])+fabs(Porg0[0][2]-Porg0[1][2])<1e-6) 
    //     { GH->levels=GH->movls; }

    if (myrank == 0)
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
 #if (PSTR == 0)
    RecursiveStep(0);
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
@@ -2173,6 +2434,7 @@ void bssn_class::Evolve(int Steps)
    // When LastDump >= DumpTime, output corresponding binary data
    if (LastDump >= DumpTime)
    {
+      STEP_TIMER_DECL(timer_dump3d);
      //       misc::tillherecheck("before Dump_Data");

      for (int lev = 0; lev < GH->levels; lev++)
@@ -2180,6 +2442,7 @@ void bssn_class::Evolve(int Steps)
 #ifdef WithShell
      SH->Dump_Data(DumpList, 0, PhysTime, dT_mon);
 #endif
+      STEP_TIMER_ADD(TB_DUMP_3D, timer_dump3d);

      LastDump = 0;

@@ -2192,10 +2455,12 @@ void bssn_class::Evolve(int Steps)
    // When Last2dDump >= d2DumpTime, output corresponding 2D data
    if (Last2dDump >= d2DumpTime)
    {
+      STEP_TIMER_DECL(timer_dump2d);
      //       misc::tillherecheck("before 2dDump_Data");

      for (int lev = 0; lev < GH->levels; lev++)
        Parallel::d2Dump_Data(GH->PatL[lev], DumpList, 0, PhysTime, dT_mon);
+      STEP_TIMER_ADD(TB_DUMP_2D, timer_dump2d);

      Last2dDump = 0;

@@ -2208,10 +2473,10 @@ void bssn_class::Evolve(int Steps)
    if (myrank == 0)
    {
      prev_clock = curr_clock;
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
      cout << endl;
      cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
-           << " Computer used " << (curr_clock - prev_clock)
+           << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
           << " seconds! " << endl;
      // cout << endl;
    }
@@ -2220,10 +2485,12 @@ void bssn_class::Evolve(int Steps)
      break;

 #if (REGLEV == 1)
+    STEP_TIMER_DECL(timer_regrid);
    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(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+    STEP_TIMER_ADD(TB_REGRID, timer_regrid);
 #endif

 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2263,10 +2530,13 @@ void bssn_class::Evolve(int Steps)
             << endl;
      }
      cout << endl;
+#if BSSN_ENABLE_STDIN_ABORT_POLL
      cout << " If you think the physical evolution time is enough for this simulation, please input 'stop' in the terminal to stop the MPI processes in the next evolution step ! " << endl;
+#endif
      // cout << endl;
    }
    
+#if BSSN_ENABLE_STDIN_ABORT_POLL
    ////////////////////////////////////////////////////////////
    // If an "abort" command is detected on stdin, terminate MPI processes
    ////////////////////////////////////////////////////////////
@@ -2294,10 +2564,12 @@ void bssn_class::Evolve(int Steps)
    }
        
    ////////////////////////////////////////////////////////////
+#endif

    // When LastCheck >= CheckTime, perform runtime checks and output status data
    if (LastCheck >= CheckTime)
    {
+      STEP_TIMER_DECL(timer_checkpoint);
      LastCheck = 0;

      CheckPoint->write_Black_Hole_position(BH_num_input, BH_num, Porg0, Porgbr, Mass);
@@ -2306,7 +2578,20 @@ void bssn_class::Evolve(int Steps)
      CheckPoint->writecheck_sh(PhysTime, SH);
 #endif
      CheckPoint->write_bssn(LastDump, Last2dDump, LastAnas);
+      STEP_TIMER_ADD(TB_CHECKPOINT, timer_checkpoint);
    }
+
+#if (BSSN_FINE_TIMING || BSSN_KERNEL_FINE_TIMING)
+    const double step_wall_seconds = MPI_Wtime() - step_wall_start;
+#endif
+#if BSSN_FINE_TIMING
+    if (ncount % BSSN_FINE_TIMING_EVERY == 0)
+      step_timing::report(myrank, nprocs, TimingMonitor, ncount, PhysTime, step_wall_seconds);
+#endif
+#if BSSN_KERNEL_FINE_TIMING
+    if (ncount % BSSN_FINE_TIMING_EVERY == 0)
+      rhs_kernel_timing_report::report(myrank, nprocs, ncount, step_wall_seconds);
+#endif
  }
  /*
  #ifdef With_AHF
@@ -2438,10 +2723,16 @@ void bssn_class::RecursiveStep(int lev)
 #endif

 #if (REGLEV == 0)
+  STEP_TIMER_DECL(timer_regrid_onelevel);
  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))
+  {
+  if (ConstraintRefreshLevels)
+    ConstraintRefreshLevels[lev] = 1;
  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(); }
+  }
+  STEP_TIMER_ADD(TB_REGRID, timer_regrid_onelevel);
 #endif
 }

@@ -3034,6 +3325,7 @@ void bssn_class::Step(int lev, int YN)

 // new code 2013-2-15, zjcao
 #if (MAPBH == 1)
+  STEP_TIMER_DECL(timer_bh_predictor);
  // for black hole position
  if (BH_num > 0 && lev == GH->levels - 1)
  {
@@ -3064,6 +3356,7 @@ void bssn_class::Step(int lev, int YN)
      }
    }
  }
+  STEP_TIMER_ADD(TB_BH_PREDICTOR, timer_bh_predictor);

  // data analysis part
  // Warning NOTE: the variables1 are used as temp storege room
@@ -3086,6 +3379,7 @@ void bssn_class::Step(int lev, int YN)
  int ERROR = 0;

  MyList<ss_patch> *sPp;
+  STEP_TIMER_DECL(timer_predictor_rhs);
  // Predictor
  MyList<Patch> *Pp = GH->PatL[lev];
  while (Pp)
@@ -3361,6 +3655,9 @@ void bssn_class::Step(int lev, int YN)
  }
 #endif

+  STEP_TIMER_ADD(TB_PREDICTOR_RHS, timer_predictor_rhs);
+
+  STEP_TIMER_DECL(timer_predictor_sync);
  Parallel::AsyncSyncState async_pre;
  Parallel::Sync_start(GH->PatL[lev], SynchList_pre, Symmetry, sync_cache_pre[lev], async_pre);

@@ -3398,6 +3695,7 @@ void bssn_class::Step(int lev, int YN)
    }
  }
 #endif
+  STEP_TIMER_ADD(TB_PREDICTOR_SYNC, timer_predictor_sync);

 #if (MAPBH == 0)
  // for black hole position
@@ -3442,6 +3740,7 @@ void bssn_class::Step(int lev, int YN)
  // corrector
  for (iter_count = 1; iter_count < 4; iter_count++)
  {
+    STEP_TIMER_DECL(timer_corrector_rhs);
    // for RK4: t0, t0+dt/2, t0+dt/2, t0+dt;
    if (iter_count == 1 || iter_count == 3)
      TRK4 += dT_lev / 2;
@@ -3721,6 +4020,9 @@ void bssn_class::Step(int lev, int YN)
    }
 #endif

