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_Input.py

@@ -13,17 +13,14 @@ import numpy
 
 ## Setting MPI processes and the output file directory
 
-File_directory   = "GW150914"                    ## output file directory
+File_directory   = "GW150914"                    ## output file directory
-Output_directory = "binary_output"               ## binary data file directory
+Output_directory = "binary_output"               ## binary data file directory
-                                                 ## The file directory name should not be too long
+                                                 ## The file directory name should not be too long
-MPI_processes    = 64                            ## number of mpi processes used in the simulation
+MPI_processes    = 64                             ## number of mpi processes used in the simulation
-OMP_Threads      = 3                             ## number of OpenMP threads used by each MPI process
+
-MPI_hosts        = ["localhost", "192.168.20.102"] ## MPI hosts for multi-node runs
+GPU_Calculation  = "no"                          ## Use GPU or not 
-MPI_processes_per_node = 32                      ## MPI ranks launched on each node in MPI_hosts
+                                                 ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
-
+CPU_Part         = 1.0
-GPU_Calculation  = "no"                          ## Use GPU or not
-                                                 ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)
-CPU_Part         = 1.0
 GPU_Part         = 0.0
 
 #################################################
@@ -53,7 +50,7 @@ Check_Time               = 100.0
 Dump_Time                = 100.0                  ## time inteval dT for dumping binary data
 D2_Dump_Time             = 100.0                  ## dump the ascii data for 2d surface after dT'
 Analysis_Time            = 0.1                    ## dump the puncture position and GW psi4 after dT"
-Evolution_Step_Number    = 10000000               ## stop the calculation after the maximal step number
+Evolution_Step_Number    = 10000000               ## stop the calculation after the maximal step number
 Courant_Factor           = 0.5                    ## Courant Factor
 Dissipation              = 0.15                   ## Kreiss-Oliger Dissipation Strength
 

AMSS_NCKU_source/bssn_class.C

@@ -36,18 +36,12 @@ using namespace std;
 #include "myglobal.h"
 #endif
 
-#include "perf.h"
+#include "perf.h"
-
+
-#include "derivatives.h"
+#include "derivatives.h"
-#include "ricci_gamma.h"
+#include "ricci_gamma.h"
-
+
-// Compile-time switch for per-timestep memory usage collection/printing.
+//================================================================================================
-// Default is OFF to reduce overhead in production runs.
-#ifndef BSSN_ENABLE_MEM_USAGE_LOG
-#define BSSN_ENABLE_MEM_USAGE_LOG 0
-#endif
-
-//================================================================================================
 
 // define bssn_class
 
@@ -2034,9 +2028,9 @@ void bssn_class::Read_Ansorg()
 
 //================================================================================================
 
-void bssn_class::Evolve(int Steps)
+void bssn_class::Evolve(int Steps)
-{
+{
-  double prev_clock = 0.0, curr_clock = 0.0;
+  clock_t prev_clock, curr_clock;
   double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
   LastAnas = 0;
 #if 0
@@ -2135,24 +2129,22 @@ void bssn_class::Evolve(int Steps)
   #endif
   */
   
-#if BSSN_ENABLE_MEM_USAGE_LOG
+  perf bssn_perf;
-  perf bssn_perf;
+  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
-  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
-#endif
 
   for (int lev = 0; lev < GH->levels; lev++)
     GH->Lt[lev] = PhysTime;
 
   GH->settrfls(trfls);
 
-  for (int ncount = 1; ncount < Steps + 1; ncount++)
+  for (int ncount = 1; ncount < Steps + 1; ncount++)
-  {
+  {
     // special for large mass ratio consideration
     //     if(fabs(Porg0[0][0]-Porg0[1][0])+fabs(Porg0[0][1]-Porg0[1][1])+fabs(Porg0[0][2]-Porg0[1][2])<1e-6) 
     //     { GH->levels=GH->movls; }
 
-    if (myrank == 0)
+    if (myrank == 0)
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
 #if (PSTR == 0)
     RecursiveStep(0);
 #elif (PSTR == 1 || PSTR == 2 || PSTR == 3)
@@ -2205,16 +2197,16 @@ void bssn_class::Evolve(int Steps)
       }
     }
 
