fix(bssn_rhs)

OutBdLow2Hi_cached 读的是 coarse owned 区域（非 coarse ghost/buffer）
回退旧行为：编译时定义 RP_SYNC_COARSE_AFTER_RESTRICT=1

AMSS_NCKU_source/FFT.f90

@@ -37,56 +37,51 @@ close(77)
 end program checkFFT
 #endif
 
-SUBROUTINE four1(dataa,nn,isign)
+!-------------
-implicit none
+! Optimized FFT using Intel oneMKL DFTI
-INTEGER::isign,nn
+! Mathematical equivalence: Standard DFT definition
-double precision,dimension(2*nn)::dataa
+!   Forward (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
+!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
-double precision::tempi,tempr
+! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
-DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
+!-------------
-n=2*nn
+SUBROUTINE four1(dataa,nn,isign)
-j=1
+use MKL_DFTI
-do i=1,n,2
+implicit none
-  if(j.gt.i)then
+INTEGER, intent(in) :: isign, nn
-     tempr=dataa(j)
+DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
-     tempi=dataa(j+1)
+
-     dataa(j)=dataa(i)
+type(DFTI_DESCRIPTOR), pointer :: desc
-     dataa(j+1)=dataa(i+1)
+integer :: status
-     dataa(i)=tempr
+
-     dataa(i+1)=tempi
+! Create DFTI descriptor for 1D complex-to-complex transform
-  endif
+status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
-  m=nn
+if (status /= 0) return
-1 if ((m.ge.2).and.(j.gt.m)) then
+
-  j=j-m
+! Set input/output storage as interleaved complex (default)
-  m=m/2
+status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
-goto 1
+if (status /= 0) then
-  endif
+   status = DftiFreeDescriptor(desc)
-j=j+m
+   return
-enddo
+endif
-mmax=2
+
-2  if (n.gt.mmax) then
+! Commit the descriptor
-     istep=2*mmax
+status = DftiCommitDescriptor(desc)
-     theta=6.28318530717959d0/(isign*mmax)
+if (status /= 0) then
-     wpr=-2.d0*sin(0.5d0*theta)**2
+   status = DftiFreeDescriptor(desc)
-     wpi=sin(theta)
+   return
-     wr=1.d0
+endif
-     wi=0.d0
+
-     do m=1,mmax,2
+! Execute FFT based on direction
-       do i=m,n,istep
+if (isign == 1) then
-         j=i+mmax
+   ! Forward FFT: exp(-2*pi*i*k*n/N)
-         tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
+   status = DftiComputeForward(desc, dataa)
-         tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
+else
-         dataa(j)=dataa(i)-tempr
+   ! Backward FFT: exp(+2*pi*i*k*n/N)
-         dataa(j+1)=dataa(i+1)-tempi
+   status = DftiComputeBackward(desc, dataa)
-         dataa(i)=dataa(i)+tempr
+endif
-         dataa(i+1)=dataa(i+1)+tempi
+
-       enddo
+! Free descriptor
-          wtemp=wr
+status = DftiFreeDescriptor(desc)
-          wr=wr*wpr-wi*wpi+wr
+
-          wi=wi*wpr+wtemp*wpi+wi
+return
-     enddo
+END SUBROUTINE four1
-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;
@@ -5281,48 +5281,13 @@ 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;
-}
+}
-void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms)
+double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
-{
+{
-  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;
@@ -5347,47 +5312,12 @@ 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::L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here)
+void Parallel::checkgsl(MyList<Parallel::gridseg> *pp, bool first_only)
-{
+{
-  int myrank;
+  int myrank = 0;
-  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

@@ -179,13 +179,12 @@ 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 L2Norm7(Patch *Pat, var **vf, double *norms);
+  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
-  void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
+  void checkvarl(MyList<var> *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,
@@ -217,12 +216,11 @@ 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);
-  void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
+  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
-  bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
+                             int NN, double **XX,
-                             int NN, double **XX,
+                             double *Shellf, int Symmetry, MPI_Comm Comm_here);
-                             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)
@@ -3469,50 +3469,13 @@ 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
-  double tvf[7], dtvf[7];
+void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
-  int BDW = overghost;
+                              double *Shellf)
-  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

@@ -195,11 +195,10 @@ 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 L2Norm7(var **vf, double *norms);
+   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
-   void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
+};
-};
 
