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
30 changed files with 3753 additions and 1416 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_node = new int[cache.max_reqs];
-  int *req_is_recv = cache.tc_req_is_recv;
+  int *req_is_recv = new int[cache.max_reqs];
-  int *completed = cache.tc_completed;
+  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_Waitall(state.req_no, cache.reqs, cache.stats);
-  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+
  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)
+  for (int node = 0; node < cpusize; node++)
-  if (cache.recv_bufs[myrank] && cache.recv_lengths[myrank] > 0)
+    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
-    data_packer(cache.recv_bufs[myrank], src[myrank], dst[myrank], myrank, UNPACK, VarList, VarList, Symmetry);
+      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;
+    AsyncSyncState() : req_no(0), active(false) {}
    int *req_is_recv;
    int pending_recv;
    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
  };
  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
@@ -736,8 +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];
 }
 //================================================================================================
@@ -2215,7 +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))
@@ -2431,7 +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
 }
@@ -2610,7 +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
 }
@@ -2777,7 +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("");
@@ -2792,7 +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("");
@@ -2811,7 +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("");
@@ -2827,7 +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("");
@@ -5748,12 +5746,6 @@ void bssn_class::SHStep()
 // 0: do not use mixing two levels data for OutBD; 1: do use
 #define MIXOUTB 0
 // In the cached Restrict->OutBdLow2Hi path, coarse Sync is usually redundant:
 // OutBdLow2Hi_cached reads coarse owned cells (build_owned_gsl type-4), not coarse ghost/buffer cells.
 // Keep a switch to restore the old behavior if needed for debugging.
 #ifndef RP_SYNC_COARSE_AFTER_RESTRICT
 #define RP_SYNC_COARSE_AFTER_RESTRICT 0
 #endif
 void bssn_class::RestrictProlong(int lev, int YN, bool BB,
                                 MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
 // we assume
@@ -5804,7 +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);
@@ -5817,9 +5809,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -5830,7 +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
@@ -5857,7 +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);
@@ -5870,9 +5860,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 //       misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
 #if (PSTR == 1 || PSTR == 2)
 //       a_stream.clear();
@@ -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
@@ -5952,19 +5940,17 @@ 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);
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      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
@@ -5976,19 +5962,17 @@ 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);
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      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
@@ -6043,19 +6027,17 @@ 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);
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      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
@@ -6069,19 +6051,17 @@ 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);
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      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
@@ -6122,7 +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
@@ -6135,7 +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
@@ -6154,16 +6134,13 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 #else
      Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
 #endif
 #if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
      Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
 #endif
    }
    Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
  }
 }
 #undef MIXOUTB
 #undef RP_SYNC_COARSE_AFTER_RESTRICT
 //================================================================================================
--- 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_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];
+            div_beta[i] = betaxx[i] + betayy[i] + betazz[i];
-            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - divb); 
+            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - div_beta[i]); 
-            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * (dxx[i] + ONE) * divb + 
+            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * gxx[i] * div_beta[i] + 
-                    TWO * ((dxx[i] + ONE) * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
+                    TWO * (gxx[i] * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
-            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * (dyy[i] + ONE) * divb + 
+            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * gyy[i] * div_beta[i] + 
-                    TWO * (gxy[i] * betaxy[i] + (dyy[i] + ONE) * betayy[i] + gyz[i] * betazy[i]);
+                    TWO * (gxy[i] * betaxy[i] + gyy[i] * betayy[i] + gyz[i] * betazy[i]);
-            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * (dzz[i] + ONE) * divb + 
+            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * gzz[i] * div_beta[i] + 
-                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + (dzz[i] + ONE) * betazz[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] * divb + 
+            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * div_beta[i] + 
-                        (dxx[i] + ONE) * betaxy[i] + gxz[i] * betazy[i] + (dyy[i] + ONE) * betayx[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 + 
+            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * div_beta[i] + 
