Switch legacy build to GCC and OpenMPI

Add optional BSSN kernel profiling switches
Remove dead chi derivative setup in BSSN RHS
2026-04-13 19:39:30 +08:00 · 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
21 changed files with 2807 additions and 1279 deletions
--- a/AMSS_NCKU_source/FFT.f90
+++ b/AMSS_NCKU_source/FFT.f90
@@ -37,51 +37,56 @@ close(77)
 end program checkFFT
 #endif

-!-------------
-! Optimized FFT using Intel oneMKL DFTI
-! Mathematical equivalence: Standard DFT definition
-!   Forward (isign=1):  X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
-!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
-! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
-!-------------
 SUBROUTINE four1(dataa,nn,isign)
-use MKL_DFTI
 implicit none
-INTEGER, intent(in) :: isign, nn
-DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
-
-type(DFTI_DESCRIPTOR), pointer :: desc
-integer :: status
-
-! Create DFTI descriptor for 1D complex-to-complex transform
-status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
-if (status /= 0) return
-
-! Set input/output storage as interleaved complex (default)
-status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
-if (status /= 0) then
-   status = DftiFreeDescriptor(desc)
-   return
+INTEGER::isign,nn
+double precision,dimension(2*nn)::dataa
+INTEGER::i,istep,j,m,mmax,n
+double precision::tempi,tempr
+DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
+n=2*nn
+j=1
+do i=1,n,2
+  if(j.gt.i)then
+     tempr=dataa(j)
+     tempi=dataa(j+1)
+     dataa(j)=dataa(i)
+     dataa(j+1)=dataa(i+1)
+     dataa(i)=tempr
+     dataa(i+1)=tempi
  endif
-
-! Commit the descriptor
-status = DftiCommitDescriptor(desc)
-if (status /= 0) then
-   status = DftiFreeDescriptor(desc)
-   return
+  m=nn
+1 if ((m.ge.2).and.(j.gt.m)) then
+  j=j-m
+  m=m/2
+goto 1
  endif
-
-! Execute FFT based on direction
-if (isign == 1) then
-   ! Forward FFT: exp(-2*pi*i*k*n/N)
-   status = DftiComputeForward(desc, dataa)
-else
-   ! Backward FFT: exp(+2*pi*i*k*n/N)
-   status = DftiComputeBackward(desc, dataa)
+j=j+m
+enddo
+mmax=2
+2  if (n.gt.mmax) then
+     istep=2*mmax
+     theta=6.28318530717959d0/(isign*mmax)
+     wpr=-2.d0*sin(0.5d0*theta)**2
+     wpi=sin(theta)
+     wr=1.d0
+     wi=0.d0
+     do m=1,mmax,2
+       do i=m,n,istep
+         j=i+mmax
+         tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
+         tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
+         dataa(j)=dataa(i)-tempr
+         dataa(j+1)=dataa(i+1)-tempi
+         dataa(i)=dataa(i)+tempr
+         dataa(i+1)=dataa(i+1)+tempi
+       enddo
+          wtemp=wr
+          wr=wr*wpr-wi*wpi+wr
+          wi=wi*wpr+wtemp*wpi+wi
+     enddo
+mmax=istep
+goto 2
 endif
-
-! Free descriptor
-status = DftiFreeDescriptor(desc)
-
 return
 END SUBROUTINE four1
--- 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/TwoPunctures.C
+++ b/AMSS_NCKU_source/TwoPunctures.C
@@ -27,7 +27,21 @@ using namespace std;
 #endif

 #include "TwoPunctures.h"
-#include <mkl_cblas.h>
+
+extern "C" {
+double cblas_ddot(const int, const double *, const int, const double *, const int);
+double cblas_dnrm2(const int, const double *, const int);
+void cblas_dgemm(const int, const int, const int,
+                 const int, const int, const int,
+                 const double, const double *, const int,
+                 const double *, const int, const double,
+                 double *, const int);
+}
+
+enum {
+  CblasRowMajor = 101,
+  CblasNoTrans = 111
+};

 TwoPunctures::TwoPunctures(double mp, double mm, double b,
                           double P_plusx, double P_plusy, double P_plusz,
--- 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;
@@ -2147,6 +2399,15 @@ 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; }
@@ -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;

@@ -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,
+        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, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
+                                     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,
+        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, // here we can not touch rhs variables, but 1 variables
-                                 RoutMAP, ErrorMonitor);
+                                     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,
+      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, // here we can not touch rhs variables, but 1 variables
-                               RoutMAP, ErrorMonitor);
+                                   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_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
@@ -2,12 +2,88 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
+#include <time.h>
 // 0-based i,j,k
 // #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
 // ex(1)=nx, ex(2)=ny, ex(3)=nz

 // 用法：a[ IDX_F(i,j,k,nx,ny) ]

+#ifndef BSSN_KERNEL_FINE_TIMING
+#define BSSN_KERNEL_FINE_TIMING 0
+#endif
+
+#if BSSN_KERNEL_FINE_TIMING
+namespace rhs_kernel_timing
+{
+    enum Bucket
+    {
+        KB_SETUP_DERIVS = 0,
+        KB_GEOM_GAMMA,
+        KB_RICCI_METRIC,
+        KB_CHI_LAPSE,
+        KB_AIJ_TRK_GAUGE,
+        KB_KO_CONSTRAINT,
+        KB_COUNT
+    };
+
+    static double local_bucket_seconds[KB_COUNT];
+
+    static const char *bucket_labels[KB_COUNT] =
+    {
+        "setup_derivs",
+        "geom_gamma",
+        "ricci_metric",
+        "chi_lapse",
+        "aij_trk_gauge",
+        "ko_constraint"
+    };
+
+    static inline double now_seconds()
+    {
+        struct timespec ts;
+        clock_gettime(CLOCK_MONOTONIC, &ts);
+        return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
+    }
+}
+
+extern "C" void f_bssn_rhs_kernel_timing_reset()
+{
+    for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
+        rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
+}
+
+extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
+{
+    return rhs_kernel_timing::KB_COUNT;
+}
+
+extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
+{
+    return rhs_kernel_timing::local_bucket_seconds;
+}
+
+extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
+{
+    if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
+        return "unknown";
+    return rhs_kernel_timing::bucket_labels[bucket_index];
+}
+
+#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
+#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
+    rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
+        rhs_kernel_timing::now_seconds() - (var_name)
+#else
+extern "C" void f_bssn_rhs_kernel_timing_reset() {}
+extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
+extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
+extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
+
+#define RHS_KERNEL_TIMER_DECL(var_name)
+#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
+#endif
+
 // C function that calculates the right-hand side for BSSN equations
 int f_compute_rhs_bssn(int *ex, double &T, 
                       double *X, double *Y, double *Z,
@@ -102,6 +178,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
    dY = Y[1] - Y[0];
    dZ = Z[1] - Z[0];