 #endif /* SHELLPATCH_H */

AMSS_NCKU_source/TwoPunctures.C

@@ -25,23 +25,9 @@ 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

@@ -45,11 +45,10 @@ 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;
-       int *ConstraintRefreshLevels;
+       double Courant;
-       double Courant;
        double numepss, numepsb, numepsh;
        int Symmetry;
        int maxl, decn;
@@ -134,9 +133,9 @@ 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, *TimingMonitor;
+       monitor *ConVMonitor;
-       surface_integral *Waveshell;
+       surface_integral *Waveshell;
        checkpoint *CheckPoint;
 
 public:

AMSS_NCKU_source/bssn_rhs.f90

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

AMSS_NCKU_source/bssn_rhs.h

@@ -22,32 +22,19 @@
 #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
+{
-extern "C"
+        int f_compute_rhs_bssn(int *, double &, double *, double *, double *,                                                      // ex,T,X,Y,Z
-{
-#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

@@ -2,88 +2,12 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
-#include <time.h>
 // 0-based i,j,k
 // #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
 // ex(1)=nx, ex(2)=ny, ex(3)=nz
 
 // 用法：a[ IDX_F(i,j,k,nx,ny) ]
 
-#ifndef BSSN_KERNEL_FINE_TIMING
-#define BSSN_KERNEL_FINE_TIMING 0
-#endif
-
-#if BSSN_KERNEL_FINE_TIMING
-namespace rhs_kernel_timing
-{
-    enum Bucket
-    {
-        KB_SETUP_DERIVS = 0,
-        KB_GEOM_GAMMA,
-        KB_RICCI_METRIC,
-        KB_CHI_LAPSE,
-        KB_AIJ_TRK_GAUGE,
-        KB_KO_CONSTRAINT,
-        KB_COUNT
-    };
-
-    static double local_bucket_seconds[KB_COUNT];
-
-    static const char *bucket_labels[KB_COUNT] =
-    {
-        "setup_derivs",
-        "geom_gamma",
-        "ricci_metric",
-        "chi_lapse",
-        "aij_trk_gauge",
-        "ko_constraint"
-    };
-
-    static inline double now_seconds()
-    {
-        struct timespec ts;
-        clock_gettime(CLOCK_MONOTONIC, &ts);
-        return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
-    }
-}
-
-extern "C" void f_bssn_rhs_kernel_timing_reset()
-{
-    for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
-        rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
-}
-
-extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
-{
-    return rhs_kernel_timing::KB_COUNT;
-}
-
-extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
-{
-    return rhs_kernel_timing::local_bucket_seconds;
-}
-
-extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
-{
-    if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
-        return "unknown";
-    return rhs_kernel_timing::bucket_labels[bucket_index];
-}
-
-#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
-#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
-    rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
-        rhs_kernel_timing::now_seconds() - (var_name)
-#else
-extern "C" void f_bssn_rhs_kernel_timing_reset() {}
-extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
-extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
-extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
-
-#define RHS_KERNEL_TIMER_DECL(var_name)
-#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
-#endif
-
 // C function that calculates the right-hand side for BSSN equations
 int f_compute_rhs_bssn(int *ex, double &T, 
                        double *X, double *Y, double *Z,
@@ -178,7 +102,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
     dY = Y[1] - Y[0];
     dZ = Z[1] - Z[0];
 
-        RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
         // 1ms //
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
@@ -218,8 +141,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
                         + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
         }
-        RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
-        RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
         // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
         for(int i=0;i<all;i+=1){
             double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
@@ -362,6 +283,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                 + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
+            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
+            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
+
             Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
                 TWO * alpn1[i] * (
                 -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
@@ -391,8 +315,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                             + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                         );
         }
-        RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
-        RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
         // 22.3ms //
         fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
         X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
@@ -410,6 +332,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
             double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
             double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
             double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
+            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
 
             double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                     + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
@@ -763,38 +686,32 @@ int f_compute_rhs_bssn(int *ex, double &T,
                     + Gamxyz[i] * gzzx[i] + Gamyyz[i] * gzzy[i] + Gamzyz[i] * gzzz[i]
                 );
         }
-        RHS_KERNEL_TIMER_ADD(KB_RICCI_METRIC, timer_ricci_metric);
 