-                        gxy[i] * betaxz[i] + (dyy[i] + ONE) * betayz[i] + gxz[i] * betaxy[i] 
+                        gxy[i] * betaxz[i] + gyy[i] * betayz[i] + gxz[i] * betaxy[i] 
-                        + (dzz[i] + ONE) * betazy[i] - gyz[i] * betaxx[i];
+                        + gzz[i] * betazy[i] - gyz[i] * betaxx[i];
-            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * divb + 
+            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * div_beta[i] + 
-                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
+                        gxx[i] * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
-                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[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] -
+            double det = gxx[i] * gyy[i] * gzz[i] + 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];
+                        gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];  
-            double lg_xx = ((dyy[i] + ONE) * (dzz[i] + ONE) - gyz[i] * gyz[i]) / det;
+            gupxx[i] = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
-            double lg_xy = -(gxy[i] * (dzz[i] + ONE) - gyz[i] * gxz[i]) / det;
+            gupxy[i] = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
-            double lg_xz = (gxy[i] * gyz[i] - (dyy[i] + ONE) * gxz[i]) / det;
+            gupxz[i] = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
-            double lg_yy = ((dxx[i] + ONE) * (dzz[i] + ONE) - gxz[i] * gxz[i]) / det;
+            gupyy[i] = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
-            double lg_yz = -((dxx[i] + ONE) * gyz[i] - gxy[i] * gxz[i]) / det;
+            gupyz[i] = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
-            double lg_zz = ((dxx[i] + ONE) * (dyy[i] + ONE) - gxy[i] * gxy[i]) / det;
+            gupzz[i] = (gxx[i] * gyy[i] - 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;
+        // 2.2ms //
-
+        if(co==0){
-            if(co==0){
+            for (int i=0;i<all;i+=1) {
                Gmx_Res[i] = Gamx[i] - (
-                    lg_xx * (lg_xx*gxxx[i] + lg_xy*gxyx[i] + lg_xz*gxzx[i]) +
+                    gupxx[i] * (gupxx[i]*gxxx[i] + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i]) +
-                    lg_xy * (lg_xx*gxyx[i] + lg_xy*gyyx[i] + lg_xz*gyzx[i]) +
+                    gupxy[i] * (gupxx[i]*gxyx[i] + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i]) +
-                    lg_xz * (lg_xx*gxzx[i] + lg_xy*gyzx[i] + lg_xz*gzzx[i]) +
+                    gupxz[i] * (gupxx[i]*gxzx[i] + gupxy[i]*gyzx[i] + gupxz[i]*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]) +
+                    gupxx[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
-                    lg_xz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
+                    gupxy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
-                    lg_xx * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
+                    gupxz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[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])
+                    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] - (
-                    lg_xx * (lg_xy*gxxx[i] + lg_yy*gxyx[i] + lg_yz*gxzx[i]) +
+                    gupxx[i] * (gupxy[i]*gxxx[i] + gupyy[i]*gxyx[i] + gupyz[i]*gxzx[i]) +
-                    lg_xy * (lg_xy*gxyx[i] + lg_yy*gyyx[i] + lg_yz*gyzx[i]) +
+                    gupxy[i] * (gupxy[i]*gxyx[i] + gupyy[i]*gyyx[i] + gupyz[i]*gyzx[i]) +
-                    lg_xz * (lg_xy*gxzx[i] + lg_yy*gyzx[i] + lg_yz*gzzx[i]) +
+                    gupxz[i] * (gupxy[i]*gxzx[i] + gupyy[i]*gyzx[i] + gupyz[i]*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]) +
+                    gupxy[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
-                    lg_yz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
+                    gupyy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
-                    lg_xy * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
+                    gupyz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[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])
+                    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] - (
-                    lg_xx * (lg_xz*gxxx[i] + lg_yz*gxyx[i] + lg_zz*gxzx[i]) +
+                    gupxx[i] * (gupxz[i]*gxxx[i] + gupyz[i]*gxyx[i] + gupzz[i]*gxzx[i]) +
-                    lg_xy * (lg_xz*gxyx[i] + lg_yz*gyyx[i] + lg_zz*gyzx[i]) +
+                    gupxy[i] * (gupxz[i]*gxyx[i] + gupyz[i]*gyyx[i] + gupzz[i]*gyzx[i]) +
-                    lg_xz * (lg_xz*gxzx[i] + lg_yz*gyzx[i] + lg_zz*gzzx[i]) +
+                    gupxz[i] * (gupxz[i]*gxzx[i] + gupyz[i]*gyzx[i] + gupzz[i]*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]) +
+                    gupxy[i] * (gupxz[i]*gxxy[i] + gupyz[i]*gxyy[i] + gupzz[i]*gxzy[i]) +
-                    lg_yz * (lg_xz*gxzy[i] + lg_yz*gyzy[i] + lg_zz*gzzy[i]) +
+                    gupyy[i] * (gupxz[i]*gxyy[i] + gupyz[i]*gyyy[i] + gupzz[i]*gyzy[i]) +
-                    lg_xz * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
+                    gupyz[i] * (gupxz[i]*gxzy[i] + gupyz[i]*gyzy[i] + gupzz[i]*gzzy[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])
+                    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])
                );
            }
            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)
+        // 5ms //
        for (int i=0;i<all;i+=1) {
-            double axx = gupxx[i]*gupxx[i]*Axx[i]
+
            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;
+        // 4ms //
-
+        for(int i=0;i<all;i+=1){
-            Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
+            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 ) -
+                -F3o2/chin1[i] * (   chix[i] * Rxx[i] +   chiy[i] * Rxy[i] +   chiz[i] * Rxz[i] ) - 
-                    gupxx[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] ) -
