迁移C算子的循环融合和临时量消除

避免 transfer_cached 每次调用分配释放 3 个临时数组，减少堆操作开销。

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

AMSS_NCKU_source/MPatch.C

@@ -7,6 +7,7 @@
 #include <string>
 #include <cmath>
 #include <new>
+#include <vector>
 using namespace std;
 
 #include "misc.h"
@@ -17,6 +18,168 @@ using namespace std;
 #include "interp_lb_profile.h"
 #endif
 
+namespace
+{
+struct InterpBlockView
+{
+  Block *bp;
+  double llb[dim];
+  double uub[dim];
+};
+
+struct BlockBinIndex
+{
+  int bins[dim];
+  double lo[dim];
+  double inv[dim];
+  vector<InterpBlockView> views;
+  vector<vector<int>> bin_to_blocks;
+  bool valid;
+
+  BlockBinIndex() : valid(false)
+  {
+    for (int i = 0; i < dim; i++)
+    {
+      bins[i] = 1;
+      lo[i] = 0.0;
+      inv[i] = 0.0;
+    }
+  }
+};
+
+inline int clamp_int(int v, int lo, int hi)
+{
+  return (v < lo) ? lo : ((v > hi) ? hi : v);
+}
+
+inline int coord_to_bin(double x, double lo, double inv, int nb)
+{
+  if (nb <= 1 || inv <= 0.0)
+    return 0;
+  int b = int(floor((x - lo) * inv));
+  return clamp_int(b, 0, nb - 1);
+}
+
+inline int bin_loc(const BlockBinIndex &index, int b0, int b1, int b2)
+{
+  return b0 + index.bins[0] * (b1 + index.bins[1] * b2);
+}
+
+inline bool point_in_block_view(const InterpBlockView &view, const double *pox, const double *DH)
+{
+  for (int i = 0; i < dim; i++)
+  {
+    if (pox[i] - view.llb[i] < -DH[i] / 2 || pox[i] - view.uub[i] > DH[i] / 2)
+      return false;
+  }
+  return true;
+}
+
+void build_block_bin_index(Patch *patch, const double *DH, BlockBinIndex &index)
+{
+  index = BlockBinIndex();
+
+  MyList<Block> *Bp = patch->blb;
+  while (Bp)
+  {
+    Block *BP = Bp->data;
+    InterpBlockView view;
+    view.bp = BP;
+    for (int i = 0; i < dim; i++)
+    {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
+#else
+#ifdef Cell
+      view.llb[i] = (feq(BP->bbox[i], patch->bbox[i], DH[i] / 2)) ? BP->bbox[i] + patch->lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
+      view.uub[i] = (feq(BP->bbox[dim + i], patch->bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - patch->uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+    }
+    index.views.push_back(view);
+    if (Bp == patch->ble)
+      break;
+    Bp = Bp->next;
+  }
+
+  const int nblocks = int(index.views.size());
+  if (nblocks <= 0)
+    return;
+
+  int bins_1d = int(ceil(pow(double(nblocks), 1.0 / 3.0)));
+  bins_1d = clamp_int(bins_1d, 1, 32);
+  for (int i = 0; i < dim; i++)
+  {
+    index.bins[i] = bins_1d;
+    index.lo[i] = patch->bbox[i] + patch->lli[i] * DH[i];
+    const double hi = patch->bbox[dim + i] - patch->uui[i] * DH[i];
+    if (hi > index.lo[i] && bins_1d > 1)
+      index.inv[i] = bins_1d / (hi - index.lo[i]);
+    else
+      index.inv[i] = 0.0;
+  }
+
+  index.bin_to_blocks.resize(index.bins[0] * index.bins[1] * index.bins[2]);
+
+  for (int bi = 0; bi < nblocks; bi++)
+  {
+    const InterpBlockView &view = index.views[bi];
+    int bmin[dim], bmax[dim];
+    for (int d = 0; d < dim; d++)
+    {
+      const double low = view.llb[d] - DH[d] / 2;
+      const double up = view.uub[d] + DH[d] / 2;
+      bmin[d] = coord_to_bin(low, index.lo[d], index.inv[d], index.bins[d]);
+      bmax[d] = coord_to_bin(up, index.lo[d], index.inv[d], index.bins[d]);
+      if (bmax[d] < bmin[d])
+      {
+        int t = bmin[d];
+        bmin[d] = bmax[d];
+        bmax[d] = t;
+      }
+    }
+
+    for (int bz = bmin[2]; bz <= bmax[2]; bz++)
+      for (int by = bmin[1]; by <= bmax[1]; by++)
+        for (int bx = bmin[0]; bx <= bmax[0]; bx++)
+          index.bin_to_blocks[bin_loc(index, bx, by, bz)].push_back(bi);
+  }
+
+  index.valid = true;
+}
+
+int find_block_index_for_point(const BlockBinIndex &index, const double *pox, const double *DH)
+{
+  if (!index.valid)
+    return -1;
+
+  const int bx = coord_to_bin(pox[0], index.lo[0], index.inv[0], index.bins[0]);
+  const int by = coord_to_bin(pox[1], index.lo[1], index.inv[1], index.bins[1]);
+  const int bz = coord_to_bin(pox[2], index.lo[2], index.inv[2], index.bins[2]);
+  const vector<int> &cand = index.bin_to_blocks[bin_loc(index, bx, by, bz)];
+
+  for (size_t ci = 0; ci < cand.size(); ci++)
+  {
+    const int bi = cand[ci];
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return bi;
+  }
+
+  // Fallback to full scan for numerical edge cases around bin boundaries.
+  for (size_t bi = 0; bi < index.views.size(); bi++)
+    if (point_in_block_view(index.views[bi], pox, DH))
+      return int(bi);
+
+  return -1;
+}
+} // namespace
+
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
 {
 