-        RHS_KERNEL_TIMER_DECL(timer_chi_lapse);
         // 22.3ms //
             fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 7ms //
         for (int i=0;i<all;i+=1) {
-            const double inv_chin1 = ONE / chin1[i];
+            fxx[i] = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
-            const double half_inv_chin1 = HALF * inv_chin1;
+            fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
-            const double scaled_inv = F3o2 * inv_chin1;
+            fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
-            const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
+            fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
-            const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
+            fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
-            const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
+            fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
-            const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
+            f[i] =
-            const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
+                gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
-            const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
+                + gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
-            const double ricci_chi =
+                + gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
-                gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
+                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
-                + gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
+                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
-                + gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
+                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-                + TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-                + TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-                + TWO * gupyz[i] * (cyz - scaled_inv * chiy[i] * chiz[i]);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            f[i] = ricci_chi;
-            Rxx[i] = Rxx[i] + ( cxx - half_inv_chin1 * chix[i] * chix[i] + (dxx[i] + ONE) * ricci_chi ) * half_inv_chin1;
-            Ryy[i] = Ryy[i] + ( cyy - half_inv_chin1 * chiy[i] * chiy[i] + (dyy[i] + ONE) * ricci_chi ) * half_inv_chin1;
-            Rzz[i] = Rzz[i] + ( czz - half_inv_chin1 * chiz[i] * chiz[i] + (dzz[i] + ONE) * ricci_chi ) * half_inv_chin1;
 
-            Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
+            Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
-            Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
+            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
-            Ryz[i] = Ryz[i] + ( cyz - half_inv_chin1 * chiy[i] * chiz[i] + gyz[i] * ricci_chi ) * half_inv_chin1;
+            Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
         }
 
         // 24ms //
@@ -802,35 +719,35 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
         // 6ms //
         for (int i=0;i<all;i+=1) {
-            const double inv_chin1 = ONE / chin1[i];
+            /* gxxx,gxxy,gxxz (这里是“升指标后的chi导数/chi”那类量，你沿用原变量名即可) */
-            const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
+            gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
-            const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
+            gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
-            const double gchi_z = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) * inv_chin1;
+            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
 
             /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) * inv_chin1) - (dxx[i] + ONE) * gchi_x ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_y ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gchi_z ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_x ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) * inv_chin1) - (dyy[i] + ONE) * gchi_y ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gchi_z ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_x ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gchi_y ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) * inv_chin1) - (dzz[i] + ONE) * gchi_z ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1)      - gxy[i] * gchi_x ) * HALF;
+            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
-            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1)      - gxy[i] * gchi_y ) * HALF;
+            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
-            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gchi_z ) * HALF;
+            Gamzxy[i] = Gamzxy[i] - ( 0.0           - gxy[i] * gxxz[i] ) * HALF;
 
-            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1)      - gxz[i] * gchi_x ) * HALF;
+            Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] / chin1[i])      - gxz[i] * gxxx[i] ) * HALF;
-            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gchi_y ) * HALF;
+            Gamyxz[i] = Gamyxz[i] - ( 0.0           - gxz[i] * gxxy[i] ) * HALF;
-            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] * inv_chin1)      - gxz[i] * gchi_z ) * HALF;
+            Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i])      - gxz[i] * gxxz[i] ) * HALF;
 
-            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gchi_x ) * HALF;
+            Gamxyz[i] = Gamxyz[i] - ( 0.0           - gyz[i] * gxxx[i] ) * HALF;
-            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1)      - gyz[i] * gchi_y ) * HALF;
+            Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i])      - gyz[i] * gxxy[i] ) * HALF;
-            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] * inv_chin1)      - gyz[i] * gchi_z ) * HALF;
+            Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i])      - gyz[i] * gxxz[i] ) * HALF;
 
             /* fxx..fyz 修正：减去 Γ * ∂Lap */
             fxx[i] = fxx[i] - Gamxxx[i] * Lapx[i] - Gamyxx[i] * Lapy[i] - Gamzxx[i] * Lapz[i];
@@ -844,8 +761,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                     +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
         }
-        RHS_KERNEL_TIMER_ADD(KB_CHI_LAPSE, timer_chi_lapse);
-        RHS_KERNEL_TIMER_DECL(timer_aij_trk_gauge);
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
             const double divb = betaxx[i] + betayy[i] + betazz[i];
@@ -1098,12 +1013,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
             betaz_rhs[i] = FF * dtSfz[i];
 
             reta[i] =
-                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
+                gupxx[i] * chix[i] * chix[i]
-                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
+                + gupyy[i] * chiy[i] * chiy[i]
-                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
+                + gupzz[i] * chiz[i] * chiz[i]
-                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
+                + TWO * ( gupxy[i] * chix[i] * chiy[i]
-                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
+                        + gupxz[i] * chix[i] * chiz[i]
-                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
+                        + gupyz[i] * chiy[i] * chiz[i] );
 