+                    gupxx[i] * (   F2o3 * Kx[i]  +  EIGHT * PI * Sx[i]            ) - 
-                    gupxy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] ) -
+                    gupxy[i] * (   F2o3 * Ky[i]  +  EIGHT * PI * Sy[i]            ) - 
-                    gupxz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] ) +
+                    gupxz[i] * (   F2o3 * Kz[i]  +  EIGHT * PI * Sz[i]            ) + 
-                                Gamxxx[i]*axx + Gamxyy[i]*ayy + Gamxzz[i]*azz +
+                                Gamxxx[i] * Rxx[i] + Gamxyy[i] * Ryy[i] + Gamxzz[i] * Rzz[i]   + 
-                        TWO * ( Gamxxy[i]*axy + Gamxxz[i]*axz + Gamxyz[i]*ayz ) );
+                        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
+                            + Gamyxx[i]*Rxx[i] + Gamyyy[i]*Ryy[i] + Gamyzz[i]*Rzz[i]
-                            + TWO * ( Gamyxy[i]*axy + Gamyxz[i]*axz + Gamyyz[i]*ayz )
+                            + 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
+                            + Gamzxx[i]*Rxx[i] + Gamzyy[i]*Ryy[i] + Gamzzz[i]*Rzz[i]
-                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
+                            + 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];
+            fxx[i] = gxxx[i] + gxyy[i] + gxzz[i];
-            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
+            fxy[i] = gxyx[i] + gyyy[i] + gyzz[i];
-            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
+            fxz[i] = gxzx[i] + gyzy[i] + gzzz[i];
-            double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
+            Gamxa[i] = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
            double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                    + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
-            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
+                        + F2o3 * Gamxa[i] * div_beta[i]
-                        - gxa * betaxx[i] - gya * betaxy[i] - gza * betaxz[i]
+                        - Gamxa[i] * betaxx[i] - Gamya[i] * betaxy[i] - Gamza[i] * betaxz[i]
-                        + F1o3 * ( gupxx[i] * lfxx + gupxy[i] * lfxy + gupxz[i] * lfxz )
+                        + 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
+                        + F2o3 * Gamya[i] * div_beta[i]
-                        - gxa * betayx[i] - gya * betayy[i] - gza * betayz[i]
+                        - Gamxa[i] * betayx[i] - Gamya[i] * betayy[i] - Gamza[i] * betayz[i]
-                        + F1o3 * ( gupxy[i] * lfxx + gupyy[i] * lfxy + gupyz[i] * lfxz )
+                        + 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
+                        + F2o3 * Gamza[i] * div_beta[i]
-                        - gxa * betazx[i] - gya * betazy[i] - gza * betazz[i]
+                        - Gamxa[i] * betazx[i] - Gamya[i] * betazy[i] - Gamza[i] * betazz[i]
-                        + F1o3 * ( gupxz[i] * lfxx + gupyz[i] * lfxy + gupzz[i] * lfxz )
+                        + 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];
+            gxxx[i] = gxx[i]*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];
+            gxyx[i] = gxx[i]*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];
+            gxzx[i] = gxx[i]*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];
+            gyyx[i] = gxx[i]*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];
+            gyzx[i] = gxx[i]*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];
+            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];
+            gxxy[i] = gxy[i]*Gamxxx[i] + gyy[i]*Gamyxx[i] + gyz[i]*Gamzxx[i];
-            gxyy[i] = gxy[i]*Gamxxy[i] + (dyy[i] + ONE)*Gamyxy[i] + gyz[i]*Gamzxy[i];
+            gxyy[i] = gxy[i]*Gamxxy[i] + gyy[i]*Gamyxy[i] + gyz[i]*Gamzxy[i];
-            gxzy[i] = gxy[i]*Gamxxz[i] + (dyy[i] + ONE)*Gamyxz[i] + gyz[i]*Gamzxz[i];
+            gxzy[i] = gxy[i]*Gamxxz[i] + gyy[i]*Gamyxz[i] + gyz[i]*Gamzxz[i];
-            gyyy[i] = gxy[i]*Gamxyy[i] + (dyy[i] + ONE)*Gamyyy[i] + gyz[i]*Gamzyy[i];
+            gyyy[i] = gxy[i]*Gamxyy[i] + gyy[i]*Gamyyy[i] + gyz[i]*Gamzyy[i];
-            gyzy[i] = gxy[i]*Gamxyz[i] + (dyy[i] + ONE)*Gamyyz[i] + gyz[i]*Gamzyz[i];
+            gyzy[i] = gxy[i]*Gamxyz[i] + gyy[i]*Gamyyz[i] + gyz[i]*Gamzyz[i];
-            gzzy[i] = gxy[i]*Gamxzz[i] + (dyy[i] + ONE)*Gamyzz[i] + gyz[i]*Gamzzz[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];
+            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + gzz[i]*Gamzxx[i];
-            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + (dzz[i] + ONE)*Gamzxy[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] + (dzz[i] + ONE)*Gamzxz[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] + (dzz[i] + ONE)*Gamzyy[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] + (dzz[i] + ONE)*Gamzyz[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] + (dzz[i] + ONE)*Gamzzz[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]
+                + gxx[i] * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
-                + gxa * gxxx[i] + gya * gxyx[i] + gza * gxzx[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]
+                + gxy[i] * Gamxy[i] + gyy[i] * Gamyy[i] + gyz[i] * Gamzy[i]
-                + gxa * gxyy[i] + gya * gyyy[i] + gza * gyzy[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]
+                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + gzz[i] * Gamzz[i]
-                + gxa * gxzz[i] + gya * gyzz[i] + gza * gzzz[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]
+                    + gxx[i] * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
-                    + gxy[i] * Gamxx[i] + (dyy[i] + ONE) * Gamyx[i] + gyz[i] * Gamzx[i]
+                    + gxy[i] * Gamxx[i] + gyy[i] * Gamyx[i] + gyz[i] * Gamzx[i]
-                    + gxa * gxyx[i] + gya * gyyx[i] + gza * gyzx[i]
+                    + Gamxa[i] * gxyx[i] + Gamya[i] * gyyx[i] + Gamza[i] * gyzx[i]