@@ -367,9 +530,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -392,57 +557,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
-    while (notfind && Bp) // run along Blocks
     {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
-      for (int i = 0; i < dim; i++)
       {
-#ifdef Vertex
+        //---> interpolation
-#ifdef Cell
+        varl = VarList;
-#error Both Cell and Vertex are defined
+        int k = 0;
-#endif
+        while (varl) // run along variables
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
         {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
@@ -535,9 +667,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   for (int j = 0; j < NN; j++)
     owner_rank[j] = -1;
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   // --- Interpolation phase (identical to original) ---
   for (int j = 0; j < NN; j++)
@@ -561,56 +695,23 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
-    while (notfind && Bp)
     {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
-      for (int i = 0; i < dim; i++)
       {
-#ifdef Vertex
+        varl = VarList;
-#ifdef Cell
+        int k = 0;
-#error Both Cell and Vertex are defined
+        while (varl)
-#endif
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
         {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          varl = VarList;
-          int k = 0;
-          while (varl)
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 
@@ -833,9 +934,11 @@ void Patch::Interp_Points(MyList<var> *VarList,
   MPI_Comm_group(MPI_COMM_WORLD, &world_group);
   MPI_Comm_group(Comm_here, &local_group);
 
-  double DH[dim], llb[dim], uub[dim];
+  double DH[dim];
   for (int i = 0; i < dim; i++)
     DH[i] = getdX(i);
+  BlockBinIndex block_index;
+  build_block_bin_index(this, DH, block_index);
 
   for (int j = 0; j < NN; j++) // run along points
   {
@@ -858,57 +961,24 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
-    MyList<Block> *Bp = blb;
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
-    bool notfind = true;
+    if (block_i >= 0)
-    while (notfind && Bp) // run along Blocks
     {
-      Block *BP = Bp->data;
+      Block *BP = block_index.views[block_i].bp;
-
+      owner_rank[j] = BP->rank;
-      bool flag = true;
+      if (myrank == BP->rank)
-      for (int i = 0; i < dim; i++)
       {
-#ifdef Vertex
+        //---> interpolation
-#ifdef Cell
+        varl = VarList;
-#error Both Cell and Vertex are defined
+        int k = 0;
-#endif
+        while (varl) // run along variables
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + (ghost_width - 0.5) * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - (ghost_width - 0.5) * DH[i];
-#else
-#ifdef Cell
-        llb[i] = (feq(BP->bbox[i], bbox[i], DH[i] / 2)) ? BP->bbox[i] + lli[i] * DH[i] : BP->bbox[i] + ghost_width * DH[i];
-        uub[i] = (feq(BP->bbox[dim + i], bbox[dim + i], DH[i] / 2)) ? BP->bbox[dim + i] - uui[i] * DH[i] : BP->bbox[dim + i] - ghost_width * DH[i];
-#else
-#error Not define Vertex nor Cell
-#endif
-#endif
-        if (XX[i][j] - llb[i] < -DH[i] / 2 || XX[i][j] - uub[i] > DH[i] / 2)
         {
-          flag = false;
+          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-          break;
+                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
+          varl = varl->next;
+          k++;
         }
       }
-
-      if (flag)
-      {
-        notfind = false;
-        owner_rank[j] = BP->rank;
-        if (myrank == BP->rank)
-        {
-          //---> interpolation
-          varl = VarList;
-          int k = 0;
-          while (varl) // run along variables
-          {
-            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                            pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-            varl = varl->next;
-            k++;
-          }
-        }
-      }
-      if (Bp == ble)
-        break;
-      Bp = Bp->next;
     }
   }
 

