prolong3 改为先算实际 stencil 窗口；只有窗口触及对称边界时才走全域 symmetry_bd，否则只复制必需窗口。restrict3 同样改成窗口判定，无触边时仅填 ii/jj/kk 必需窗口。

perf(restrict3): shrink X-pass ii sweep to required overlap window
- compute fi_min/fi_max from output i-range and derive ii_lo/ii_hi - replace full ii sweep (-1:extf(1)) with windowed sweep in Z/Y precompute passes - keep stencil math unchanged; add bounds sanity check for ii window
2026-03-02 18:10:38 +08:00 · 2026-03-02 18:10:38 +08:00 · 2026-03-02 18:10:35 +08:00 · 2026-03-02 14:11:52 +08:00 · 2026-03-02 14:08:27 +08:00 · 2026-03-02 14:08:13 +08:00
31 changed files with 4148 additions and 1853 deletions
--- a/AMSS_NCKU_source/Parallel.C
+++ b/AMSS_NCKU_source/Parallel.C
@@ -4320,7 +4320,7 @@ Parallel::SyncCache::SyncCache()
    : valid(false), cpusize(0), combined_src(0), combined_dst(0),
      send_lengths(0), recv_lengths(0), send_bufs(0), recv_bufs(0),
      send_buf_caps(0), recv_buf_caps(0), reqs(0), stats(0), max_reqs(0),
-      lengths_valid(false), tc_req_node(0), tc_req_is_recv(0), tc_completed(0)
+      lengths_valid(false)
 {
 }
 // SyncCache invalidate: free grid segment lists but keep buffers
@@ -4359,15 +4359,11 @@ void Parallel::SyncCache::destroy()
  if (recv_bufs) delete[] recv_bufs;
  if (reqs) delete[] reqs;
  if (stats) delete[] stats;
-  if (tc_req_node) delete[] tc_req_node;
-  if (tc_req_is_recv) delete[] tc_req_is_recv;
-  if (tc_completed) delete[] tc_completed;
  combined_src = combined_dst = 0;
  send_lengths = recv_lengths = 0;
  send_buf_caps = recv_buf_caps = 0;
  send_bufs = recv_bufs = 0;
  reqs = 0; stats = 0;
-  tc_req_node = 0; tc_req_is_recv = 0; tc_completed = 0;
  cpusize = 0; max_reqs = 0;
 }
 // transfer_cached: reuse pre-allocated buffers from SyncCache
@@ -4383,9 +4379,9 @@ void Parallel::transfer_cached(MyList<Parallel::gridseg> **src, MyList<Parallel:
  int req_no = 0;
  int pending_recv = 0;
  int node;
-  int *req_node = cache.tc_req_node;
-  int *req_is_recv = cache.tc_req_is_recv;
-  int *completed = cache.tc_completed;
+  int *req_node = new int[cache.max_reqs];
+  int *req_is_recv = new int[cache.max_reqs];
+  int *completed = new int[cache.max_reqs];

  // Post receives first so peers can progress rendezvous early.
  for (node = 0; node < cpusize; node++)
@@ -4470,7 +4466,12 @@ void Parallel::transfer_cached(MyList<Parallel::gridseg> **src, MyList<Parallel:

  if (self_len > 0)
    data_packer(cache.recv_bufs[myrank], src[myrank], dst[myrank], myrank, UNPACK, VarList1, VarList2, Symmetry);
+
+  delete[] req_node;
+  delete[] req_is_recv;
+  delete[] completed;
 }
+// Sync_cached: build grid segment lists on first call, reuse on subsequent calls
 void Parallel::Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry, SyncCache &cache)
 {
  if (!cache.valid)
@@ -4498,9 +4499,6 @@ void Parallel::Sync_cached(MyList<Patch> *PatL, MyList<var> *VarList, int Symmet
      cache.max_reqs = 2 * cpusize;
      cache.reqs = new MPI_Request[cache.max_reqs];
      cache.stats = new MPI_Status[cache.max_reqs];
-      cache.tc_req_node = new int[cache.max_reqs];
-      cache.tc_req_is_recv = new int[cache.max_reqs];
-      cache.tc_completed = new int[cache.max_reqs];
    }

    for (int node = 0; node < cpusize; node++)
@@ -4601,9 +4599,6 @@ void Parallel::Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetr
      cache.max_reqs = 2 * cpusize;
      cache.reqs = new MPI_Request[cache.max_reqs];
      cache.stats = new MPI_Status[cache.max_reqs];
-      cache.tc_req_node = new int[cache.max_reqs];
-      cache.tc_req_is_recv = new int[cache.max_reqs];
-      cache.tc_completed = new int[cache.max_reqs];
    }

    for (int node = 0; node < cpusize; node++)
@@ -4674,11 +4669,6 @@ void Parallel::Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetr
  int cpusize = cache.cpusize;
  state.req_no = 0;
  state.active = true;
-  state.pending_recv = 0;
-  // Allocate tracking arrays
-  delete[] state.req_node; delete[] state.req_is_recv;
-  state.req_node = new int[cache.max_reqs];
-  state.req_is_recv = new int[cache.max_reqs];

  MyList<Parallel::gridseg> **src = cache.combined_src;
  MyList<Parallel::gridseg> **dst = cache.combined_dst;
@@ -4723,8 +4713,6 @@ void Parallel::Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetr
          cache.send_buf_caps[node] = slength;
        }
        data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList, VarList, Symmetry);
-        state.req_node[state.req_no] = node;
-        state.req_is_recv[state.req_no] = 0;
        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 2, MPI_COMM_WORLD, cache.reqs + state.req_no++);
      }
      int rlength;
@@ -4742,60 +4730,29 @@ void Parallel::Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetr
          cache.recv_bufs[node] = new double[rlength];
          cache.recv_buf_caps[node] = rlength;
        }
-        state.req_node[state.req_no] = node;
-        state.req_is_recv[state.req_no] = 1;
-        state.pending_recv++;
        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 2, MPI_COMM_WORLD, cache.reqs + state.req_no++);
      }
    }
  }
  cache.lengths_valid = true;
 }
-// Sync_finish: progressive unpack as receives complete, then wait for sends
+// Sync_finish: wait for async MPI operations and unpack
 void Parallel::Sync_finish(SyncCache &cache, AsyncSyncState &state,
                           MyList<var> *VarList, int Symmetry)
 {
  if (!state.active)
    return;

-  int myrank;
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  MPI_Waitall(state.req_no, cache.reqs, cache.stats);
+
+  int cpusize = cache.cpusize;
  MyList<Parallel::gridseg> **src = cache.combined_src;
  MyList<Parallel::gridseg> **dst = cache.combined_dst;

-  // Unpack local data first (no MPI needed)
-  if (cache.recv_bufs[myrank] && cache.recv_lengths[myrank] > 0)
-    data_packer(cache.recv_bufs[myrank], src[myrank], dst[myrank], myrank, UNPACK, VarList, VarList, Symmetry);
+  for (int node = 0; node < cpusize; node++)
+    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
+      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList, VarList, Symmetry);

-  // Progressive unpack of remote receives
-  if (state.pending_recv > 0 && state.req_no > 0)
-  {
-    int pending = state.pending_recv;
-    int *completed = new int[cache.max_reqs];
-    while (pending > 0)
-    {
-      int outcount = 0;
-      MPI_Waitsome(state.req_no, cache.reqs, &outcount, completed, cache.stats);
-      if (outcount == MPI_UNDEFINED) break;
-      for (int i = 0; i < outcount; i++)
-      {
-        int idx = completed[i];
-        if (idx >= 0 && state.req_is_recv[idx])
-        {
-          int recv_node = state.req_node[idx];
-          data_packer(cache.recv_bufs[recv_node], src[recv_node], dst[recv_node], recv_node, UNPACK, VarList, VarList, Symmetry);
-          pending--;
-        }
-      }
-    }
-    delete[] completed;
-  }
-
-  // Wait for remaining sends
-  if (state.req_no > 0) MPI_Waitall(state.req_no, cache.reqs, cache.stats);
-
-  delete[] state.req_node; state.req_node = 0;
-  delete[] state.req_is_recv; state.req_is_recv = 0;
  state.active = false;
 }
 // collect buffer grid segments or blocks for the periodic boundary condition of given patch
@@ -5862,9 +5819,6 @@ void Parallel::Restrict_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
      cache.max_reqs = 2 * cpusize;
      cache.reqs = new MPI_Request[cache.max_reqs];
      cache.stats = new MPI_Status[cache.max_reqs];
-      cache.tc_req_node = new int[cache.max_reqs];
-      cache.tc_req_is_recv = new int[cache.max_reqs];
-      cache.tc_completed = new int[cache.max_reqs];
    }

    MyList<Parallel::gridseg> *dst = build_complete_gsl(PatcL);
@@ -5911,9 +5865,6 @@ void Parallel::OutBdLow2Hi_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
      cache.max_reqs = 2 * cpusize;
      cache.reqs = new MPI_Request[cache.max_reqs];
      cache.stats = new MPI_Status[cache.max_reqs];
-      cache.tc_req_node = new int[cache.max_reqs];
-      cache.tc_req_is_recv = new int[cache.max_reqs];
-      cache.tc_completed = new int[cache.max_reqs];
    }

    MyList<Parallel::gridseg> *dst = build_buffer_gsl(PatfL);
@@ -5960,9 +5911,6 @@ void Parallel::OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
      cache.max_reqs = 2 * cpusize;
      cache.reqs = new MPI_Request[cache.max_reqs];
      cache.stats = new MPI_Status[cache.max_reqs];
-      cache.tc_req_node = new int[cache.max_reqs];
-      cache.tc_req_is_recv = new int[cache.max_reqs];
-      cache.tc_completed = new int[cache.max_reqs];
    }

    MyList<Parallel::gridseg> *dst = build_buffer_gsl(PatfL);
--- a/AMSS_NCKU_source/Parallel.h
+++ b/AMSS_NCKU_source/Parallel.h
@@ -108,9 +108,6 @@ namespace Parallel
    MPI_Status *stats;
    int max_reqs;
    bool lengths_valid;
-    int *tc_req_node;
-    int *tc_req_is_recv;
-    int *tc_completed;
    SyncCache();
    void invalidate();
    void destroy();
@@ -124,10 +121,7 @@ namespace Parallel
  struct AsyncSyncState {
    int req_no;
    bool active;
-    int *req_node;
-    int *req_is_recv;
-    int pending_recv;
-    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
+    AsyncSyncState() : req_no(0), active(false) {}
  };

  void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,
--- a/AMSS_NCKU_source/bssn_class.C
+++ b/AMSS_NCKU_source/bssn_class.C
@@ -41,12 +41,6 @@ using namespace std;
 #include "derivatives.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
@@ -742,8 +736,6 @@ void bssn_class::Initialize()
  sync_cache_cor = new Parallel::SyncCache[GH->levels];
  sync_cache_rp_coarse = new Parallel::SyncCache[GH->levels];
  sync_cache_rp_fine = new Parallel::SyncCache[GH->levels];
-  sync_cache_restrict = new Parallel::SyncCache[GH->levels];
-  sync_cache_outbd = new Parallel::SyncCache[GH->levels];
 }

 //================================================================================================
@@ -2135,10 +2127,8 @@ void bssn_class::Evolve(int Steps)
  #endif
  */
  
-#if BSSN_ENABLE_MEM_USAGE_LOG
  perf bssn_perf;
  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;
@@ -2223,7 +2213,7 @@ void bssn_class::Evolve(int Steps)
    GH->Regrid(Symmetry, BH_num, Porgbr, Porg0,
               SynchList_cor, OldStateList, StateList, SynchList_pre,
               fgt(PhysTime - dT_mon, StartTime, dT_mon / 2), ErrorMonitor);
-    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+    for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif

 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2232,7 +2222,6 @@ 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
    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
                          &peak_min, &peak_avg, &peak_max, nprocs);
@@ -2248,7 +2237,6 @@ void bssn_class::Evolve(int Steps)
             (double)peak_max / (1024.0 * 1024.0));
      cout << endl;
    }
-#endif
    
    // Output puncture positions at each step
    if (myrank == 0)
@@ -2441,7 +2429,7 @@ void bssn_class::RecursiveStep(int lev)
  if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                      SynchList_cor, OldStateList, StateList, SynchList_pre,
                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 }

@@ -2620,7 +2608,7 @@ void bssn_class::ParallelStep()
  if (GH->Regrid_Onelevel(GH->mylev, Symmetry, BH_num, Porgbr, Porg0,
                      SynchList_cor, OldStateList, StateList, SynchList_pre,
                      fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+  for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }
 #endif
 }

@@ -2787,7 +2775,7 @@ void bssn_class::ParallelStep()
        if (GH->Regrid_Onelevel(lev + 1, Symmetry, BH_num, Porgbr, Porg0,
                            SynchList_cor, OldStateList, StateList, SynchList_pre,
                            fgt(PhysTime - dT_levp1, StartTime, dT_levp1 / 2), ErrorMonitor))
-        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+        for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }

        //               a_stream.clear();
        //               a_stream.str("");
@@ -2802,7 +2790,7 @@ void bssn_class::ParallelStep()
      if (GH->Regrid_Onelevel(lev, Symmetry, BH_num, Porgbr, Porg0,
                          SynchList_cor, OldStateList, StateList, SynchList_pre,
                          fgt(PhysTime - dT_lev, StartTime, dT_lev / 2), ErrorMonitor))
-      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+      for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }

      //               a_stream.clear();
      //               a_stream.str("");
@@ -2821,7 +2809,7 @@ void bssn_class::ParallelStep()
          if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                              SynchList_cor, OldStateList, StateList, SynchList_pre,
                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }

          //               a_stream.clear();
          //               a_stream.str("");
@@ -2837,7 +2825,7 @@ void bssn_class::ParallelStep()
          if (GH->Regrid_Onelevel(lev - 1, Symmetry, BH_num, Porgbr, Porg0,
                              SynchList_cor, OldStateList, StateList, SynchList_pre,
                              fgt(PhysTime - dT_lev, StartTime, dT_levm1 / 2), ErrorMonitor))
-          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); sync_cache_restrict[il].invalidate(); sync_cache_outbd[il].invalidate(); }
+          for (int il = 0; il < GH->levels; il++) { sync_cache_pre[il].invalidate(); sync_cache_cor[il].invalidate(); sync_cache_rp_coarse[il].invalidate(); sync_cache_rp_fine[il].invalidate(); }

          //               a_stream.clear();
          //               a_stream.str("");
@@ -5808,7 +5796,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif

 #if (RPB == 0)
-      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
+      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
 #elif (RPB == 1)
      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -5832,7 +5820,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5859,7 +5847,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif

 #if (RPB == 0)
-      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
+      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #elif (RPB == 1)
      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
@@ -5883,7 +5871,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -5952,7 +5940,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
      }

 #if (RPB == 0)
-      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
+      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
 #elif (RPB == 1)
      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SynchList_pre,Symmetry);
      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -5962,7 +5950,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5974,7 +5962,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
    else // no time refinement levels and for all same time levels
    {
 #if (RPB == 0)
-      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
+      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #elif (RPB == 1)
      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SL,SL,Symmetry);
      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
@@ -5984,7 +5972,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -6039,7 +6027,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
      }

