Switch legacy build to GCC and OpenMPI

Reviewed-on: #3

AMSS_NCKU_source/FFT.f90

@@ -37,51 +37,56 @@ close(77)
 end program checkFFT
 #endif
 
-!-------------
+SUBROUTINE four1(dataa,nn,isign)
-! Optimized FFT using Intel oneMKL DFTI
+implicit none
-! Mathematical equivalence: Standard DFT definition
+INTEGER::isign,nn
-!   Forward (isign=1):  X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
+double precision,dimension(2*nn)::dataa
-!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
+INTEGER::i,istep,j,m,mmax,n
-! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
+double precision::tempi,tempr
-!-------------
+DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
-SUBROUTINE four1(dataa,nn,isign)
+n=2*nn
-use MKL_DFTI
+j=1
-implicit none
+do i=1,n,2
-INTEGER, intent(in) :: isign, nn
+  if(j.gt.i)then
-DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
+     tempr=dataa(j)
-
+     tempi=dataa(j+1)
-type(DFTI_DESCRIPTOR), pointer :: desc
+     dataa(j)=dataa(i)
-integer :: status
+     dataa(j+1)=dataa(i+1)
-
+     dataa(i)=tempr
-! Create DFTI descriptor for 1D complex-to-complex transform
+     dataa(i+1)=tempi
-status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
+  endif
-if (status /= 0) return
+  m=nn
-
+1 if ((m.ge.2).and.(j.gt.m)) then
-! Set input/output storage as interleaved complex (default)
+  j=j-m
-status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
+  m=m/2
-if (status /= 0) then
+goto 1
-   status = DftiFreeDescriptor(desc)
+  endif
-   return
+j=j+m
-endif
+enddo
-
+mmax=2
-! Commit the descriptor
+2  if (n.gt.mmax) then
-status = DftiCommitDescriptor(desc)
+     istep=2*mmax
-if (status /= 0) then
+     theta=6.28318530717959d0/(isign*mmax)
-   status = DftiFreeDescriptor(desc)
+     wpr=-2.d0*sin(0.5d0*theta)**2
-   return
+     wpi=sin(theta)
-endif
+     wr=1.d0
-
+     wi=0.d0
-! Execute FFT based on direction
+     do m=1,mmax,2
-if (isign == 1) then
+       do i=m,n,istep
-   ! Forward FFT: exp(-2*pi*i*k*n/N)
+         j=i+mmax
-   status = DftiComputeForward(desc, dataa)
+         tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
-else
+         tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
-   ! Backward FFT: exp(+2*pi*i*k*n/N)
+         dataa(j)=dataa(i)-tempr
-   status = DftiComputeBackward(desc, dataa)
+         dataa(j+1)=dataa(i+1)-tempi
-endif
+         dataa(i)=dataa(i)+tempr
-
+         dataa(i+1)=dataa(i+1)+tempi
-! Free descriptor
+       enddo
-status = DftiFreeDescriptor(desc)
+          wtemp=wr
-
+          wr=wr*wpr-wi*wpi+wr
-return
+          wi=wi*wpr+wtemp*wpi+wi
-END SUBROUTINE four1
+     enddo
+mmax=istep
+goto 2
+endif
+return
+END SUBROUTINE four1

AMSS_NCKU_source/Parallel.C

@@ -5253,10 +5253,10 @@ void Parallel::PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry)
   delete[] transfer_src;
   delete[] transfer_dst;
 }
-double Parallel::L2Norm(Patch *Pat, var *vf)
+double Parallel::L2Norm(Patch *Pat, var *vf)
-{
+{
-  int myrank;
+  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
 
   double tvf, dtvf = 0;
   int BDW = ghost_width;
@@ -5281,13 +5281,48 @@ double Parallel::L2Norm(Patch *Pat, var *vf)
   MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   tvf = sqrt(tvf);
-
+
-  return tvf;
+  return tvf;
-}
+}
-double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
+void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms)
-{
+{
-  int myrank;
+  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &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;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
 
   double tvf, dtvf = 0;
   int BDW = ghost_width;
@@ -5312,12 +5347,47 @@ double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
   MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
 
   tvf = sqrt(tvf);
-
+
-  return tvf;
+  return tvf;
-}
+}
-void Parallel::checkgsl(MyList<Parallel::gridseg> *pp, bool first_only)
+void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here)
-{
+{
-  int myrank = 0;
+  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;
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
   if (myrank == 0)
   {