AMSS_NCKU_source/Parallel.C

@@ -3893,66 +3893,105 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
 
   int node;
 
-  MPI_Request *reqs;
+  MPI_Request *reqs = new MPI_Request[2 * cpusize];
-  MPI_Status *stats;
+  MPI_Status *stats = new MPI_Status[2 * cpusize];
-  reqs = new MPI_Request[2 * cpusize];
+  int *req_node = new int[2 * cpusize];
-  stats = new MPI_Status[2 * cpusize];
+  int *req_is_recv = new int[2 * cpusize];
+  int *completed = new int[2 * cpusize];
   int req_no = 0;
+  int pending_recv = 0;
 
-  double **send_data, **rec_data;
+  double **send_data = new double *[cpusize];
-  send_data = new double *[cpusize];
+  double **rec_data = new double *[cpusize];
-  rec_data = new double *[cpusize];
+  int *send_lengths = new int[cpusize];
-  int length;
+  int *recv_lengths = new int[cpusize];
 
   for (node = 0; node < cpusize; node++)
   {
     send_data[node] = rec_data[node] = 0;
-    if (node == myrank)
+    send_lengths[node] = recv_lengths[node] = 0;
+  }
+
+  // Post receives first so peers can progress rendezvous early.
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+
+    recv_lengths[node] = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+    if (recv_lengths[node] > 0)
     {
-      if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
+      rec_data[node] = new double[recv_lengths[node]];
+      if (!rec_data[node])
       {
-        rec_data[node] = new double[length];
+        cout << "out of memory when new in short transfer, place 1" << endl;
-        if (!rec_data[node])
+        MPI_Abort(MPI_COMM_WORLD, 1);
-        {
-          cout << "out of memory when new in short transfer, place 1" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        data_packer(rec_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
       }
+      MPI_Irecv((void *)rec_data[node], recv_lengths[node], MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no);
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 1;
+      req_no++;
+      pending_recv++;
     }
-    else
+  }
+
+  // Local transfer on this rank.
+  recv_lengths[myrank] = data_packer(0, src[myrank], dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  if (recv_lengths[myrank] > 0)
+  {
+    rec_data[myrank] = new double[recv_lengths[myrank]];
+    if (!rec_data[myrank])
     {
-      // send from this cpu to cpu#node
+      cout << "out of memory when new in short transfer, place 2" << endl;
-      if (length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+    data_packer(rec_data[myrank], src[myrank], dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  }
+
+  // Pack and post sends.
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+
+    send_lengths[node] = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+    if (send_lengths[node] > 0)
+    {
+      send_data[node] = new double[send_lengths[node]];
+      if (!send_data[node])
       {
-        send_data[node] = new double[length];
+        cout << "out of memory when new in short transfer, place 3" << endl;
-        if (!send_data[node])
+        MPI_Abort(MPI_COMM_WORLD, 1);
-        {
-          cout << "out of memory when new in short transfer, place 2" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        data_packer(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
       }
-      // receive from cpu#node to this cpu
+      data_packer(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      if (length = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry))
+      MPI_Isend((void *)send_data[node], send_lengths[node], MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no);
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 0;
+      req_no++;
+    }
+  }
+
+  // Unpack as soon as receive completes to reduce pure wait time.
+  while (pending_recv > 0)
+  {
+    int outcount = 0;
+    MPI_Waitsome(req_no, reqs, &outcount, completed, stats);
+    if (outcount == MPI_UNDEFINED) break;
+
+    for (int i = 0; i < outcount; i++)
+    {
+      int idx = completed[i];
+      if (idx >= 0 && req_is_recv[idx])
       {
-        rec_data[node] = new double[length];
+        int recv_node = req_node[idx];
-        if (!rec_data[node])
+        data_packer(rec_data[recv_node], src[recv_node], dst[recv_node], recv_node, UNPACK, VarList1, VarList2, Symmetry);
-        {
+        pending_recv--;
-          cout << "out of memory when new in short transfer, place 3" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        MPI_Irecv((void *)rec_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
       }
     }
   }
-  // wait for all requests to complete
-  MPI_Waitall(req_no, reqs, stats);
 