+        RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
        // 1ms //
        for(int i=0;i<all;i+=1){
            alpn1[i] = Lap[i] + 1.0;
@@ -141,6 +218,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
        }
+        RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
+        RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
        // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
        for(int i=0;i<all;i+=1){
            double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
@@ -283,9 +362,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
-            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
-            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
-
            Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
                TWO * alpn1[i] * (
                -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
@@ -315,6 +391,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                        );
        }
+        RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
+        RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
        // 22.3ms //
        fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
        X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
@@ -332,7 +410,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
            double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
-            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;

            double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                    + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
@@ -686,69 +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];
@@ -762,6 +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];
@@ -1062,6 +1146,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
            #endif
        }
+        RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
+        RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
        // advection + KO dissipation with shared symmetry buffer
        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
@@ -1193,6 +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/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/gaussj.C
+++ b/AMSS_NCKU_source/gaussj.C
@@ -17,65 +17,103 @@ using namespace std;
 #include <math.h>
 #endif

-// Intel oneMKL LAPACK interface
-#include <mkl_lapacke.h>
-/* Linear equation solution using Intel oneMKL LAPACK.
+/* Linear equation solution by Gauss-Jordan elimination.
 a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
 containing the right-hand side vectors. On output a is
 replaced by its matrix inverse, and b is replaced by the
-corresponding set of solution vectors.
-
-Mathematical equivalence:
-  Solves: A * x = b  =>  x = A^(-1) * b
-  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
-  within numerical precision. */
+corresponding set of solution vectors. */

 int gaussj(double *a, double *b, int n)
 {
-  // Allocate pivot array and workspace
-  lapack_int *ipiv = new lapack_int[n];
-  lapack_int info;
+  double swap;

-  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
-  double *a_copy = new double[n * n];
-  for (int i = 0; i < n * n; i++) {
-    a_copy[i] = a[i];
+  int *indxc, *indxr, *ipiv;
+  indxc = new int[n];
+  indxr = new int[n];
+  ipiv = new int[n];
+
+  int i, icol, irow, j, k, l, ll;
+  double big, dum, pivinv;
+
+  for (j = 0; j < n; j++)
+    ipiv[j] = 0;
+  for (i = 0; i < n; i++)
+  {
+    big = 0.0;
+    for (j = 0; j < n; j++)
+      if (ipiv[j] != 1)
+        for (k = 0; k < n; k++)
+        {
+          if (ipiv[k] == 0)
+          {
+            if (fabs(a[j * n + k]) >= big)
+            {
+              big = fabs(a[j * n + k]);
+              irow = j;
+              icol = k;
+            }
+          }
+          else if (ipiv[k] > 1)
+          {
+            cout << "gaussj: Singular Matrix-1" << endl;
+            return 1;
+          }
        }

-  // Step 1: Solve linear system A*x = b using LU decomposition
-  // LAPACKE_dgesv uses column-major by default, but we use row-major
-  info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
+    ipiv[icol] = ipiv[icol] + 1;
+    if (irow != icol)
+    {
+      for (l = 0; l < n; l++)
+      {
+        swap = a[irow * n + l];
+        a[irow * n + l] = a[icol * n + l];
+        a[icol * n + l] = swap;
+      }

-  if (info != 0) {
-    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
-    delete[] ipiv;
-    delete[] a_copy;
+      swap = b[irow];
+      b[irow] = b[icol];
+      b[icol] = swap;
+    }
+
+    indxr[i] = irow;
+    indxc[i] = icol;
+
+    if (a[icol * n + icol] == 0.0)
+    {
+      cout << "gaussj: Singular Matrix-2" << endl;
      return 1;
    }

-  // Step 2: Compute matrix inverse A^(-1) using LU factorization
-  // First do LU factorization of original matrix a
-  info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
-
-  if (info != 0) {
-    cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
-    delete[] ipiv;
-    delete[] a_copy;
-    return 1;
+    pivinv = 1.0 / a[icol * n + icol];
+    a[icol * n + icol] = 1.0;
+    for (l = 0; l < n; l++)
+      a[icol * n + l] *= pivinv;
+    b[icol] *= pivinv;
+    for (ll = 0; ll < n; ll++)
+      if (ll != icol)
+      {
+        dum = a[ll * n + icol];
+        a[ll * n + icol] = 0.0;
+        for (l = 0; l < n; l++)
+          a[ll * n + l] -= a[icol * n + l] * dum;
+        b[ll] -= b[icol] * dum;
+      }
  }

-  // Then compute inverse from LU factorization
-  info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
-
-  if (info != 0) {
-    cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
-    delete[] ipiv;
-    delete[] a_copy;
-    return 1;
+  for (l = n - 1; l >= 0; l--)
+  {
+    if (indxr[l] != indxc[l])
+      for (k = 0; k < n; k++)
+      {
+        swap = a[k * n + indxr[l]];
+        a[k * n + indxr[l]] = a[k * n + indxc[l]];
+        a[k * n + indxc[l]] = swap;
+      }
  }

+  delete[] indxc;
+  delete[] indxr;
  delete[] ipiv;
-  delete[] a_copy;

  return 0;
 }
--- 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
@@ -8,27 +8,16 @@ include makefile.inc
 POLINT6_USE_BARY ?= 1
 POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)

-## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
-##   make                        -> opt  (PGO-guided, maximum performance)
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+## Legacy GNU/OpenMPI flags
+CXXBASEFLAGS = -O3 -march=native -Wno-deprecated -Dfortran3 -Dnewc $(INTERP_LB_FLAGS)
+F90BASEFLAGS = -O3 -march=native -cpp -fallow-argument-mismatch $(POLINT6_FLAG)

 ifeq ($(PGO_MODE),instrument)
-## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+CXXAPPFLAGS = $(CXXBASEFLAGS)
+f90appflags = $(F90BASEFLAGS)
 else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-## PGO has been turned off, now tested and found to be negative optimization
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+CXXAPPFLAGS = $(CXXBASEFLAGS)
+f90appflags = $(F90BASEFLAGS)
 endif

 .SUFFIXES: .o .f90 .C .for .cu
@@ -68,16 +57,13 @@ lopsided_kodis_c.o: lopsided_kodis_c.C
 #	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@

 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
-TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
-TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=$(TP_PROFDATA) \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
+TP_OPTFLAGS = $(CXXBASEFLAGS) $(TP_OPENMP_FLAGS)

 TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -c $< -o $@

 TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -c $< -o $@

 # Input files

@@ -185,7 +171,7 @@ ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILE
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)

 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)

 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -1,33 +1,27 @@
-## GCC version (commented out)
-## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
+## Legacy GNU/OpenMPI toolchain configuration

-## Intel oneAPI version with oneMKL (Optimized for performance)
-filein  = -I/usr/include/ -I${MKLROOT}/include
+## OpenMPI wrappers are installed but may not be on PATH.
+OMPI_BIN ?= /usr/lib64/openmpi/bin