 #if (RPB == 0)
-      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
+      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry);
 #elif (RPB == 1)
      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,SynchList_pre,Symmetry);
      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
@@ -6049,7 +6037,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6063,7 +6051,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
      if (myrank == 0)
        cout << "===: " << GH->Lt[lev - 1] << "," << GH->Lt[lev] + dT_lev << endl;
 #if (RPB == 0)
-      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry, sync_cache_restrict[lev]);
+      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
 #elif (RPB == 1)
      //       Parallel::Restrict_bam(GH->PatL[lev-1],GH->PatL[lev],SynchList_cor,StateList,Symmetry);
      Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
@@ -6073,7 +6061,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif
@@ -6114,7 +6102,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)

 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6127,7 +6115,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
    {
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
+      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #elif (MIXOUTB == 1)
      Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif
--- a/AMSS_NCKU_source/bssn_class.h
+++ b/AMSS_NCKU_source/bssn_class.h
@@ -130,8 +130,6 @@ public:
       Parallel::SyncCache *sync_cache_cor;  // per-level cache for corrector sync
       Parallel::SyncCache *sync_cache_rp_coarse;  // RestrictProlong sync on PatL[lev-1]
       Parallel::SyncCache *sync_cache_rp_fine;    // RestrictProlong sync on PatL[lev]
-       Parallel::SyncCache *sync_cache_restrict;   // cached Restrict in RestrictProlong
-       Parallel::SyncCache *sync_cache_outbd;      // cached OutBdLow2Hi in RestrictProlong

       monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
       monitor *ConVMonitor;
--- a/AMSS_NCKU_source/bssn_rhs.f90
+++ b/AMSS_NCKU_source/bssn_rhs.f90
@@ -62,7 +62,6 @@
  real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
 !  gont = 0: success; gont = 1: something wrong
  integer::gont
-  integer :: i,j,k

 !~~~~~~> Other variables:

@@ -86,13 +85,6 @@

  real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
  real*8            :: dX, dY, dZ, PI
-  real*8            :: divb_loc,det_loc
-  real*8            :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
-  real*8            :: Rxx_loc,Rxy_loc,Rxz_loc,Ryy_loc,Ryz_loc,Rzz_loc
-  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
@@ -105,7 +97,7 @@
 #endif

 #if (GAUGE == 6 || GAUGE == 7)
-  integer :: BHN
+  integer :: BHN,i,j,k
  real*8, dimension(9) :: Porg
  real*8, dimension(3) :: Mass
  real*8 :: r1,r2,M,A,w1,w2,C1,C2
@@ -153,24 +145,22 @@
  dY = Y(2) - Y(1)
  dZ = Z(2) - Z(1)

-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    alpn1(i,j,k) = Lap(i,j,k) + ONE
-    chin1(i,j,k) = chi(i,j,k) + 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
+  alpn1 = Lap + ONE
+  chin1 = chi + ONE
+  gxx = dxx + ONE
+  gyy = dyy + ONE
+  gzz = dzz + ONE

  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)
  
+  div_beta = betaxx + betayy + betazz
+ 
  call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)

+  chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
+
  call fderivs(ex,dxx,gxxx,gxxy,gxxz,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,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
@@ -178,179 +168,151 @@
  call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
  call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)

-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
-    div_beta(i,j,k) = divb_loc
+  gxx_rhs = - TWO * alpn1 * Axx    -  F2o3 * gxx * div_beta          + &
+              TWO *(  gxx * betaxx +   gxy * betayx +   gxz * betazx)

-    chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
+  gyy_rhs = - TWO * alpn1 * Ayy    -  F2o3 * gyy * div_beta          + &
+              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 + &
-         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) )
+  gzz_rhs = - TWO * alpn1 * Azz    -  F2o3 * gzz * div_beta          + &
+              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 + &
-         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) )
+  gxy_rhs = - TWO * alpn1 * Axy    +  F1o3 * gxy    * div_beta       + &
+                      gxx * betaxy                  +   gxz * betazy + &
+                                       gyy * betayx +   gyz * betazx   &
+                                                    -   gxy * betazz

-    gzz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Azz(i,j,k) - F2o3 * gzz(i,j,k) * divb_loc + &
-         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 * betaxz +   gyy * betayz                  + &
+                      gxz * betaxy                  +   gzz * betazy   &
+                                                    -   gyz * betaxx
 
-    gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
-         gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
-         gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
+  gxz_rhs = - TWO * alpn1 * Axz    +  F1o3 * gxz    * div_beta       + &
+                      gxx * betaxz +   gxy * betayz                  + &
+                                       gyz * betayx +   gzz * betazx   &
+                                                    -   gxz * betayy     !rhs for gij

-    gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
-         gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
-         gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
-
-    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) + &
-         gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
-
-    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) + &
-         gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) - gxz(i,j,k) * gyy(i,j,k) * gxz(i,j,k) - &
-         gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
-    gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
-    gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
-    gupxz_loc = ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) / det_loc
-    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
-    gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
-    gupxx(i,j,k) = gupxx_loc
-    gupxy(i,j,k) = gupxy_loc
-    gupxz(i,j,k) = gupxz_loc
-    gupyy(i,j,k) = gupyy_loc
-    gupyz(i,j,k) = gupyz_loc
-    gupzz(i,j,k) = gupzz_loc
+! invert tilted metric
+  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+  gupxx =   ( gyy * gzz - gyz * gyz ) / gupzz
+  gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
+  gupxz =   ( gxy * gyz - gyy * gxz ) / gupzz
+  gupyy =   ( gxx * gzz - gxz * gxz ) / gupzz
+  gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
+  gupzz =   ( gxx * gyy - gxy * gxy ) / gupzz

  if(co == 0)then
-      Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
-           gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
-           gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
-           gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
-           gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
-           gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
-           gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
-           gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
-           gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
-           gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
-      Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
-           gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
-           gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
-           gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
-           gupxy_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
-           gupyy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
-           gupyz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
-           gupxy_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
-           gupyy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
-           gupyz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
-      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)) + &
-           gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
-           gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
-           gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
-           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)) + &
-           gupxz_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
-           gupyz_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
-           gupzz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
+! Gam^i_Res = Gam^i + gup^ij_,j
+  Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
+                   +gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
+                   +gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
+                   +gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+                   +gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+                   +gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+                   +gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+                   +gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+                   +gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
+  Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
+                   +gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
+                   +gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
+                   +gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+                   +gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+                   +gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+                   +gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+                   +gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+                   +gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
+  Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
+                   +gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
+                   +gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
+                   +gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
+                   +gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
+                   +gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
+                   +gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+                   +gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+                   +gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
  endif

-    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)))
-    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)))
+! second kind of connection
+  Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
+  Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
+  Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
 
-    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)))
-    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)))
+  Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
+  Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
+  Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))

-    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))
-    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))
+  Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
+  Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
+  Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)

-    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)) )
-    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)) )
-    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)) )
+  Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
+  Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
+  Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )

-    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) )
-    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) )
+  Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
+  Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
+  Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )

-    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) )
-    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) )
-  enddo
-  enddo
-  enddo
+  Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
+  Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
+  Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
 ! Raise indices of \tilde A_{ij} and store in R_ij

+  Rxx =    gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
+      TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
+
+  Ryy =    gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
+      TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
+
+  Rzz =    gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
+      TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
+
+  Rxy =    gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
+          (gupxx * gupyy       + gupxy * gupxy)* Axy                       + &
+          (gupxx * gupyz       + gupxz * gupxy)* Axz                       + &
+          (gupxy * gupyz       + gupxz * gupyy)* Ayz
+
+  Rxz =    gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
+          (gupxx * gupyz       + gupxy * gupxz)* Axy                       + &
+          (gupxx * gupzz       + gupxz * gupxz)* Axz                       + &
+          (gupxy * gupzz       + gupxz * gupyz)* Ayz
+
+  Ryz =    gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
+          (gupxy * gupyz       + gupyy * gupxz)* Axy                       + &
+          (gupxy * gupzz       + gupyz * gupxz)* Axz                       + &
+          (gupyy * gupzz       + gupyz * gupyz)* 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)
  call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    gupxx_loc = gupxx(i,j,k)
-    gupxy_loc = gupxy(i,j,k)
-    gupxz_loc = gupxz(i,j,k)
-    gupyy_loc = gupyy(i,j,k)
-    gupyz_loc = gupyz(i,j,k)
-    gupzz_loc = gupzz(i,j,k)

-    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) + &
-         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) + &
-         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))
-    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) + &
-         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))
-    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) + &
-         (gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
-         (gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
-         (gupxy_loc * gupyz_loc + gupxz_loc * gupyy_loc) * Ayz(i,j,k)
-    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) + &
-         (gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
-         (gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
-    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_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
-         (gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
-         (gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
-    Rxx(i,j,k) = Rxx_loc
-    Ryy(i,j,k) = Ryy_loc
-    Rzz(i,j,k) = Rzz_loc
-    Rxy(i,j,k) = Rxy_loc
-    Rxz(i,j,k) = Rxz_loc
-    Ryz(i,j,k) = Ryz_loc
+   Gamx_rhs = - TWO * (   Lapx * Rxx +   Lapy * Rxy +   Lapz * Rxz ) + &
+        TWO * alpn1 * (                                                &
+        -F3o2/chin1 * (   chix * Rxx +   chiy * Rxy +   chiz * Rxz ) - &
+              gupxx * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
+              gupxy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
+              gupxz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+                        Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz   + &
+                TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )

-    Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
-         TWO * alpn1(i,j,k) * ( &
-         -F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
-         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 = - TWO * (   Lapx * Rxy +   Lapy * Ryy +   Lapz * Ryz ) + &
+        TWO * alpn1 * (                                                &
+        -F3o2/chin1 * (   chix * Rxy +  chiy * Ryy +    chiz * Ryz ) - &
+              gupxy * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
+              gupyy * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
+              gupyz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+                        Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz   + &
+                TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )

-    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
+   Gamz_rhs = - TWO * (   Lapx * Rxz +   Lapy * Ryz +   Lapz * Rzz ) + &
+        TWO * alpn1 * (                                                &
+        -F3o2/chin1 * (   chix * Rxz +  chiy * Ryz +    chiz * Rzz ) - &
+              gupxz * (   F2o3 * Kx  +  EIGHT * PI * Sx            ) - &
+              gupyz * (   F2o3 * Ky  +  EIGHT * PI * Sy            ) - &
+              gupzz * (   F2o3 * Kz  +  EIGHT * PI * Sz            ) + &
+                        Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz   + &
+                TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )

  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)

+  fxx = gxxx + gxyy + gxzz
+  fxy = gxyx + gyyy + gyzz
+  fxz = gxzx + gyzy + gzzz
+
+  Gamxa =       gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
+          TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
+  Gamya =       gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
+          TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
+  Gamza =       gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
+          TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
+
  call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
  call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
  call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    divb_loc = div_beta(i,j,k)
-    fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
-    fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
-    fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)

-    gupxx_loc = gupxx(i,j,k)
-    gupxy_loc = gupxy(i,j,k)
-    gupxz_loc = gupxz(i,j,k)
-    gupyy_loc = gupyy(i,j,k)
-    gupyz_loc = gupyz(i,j,k)
-    gupzz_loc = gupzz(i,j,k)
+  Gamx_rhs =               Gamx_rhs +  F2o3 *  Gamxa * div_beta        - &
+                     Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz  + &
+             F1o3 * (gupxx * fxx    + gupxy * fxy    + gupxz * fxz    ) + &
+                     gupxx * gxxx   + gupyy * gyyx   + gupzz * gzzx    + &
+              TWO * (gupxy * gxyx   + gupxz * gxzx   + gupyz * gyzx  )

-    Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
-         TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
-    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))
-    Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
-         TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
-    Gamxa(i,j,k) = Gamxa_loc
-    Gamya(i,j,k) = Gamya_loc
-    Gamza(i,j,k) = Gamza_loc
+  Gamy_rhs =               Gamy_rhs +  F2o3 *  Gamya * div_beta        - &
+                     Gamxa * betayx - Gamya * betayy - Gamza * betayz  + &
+             F1o3 * (gupxy * fxx    + gupyy * fxy    + gupyz * fxz    ) + &
+                     gupxx * gxxy   + gupyy * gyyy   + gupzz * gzzy    + &
+              TWO * (gupxy * gxyy   + gupxz * gxzy   + gupyz * gyzy  )

-    Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
-         Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
-         F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
-         gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
-         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
+  Gamz_rhs =               Gamz_rhs +  F2o3 *  Gamza * div_beta        - &
+                     Gamxa * betazx - Gamya * betazy - Gamza * betazz  + &
+             F1o3 * (gupxz * fxx    + gupyz * fxy    + gupzz * fxz    ) + &
+                     gupxx * gxxz   + gupyy * gyyz   + gupzz * gzzz    + &
+              TWO * (gupxy * gxyz   + gupxz * gxzz   + gupyz * gyzz  )    !rhs for Gam^i

 !first kind of connection stored in gij,k
  gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
@@ -658,187 +604,189 @@
 !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)

-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    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)
-    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)
-    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)
-    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)
-    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)
+  fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
+  fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
+  fxz = fxz - Gamxxz * chix - Gamyxz * chiy - Gamzxz * chiz
+  fyy = fyy - Gamxyy * chix - Gamyyy * chiy - Gamzyy * chiz
+  fyz = fyz - Gamxyz * chix - Gamyyz * chiy - Gamzyz * chiz
+  fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
+! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f

-    chin_loc = chin1(i,j,k)
-    f_loc = gupxx(i,j,k) * (fxx(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chix(i,j,k)) + &
-            gupyy(i,j,k) * (fyy(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiy(i,j,k)) + &
-            gupzz(i,j,k) * (fzz(i,j,k) - F3o2/chin_loc * chiz(i,j,k) * chiz(i,j,k)) + &
-            TWO * gupxy(i,j,k) * (fxy(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiy(i,j,k)) + &
-            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))
-    f(i,j,k) = f_loc
+  f =        gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
+             gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
+             gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
+       TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
+       TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
+       TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz ) 
+! Add chi part to Ricci tensor:

-    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
-    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
-    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
-    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
-    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
-  enddo
-  enddo
-  enddo
+  Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * f)/chin1/TWO
+  Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * f)/chin1/TWO
+  Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/TWO
+  Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/TWO
+  Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/TWO
+  Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO

 ! covariant second derivatives of the lapse respect to physical metric
  call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
                SYM,SYM,SYM,symmetry,Lev)