AMSS_NCKU_source/Parallel.h

@@ -179,12 +179,13 @@ namespace Parallel
   MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
   MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
   MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
-  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
+  void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
-                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
+                         MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
-  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
+  void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
-  double L2Norm(Patch *Pat, var *vf);
+  double L2Norm(Patch *Pat, var *vf);
-  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
+  void L2Norm7(Patch *Pat, var **vf, double *norms);
-  void checkvarl(MyList<var> *pp, bool first_only);
+  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);
   MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
   void prepare_inter_time_level(Patch *Pat,
@@ -216,11 +217,12 @@ namespace Parallel
   void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
   bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
   void checkpatchlist(MyList<Patch> *PatL, bool buflog);
-
+
-  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
+  double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
-  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
+  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
-                             int NN, double **XX,
+  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
+                             int NN, double **XX,
+                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
 #if (PSTR == 1 || PSTR == 2 || PSTR == 3)
   MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
                             bool periodic, int start_rank, int end_rank, int nodes = 0);

AMSS_NCKU_source/ShellPatch.C

@@ -3439,10 +3439,10 @@ void ShellPatch::write_Pablo_file_ss(int *ext, double xmin, double xmax, double
   delete[] Z;
 }
 
-double ShellPatch::L2Norm(var *vf)
+double ShellPatch::L2Norm(var *vf)
-{
+{
-  double tvf, dtvf = 0;
+  double tvf, dtvf = 0;
-  int BDW = overghost;
+  int BDW = overghost;
 
   MyList<ss_patch> *sPp = PatL;
   while (sPp)
@@ -3469,13 +3469,50 @@ double ShellPatch::L2Norm(var *vf)
   MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
 
   tvf = sqrt(tvf);
-
+
-  return tvf;
+  return tvf;
-}
+}
-
+void ShellPatch::L2Norm7(var **vf, double *norms)
-// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
+{
-void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
+  double tvf[7], dtvf[7];
-                              double *Shellf)
+  int BDW = overghost;
+  for (int i = 0; i < 7; i++)
+    dtvf[i] = 0;
+
+  MyList<ss_patch> *sPp = PatL;
+  while (sPp)
+  {
+    MyList<Block> *Bp = sPp->data->blb;
+    while (Bp)
+    {
+      Block *cg = Bp->data;
+      if (myrank == cg->rank)
+      {
+        f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
+                        sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2],
+                        sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
+                        cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
+                        cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
+                        cg->fgfs[vf[6]->sgfn], tvf, BDW);
+        for (int i = 0; i < 7; i++)
+          dtvf[i] += tvf[i];
+      }
+      if (Bp == sPp->data->ble)
+        break;
+      Bp = Bp->next;
+    }
+    sPp = sPp->next;
+  }
+
+  MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+  for (int i = 0; i < 7; i++)
+    norms[i] = sqrt(tvf[i]);
+}
+
+// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
+void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
+                              double *Shellf)
 {
   MyList<var> *varl;
   int num_var = 0;

AMSS_NCKU_source/ShellPatch.h

@@ -195,10 +195,11 @@ public:
    bool Interp_One_Point(MyList<var> *VarList,
                          double *XX, /*input global Cartesian coordinate*/
                          double *Shellf, int Symmetry);
-   void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
+   void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
-                            char *filename, int sst);
+                            char *filename, int sst);
-   double L2Norm(var *vf);
+   double L2Norm(var *vf);
-   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
+   void L2Norm7(var **vf, double *norms);
-};
+   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
+};
 
 #endif /* SHELLPATCH_H */

AMSS_NCKU_source/TwoPunctures.C

@@ -25,9 +25,23 @@ using namespace std;
 #include <math.h>
 #include <complex.h>
 #endif
-
+
-#include "TwoPunctures.h"
+#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,

AMSS_NCKU_source/bssn_class.h

@@ -45,10 +45,11 @@ public:
        int checkrun;
        char checkfilename[50];
        int Steps;
-       double StartTime, TotalTime;
+       double StartTime, TotalTime;
-       double AnasTime, DumpTime, d2DumpTime, CheckTime;
+       double AnasTime, DumpTime, d2DumpTime, CheckTime;
-       double LastAnas, LastConsOut;
+       double LastAnas, LastConsOut;
-       double Courant;
+       int *ConstraintRefreshLevels;
+       double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
        int maxl, decn;
@@ -133,9 +134,9 @@ public:
        Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
        Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong
 