-## 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
+## Wrapper compilers
+f90          = $(OMPI_BIN)/mpifort
+f77          = $(OMPI_BIN)/mpifort
+CXX          = $(OMPI_BIN)/mpicxx
+CC           = $(OMPI_BIN)/mpicc
+CLINKER      = $(OMPI_BIN)/mpicxx

-## Memory allocator switch
-##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
-##   0           : use system default allocator (ptmalloc)
-USE_TBBMALLOC ?= 1
-TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
-ifneq ($(wildcard $(TBBMALLOC_SO)),)
-TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
-else
-TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
-endif
-ifeq ($(USE_TBBMALLOC),1)
-LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
-endif
+## Extra include flags are not needed when using the OpenMPI wrappers.
+filein       =

-## 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
-PGO_MODE ?= opt
+## BLAS/LAPACK backend:
+## OpenBLAS on this system provides BLAS, CBLAS and LAPACK symbols.
+BLAS_LAPACK_LIB ?= /lib64/libopenblaso.so.0
+LDLIBS  = $(BLAS_LAPACK_LIB) -lgfortran -lpthread -lm -ldl
+
+## PGO build mode switch
+##   off        : default legacy GNU build without PGO
+##   instrument : accepted for compatibility, currently same as off
+PGO_MODE ?= off

 ## Interp_Points load balance profiling mode
 ##   off        : (default) no load balance instrumentation
@@ -49,17 +43,13 @@ endif
 USE_CXX_KERNELS ?= 1

 ## RK4 kernel implementation switch
-##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
+##   1 (default) : use C/C++ rewrite of rungekutta4_rout
 ##   0           : use original Fortran rungekutta4_rout.o
 USE_CXX_RK4 ?= 1

-f90          = ifx
-f77          = ifx
-CXX          = icpx
-CC           = icx
-CLINKER      = mpiicpx
+## OpenMP is only used for TwoPunctures on the legacy toolchain.
+TP_OPENMP_FLAGS ?= -fopenmp

 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
--- a/AMSS_NCKU_source/surface_integral.C
+++ b/AMSS_NCKU_source/surface_integral.C
@@ -36,7 +36,14 @@ using namespace std;
 //| Constructor
 //|============================================================================

-surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry)
+surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry),
+                                                    wave_cache_spinw(-1),
+                                                    wave_cache_maxl(-1),
+                                                    wave_cache_modes(0),
+                                                    wave_theta_pos(0),
+                                                    wave_theta_neg(0),
+                                                    wave_phi_cos(0),
+                                                    wave_phi_sin(0)
 {
  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
  MPI_Comm_size(MPI_COMM_WORLD, &cpusize);
@@ -182,6 +189,7 @@ surface_integral::surface_integral(int iSymmetry) : Symmetry(iSymmetry)
 //|============================================================================
 surface_integral::~surface_integral()
 {
+  clear_wave_cache();
  delete[] nx_g;
  delete[] ny_g;
  delete[] nz_g;
@@ -190,6 +198,65 @@ surface_integral::~surface_integral()
  delete[] wtcostheta;
 #endif
 }
+void surface_integral::clear_wave_cache()
+{
+  delete[] wave_theta_pos;
+  delete[] wave_theta_neg;
+  delete[] wave_phi_cos;
+  delete[] wave_phi_sin;
+  wave_theta_pos = 0;
+  wave_theta_neg = 0;
+  wave_phi_cos = 0;
+  wave_phi_sin = 0;
+  wave_cache_spinw = -1;
+  wave_cache_maxl = -1;
+  wave_cache_modes = 0;
+}
+void surface_integral::build_wave_cache(int spinw, int maxl)
+{
+  if (wave_cache_spinw == spinw && wave_cache_maxl == maxl && wave_theta_pos && wave_theta_neg && wave_phi_cos && wave_phi_sin)
+    return;
+
+  clear_wave_cache();
+
+  int modes = 0;
+  for (int pl = spinw; pl < maxl + 1; pl++)
+    for (int pm = -pl; pm < pl + 1; pm++)
+      modes++;
+
+  wave_theta_pos = new double[modes * N_theta];
+  wave_theta_neg = new double[modes * N_theta];
+  wave_phi_cos = new double[modes * N_phi];
+  wave_phi_sin = new double[modes * N_phi];
+
+  int countlm = 0;
+  for (int pl = spinw; pl < maxl + 1; pl++)
+    for (int pm = -pl; pm < pl + 1; pm++)
+    {
+      const double prefactor = sqrt((2 * pl + 1.0) / 4.0 / PI);
+      for (int i = 0; i < N_theta; i++)
+      {
+#ifdef GaussInt
+        const double weight = wtcostheta[i];
+#else
+        const double weight = 1.0;
+#endif
+        wave_theta_pos[countlm * N_theta + i] = prefactor * misc::Wigner_d_function(pl, pm, spinw, arcostheta[i]) * weight;
+        wave_theta_neg[countlm * N_theta + i] = prefactor * misc::Wigner_d_function(pl, pm, spinw, -arcostheta[i]) * weight;
+      }
+      for (int j = 0; j < N_phi; j++)
+      {
+        const double phase = pm * (j + 0.5) * dphi;
+        wave_phi_cos[countlm * N_phi + j] = cos(phase);
+        wave_phi_sin[countlm * N_phi + j] = sin(phase);
+      }
+      countlm++;
+    }
+
+  wave_cache_spinw = spinw;
+  wave_cache_maxl = maxl;
+  wave_cache_modes = modes;
+}
 //|----------------------------------------------------------------
 //  spin weighted spinw component of psi4, general routine
 //  l takes from spinw to maxl; m takes from -l to l
@@ -264,6 +331,39 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
    lpsy = 8;

  double psi4RR, psi4II;
+  if (Symmetry == 0 || Symmetry == 1)
+  {
+    build_wave_cache(spinw, maxl);
+    for (n = Nmin; n <= Nmax; n++)
+    {
+      i = int(n / N_phi);
+      j = n - i * N_phi;
+
+      const double psi4RR0 = shellf[InList * n];
+      const double psi4II0 = shellf[InList * n + 1];
+      const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
+      const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
+      for (int countlm = 0; countlm < wave_cache_modes; countlm++)
+      {
+        const int theta_idx = countlm * N_theta + i;
+        const int phi_idx = countlm * N_phi + j;
+        const double theta_pos = wave_theta_pos[theta_idx];
+        const double cosmphi_here = wave_phi_cos[phi_idx];
+        const double sinmphi_here = wave_phi_sin[phi_idx];
+
+        RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
+        IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
+        if (Symmetry == 1)
+        {
+          const double theta_neg = wave_theta_neg[theta_idx];
+          RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
+          IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
+        }
+      }
+    }
+  }
+  else
+  {
    for (n = Nmin; n <= Nmax; n++)
    {
      //       need round off always
@@ -348,6 +448,7 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
          countlm++; // no sanity check for countlm and NN which should be noted in the input parameters
        }
    }
+  }