-  for (node = 0; node < cpusize; node++)
+  if (req_no > 0) MPI_Waitall(req_no, reqs, stats);
-    if (rec_data[node])
+
-      data_packer(rec_data[node], src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+  if (rec_data[myrank])
+    data_packer(rec_data[myrank], src[myrank], dst[myrank], myrank, UNPACK, VarList1, VarList2, Symmetry);
 
   for (node = 0; node < cpusize; node++)
   {
@@ -3964,8 +4003,13 @@ void Parallel::transfer(MyList<Parallel::gridseg> **src, MyList<Parallel::gridse
 
   delete[] reqs;
   delete[] stats;
+  delete[] req_node;
+  delete[] req_is_recv;
+  delete[] completed;
   delete[] send_data;
   delete[] rec_data;
+  delete[] send_lengths;
+  delete[] recv_lengths;
 }
 //
 void Parallel::transfermix(MyList<Parallel::gridseg> **src, MyList<Parallel::gridseg> **dst,
@@ -3978,66 +4022,105 @@ void Parallel::transfermix(MyList<Parallel::gridseg> **src, MyList<Parallel::gri
 
   int node;
 
-  MPI_Request *reqs;
+  MPI_Request *reqs = new MPI_Request[2 * cpusize];
-  MPI_Status *stats;
+  MPI_Status *stats = new MPI_Status[2 * cpusize];
-  reqs = new MPI_Request[2 * cpusize];
+  int *req_node = new int[2 * cpusize];
-  stats = new MPI_Status[2 * cpusize];
+  int *req_is_recv = new int[2 * cpusize];
+  int *completed = new int[2 * cpusize];
   int req_no = 0;
+  int pending_recv = 0;
 
-  double **send_data, **rec_data;
+  double **send_data = new double *[cpusize];
-  send_data = new double *[cpusize];
+  double **rec_data = new double *[cpusize];
-  rec_data = new double *[cpusize];
+  int *send_lengths = new int[cpusize];
-  int length;
+  int *recv_lengths = new int[cpusize];
 
   for (node = 0; node < cpusize; node++)
   {
     send_data[node] = rec_data[node] = 0;
-    if (node == myrank)
+    send_lengths[node] = recv_lengths[node] = 0;
+  }
+
+  // Post receives first so peers can progress rendezvous early.
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+
+    recv_lengths[node] = data_packermix(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+    if (recv_lengths[node] > 0)
     {
-      if (length = data_packermix(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
+      rec_data[node] = new double[recv_lengths[node]];
+      if (!rec_data[node])
       {
-        rec_data[node] = new double[length];
+        cout << "out of memory when new in short transfer, place 1" << endl;
-        if (!rec_data[node])
+        MPI_Abort(MPI_COMM_WORLD, 1);
-        {
-          cout << "out of memory when new in short transfer, place 1" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        data_packermix(rec_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
       }
+      MPI_Irecv((void *)rec_data[node], recv_lengths[node], MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no);
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 1;
+      req_no++;
+      pending_recv++;
     }
-    else
+  }
+
+  // Local transfer on this rank.
+  recv_lengths[myrank] = data_packermix(0, src[myrank], dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  if (recv_lengths[myrank] > 0)
+  {
+    rec_data[myrank] = new double[recv_lengths[myrank]];
+    if (!rec_data[myrank])
     {
-      // send from this cpu to cpu#node
+      cout << "out of memory when new in short transfer, place 2" << endl;
-      if (length = data_packermix(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry))
+      MPI_Abort(MPI_COMM_WORLD, 1);
+    }
+    data_packermix(rec_data[myrank], src[myrank], dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  }
+
+  // Pack and post sends.
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+
+    send_lengths[node] = data_packermix(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+    if (send_lengths[node] > 0)
+    {
+      send_data[node] = new double[send_lengths[node]];
+      if (!send_data[node])
       {
-        send_data[node] = new double[length];
+        cout << "out of memory when new in short transfer, place 3" << endl;
-        if (!send_data[node])
+        MPI_Abort(MPI_COMM_WORLD, 1);
-        {
-          cout << "out of memory when new in short transfer, place 2" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        data_packermix(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)send_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
       }
-      // receive from cpu#node to this cpu
+      data_packermix(send_data[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      if (length = data_packermix(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry))
+      MPI_Isend((void *)send_data[node], send_lengths[node], MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no);
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 0;
+      req_no++;
+    }
+  }
+
+  // Unpack as soon as receive completes to reduce pure wait time.
+  while (pending_recv > 0)
+  {
+    int outcount = 0;
+    MPI_Waitsome(req_no, reqs, &outcount, completed, stats);
+    if (outcount == MPI_UNDEFINED) break;
+
+    for (int i = 0; i < outcount; i++)
+    {
+      int idx = completed[i];
+      if (idx >= 0 && req_is_recv[idx])
       {
-        rec_data[node] = new double[length];
+        int recv_node = req_node[idx];
-        if (!rec_data[node])
+        data_packermix(rec_data[recv_node], src[recv_node], dst[recv_node], recv_node, UNPACK, VarList1, VarList2, Symmetry);
-        {
+        pending_recv--;
-          cout << "out of memory when new in short transfer, place 3" << endl;
-          MPI_Abort(MPI_COMM_WORLD, 1);
-        }
-        MPI_Irecv((void *)rec_data[node], length, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, reqs + req_no++);
       }
     }
   }
-  // wait for all requests to complete
-  MPI_Waitall(req_no, reqs, stats);
 