-    if (myrank == 0)
+    if (myrank == 0)
-    {
+    {
-      prev_clock = curr_clock;
+      prev_clock = curr_clock;
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
-      cout << endl;
+      cout << endl;
-      cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
+      cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime << "   "
-           << " Computer used " << (curr_clock - prev_clock)
+           << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) 
-           << " seconds! " << endl;
+           << " seconds! " << endl;
-      // cout << endl;
+      // cout << endl;
-    }
+    }
 
     if (PhysTime >= TotalTime)
       break;
@@ -2232,23 +2224,21 @@ void bssn_class::Evolve(int Steps)
 //		fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
 #endif
 
-#if BSSN_ENABLE_MEM_USAGE_LOG
+    // Retrieve memory usage information used during computation; master process prints it
-    // Retrieve memory usage information used during computation; master process prints it
+    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
-    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
+                          &peak_min, &peak_avg, &peak_max, nprocs);
-                          &peak_min, &peak_avg, &peak_max, nprocs);
+    if (myrank == 0)
-    if (myrank == 0)
+    {
-    {
+      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
-      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
+             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
-             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
+             (double)current_min / (1024.0 * 1024.0),
-             (double)current_min / (1024.0 * 1024.0),
+             (double)current_avg / (1024.0 * 1024.0),
-             (double)current_avg / (1024.0 * 1024.0),
+             (double)current_max / (1024.0 * 1024.0),
-             (double)current_max / (1024.0 * 1024.0),
+             (double)peak_min / (1024.0 * 1024.0),
-             (double)peak_min / (1024.0 * 1024.0),
+             (double)peak_avg / (1024.0 * 1024.0),
-             (double)peak_avg / (1024.0 * 1024.0),
+             (double)peak_max / (1024.0 * 1024.0));
-             (double)peak_max / (1024.0 * 1024.0));
+      cout << endl;
-      cout << endl;
+    }
-    }
-#endif
     
     // Output puncture positions at each step
     if (myrank == 0)
@@ -5755,11 +5745,17 @@ void bssn_class::SHStep()
 
 //================================================================================================
 
-// 0: do not use mixing two levels data for OutBD; 1: do use
+// 0: do not use mixing two levels data for OutBD; 1: do use
-
+
-#define MIXOUTB 0
+#define MIXOUTB 0
-void bssn_class::RestrictProlong(int lev, int YN, bool BB,
+// In the cached Restrict->OutBdLow2Hi path, coarse Sync is usually redundant:
-                                 MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
+// OutBdLow2Hi_cached reads coarse owned cells (build_owned_gsl type-4), not coarse ghost/buffer cells.
+// Keep a switch to restore the old behavior if needed for debugging.
+#ifndef RP_SYNC_COARSE_AFTER_RESTRICT
+#define RP_SYNC_COARSE_AFTER_RESTRICT 0
+#endif
+void bssn_class::RestrictProlong(int lev, int YN, bool BB,
+                                 MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
 // we assume
 // StateList      1   -----------
 //
@@ -5821,7 +5817,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5872,7 +5870,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
 
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5958,7 +5958,9 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
@@ -5980,7 +5982,9 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
@@ -6045,7 +6049,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
@@ -6069,7 +6075,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
 #endif
 
-      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
@@ -6093,7 +6101,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 //================================================================================================
 
-void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
+void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 {
   if (lev > 0)
   {
@@ -6146,15 +6154,18 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 #else
       Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
 #endif
-      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
+      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
+#endif
     }
 
     Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
   }
-}
+}
-#undef MIXOUTB
+#undef MIXOUTB
-
+#undef RP_SYNC_COARSE_AFTER_RESTRICT
-//================================================================================================
+
+//================================================================================================
 
 
 

AMSS_NCKU_source/bssn_gpu_class.C

@@ -1891,7 +1891,7 @@ void bssn_class::Read_Ansorg()
 void bssn_class::Evolve(int Steps)
 {
 