-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    chin_loc = chin1(i,j,k)
-    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
-    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
-    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
+  gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
+  gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
+  gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
+! now get physical second kind of connection
+  Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
+  Gamyxx = Gamyxx - (                     - gxx * gxxy )*HALF
+  Gamzxx = Gamzxx - (                     - gxx * gxxz )*HALF
+  Gamxyy = Gamxyy - (                     - gyy * gxxx )*HALF
+  Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
+  Gamzyy = Gamzyy - (                     - gyy * gxxz )*HALF
+  Gamxzz = Gamxzz - (                     - gzz * gxxx )*HALF
+  Gamyzz = Gamyzz - (                     - gzz * gxxy )*HALF
+  Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
+  Gamxxy = Gamxxy - (  chiy        /chin1 - gxy * gxxx )*HALF
+  Gamyxy = Gamyxy - (         chix /chin1 - gxy * gxxy )*HALF
+  Gamzxy = Gamzxy - (                     - gxy * gxxz )*HALF
+  Gamxxz = Gamxxz - (  chiz        /chin1 - gxz * gxxx )*HALF
+  Gamyxz = Gamyxz - (                     - gxz * gxxy )*HALF
+  Gamzxz = Gamzxz - (         chix /chin1 - gxz * gxxz )*HALF
+  Gamxyz = Gamxyz - (                     - gyz * gxxx )*HALF
+  Gamyyz = Gamyyz - (  chiz        /chin1 - gyz * gxxy )*HALF
+  Gamzyz = Gamzyz - (         chiy /chin1 - gyz * gxxz )*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
-    Gamyxx(i,j,k) = Gamyxx(i,j,k) - (                                   - gxx(i,j,k) * gxxy(i,j,k) )*HALF
-    Gamzxx(i,j,k) = Gamzxx(i,j,k) - (                                   - gxx(i,j,k) * gxxz(i,j,k) )*HALF
-    Gamxyy(i,j,k) = Gamxyy(i,j,k) - (                                   - gyy(i,j,k) * gxxx(i,j,k) )*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
-    Gamzyy(i,j,k) = Gamzyy(i,j,k) - (                                   - gyy(i,j,k) * gxxz(i,j,k) )*HALF
-    Gamxzz(i,j,k) = Gamxzz(i,j,k) - (                                   - gzz(i,j,k) * gxxx(i,j,k) )*HALF
-    Gamyzz(i,j,k) = Gamyzz(i,j,k) - (                                   - gzz(i,j,k) * gxxy(i,j,k) )*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
-    Gamyxy(i,j,k) = Gamyxy(i,j,k) - ( chix(i,j,k) /chin_loc - gxy(i,j,k) * gxxy(i,j,k) )*HALF
-    Gamzxy(i,j,k) = Gamzxy(i,j,k) - (                     - gxy(i,j,k) * gxxz(i,j,k) )*HALF
-    Gamxxz(i,j,k) = Gamxxz(i,j,k) - ( chiz(i,j,k) /chin_loc - gxz(i,j,k) * gxxx(i,j,k) )*HALF
-    Gamyxz(i,j,k) = Gamyxz(i,j,k) - (                     - gxz(i,j,k) * gxxy(i,j,k) )*HALF
-    Gamzxz(i,j,k) = Gamzxz(i,j,k) - ( chix(i,j,k) /chin_loc - gxz(i,j,k) * gxxz(i,j,k) )*HALF
-    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
-    Gamzyz(i,j,k) = Gamzyz(i,j,k) - ( chiy(i,j,k) /chin_loc - gyz(i,j,k) * gxxz(i,j,k) )*HALF
+  fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
+  fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
+  fzz = fzz - Gamxzz*Lapx - Gamyzz*Lapy - Gamzzz*Lapz
+  fxy = fxy - Gamxxy*Lapx - Gamyxy*Lapy - Gamzxy*Lapz
+  fxz = fxz - Gamxxz*Lapx - Gamyxz*Lapy - Gamzxz*Lapz
+  fyz = fyz - Gamxyz*Lapx - Gamyyz*Lapy - Gamzyz*Lapz

-    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)
-    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)
-    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)
-    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)
-    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)
-    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)
+! store D^i D_i Lap in trK_rhs upto chi
+  trK_rhs =    gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz )
+#if 1        
+!! follow bam code
+  S =  chin1 * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
+     TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
+  f = F2o3 * trK * trK -(&
+       gupxx * ( &
+       gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
+       TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz) ) + &
+       gupyy * ( &
+       gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
+       TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz) ) + &
+       gupzz * ( &
+       gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
+       TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz) ) + &
+       TWO * ( &
+       gupxy * ( &
+       gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
+       gupxy * (Axx * Ayy + Axy * Axy) + &
+       gupxz * (Axx * Ayz + Axz * Axy) + &
+       gupyz * (Axy * Ayz + Axz * Ayy) ) + &
+       gupxz * ( &
+       gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
+       gupxy * (Axx * Ayz + Axy * Axz) + &
+       gupxz * (Axx * Azz + Axz * Axz) + &
+       gupyz * (Axy * Azz + Axz * Ayz) ) + &
+       gupyz * ( &
+       gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
+       gupxy * (Axy * Ayz + Ayy * Axz) + &
+       gupxz * (Axy * Azz + Ayz * Axz) + &
+       gupyz * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
+  f = - F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
  
-    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(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k))
-  enddo
-  enddo
-  enddo
-  do k=1,ex(3)
-  do j=1,ex(2)
-  do i=1,ex(1)
-    divb_loc = div_beta(i,j,k)
-    chin_loc = chin1(i,j,k)
+  fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
+  fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
+  fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
+  fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
+  fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
+  fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
+#else        
+! Add lapse and S_ij parts to Ricci tensor:

-    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) + &
-           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)) )
-    S(i,j,k) = S_loc
+  fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
+  fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
+  fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
+  fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
+  fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
+  fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz

-    f_loc = F2o3 * trK(i,j,k) * trK(i,j,k) - ( &
-            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) + &
-                             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(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + &
-                                    gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k)) ) + &
-            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) + &
-                             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) + gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
-                                    gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k)) ) + &
-            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) + &
-                             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) + &
-                                    gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k)) ) + &
-            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) + &
-                                     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)) + &
-                                     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)) ) + &
-                    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) + &
-                                     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)) + &
-                                     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)) ) + &
-                    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) + &
-                                     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)) + &
-                                     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)) ) ) ) - &
-            F16 * PI * rho(i,j,k) + EIGHT * PI * S_loc
+! Compute trace-free part (note: chi^-1 and chi cancel!):

-    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(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
-            alpn1(i,j,k)/chin_loc * f_loc )
-    f(i,j,k) = f_loc
+  f = F1o3 *(  gupxx * fxx + gupyy * fyy + gupzz * fzz + &
+        TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) )
+#endif

-    l_fxx = alpn1(i,j,k) * (Rxx(i,j,k) - EIGHT * PI * Sxx(i,j,k)) - fxx(i,j,k)
-    l_fxy = alpn1(i,j,k) * (Rxy(i,j,k) - EIGHT * PI * Sxy(i,j,k)) - fxy(i,j,k)
-    l_fxz = alpn1(i,j,k) * (Rxz(i,j,k) - EIGHT * PI * Sxz(i,j,k)) - fxz(i,j,k)
-    l_fyy = alpn1(i,j,k) * (Ryy(i,j,k) - EIGHT * PI * Syy(i,j,k)) - fyy(i,j,k)
-    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)
+  Axx_rhs = fxx - gxx * f
+  Ayy_rhs = fyy - gyy * f
+  Azz_rhs = fzz - gzz * f
+  Axy_rhs = fxy - gxy * f
+  Axz_rhs = fxz - gxz * f
+  Ayz_rhs = fyz - gyz * f

-    Axx_rhs(i,j,k) = l_fxx - gxx(i,j,k) * f_loc
-    Ayy_rhs(i,j,k) = l_fyy - gyy(i,j,k) * f_loc
-    Azz_rhs(i,j,k) = l_fzz - gzz(i,j,k) * f_loc
-    Axy_rhs(i,j,k) = l_fxy - gxy(i,j,k) * f_loc
-    Axz_rhs(i,j,k) = l_fxz - gxz(i,j,k) * f_loc
-    Ayz_rhs(i,j,k) = l_fyz - gyz(i,j,k) * f_loc
+! Now: store A_il A^l_j into fij:

-    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) + &
-                 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(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k))
-    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) + &
-                 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) + &
-                 gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k))
-    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) + &
-                 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) + gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k))
-    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) + &
-                 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)) + &
-                 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))
-    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) + &
-                 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)) + &
-                 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))
-    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) + &
-                 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)) + &
-                 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))
+  fxx =       gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
+       TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
+  fyy =       gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
+       TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
+  fzz =       gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
+       TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
+  fxy =       gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
+              gupxy *(Axx * Ayy + Axy * Axy)                            + &
+              gupxz *(Axx * Ayz + Axz * Axy)                            + &
+              gupyz *(Axy * Ayz + Axz * Ayy)
+  fxz =       gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
+              gupxy *(Axx * Ayz + Axy * Axz)                            + &
+              gupxz *(Axx * Azz + Axz * Axz)                            + &
+              gupyz *(Axy * Azz + Axz * Ayz)
+  fyz =       gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
+              gupxy *(Axy * Ayz + Ayy * Axz)                            + &
+              gupxz *(Axy * Azz + Ayz * Axz)                            + &
+              gupyz *(Ayy * Azz + Ayz * Ayz)

-    trK_rhs(i,j,k) = chin_loc * trK_rhs(i,j,k)
+  f = chin1
+! store D^i D_i Lap in trK_rhs
+  trK_rhs = f*trK_rhs
          
-    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)) + &
-                     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)) - &
-                     F2o3 * Axx(i,j,k) * divb_loc
-    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)) - &
-                     F2o3 * Ayy(i,j,k) * divb_loc
-    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)) + &
-                     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)) - &
-                     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)) + &
-                     Axx(i,j,k) * betaxy(i,j,k) + Axz(i,j,k) * betazy(i,j,k) + Ayy(i,j,k) * betayx(i,j,k) + &
-                     Ayz(i,j,k) * betazx(i,j,k) + F1o3 * Axy(i,j,k) * divb_loc - Axy(i,j,k) * betazz(i,j,k)
-    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)) + &
-                     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(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(i,j,k) * betaxz(i,j,k) + Axy(i,j,k) * betayz(i,j,k) + Ayz(i,j,k) * betayx(i,j,k) + &
-                     Azz(i,j,k) * betazx(i,j,k) + F1o3 * Axz(i,j,k) * divb_loc - Axz(i,j,k) * betayy(i,j,k)
+  Axx_rhs =           f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx)  + &
+           TWO * (  Axx * betaxx +   Axy * betayx +   Axz * betazx )- &
+             F2o3 * Axx * div_beta

-    trK_rhs(i,j,k) = - trK_rhs(i,j,k) + alpn1(i,j,k) * ( F1o3 * trK(i,j,k) * trK(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(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
-                    FOUR * PI * (rho(i,j,k) + S_loc) )
-  enddo
-  enddo
-  enddo
+  Ayy_rhs =           f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy)  + &
+           TWO * (  Axy * betaxy +   Ayy * betayy +   Ayz * betazy )- &
+             F2o3 * Ayy * div_beta
+
+  Azz_rhs =           f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz)  + &
+           TWO * (  Axz * betaxz +   Ayz * betayz +   Azz * betazz )- &
+             F2o3 * Azz * div_beta
+
+  Axy_rhs =           f * Axy_rhs+ alpn1 *( trK * Axy  - TWO * fxy )+ &
+                    Axx * betaxy                  +   Axz * betazy  + &
+                                     Ayy * betayx +   Ayz * betazx  + &
+             F1o3 * Axy * div_beta                -   Axy * betazz
+
+  Ayz_rhs =           f * Ayz_rhs+ alpn1 *( trK * Ayz  - TWO * fyz )+ &
+                    Axy * betaxz +   Ayy * betayz                   + &
+                    Axz * betaxy                  +   Azz * betazy  + &
+             F1o3 * Ayz * div_beta                -   Ayz * betaxx
+ 
+  Axz_rhs =           f * Axz_rhs+ alpn1 *( trK * Axz  - TWO * fxz )+ &
+                    Axx * betaxz +   Axy * betayz                   + &
+                                     Ayz * betayx +   Azz * betazx  + &
+             F1o3 * Axz * div_beta                -   Axz * betayy      !rhs for Aij
+
+! Compute trace of S_ij
+
+  S =  f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
+     TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
+
+  trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK         + &
+                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.

-  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,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,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)
--- a/AMSS_NCKU_source/bssn_rhs_c.C
+++ b/AMSS_NCKU_source/bssn_rhs_c.C
@@ -39,6 +39,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
    // printf("nx=%d ny=%d nz=%d all=%d\n", nx, ny, nz, all);

    // temp variable
+    double gxx[all],gyy[all],gzz[all];
    double chix[all],chiy[all],chiz[all];
    double gxxx[all],gxyx[all],gxzx[all],gyyx[all],gyzx[all],gzzx[all];
    double gxxy[all],gxyy[all],gxzy[all],gyyy[all],gyzy[all],gzzy[all];
@@ -50,9 +51,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
    double Gamxx[all],Gamxy[all],Gamxz[all];
    double Gamyx[all],Gamyy[all],Gamyz[all];
    double Gamzx[all],Gamzy[all],Gamzz[all];
-    double Kx[all], Ky[all], Kz[all], S[all];
+    double Kx[all], Ky[all], Kz[all], div_beta[all], S[all];
    double f[all], fxx[all], fxy[all], fxz[all], fyy[all], fyz[all], fzz[all];
-    double alpn1[all], chin1[all];
+    double Gamxa[all], Gamya[all], Gamza[all], alpn1[all], chin1[all];
    double gupxx[all], gupxy[all], gupxz[all];
    double gupyy[all], gupyz[all], gupzz[all];
    double SSS[3] = { 1.0,  1.0,  1.0};
@@ -106,6 +107,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
        for(int i=0;i<all;i+=1){
            alpn1[i] = Lap[i] + 1.0;
            chin1[i] = chi[i] + 1.0;
+            gxx[i] = dxx[i] + 1.0;
+            gyy[i] = dyy[i] + 1.0;
+            gzz[i] = dzz[i] + 1.0;
        }
        // 9ms //
        fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev);
@@ -123,196 +127,231 @@ int f_compute_rhs_bssn(int *ex, double &T,