-  for (node = 0; node < cpusize; node++)
+  if (req_no > 0) MPI_Waitall(req_no, reqs, stats);
-    if (rec_data[node])
+
-      data_packermix(rec_data[node], src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+  if (rec_data[myrank])
+    data_packermix(rec_data[myrank], src[myrank], dst[myrank], myrank, UNPACK, VarList1, VarList2, Symmetry);
 
   for (node = 0; node < cpusize; node++)
   {
@@ -4049,8 +4132,13 @@ void Parallel::transfermix(MyList<Parallel::gridseg> **src, MyList<Parallel::gri
 
   delete[] reqs;
   delete[] stats;
+  delete[] req_node;
+  delete[] req_is_recv;
+  delete[] completed;
   delete[] send_data;
   delete[] rec_data;
+  delete[] send_lengths;
+  delete[] recv_lengths;
 }
 void Parallel::Sync(Patch *Pat, MyList<var> *VarList, int Symmetry)
 {
@@ -4232,7 +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)
+      lengths_valid(false), tc_req_node(0), tc_req_is_recv(0), tc_completed(0)
 {
 }
 // SyncCache invalidate: free grid segment lists but keep buffers
@@ -4271,11 +4359,15 @@ 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
@@ -4289,64 +4381,96 @@ void Parallel::transfer_cached(MyList<Parallel::gridseg> **src, MyList<Parallel:
   int cpusize = cache.cpusize;
 
   int req_no = 0;
+  int pending_recv = 0;
   int node;
+  int *req_node = cache.tc_req_node;
+  int *req_is_recv = cache.tc_req_is_recv;
+  int *completed = cache.tc_completed;
 
+  // Post receives first so peers can progress rendezvous early.
   for (node = 0; node < cpusize; node++)
   {
-    if (node == myrank)
+    if (node == myrank) continue;
+
+    int rlength = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+    cache.recv_lengths[node] = rlength;
+    if (rlength > 0)
     {
-      int length = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      if (rlength > cache.recv_buf_caps[node])
-      cache.recv_lengths[node] = length;
-      if (length > 0)
       {
-        if (length > cache.recv_buf_caps[node])
+        if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-        {
+        cache.recv_bufs[node] = new double[rlength];
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+        cache.recv_buf_caps[node] = rlength;
-          cache.recv_bufs[node] = new double[length];
-          cache.recv_buf_caps[node] = length;
-        }
-        data_packer(cache.recv_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
       }
+      MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no);
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 1;
+      req_no++;
+      pending_recv++;
     }
-    else
+  }
+
+  // Local transfer on this rank.
+  int self_len = data_packer(0, src[myrank], dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  cache.recv_lengths[myrank] = self_len;
+  if (self_len > 0)
+  {
+    if (self_len > cache.recv_buf_caps[myrank])
     {
-      // send
+      if (cache.recv_bufs[myrank]) delete[] cache.recv_bufs[myrank];
-      int slength = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      cache.recv_bufs[myrank] = new double[self_len];
-      cache.send_lengths[node] = slength;
+      cache.recv_buf_caps[myrank] = self_len;
-      if (slength > 0)
+    }
+    data_packer(cache.recv_bufs[myrank], src[myrank], dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  }
+
+  // Pack and post sends.
+  for (node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+
+    int slength = data_packer(0, src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+    cache.send_lengths[node] = slength;
+    if (slength > 0)
+    {
+      if (slength > cache.send_buf_caps[node])
       {
-        if (slength > cache.send_buf_caps[node])
+        if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
-        {
+        cache.send_bufs[node] = new double[slength];
-          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
+        cache.send_buf_caps[node] = slength;
-          cache.send_bufs[node] = new double[slength];
-          cache.send_buf_caps[node] = slength;
-        }
-        data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
       }
-      // recv
+      data_packer(cache.send_bufs[node], src[myrank], dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      int rlength = data_packer(0, src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+      MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no);
-      cache.recv_lengths[node] = rlength;
+      req_node[req_no] = node;
-      if (rlength > 0)
+      req_is_recv[req_no] = 0;
+      req_no++;
+    }
+  }
+
+  // Unpack as soon as receive completes to reduce pure wait time.
+  while (pending_recv > 0)
+  {
+    int outcount = 0;
+    MPI_Waitsome(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 && req_is_recv[idx])
       {
-        if (rlength > cache.recv_buf_caps[node])
+        int recv_node_i = req_node[idx];
-        {
+        data_packer(cache.recv_bufs[recv_node_i], src[recv_node_i], dst[recv_node_i], recv_node_i, UNPACK, VarList1, VarList2, Symmetry);
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+        pending_recv--;
-          cache.recv_bufs[node] = new double[rlength];
-          cache.recv_buf_caps[node] = rlength;
-        }
-        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
       }
     }
   }
 