-  double prev_clock = 0.0, curr_clock = 0.0;
+  clock_t prev_clock, curr_clock;
   double LastDump = 0.0, LastCheck = 0.0, Last2dDump = 0.0;
   LastAnas = 0;
 #if 0
@@ -2035,12 +2035,10 @@ void bssn_class::Evolve(int Steps)
 
   GH->settrfls(trfls);
 
-  for (int ncount = 1; ncount < Steps + 1; ncount++)
+  for (int ncount = 1; ncount < Steps + 1; ncount++)
-  {
+  {
-    if (myrank == 0)
+    cout << "Before Step: " << ncount << " My Rank: " << myrank 
-      curr_clock = MPI_Wtime();
+         << " takes " << MPI_Wtime() - beg_time << " seconds!" << endl;
-    cout << "Before Step: " << ncount << " My Rank: " << myrank 
-         << " takes " << MPI_Wtime() - beg_time << " seconds!" << endl;
     beg_time = MPI_Wtime();
 #if (PSTR == 0)
     RecursiveStep(0);
@@ -2097,10 +2095,10 @@ void bssn_class::Evolve(int Steps)
 
     if (myrank == 0)
     {
-      prev_clock = curr_clock;
+      prev_clock = curr_clock;
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
-      cout << "Timestep # " << ncount << ": integrating to time: " << PhysTime << endl;
+      cout << "Timestep # " << ncount << ": integrating to time: " << PhysTime << endl;
-      cout << "used " << (curr_clock - prev_clock) << " seconds!" << endl;
+      cout << "used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds!" << endl;
     }
 
     if (PhysTime >= TotalTime)

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_c.C

@@ -2,24 +2,6 @@
 #include "bssn_rhs.h"
 #include "share_func.h"
 #include "tool.h"
-
-#ifdef _OPENMP
-#define BSSN_OMP_TASK_GROUP_BEGIN \
-    _Pragma("omp parallel")       \
-    {                             \
-        _Pragma("omp single nowait") \
-        {
-#define BSSN_OMP_TASK_CALL(...) \
-            _Pragma("omp task") { __VA_ARGS__; }
-#define BSSN_OMP_TASK_GROUP_END \
-            _Pragma("omp taskwait") \
-        } \
-    }
-#else
-#define BSSN_OMP_TASK_GROUP_BEGIN {
-#define BSSN_OMP_TASK_CALL(...) { __VA_ARGS__; }
-#define BSSN_OMP_TASK_GROUP_END }
-#endif
 // 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
@@ -126,20 +108,18 @@ int f_compute_rhs_bssn(int *ex, double &T,
             chin1[i] = chi[i] + 1.0;
         }
         // 9ms //
-        BSSN_OMP_TASK_GROUP_BEGIN
+        fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev))
+        fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev))
+        fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev))
+        fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev))
+        fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev))
+        fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev))
+        fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev))
+        fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev))
+        fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev))
+        fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev))
+        fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev))
+        fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev))
-        BSSN_OMP_TASK_GROUP_END
 
         // 3ms //
         for(int i=0;i<all;i+=1){
@@ -336,14 +316,15 @@ int f_compute_rhs_bssn(int *ex, double &T,
                         );
         }
         // 22.3ms //
-        BSSN_OMP_TASK_GROUP_BEGIN
+        fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
-        BSSN_OMP_TASK_CALL(fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev))
+        X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fdderivs(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev))
+        fdderivs(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,
-        BSSN_OMP_TASK_CALL(fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev))
+        X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev))
+        fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,
-        BSSN_OMP_TASK_CALL(fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev))
+        X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev);
-        BSSN_OMP_TASK_CALL(fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev))
+        fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev);
-        BSSN_OMP_TASK_GROUP_END
+        fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev);
+        fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev);
 
         // Fused: fxx/Gamxa + Gamma_rhs part 2 (2 loops -> 1)
         for(int i=0;i<all;i+=1){
@@ -735,7 +716,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
         // 24ms //
         fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
-        fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
 