        // 3ms //
        for(int i=0;i<all;i+=1){
-            const double divb = betaxx[i] + betayy[i] + betazz[i];
-            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - divb); 
-            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * (dxx[i] + ONE) * divb + 
-                    TWO * ((dxx[i] + ONE) * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
-            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * (dyy[i] + ONE) * divb + 
-                    TWO * (gxy[i] * betaxy[i] + (dyy[i] + ONE) * betayy[i] + gyz[i] * betazy[i]);
-            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * (dzz[i] + ONE) * divb + 
-                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + (dzz[i] + ONE) * betazz[i]);
-            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * divb + 
-                        (dxx[i] + ONE) * betaxy[i] + gxz[i] * betazy[i] + (dyy[i] + ONE) * betayx[i] 
+            div_beta[i] = betaxx[i] + betayy[i] + betazz[i];
+            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - div_beta[i]); 
+            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * gxx[i] * div_beta[i] + 
+                    TWO * (gxx[i] * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
+            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * gyy[i] * div_beta[i] + 
+                    TWO * (gxy[i] * betaxy[i] + gyy[i] * betayy[i] + gyz[i] * betazy[i]);
+            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * gzz[i] * div_beta[i] + 
+                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + gzz[i] * betazz[i]);
+            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * div_beta[i] + 
+                        gxx[i] * betaxy[i] + gxz[i] * betazy[i] + gyy[i] * betayx[i] 
                        + gyz[i] * betazx[i] - gxy[i] * betazz[i];        
-            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * divb + 
-                        gxy[i] * betaxz[i] + (dyy[i] + ONE) * betayz[i] + gxz[i] * betaxy[i] 
-                        + (dzz[i] + ONE) * betazy[i] - gyz[i] * betaxx[i];
-            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * divb + 
-                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
-                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
+            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * div_beta[i] + 
+                        gxy[i] * betaxz[i] + gyy[i] * betayz[i] + gxz[i] * betaxy[i] 
+                        + gzz[i] * betazy[i] - gyz[i] * betaxx[i];
+            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * div_beta[i] + 
+                        gxx[i] * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
+                        + gzz[i] * betazx[i] - gxz[i] * betayy[i];                  
        }
-        // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
+        // 1ms //
        for(int i=0;i<all;i+=1){
-            double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
-                        gxz[i] * (dyy[i] + ONE) * gxz[i] - gxy[i] * gxy[i] * (dzz[i] + ONE) - (dxx[i] + ONE) * gyz[i] * gyz[i];
-            double lg_xx = ((dyy[i] + ONE) * (dzz[i] + ONE) - gyz[i] * gyz[i]) / det;
-            double lg_xy = -(gxy[i] * (dzz[i] + ONE) - gyz[i] * gxz[i]) / det;
-            double lg_xz = (gxy[i] * gyz[i] - (dyy[i] + ONE) * gxz[i]) / det;
-            double lg_yy = ((dxx[i] + ONE) * (dzz[i] + ONE) - gxz[i] * gxz[i]) / det;
-            double lg_yz = -((dxx[i] + ONE) * gyz[i] - gxy[i] * gxz[i]) / det;
-            double lg_zz = ((dxx[i] + ONE) * (dyy[i] + ONE) - gxy[i] * gxy[i]) / det;
-            gupxx[i] = lg_xx; gupxy[i] = lg_xy; gupxz[i] = lg_xz;
-            gupyy[i] = lg_yy; gupyz[i] = lg_yz; gupzz[i] = lg_zz;
-
+            double det = gxx[i] * gyy[i] * gzz[i] + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] - 
+                        gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];  
+            gupxx[i] = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
+            gupxy[i] = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
+            gupxz[i] = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
+            gupyy[i] = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
+            gupyz[i] = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
+            gupzz[i] = (gxx[i] * gyy[i] - gxy[i] * gxy[i]) / det;   
+        }
+        // 2.2ms //
        if(co==0){
-                Gmx_Res[i] = Gamx[i] - (
-                    lg_xx * (lg_xx*gxxx[i] + lg_xy*gxyx[i] + lg_xz*gxzx[i]) +
-                    lg_xy * (lg_xx*gxyx[i] + lg_xy*gyyx[i] + lg_xz*gyzx[i]) +
-                    lg_xz * (lg_xx*gxzx[i] + lg_xy*gyzx[i] + lg_xz*gzzx[i]) +
-                    lg_xx * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
-                    lg_xy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
-                    lg_xz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
-                    lg_xx * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-                    lg_xy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    lg_xz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                );
-                Gmy_Res[i] = Gamy[i] - (
-                    lg_xx * (lg_xy*gxxx[i] + lg_yy*gxyx[i] + lg_yz*gxzx[i]) +
-                    lg_xy * (lg_xy*gxyx[i] + lg_yy*gyyx[i] + lg_yz*gyzx[i]) +
-                    lg_xz * (lg_xy*gxzx[i] + lg_yy*gyzx[i] + lg_yz*gzzx[i]) +
-                    lg_xy * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
-                    lg_yy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
-                    lg_yz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
-                    lg_xy * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-                    lg_yy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    lg_yz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                );
-                Gmz_Res[i] = Gamz[i] - (
-                    lg_xx * (lg_xz*gxxx[i] + lg_yz*gxyx[i] + lg_zz*gxzx[i]) +
-                    lg_xy * (lg_xz*gxyx[i] + lg_yz*gyyx[i] + lg_zz*gyzx[i]) +
-                    lg_xz * (lg_xz*gxzx[i] + lg_yz*gyzx[i] + lg_zz*gzzx[i]) +
-                    lg_xy * (lg_xz*gxxy[i] + lg_yz*gxyy[i] + lg_zz*gxzy[i]) +
-                    lg_yy * (lg_xz*gxyy[i] + lg_yz*gyyy[i] + lg_zz*gyzy[i]) +
-                    lg_yz * (lg_xz*gxzy[i] + lg_yz*gyzy[i] + lg_zz*gzzy[i]) +
-                    lg_xz * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-                    lg_yz * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    lg_zz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                );
-            }
-
-            Gamxxx[i] = HALF * ( lg_xx*gxxx[i]
-                            + lg_xy*(TWO*gxyx[i] - gxxy[i])
-                            + lg_xz*(TWO*gxzx[i] - gxxz[i]) );
-            Gamyxx[i] = HALF * ( lg_xy*gxxx[i]
-                            + lg_yy*(TWO*gxyx[i] - gxxy[i])
-                            + lg_yz*(TWO*gxzx[i] - gxxz[i]) );
-            Gamzxx[i] = HALF * ( lg_xz*gxxx[i]
-                            + lg_yz*(TWO*gxyx[i] - gxxy[i])
-                            + lg_zz*(TWO*gxzx[i] - gxxz[i]) );
-            Gamxyy[i] = HALF * ( lg_xx*(TWO*gxyy[i] - gyyx[i])
-                            + lg_xy*gyyy[i]
-                            + lg_xz*(TWO*gyzy[i] - gyyz[i]) );
-            Gamyyy[i] = HALF * ( lg_xy*(TWO*gxyy[i] - gyyx[i])
-                            + lg_yy*gyyy[i]
-                            + lg_yz*(TWO*gyzy[i] - gyyz[i]) );
-            Gamzyy[i] = HALF * ( lg_xz*(TWO*gxyy[i] - gyyx[i])
-                            + lg_yz*gyyy[i]
-                            + lg_zz*(TWO*gyzy[i] - gyyz[i]) );
-            Gamxzz[i] = HALF * ( lg_xx*(TWO*gxzz[i] - gzzx[i])
-                            + lg_xy*(TWO*gyzz[i] - gzzy[i])
-                            + lg_xz*gzzz[i] );
-            Gamyzz[i] = HALF * ( lg_xy*(TWO*gxzz[i] - gzzx[i])
-                            + lg_yy*(TWO*gyzz[i] - gzzy[i])
-                            + lg_yz*gzzz[i] );
-            Gamzzz[i] = HALF * ( lg_xz*(TWO*gxzz[i] - gzzx[i])
-                            + lg_yz*(TWO*gyzz[i] - gzzy[i])
-                            + lg_zz*gzzz[i] );
-            Gamxxy[i] = HALF * ( lg_xx*gxxy[i]
-                            + lg_xy*gyyx[i]
-                            + lg_xz*(gxzy[i] + gyzx[i] - gxyz[i]) );
-            Gamyxy[i] = HALF * ( lg_xy*gxxy[i]
-                            + lg_yy*gyyx[i]
-                            + lg_yz*(gxzy[i] + gyzx[i] - gxyz[i]) );
-            Gamzxy[i] = HALF * ( lg_xz*gxxy[i]
-                            + lg_yz*gyyx[i]
-                            + lg_zz*(gxzy[i] + gyzx[i] - gxyz[i]) );
-            Gamxxz[i] = HALF * ( lg_xx*gxxz[i]
-                            + lg_xy*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + lg_xz*gzzx[i] );
-            Gamyxz[i] = HALF * ( lg_xy*gxxz[i]
-                            + lg_yy*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + lg_yz*gzzx[i] );
-            Gamzxz[i] = HALF * ( lg_xz*gxxz[i]
-                            + lg_yz*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + lg_zz*gzzx[i] );
-            Gamxyz[i] = HALF * ( lg_xx*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + lg_xy*gyyz[i]
-                            + lg_xz*gzzy[i] );
-            Gamyyz[i] = HALF * ( lg_xy*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + lg_yy*gyyz[i]
-                            + lg_yz*gzzy[i] );
-            Gamzyz[i] = HALF * ( lg_xz*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + lg_yz*gyyz[i]
-                            + lg_zz*gzzy[i] );
-        }
-        // Fused: A^{ij} raise-index + Gamma_rhs part 1 (2 loops -> 1)
            for (int i=0;i<all;i+=1) {
-            double axx = gupxx[i]*gupxx[i]*Axx[i]
+                Gmx_Res[i] = Gamx[i] - (
+                    gupxx[i] * (gupxx[i]*gxxx[i] + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i]) +
+                    gupxy[i] * (gupxx[i]*gxyx[i] + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i]) +
+                    gupxz[i] * (gupxx[i]*gxzx[i] + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i]) +
+
+                    gupxx[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
+                    gupxy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
+                    gupxz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
+
+                    gupxx[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    gupxy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
+                    gupxz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
+                );
+
+                Gmy_Res[i] = Gamy[i] - (
+                    gupxx[i] * (gupxy[i]*gxxx[i] + gupyy[i]*gxyx[i] + gupyz[i]*gxzx[i]) +
+                    gupxy[i] * (gupxy[i]*gxyx[i] + gupyy[i]*gyyx[i] + gupyz[i]*gyzx[i]) +
+                    gupxz[i] * (gupxy[i]*gxzx[i] + gupyy[i]*gyzx[i] + gupyz[i]*gzzx[i]) +
+
+                    gupxy[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
+                    gupyy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
+                    gupyz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
+
+                    gupxy[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    gupyy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
+                    gupyz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
+                );
+
+                Gmz_Res[i] = Gamz[i] - (
+                    gupxx[i] * (gupxz[i]*gxxx[i] + gupyz[i]*gxyx[i] + gupzz[i]*gxzx[i]) +
+                    gupxy[i] * (gupxz[i]*gxyx[i] + gupyz[i]*gyyx[i] + gupzz[i]*gyzx[i]) +
+                    gupxz[i] * (gupxz[i]*gxzx[i] + gupyz[i]*gyzx[i] + gupzz[i]*gzzx[i]) +
+
+                    gupxy[i] * (gupxz[i]*gxxy[i] + gupyz[i]*gxyy[i] + gupzz[i]*gxzy[i]) +
+                    gupyy[i] * (gupxz[i]*gxyy[i] + gupyz[i]*gyyy[i] + gupzz[i]*gyzy[i]) +
+                    gupyz[i] * (gupxz[i]*gxzy[i] + gupyz[i]*gyzy[i] + gupzz[i]*gzzy[i]) +
+
+                    gupxz[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    gupyz[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
+                    gupzz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
+                );
+            }
+        }
+        // 5ms //
+        for (int i=0;i<all;i+=1) {
+
+            Gamxxx[i] = HALF * ( gupxx[i]*gxxx[i]
+                            + gupxy[i]*(TWO*gxyx[i] - gxxy[i])
+                            + gupxz[i]*(TWO*gxzx[i] - gxxz[i]) );
+
+            Gamyxx[i] = HALF * ( gupxy[i]*gxxx[i]
+                            + gupyy[i]*(TWO*gxyx[i] - gxxy[i])
+                            + gupyz[i]*(TWO*gxzx[i] - gxxz[i]) );
+
+            Gamzxx[i] = HALF * ( gupxz[i]*gxxx[i]
+                            + gupyz[i]*(TWO*gxyx[i] - gxxy[i])
+                            + gupzz[i]*(TWO*gxzx[i] - gxxz[i]) );
+
+            Gamxyy[i] = HALF * ( gupxx[i]*(TWO*gxyy[i] - gyyx[i])
+                            + gupxy[i]*gyyy[i]
+                            + gupxz[i]*(TWO*gyzy[i] - gyyz[i]) );
+
+            Gamyyy[i] = HALF * ( gupxy[i]*(TWO*gxyy[i] - gyyx[i])
+                            + gupyy[i]*gyyy[i]
+                            + gupyz[i]*(TWO*gyzy[i] - gyyz[i]) );
+
+            Gamzyy[i] = HALF * ( gupxz[i]*(TWO*gxyy[i] - gyyx[i])
+                            + gupyz[i]*gyyy[i]
+                            + gupzz[i]*(TWO*gyzy[i] - gyyz[i]) );
+
+            Gamxzz[i] = HALF * ( gupxx[i]*(TWO*gxzz[i] - gzzx[i])
+                            + gupxy[i]*(TWO*gyzz[i] - gzzy[i])
+                            + gupxz[i]*gzzz[i] );
+
+            Gamyzz[i] = HALF * ( gupxy[i]*(TWO*gxzz[i] - gzzx[i])
+                            + gupyy[i]*(TWO*gyzz[i] - gzzy[i])
+                            + gupyz[i]*gzzz[i] );
+
+            Gamzzz[i] = HALF * ( gupxz[i]*(TWO*gxzz[i] - gzzx[i])
+                            + gupyz[i]*(TWO*gyzz[i] - gzzy[i])
+                            + gupzz[i]*gzzz[i] );
+
+            Gamxxy[i] = HALF * ( gupxx[i]*gxxy[i]
+                            + gupxy[i]*gyyx[i]
+                            + gupxz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
+
+            Gamyxy[i] = HALF * ( gupxy[i]*gxxy[i]
+                            + gupyy[i]*gyyx[i]
+                            + gupyz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
+
+            Gamzxy[i] = HALF * ( gupxz[i]*gxxy[i]
+                            + gupyz[i]*gyyx[i]
+                            + gupzz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
+
+            Gamxxz[i] = HALF * ( gupxx[i]*gxxz[i]
+                            + gupxy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + gupxz[i]*gzzx[i] );
+
+            Gamyxz[i] = HALF * ( gupxy[i]*gxxz[i]
+                            + gupyy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + gupyz[i]*gzzx[i] );
+
+            Gamzxz[i] = HALF * ( gupxz[i]*gxxz[i]
+                            + gupyz[i]*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + gupzz[i]*gzzx[i] );
+
+            Gamxyz[i] = HALF * ( gupxx[i]*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + gupxy[i]*gyyz[i]
+                            + gupxz[i]*gzzy[i] );
+
+            Gamyyz[i] = HALF * ( gupxy[i]*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + gupyy[i]*gyyz[i]
+                            + gupyz[i]*gzzy[i] );
+
+            Gamzyz[i] = HALF * ( gupxz[i]*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + gupyz[i]*gyyz[i]
+                            + gupzz[i]*gzzy[i] );
+
+        }
+        // 1.8ms //
+        for (int i=0;i<all;i+=1) {
+
+            Rxx[i] = gupxx[i]*gupxx[i]*Axx[i]
                + gupxy[i]*gupxy[i]*Ayy[i]
                + gupxz[i]*gupxz[i]*Azz[i]
                + TWO * ( gupxx[i]*gupxy[i]*Axy[i]
                        + gupxx[i]*gupxz[i]*Axz[i]
                        + gupxy[i]*gupxz[i]*Ayz[i] );
-            double ayy = gupxy[i]*gupxy[i]*Axx[i]
+
+            Ryy[i] = gupxy[i]*gupxy[i]*Axx[i]
                + gupyy[i]*gupyy[i]*Ayy[i]
                + gupyz[i]*gupyz[i]*Azz[i]
                + TWO * ( gupxy[i]*gupyy[i]*Axy[i]
                        + gupxy[i]*gupyz[i]*Axz[i]
                        + gupyy[i]*gupyz[i]*Ayz[i] );
-            double azz = gupxz[i]*gupxz[i]*Axx[i]
+
+            Rzz[i] = gupxz[i]*gupxz[i]*Axx[i]
                + gupyz[i]*gupyz[i]*Ayy[i]
                + gupzz[i]*gupzz[i]*Azz[i]
                + TWO * ( gupxz[i]*gupyz[i]*Axy[i]
                        + gupxz[i]*gupzz[i]*Axz[i]
                        + gupyz[i]*gupzz[i]*Ayz[i] );
-            double axy = gupxx[i]*gupxy[i]*Axx[i]
+
+            Rxy[i] = gupxx[i]*gupxy[i]*Axx[i]
                + gupxy[i]*gupyy[i]*Ayy[i]
                + gupxz[i]*gupyz[i]*Azz[i]
                + ( gupxx[i]*gupyy[i] + gupxy[i]*gupxy[i] ) * Axy[i]
                + ( gupxx[i]*gupyz[i] + gupxz[i]*gupxy[i] ) * Axz[i]
                + ( gupxy[i]*gupyz[i] + gupxz[i]*gupyy[i] ) * Ayz[i];
-            double axz = gupxx[i]*gupxz[i]*Axx[i]
+
+            Rxz[i] = gupxx[i]*gupxz[i]*Axx[i]
                + gupxy[i]*gupyz[i]*Ayy[i]
                + gupxz[i]*gupzz[i]*Azz[i]
                + ( gupxx[i]*gupyz[i] + gupxy[i]*gupxz[i] ) * Axy[i]
                + ( gupxx[i]*gupzz[i] + gupxz[i]*gupxz[i] ) * Axz[i]
                + ( gupxy[i]*gupzz[i] + gupxz[i]*gupyz[i] ) * Ayz[i];
-            double ayz = gupxy[i]*gupxz[i]*Axx[i]
+
+            Ryz[i] = gupxy[i]*gupxz[i]*Axx[i]
                + gupyy[i]*gupyz[i]*Ayy[i]
                + gupyz[i]*gupzz[i]*Azz[i]
                + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
-            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
-            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
-
-            Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
+        }
+        // 4ms //
+        for(int i=0;i<all;i+=1){
+            Gamx_rhs[i] = - TWO * (   Lapx[i] * Rxx[i] +   Lapy[i] * Rxy[i] +   Lapz[i] * Rxz[i] ) + 
                TWO * alpn1[i] * (                                                
-                -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
-                    gupxx[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] ) -
-                    gupxy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] ) -
-                    gupxz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] ) +
-                                Gamxxx[i]*axx + Gamxyy[i]*ayy + Gamxzz[i]*azz +
-                        TWO * ( Gamxxy[i]*axy + Gamxxz[i]*axz + Gamxyz[i]*ayz ) );
+                -F3o2/chin1[i] * (   chix[i] * Rxx[i] +   chiy[i] * Rxy[i] +   chiz[i] * Rxz[i] ) - 
+                    gupxx[i] * (   F2o3 * Kx[i]  +  EIGHT * PI * Sx[i]            ) - 
+                    gupxy[i] * (   F2o3 * Ky[i]  +  EIGHT * PI * Sy[i]            ) - 
+                    gupxz[i] * (   F2o3 * Kz[i]  +  EIGHT * PI * Sz[i]            ) + 
+                                Gamxxx[i] * Rxx[i] + Gamxyy[i] * Ryy[i] + Gamxzz[i] * Rzz[i]   + 
+                        TWO * ( Gamxxy[i] * Rxy[i] + Gamxxz[i] * Rxz[i] + Gamxyz[i] * Ryz[i] ) );