  for (int ii = 0; ii < NN; ii++)
  {
@@ -466,6 +567,39 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
    lpsy = 8;

  double psi4RR, psi4II;
+  if (Symmetry == 0 || Symmetry == 1)
+  {
+    build_wave_cache(spinw, maxl);
+    for (n = Nmin; n <= Nmax; n++)
+    {
+      i = int(n / N_phi);
+      j = n - i * N_phi;
+
+      const double psi4RR0 = shellf[InList * n];
+      const double psi4II0 = shellf[InList * n + 1];
+      const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
+      const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
+      for (int countlm = 0; countlm < wave_cache_modes; countlm++)
+      {
+        const int theta_idx = countlm * N_theta + i;
+        const int phi_idx = countlm * N_phi + j;
+        const double theta_pos = wave_theta_pos[theta_idx];
+        const double cosmphi_here = wave_phi_cos[phi_idx];
+        const double sinmphi_here = wave_phi_sin[phi_idx];
+
+        RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
+        IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
+        if (Symmetry == 1)
+        {
+          const double theta_neg = wave_theta_neg[theta_idx];
+          RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
+          IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
+        }
+      }
+    }
+  }
+  else
+  {
    for (n = Nmin; n <= Nmax; n++)
    {
      //       need round off always
@@ -550,6 +684,7 @@ void surface_integral::surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *
          countlm++; // no sanity check for countlm and NN which should be noted in the input parameters
        }
    }
+  }

  for (int ii = 0; ii < NN; ii++)
  {
@@ -2319,7 +2454,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
                                     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)
+                                     double *Rout, monitor *Monitor, bool refresh_mass_fields)
 {
  if (myrank == 0 && GH->grids[lev] != 1)
    if (Monitor && Monitor->outfile)
@@ -2329,6 +2464,8 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var

  double mass, px, py, pz, sx, sy, sz;

+  if (refresh_mass_fields)
+  {
    MyList<Patch> *Pp = GH->PatL[lev];
    while (Pp)
    {
@@ -2352,6 +2489,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
      }
      Pp = Pp->next;
    }
+  }

  const int InList = 17;

@@ -2581,7 +2719,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
                                     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)
 {
  int lmyrank;
  MPI_Comm_rank(Comm_here, &lmyrank);
@@ -2593,6 +2731,8 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var

  double mass, px, py, pz, sx, sy, sz;

+  if (refresh_mass_fields)
+  {
    MyList<Patch> *Pp = GH->PatL[lev];
    while (Pp)
    {
@@ -2616,6 +2756,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var
      }
      Pp = Pp->next;
    }
+  }

  const int InList = 17;

@@ -2853,7 +2994,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
                                     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)
+                                     double *Rout, monitor *Monitor, bool refresh_mass_fields)
 {
  if (lev != 0)
  {
@@ -2869,6 +3010,8 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c

  double mass, px, py, pz, sx, sy, sz;

+  if (refresh_mass_fields)
+  {
    MyList<ss_patch> *Pp = GH->PatL;
    while (Pp)
    {
@@ -2903,6 +3046,7 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
      }
      Pp = Pp->next;
    }
+  }

  const int InList = 17;