         // 6ms //
         for (int i=0;i<all;i+=1) {
@@ -1033,12 +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 );
@@ -1051,12 +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 );
@@ -1082,32 +1062,30 @@ int f_compute_rhs_bssn(int *ex, double &T,
             #endif
         }
         // advection + KO dissipation with shared symmetry buffer
-        BSSN_OMP_TASK_GROUP_BEGIN
+        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps))
+        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps))
+        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps))
+        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps))
+        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps))
+        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps))
+        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps))
+        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps))
+        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps))
+        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps))
+        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps))
+        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps))
+        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps))
+        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps))
+        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps))
+        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        BSSN_OMP_TASK_CALL(lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps))
-        BSSN_OMP_TASK_GROUP_END
         // 2ms //
         if(co==0){
             for (int i=0;i<all;i+=1) {
@@ -1154,14 +1132,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
             }
 
             // 1ms //
-            BSSN_OMP_TASK_GROUP_BEGIN
+            fderivs(ex,Axx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
-            BSSN_OMP_TASK_CALL(fderivs(ex,Axx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0))
+            fderivs(ex,Axy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0);
-            BSSN_OMP_TASK_CALL(fderivs(ex,Axy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,0))
+            fderivs(ex,Axz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0);
-            BSSN_OMP_TASK_CALL(fderivs(ex,Axz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,0))
+            fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
-            BSSN_OMP_TASK_CALL(fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0))
+            fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
-            BSSN_OMP_TASK_CALL(fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0))
+            fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
-            BSSN_OMP_TASK_CALL(fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0))
-            BSSN_OMP_TASK_GROUP_END
             // 7ms //
             for (int i=0;i<all;i+=1) {
                 gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]

AMSS_NCKU_source/fdderivs_c.C

@@ -41,8 +41,8 @@ void fdderivs(const int ex[3],
     const size_t nz = (size_t)ex3 + 2;
     const size_t fh_size = nx * ny * nz;
 
-    static thread_local double *fh = NULL;
+    static double *fh = NULL;
-    static thread_local size_t cap = 0;
+    static size_t cap = 0;
 
     if (fh_size > cap) {
         free(fh);

AMSS_NCKU_source/fderivs_c.C

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

AMSS_NCKU_source/lopsided_kodis_c.C

@@ -43,13 +43,7 @@ void lopsided_kodis(const int ex[3],
     const size_t nz = (size_t)ex3 + 3;
     const size_t fh_size = nx * ny * nz;
 
-    static thread_local double *fh = NULL;
+    double *fh = (double*)malloc(fh_size * sizeof(double));
-    static thread_local size_t cap = 0;
-    if (fh_size > cap) {
-        free(fh);
-        fh = (double*)aligned_alloc(64, fh_size * sizeof(double));
-        cap = fh_size;
-    }
     if (!fh) return;
 
     symmetry_bd(3, ex, f, fh, SoA);
@@ -249,4 +243,6 @@ void lopsided_kodis(const int ex[3],
             }
         }
     }
+
+    free(fh);
 }

AMSS_NCKU_source/makefile

@@ -16,7 +16,7 @@ PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 ifeq ($(PGO_MODE),instrument)
 ## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
 CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS) $(OPENMP_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
               -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
@@ -26,7 +26,7 @@ else
 
 
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS) $(OPENMP_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
               -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
@@ -64,8 +64,8 @@ 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
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata

AMSS_NCKU_source/makefile.inc

@@ -29,9 +29,6 @@ endif
 ##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
 PGO_MODE ?= opt
 
-## OpenMP switch for C/C++ kernels
-OPENMP_FLAGS ?= -qopenmp
-
 ## Interp_Points load balance profiling mode
 ##   off        : (default) no load balance instrumentation
 ##   profile    : Pass 1 — instrument Interp_Points to collect timing profile