+    STEP_TIMER_ADD(TB_CORRECTOR_RHS, timer_corrector_rhs);
+
+    STEP_TIMER_DECL(timer_corrector_sync);
    Parallel::AsyncSyncState async_cor;
    Parallel::Sync_start(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_cor[lev], async_cor);

@@ -3760,8 +4062,10 @@ void bssn_class::Step(int lev, int YN)
      }
    }
 #endif
+    STEP_TIMER_ADD(TB_CORRECTOR_SYNC, timer_corrector_sync);

 #if (MAPBH == 0)
+    STEP_TIMER_DECL(timer_bh_corrector);
    // for black hole position
    if (BH_num > 0 && lev == GH->levels - 1)
    {
@@ -3794,11 +4098,13 @@ void bssn_class::Step(int lev, int YN)
        }
      }
    }
+    STEP_TIMER_ADD(TB_BH_CORRECTOR, timer_bh_corrector);
 #endif

    // swap time level
    if (iter_count < 3)
    {
+      STEP_TIMER_DECL(timer_state_swap);
      Pp = GH->PatL[lev];
      while (Pp)
      {
@@ -3845,9 +4151,11 @@ void bssn_class::Step(int lev, int YN)
        }
      }
 #endif
+      STEP_TIMER_ADD(TB_STATE_SWAP, timer_state_swap);
    }
  }
 #if (RPS == 0)
+  STEP_TIMER_DECL(timer_restrict_prolong);
  // mesh refinement boundary part
  RestrictProlong(lev, YN, BB);

@@ -3868,6 +4176,7 @@ void bssn_class::Step(int lev, int YN)
  }
 #endif

+  STEP_TIMER_ADD(TB_RESTRICT_PROLONG, timer_restrict_prolong);
 #endif
  // note the data structure before update
  // SynchList_cor 1   -----------
@@ -3876,6 +4185,7 @@ void bssn_class::Step(int lev, int YN)
  //
  // OldStateList  old -----------
  // update
+  STEP_TIMER_DECL(timer_state_commit);
  Pp = GH->PatL[lev];
  while (Pp)
  {
@@ -3932,6 +4242,7 @@ void bssn_class::Step(int lev, int YN)
      Porg0[ithBH][2] = Porg1[ithBH][2];
    }
  }
+  STEP_TIMER_ADD(TB_STATE_SWAP, timer_state_commit);
 }

 //================================================================================================
@@ -4258,7 +4569,9 @@ void bssn_class::Step(int lev, int YN)
    }
  }
 #endif
+  STEP_TIMER_ADD(TB_PREDICTOR_SYNC, timer_predictor_sync);

+  STEP_TIMER_DECL(timer_bh_predictor);
  // for black hole position
  if (BH_num > 0 && lev == GH->levels - 1)
  {
@@ -4297,6 +4610,7 @@ void bssn_class::Step(int lev, int YN)
  {
    AnalysisStuff(lev, dT_lev);
  }
+  STEP_TIMER_ADD(TB_BH_PREDICTOR, timer_bh_predictor);
  // corrector
  for (iter_count = 1; iter_count < 3; iter_count++)
  {
@@ -5767,6 +6081,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //
 // SynchList_cor  old -----------
 {
+  STEP_TIMER_DECL(timer_restrict_prolong);
 #if (PSTR == 1 || PSTR == 2)
 //  stringstream a_stream;
 //  a_stream.setf(ios::left);
@@ -5909,6 +6224,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //    misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
  }
+  STEP_TIMER_ADD(TB_RESTRICT_PROLONG, timer_restrict_prolong);
 }

 //================================================================================================
@@ -5928,6 +6244,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 //
 // SynchList_cor  old -----------
 {
+  STEP_TIMER_DECL(timer_restrict_prolong);
  //  misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"starting RestrictProlong_aux");

  if (lev >= GH->levels - 1)
@@ -5996,6 +6313,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,

    Parallel::Sync_cached(GH->PatL[lev], SL, Symmetry, sync_cache_rp_fine[lev]);
  }
+  STEP_TIMER_ADD(TB_RESTRICT_PROLONG, timer_restrict_prolong);
 }

 //================================================================================================
@@ -6006,6 +6324,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,

 void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 {
+  STEP_TIMER_DECL(timer_restrict_prolong);
  double dT_lev = dT * pow(0.5, Mymax(lev, trfls));
  // we assume  for fine
  // SynchList_cor 1   -----------
@@ -6085,6 +6404,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)

    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
  }
+  STEP_TIMER_ADD(TB_RESTRICT_PROLONG, timer_restrict_prolong);
 }

 //================================================================================================
@@ -6835,18 +7155,15 @@ void bssn_class::compute_Porg_rhs(double **BH_PS,double **BH_RHS,var *forx,var *

 void bssn_class::compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, var *fory, var *forz, int ilev)
 {
-  const int InList = 3;
+  MyList<var> DG_List_x(forx);
+  MyList<var> DG_List_y(fory);
+  MyList<var> DG_List_z(forz);
+  DG_List_x.next = &DG_List_y;
+  DG_List_y.next = &DG_List_z;

-  MyList<var> *DG_List = new MyList<var>(forx);
-  DG_List->insert(fory);
-  DG_List->insert(forz);
-
-  double *x1, *y1, *z1;
-  double *shellf;
-  shellf = new double[3];
-  double *pox[3];
-  for (int i = 0; i < 3; i++)
-    pox[i] = new double[1];
+  double shellf[3];
+  double pox_buf[3][1];
+  double *pox[3] = {pox_buf[0], pox_buf[1], pox_buf[2]};

  for (int n = 0; n < BH_num; n++)
  {
@@ -6857,9 +7174,9 @@ void bssn_class::compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, va
    int lev = ilev;

 #if (PSTR == 0)
-    while (!Parallel::PatList_Interp_Points(GH->PatL[lev], DG_List, 1, pox, shellf, Symmetry))
+    while (!Parallel::PatList_Interp_Points(GH->PatL[lev], &DG_List_x, 1, pox, shellf, Symmetry))
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
-    while (!Parallel::PatList_Interp_Points(GH->PatL[lev], DG_List, 1, pox, shellf, Symmetry, GH->Commlev[lev]))
+    while (!Parallel::PatList_Interp_Points(GH->PatL[lev], &DG_List_x, 1, pox, shellf, Symmetry, GH->Commlev[lev]))
 #endif
    {
      lev--;
@@ -6868,7 +7185,7 @@ void bssn_class::compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, va
        ErrorMonitor->outfile << "fail to find black holes at t = " << PhysTime << endl;
        for (n = 0; n < BH_num; n++)
          ErrorMonitor->outfile << "(x,y,z) = (" 
-                                << pox[0][n] << "," << pox[1][n] << "," << pox[2][n] 
+                                << BH_PS[n][0] << "," << BH_PS[n][1] << "," << BH_PS[n][2] 
                                << ")" << endl;
        break;
      }
@@ -6881,11 +7198,6 @@ void bssn_class::compute_Porg_rhs(double **BH_PS, double **BH_RHS, var *forx, va
      BH_RHS[n][2] = -shellf[2];
    }
  }
-
-  DG_List->clearList();
-  delete[] shellf;
-  for (int i = 0; i < 3; i++)
-    delete[] pox[i];
 }
 #endif