-       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
+       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
-       monitor *ConVMonitor;
+       monitor *ConVMonitor, *TimingMonitor;
-       surface_integral *Waveshell;
+       surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
 public:

AMSS_NCKU_source/bssn_rhs.h

@@ -22,19 +22,32 @@
 #define f_compute_rhs_Z4c_ss COMPUTE_RHS_Z4C_SS
 #define f_compute_constraint_fr COMPUTE_CONSTRAINT_FR
 #endif
-#ifdef fortran3
+#ifdef fortran3
-#define f_compute_rhs_bssn compute_rhs_bssn_
+#define f_compute_rhs_bssn compute_rhs_bssn_
 #define f_compute_rhs_bssn_ss compute_rhs_bssn_ss_
 #define f_compute_rhs_bssn_escalar compute_rhs_bssn_escalar_
 #define f_compute_rhs_bssn_escalar_ss compute_rhs_bssn_escalar_ss_
 #define f_compute_rhs_Z4c compute_rhs_z4c_
 #define f_compute_rhs_Z4cnot compute_rhs_z4cnot_
 #define f_compute_rhs_Z4c_ss compute_rhs_z4c_ss_
-#define f_compute_constraint_fr compute_constraint_fr_
+#define f_compute_constraint_fr compute_constraint_fr_
-#endif
+#endif
-extern "C"
+
-{
+#ifdef __cplusplus
-        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
+extern "C"
+{
+#endif
+        void f_bssn_rhs_kernel_timing_reset();
+        int f_bssn_rhs_kernel_timing_bucket_count();
+        const double *f_bssn_rhs_kernel_timing_local_seconds();
+        const char *f_bssn_rhs_kernel_timing_label(int);
+#ifdef __cplusplus
+}
+#endif
+
+extern "C"
+{
+        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
                                double *, double *,                                                                                 // chi, trK
                                double *, double *, double *, double *, double *, double *,                                         // gij
                                double *, double *, double *, double *, double *, double *,                                         // Aij

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];
+            const double inv_chin1 = ONE / chin1[i];
-            fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
+            const double half_inv_chin1 = HALF * inv_chin1;
-            fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
+            const double scaled_inv = F3o2 * inv_chin1;
-            fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
+            const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
-            fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
+            const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
-            fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
+            const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
-            f[i] =
+            const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
-                gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
+            const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
-                + gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
+            const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
-                + gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
+            const double ricci_chi =
-                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
+                gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
-                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
+                + gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
-                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
+                + gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+                + TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+                + TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+                + 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);
+            Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
-            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
+            Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
-            Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
+            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) */
+            const double inv_chin1 = ONE / chin1[i];
-            gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
+            const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
-            gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
+            const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
-            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
+            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;
+            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) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
+            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) * gxxz[i] ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_z ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_x ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * 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) * gxxz[i] ) * 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;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_x ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_y ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * 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;
+            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1)      - gxy[i] * gchi_x ) * HALF;
-            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
+            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1)      - gxy[i] * gchi_y ) * HALF;
-            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gxxz[i] ) * 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;
+            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1)      - gxz[i] * gchi_x ) * HALF;
-            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gxxy[i] ) * HALF;
+            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gchi_y ) * HALF;
-            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i])      - gxz[i] * gxxz[i] ) * 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;
+            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gchi_x ) * HALF;
-            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i])      - gyz[i] * gxxy[i] ) * HALF;
+            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1)      - gyz[i] * gchi_y ) * HALF;
-            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i])      - gyz[i] * gxxz[i] ) * 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);
@@ -1139,60 +1225,61 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
             fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
             fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
-        }
+            // 7ms //
-        // 7ms //
+            for (int i=0;i<all;i+=1) {
-        for (int i=0;i<all;i+=1) {
+                gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
-            gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
+                                      + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
-                                  + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
+                gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-            gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                      + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
-                                  + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
+                gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-            gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                      + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
-                                  + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
+                gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
-            gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
+                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
-                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
+                gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
-            gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
+                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
-                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
+                gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
-            gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
+                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
-                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
+                gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-            gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                      + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
-                                  + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
+                gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
-            gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
+                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
-                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
+                gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-            gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
-                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
+                gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
-            gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
+                                      + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
-                                  + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
+                gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-            gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                      + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
-                                  + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
+                gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
-            gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
+                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
-                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
+                gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-            gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                      + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
-                                  + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
+                gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-            gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                      + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
-                                  + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
+                gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
-            gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
+                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
-                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
+                gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-            gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                      + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
-                                  + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
+                gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
-            gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
+                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
-                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
+                gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
-            gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
+                                      + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
-                                  + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
 