-                    + gxa * gxxy[i] + gya * gxyy[i] + gza * gxzy[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]
+                    + gxx[i] * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
-                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + (dzz[i] + ONE) * Gamzx[i]
+                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + gzz[i] * Gamzx[i]
-                    + gxa * gxzx[i] + gya * gyzx[i] + gza * gzzx[i]
+                    + Gamxa[i] * gxzx[i] + Gamya[i] * gyzx[i] + Gamza[i] * gzzx[i]
-                    + gxa * gxxz[i] + gya * gxyz[i] + gza * gxzz[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]
+                    + gxy[i] * Gamxz[i] + gyy[i] * Gamyz[i] + gyz[i] * Gamzz[i]
-                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + (dzz[i] + ONE) * Gamzy[i]
+                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + gzz[i] * Gamzy[i]
-                    + gxa * gxzy[i] + gya * gyzy[i] + gza * gzzy[i]
+                    + Gamxa[i] * gxzy[i] + Gamya[i] * gyzy[i] + Gamza[i] * gzzy[i]
-                    + gxa * gxyz[i] + gya * gyyz[i] + gza * gyzz[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);
+            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) + (dyy[i] + ONE) * 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) + (dzz[i] + ONE) * 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);
@@ -716,6 +750,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
        // 24ms //
        fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
        fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
        // 6ms //
        for (int i=0;i<all;i+=1) {
@@ -725,17 +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;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - gxx[i] * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - gxx[i] * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - gxx[i] * gxxz[i] ) * HALF;
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - gyy[i] * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - gyy[i] * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[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;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - gzz[i] * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - gzz[i] * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / 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;
@@ -757,13 +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]
@@ -814,20 +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];
+            fxx[i] = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
-            double l_fxy = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
+            fxy[i] = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
-            double l_fxz = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
+            fxz[i] = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
-            double l_fyy = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
+            fyy[i] = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
-            double l_fyz = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
+            fyz[i] = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
-            double l_fzz = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[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];
+            Axx_rhs[i] = fxx[i] - gxx[i] * f[i];
-            Ayy_rhs[i] = l_fyy - (dyy[i] + ONE) * f[i];
+            Ayy_rhs[i] = fyy[i] - gyy[i] * f[i];
-            Azz_rhs[i] = l_fzz - (dzz[i] + ONE) * f[i];
+            Azz_rhs[i] = fzz[i] - gzz[i] * f[i];
-            Axy_rhs[i] = l_fxy - gxy[i] * f[i];
+            Axy_rhs[i] = fxy[i] - gxy[i] * f[i];
-            Axz_rhs[i] = l_fxz - gxz[i] * f[i];
+            Axz_rhs[i] = fxz[i] - gxz[i] * f[i];
-            Ayz_rhs[i] = l_fyz - gyz[i] * f[i];
+            Ayz_rhs[i] = fyz[i] - gyz[i] * f[i];
            /* Now: store A_il A^l_j into fij: */
            fxx[i] =
@@ -889,19 +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]
@@ -910,7 +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] =
@@ -920,7 +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] =
@@ -930,7 +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 */
@@ -1013,12 +1052,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
            betaz_rhs[i] = FF * dtSfz[i];
            reta[i] =
-                gupxx[i] * chix[i] * chix[i]
+                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
-                + gupyy[i] * chiy[i] * chiy[i]
+                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
-                + gupzz[i] * chiz[i] * chiz[i]
+                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
-                + TWO * ( gupxy[i] * chix[i] * chiy[i]
+                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
-                        + gupxz[i] * chix[i] * chiz[i]
+                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
-                        + gupyz[i] * chiy[i] * chiz[i] );
+                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
            #if (GAUGE == 2)
            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
@@ -1031,12 +1070,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
            dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
            #elif (GAUGE == 4 || GAUGE == 5)
            reta[i] =
-                gupxx[i] * chix[i] * chix[i]
+                gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
-                + gupyy[i] * chiy[i] * chiy[i]
+                + gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
-                + gupzz[i] * chiz[i] * chiz[i]
+                + gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
-                + TWO * ( gupxy[i] * chix[i] * chiy[i]
+                + TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
-                        + gupxz[i] * chix[i] * chiz[i]
+                        + gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