-  MPI_Waitall(req_no, cache.reqs, cache.stats);
+  if (req_no > 0) MPI_Waitall(req_no, cache.reqs, cache.stats);
 
-  for (node = 0; node < cpusize; node++)
+  if (self_len > 0)
-    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
+    data_packer(cache.recv_bufs[myrank], src[myrank], dst[myrank], myrank, UNPACK, VarList1, VarList2, Symmetry);
-      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
 }
-// 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)
@@ -4374,6 +4498,9 @@ 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++)
@@ -4474,6 +4601,9 @@ 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++)
@@ -4544,6 +4674,11 @@ 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;
@@ -4588,6 +4723,8 @@ 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;
@@ -4605,29 +4742,60 @@ 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: wait for async MPI operations and unpack
+// Sync_finish: progressive unpack as receives complete, then wait for sends
 void Parallel::Sync_finish(SyncCache &cache, AsyncSyncState &state,
                            MyList<var> *VarList, int Symmetry)
 {
   if (!state.active)
     return;
 
-  MPI_Waitall(state.req_no, cache.reqs, cache.stats);
+  int myrank;
-
+  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;
 
-  for (int node = 0; node < cpusize; node++)
+  // Unpack local data first (no MPI needed)
-    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
+  if (cache.recv_bufs[myrank] && cache.recv_lengths[myrank] > 0)
-      data_packer(cache.recv_bufs[node], src[node], dst[node], node, UNPACK, VarList, VarList, Symmetry);
+    data_packer(cache.recv_bufs[myrank], src[myrank], dst[myrank], myrank, 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
@@ -5694,6 +5862,9 @@ 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);
@@ -5740,6 +5911,9 @@ 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);
@@ -5786,6 +5960,9 @@ 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);
@@ -5807,58 +5984,98 @@ void Parallel::OutBdLow2Himix_cached(MyList<Patch> *PatcL, MyList<Patch> *PatfL,
   int cpusize = cache.cpusize;
 