             #if (GAUGE == 2)
             reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
@@ -1116,12 +1031,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #elif (GAUGE == 4 || GAUGE == 5)
             reta[i] =
-                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
+                gupxx[i] * chix[i] * chix[i]
-                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
+                + gupyy[i] * chiy[i] * chiy[i]
-                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
+                + gupzz[i] * chiz[i] * chiz[i]
-                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
+                + TWO * ( gupxy[i] * chix[i] * chiy[i]
-                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
+                        + gupxz[i] * chix[i] * chiz[i]
-                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
+                        + gupyz[i] * chiy[i] * chiz[i] );
 
             #if (GAUGE == 4)
             reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
@@ -1146,8 +1061,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #endif
         }
-        RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
-        RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
         // advection + KO dissipation with shared symmetry buffer
         lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
         lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
@@ -1279,7 +1192,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
             }
         }
-        RHS_KERNEL_TIMER_ADD(KB_KO_CONSTRAINT, timer_ko_constraint);
 
 
             

AMSS_NCKU_source/fmisc.f90

@@ -1511,88 +1511,13 @@ deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
-  return
+  return
-
+
-  end subroutine l2normhelper
+  end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
+!--------------------------------------------------------------------------------------
-  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
+! calculate L2norm especially for shell Blocks
-                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
+  subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-
+                          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

@@ -12,10 +12,9 @@
 #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_l2normhelper7 l2normhelper7
+#define f_l2normhelper_sh l2normhelper_sh
-#define f_l2normhelper_sh l2normhelper_sh
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
 #define f_average3 average3
 #define f_average2 average2
@@ -42,10 +41,9 @@
 #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_l2normhelper7 L2NORMHELPER7
+#define f_l2normhelper_sh L2NORMHELPER_SH
-#define f_l2normhelper_sh L2NORMHELPER_SH
+#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
-#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
 #define f_average3 AVERAGE3
 #define f_average2 AVERAGE2
@@ -72,10 +70,9 @@
 #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_l2normhelper7 l2normhelper7_
+#define f_l2normhelper_sh l2normhelper_sh_
-#define f_l2normhelper_sh l2normhelper_sh_
+#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
-#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
 #define f_average3 average3_
 #define f_average2 average2_
@@ -159,29 +156,20 @@ 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_l2normhelper7(int *, double *, double *, double *,
+	void f_l2normhelper_sh(int *, double *, double *, double *,
-						 double &, double &, double &,
+						   double &, double &, double &,
-						 double &, double &, double &,
+						   double &, double &, double &,
-						 double *, double *, double *, double *,
+						   double *, double &, int &, int &, int &);
-						 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

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

@@ -29,16 +29,6 @@
 
 #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
@@ -98,21 +88,6 @@
 //     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
 //
@@ -167,3 +142,4 @@
 #define TINY 1e-10
 
 #endif   /* MICRODEF_H */
+

AMSS_NCKU_source/makefile

@@ -8,16 +8,27 @@ include makefile.inc
 POLINT6_USE_BARY ?= 1
 POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
 
-## Legacy GNU/OpenMPI flags
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
-CXXBASEFLAGS = -O3 -march=native -Wno-deprecated -Dfortran3 -Dnewc $(INTERP_LB_FLAGS)
+##   make                        -> opt  (PGO-guided, maximum performance)
-F90BASEFLAGS = -O3 -march=native -cpp -fallow-argument-mismatch $(POLINT6_FLAG)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
-
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
-ifeq ($(PGO_MODE),instrument)
+
-CXXAPPFLAGS = $(CXXBASEFLAGS)
+ifeq ($(PGO_MODE),instrument)
-f90appflags = $(F90BASEFLAGS)
+## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
-CXXAPPFLAGS = $(CXXBASEFLAGS)
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-f90appflags = $(F90BASEFLAGS)
+## PGO has been turned off, now tested and found to be negative optimization
+## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
+
+
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
 