@@ -7108,6 +7420,10 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
    IP = new double[NN];
    RoutMAP = new double[7];
    double Rex = maxrex;
+    bool patch_mass_prepared = false;
+#ifdef WithShell
+    bool shell_mass_prepared = false;
+#endif
    for (int i = 0; i < decn; i++)
    {
 #ifdef Point_Psi4
@@ -7135,7 +7451,8 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
+                                 RoutMAP, ErrorMonitor, !patch_mass_prepared);
+        patch_mass_prepared = true;
      }
      else
      {
@@ -7143,44 +7460,52 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
+                                 RoutMAP, ErrorMonitor, !shell_mass_prepared);
+        shell_mass_prepared = true;
      }
 #else
      Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
                               gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
                               Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
                               Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor);
+                               RoutMAP, ErrorMonitor, !patch_mass_prepared);
+      patch_mass_prepared = true;
 #endif
 #else
 //        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"before surface integral");
 #ifdef WithShell
      if (lev > 0 || Rex < GH->bbox[0][0][3])
      {
-        Waveshell->surf_Wave(Rex, lev, GH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor);
-        Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
+        Waveshell->surf_WaveMassPAng(Rex, lev, GH,
+                                     Rpsi4, Ipsi4, 2, maxl, NN, RP, IP,
+                                     phi0, trK0,
+                                     gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
+                                     Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
+                                     Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1,
+                                     RoutMAP, ErrorMonitor, !patch_mass_prepared);
+        patch_mass_prepared = true;
      }
      else
      {
-        Waveshell->surf_Wave(Rex, lev, SH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor);
-        Waveshell->surf_MassPAng(Rex, lev, SH, phi0, trK0,
-                                 gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                                 Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                                 Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
+        Waveshell->surf_WaveMassPAng(Rex, lev, SH,
+                                     Rpsi4, Ipsi4, 2, maxl, NN, RP, IP,
+                                     phi0, trK0,
+                                     gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
+                                     Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
+                                     Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1,
+                                     RoutMAP, ErrorMonitor, !shell_mass_prepared);
+        shell_mass_prepared = true;
      }
 #else
 #if (PSTR == 0)
-      Waveshell->surf_Wave(Rex, lev, GH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor);
-      Waveshell->surf_MassPAng(Rex, lev, GH, phi0, trK0,
-                               gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
-                               Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
-                               Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor);
+      Waveshell->surf_WaveMassPAng(Rex, lev, GH,
+                                   Rpsi4, Ipsi4, 2, maxl, NN, RP, IP,
+                                   phi0, trK0,
+                                   gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
+                                   Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
+                                   Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1,
+                                   RoutMAP, ErrorMonitor, !patch_mass_prepared);
+      patch_mass_prepared = true;
 #elif (PSTR == 1 || PSTR == 2)
      Waveshell->surf_Wave(Rex, lev, GH, Rpsi4, Ipsi4, 2, maxl, NN, RP, IP, ErrorMonitor, GH->Commlev[lev]);
      //        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"after surf_Wave");
@@ -7188,7 +7513,8 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
                               gxx0, gxy0, gxz0, gyy0, gyz0, gzz0,
                               Axx0, Axy0, Axz0, Ayy0, Ayz0, Azz0,
                               Gmx0, Gmy0, Gmz0, Sfx1, Sfy1, Sfz1, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor, GH->Commlev[lev]);
+                               RoutMAP, ErrorMonitor, GH->Commlev[lev], !patch_mass_prepared);
+      patch_mass_prepared = true;
 #endif
 #endif
 //        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"end surface integral");
@@ -7261,7 +7587,7 @@ void bssn_class::Constraint_Out()
    for (int lev = 0; lev < GH->levels; lev++)
    {
      // make sure the data consistent for higher levels
-      if (lev > 0) // if the constrait quantities can be reused from the step rhs calculation
+      if (lev > 0 && ConstraintRefreshLevels && ConstraintRefreshLevels[lev]) // only refresh levels whose grid layout changed after evolution
      {
        double TRK4 = PhysTime;
        double ndeps = numepsb;
@@ -7415,35 +7741,18 @@ void bssn_class::Constraint_Out()
 #if (PSTR == 1 || PSTR == 2)
    double ConV_h[7];
 #endif
+    var *ConstraintVars[7] = {Cons_Ham, Cons_Px, Cons_Py, Cons_Pz, Cons_Gx, Cons_Gy, Cons_Gz};

 #ifdef WithShell
-    ConV[0] = SH->L2Norm(Cons_Ham);
-    ConV[1] = SH->L2Norm(Cons_Px);
-    ConV[2] = SH->L2Norm(Cons_Py);
-    ConV[3] = SH->L2Norm(Cons_Pz);
-    ConV[4] = SH->L2Norm(Cons_Gx);
-    ConV[5] = SH->L2Norm(Cons_Gy);
-    ConV[6] = SH->L2Norm(Cons_Gz);
+    SH->L2Norm7(ConstraintVars, ConV);
    ConVMonitor->writefile(PhysTime, 7, ConV);
 #endif
    for (int levi = 0; levi < GH->levels; levi++)
    {
 #if (PSTR == 0)
-      ConV[0] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Ham);
-      ConV[1] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Px);
-      ConV[2] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Py);
-      ConV[3] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Pz);
-      ConV[4] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gx);
-      ConV[5] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gy);
-      ConV[6] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gz);
+      Parallel::L2Norm7(GH->PatL[levi]->data, ConstraintVars, ConV);
 #elif (PSTR == 1 || PSTR == 2)
-      ConV[0] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Ham, GH->Commlev[levi]);
-      ConV[1] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Px, GH->Commlev[levi]);
-      ConV[2] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Py, GH->Commlev[levi]);
-      ConV[3] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Pz, GH->Commlev[levi]);
-      ConV[4] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gx, GH->Commlev[levi]);
-      ConV[5] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gy, GH->Commlev[levi]);
-      ConV[6] = Parallel::L2Norm(GH->PatL[levi]->data, Cons_Gz, GH->Commlev[levi]);
+      Parallel::L2Norm7(GH->PatL[levi]->data, ConstraintVars, ConV, GH->Commlev[levi]);
      //        misc::tillherecheck("before collect data to cpu0");
      // MPI_ALLREDUCE( sendbuf, recvbuf, count, datatype, op, comm), sendbu and recvbuf must be different
      if (levi > 0)
@@ -7474,6 +7783,9 @@ void bssn_class::Constraint_Out()
    Interp_Constraint(false);