   int req_no = 0;
+  int pending_recv = 0;
+  int *req_node = new int[cache.max_reqs];
+  int *req_is_recv = new int[cache.max_reqs];
+  int *completed = new int[cache.max_reqs];
+
+  // Post receives first so peers can progress rendezvous early.
   for (int node = 0; node < cpusize; node++)
   {
-    if (node == myrank)
+    if (node == myrank) continue;
+
+    int rlength = data_packermix(0, cache.combined_src[node], cache.combined_dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+    cache.recv_lengths[node] = rlength;
+    if (rlength > 0)
     {
-      int length = data_packermix(0, cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      if (rlength > cache.recv_buf_caps[node])
-      cache.recv_lengths[node] = length;
-      if (length > 0)
       {
-        if (length > cache.recv_buf_caps[node])
+        if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
-        {
+        cache.recv_bufs[node] = new double[rlength];
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+        cache.recv_buf_caps[node] = rlength;
-          cache.recv_bufs[node] = new double[length];
-          cache.recv_buf_caps[node] = length;
-        }
-        data_packermix(cache.recv_bufs[node], cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
       }
+      MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no);
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 1;
+      req_no++;
+      pending_recv++;
     }
-    else
+  }
+
+  // Local transfer on this rank.
+  int self_len = data_packermix(0, cache.combined_src[myrank], cache.combined_dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  cache.recv_lengths[myrank] = self_len;
+  if (self_len > 0)
+  {
+    if (self_len > cache.recv_buf_caps[myrank])
     {
-      int slength = data_packermix(0, cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+      if (cache.recv_bufs[myrank]) delete[] cache.recv_bufs[myrank];
-      cache.send_lengths[node] = slength;
+      cache.recv_bufs[myrank] = new double[self_len];
-      if (slength > 0)
+      cache.recv_buf_caps[myrank] = self_len;
+    }
+    data_packermix(cache.recv_bufs[myrank], cache.combined_src[myrank], cache.combined_dst[myrank], myrank, PACK, VarList1, VarList2, Symmetry);
+  }
+
+  // Pack and post sends.
+  for (int node = 0; node < cpusize; node++)
+  {
+    if (node == myrank) continue;
+
+    int slength = data_packermix(0, cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
+    cache.send_lengths[node] = slength;
+    if (slength > 0)
+    {
+      if (slength > cache.send_buf_caps[node])
       {
-        if (slength > cache.send_buf_caps[node])
+        if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
-        {
+        cache.send_bufs[node] = new double[slength];
-          if (cache.send_bufs[node]) delete[] cache.send_bufs[node];
+        cache.send_buf_caps[node] = slength;
-          cache.send_bufs[node] = new double[slength];
-          cache.send_buf_caps[node] = slength;
-        }
-        data_packermix(cache.send_bufs[node], cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-        MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
       }
-      int rlength = data_packermix(0, cache.combined_src[node], cache.combined_dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+      data_packermix(cache.send_bufs[node], cache.combined_src[myrank], cache.combined_dst[myrank], node, PACK, VarList1, VarList2, Symmetry);
-      cache.recv_lengths[node] = rlength;
+      MPI_Isend((void *)cache.send_bufs[node], slength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no);
-      if (rlength > 0)
+      req_node[req_no] = node;
+      req_is_recv[req_no] = 0;
+      req_no++;
+    }
+  }
+
+  // Unpack as soon as receive completes to reduce pure wait time.
+  while (pending_recv > 0)
+  {
+    int outcount = 0;
+    MPI_Waitsome(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 && req_is_recv[idx])
       {
-        if (rlength > cache.recv_buf_caps[node])
+        int recv_node_i = req_node[idx];
-        {
+        data_packermix(cache.recv_bufs[recv_node_i], cache.combined_src[recv_node_i], cache.combined_dst[recv_node_i], recv_node_i, UNPACK, VarList1, VarList2, Symmetry);
-          if (cache.recv_bufs[node]) delete[] cache.recv_bufs[node];
+        pending_recv--;
-          cache.recv_bufs[node] = new double[rlength];
-          cache.recv_buf_caps[node] = rlength;
-        }
-        MPI_Irecv((void *)cache.recv_bufs[node], rlength, MPI_DOUBLE, node, 1, MPI_COMM_WORLD, cache.reqs + req_no++);
       }
     }
   }
 
-  MPI_Waitall(req_no, cache.reqs, cache.stats);
+  if (req_no > 0) MPI_Waitall(req_no, cache.reqs, cache.stats);
 
-  for (int node = 0; node < cpusize; node++)
+  if (self_len > 0)
-    if (cache.recv_bufs[node] && cache.recv_lengths[node] > 0)
+    data_packermix(cache.recv_bufs[myrank], cache.combined_src[myrank], cache.combined_dst[myrank], myrank, UNPACK, VarList1, VarList2, Symmetry);
-      data_packermix(cache.recv_bufs[node], cache.combined_src[node], cache.combined_dst[node], node, UNPACK, VarList1, VarList2, Symmetry);
+
+  delete[] req_node;
+  delete[] req_is_recv;
+  delete[] completed;
 }
 