@@ -3128,6 +3272,626 @@ void surface_integral::surf_MassPAng(double rex, int lev, ShellPatch *GH, var *c
  delete[] shellf;
  DG_List->clearList();
 }
+void surface_integral::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)
+{
+  if (Symmetry != 0 && Symmetry != 1)
+  {
+    surf_Wave(rex, lev, GH, Rpsi4, Ipsi4, spinw, maxl, NN, RP, IP, Monitor);
+    surf_MassPAng(rex, lev, GH, chi, trK,
+                  gxx, gxy, gxz, gyy, gyz, gzz,
+                  Axx, Axy, Axz, Ayy, Ayz, Azz,
+                  Gmx, Gmy, Gmz,
+                  Sfx_rhs, Sfy_rhs, Sfz_rhs,
+                  Rout, Monitor, refresh_mass_fields);
+    return;
+  }
+
+  if (myrank == 0 && GH->grids[lev] != 1)
+    if (Monitor && Monitor->outfile)
+      Monitor->outfile << "WARNING: surface integral on multipatches" << endl;
+    else
+      cout << "WARNING: surface integral on multipatches" << endl;
+
+  if (refresh_mass_fields)
+  {
+    MyList<Patch> *Pp = GH->PatL[lev];
+    while (Pp)
+    {
+      MyList<Block> *BP = Pp->data->blb;
+      while (BP)
+      {
+        Block *cg = BP->data;
+        if (myrank == cg->rank)
+        {
+          f_admmass_bssn(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                         cg->fgfs[chi->sgfn], cg->fgfs[trK->sgfn],
+                         cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
+                         cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
+                         cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
+                         cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
+                         Symmetry);
+        }
+        if (BP == Pp->data->ble)
+          break;
+        BP = BP->next;
+      }
+      Pp = Pp->next;
+    }
+  }
+
+  const int InList = 19;
+  const int idx_rpsi4 = 0, idx_ipsi4 = 1;
+  const int idx_sfx = 2, idx_sfy = 3, idx_sfz = 4;
+  const int idx_chi = 5, idx_trk = 6;
+  const int idx_gxx = 7, idx_gxy = 8, idx_gxz = 9, idx_gyy = 10, idx_gyz = 11, idx_gzz = 12;
+  const int idx_axx = 13, idx_axy = 14, idx_axz = 15, idx_ayy = 16, idx_ayz = 17, idx_azz = 18;
+
+  MyList<var> *DG_List = new MyList<var>(Rpsi4);
+  DG_List->insert(Ipsi4);
+  DG_List->insert(Sfx_rhs);
+  DG_List->insert(Sfy_rhs);
+  DG_List->insert(Sfz_rhs);
+  DG_List->insert(chi);
+  DG_List->insert(trK);
+  DG_List->insert(gxx);
+  DG_List->insert(gxy);
+  DG_List->insert(gxz);
+  DG_List->insert(gyy);
+  DG_List->insert(gyz);
+  DG_List->insert(gzz);
+  DG_List->insert(Axx);
+  DG_List->insert(Axy);
+  DG_List->insert(Axz);
+  DG_List->insert(Ayy);
+  DG_List->insert(Ayz);
+  DG_List->insert(Azz);
+
+  int n;
+  double *pox[3];
+  for (int ia = 0; ia < 3; ia++)
+    pox[ia] = 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;
+  Lp = n_tot - cpusize * mp;
+  if (Lp > myrank)
+  {
+    Nmin = myrank * mp + myrank;
+    Nmax = Nmin + mp;
+  }
+  else
+  {
+    Nmin = myrank * mp + Lp;
+    Nmax = Nmin + mp - 1;
+  }
+
+  double *shellf = new double[n_tot * InList];
+  GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
+
+  double *RP_out = new double[NN];
+  double *IP_out = new double[NN];
+  for (int ii = 0; ii < NN; ii++)
+  {
+    RP_out[ii] = 0.0;
+    IP_out[ii] = 0.0;
+  }
+
+  double Mass_out = 0.0;
+  double ang_outx = 0.0, ang_outy = 0.0, ang_outz = 0.0;
+  double p_outx = 0.0, p_outy = 0.0, p_outz = 0.0;
+  const double f1o8 = 0.125;
+
+  build_wave_cache(spinw, maxl);
+
+  for (n = Nmin; n <= Nmax; n++)
+  {
+    const int base = InList * n;
+    const int i = int(n / N_phi);
+    const int j = n - i * N_phi;
+
+    const double psi4RR0 = shellf[base + idx_rpsi4];
+    const double psi4II0 = shellf[base + idx_ipsi4];
+    const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
+    const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
+    for (int countlm = 0; countlm < wave_cache_modes; countlm++)
+    {
+      const int theta_idx = countlm * N_theta + i;
+      const int phi_idx = countlm * N_phi + j;
+      const double theta_pos = wave_theta_pos[theta_idx];
+      const double cosmphi_here = wave_phi_cos[phi_idx];
+      const double sinmphi_here = wave_phi_sin[phi_idx];
+
+      RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
+      IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
+      if (Symmetry == 1)
+      {
+        const double theta_neg = wave_theta_neg[theta_idx];
+        RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
+        IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
+      }
+    }
+
+    double Chi = shellf[base + idx_chi];
+    double TRK = shellf[base + idx_trk];
+    double Gxx = shellf[base + idx_gxx] + 1.0;
+    double Gxy = shellf[base + idx_gxy];
+    double Gxz = shellf[base + idx_gxz];
+    double Gyy = shellf[base + idx_gyy] + 1.0;
+    double Gyz = shellf[base + idx_gyz];
+    double Gzz = shellf[base + idx_gzz] + 1.0;
+    double axx = shellf[base + idx_axx];
+    double axy = shellf[base + idx_axy];
+    double axz = shellf[base + idx_axz];
+    double ayy = shellf[base + idx_ayy];
+    double ayz = shellf[base + idx_ayz];
+    double azz = shellf[base + idx_azz];
+
+    Chi = 1.0 / (1.0 + Chi);
+    const double Psi = Chi * sqrt(Chi);
+
+#ifdef GaussInt
+    const double theta_weight = wtcostheta[i];
+    Mass_out += (shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n]) * theta_weight;
+#else
+    const double theta_weight = 1.0;
+    Mass_out += shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n];
+#endif
+
+    double detg = Gxx * Gyy * Gzz + Gxy * Gyz * Gxz + Gxz * Gxy * Gyz -
+                  Gxz * Gyy * Gxz - Gxy * Gxy * Gzz - Gxx * Gyz * Gyz;
+    const double gupxx = (Gyy * Gzz - Gyz * Gyz) / detg;
+    const double gupxy = -(Gxy * Gzz - Gyz * Gxz) / detg;
+    const double gupxz = (Gxy * Gyz - Gyy * Gxz) / detg;
+    const double gupyy = (Gxx * Gzz - Gxz * Gxz) / detg;
+    const double gupyz = -(Gxx * Gyz - Gxy * Gxz) / detg;
+    const double gupzz = (Gxx * Gyy - Gxy * Gxy) / detg;
+
+    const double aupxx = gupxx * axx + gupxy * axy + gupxz * axz;
+    const double aupxy = gupxx * axy + gupxy * ayy + gupxz * ayz;
+    const double aupxz = gupxx * axz + gupxy * ayz + gupxz * azz;
+    const double aupyx = gupxy * axx + gupyy * axy + gupyz * axz;
+    const double aupyy = gupxy * axy + gupyy * ayy + gupyz * ayz;
+    const double aupyz = gupxy * axz + gupyy * ayz + gupyz * azz;
+    const double aupzx = gupxz * axx + gupyz * axy + gupzz * axz;
+    const double aupzy = gupxz * axy + gupyz * ayy + gupzz * ayz;
+    const double aupzz = gupxz * axz + gupyz * ayz + gupzz * azz;
+
+    if (Symmetry == 0)
+    {
+      ang_outx += f1o8 * Psi * (nx_g[n] * (pox[1][n] * aupxz - pox[2][n] * aupxy) + ny_g[n] * (pox[1][n] * aupyz - pox[2][n] * aupyy) + nz_g[n] * (pox[1][n] * aupzz - pox[2][n] * aupzy)) * theta_weight;
+      ang_outy += f1o8 * Psi * (nx_g[n] * (pox[2][n] * aupxx - pox[0][n] * aupxz) + ny_g[n] * (pox[2][n] * aupyx - pox[0][n] * aupyz) + nz_g[n] * (pox[2][n] * aupzx - pox[0][n] * aupzz)) * theta_weight;
+      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
+    }
+    else
+    {
+      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
+    }
+
+    axx = Chi * (axx + Gxx * TRK / 3.0);
+    axy = Chi * (axy + Gxy * TRK / 3.0);
+    axz = Chi * (axz + Gxz * TRK / 3.0);
+    ayy = Chi * (ayy + Gyy * TRK / 3.0);
+    ayz = Chi * (ayz + Gyz * TRK / 3.0);
+    azz = Chi * (azz + Gzz * TRK / 3.0);
+
+    axx -= TRK;
+    ayy -= TRK;
+    azz -= TRK;
+