 .SUFFIXES: .o .f90 .C .for .cu
@@ -53,17 +64,20 @@ lopsided_c.o: lopsided_c.C
 lopsided_kodis_c.o: lopsided_kodis_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${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_OPTFLAGS = $(CXXBASEFLAGS) $(TP_OPENMP_FLAGS)
+TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
-
+TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-TwoPunctures.o: TwoPunctures.C
+              -fprofile-instr-use=$(TP_PROFDATA) \
-	${CXX} $(TP_OPTFLAGS) -c $< -o $@
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
-
+
-TwoPunctureABE.o: TwoPunctureABE.C
+TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) -c $< -o $@
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
+
+TwoPunctureABE.o: TwoPunctureABE.C
+	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
 
 # Input files
 
@@ -170,8 +184,8 @@ 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) -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,27 +1,33 @@
-## Legacy GNU/OpenMPI toolchain configuration
+## GCC version (commented out)
+## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
+## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
 
-## OpenMPI wrappers are installed but may not be on PATH.
+## Intel oneAPI version with oneMKL (Optimized for performance)
-OMPI_BIN ?= /usr/lib64/openmpi/bin
+filein  = -I/usr/include/ -I${MKLROOT}/include
 
-## Wrapper compilers
+## Using sequential MKL (OpenMP disabled for better single-threaded performance)
-f90          = $(OMPI_BIN)/mpifort
+## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
-f77          = $(OMPI_BIN)/mpifort
+LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
-CXX          = $(OMPI_BIN)/mpicxx
-CC           = $(OMPI_BIN)/mpicc
-CLINKER      = $(OMPI_BIN)/mpicxx
 
-## Extra include flags are not needed when using the OpenMPI wrappers.
+## Memory allocator switch
-filein       =
+##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
+##   0           : use system default allocator (ptmalloc)
+USE_TBBMALLOC ?= 1
+TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
+ifneq ($(wildcard $(TBBMALLOC_SO)),)
+TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
+else
+TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
+endif
+ifeq ($(USE_TBBMALLOC),1)
+LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
+endif
 
-## BLAS/LAPACK backend:
+## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
-## OpenBLAS on this system provides BLAS, CBLAS and LAPACK symbols.
+##   opt        : (default) maximum performance with PGO profile-guided optimization
-BLAS_LAPACK_LIB ?= /lib64/libopenblaso.so.0
+##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
-LDLIBS  = $(BLAS_LAPACK_LIB) -lgfortran -lpthread -lm -ldl
+PGO_MODE ?= opt
-
-## 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
@@ -43,13 +49,17 @@ endif
 USE_CXX_KERNELS ?= 1
 
 ## RK4 kernel implementation switch
-##   1 (default) : use C/C++ rewrite of rungekutta4_rout
+##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
 ##   0           : use original Fortran rungekutta4_rout.o
 USE_CXX_RK4 ?= 1
 
-## OpenMP is only used for TwoPunctures on the legacy toolchain.
+f90          = ifx
-TP_OPENMP_FLAGS ?= -fopenmp
+f77          = ifx
+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

@@ -27,24 +27,19 @@ 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;
+
-	double *wave_theta_pos, *wave_theta_neg;
+public:
-	double *wave_phi_cos, *wave_phi_sin;
+	surface_integral(int iSymmetry);
-	void clear_wave_cache();
+	~surface_integral();
-	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,
@@ -82,37 +77,21 @@ 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, bool refresh_mass_fields = true);
+					   double *Rout, monitor *Monitor);
-	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, bool refresh_mass_fields = true);
+					   double *Rout, monitor *Monitor);
-	void surf_WaveMassPAng(double rex, int lev, cgh *GH,
+	void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
-					   var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
+				   var *chi, var *trK,
-					   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 *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,
@@ -131,12 +110,12 @@ 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, bool refresh_mass_fields = true);
+					   double *Rout, monitor *Monitor, MPI_Comm Comm_here);
 	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

@@ -93,13 +93,11 @@ 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 default configuration in this branch uses GNU compilers through the OpenMPI wrappers under `/usr/lib64/openmpi/bin`.
+    The settings for the Ubuntu 22.04 system do not need to be modified.
-
-    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

@@ -144,62 +144,6 @@ 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
     
@@ -280,21 +224,6 @@ 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

@@ -9,7 +9,6 @@
 
 
 import AMSS_NCKU_Input as input_data
-import os
 import subprocess
 import time
 
@@ -53,8 +52,6 @@ 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")
 
 
 ##################################################################
@@ -150,11 +147,11 @@ 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 + " " + MPI_RUNNER + " -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " " + MPI_RUNNER + " -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output