-            Gamy_rhs[i] = -TWO * ( Lapx[i]*axy + Lapy[i]*ayy + Lapz[i]*ayz )
+            Gamy_rhs[i] = -TWO * ( Lapx[i]*Rxy[i] + Lapy[i]*Ryy[i] + Lapz[i]*Ryz[i] )
                        +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*axy + chiy[i]*ayy + chiz[i]*ayz )
+                            -F3o2/chin1[i] * ( chix[i]*Rxy[i] + chiy[i]*Ryy[i] + chiz[i]*Ryz[i] )
                            - gupxy[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                            - gupyy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                            - gupyz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamyxx[i]*axx + Gamyyy[i]*ayy + Gamyzz[i]*azz
-                            + TWO * ( Gamyxy[i]*axy + Gamyxz[i]*axz + Gamyyz[i]*ayz )
+                            + Gamyxx[i]*Rxx[i] + Gamyyy[i]*Ryy[i] + Gamyzz[i]*Rzz[i]
+                            + TWO * ( Gamyxy[i]*Rxy[i] + Gamyxz[i]*Rxz[i] + Gamyyz[i]*Ryz[i] )
                        );

-            Gamz_rhs[i] = -TWO * ( Lapx[i]*axz + Lapy[i]*ayz + Lapz[i]*azz )
+            Gamz_rhs[i] = -TWO * ( Lapx[i]*Rxz[i] + Lapy[i]*Ryz[i] + Lapz[i]*Rzz[i] )
                        +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*axz + chiy[i]*ayz + chiz[i]*azz )
+                            -F3o2/chin1[i] * ( chix[i]*Rxz[i] + chiy[i]*Ryz[i] + chiz[i]*Rzz[i] )
                            - gupxz[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                            - gupyz[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                            - gupzz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamzxx[i]*axx + Gamzyy[i]*ayy + Gamzzz[i]*azz
-                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
+                            + Gamzxx[i]*Rxx[i] + Gamzyy[i]*Ryy[i] + Gamzzz[i]*Rzz[i]
+                            + TWO * ( Gamzxy[i]*Rxy[i] + Gamzxz[i]*Rxz[i] + Gamzyz[i]*Ryz[i] )
                        );
        }
        // 22.3ms //
@@ -326,63 +365,65 @@ int f_compute_rhs_bssn(int *ex, double &T,
        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)
+        // 3.5ms //
        for(int i=0;i<all;i+=1){
-            const double divb = betaxx[i] + betayy[i] + betazz[i];
-            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
-            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
-            double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
-            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
-
-            double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
+            fxx[i] = gxxx[i] + gxyy[i] + gxzz[i];
+            fxy[i] = gxyx[i] + gyyy[i] + gyzz[i];
+            fxz[i] = gxzx[i] + gyzy[i] + gzzz[i];
+            Gamxa[i] = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                    + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
-            double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
+
+            Gamya[i] = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
                    + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
-            double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
+
+            Gamza[i] = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
                    + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
+        }
+        // 3.9ms //
+        for(int i=0;i<all;i+=1){
            Gamx_rhs[i] = Gamx_rhs[i]
-                        + F2o3 * gxa * divb
-                        - gxa * betaxx[i] - gya * betaxy[i] - gza * betaxz[i]
-                        + F1o3 * ( gupxx[i] * lfxx + gupxy[i] * lfxy + gupxz[i] * lfxz )
+                        + F2o3 * Gamxa[i] * div_beta[i]
+                        - Gamxa[i] * betaxx[i] - Gamya[i] * betaxy[i] - Gamza[i] * betaxz[i]
+                        + F1o3 * ( gupxx[i] * fxx[i] + gupxy[i] * fxy[i] + gupxz[i] * fxz[i] )
                        + gupxx[i] * gxxx[i] + gupyy[i] * gyyx[i] + gupzz[i] * gzzx[i]
                        + TWO * ( gupxy[i] * gxyx[i] + gupxz[i] * gxzx[i] + gupyz[i] * gyzx[i] );

            Gamy_rhs[i] = Gamy_rhs[i]
-                        + F2o3 * gya * divb
-                        - gxa * betayx[i] - gya * betayy[i] - gza * betayz[i]
-                        + F1o3 * ( gupxy[i] * lfxx + gupyy[i] * lfxy + gupyz[i] * lfxz )
+                        + F2o3 * Gamya[i] * div_beta[i]
+                        - Gamxa[i] * betayx[i] - Gamya[i] * betayy[i] - Gamza[i] * betayz[i]
+                        + F1o3 * ( gupxy[i] * fxx[i] + gupyy[i] * fxy[i] + gupyz[i] * fxz[i] )
                        + gupxx[i] * gxxy[i] + gupyy[i] * gyyy[i] + gupzz[i] * gzzy[i]
                        + TWO * ( gupxy[i] * gxyy[i] + gupxz[i] * gxzy[i] + gupyz[i] * gyzy[i] );

            Gamz_rhs[i] = Gamz_rhs[i]
-                        + F2o3 * gza * divb
-                        - gxa * betazx[i] - gya * betazy[i] - gza * betazz[i]
-                        + F1o3 * ( gupxz[i] * lfxx + gupyz[i] * lfxy + gupzz[i] * lfxz )
+                        + F2o3 * Gamza[i] * div_beta[i]
+                        - Gamxa[i] * betazx[i] - Gamya[i] * betazy[i] - Gamza[i] * betazz[i]
+                        + F1o3 * ( gupxz[i] * fxx[i] + gupyz[i] * fxy[i] + gupzz[i] * fxz[i] )
                        + gupxx[i] * gxxz[i] + gupyy[i] * gyyz[i] + gupzz[i] * gzzz[i]
                        + TWO * ( gupxy[i] * gxyz[i] + gupxz[i] * gxzz[i] + gupyz[i] * gyzz[i] );
        }
        // 4.4ms //
        for (int i=0;i<all;i+=1) {
-            gxxx[i] = (dxx[i] + ONE)*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
-            gxyx[i] = (dxx[i] + ONE)*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
-            gxzx[i] = (dxx[i] + ONE)*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
-            gyyx[i] = (dxx[i] + ONE)*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
-            gyzx[i] = (dxx[i] + ONE)*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
-            gzzx[i] = (dxx[i] + ONE)*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
+            gxxx[i] = gxx[i]*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
+            gxyx[i] = gxx[i]*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
+            gxzx[i] = gxx[i]*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
+            gyyx[i] = gxx[i]*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
+            gyzx[i] = gxx[i]*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
+            gzzx[i] = gxx[i]*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];

-            gxxy[i] = gxy[i]*Gamxxx[i] + (dyy[i] + ONE)*Gamyxx[i] + gyz[i]*Gamzxx[i];
-            gxyy[i] = gxy[i]*Gamxxy[i] + (dyy[i] + ONE)*Gamyxy[i] + gyz[i]*Gamzxy[i];
-            gxzy[i] = gxy[i]*Gamxxz[i] + (dyy[i] + ONE)*Gamyxz[i] + gyz[i]*Gamzxz[i];
-            gyyy[i] = gxy[i]*Gamxyy[i] + (dyy[i] + ONE)*Gamyyy[i] + gyz[i]*Gamzyy[i];
-            gyzy[i] = gxy[i]*Gamxyz[i] + (dyy[i] + ONE)*Gamyyz[i] + gyz[i]*Gamzyz[i];
-            gzzy[i] = gxy[i]*Gamxzz[i] + (dyy[i] + ONE)*Gamyzz[i] + gyz[i]*Gamzzz[i];
+            gxxy[i] = gxy[i]*Gamxxx[i] + gyy[i]*Gamyxx[i] + gyz[i]*Gamzxx[i];
+            gxyy[i] = gxy[i]*Gamxxy[i] + gyy[i]*Gamyxy[i] + gyz[i]*Gamzxy[i];
+            gxzy[i] = gxy[i]*Gamxxz[i] + gyy[i]*Gamyxz[i] + gyz[i]*Gamzxz[i];
+            gyyy[i] = gxy[i]*Gamxyy[i] + gyy[i]*Gamyyy[i] + gyz[i]*Gamzyy[i];
+            gyzy[i] = gxy[i]*Gamxyz[i] + gyy[i]*Gamyyz[i] + gyz[i]*Gamzyz[i];
+            gzzy[i] = gxy[i]*Gamxzz[i] + gyy[i]*Gamyzz[i] + gyz[i]*Gamzzz[i];

-            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + (dzz[i] + ONE)*Gamzxx[i];
-            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + (dzz[i] + ONE)*Gamzxy[i];
-            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + (dzz[i] + ONE)*Gamzxz[i];
-            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + (dzz[i] + ONE)*Gamzyy[i];
-            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + (dzz[i] + ONE)*Gamzyz[i];
-            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + (dzz[i] + ONE)*Gamzzz[i];
+            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + gzz[i]*Gamzxx[i];
+            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + gzz[i]*Gamzxy[i];
+            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + gzz[i]*Gamzxz[i];
+            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + gzz[i]*Gamzyy[i];
+            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + gzz[i]*Gamzyz[i];
+            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + gzz[i]*Gamzzz[i];
        }
        // 22.2ms //
            fdderivs(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
@@ -430,17 +471,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
        // 14ms //
        /* 假设 all = ex1*ex2*ex3，所有量都是 length=all 的 double 数组（已按同一扁平化规则排布） */
        for (int i = 0; i < all; i += 1) {
-            const double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
-                            + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
-            const double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
-                            + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
-            const double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
-                            + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
-
            Rxx[i] =
                -HALF * Rxx[i]
-                + (dxx[i] + ONE) * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
-                + gxa * gxxx[i] + gya * gxyx[i] + gza * gxzx[i]
+                + gxx[i] * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
+                + Gamxa[i] * gxxx[i] + Gamya[i] * gxyx[i] + Gamza[i] * gxzx[i]
                + gupxx[i] * (
                    TWO * (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxyx[i] + Gamzxx[i] * gxzx[i]) +
                        (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxxy[i] + Gamzxx[i] * gxxz[i])
@@ -474,8 +508,8 @@ int f_compute_rhs_bssn(int *ex, double &T,

            Ryy[i] =
                -HALF * Ryy[i]
-                + gxy[i] * Gamxy[i] + (dyy[i] + ONE) * Gamyy[i] + gyz[i] * Gamzy[i]
-                + gxa * gxyy[i] + gya * gyyy[i] + gza * gyzy[i]
+                + gxy[i] * Gamxy[i] + gyy[i] * Gamyy[i] + gyz[i] * Gamzy[i]
+                + Gamxa[i] * gxyy[i] + Gamya[i] * gyyy[i] + Gamza[i] * gyzy[i]
                + gupxx[i] * (
                    TWO * (Gamxxy[i] * gxxy[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxzy[i]) +
                        (Gamxxy[i] * gxyx[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxyz[i])
@@ -509,8 +543,8 @@ int f_compute_rhs_bssn(int *ex, double &T,