AMSS_NCKU_source/scalar_class.C

@@ -317,9 +317,9 @@ void scalar_class::Setup_Initial_Data()
 #endif
   }
 }
-void scalar_class::Evolve(int Steps)
+void scalar_class::Evolve(int Steps)
-{
+{
-  double prev_clock = 0.0, curr_clock = 0.0;
+  clock_t prev_clock, curr_clock;
   double LastDump = 0.0, LastCheck = 0.0;
   LastAnas = 0;
 
@@ -327,8 +327,8 @@ void scalar_class::Evolve(int Steps)
 
   for (int ncount = 1; ncount < Steps + 1; ncount++)
   {
-    if (myrank == 0)
+    if (myrank == 0)
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
     RecursiveStep(0);
 
     LastDump += dT_mon;
@@ -343,13 +343,13 @@ void scalar_class::Evolve(int Steps)
 #endif
       LastDump = 0;
     }
-    if (myrank == 0)
+    if (myrank == 0)
-    {
+    {
-      prev_clock = curr_clock;
+      prev_clock = curr_clock;
-      curr_clock = MPI_Wtime();
+      curr_clock = clock();
-      cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime
+      cout << " Timestep # " << ncount << ": integrating to time: " << PhysTime
-           << " Computer used " << (curr_clock - prev_clock) << " seconds! " << endl;
+           << " Computer used " << (double)(curr_clock - prev_clock) / ((double)CLOCKS_PER_SEC) << " seconds! " << endl;
-    }
+    }
     if (PhysTime >= TotalTime)
       break;
   }

makefile_and_run.py

@@ -9,7 +9,6 @@
 
 
 import AMSS_NCKU_Input as input_data
-import os
 import subprocess
 import time
 
@@ -55,44 +54,6 @@ NUMACTL_CPU_BIND = get_last_n_cores_per_socket(n=32)
 BUILD_JOBS = 64
 
 
-def build_abe_runtime_env():
-    """Inject OpenMP runtime settings only for the main ABE evolution run."""
-    runtime_env = os.environ.copy()
-    omp_threads = max(1, int(getattr(input_data, "OMP_Threads", 1)))
-    runtime_env["OMP_NUM_THREADS"] = str(omp_threads)
-    return runtime_env
-
-
-def build_twopuncture_runtime_env():
-    """Let TwoPunctureABE use the runtime default instead of the ABE OMP override."""
-    runtime_env = os.environ.copy()
-    runtime_env.pop("OMP_NUM_THREADS", None)
-    runtime_env.pop("OMP_THREAD_LIMIT", None)
-    return runtime_env
-
-
-def build_mpi_launch_args():
-    """Build optional host-distribution arguments for mpirun."""
-    hosts = list(getattr(input_data, "MPI_hosts", []))
-    ppn = int(getattr(input_data, "MPI_processes_per_node", 0))
-
-    if not hosts:
-        return ""
-
-    if ppn > 0:
-        expected = len(hosts) * ppn
-        if int(input_data.MPI_processes) != expected:
-            raise ValueError(
-                f"MPI_processes={input_data.MPI_processes} does not match "
-                f"len(MPI_hosts) * MPI_processes_per_node = {expected}"
-            )
-
-    launch_args = f"-hosts {','.join(hosts)}"
-    if ppn > 0:
-        launch_args += f" -ppn {ppn}"
-    return launch_args
-
-
 ##################################################################
 
 
@@ -182,38 +143,19 @@ def run_ABE():
     print(                                                      )
     print( " Running the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                      )
-    print( f" MPI processes = {input_data.MPI_processes}, OMP threads per process = {max(1, int(getattr(input_data, 'OMP_Threads', 1)))}" )
-    if getattr(input_data, "MPI_hosts", []):
-        print( f" MPI hosts = {getattr(input_data, 'MPI_hosts', [])}, MPI ranks per node = {int(getattr(input_data, 'MPI_processes_per_node', 0))}" )
-        print( " Multi-node runs require the working directory to be visible on all MPI hosts. " )
-    print(                                                                                                      )
 