-            movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
+                movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
-                        + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
+                            + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
-                        + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
+                            + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
-            movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
+                movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
-                        + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
+                            + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
-                        + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
+                            + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
-            movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
+                movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
-                        + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
+                            + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
-                        + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
+                            + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
 
-            movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
+                movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
-            movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
+                movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
-            movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+                movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+            }
         }
+        RHS_KERNEL_TIMER_ADD(KB_KO_CONSTRAINT, timer_ko_constraint);
 
 
             

AMSS_NCKU_source/fdderivs_c.C

@@ -71,106 +71,131 @@ void fdderivs(const int ex[3],
     const double Fdxdz = F1o144 / (dX * dZ);
     const double Fdydz = F1o144 / (dY * dZ);
 
-    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
+    /* 只清零不被主循环覆盖的边界面 */
-    for (size_t p = 0; p < all; ++p) {
+    {
-        fxx[p] = ZEO; fxy[p] = ZEO; fxz[p] = ZEO;
+        /* 高边界：k0=ex3-1 */
-        fyy[p] = ZEO; fyz[p] = ZEO; fzz[p] = ZEO;
+        for (int j0 = 0; j0 < ex2; ++j0)
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+        /* 高边界：j0=ex2-1 */
+        for (int k0 = 0; k0 < ex3 - 1; ++k0)
+            for (int i0 = 0; i0 < ex1; ++i0) {
+                const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+        /* 高边界：i0=ex1-1 */
+        for (int k0 = 0; k0 < ex3 - 1; ++k0)
+            for (int j0 = 0; j0 < ex2 - 1; ++j0) {
+                const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
+                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+            }
+
+        /* 低边界：当二阶模板也不可用时，对应 i0/j0/k0=0 面 */
+        if (kminF == 1) {
+            for (int j0 = 0; j0 < ex2; ++j0)
+                for (int i0 = 0; i0 < ex1; ++i0) {
+                    const size_t p = idx_ex(i0, j0, 0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+        if (jminF == 1) {
+            for (int k0 = 0; k0 < ex3; ++k0)
+                for (int i0 = 0; i0 < ex1; ++i0) {
+                    const size_t p = idx_ex(i0, 0, k0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
+        if (iminF == 1) {
+            for (int k0 = 0; k0 < ex3; ++k0)
+                for (int j0 = 0; j0 < ex2; ++j0) {
+                    const size_t p = idx_ex(0, j0, k0, ex);
+                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
+                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
+                }
+        }
     }
 
-    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
+    /*
-    // only compute when x/y/z all satisfy the same-order stencil at this point.
+     * 两段式：
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+     * 1) 二阶可用区域先计算二阶模板
-        const int kF = k0 + 1;
+     * 2) 高阶可用区域再覆盖四阶模板
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+     */
-            const int jF = j0 + 1;
+    const int i2_lo = (iminF > 0) ? iminF : 0;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+    const int j2_lo = (jminF > 0) ? jminF : 0;
-                const int iF = i0 + 1;
+    const int k2_lo = (kminF > 0) ? kminF : 0;
-                const size_t p = idx_ex(i0, j0, k0, ex);
+    const int i2_hi = ex1 - 2;
+    const int j2_hi = ex2 - 2;
+    const int k2_hi = ex3 - 2;
+
+    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+    const int i4_hi = ex1 - 3;
+    const int j4_hi = ex2 - 3;
+    const int k4_hi = ex3 - 3;
+
+    /*
+     * Strategy A:
+     * Avoid redundant work in overlap of 2nd/4th-order regions.
+     * Only compute 2nd-order on shell points that are NOT overwritten by
+     * the 4th-order pass.
+     */
+    const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
+
+    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                    if (has4 &&
+                        i0 >= i4_lo && i0 <= i4_hi &&
+                        j0 >= j4_lo && j0 <= j4_hi &&
+                        k0 >= k4_lo && k0 <= k4_hi) {
+                        continue;
+                    }
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
 