    LastConsOut = 0;
+    if (ConstraintRefreshLevels)
+      for (int lev = 0; lev < GH->levels; lev++)
+        ConstraintRefreshLevels[lev] = 0;
  }
 }

--- a/AMSS_NCKU_source/bssn_class.h
+++ b/AMSS_NCKU_source/bssn_class.h
@@ -48,6 +48,7 @@ public:
       double StartTime, TotalTime;
       double AnasTime, DumpTime, d2DumpTime, CheckTime;
       double LastAnas, LastConsOut;
+       int *ConstraintRefreshLevels;
       double Courant;
       double numepss, numepsb, numepsh;
       int Symmetry;
@@ -134,7 +135,7 @@ public:
       Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong

       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
-       monitor *ConVMonitor;
+       monitor *ConVMonitor, *TimingMonitor;
       surface_integral *Waveshell;
       checkpoint *CheckPoint;

--- a/AMSS_NCKU_source/bssn_gpu_class.C
+++ b/AMSS_NCKU_source/bssn_gpu_class.C
@@ -1891,7 +1891,7 @@ void bssn_class::Read_Ansorg()
 void bssn_class::Evolve(int Steps)
 {

-  double prev_clock = 0.0, curr_clock = 0.0;
+  clock_t prev_clock, curr_clock;
  double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
  LastAnas = 0;
 #if 0
@@ -2037,8 +2037,6 @@ void bssn_class::Evolve(int Steps)

  for (int ncount = 1; ncount < Steps + 1; ncount++)
  {
-    if (myrank == 0)
-      curr_clock = MPI_Wtime();
    cout << "Before Step: " << ncount << " My Rank: " << myrank 
         << " takes " << MPI_Wtime() - beg_time << " seconds!" << endl;
    beg_time = MPI_Wtime();
@@ -2098,9 +2096,9 @@ void bssn_class::Evolve(int Steps)
    if (myrank == 0)
    {
      prev_clock = curr_clock;
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
      cout << "Timestep # " << ncount << ": integrating to time: " << PhysTime << endl;
-      cout << "used " << (curr_clock - prev_clock) << " seconds!" << endl;
+      cout << "used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
    }

    if (PhysTime >= TotalTime)
--- a/AMSS_NCKU_source/bssn_rhs.h
+++ b/AMSS_NCKU_source/bssn_rhs.h
@@ -32,6 +32,19 @@
 #define f_compute_rhs_Z4c_ss compute_rhs_z4c_ss_
 #define f_compute_constraint_fr compute_constraint_fr_
 #endif
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+        void f_bssn_rhs_kernel_timing_reset();
+        int f_bssn_rhs_kernel_timing_bucket_count();
+        const double *f_bssn_rhs_kernel_timing_local_seconds();
+        const char *f_bssn_rhs_kernel_timing_label(int);
+#ifdef __cplusplus
+}
+#endif
+
 extern "C"
 {
        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
--- a/AMSS_NCKU_source/bssn_rhs_c.C
+++ b/AMSS_NCKU_source/bssn_rhs_c.C
@@ -2,30 +2,88 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
-
-#ifdef _OPENMP
-#define BSSN_OMP_TASK_GROUP_BEGIN \
-    _Pragma("omp parallel")       \
-    {                             \
-        _Pragma("omp single nowait") \
-        {
-#define BSSN_OMP_TASK_CALL(...) \
-            _Pragma("omp task") { __VA_ARGS__; }
-#define BSSN_OMP_TASK_GROUP_END \
-            _Pragma("omp taskwait") \
-        } \
-    }
-#else
-#define BSSN_OMP_TASK_GROUP_BEGIN {
-#define BSSN_OMP_TASK_CALL(...) { __VA_ARGS__; }
-#define BSSN_OMP_TASK_GROUP_END }
-#endif
+#include <time.h>
 // 0-based i,j,k
 // #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
 // ex(1)=nx, ex(2)=ny, ex(3)=nz

 // 用法：a[ IDX_F(i,j,k,nx,ny) ]

+#ifndef BSSN_KERNEL_FINE_TIMING
+#define BSSN_KERNEL_FINE_TIMING 0
+#endif
+
+#if BSSN_KERNEL_FINE_TIMING
+namespace rhs_kernel_timing
+{
+    enum Bucket
+    {
+        KB_SETUP_DERIVS = 0,
+        KB_GEOM_GAMMA,
+        KB_RICCI_METRIC,
+        KB_CHI_LAPSE,
+        KB_AIJ_TRK_GAUGE,
+        KB_KO_CONSTRAINT,
+        KB_COUNT
+    };
+
+    static double local_bucket_seconds[KB_COUNT];
+
+    static const char *bucket_labels[KB_COUNT] =
+    {
+        "setup_derivs",
+        "geom_gamma",
+        "ricci_metric",
+        "chi_lapse",
+        "aij_trk_gauge",
+        "ko_constraint"
+    };
+
+    static inline double now_seconds()
+    {
+        struct timespec ts;
+        clock_gettime(CLOCK_MONOTONIC, &ts);
+        return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
+    }
+}
+
+extern "C" void f_bssn_rhs_kernel_timing_reset()
+{
+    for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
+        rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
+}
+
+extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
+{
+    return rhs_kernel_timing::KB_COUNT;
+}
+
+extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
+{
+    return rhs_kernel_timing::local_bucket_seconds;
+}
+
+extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
+{
+    if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
+        return "unknown";
+    return rhs_kernel_timing::bucket_labels[bucket_index];
+}
+
+#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
+#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
+    rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
+        rhs_kernel_timing::now_seconds() - (var_name)
+#else
+extern "C" void f_bssn_rhs_kernel_timing_reset() {}
+extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
+extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
+extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
+
+#define RHS_KERNEL_TIMER_DECL(var_name)
+#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
+#endif
+
 // C function that calculates the right-hand side for BSSN equations
 int f_compute_rhs_bssn(int *ex, double &T, 
                       double *X, double *Y, double *Z,
@@ -120,26 +178,25 @@ int f_compute_rhs_bssn(int *ex, double &T,
    dY = Y[1] - Y[0];
    dZ = Z[1] - Z[0];

+        RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
        // 1ms //
        for(int i=0;i<all;i+=1){
            alpn1[i] = Lap[i] + 1.0;
            chin1[i] = chi[i] + 1.0;
        }
        // 9ms //
-        BSSN_OMP_TASK_GROUP_BEGIN
-        BSSN_OMP_TASK_CALL(fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev))
-        BSSN_OMP_TASK_GROUP_END
+        fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev);
+        fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev);
+        fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev);
+        fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
+        fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
+        fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev);
+        fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev);
+        fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
+        fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev);
+        fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
+        fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
+        fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);