            Rzz[i] =
                -HALF * Rzz[i]
-                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + (dzz[i] + ONE) * Gamzz[i]
-                + gxa * gxzz[i] + gya * gyzz[i] + gza * gzzz[i]
+                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + gzz[i] * Gamzz[i]
+                + Gamxa[i] * gxzz[i] + Gamya[i] * gyzz[i] + Gamza[i] * gzzz[i]
                + gupxx[i] * (
                    TWO * (Gamxxz[i] * gxxz[i] + Gamyxz[i] * gxyz[i] + Gamzxz[i] * gxzz[i]) +
                        (Gamxxz[i] * gxzx[i] + Gamyxz[i] * gxzy[i] + Gamzxz[i] * gxzz[i])
@@ -545,10 +579,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
            Rxy[i] =
                HALF * (
                    -Rxy[i]
-                    + (dxx[i] + ONE) * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
-                    + gxy[i] * Gamxx[i] + (dyy[i] + ONE) * Gamyx[i] + gyz[i] * Gamzx[i]
-                    + gxa * gxyx[i] + gya * gyyx[i] + gza * gyzx[i]
-                    + gxa * gxxy[i] + gya * gxyy[i] + gza * gxzy[i]
+                    + gxx[i] * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
+                    + gxy[i] * Gamxx[i] + gyy[i] * Gamyx[i] + gyz[i] * Gamzx[i]
+                    + Gamxa[i] * gxyx[i] + Gamya[i] * gyyx[i] + Gamza[i] * gyzx[i]
+                    + Gamxa[i] * gxxy[i] + Gamya[i] * gxyy[i] + Gamza[i] * gxzy[i]
                )
                + gupxx[i] * (
                    Gamxxx[i] * gxxy[i] + Gamyxx[i] * gxyy[i] + Gamzxx[i] * gxzy[i]
@@ -593,10 +627,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
            Rxz[i] =
                HALF * (
                    -Rxz[i]
-                    + (dxx[i] + ONE) * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
-                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + (dzz[i] + ONE) * Gamzx[i]
-                    + gxa * gxzx[i] + gya * gyzx[i] + gza * gzzx[i]
-                    + gxa * gxxz[i] + gya * gxyz[i] + gza * gxzz[i]
+                    + gxx[i] * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
+                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + gzz[i] * Gamzx[i]
+                    + Gamxa[i] * gxzx[i] + Gamya[i] * gyzx[i] + Gamza[i] * gzzx[i]
+                    + Gamxa[i] * gxxz[i] + Gamya[i] * gxyz[i] + Gamza[i] * gxzz[i]
                )
                + gupxx[i] * (
                    Gamxxx[i] * gxxz[i] + Gamyxx[i] * gxyz[i] + Gamzxx[i] * gxzz[i]
@@ -641,10 +675,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
            Ryz[i] =
                HALF * (
                    -Ryz[i]
-                    + gxy[i] * Gamxz[i] + (dyy[i] + ONE) * Gamyz[i] + gyz[i] * Gamzz[i]
-                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + (dzz[i] + ONE) * Gamzy[i]
-                    + gxa * gxzy[i] + gya * gyzy[i] + gza * gzzy[i]
-                    + gxa * gxyz[i] + gya * gyyz[i] + gza * gyzz[i]
+                    + gxy[i] * Gamxz[i] + gyy[i] * Gamyz[i] + gyz[i] * Gamzz[i]
+                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + gzz[i] * Gamzy[i]
+                    + Gamxa[i] * gxzy[i] + Gamya[i] * gyzy[i] + Gamza[i] * gzzy[i]
+                    + Gamxa[i] * gxyz[i] + Gamya[i] * gyyz[i] + Gamza[i] * gyzz[i]
                )
                + gupxx[i] * (
                    Gamxxy[i] * gxxz[i] + Gamyxy[i] * gxyz[i] + Gamzxy[i] * gxzz[i]
@@ -705,9 +739,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
                + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
                + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + gxx[i] * f[i] ) / (chin1[i] * TWO);
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + gyy[i] * f[i] ) / (chin1[i] * TWO);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + gzz[i] * f[i] ) / (chin1[i] * TWO);

            Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
            Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
@@ -726,17 +760,17 @@ int f_compute_rhs_bssn(int *ex, double &T,
            gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];

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

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

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

            Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
            Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
@@ -758,13 +792,14 @@ int f_compute_rhs_bssn(int *ex, double &T,
            fxy[i] = fxy[i] - Gamxxy[i] * Lapx[i] - Gamyxy[i] * Lapy[i] - Gamzxy[i] * Lapz[i];
            fxz[i] = fxz[i] - Gamxxz[i] * Lapx[i] - Gamyxz[i] * Lapy[i] - Gamzxz[i] * Lapz[i];
            fyz[i] = fyz[i] - Gamxyz[i] * Lapx[i] - Gamyyz[i] * Lapy[i] - Gamzyz[i] * Lapz[i];
-
+        }
+        // 1ms //
+        for (int i=0;i<all;i+=1) {
            trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                    +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
        }
        // 2.5ms //
        for (int i=0;i<all;i+=1) {
-            const double divb = betaxx[i] + betayy[i] + betazz[i];

            S[i] = chin1[i] * (
                    gupxx[i] * Sxx[i] + gupyy[i] * Syy[i] + gupzz[i] * Szz[i]
@@ -815,20 +850,23 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + (alpn1[i] / chin1[i]) * f[i]
            );

-            double l_fxx = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
-            double l_fxy = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
-            double l_fxz = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
-            double l_fyy = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
-            double l_fyz = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
-            double l_fzz = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
+            fxx[i] = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
+            fxy[i] = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
+            fxz[i] = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
+            fyy[i] = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
+            fyz[i] = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
+            fzz[i] = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
+        }
+        // 8ms //
+        for (int i=0;i<all;i+=1) {

            /* Aij_rhs = fij - gij * f */
-            Axx_rhs[i] = l_fxx - (dxx[i] + ONE) * f[i];
-            Ayy_rhs[i] = l_fyy - (dyy[i] + ONE) * f[i];
-            Azz_rhs[i] = l_fzz - (dzz[i] + ONE) * f[i];
-            Axy_rhs[i] = l_fxy - gxy[i] * f[i];
-            Axz_rhs[i] = l_fxz - gxz[i] * f[i];
-            Ayz_rhs[i] = l_fyz - gyz[i] * f[i];
+            Axx_rhs[i] = fxx[i] - gxx[i] * f[i];
+            Ayy_rhs[i] = fyy[i] - gyy[i] * f[i];
+            Azz_rhs[i] = fzz[i] - gzz[i] * f[i];
+            Axy_rhs[i] = fxy[i] - gxy[i] * f[i];
+            Axz_rhs[i] = fxz[i] - gxz[i] * f[i];
+            Ayz_rhs[i] = fyz[i] - gyz[i] * f[i];

            /* Now: store A_il A^l_j into fij: */
            fxx[i] =
@@ -890,19 +928,19 @@ int f_compute_rhs_bssn(int *ex, double &T,
                f[i] * Axx_rhs[i]
                + alpn1[i] * ( trK[i] * Axx[i] - TWO * fxx[i] )
                + TWO * ( Axx[i] * betaxx[i] + Axy[i] * betayx[i] + Axz[i] * betazx[i] )
-                - F2o3 * Axx[i] * divb;
+                - F2o3 * Axx[i] * div_beta[i];

            Ayy_rhs[i] =
                f[i] * Ayy_rhs[i]
                + alpn1[i] * ( trK[i] * Ayy[i] - TWO * fyy[i] )
                + TWO * ( Axy[i] * betaxy[i] + Ayy[i] * betayy[i] + Ayz[i] * betazy[i] )
-                - F2o3 * Ayy[i] * divb;
+                - F2o3 * Ayy[i] * div_beta[i];

            Azz_rhs[i] =
                f[i] * Azz_rhs[i]
                + alpn1[i] * ( trK[i] * Azz[i] - TWO * fzz[i] )
                + TWO * ( Axz[i] * betaxz[i] + Ayz[i] * betayz[i] + Azz[i] * betazz[i] )
-                - F2o3 * Azz[i] * divb;
+                - F2o3 * Azz[i] * div_beta[i];

            Axy_rhs[i] =
                f[i] * Axy_rhs[i]
@@ -911,7 +949,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + Axz[i] * betazy[i]
                + Ayy[i] * betayx[i]
                + Ayz[i] * betazx[i]
-                + F1o3 * Axy[i] * divb
+                + F1o3 * Axy[i] * div_beta[i]
                - Axy[i] * betazz[i];

            Ayz_rhs[i] =
@@ -921,7 +959,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + Ayy[i] * betayz[i]
                + Axz[i] * betaxy[i]
                + Azz[i] * betazy[i]
-                + F1o3 * Ayz[i] * divb
+                + F1o3 * Ayz[i] * div_beta[i]
                - Ayz[i] * betaxx[i];

            Axz_rhs[i] =
@@ -931,7 +969,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                + Axy[i] * betayz[i]
                + Ayz[i] * betayx[i]
                + Azz[i] * betazx[i]
-                + F1o3 * Axz[i] * divb
+                + F1o3 * Axz[i] * div_beta[i]
                - Axz[i] * betayy[i];

            /* Compute trace of S_ij */
@@ -1062,31 +1100,58 @@ int f_compute_rhs_bssn(int *ex, double &T,
            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
            #endif
        }
-        // advection + KO dissipation with shared symmetry buffer
-        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
+        // 26ms //
+        lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS);
+        lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA);
+        lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA);
+        lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS);
+        lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA);
+        lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA);
+        lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS);
+        // 20ms //
+        if(eps>0){
+            kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps);
+            kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps);
+            kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps);
+            kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps);
+            kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps);
+            kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps);
+            kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps);
+            kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps);
+            kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps);
+            kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps);
+        }
        // 2ms //
        if(co==0){
            for (int i=0;i<all;i+=1) {
@@ -1139,6 +1204,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
            fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
            fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
            fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
+        }
        // 7ms //
        for (int i=0;i<all;i+=1) {
            gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
@@ -1192,7 +1258,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
            movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
            movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
        }
-        }


            
--- a/AMSS_NCKU_source/bssn_rhs_cuda.cu
+++ b/AMSS_NCKU_source/bssn_rhs_cuda.cu
--- a/AMSS_NCKU_source/bssn_rhs_cuda.h
+++ b/AMSS_NCKU_source/bssn_rhs_cuda.h
@@ -0,0 +1,36 @@
+#ifndef BSSN_RHS_CUDA_H
+#define BSSN_RHS_CUDA_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+int f_compute_rhs_bssn(int *ex, double &T,
+                       double *X, double *Y, double *Z,
+                       double *chi, double *trK,
+                       double *dxx, double *gxy, double *gxz, double *dyy, double *gyz, double *dzz,
+                       double *Axx, double *Axy, double *Axz, double *Ayy, double *Ayz, double *Azz,
+                       double *Gamx, double *Gamy, double *Gamz,
+                       double *Lap, double *betax, double *betay, double *betaz,
+                       double *dtSfx, double *dtSfy, double *dtSfz,
+                       double *chi_rhs, double *trK_rhs,
+                       double *gxx_rhs, double *gxy_rhs, double *gxz_rhs, double *gyy_rhs, double *gyz_rhs, double *gzz_rhs,
+                       double *Axx_rhs, double *Axy_rhs, double *Axz_rhs, double *Ayy_rhs, double *Ayz_rhs, double *Azz_rhs,
+                       double *Gamx_rhs, double *Gamy_rhs, double *Gamz_rhs,
+                       double *Lap_rhs, double *betax_rhs, double *betay_rhs, double *betaz_rhs,
+                       double *dtSfx_rhs, double *dtSfy_rhs, double *dtSfz_rhs,
+                       double *rho, double *Sx, double *Sy, double *Sz,
+                       double *Sxx, double *Sxy, double *Sxz, double *Syy, double *Syz, double *Szz,
+                       double *Gamxxx, double *Gamxxy, double *Gamxxz, double *Gamxyy, double *Gamxyz, double *Gamxzz,
+                       double *Gamyxx, double *Gamyxy, double *Gamyxz, double *Gamyyy, double *Gamyyz, double *Gamyzz,
+                       double *Gamzxx, double *Gamzxy, double *Gamzxz, double *Gamzyy, double *Gamzyz, double *Gamzzz,
+                       double *Rxx, double *Rxy, double *Rxz, double *Ryy, double *Ryz, double *Rzz,
+                       double *ham_Res, double *movx_Res, double *movy_Res, double *movz_Res,
+                       double *Gmx_Res, double *Gmy_Res, double *Gmz_Res,
+                       int &Symmetry, int &Lev, double &eps, int &co);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
--- a/AMSS_NCKU_source/diff_newwb.f90
+++ b/AMSS_NCKU_source/diff_newwb.f90
@@ -1513,7 +1513,6 @@
  real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
  real*8, dimension(3) :: SoA
  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  integer :: i_core_min,i_core_max,j_core_min,j_core_max,k_core_min,k_core_max
  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
  real*8  :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
  integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
@@ -1566,47 +1565,9 @@
  fxz = ZEO
  fyz = ZEO

-  i_core_min = max(1, imin+2)
-  i_core_max = min(ex(1), imax-2)
-  j_core_min = max(1, jmin+2)
-  j_core_max = min(ex(2), jmax-2)
-  k_core_min = max(1, kmin+2)
-  k_core_max = min(ex(3), kmax-2)
-
-  if(i_core_min <= i_core_max .and. j_core_min <= j_core_max .and. k_core_min <= k_core_max)then
-   do k=k_core_min,k_core_max
-   do j=j_core_min,j_core_max
-   do i=i_core_min,i_core_max
-! interior points always use 4th-order stencils without branch checks
-      fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-                          -fh(i+2,j,k)+F16*fh(i+1,j,k)              )
-      fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-                          -fh(i,j+2,k)+F16*fh(i,j+1,k)              )
-      fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-                          -fh(i,j,k+2)+F16*fh(i,j,k+1)              )
-      fxy(i,j,k) = Fdxdy*(     (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k))  &
-                          -F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k))  &
-                          +F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k))  &
-                          -    (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
-      fxz(i,j,k) = Fdxdz*(     (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2))  &
-                          -F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1))  &
-                          +F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1))  &
-                          -    (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
-      fyz(i,j,k) = Fdydz*(     (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2))  &
-                          -F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1))  &
-                          +F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1))  &
-                          -    (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
-   enddo
-   enddo
-   enddo
-  endif
-
  do k=1,ex(3)
  do j=1,ex(2)
  do i=1,ex(1)
-      if(i>=i_core_min .and. i<=i_core_max .and. &
-         j>=j_core_min .and. j<=j_core_max .and. &
-         k>=k_core_min .and. k<=k_core_max) cycle
 !~~~~~~ fxx
        if(i+2 <= imax .and. i-2 >= imin)then
 !
--- a/AMSS_NCKU_source/fderivs_c.C
+++ b/AMSS_NCKU_source/fderivs_c.C
@@ -81,63 +81,26 @@ void fderivs(const int ex[3],
    }

    /*
-     * 两段式：
-     * 1) 先在二阶可用区域计算二阶模板
-     * 2) 再在高阶可用区域覆盖为四阶模板
+     * Fortran loops:
+     * do k=1,ex3-1
+     * do j=1,ex2-1
+     * do i=1,ex1-1
     *
-     * 与原 if/elseif 逻辑等价，但减少逐点分支判断。
+     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
     */
-    const int i2_lo = (iminF > 0) ? iminF : 0;
-    const int j2_lo = (jminF > 0) ? jminF : 0;
-    const int k2_lo = (kminF > 0) ? kminF : 0;
-    const int i2_hi = ex1 - 2;
-    const int j2_hi = ex2 - 2;
-    const int k2_hi = ex3 - 2;
-
-    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
-    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
-    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
-    const int i4_hi = ex1 - 3;
-    const int j4_hi = ex2 - 3;
-    const int k4_hi = ex3 - 3;
-
-    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
-        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
        const int kF = k0 + 1;
-            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
            const int jF = j0 + 1;
-                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
-
-                    fx[p] = d2dx * (
-                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fy[p] = d2dy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fz[p] = d2dz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-                }
-            }
-        }
-    }
-
-    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
-        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
                const int iF = i0 + 1;
                const size_t p = idx_ex(i0, j0, k0, ex);