-                        + gupyz[i] * chiy[i] * chiz[i] );
+                        + gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
            #if (GAUGE == 4)
            reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
@@ -1061,31 +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
+        // 26ms //
-        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
+        lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA);
-        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
+        lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS);
-        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
+        lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA);
-        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
+        lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS);
-        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
+        lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS);
-        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
+        lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA);
-        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
+        lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA);
-        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
+        lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS);
-        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
+        lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS);
-        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
+        lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS);
-        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
+        lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA);
-        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
+        lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA);
-        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
+        lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA);
-        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
+        lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS);
-        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
+        lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS);
-        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
+        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) {
@@ -1138,59 +1204,59 @@ 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) {
+        // 7ms //
-                gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
+        for (int i=0;i<all;i+=1) {
-                                      + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
+            gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
-                gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                  + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
-                                      + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
+            gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-                gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                  + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
-                                      + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
+            gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-                gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
+                                  + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
-                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
+            gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
-                gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
+                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
-                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
+            gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
-                gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
+                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
-                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
+            gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
-                gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
-                                      + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
+            gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-                gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
+                                  + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
-                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
+            gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
-                gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
-                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
+            gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-                gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
+                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
-                                      + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
+            gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
-                gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                  + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
-                                      + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
+            gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-                gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
+                                  + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
-                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
+            gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
-                gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
-                                      + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