-                if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
-                    (jF + 2 <= jmaxF && jF - 2 >= jminF) &&
-                    (kF + 2 <= kmaxF && kF - 2 >= kminF)) {
-                    fxx[p] = Fdxdx * (
-                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-                    fyy[p] = Fdydy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-                    fzz[p] = Fdzdz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-                    fxy[p] = Fdxdy * (
-                           (fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)] +
-                            F8 * fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)])
-                        - F8 * (fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] +
-                                F8 * fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)])
-                        + F8 * (fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
-                                F8 * fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)])
-                           - (fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)] +
-                              F8 * fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)])
-                    );
-                    fxz[p] = Fdxdz * (
-                           (fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)] +
-                            F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)])
-                        - F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] +
-                                F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)])
-                        + F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
-                                F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)])
-                           - (fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)] +
-                              F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)])
-                    );
-                    fyz[p] = Fdydz * (
-                           (fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)] +
-                            F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)])
-                        - F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] +
-                                F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)])
-                        + F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
-                                F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)])
-                           - (fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)] +
-                              F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)])
-                    );
-                } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
-                           (jF + 1 <= jmaxF && jF - 1 >= jminF) &&
-                           (kF + 1 <= kmaxF && kF - 1 >= kminF)) {
                     fxx[p] = Sdxdx * (
                         fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
                     );
+
                     fyy[p] = Sdydy * (
                         fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
                     );
+
                     fzz[p] = Sdzdz * (
                         fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
                     );
+
                     fxy[p] = Sdxdy * (
                         fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
                         fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
                         fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
                         fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
                     );
+
                     fxz[p] = Sdxdz * (
                         fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
                         fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
                         fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
                         fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
                     );
+
                     fyz[p] = Sdydz * (
                         fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
                         fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
@@ -182,5 +207,126 @@ void fdderivs(const int ex[3],
         }
     }
 
+    if (has4) {
+        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fxx[p] = Fdxdx * (
+                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fyy[p] = Fdydy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fzz[p] = Fdzdz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+
+                    {
+                        const double t_jm2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
+
+                        const double t_jm1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
+
+                        const double t_jp1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
+
+                        const double t_jp2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
+
+                        fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
+                    }
+
+                    {
+                        const double t_km2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
+
+                        const double t_km1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
+
+                        const double t_kp1 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
+
+                        const double t_kp2 =
+                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
+
+                        fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                    }
+
+                    {
+                        const double t_km2 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
+
+                        const double t_km1 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
+
+                        const double t_kp1 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
+
+                        const double t_kp2 =
+                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
+                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
+                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
+                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
+
+                        fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
+                    }
+                }
+            }
+        }
+    }
+
     // free(fh);
 }

AMSS_NCKU_source/fderivs_c.C

@@ -80,48 +80,46 @@ void fderivs(const int ex[3],
         fz[p] = ZEO;
     }
 
-    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
+    /*
-    // only compute when x/y/z all satisfy the same-order stencil at this point.
+     * 两段式：
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+     * 1) 先在二阶可用区域计算二阶模板
-        const int kF = k0 + 1;
+     * 2) 再在高阶可用区域覆盖为四阶模板
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+     *
-            const int jF = j0 + 1;
+     * 与原 if/elseif 逻辑等价，但减少逐点分支判断。
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+     */
-                const int iF = i0 + 1;
+    const int i2_lo = (iminF > 0) ? iminF : 0;
-                const size_t p = idx_ex(i0, j0, k0, ex);
+    const int j2_lo = (jminF > 0) ? jminF : 0;
+    const int k2_lo = (kminF > 0) ? kminF : 0;
+    const int i2_hi = ex1 - 2;
+    const int j2_hi = ex2 - 2;
+    const int k2_hi = ex3 - 2;
+
+    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+    const int i4_hi = ex1 - 3;
+    const int j4_hi = ex2 - 3;
+    const int k4_hi = ex3 - 3;
+
+    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
 
-                if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
-                    (jF + 2 <= jmaxF && jF - 2 >= jminF) &&
-                    (kF + 2 <= kmaxF && kF - 2 >= kminF)) {
-                    fx[p] = d12dx * (
-                        fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
-                        EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                        EIT * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)]
-                    );
-                    fy[p] = d12dy * (
-                        fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] -
-                        EIT * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                        EIT * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)]
-                    );
-                    fz[p] = d12dz * (
-                        fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] -
-                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
-                    );
-                } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
-                           (jF + 1 <= jmaxF && jF - 1 >= jminF) &&
-                           (kF + 1 <= kmaxF && kF - 1 >= kminF)) {
                     fx[p] = d2dx * (
                         -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
                          fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
                     );
+
                     fy[p] = d2dy * (
                         -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
                          fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
                     );
+
                     fz[p] = d2dz * (
                         -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
                          fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
@@ -131,5 +129,39 @@ void fderivs(const int ex[3],
         }
     }
 