     ## Define the command to run; cast other values to strings as needed
-    mpi_launch_args = build_mpi_launch_args()
     
     if (input_data.GPU_Calculation == "no"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun "
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
-        if mpi_launch_args:
-            mpi_command += mpi_launch_args + " "
-        mpi_command += "-np " + str(input_data.MPI_processes) + " ./ABE"
         #mpi_command         = " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = NUMACTL_CPU_BIND + " mpirun "
+        mpi_command         = NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
-        if mpi_launch_args:
-            mpi_command += mpi_launch_args + " "
-        mpi_command += "-np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
  
     ## Execute the MPI command and stream output
-    mpi_process = subprocess.Popen(
+    mpi_process = subprocess.Popen(mpi_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
-        mpi_command,
-        shell=True,
-        stdout=subprocess.PIPE,
-        stderr=subprocess.STDOUT,
-        text=True,
-        env=build_abe_runtime_env(),
-    )
 
     ## Write ABE run output to file while printing to stdout
     with open(mpi_command_outfile, 'w') as file0:  
@@ -253,14 +195,7 @@ def run_TwoPunctureABE():
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output
-    TwoPuncture_process = subprocess.Popen(
+    TwoPuncture_process = subprocess.Popen(TwoPuncture_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True)
-        TwoPuncture_command,
-        shell=True,
-        stdout=subprocess.PIPE,
-        stderr=subprocess.STDOUT,
-        text=True,
-        env=build_twopuncture_runtime_env(),
-    )
 
     ## Write TwoPunctureABE run output to file while printing to stdout
     with open(TwoPuncture_command_outfile, 'w') as file0:  

setup.py

@@ -65,14 +65,10 @@ def print_input_data( File_directory ):
         
     print( "------------------------------------------------------------------------------------------" )
     print(                                                                                           )
-    print( " Printing the basic parameter and setting in the AMSS-NCKU simulation "                  )
+    print( " Printing the basic parameter and setting in the AMSS-NCKU simulation "                  )
-    print(                                                                                           )
+    print(                                                                                           )
-    print( " The number of MPI processes in the AMSS-NCKU simulation = ", input_data.MPI_processes   )
+    print( " The number of MPI processes in the AMSS-NCKU simulation = ", input_data.MPI_processes   ) 
-    print( " The number of OMP threads per MPI process         = ", input_data.OMP_Threads           )
+    print(                                                                                           )
-    if getattr(input_data, "MPI_hosts", []):
-        print( " The MPI host list in the AMSS-NCKU simulation   = ", input_data.MPI_hosts             )
-        print( " The number of MPI ranks launched per host       = ", input_data.MPI_processes_per_node )
-    print(                                                                                           )
     print( " The form of computational equation  = ",            input_data.Equation_Class           )
     print( " The initial data in this simulation = ",            input_data.Initial_Data_Method      )
     print(                                                                                           )
@@ -144,14 +140,10 @@ def print_input_data( File_directory ):
     file0    = open(filepath, 'w')
     
     print(                                                                                              file=file0 )
-    print( " Printing the basic parameter and setting in the AMSS-NCKU simulation ",                    file=file0 )
+    print( " Printing the basic parameter and setting in the AMSS-NCKU simulation ",                    file=file0 )
-    print(                                                                                              file=file0 )
+    print(                                                                                              file=file0 )
-    print( " The number of MPI processes in the AMSS-NCKU simulation = ", input_data.MPI_processes,     file=file0 )
+    print( " The number of MPI processes in the AMSS-NCKU simulation = ", input_data.MPI_processes,     file=file0 ) 
-    print( " The number of OMP threads per MPI process         = ", input_data.OMP_Threads,             file=file0 )
+    print(                                                                                              file=file0 )
-    if getattr(input_data, "MPI_hosts", []):
-        print( " The MPI host list in the AMSS-NCKU simulation   = ", input_data.MPI_hosts,               file=file0 )
-        print( " The number of MPI ranks launched per host       = ", input_data.MPI_processes_per_node,   file=file0 )
-    print(                                                                                              file=file0 )
     print( " The form of computational equation  = ",            input_data.Equation_Class,             file=file0 )
     print( " The initial data in this simulation = ",            input_data.Initial_Data_Method,        file=file0 )
     print(                                                                                              file=file0 )