+            gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-                gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                  + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
-                                      + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
+            gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-                gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
+                                  + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
-                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
+            gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
-                gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
-                                      + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
+            gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-                gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
+                                  + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
-                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
+            gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
-                gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
+                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
-                                      + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
+            gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
                                  + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
-                movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
+            movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
-                            + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
+                        + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
-                            + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
+                        + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
-                movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
+            movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
-                            + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
+                        + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
-                            + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
+                        + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
-                movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
+            movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
-                            + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
+                        + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
-                            + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
+                        + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
-                movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
+            movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
-                movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
+            movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
-                movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+            movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
            }
        }
--- 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：
+     * Fortran loops:
-     * 1) 先在二阶可用区域计算二阶模板
+     * do k=1,ex3-1
-     * 2) 再在高阶可用区域覆盖为四阶模板
+     * 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;
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-    const int j2_lo = (jminF > 0) ? jminF : 0;
+        const int kF = k0 + 1;
-    const int k2_lo = (kminF > 0) ? kminF : 0;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-    const int i2_hi = ex1 - 2;
+            const int jF = j0 + 1;
-    const int j2_hi = ex2 - 2;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-    const int k2_hi = ex3 - 2;
+                const int iF = i0 + 1;
-
+                const size_t p = idx_ex(i0, j0, k0, ex);
    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
    const int i4_hi = ex1 - 3;
    const int j4_hi = ex2 - 3;
    const int k4_hi = ex3 - 3;
    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
            const int kF = k0 + 1;
            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
                const int jF = j0 + 1;
                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
                    const int iF = i0 + 1;
                    const size_t p = idx_ex(i0, j0, k0, ex);
                    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) {
                    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
+    for (int k0 = 0; k0 < ex3; ++k0) {
    // 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) {
        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）
@@ -109,6 +100,7 @@ void kodis(const int ex[3],
                    // Fortran:
                    // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
                    f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
                }
            }
        }
    }
--- 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) \
+## opt (default): maximum performance with PGO profile data
 ## PGO has been turned off, now tested and found to be negative optimization
 ## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
              -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 $@
@@ -61,9 +63,6 @@ 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
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
@@ -87,12 +86,16 @@ ifeq ($(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)
+ABE: $(C++FILES) $(CFILES_CUDA) $(F90FILES) $(F77FILES) $(AHFDOBJS)
-	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES) $(CFILES) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(LDLIBS)
+	$(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