+    p_outx += f1o8 * Psi * (nx_g[n] * axx + ny_g[n] * axy + nz_g[n] * axz) * theta_weight;
+    p_outy += f1o8 * Psi * (nx_g[n] * axy + ny_g[n] * ayy + nz_g[n] * ayz) * theta_weight;
+    if (Symmetry == 0)
+      p_outz += f1o8 * Psi * (nx_g[n] * axz + ny_g[n] * ayz + nz_g[n] * azz) * theta_weight;
+  }
+
+  for (int ii = 0; ii < NN; ii++)
+  {
+#ifdef GaussInt
+    RP_out[ii] = RP_out[ii] * rex * dphi;
+    IP_out[ii] = IP_out[ii] * rex * dphi;
+#else
+    RP_out[ii] = RP_out[ii] * rex * dphi * dcostheta;
+    IP_out[ii] = IP_out[ii] * rex * dphi * dcostheta;
+#endif
+  }
+
+  double mass, px, py, pz, sx, sy, sz;
+  {
+    double *reduce_out = new double[2 * NN + 7];
+    double *reduce_in = new double[2 * NN + 7];
+    memcpy(reduce_out, RP_out, NN * sizeof(double));
+    memcpy(reduce_out + NN, IP_out, NN * sizeof(double));
+    reduce_out[2 * NN + 0] = Mass_out;
+    reduce_out[2 * NN + 1] = ang_outx;
+    reduce_out[2 * NN + 2] = ang_outy;
+    reduce_out[2 * NN + 3] = ang_outz;
+    reduce_out[2 * NN + 4] = p_outx;
+    reduce_out[2 * NN + 5] = p_outy;
+    reduce_out[2 * NN + 6] = p_outz;
+    MPI_Allreduce(reduce_out, reduce_in, 2 * NN + 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, reduce_in, NN * sizeof(double));
+    memcpy(IP, reduce_in + NN, NN * sizeof(double));
+    mass = reduce_in[2 * NN + 0];
+    sx = reduce_in[2 * NN + 1];
+    sy = reduce_in[2 * NN + 2];
+    sz = reduce_in[2 * NN + 3];
+    px = reduce_in[2 * NN + 4];
+    py = reduce_in[2 * NN + 5];
+    pz = reduce_in[2 * NN + 6];
+    delete[] reduce_out;
+    delete[] reduce_in;
+  }
+
+#ifdef GaussInt
+  mass = mass * rex * rex * dphi * factor;
+
+  sx = sx * rex * rex * dphi * (1.0 / PI) * factor;
+  sy = sy * rex * rex * dphi * (1.0 / PI) * factor;
+  sz = sz * rex * rex * dphi * (1.0 / PI) * factor;
+
+  px = px * rex * rex * dphi * (1.0 / PI) * factor;
+  py = py * rex * rex * dphi * (1.0 / PI) * factor;
+  pz = pz * rex * rex * dphi * (1.0 / PI) * factor;
+#else
+  mass = mass * rex * rex * dphi * dcostheta * factor;
+
+  sx = sx * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  sy = sy * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  sz = sz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+
+  px = px * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  py = py * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  pz = pz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+#endif
+
+  Rout[0] = mass;
+  Rout[1] = px;
+  Rout[2] = py;
+  Rout[3] = pz;
+  Rout[4] = sx;
+  Rout[5] = sy;
+  Rout[6] = sz;
+
+  delete[] pox[0];
+  delete[] pox[1];
+  delete[] pox[2];
+  delete[] shellf;
+  delete[] RP_out;
+  delete[] IP_out;
+  DG_List->clearList();
+}
+void surface_integral::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)
+{
+  if (Symmetry != 0 && Symmetry != 1)
+  {
+    surf_Wave(rex, lev, GH, Rpsi4, Ipsi4, spinw, maxl, NN, RP, IP, Monitor);
+    surf_MassPAng(rex, lev, GH, chi, trK,
+                  gxx, gxy, gxz, gyy, gyz, gzz,
+                  Axx, Axy, Axz, Ayy, Ayz, Azz,
+                  Gmx, Gmy, Gmz,
+                  Sfx_rhs, Sfy_rhs, Sfz_rhs,
+                  Rout, Monitor, refresh_mass_fields);
+    return;
+  }
+
+  if (lev != 0)
+  {
+    if (myrank == 0)
+    {
+      if (Monitor && Monitor->outfile)
+        Monitor->outfile << "WARNING: shell surface integral not on level 0" << endl;
+      else
+        cout << "WARNING: shell surface integral not on level 0" << endl;
+    }
+    return;
+  }
+
+  if (refresh_mass_fields)
+  {
+    MyList<ss_patch> *Pp = GH->PatL;
+    while (Pp)
+    {
+      MyList<Block> *BL = Pp->data->blb;
+      int fngfs = Pp->data->fngfs;
+      while (BL)
+      {
+        Block *cg = BL->data;
+        if (myrank == cg->rank)
+        {
+          f_admmass_bssn_ss(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                            cg->fgfs[fngfs + ShellPatch::gx], cg->fgfs[fngfs + ShellPatch::gy], cg->fgfs[fngfs + ShellPatch::gz],
+                            cg->fgfs[fngfs + ShellPatch::drhodx], cg->fgfs[fngfs + ShellPatch::drhody], cg->fgfs[fngfs + ShellPatch::drhodz],
+                            cg->fgfs[fngfs + ShellPatch::dsigmadx], cg->fgfs[fngfs + ShellPatch::dsigmady], cg->fgfs[fngfs + ShellPatch::dsigmadz],
+                            cg->fgfs[fngfs + ShellPatch::dRdx], cg->fgfs[fngfs + ShellPatch::dRdy], cg->fgfs[fngfs + ShellPatch::dRdz],
+                            cg->fgfs[fngfs + ShellPatch::drhodxx], cg->fgfs[fngfs + ShellPatch::drhodxy], cg->fgfs[fngfs + ShellPatch::drhodxz],
+                            cg->fgfs[fngfs + ShellPatch::drhodyy], cg->fgfs[fngfs + ShellPatch::drhodyz], cg->fgfs[fngfs + ShellPatch::drhodzz],
+                            cg->fgfs[fngfs + ShellPatch::dsigmadxx], cg->fgfs[fngfs + ShellPatch::dsigmadxy], cg->fgfs[fngfs + ShellPatch::dsigmadxz],
+                            cg->fgfs[fngfs + ShellPatch::dsigmadyy], cg->fgfs[fngfs + ShellPatch::dsigmadyz], cg->fgfs[fngfs + ShellPatch::dsigmadzz],
+                            cg->fgfs[fngfs + ShellPatch::dRdxx], cg->fgfs[fngfs + ShellPatch::dRdxy], cg->fgfs[fngfs + ShellPatch::dRdxz],
+                            cg->fgfs[fngfs + ShellPatch::dRdyy], cg->fgfs[fngfs + ShellPatch::dRdyz], cg->fgfs[fngfs + ShellPatch::dRdzz],
+                            cg->fgfs[chi->sgfn], cg->fgfs[trK->sgfn],
+                            cg->fgfs[gxx->sgfn], cg->fgfs[gxy->sgfn], cg->fgfs[gxz->sgfn], cg->fgfs[gyy->sgfn], cg->fgfs[gyz->sgfn], cg->fgfs[gzz->sgfn],
+                            cg->fgfs[Axx->sgfn], cg->fgfs[Axy->sgfn], cg->fgfs[Axz->sgfn], cg->fgfs[Ayy->sgfn], cg->fgfs[Ayz->sgfn], cg->fgfs[Azz->sgfn],
+                            cg->fgfs[Gmx->sgfn], cg->fgfs[Gmy->sgfn], cg->fgfs[Gmz->sgfn],
+                            cg->fgfs[Sfx_rhs->sgfn], cg->fgfs[Sfy_rhs->sgfn], cg->fgfs[Sfz_rhs->sgfn],
+                            Symmetry, Pp->data->sst);
+        }
+        if (BL == Pp->data->ble)
+          break;
+        BL = BL->next;
+      }
+      Pp = Pp->next;
+    }
+  }
+
+  const int InList = 19;
+  const int idx_rpsi4 = 0, idx_ipsi4 = 1;
+  const int idx_sfx = 2, idx_sfy = 3, idx_sfz = 4;
+  const int idx_chi = 5, idx_trk = 6;
+  const int idx_gxx = 7, idx_gxy = 8, idx_gxz = 9, idx_gyy = 10, idx_gyz = 11, idx_gzz = 12;
+  const int idx_axx = 13, idx_axy = 14, idx_axz = 15, idx_ayy = 16, idx_ayz = 17, idx_azz = 18;
+
+  MyList<var> *DG_List = new MyList<var>(Rpsi4);
+  DG_List->insert(Ipsi4);
+  DG_List->insert(Sfx_rhs);
+  DG_List->insert(Sfy_rhs);
+  DG_List->insert(Sfz_rhs);
+  DG_List->insert(chi);
+  DG_List->insert(trK);
+  DG_List->insert(gxx);
+  DG_List->insert(gxy);
+  DG_List->insert(gxz);
+  DG_List->insert(gyy);
+  DG_List->insert(gyz);
+  DG_List->insert(gzz);
+  DG_List->insert(Axx);
+  DG_List->insert(Axy);
+  DG_List->insert(Axz);
+  DG_List->insert(Ayy);
+  DG_List->insert(Ayz);
+  DG_List->insert(Azz);
+
+  int n;
+  double *pox[3];
+  for (int ia = 0; ia < 3; ia++)
+    pox[ia] = 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 = new double[n_tot * InList];
+  GH->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry);
+
+  int mp, Lp, Nmin, Nmax;
+  mp = n_tot / cpusize;
+  Lp = n_tot - cpusize * mp;
+
+  if (Lp > myrank)
+  {
+    Nmin = myrank * mp + myrank;
+    Nmax = Nmin + mp;
+  }
+  else
+  {
+    Nmin = myrank * mp + Lp;
+    Nmax = Nmin + mp - 1;
+  }
+
+  double *RP_out = new double[NN];
+  double *IP_out = new double[NN];
+  for (int ii = 0; ii < NN; ii++)
+  {
+    RP_out[ii] = 0.0;
+    IP_out[ii] = 0.0;
+  }
+
+  double Mass_out = 0.0;