        // 3ms //
        for(int i=0;i<all;i+=1){
@@ -161,6 +218,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
        }
+        RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
+        RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
        // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
        for(int i=0;i<all;i+=1){
            double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
@@ -303,9 +362,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
-            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
-            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
-
            Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
                TWO * alpn1[i] * (
                -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
@@ -335,15 +391,18 @@ int f_compute_rhs_bssn(int *ex, double &T,
                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                        );
        }
+        RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
+        RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
        // 22.3ms //
-        BSSN_OMP_TASK_GROUP_BEGIN
-        BSSN_OMP_TASK_CALL(fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fdderivs(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev))
-        BSSN_OMP_TASK_CALL(fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev))
-        BSSN_OMP_TASK_GROUP_END
+        fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
+        X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
+        fdderivs(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,
+        X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev);
+        fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,
+        X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev);
+        fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev);
+        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);

        // Fused: fxx/Gamxa + Gamma_rhs part 2 (2 loops -> 1)
        for(int i=0;i<all;i+=1){
@@ -351,7 +410,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
            double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
-            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;

            double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                    + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
@@ -705,69 +763,74 @@ int f_compute_rhs_bssn(int *ex, double &T,
                    + Gamxyz[i] * gzzx[i] + Gamyyz[i] * gzzy[i] + Gamzyz[i] * gzzz[i]
                );
        }
+        RHS_KERNEL_TIMER_ADD(KB_RICCI_METRIC, timer_ricci_metric);

+        RHS_KERNEL_TIMER_DECL(timer_chi_lapse);
        // 22.3ms //
            fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);

        // 7ms //
        for (int i=0;i<all;i+=1) {
-            fxx[i] = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
-            fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
-            fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
-            fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
-            fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
-            fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
-            f[i] =
-                gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
-                + gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
-                + gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
-                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
-                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
-                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+            const double inv_chin1 = ONE / chin1[i];
+            const double half_inv_chin1 = HALF * inv_chin1;
+            const double scaled_inv = F3o2 * inv_chin1;
+            const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
+            const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
+            const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
+            const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
+            const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
+            const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
+            const double ricci_chi =
+                gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
+                + gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
+                + gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
+                + TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
+                + TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
+                + TWO * gupyz[i] * (cyz - scaled_inv * chiy[i] * chiz[i]);
+            f[i] = ricci_chi;
+            Rxx[i] = Rxx[i] + ( cxx - half_inv_chin1 * chix[i] * chix[i] + (dxx[i] + ONE) * ricci_chi ) * half_inv_chin1;
+            Ryy[i] = Ryy[i] + ( cyy - half_inv_chin1 * chiy[i] * chiy[i] + (dyy[i] + ONE) * ricci_chi ) * half_inv_chin1;
+            Rzz[i] = Rzz[i] + ( czz - half_inv_chin1 * chiz[i] * chiz[i] + (dzz[i] + ONE) * ricci_chi ) * half_inv_chin1;

-            Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
-            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
-            Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
+            Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
+            Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
+            Ryz[i] = Ryz[i] + ( cyz - half_inv_chin1 * chiy[i] * chiz[i] + gyz[i] * ricci_chi ) * half_inv_chin1;
        }

        // 24ms //
        fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
-        fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);

        // 6ms //
        for (int i=0;i<all;i+=1) {
-            /* gxxx,gxxy,gxxz (这里是“升指标后的chi导数/chi”那类量，你沿用原变量名即可) */
-            gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
-            gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
-            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
+            const double inv_chin1 = ONE / chin1[i];
+            const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
+            const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
+            const double gchi_z = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) * inv_chin1;

            /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) * inv_chin1) - (dxx[i] + ONE) * gchi_x ) * HALF;
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_y ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_z ) * HALF;

-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_x ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) * inv_chin1) - (dyy[i] + ONE) * gchi_y ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_z ) * HALF;

-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_x ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_y ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) * inv_chin1) - (dzz[i] + ONE) * gchi_z ) * HALF;

-            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
-            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
-            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gxxz[i] ) * HALF;
+            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1)      - gxy[i] * gchi_x ) * HALF;
+            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1)      - gxy[i] * gchi_y ) * HALF;
+            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gchi_z ) * HALF;

-            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] / chin1[i])      - gxz[i] * gxxx[i] ) * HALF;
-            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gxxy[i] ) * HALF;
-            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i])      - gxz[i] * gxxz[i] ) * HALF;
+            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1)      - gxz[i] * gchi_x ) * HALF;
+            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gchi_y ) * HALF;
+            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] * inv_chin1)      - gxz[i] * gchi_z ) * HALF;

-            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gxxx[i] ) * HALF;
-            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i])      - gyz[i] * gxxy[i] ) * HALF;
-            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i])      - gyz[i] * gxxz[i] ) * HALF;
+            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gchi_x ) * HALF;
+            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1)      - gyz[i] * gchi_y ) * HALF;
+            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] * inv_chin1)      - gyz[i] * gchi_z ) * HALF;

            /* fxx..fyz 修正：减去 Γ * ∂Lap */
            fxx[i] = fxx[i] - Gamxxx[i] * Lapx[i] - Gamyxx[i] * Lapy[i] - Gamzxx[i] * Lapz[i];
@@ -781,6 +844,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
            trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                    +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
        }
+        RHS_KERNEL_TIMER_ADD(KB_CHI_LAPSE, timer_chi_lapse);
+        RHS_KERNEL_TIMER_DECL(timer_aij_trk_gauge);
        // 2.5ms //
        for (int i=0;i<all;i+=1) {
            const double divb = betaxx[i] + betayy[i] + betazz[i];
@@ -1081,33 +1146,33 @@ int f_compute_rhs_bssn(int *ex, double &T,
            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
            #endif
        }
+        RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
+        RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
        // advection + KO dissipation with shared symmetry buffer
-        BSSN_OMP_TASK_GROUP_BEGIN
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps))
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps))
-        BSSN_OMP_TASK_GROUP_END
+        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
+        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
+        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
+        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
+        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
+        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
+        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
+        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
+        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
+        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
+        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
+        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
+        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
+        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
+        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
        // 2ms //
        if(co==0){
            for (int i=0;i<all;i+=1) {
@@ -1154,14 +1219,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
            }

            // 1ms //
-            BSSN_OMP_TASK_GROUP_BEGIN
-            BSSN_OMP_TASK_CALL(fderivs(ex,Axx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0))
-            BSSN_OMP_TASK_CALL(fderivs(ex,Axy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0))
-            BSSN_OMP_TASK_CALL(fderivs(ex,Axz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0))
-            BSSN_OMP_TASK_CALL(fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0))
-            BSSN_OMP_TASK_CALL(fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0))
-            BSSN_OMP_TASK_CALL(fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0))
-            BSSN_OMP_TASK_GROUP_END
+            fderivs(ex,Axx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
+            fderivs(ex,Axy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0);
+            fderivs(ex,Axz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0);
+            fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
+            fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
+            fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
            // 7ms //
            for (int i=0;i<all;i+=1) {
                gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
@@ -1216,6 +1279,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
            }
        }
+        RHS_KERNEL_TIMER_ADD(KB_KO_CONSTRAINT, timer_ko_constraint);