+                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
+                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+                {
                    fx[p] = d12dx * (
                        fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
                        EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
@@ -159,6 +122,26 @@ void fderivs(const int ex[3],
                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
                    );
                }
+                // elseif(i+1 <= imax .and. i-1 >= imin ...)
+                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
+                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
+                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
+                {
+                    fx[p] = d2dx * (
+                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d2dy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fz[p] = d2dz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                }
            }
        }
    }
--- a/AMSS_NCKU_source/fmisc.f90
+++ b/AMSS_NCKU_source/fmisc.f90
@@ -1327,6 +1327,35 @@ end subroutine d2dump

  return
  end subroutine polint
+
+  subroutine polint0(xa, ya, y, ordn)
+  ! Lagrange interpolation at x=0, O(n) direct formula
+  implicit none
+  integer, intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa, ya
+  real*8, intent(out) :: y
+
+  integer :: j, k
+  real*8 :: wj
+
+  y = 0.d0
+  do j = 1, ordn
+    wj = 1.d0
+    do k = 1, ordn
+      if (k .ne. j) then
+        wj = wj * xa(k) / (xa(k) - xa(j))
+      endif
+    enddo
+    y = y + wj * ya(j)
+  enddo
+
+  return
+  end subroutine polint0
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
 !------------------------------------------------------------------------------
 ! Compute Lagrange interpolation basis weights for one target point.
 !------------------------------------------------------------------------------
--- a/AMSS_NCKU_source/interp_lb_profile_data.h
+++ b/AMSS_NCKU_source/interp_lb_profile_data.h
@@ -1,5 +1,3 @@
-/* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
-/* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
 /* Auto-generated from interp_lb_profile.bin — do not edit */
 #ifndef INTERP_LB_PROFILE_DATA_H
 #define INTERP_LB_PROFILE_DATA_H
--- a/AMSS_NCKU_source/kodiss_c.C
+++ b/AMSS_NCKU_source/kodiss_c.C
@@ -63,28 +63,19 @@ void kodis(const int ex[3],
     * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
     * 并定义 Fortran index: iF=i0+1, ...
     */
-    // 收紧循环范围：只遍历满足 iF±3/jF±3/kF±3 条件的内部点
-    // iF-3 >= iminF => iF >= iminF+3 => i0 >= iminF+2 (因为 iF=i0+1)
-    // iF+3 <= imaxF => iF <= imaxF-3 => i0 <= imaxF-4
-    const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
-    const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
-    const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
-    const int i0_hi = imaxF - 4;  // inclusive
-    const int j0_hi = jmaxF - 4;
-    const int k0_hi = kmaxF - 4;
-
-    if (i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi) {
-        free(fh);
-        return;
-    }
-
-    for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+    for (int k0 = 0; k0 < ex3; ++k0) {
        const int kF = k0 + 1;
-        for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+        for (int j0 = 0; j0 < ex2; ++j0) {
            const int jF = j0 + 1;
-            for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+            for (int i0 = 0; i0 < ex1; ++i0) {
                const int iF = i0 + 1;

+                // Fortran if 条件：
+                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
+                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
+                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
+                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
+                {
                    const size_t p = idx_ex(i0, j0, k0, ex);

                    // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
@@ -112,6 +103,7 @@ void kodis(const int ex[3],
                }
            }
        }
+    }

    free(fh);
 }
--- a/AMSS_NCKU_source/lopsided_kodis_c.C
+++ b/AMSS_NCKU_source/lopsided_kodis_c.C
@@ -1,248 +0,0 @@
-#include "tool.h"
-
-/*
- * Combined advection (lopsided) + KO dissipation (kodis).
- * Uses one shared symmetry_bd buffer per call.
- */
-void lopsided_kodis(const int ex[3],
-                    const double *X, const double *Y, const double *Z,
-                    const double *f, double *f_rhs,
-                    const double *Sfx, const double *Sfy, const double *Sfz,
-                    int Symmetry, const double SoA[3], double eps)
-{
-    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
-    const double F6 = 6.0, F18 = 18.0;
-    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
-    const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
-    const double cof = 64.0; // 2^6
-
-    const int NO_SYMM = 0, EQ_SYMM = 1;
-
-    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
-
-    const double dX = X[1] - X[0];
-    const double dY = Y[1] - Y[0];
-    const double dZ = Z[1] - Z[0];
-
-    const double d12dx = ONE / F12 / dX;
-    const double d12dy = ONE / F12 / dY;
-    const double d12dz = ONE / F12 / dZ;
-
-    const int imaxF = ex1;
-    const int jmaxF = ex2;
-    const int kmaxF = ex3;
-
-    int iminF = 1, jminF = 1, kminF = 1;
-    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
-    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
-    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
-
-    // fh for Fortran-style domain (-2:ex1,-2:ex2,-2:ex3)
-    const size_t nx = (size_t)ex1 + 3;
-    const size_t ny = (size_t)ex2 + 3;
-    const size_t nz = (size_t)ex3 + 3;
-    const size_t fh_size = nx * ny * nz;
-
-    double *fh = (double*)malloc(fh_size * sizeof(double));
-    if (!fh) return;
-
-    symmetry_bd(3, ex, f, fh, SoA);
-
-    // Advection (same stencil logic as lopsided_c.C)
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-        const int kF = k0 + 1;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-            const int jF = j0 + 1;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-                const int iF = i0 + 1;
-                const size_t p = idx_ex(i0, j0, k0, ex);
-
-                const double sfx = Sfx[p];
-                if (sfx > ZEO) {
-                    if (i0 <= ex1 - 4) {
-                        f_rhs[p] += sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
-                    } else if (i0 <= ex1 - 3) {
-                        f_rhs[p] += sfx * d12dx *
-                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
-                    } else if (i0 <= ex1 - 2) {
-                        f_rhs[p] -= sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
-                    }
-                } else if (sfx < ZEO) {
-                    if ((i0 - 2) >= iminF) {
-                        f_rhs[p] -= sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
-                    } else if ((i0 - 1) >= iminF) {
-                        f_rhs[p] += sfx * d12dx *
-                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
-                    } else if (i0 >= iminF) {
-                        f_rhs[p] += sfx * d12dx *
-                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
-                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
-                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
-                    }
-                }
-
-                const double sfy = Sfy[p];
-                if (sfy > ZEO) {
-                    if (j0 <= ex2 - 4) {
-                        f_rhs[p] += sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
-                    } else if (j0 <= ex2 - 3) {
-                        f_rhs[p] += sfy * d12dy *
-                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
-                    } else if (j0 <= ex2 - 2) {
-                        f_rhs[p] -= sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
-                    }
-                } else if (sfy < ZEO) {
-                    if ((j0 - 2) >= jminF) {
-                        f_rhs[p] -= sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
-                    } else if ((j0 - 1) >= jminF) {
-                        f_rhs[p] += sfy * d12dy *
-                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
-                    } else if (j0 >= jminF) {
-                        f_rhs[p] += sfy * d12dy *
-                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
-                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
-                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
-                    }
-                }
-
-                const double sfz = Sfz[p];
-                if (sfz > ZEO) {
-                    if (k0 <= ex3 - 4) {
-                        f_rhs[p] += sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
-                    } else if (k0 <= ex3 - 3) {
-                        f_rhs[p] += sfz * d12dz *
-                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
-                    } else if (k0 <= ex3 - 2) {
-                        f_rhs[p] -= sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
-                    }
-                } else if (sfz < ZEO) {
-                    if ((k0 - 2) >= kminF) {
-                        f_rhs[p] -= sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
-                    } else if ((k0 - 1) >= kminF) {
-                        f_rhs[p] += sfz * d12dz *
-                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
-                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
-                    } else if (k0 >= kminF) {
-                        f_rhs[p] += sfz * d12dz *
-                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
-                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
-                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
-                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
-                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
-                    }
-                }
-            }
-        }
-    }
-
-    // KO dissipation (same domain restriction as kodiss_c.C)
-    if (eps > ZEO) {
-        const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
-        const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
-        const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
-        const int i0_hi = imaxF - 4; // inclusive
-        const int j0_hi = jmaxF - 4;
-        const int k0_hi = kmaxF - 4;
-
-        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
-            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
-                const int kF = k0 + 1;
-                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
-                    const int jF = j0 + 1;
-                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
-                        const int iF = i0 + 1;
-                        const size_t p = idx_ex(i0, j0, k0, ex);
-
-                        const double Dx_term =
-                            ((fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
-                             SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
-                             FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
-                             TWT *  fh[idx_fh_F(iF,     jF, kF, ex)]) / dX;
-
-                        const double Dy_term =
-                            ((fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
-                             SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
-                             FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
-                             TWT *  fh[idx_fh_F(iF, jF,     kF, ex)]) / dY;
-
-                        const double Dz_term =
-                            ((fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
-                             SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
-                             FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
-                             TWT *  fh[idx_fh_F(iF, jF, kF,     ex)]) / dZ;
-
-                        f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
-                    }
-                }
-            }
-        }
-    }
-
-    free(fh);
-}
--- a/AMSS_NCKU_source/makefile
+++ b/AMSS_NCKU_source/makefile
@@ -20,14 +20,12 @@ CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
-## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-## PGO has been turned off, now tested and found to be negative optimization
-## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-
-
+## opt (default): maximum performance with PGO profile data
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(PROFDATA) \
              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=$(PROFDATA) \
              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif

@@ -45,6 +43,10 @@ endif
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)

+# CUDA rewrite of BSSN RHS (drop-in replacement for bssn_rhs_c + stencil helpers)
+bssn_rhs_cuda.o: bssn_rhs_cuda.cu macrodef.h
+	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
+
 # C rewrite of BSSN RHS kernel and helpers
 bssn_rhs_c.o: bssn_rhs_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
@@ -61,12 +63,9 @@ kodiss_c.o: kodiss_c.C
 lopsided_c.o: lopsided_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@

-lopsided_kodis_c.o: lopsided_kodis_c.C
+interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@

-#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
 TP_OPTFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
@@ -87,12 +86,16 @@ ifeq ($(USE_CXX_KERNELS),0)
 CFILES =
 else
 # C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o
 endif

+# CUDA rewrite: bssn_rhs_cuda.o replaces all CFILES (stencils are built-in)
+CFILES_CUDA = bssn_rhs_cuda.o
+
 ## RK4 kernel switch (independent from USE_CXX_KERNELS)
 ifeq ($(USE_CXX_RK4),1)
 CFILES += rungekutta4_rout_c.o
+CFILES_CUDA += rungekutta4_rout_c.o
 RK4_F90_OBJ =
 else
 RK4_F90_OBJ = rungekutta4_rout.o
@@ -178,8 +181,11 @@ $(CUDAFILES): bssn_gpu.h gpu_mem.h gpu_rhsSS_mem.h
 misc.o : zbesh.o

 # projects
-ABE: $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+ABE: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)
+
+ABE_CUDA: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS) -lcudart $(CUDA_LIB_PATH)

 ABEGPU: $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
@@ -188,4 +194,4 @@ TwoPunctureABE: $(TwoPunctureFILES)
 	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)

 clean:
-	rm *.o ABE ABEGPU TwoPunctureABE make.log -f
+	rm *.o ABE ABE_CUDA ABEGPU TwoPunctureABE make.log -f
--- a/AMSS_NCKU_source/makefile.inc
+++ b/AMSS_NCKU_source/makefile.inc
@@ -62,4 +62,4 @@ CLINKER      = mpiicpx
 Cu = nvcc
 CUDA_LIB_PATH = -L/usr/lib/cuda/lib64 -I/usr/include -I/usr/lib/cuda/include
 #CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -arch compute_13 -code compute_13,sm_13 -Dfortran3 -Dnewc
-CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc
+CUDA_APP_FLAGS = -c -g -O3 --ptxas-options=-v -Dfortran3 -Dnewc -arch=sm_80
--- a/AMSS_NCKU_source/prolongrestrict_cell.f90
+++ b/AMSS_NCKU_source/prolongrestrict_cell.f90
@@ -217,7 +217,6 @@
  real*8,dimension(2*ghost_width) :: X,Y,Z
  real*8, dimension(2*ghost_width,2*ghost_width) :: tmp2
  real*8, dimension(2*ghost_width) :: tmp1
-  real*8 :: ddy
  real*8,dimension(3) :: ccp

 #if (ghost_width == 2)
@@ -580,7 +579,7 @@
            tmp1(ghost_width-cxI(1)+cxB(1)  :ghost_width-cxI(1)+cxT(1)  ) = funf(cxB(1):cxT(1),j,k)
         endif

-         call polint(X,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(X,tmp1,funf(i,j,k),2*ghost_width)

 ! for y direction
       elseif(sum(fg).eq.2.and.fg(2) .eq. 0.and. &
@@ -690,7 +689,7 @@
            tmp1(ghost_width-cxI(2)+cxB(2)  :ghost_width-cxI(2)+cxT(2)  ) = funf(i,cxB(2):cxT(2),k)
         endif

-         call polint(Y,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Y,tmp1,funf(i,j,k),2*ghost_width)

 ! for z direction
       elseif(sum(fg).eq.2.and.fg(3) .eq. 0.and. &
@@ -802,7 +801,7 @@
            tmp1(ghost_width-cxI(3)+cxB(3)  :ghost_width-cxI(3)+cxT(3)  ) = funf(i,j,cxB(3):cxT(3))
         endif

-         call polint(Z,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Z,tmp1,funf(i,j,k),2*ghost_width)

 #else

--- a/AMSS_NCKU_source/prolongrestrict_vertex.f90
+++ b/AMSS_NCKU_source/prolongrestrict_vertex.f90
@@ -217,7 +217,6 @@
  real*8,dimension(2*ghost_width) :: X,Y,Z
  real*8, dimension(2*ghost_width,2*ghost_width) :: tmp2
  real*8, dimension(2*ghost_width) :: tmp1
-  real*8 :: ddy

 #if (ghost_width == 2)
  real*8, parameter :: C1=-1.d0/16,C2=9.d0/16
@@ -470,7 +469,7 @@

         tmp1(cxB(1)+ghost_width-i+1:cxT(1)+ghost_width-i+1) = fh(cxB(1):cxT(1),j,k)

-         call polint(X,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(X,tmp1,funf(i,j,k),2*ghost_width)

 ! for y direction
       elseif (fg(2) .eq. 0)then
@@ -529,7 +528,7 @@

         tmp1(cxB(2)+ghost_width-j+1:cxT(2)+ghost_width-j+1) = fh(i,cxB(2):cxT(2),k)

-         call polint(Y,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Y,tmp1,funf(i,j,k),2*ghost_width)

 ! for z direction
       else
@@ -588,7 +587,7 @@

         tmp1(cxB(3)+ghost_width-k+1:cxT(3)+ghost_width-k+1) = fh(i,j,cxB(3):cxT(3))