+    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fx[p] = d12dx * (
+                        fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d12dy * (
+                        fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)]
+                    );
+
+                    fz[p] = d12dz * (
+                        fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] -
+                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                        EIT * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
+                    );
+                }
+            }
+        }
+    }
+
     // free(fh);
 }

AMSS_NCKU_source/fmisc.f90

@@ -1511,13 +1511,88 @@ deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
-  return
+  return
-
+
-  end subroutine l2normhelper
+  end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
+!--------------------------------------------------------------------------------------
-! calculate L2norm especially for shell Blocks
+  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
-                          f,f_out,gw,ogw,Symmetry)
+
+  implicit none
+!~~~~~~> Input parameters:
+  integer,intent(in ):: ex(1:3)
+  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
+  integer,intent(in)::gw
+  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
+  real*8, intent(out) :: f_out(7)
+!~~~~~~> Other variables:
+
+  real*8            :: dX, dY, dZ
+  integer::imin,jmin,kmin
+  integer::imax,jmax,kmax
+  integer::i,j,k
+  real*8 :: s1,s2,s3,s4,s5,s6,s7
+
+  dX = X(2) - X(1)
+  dY = Y(2) - Y(1)
+  dZ = Z(2) - Z(1)
+
+! for ghost zone
+   imin = gw+1
+   jmin = gw+1
+   kmin = gw+1
+
+   imax = ex(1) - gw
+   jmax = ex(2) - gw
+   kmax = ex(3) - gw
+
+!for patch boundary (i.e., not ghost boundary)
+
+if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
+if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
+if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
+if(dabs(X(1)-xmin) < dX) imin = 1
+if(dabs(Y(1)-ymin) < dY) jmin = 1
+if(dabs(Z(1)-zmin) < dZ) kmin = 1
+
+  s1 = 0.d0
+  s2 = 0.d0
+  s3 = 0.d0
+  s4 = 0.d0
+  s5 = 0.d0
+  s6 = 0.d0
+  s7 = 0.d0
+
+  do k=kmin,kmax
+    do j=jmin,jmax
+!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
+      do i=imin,imax
+        s1 = s1 + f1(i,j,k)*f1(i,j,k)
+        s2 = s2 + f2(i,j,k)*f2(i,j,k)
+        s3 = s3 + f3(i,j,k)*f3(i,j,k)
+        s4 = s4 + f4(i,j,k)*f4(i,j,k)
+        s5 = s5 + f5(i,j,k)*f5(i,j,k)
+        s6 = s6 + f6(i,j,k)*f6(i,j,k)
+        s7 = s7 + f7(i,j,k)*f7(i,j,k)
+      enddo
+    enddo
+  enddo
+
+  f_out(1) = s1*dX*dY*dZ
+  f_out(2) = s2*dX*dY*dZ
+  f_out(3) = s3*dX*dY*dZ
+  f_out(4) = s4*dX*dY*dZ
+  f_out(5) = s5*dX*dY*dZ
+  f_out(6) = s6*dX*dY*dZ
+  f_out(7) = s7*dX*dY*dZ
+
+  return
+
+  end subroutine l2normhelper7
+!--------------------------------------------------------------------------------------
+! calculate L2norm especially for shell Blocks
+  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+                          f,f_out,gw,ogw,Symmetry)
 
   implicit none
 !~~~~~~> Input parameters:

AMSS_NCKU_source/fmisc.h

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

AMSS_NCKU_source/gaussj.C

@@ -17,68 +17,106 @@ using namespace std;
 #include <math.h>
 #endif
 
-// Intel oneMKL LAPACK interface
+/* Linear equation solution by Gauss-Jordan elimination.
-#include <mkl_lapacke.h>
+a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
-/* Linear equation solution using Intel oneMKL LAPACK.
+containing the right-hand side vectors. On output a is
-a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
+replaced by its matrix inverse, and b is replaced by the
-containing the right-hand side vectors. On output a is
+corresponding set of solution vectors. */
-replaced by its matrix inverse, and b is replaced by the
+
-corresponding set of solution vectors.
+int gaussj(double *a, double *b, int n)
-
+{
-Mathematical equivalence:
+  double swap;
-  Solves: A * x = b  =>  x = A^(-1) * b
+
-  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
+  int *indxc, *indxr, *ipiv;
-  within numerical precision. */
+  indxc = new int[n];
-
+  indxr = new int[n];
-int gaussj(double *a, double *b, int n)
+  ipiv = new int[n];
-{
+
-  // Allocate pivot array and workspace
+  int i, icol, irow, j, k, l, ll;
-  lapack_int *ipiv = new lapack_int[n];
+  double big, dum, pivinv;
-  lapack_int info;
+
-
+  for (j = 0; j < n; j++)
-  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
+    ipiv[j] = 0;
-  double *a_copy = new double[n * n];
+  for (i = 0; i < n; i++)
-  for (int i = 0; i < n * n; i++) {
+  {
-    a_copy[i] = a[i];
+    big = 0.0;
-  }
+    for (j = 0; j < n; j++)
-
+      if (ipiv[j] != 1)
-  // Step 1: Solve linear system A*x = b using LU decomposition
+        for (k = 0; k < n; k++)
-  // 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);
+          if (ipiv[k] == 0)
-
+          {
-  if (info != 0) {
+            if (fabs(a[j * n + k]) >= big)
-    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
+            {
-    delete[] ipiv;
+              big = fabs(a[j * n + k]);
-    delete[] a_copy;
+              irow = j;
-    return 1;
+              icol = k;
-  }
+            }
-
+          }
-  // Step 2: Compute matrix inverse A^(-1) using LU factorization
+          else if (ipiv[k] > 1)
-  // First do LU factorization of original matrix a
+          {
-  info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
+            cout << "gaussj: Singular Matrix-1" << endl;
-
+            return 1;
-  if (info != 0) {
+          }
-    cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
+        }
-    delete[] ipiv;
+
-    delete[] a_copy;
+    ipiv[icol] = ipiv[icol] + 1;
-    return 1;
+    if (irow != icol)
-  }
+    {
-
+      for (l = 0; l < n; l++)
-  // Then compute inverse from LU factorization
+      {
-  info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
+        swap = a[irow * n + l];
-
+        a[irow * n + l] = a[icol * n + l];
-  if (info != 0) {
+        a[icol * n + l] = swap;
-    cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
+      }
-    delete[] ipiv;
+
-    delete[] a_copy;
+      swap = b[irow];
-    return 1;
+      b[irow] = b[icol];
-  }
+      b[icol] = swap;
-
+    }
-  delete[] ipiv;
+
-  delete[] a_copy;
+    indxr[i] = irow;
-
+    indxc[i] = icol;
-  return 0;
+
-}
+    if (a[icol * n + icol] == 0.0)
+    {
+      cout << "gaussj: Singular Matrix-2" << endl;
+      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;
+      }
+  }
+
+  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;
+
+  return 0;
+}
 // for check usage
 /*
 int main()

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 */
-

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)
+## Legacy GNU/OpenMPI flags
-##   make                        -> opt  (PGO-guided, maximum performance)
+CXXBASEFLAGS = -O3 -march=native -Wno-deprecated -Dfortran3 -Dnewc $(INTERP_LB_FLAGS)
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+F90BASEFLAGS = -O3 -march=native -cpp -fallow-argument-mismatch $(POLINT6_FLAG)
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+
-
+ifeq ($(PGO_MODE),instrument)
-ifeq ($(PGO_MODE),instrument)
+CXXAPPFLAGS = $(CXXBASEFLAGS)
-## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
+f90appflags = $(F90BASEFLAGS)
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
+CXXAPPFLAGS = $(CXXBASEFLAGS)
-## PGO has been turned off, now tested and found to be negative optimization
+f90appflags = $(F90BASEFLAGS)
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
 
 .SUFFIXES: .o .f90 .C .for .cu
@@ -67,17 +56,14 @@ lopsided_kodis_c.o: lopsided_kodis_c.C
 #interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
 #	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
+## 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 = $(CXXBASEFLAGS) $(TP_OPENMP_FLAGS)
-TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+
-              -fprofile-instr-use=$(TP_PROFDATA) \
+TwoPunctures.o: TwoPunctures.C
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
+	${CXX} $(TP_OPTFLAGS) -c $< -o $@
-
+
-TwoPunctures.o: TwoPunctures.C
+TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -c $< -o $@
-
-TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 # Input files
 
@@ -184,8 +170,8 @@ ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
 ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
-TwoPunctureABE: $(TwoPunctureFILES)
+TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,33 +1,27 @@
-## GCC version (commented out)
+## Legacy GNU/OpenMPI toolchain configuration
-## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
-## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
 
-## Intel oneAPI version with oneMKL (Optimized for performance)
+## OpenMPI wrappers are installed but may not be on PATH.
-filein  = -I/usr/include/ -I${MKLROOT}/include
+OMPI_BIN ?= /usr/lib64/openmpi/bin
 