+  double ang_outx = 0.0, ang_outy = 0.0, ang_outz = 0.0;
+  double p_outx = 0.0, p_outy = 0.0, p_outz = 0.0;
+  const double f1o8 = 0.125;
+
+  build_wave_cache(spinw, maxl);
+
+  for (n = Nmin; n <= Nmax; n++)
+  {
+    const int base = InList * n;
+    const int i = int(n / N_phi);
+    const int j = n - i * N_phi;
+
+    const double psi4RR0 = shellf[base + idx_rpsi4];
+    const double psi4II0 = shellf[base + idx_ipsi4];
+    const double psi4RR1 = Rpsi4->SoA[2] * psi4RR0;
+    const double psi4II1 = Ipsi4->SoA[2] * psi4II0;
+    for (int countlm = 0; countlm < wave_cache_modes; countlm++)
+    {
+      const int theta_idx = countlm * N_theta + i;
+      const int phi_idx = countlm * N_phi + j;
+      const double theta_pos = wave_theta_pos[theta_idx];
+      const double cosmphi_here = wave_phi_cos[phi_idx];
+      const double sinmphi_here = wave_phi_sin[phi_idx];
+
+      RP_out[countlm] += theta_pos * (psi4RR0 * cosmphi_here + psi4II0 * sinmphi_here);
+      IP_out[countlm] += theta_pos * (psi4II0 * cosmphi_here - psi4RR0 * sinmphi_here);
+      if (Symmetry == 1)
+      {
+        const double theta_neg = wave_theta_neg[theta_idx];
+        RP_out[countlm] += theta_neg * (psi4RR1 * cosmphi_here + psi4II1 * sinmphi_here);
+        IP_out[countlm] += theta_neg * (psi4II1 * cosmphi_here - psi4RR1 * sinmphi_here);
+      }
+    }
+
+    double Chi = shellf[base + idx_chi];
+    double TRK = shellf[base + idx_trk];
+    double Gxx = shellf[base + idx_gxx] + 1.0;
+    double Gxy = shellf[base + idx_gxy];
+    double Gxz = shellf[base + idx_gxz];
+    double Gyy = shellf[base + idx_gyy] + 1.0;
+    double Gyz = shellf[base + idx_gyz];
+    double Gzz = shellf[base + idx_gzz] + 1.0;
+    double axx = shellf[base + idx_axx];
+    double axy = shellf[base + idx_axy];
+    double axz = shellf[base + idx_axz];
+    double ayy = shellf[base + idx_ayy];
+    double ayz = shellf[base + idx_ayz];
+    double azz = shellf[base + idx_azz];
+
+    Chi = 1.0 / (1.0 + Chi);
+    const double Psi = Chi * sqrt(Chi);
+
+#ifdef GaussInt
+    const double theta_weight = wtcostheta[i];
+    Mass_out += (shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n]) * theta_weight;
+#else
+    const double theta_weight = 1.0;
+    Mass_out += shellf[base + idx_sfx] * nx_g[n] + shellf[base + idx_sfy] * ny_g[n] + shellf[base + idx_sfz] * nz_g[n];
+#endif
+
+    double detg = Gxx * Gyy * Gzz + Gxy * Gyz * Gxz + Gxz * Gxy * Gyz -
+                  Gxz * Gyy * Gxz - Gxy * Gxy * Gzz - Gxx * Gyz * Gyz;
+    const double gupxx = (Gyy * Gzz - Gyz * Gyz) / detg;
+    const double gupxy = -(Gxy * Gzz - Gyz * Gxz) / detg;
+    const double gupxz = (Gxy * Gyz - Gyy * Gxz) / detg;
+    const double gupyy = (Gxx * Gzz - Gxz * Gxz) / detg;
+    const double gupyz = -(Gxx * Gyz - Gxy * Gxz) / detg;
+    const double gupzz = (Gxx * Gyy - Gxy * Gxy) / detg;
+
+    const double aupxx = gupxx * axx + gupxy * axy + gupxz * axz;
+    const double aupxy = gupxx * axy + gupxy * ayy + gupxz * ayz;
+    const double aupxz = gupxx * axz + gupxy * ayz + gupxz * azz;
+    const double aupyx = gupxy * axx + gupyy * axy + gupyz * axz;
+    const double aupyy = gupxy * axy + gupyy * ayy + gupyz * ayz;
+    const double aupyz = gupxy * axz + gupyy * ayz + gupyz * azz;
+    const double aupzx = gupxz * axx + gupyz * axy + gupzz * axz;
+    const double aupzy = gupxz * axy + gupyz * ayy + gupzz * ayz;
+    const double aupzz = gupxz * axz + gupyz * ayz + gupzz * azz;
+
+    if (Symmetry == 0)
+    {
+      ang_outx += f1o8 * Psi * (nx_g[n] * (pox[1][n] * aupxz - pox[2][n] * aupxy) + ny_g[n] * (pox[1][n] * aupyz - pox[2][n] * aupyy) + nz_g[n] * (pox[1][n] * aupzz - pox[2][n] * aupzy)) * theta_weight;
+      ang_outy += f1o8 * Psi * (nx_g[n] * (pox[2][n] * aupxx - pox[0][n] * aupxz) + ny_g[n] * (pox[2][n] * aupyx - pox[0][n] * aupyz) + nz_g[n] * (pox[2][n] * aupzx - pox[0][n] * aupzz)) * theta_weight;
+      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
+    }
+    else
+    {
+      ang_outz += f1o8 * Psi * (nx_g[n] * (pox[0][n] * aupxy - pox[1][n] * aupxx) + ny_g[n] * (pox[0][n] * aupyy - pox[1][n] * aupyx) + nz_g[n] * (pox[0][n] * aupzy - pox[1][n] * aupzx)) * theta_weight;
+    }
+
+    axx = Chi * (axx + Gxx * TRK / 3.0);
+    axy = Chi * (axy + Gxy * TRK / 3.0);
+    axz = Chi * (axz + Gxz * TRK / 3.0);
+    ayy = Chi * (ayy + Gyy * TRK / 3.0);
+    ayz = Chi * (ayz + Gyz * TRK / 3.0);
+    azz = Chi * (azz + Gzz * TRK / 3.0);
+
+    axx -= TRK;
+    ayy -= TRK;
+    azz -= TRK;
+
+    p_outx += f1o8 * Psi * (nx_g[n] * axx + ny_g[n] * axy + nz_g[n] * axz) * theta_weight;
+    p_outy += f1o8 * Psi * (nx_g[n] * axy + ny_g[n] * ayy + nz_g[n] * ayz) * theta_weight;
+    if (Symmetry == 0)
+      p_outz += f1o8 * Psi * (nx_g[n] * axz + ny_g[n] * ayz + nz_g[n] * azz) * theta_weight;
+  }
+
+  for (int ii = 0; ii < NN; ii++)
+  {
+#ifdef GaussInt
+    RP_out[ii] = RP_out[ii] * rex * dphi;
+    IP_out[ii] = IP_out[ii] * rex * dphi;
+#else
+    RP_out[ii] = RP_out[ii] * rex * dphi * dcostheta;
+    IP_out[ii] = IP_out[ii] * rex * dphi * dcostheta;
+#endif
+  }
+
+  double mass, px, py, pz, sx, sy, sz;
+  {
+    double *reduce_out = new double[2 * NN + 7];
+    double *reduce_in = new double[2 * NN + 7];
+    memcpy(reduce_out, RP_out, NN * sizeof(double));
+    memcpy(reduce_out + NN, IP_out, NN * sizeof(double));
+    reduce_out[2 * NN + 0] = Mass_out;
+    reduce_out[2 * NN + 1] = ang_outx;
+    reduce_out[2 * NN + 2] = ang_outy;
+    reduce_out[2 * NN + 3] = ang_outz;
+    reduce_out[2 * NN + 4] = p_outx;
+    reduce_out[2 * NN + 5] = p_outy;
+    reduce_out[2 * NN + 6] = p_outz;
+    MPI_Allreduce(reduce_out, reduce_in, 2 * NN + 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+    memcpy(RP, reduce_in, NN * sizeof(double));
+    memcpy(IP, reduce_in + NN, NN * sizeof(double));
+    mass = reduce_in[2 * NN + 0];
+    sx = reduce_in[2 * NN + 1];
+    sy = reduce_in[2 * NN + 2];
+    sz = reduce_in[2 * NN + 3];
+    px = reduce_in[2 * NN + 4];
+    py = reduce_in[2 * NN + 5];
+    pz = reduce_in[2 * NN + 6];
+    delete[] reduce_out;
+    delete[] reduce_in;
+  }
+
+#ifdef GaussInt
+  mass = mass * rex * rex * dphi * factor;
+
+  sx = sx * rex * rex * dphi * (1.0 / PI) * factor;
+  sy = sy * rex * rex * dphi * (1.0 / PI) * factor;
+  sz = sz * rex * rex * dphi * (1.0 / PI) * factor;
+
+  px = px * rex * rex * dphi * (1.0 / PI) * factor;
+  py = py * rex * rex * dphi * (1.0 / PI) * factor;
+  pz = pz * rex * rex * dphi * (1.0 / PI) * factor;
+#else
+  mass = mass * rex * rex * dphi * dcostheta * factor;
+
+  sx = sx * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  sy = sy * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  sz = sz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+
+  px = px * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  py = py * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+  pz = pz * rex * rex * dphi * dcostheta * (1.0 / PI) * factor;
+#endif
+
+  Rout[0] = mass;
+  Rout[1] = px;
+  Rout[2] = py;
+  Rout[3] = pz;
+  Rout[4] = sx;
+  Rout[5] = sy;
+  Rout[6] = sz;
+
+  delete[] pox[0];
+  delete[] pox[1];
+  delete[] pox[2];
+  delete[] shellf;
+  delete[] RP_out;
+  delete[] IP_out;
+  DG_List->clearList();
+}
 //|----------------------------------------------------------------
 //  do not discriminate box and shell
 //  for Gravitational wave specially symmetric case
--- 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/README.md
+++ b/README.md
@@ -97,7 +97,9 @@ Here, we take the Ubuntu 22.04 system as an example