            
--- a/AMSS_NCKU_source/fdderivs_c.C
+++ b/AMSS_NCKU_source/fdderivs_c.C
@@ -41,8 +41,8 @@ void fdderivs(const int ex[3],
    const size_t nz = (size_t)ex3 + 2;
    const size_t fh_size = nx * ny * nz;

-    static thread_local double *fh = NULL;
-    static thread_local size_t cap = 0;
+    static double *fh = NULL;
+    static size_t cap = 0;

    if (fh_size > cap) {
        free(fh);
--- a/AMSS_NCKU_source/fderivs_c.C
+++ b/AMSS_NCKU_source/fderivs_c.C
@@ -50,8 +50,8 @@ void fderivs(const int ex[3],
    const size_t ny = (size_t)ex2 + 2;
    const size_t nz = (size_t)ex3 + 2;
    const size_t fh_size = nx * ny * nz;
-    static thread_local double *fh = NULL;
-    static thread_local size_t cap = 0;
+    static double *fh = NULL;
+    static size_t cap = 0;

    if (fh_size > cap) {
        free(fh);
--- a/AMSS_NCKU_source/fmisc.f90
+++ b/AMSS_NCKU_source/fmisc.f90
@@ -1514,6 +1514,81 @@ f_out = f_out*dX*dY*dZ
  return

  end subroutine l2normhelper
+!--------------------------------------------------------------------------------------
+  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
+
+  implicit none
+!~~~~~~> Input parameters:
+  integer,intent(in ):: ex(1:3)
+  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
+  integer,intent(in)::gw
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
+  real*8, intent(out) :: f_out(7)
+!~~~~~~> Other variables:
+
+  real*8            :: dX, dY, dZ
+  integer::imin,jmin,kmin
+  integer::imax,jmax,kmax
+  integer::i,j,k
+  real*8 :: s1,s2,s3,s4,s5,s6,s7
+
+  dX = X(2) - X(1)
+  dY = Y(2) - Y(1)
+  dZ = Z(2) - Z(1)
+
+! for ghost zone
+   imin = gw+1
+   jmin = gw+1
+   kmin = gw+1
+
+   imax = ex(1) - gw
+   jmax = ex(2) - gw
+   kmax = ex(3) - gw
+
+!for patch boundary (i.e., not ghost boundary)
+
+if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
+if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
+if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
+if(dabs(X(1)-xmin) < dX) imin = 1
+if(dabs(Y(1)-ymin) < dY) jmin = 1
+if(dabs(Z(1)-zmin) < dZ) kmin = 1
+
+  s1 = 0.d0
+  s2 = 0.d0
+  s3 = 0.d0
+  s4 = 0.d0
+  s5 = 0.d0
+  s6 = 0.d0
+  s7 = 0.d0
+
+  do k=kmin,kmax
+    do j=jmin,jmax
+!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
+      do i=imin,imax
+        s1 = s1 + f1(i,j,k)*f1(i,j,k)
+        s2 = s2 + f2(i,j,k)*f2(i,j,k)
+        s3 = s3 + f3(i,j,k)*f3(i,j,k)
+        s4 = s4 + f4(i,j,k)*f4(i,j,k)
+        s5 = s5 + f5(i,j,k)*f5(i,j,k)
+        s6 = s6 + f6(i,j,k)*f6(i,j,k)
+        s7 = s7 + f7(i,j,k)*f7(i,j,k)
+      enddo
+    enddo
+  enddo
+
+  f_out(1) = s1*dX*dY*dZ
+  f_out(2) = s2*dX*dY*dZ
+  f_out(3) = s3*dX*dY*dZ
+  f_out(4) = s4*dX*dY*dZ
+  f_out(5) = s5*dX*dY*dZ
+  f_out(6) = s6*dX*dY*dZ
+  f_out(7) = s7*dX*dY*dZ
+
+  return
+
+  end subroutine l2normhelper7
 !--------------------------------------------------------------------------------------
 ! calculate L2norm especially for shell Blocks
  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
--- a/AMSS_NCKU_source/fmisc.h
+++ b/AMSS_NCKU_source/fmisc.h
@@ -13,6 +13,7 @@
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
 #define f_l2normhelper l2normhelper
+#define f_l2normhelper7 l2normhelper7
 #define f_l2normhelper_sh l2normhelper_sh
 #define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
@@ -42,6 +43,7 @@
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
 #define f_l2normhelper L2NORMHELPER
+#define f_l2normhelper7 L2NORMHELPER7
 #define f_l2normhelper_sh L2NORMHELPER_SH
 #define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
@@ -71,6 +73,7 @@
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
 #define f_l2normhelper l2normhelper_
+#define f_l2normhelper7 l2normhelper7_
 #define f_l2normhelper_sh l2normhelper_sh_
 #define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
@@ -164,6 +167,15 @@ extern "C"
 						double *, double &, int &);
 }

+extern "C"
+{
+	void f_l2normhelper7(int *, double *, double *, double *,
+						 double &, double &, double &,
+						 double &, double &, double &,
+						 double *, double *, double *, double *,
+						 double *, double *, double *, double *, int &);
+}
+
 extern "C"
 {
 	void f_l2normhelper_sh(int *, double *, double *, double *,
--- a/AMSS_NCKU_source/lopsided_kodis_c.C
+++ b/AMSS_NCKU_source/lopsided_kodis_c.C
@@ -43,13 +43,7 @@ void lopsided_kodis(const int ex[3],
    const size_t nz = (size_t)ex3 + 3;
    const size_t fh_size = nx * ny * nz;

-    static thread_local double *fh = NULL;
-    static thread_local size_t cap = 0;
-    if (fh_size > cap) {
-        free(fh);
-        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
-        cap = fh_size;
-    }
+    double *fh = (double*)malloc(fh_size * sizeof(double));
    if (!fh) return;

    symmetry_bd(3, ex, f, fh, SoA);
@@ -249,4 +243,6 @@ void lopsided_kodis(const int ex[3],
            }
        }
    }
+
+    free(fh);
 }
--- a/AMSS_NCKU_source/macrodef.h
+++ b/AMSS_NCKU_source/macrodef.h
@@ -29,6 +29,16 @@

 #define REGLEV 0

+#define BSSN_FINE_TIMING 0
+
+#define BSSN_FINE_TIMING_EVERY 1
+
+#define BSSN_FINE_TIMING_TOPN 8
+
+#define BSSN_KERNEL_FINE_TIMING 0
+
+#define BSSN_ENABLE_STDIN_ABORT_POLL 0
+
 //#define USE_GPU

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

 #endif   /* MICRODEF_H */
-
--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -16,7 +16,7 @@ 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 \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS) $(OPENMP_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
@@ -26,7 +26,7 @@ else