-## Using sequential MKL (OpenMP disabled for better single-threaded performance)
+## Wrapper compilers
-## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
+f90          = $(OMPI_BIN)/mpifort
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
+f77          = $(OMPI_BIN)/mpifort
+CXX          = $(OMPI_BIN)/mpicxx
+CC           = $(OMPI_BIN)/mpicc
+CLINKER      = $(OMPI_BIN)/mpicxx
 
-## Memory allocator switch
+## Extra include flags are not needed when using the OpenMPI wrappers.
-##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
+filein       =
-##   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
 
-## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
+## BLAS/LAPACK backend:
-##   opt        : (default) maximum performance with PGO profile-guided optimization
+## OpenBLAS on this system provides BLAS, CBLAS and LAPACK symbols.
-##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
+BLAS_LAPACK_LIB ?= /lib64/libopenblaso.so.0
-PGO_MODE ?= opt
+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
@@ -46,20 +40,16 @@ endif
 ## Kernel implementation switch
 ##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
 ##   0           : fall back to original Fortran kernels
-USE_CXX_KERNELS ?= 0
+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 ?= 0
+USE_CXX_RK4 ?= 1
 
-f90          = ifx
+## OpenMP is only used for TwoPunctures on the legacy toolchain.
-f77          = ifx
+TP_OPENMP_FLAGS ?= -fopenmp
-CXX          = icpx
-CC           = icx
-CLINKER      = mpiicpx
 
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
-#CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
 CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc

AMSS_NCKU_source/surface_integral.h

@@ -27,19 +27,24 @@ using namespace std;
 class surface_integral
 {
 
-private:
+private:
-	int Symmetry, factor;
+	int Symmetry, factor;
-	int N_theta, N_phi; // Number of points in Theta & Phi directions
+	int N_theta, N_phi; // Number of points in Theta & Phi directions
-	double dphi, dcostheta;
+	double dphi, dcostheta;
-	double *arcostheta, *wtcostheta;
+	double *arcostheta, *wtcostheta;
-	int n_tot; // size of arrays
+	int n_tot; // size of arrays
-
+
-	double *nx_g, *ny_g, *nz_g; // global list of unit normals
+	double *nx_g, *ny_g, *nz_g; // global list of unit normals
-	int myrank, cpusize;
+	int myrank, cpusize;
-
+	int wave_cache_spinw, wave_cache_maxl, wave_cache_modes;
-public:
+	double *wave_theta_pos, *wave_theta_neg;
-	surface_integral(int iSymmetry);
+	double *wave_phi_cos, *wave_phi_sin;
-	~surface_integral();
+	void clear_wave_cache();
+	void build_wave_cache(int spinw, int maxl);
+
+public:
+	surface_integral(int iSymmetry);
+	~surface_integral();
 
 	void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
 				   int spinw, int maxl, int NN, double *RP, double *IP,
@@ -77,21 +82,37 @@ public:
 								 double &, double &, double &, double &, double &, double &, double &,
 								 double &, double &, double &, double &, double &, double &,
 								 double &, double &)); // NN is the length of RP and IP
-	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
+	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   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,
+	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 *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
-					   double *Rout, monitor *Monitor);
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
-	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
+	void surf_WaveMassPAng(double rex, int lev, cgh *GH,
-				   var *chi, var *trK,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
-				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
+					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+					   var *chi, var *trK,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
+					   double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
+	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
+				   var *chi, var *trK,
+				   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
 				   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
 				   var *chix, var *chiy, var *chiz,
 				   var *trKx, var *trKy, var *trKz,
@@ -110,12 +131,12 @@ public:
 	bool SR_Interp_Points(MyList<var> *VarList, cgh *GH, ShellPatch *SH,
 						  int NN, double **XX, double *Shellf);
 
-	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
+	void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
-					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
+					   var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
-					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
+					   var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
-					   var *Gmx, var *Gmy, var *Gmz,
+					   var *Gmx, var *Gmy, var *Gmz,
-					   var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
+					   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);

README.md

@@ -93,11 +93,13 @@ Here, we take the Ubuntu 22.04 system as an example
 
 #### How to use AMSS-NCKU
 
-0.  Setting the parameters for compilation
+0.  Setting the parameters for compilation
-
+
-    Modify the makefile.inc file in the AMSS_NCKU_source directory and change the settings according to your computer.
+    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.
 

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 )

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