    Modify the makefile.inc file in the AMSS_NCKU_source directory and change the settings according to your computer.

-    The settings for the Ubuntu 22.04 system do not need to be modified.
+    The default configuration in this branch uses GNU compilers through the OpenMPI wrappers under `/usr/lib64/openmpi/bin`.
+
+    If your OpenMPI installation is in another location, update `OMPI_BIN` in `AMSS_NCKU_source/makefile.inc` or export `AMSS_OPENMPI_BIN` before running the Python launcher.

 1.  Enter the AMSS-NCKU Python code folder and modify the input.

--- 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
@@ -9,6 +9,7 @@


 import AMSS_NCKU_Input as input_data
+import os
 import subprocess
 import time

@@ -52,6 +53,8 @@ NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)

 ## Build parallelism: match the number of bound cores
 BUILD_JOBS = 64
+OPENMPI_BIN = os.environ.get("AMSS_OPENMPI_BIN", "/usr/lib64/openmpi/bin")
+MPI_RUNNER = os.path.join(OPENMPI_BIN, "mpirun")


 ##################################################################
@@ -147,11 +150,11 @@ def run_ABE():
    ## Define the command to run; cast other values to strings as needed
    
    if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = NUMACTL_CPU_BIND + " " + MPI_RUNNER + " -np " + str(input_data.MPI_processes) + " ./ABE"
        #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
        mpi_command_outfile = "ABE_out.log"
    elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " " + MPI_RUNNER + " -np " + str(input_data.MPI_processes) + " ./ABEGPU"
        mpi_command_outfile = "ABEGPU_out.log"
 
    ## Execute the MPI command and stream output
Author	SHA1	Message	Date
CGH0S7	3f3f16e881	Switch legacy build to GCC and OpenMPI	2026-04-13 19:39:30 +08:00
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