 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS) $(OPENMP_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -29,9 +29,6 @@ endif
 ##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
 PGO_MODE ?= opt

-## OpenMP switch for C/C++ kernels
-OPENMP_FLAGS ?= -qopenmp
-
 ## Interp_Points load balance profiling mode
 ##   off        : (default) no load balance instrumentation
 ##   profile    : Pass 1 — instrument Interp_Points to collect timing profile
--- a/AMSS_NCKU_source/scalar_class.C
+++ b/AMSS_NCKU_source/scalar_class.C
@@ -319,7 +319,7 @@ void scalar_class::Setup_Initial_Data()
 }
 void scalar_class::Evolve(int Steps)
 {
-  double prev_clock = 0.0, curr_clock = 0.0;
+  clock_t prev_clock, curr_clock;
  double LastDump = 0.0, LastCheck = 0.0;
  LastAnas = 0;

@@ -328,7 +328,7 @@ void scalar_class::Evolve(int Steps)
  for (int ncount = 1; ncount < Steps + 1; ncount++)
  {
    if (myrank == 0)
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
    RecursiveStep(0);

    LastDump += dT_mon;
@@ -346,9 +346,9 @@ void scalar_class::Evolve(int Steps)
    if (myrank == 0)
    {
      prev_clock = curr_clock;
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
      cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime
-           << " Computer used " << (curr_clock - prev_clock) << " seconds! " << endl;
+           << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds! " << endl;
    }
    if (PhysTime >= TotalTime)
      break;
--- a/AMSS_NCKU_source/surface_integral.C
+++ b/AMSS_NCKU_source/surface_integral.C
--- a/AMSS_NCKU_source/surface_integral.h
+++ b/AMSS_NCKU_source/surface_integral.h
@@ -36,6 +36,11 @@ private:

 	double *nx_g, *ny_g, *nz_g; // global list of unit normals
 	int myrank, cpusize;
+	int wave_cache_spinw, wave_cache_maxl, wave_cache_modes;
+	double *wave_theta_pos, *wave_theta_neg;
+	double *wave_phi_cos, *wave_phi_sin;
+	void clear_wave_cache();
+	void build_wave_cache(int spinw, int maxl);

 public:
 	surface_integral(int iSymmetry);
@@ -82,13 +87,29 @@ public:
 					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 					   var *Gmx, var *Gmy, var *Gmz,
 					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
 	void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
 					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
 					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 					   var *Gmx, var *Gmy, var *Gmz,
 					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, cgh *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
 	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
 				   var *chi, var *trK,
 				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
@@ -115,7 +136,7 @@ public:
 					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 					   var *Gmx, var *Gmy, var *Gmz,
 					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
-					   double *Rout, monitor *Monitor, MPI_Comm Comm_here);
+					   double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields = true);
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
 				   monitor *Monitor, MPI_Comm Comm_here);
--- a/generate_macrodef.py
+++ b/generate_macrodef.py
@@ -144,6 +144,62 @@ def generate_macrodef_h():
    print( "#define REGLEV 0",      file=file1 )
    print(                          file=file1 )

+    # Define fine-grained timing/debug macros.
+    # All of them default to OFF so production builds do not pay profiling overhead.
+
+    fine_timing = getattr(input_data, "Fine_Timing",
+                  getattr(input_data, "Finegrained_Timing", "no"))
+    kernel_fine_timing = getattr(input_data, "Kernel_Fine_Timing",
+                          getattr(input_data, "BSSN_Kernel_Fine_Timing", "no"))
+    stdin_abort_poll = getattr(input_data, "Enable_Stdin_Abort_Poll",
+                       getattr(input_data, "Stdin_Abort_Poll", "no"))
+    timing_report_every = max(1, int(getattr(
+        input_data, "Timing_Every_Steps",
+        getattr(input_data, "Timing_Report_Every", 1))))
+    timing_top_hotspots = max(1, int(getattr(
+        input_data, "Timing_Top_Hotspots", 8)))
+
+    if ( fine_timing == "yes" ):
+        print( "#define BSSN_FINE_TIMING 1", file=file1 )
+        print(                               file=file1 )
+    elif ( fine_timing == "no" ):
+        print( "#define BSSN_FINE_TIMING 0", file=file1 )
+        print(                               file=file1 )
+    else:
+        print( "Fine_Timing setting error!!!" )
+        print()
+        print( "# Fine_Timing setting error!!!", file=file1 )
+        print(                                   file=file1 )
+
+    print( f"#define BSSN_FINE_TIMING_EVERY {timing_report_every}", file=file1 )
+    print(                                                          file=file1 )
+    print( f"#define BSSN_FINE_TIMING_TOPN {timing_top_hotspots}",  file=file1 )
+    print(                                                          file=file1 )
+
+    if ( kernel_fine_timing == "yes" ):
+        print( "#define BSSN_KERNEL_FINE_TIMING 1", file=file1 )
+        print(                                      file=file1 )
+    elif ( kernel_fine_timing == "no" ):
+        print( "#define BSSN_KERNEL_FINE_TIMING 0", file=file1 )
+        print(                                      file=file1 )
+    else:
+        print( "Kernel_Fine_Timing setting error!!!" )
+        print()
+        print( "# Kernel_Fine_Timing setting error!!!", file=file1 )
+        print(                                          file=file1 )
+
+    if ( stdin_abort_poll == "yes" ):
+        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 1", file=file1 )
+        print(                                           file=file1 )
+    elif ( stdin_abort_poll == "no" ):
+        print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 0", file=file1 )
+        print(                                           file=file1 )
+    else:
+        print( "Enable_Stdin_Abort_Poll setting error!!!" )
+        print()
+        print( "# Enable_Stdin_Abort_Poll setting error!!!", file=file1 )
+        print(                                               file=file1 )
+
    # Define macro USE_GPU
    # use GPU or not
    
@@ -224,6 +280,21 @@ def generate_macrodef_h():
    print( "//     0: for every level;",                                                 file=file1 ) 
    print( "//     1: for all",                                                          file=file1 )
    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING",                                                 file=file1 )
+    print( "//     enable fine-grained per-timestep timing monitor",                     file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING_EVERY",                                           file=file1 )
+    print( "//     report timing every N coarse timesteps",                              file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_FINE_TIMING_TOPN",                                            file=file1 )
+    print( "//     number of hottest timing buckets shown in stdout",                    file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_KERNEL_FINE_TIMING",                                          file=file1 )
+    print( "//     enable split timing inside compute_rhs_bssn",                         file=file1 )
+    print( "//",                                                                         file=file1 )
+    print( "// define BSSN_ENABLE_STDIN_ABORT_POLL",                                     file=file1 )
+    print( "//     poll stdin and broadcast abort flag every coarse step",               file=file1 )
+    print( "//",                                                                         file=file1 )
    print( "// define USE_GPU",                                                          file=file1 )
    print( "//     use gpu or not",                                                      file=file1 )
    print( "//",                                                                         file=file1 )
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -9,7 +9,6 @@


 import AMSS_NCKU_Input as input_data
-import os
 import subprocess
 import time

@@ -55,44 +54,6 @@ NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
 BUILD_JOBS = 64