-         call polint(Z,tmp1,0.d0,funf(i,j,k),ddy,2*ghost_width)
+         call polint0(Z,tmp1,funf(i,j,k),2*ghost_width)

       endif
      
--- a/AMSS_NCKU_source/rungekutta4_rout_c.C
+++ b/AMSS_NCKU_source/rungekutta4_rout_c.C
@@ -2,7 +2,6 @@
 #include <cstdio>
 #include <cstdlib>
 #include <cstddef>
-#include <complex>
 #include <immintrin.h>

 namespace {
@@ -118,62 +117,6 @@ inline void rk4_stage3(std::size_t n,

 extern "C" {

-void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
-    constexpr double F1o6 = 1.0 / 6.0;
-    constexpr double HLF = 0.5;
-    constexpr double TWO = 2.0;
-
-    switch (RK4) {
-    case 0:
-        f1 = f0 + HLF * dT * f_rhs;
-        break;
-    case 1:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + HLF * dT * f1;
-        break;
-    case 2:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + dT * f1;
-        break;
-    case 3:
-        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
-        break;
-    default:
-        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-}
-
-void rungekutta4_cplxscalar_(double &dT,
-                             std::complex<double> &f0,
-                             std::complex<double> &f1,
-                             std::complex<double> &f_rhs,
-                             int &RK4) {
-    constexpr double F1o6 = 1.0 / 6.0;
-    constexpr double HLF = 0.5;
-    constexpr double TWO = 2.0;
-
-    switch (RK4) {
-    case 0:
-        f1 = f0 + HLF * dT * f_rhs;
-        break;
-    case 1:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + HLF * dT * f1;
-        break;
-    case 2:
-        f_rhs = f_rhs + TWO * f1;
-        f1 = f0 + dT * f1;
-        break;
-    case 3:
-        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
-        break;
-    default:
-        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
-        std::abort();
-    }
-}
-
 int f_rungekutta4_rout(int *ex, double &dT,
                       double *f0, double *f1, double *f_rhs,
                       int &RK4) {
--- a/AMSS_NCKU_source/tool.h
+++ b/AMSS_NCKU_source/tool.h
@@ -25,9 +25,3 @@ void lopsided(const int ex[3],
              const double *f, double *f_rhs,
              const double *Sfx, const double *Sfy, const double *Sfz,
              int Symmetry, const double SoA[3]);
-
-void lopsided_kodis(const int ex[3],
-                    const double *X, const double *Y, const double *Z,
-                    const double *f, double *f_rhs,
-                    const double *Sfx, const double *Sfy, const double *Sfz,
-                    int Symmetry, const double SoA[3], double eps);
--- a/makefile_and_run.py
+++ b/makefile_and_run.py
@@ -70,7 +70,7 @@ def makefile_ABE():

    ## Build command with CPU binding to nohz_full cores
    if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=optimize ABE"
    elif (input_data.GPU_Calculation == "yes"):
        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
    else:
--- a/pgo_profile/PGO_Profile_Analysis.md
+++ b/pgo_profile/PGO_Profile_Analysis.md
@@ -0,0 +1,97 @@
+# AMSS-NCKU PGO Profile Analysis Report
+
+## 1. Profiling Environment
+
+| Item | Value |
+|------|-------|
+| Compiler | Intel oneAPI DPC++/C++ 2025.3.0 (icpx/ifx) |
+| Instrumentation Flag | `-fprofile-instr-generate` |
+| Optimization Level (instrumented) | `-O2 -xHost -fma` |
+| MPI Processes | 1 (single process to avoid MPI+instrumentation deadlock) |
+| Profile File | `default_9725750769337483397_0.profraw` (327 KB) |
+| Merged Profile | `default.profdata` (394 KB) |
+| llvm-profdata | `/home/intel/oneapi/compiler/2025.3/bin/compiler/llvm-profdata` |
+
+## 2. Reduced Simulation Parameters (for profiling run)
+
+| Parameter | Production Value | Profiling Value |
+|-----------|-----------------|-----------------|
+| MPI_processes | 64 | 1 |
+| grid_level | 9 | 4 |
+| static_grid_level | 5 | 3 |
+| static_grid_number | 96 | 24 |
+| moving_grid_number | 48 | 16 |
+| largest_box_xyz_max | 320^3 | 160^3 |
+| Final_Evolution_Time | 1000.0 | 10.0 |
+| Evolution_Step_Number | 10,000,000 | 1,000 |
+| Detector_Number | 12 | 2 |
+
+## 3. Profile Summary
+
+| Metric | Value |
+|--------|-------|
+| Total instrumented functions | 1,392 |
+| Functions with non-zero counts | 117 (8.4%) |
+| Functions with zero counts | 1,275 (91.6%) |
+| Maximum function entry count | 386,459,248 |
+| Maximum internal block count | 370,477,680 |
+| Total block count | 4,198,023,118 |
+
+## 4. Top 20 Hotspot Functions
+
+| Rank | Total Count | Max Block Count | Function | Category |
+|------|------------|-----------------|----------|----------|
+| 1 | 1,241,601,732 | 370,477,680 | `polint_` | Interpolation |
+| 2 | 755,994,435 | 230,156,640 | `prolong3_` | Grid prolongation |
+| 3 | 667,964,095 | 3,697,792 | `compute_rhs_bssn_` | BSSN RHS evolution |
+| 4 | 539,736,051 | 386,459,248 | `symmetry_bd_` | Symmetry boundary |
+| 5 | 277,310,808 | 53,170,728 | `lopsided_` | Lopsided FD stencil |
+| 6 | 155,534,488 | 94,535,040 | `decide3d_` | 3D grid decision |
+| 7 | 119,267,712 | 19,266,048 | `rungekutta4_rout_` | RK4 time integrator |
+| 8 | 91,574,616 | 48,824,160 | `kodis_` | Kreiss-Oliger dissipation |
+| 9 | 67,555,389 | 43,243,680 | `fderivs_` | Finite differences |
+| 10 | 55,296,000 | 42,246,144 | `misc::fact(int)` | Factorial utility |
+| 11 | 43,191,071 | 27,663,328 | `fdderivs_` | 2nd-order FD derivatives |
+| 12 | 36,233,965 | 22,429,440 | `restrict3_` | Grid restriction |
+| 13 | 24,698,512 | 17,231,520 | `polin3_` | Polynomial interpolation |
+| 14 | 22,962,942 | 20,968,768 | `copy_` | Data copy |
+| 15 | 20,135,696 | 17,259,168 | `Ansorg::barycentric(...)` | Spectral interpolation |
+| 16 | 14,650,224 | 7,224,768 | `Ansorg::barycentric_omega(...)` | Spectral weights |
+| 17 | 13,242,296 | 2,871,920 | `global_interp_` | Global interpolation |
+| 18 | 12,672,000 | 7,734,528 | `sommerfeld_rout_` | Sommerfeld boundary |
+| 19 | 6,872,832 | 1,880,064 | `sommerfeld_routbam_` | Sommerfeld boundary (BAM) |
+| 20 | 5,709,900 | 2,809,632 | `l2normhelper_` | L2 norm computation |
+
+## 5. Hotspot Category Breakdown
+
+Top 20 functions account for ~98% of total execution counts:
+
+| Category | Functions | Combined Count | Share |
+|----------|-----------|---------------|-------|
+| Interpolation / Prolongation / Restriction | polint_, prolong3_, restrict3_, polin3_, global_interp_, Ansorg::* | ~2,093M | ~50% |
+| BSSN RHS + FD stencils | compute_rhs_bssn_, lopsided_, fderivs_, fdderivs_ | ~1,056M | ~25% |
+| Boundary conditions | symmetry_bd_, sommerfeld_rout_, sommerfeld_routbam_ | ~559M | ~13% |
+| Time integration | rungekutta4_rout_ | ~119M | ~3% |
+| Dissipation | kodis_ | ~92M | ~2% |
+| Utilities | misc::fact, decide3d_, copy_, l2normhelper_ | ~256M | ~6% |
+
+## 6. Conclusions
+
+1. **Profile data is valid**: 1,392 functions instrumented, 117 exercised with ~4.2 billion total counts.
+2. **Hotspot concentration is high**: Top 5 functions alone account for ~76% of all counts, which is ideal for PGO — the compiler has strong branch/layout optimization targets.
+3. **Fortran numerical kernels dominate**: `polint_`, `prolong3_`, `compute_rhs_bssn_`, `symmetry_bd_`, `lopsided_` are all Fortran routines in the inner evolution loop. PGO will optimize their branch prediction and basic block layout.
+4. **91.6% of functions have zero counts**: These are code paths for unused features (GPU, BSSN-EScalar, BSSN-EM, Z4C, etc.). PGO will deprioritize them, improving instruction cache utilization.
+5. **Profile is representative**: Despite the reduced grid size, the code path coverage matches production — the same kernels (RHS, prolongation, restriction, boundary) are exercised. PGO branch probabilities from this profile will transfer well to full-scale runs.
+
+## 7. PGO Phase 2 Usage
+
+To apply the profile, use the following flags in `makefile.inc`:
+
+```makefile
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
+              -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
+              -align array64byte -fpp -I${MKLROOT}/include
+```
--- a/pgo_profile/default.profdata
+++ b/pgo_profile/default.profdata
--- a/pgo_profile/default_9726853898452064389_0.profdata
+++ b/pgo_profile/default_9726853898452064389_0.profdata
--- a/pgo_profile/default.profdata.backup
+++ b/pgo_profile/default.profdata.backup
--- a/pgo_profile/default.profdata.backup2
+++ b/pgo_profile/default.profdata.backup2
--- a/pgo_profile/default.profdatabackup3
+++ b/pgo_profile/default.profdatabackup3
--- a/pgo_profile/default_15874826282416242821_0_58277.profraw
+++ b/pgo_profile/default_15874826282416242821_0_58277.profraw
--- a/pgo_profile/default_9725750769337483397_0.profraw
+++ b/pgo_profile/default_9725750769337483397_0.profraw
--- a/pgo_profile/default_9725923726611433605_0.profraw
+++ b/pgo_profile/default_9725923726611433605_0.profraw
--- a/pgo_profile/default_9726420327935033477_0.profraw
+++ b/pgo_profile/default_9726420327935033477_0.profraw
Author	SHA1	Message	Date
ianchb	43975017eb	prolong3 改为先算实际 stencil 窗口；只有窗口触及对称边界时才走全域 symmetry_bd，否则只复制必需窗口。restrict3 同样改成窗口判定，无触边时仅填 ii/jj/kk 必需窗口。	2026-03-02 18:10:38 +08:00
ianchb	485667ef4c	perf(restrict3): shrink X-pass ii sweep to required overlap window - compute fi_min/fi_max from output i-range and derive ii_lo/ii_hi - replace full ii sweep (-1:extf(1)) with windowed sweep in Z/Y precompute passes - keep stencil math unchanged; add bounds sanity check for ii window	2026-03-02 18:10:38 +08:00
ianchb	2a977ce82e	perf(MPatch): 用空间 bin 索引加速 Interp_Points 的 block 归属查找 - 为 Patch::Interp_Points 三个重载引入 BlockBinIndex（候选筛选 + 全扫回退） - 保持原 point-in-block 判定与后续插值/通信流程不变 - 将逐点线性扫块从 O(N_pointsN_blocks) 降为近似 O(N_pointsk) - 测试：bin 上限如果太大，会引入不必要的索引构建开销。将 bins 上限设为 16。 Co-authored-by: gpt-5.3-codex	2026-03-02 18:10:35 +08:00
CGH0S7	160e2a0369	fix prolong/restrict index bounds after cherry-pick `12e1f63`	2026-03-02 14:11:52 +08:00
ianchb	01410de05a	refactor(Parallel): streamline MPI communication by consolidating request handling and memory management	2026-03-02 14:08:27 +08:00
jaunatisblue	83c826eb49	prolong3: 减少Z-pass 冗余计算	2026-03-02 14:08:13 +08:00
ianchb	43ddaab903	fix: add C RK4 kernel to CFILES_CUDA	2026-03-02 12:19:52 +08:00
ianchb	5839755c2f	compute div_beta on-the-fly to remove temp array	2026-03-02 12:12:58 +08:00
ianchb	a893b4007c	merge lopsided+kodis	2026-03-02 12:12:26 +08:00
CGH0S7	ad5ff03615	build: switch allocator option to oneTBB tbbmalloc (cherry picked from commit `e29ca2dca9`)	2026-03-02 11:53:30 +08:00
CGH0S7	b4bc0ef269	先关闭绑核心，发现速度对比：不绑定核心+SCX>绑核心+SCX (cherry picked from commit `1eba73acbe`)	2026-03-02 11:53:13 +08:00
CGH0S7	b185f84cce	Add switchable C RK4 kernel and build toggle (cherry picked from commit `b91cfff301`)	2026-03-02 11:53:00 +08:00
ianchb	71f6eb7b44	Remove profiling code	2026-03-02 11:29:48 +08:00
CGH0S7	90620c2aec	Optimize fdderivs: skip redundant 2nd-order work in 4th-order overlap	2026-03-02 11:04:04 +08:00
jaunatisblue	f561522d89	prolong3：提升cache命中率	2026-03-02 11:02:19 +08:00
jaunatisblue	3f4715b8cc	修改prolong	2026-03-02 11:02:17 +08:00
jaunatisblue	710ea8f76b	对prolong3做访存优化	2026-03-02 11:02:12 +08:00
CGH0S7	5cf891359d	Optimize symmetry_bd with stride-based fast paths (cherry picked from commit `16013081e0`)	2026-03-02 11:01:49 +08:00
CGH0S7	222747449a	Optimize average2: use DO CONCURRENT loop form (cherry picked from commit `1a518cd3f6`)	2026-03-02 11:01:45 +08:00
CGH0S7	14de4d535e	Optimize average2: replace array expression with explicit loops (cherry picked from commit `1dc622e516`)	2026-03-02 11:01:42 +08:00
CGH0S7	787295692a	Optimize prolong3: hoist bounds check out of inner loop (cherry picked from commit `3046a0ccde`)	2026-03-02 11:01:39 +08:00
CGH0S7	335f2f23fe	Optimize prolong3: replace parity branches with coefficient lookup (cherry picked from commit `d4ec69c98a`)	2026-03-02 11:01:37 +08:00
CGH0S7	7109474a14	Optimize prolong3: precompute coarse index/parity maps (cherry picked from commit `2c0a3055d4`)	2026-03-02 11:01:31 +08:00
CGH0S7	e7a02e8f72	perf(polint): add uniform-grid fast path for barycentric n=6	2026-03-01 14:13:51 +08:00
CGH0S7	8dad910c6c	perf(polint): add switchable barycentric ordn=6 path	2026-03-01 14:13:51 +08:00
CGH0S7	01b4cf71d1	perf(polin3): switch to lagrange-weight tensor contraction	2026-03-01 14:13:04 +08:00
CGH0S7	66dabe8cc4	perf(polint): add ordn=6 specialized neville path	2026-03-01 14:12:22 +08:00
ianchb	abf2f640e4	add fused symmetry packing kernels for orders 2 and 3 in BSSN RHS	2026-02-28 15:35:14 +08:00
ianchb	94f40627aa	refine GPU dispatch initialization and optimize H2D/D2H data transfers	2026-02-28 15:23:41 +08:00
ianchb	d94c31c5c4	[WIP]Implement multi-GPU support in BSSN RHS and add profiling for H2D/D2H transfers	2026-02-28 11:12:14 +08:00
ianchb	724e9cd415	[WIP]Add CUDA support for BSSN RHS with new kernel and update makefiles	2026-02-28 11:12:13 +08:00
ianchb	c001939461	Add Lagrange interpolation subroutine and update calls in prolongrestrict modules	2026-02-28 11:12:13 +08:00
ianchb	94d236385d	Revert "skip redundant MPI ghost cell syncs for stages 0, 1 & 2" This reverts commit `f7ada421cf`.	2026-02-28 11:12:12 +08:00
ianchb	780f1c80d0	skip redundant MPI ghost cell syncs for stages 0, 1 & 2 BSSN 每个 RK4 时间步执行 4 次 MPI ghost zone 同步： Stage 0（预测）结束后：Parallel::Sync(SynchList_pre) Stage 1（校正 1）结束后：Parallel::Sync(SynchList_cor) Stage 2（校正 2）结束后：Parallel::Sync(SynchList_cor) Stage 3（校正 3）结束后：Parallel::Sync(SynchList_cor) ← 必要（为下一步提供 ghost） bssnEM_class.C、Z4c_class.C 结构相同，一起修改了	2026-02-28 11:12:09 +08:00