-def build_abe_runtime_env():
-    """Inject OpenMP runtime settings only for the main ABE evolution run."""
-    runtime_env = os.environ.copy()
-    omp_threads = max(1, int(getattr(input_data, "OMP_Threads", 1)))
-    runtime_env["OMP_NUM_THREADS"] = str(omp_threads)
-    return runtime_env
-
-
-def build_twopuncture_runtime_env():
-    """Let TwoPunctureABE use the runtime default instead of the ABE OMP override."""
-    runtime_env = os.environ.copy()
-    runtime_env.pop("OMP_NUM_THREADS", None)
-    runtime_env.pop("OMP_THREAD_LIMIT", None)
-    return runtime_env
-
-
-def build_mpi_launch_args():
-    """Build optional host-distribution arguments for mpirun."""
-    hosts = list(getattr(input_data, "MPI_hosts", []))
-    ppn = int(getattr(input_data, "MPI_processes_per_node", 0))
-
-    if not hosts:
-        return ""
-
-    if ppn > 0:
-        expected = len(hosts) * ppn
-        if int(input_data.MPI_processes) != expected:
-            raise ValueError(
-                f"MPI_processes={input_data.MPI_processes} does not match "
-                f"len(MPI_hosts) * MPI_processes_per_node = {expected}"
-            )
-
-    launch_args = f"-hosts {','.join(hosts)}"
-    if ppn > 0:
-        launch_args += f" -ppn {ppn}"
-    return launch_args
-
-
 ##################################################################


@@ -182,38 +143,19 @@ def run_ABE():
    print(                                                      )
    print( " Running the AMSS-NCKU executable file ABE/ABEGPU " ) 
    print(                                                      )
-    print( f" MPI processes = {input_data.MPI_processes}, OMP threads per process = {max(1, int(getattr(input_data, 'OMP_Threads', 1)))}" )
-    if getattr(input_data, "MPI_hosts", []):
-        print( f" MPI hosts = {getattr(input_data, 'MPI_hosts', [])}, MPI ranks per node = {int(getattr(input_data, 'MPI_processes_per_node', 0))}" )
-        print( " Multi-node runs require the working directory to be visible on all MPI hosts. " )
-    print(                                                                                                      )

    ## Define the command to run; cast other values to strings as needed
-    mpi_launch_args = build_mpi_launch_args()
    
    if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun "
-        if mpi_launch_args:
-            mpi_command += mpi_launch_args + " "
-        mpi_command += "-np " + str(input_data.MPI_processes) + " ./ABE"
+        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 "
-        if mpi_launch_args:
-            mpi_command += mpi_launch_args + " "
-        mpi_command += "-np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        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,
-        env=build_abe_runtime_env(),
-    )
+    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)

    ## Write ABE run output to file while printing to stdout
    with open(mpi_command_outfile, 'w') as file0:  
@@ -253,14 +195,7 @@ def run_TwoPunctureABE():
    TwoPuncture_command_outfile = "TwoPunctureABE_out.log"

    ## Execute the command with subprocess.Popen and stream output
-    TwoPuncture_process = subprocess.Popen(
-        TwoPuncture_command,
-        shell=True,
-        stdout=subprocess.PIPE,
-        stderr=subprocess.STDOUT,
-        text=True,
-        env=build_twopuncture_runtime_env(),
-    )
+    TwoPuncture_process = subprocess.Popen(TwoPuncture_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)

    ## Write TwoPunctureABE run output to file while printing to stdout
    with open(TwoPuncture_command_outfile, 'w') as file0:  
--- a/setup.py
+++ b/setup.py
@@ -68,10 +68,6 @@ def print_input_data( File_directory ):
    print( " Printing the basic parameter and setting in the AMSS-NCKU simulation "                  )
    print(                                                                                           )
    print( " The number of MPI processes in the AMSS-NCKU simulation = ", input_data.MPI_processes   ) 
-    print( " The number of OMP threads per MPI process         = ", input_data.OMP_Threads           )
-    if getattr(input_data, "MPI_hosts", []):
-        print( " The MPI host list in the AMSS-NCKU simulation   = ", input_data.MPI_hosts             )
-        print( " The number of MPI ranks launched per host       = ", input_data.MPI_processes_per_node )
    print(                                                                                           )
    print( " The form of computational equation  = ",            input_data.Equation_Class           )
    print( " The initial data in this simulation = ",            input_data.Initial_Data_Method      )
@@ -147,10 +143,6 @@ def print_input_data( File_directory ):
    print( " Printing the basic parameter and setting in the AMSS-NCKU simulation ",                    file=file0 )
    print(                                                                                              file=file0 )
    print( " The number of MPI processes in the AMSS-NCKU simulation = ", input_data.MPI_processes,     file=file0 ) 
-    print( " The number of OMP threads per MPI process         = ", input_data.OMP_Threads,             file=file0 )
-    if getattr(input_data, "MPI_hosts", []):
-        print( " The MPI host list in the AMSS-NCKU simulation   = ", input_data.MPI_hosts,               file=file0 )
-        print( " The number of MPI ranks launched per host       = ", input_data.MPI_processes_per_node,   file=file0 )
    print(                                                                                              file=file0 )
    print( " The form of computational equation  = ",            input_data.Equation_Class,             file=file0 )
    print( " The initial data in this simulation = ",            input_data.Initial_Data_Method,        file=file0 )
Author	SHA1	Message	Date
CGH0S7	9c31384b2f	Add optional BSSN kernel profiling switches	2026-04-13 16:51:06 +08:00
CGH0S7	e4e741caa1	Remove dead chi derivative setup in BSSN RHS	2026-04-13 15:55:43 +08:00
CGH0S7	65e0f95f40	Localize chi Ricci intermediates in RHS	2026-04-13 15:14:31 +08:00
CGH0S7	f9fbf97e64	Elide dead stores in BSSN RHS hot path	2026-04-13 15:10:22 +08:00
CGH0S7	968522995b	Add fine-grained step timing and trim BH RHS overhead	2026-04-13 14:50:55 +08:00
CGH0S7	f3988ac8ca	Merge wave and mass extraction interpolation	2026-04-13 13:17:36 +08:00
CGH0S7	e4c25eb21f	Cache wave extraction angular kernels	2026-04-13 12:40:20 +08:00
CGH0S7	4b10519876	Reuse mass integrand across detector radii	2026-04-13 11:55:41 +08:00
CGH0S7	3a58273501	Batch constraint norm reductions	2026-04-13 11:48:02 +08:00
CGH0S7	5c65cea2f0	Optimize constraint refresh after regrid	2026-04-13 11:39:50 +08:00