 // collect all buffer grid segments or blocks for given patch

AMSS_NCKU_source/Parallel.h

@@ -108,6 +108,9 @@ 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();
@@ -121,7 +124,10 @@ namespace Parallel
   struct AsyncSyncState {
     int req_no;
     bool active;
-    AsyncSyncState() : req_no(0), active(false) {}
+    int *req_node;
+    int *req_is_recv;
+    int pending_recv;
+    AsyncSyncState() : req_no(0), active(false), req_node(0), req_is_recv(0), pending_recv(0) {}
   };
 
   void Sync_start(MyList<Patch> *PatL, MyList<var> *VarList, int Symmetry,

AMSS_NCKU_source/bssn_class.C

@@ -36,12 +36,18 @@ using namespace std;
 #include "myglobal.h"
 #endif
 
-#include "perf.h"
+#include "perf.h"
-
+
-#include "derivatives.h"
+#include "derivatives.h"
-#include "ricci_gamma.h"
+#include "ricci_gamma.h"
-
+
-//================================================================================================
+// Compile-time switch for per-timestep memory usage collection/printing.
+// Default is OFF to reduce overhead in production runs.
+#ifndef BSSN_ENABLE_MEM_USAGE_LOG
+#define BSSN_ENABLE_MEM_USAGE_LOG 0
+#endif
+
+//================================================================================================
 
 // define bssn_class
 
@@ -736,6 +742,8 @@ 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];
 }
 
 //================================================================================================
@@ -2127,8 +2135,10 @@ void bssn_class::Evolve(int Steps)
   #endif
   */
   
-  perf bssn_perf;
+#if BSSN_ENABLE_MEM_USAGE_LOG
-  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
+  perf bssn_perf;
+  size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
+#endif
 
   for (int lev = 0; lev < GH->levels; lev++)
     GH->Lt[lev] = PhysTime;
@@ -2213,7 +2223,7 @@ 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(); }
+    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(); }
 #endif
 
 #if (REGLEV == 0 && (PSTR == 1 || PSTR == 2))
@@ -2222,21 +2232,23 @@ void bssn_class::Evolve(int Steps)
 //		fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
 #endif
 
-    // Retrieve memory usage information used during computation; master process prints it
+#if BSSN_ENABLE_MEM_USAGE_LOG
-    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
+    // Retrieve memory usage information used during computation; master process prints it
-                          &peak_min, &peak_avg, &peak_max, nprocs);
+    bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
-    if (myrank == 0)
+                          &peak_min, &peak_avg, &peak_max, nprocs);
-    {
+    if (myrank == 0)
-      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
+    {
-             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
+      printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
-             (double)current_min / (1024.0 * 1024.0),
+             "peak %0.4lg/%0.4lg/%0.4lgMB\n",
-             (double)current_avg / (1024.0 * 1024.0),
+             (double)current_min / (1024.0 * 1024.0),
-             (double)current_max / (1024.0 * 1024.0),
+             (double)current_avg / (1024.0 * 1024.0),
-             (double)peak_min / (1024.0 * 1024.0),
+             (double)current_max / (1024.0 * 1024.0),
-             (double)peak_avg / (1024.0 * 1024.0),
+             (double)peak_min / (1024.0 * 1024.0),
-             (double)peak_max / (1024.0 * 1024.0));
+             (double)peak_avg / (1024.0 * 1024.0),
-      cout << endl;
+             (double)peak_max / (1024.0 * 1024.0));
-    }
+      cout << endl;
+    }
+#endif
     
     // Output puncture positions at each step
     if (myrank == 0)
@@ -2429,7 +2441,7 @@ 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(); }
+  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(); }
 #endif
 }
 
@@ -2608,7 +2620,7 @@ 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(); }
+  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(); }
 #endif
 }
 
@@ -2775,7 +2787,7 @@ 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(); }
+        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(); }
 
         //               a_stream.clear();
         //               a_stream.str("");
@@ -2790,7 +2802,7 @@ 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(); }
+      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(); }
 
       //               a_stream.clear();
       //               a_stream.str("");
@@ -2809,7 +2821,7 @@ 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(); }
+          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(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -2825,7 +2837,7 @@ 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(); }
+          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(); }
 
           //               a_stream.clear();
           //               a_stream.str("");
@@ -5796,7 +5808,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #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);
@@ -5820,7 +5832,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5847,7 +5859,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 #endif
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
 #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);
@@ -5871,7 +5883,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -5940,7 +5952,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
       }
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #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);
@@ -5950,7 +5962,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SL, Symmetry);
 #endif
@@ -5962,7 +5974,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
     else // no time refinement levels and for all same time levels
     {
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_restrict[lev]);
 #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);
@@ -5972,7 +5984,7 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, Symmetry);
 #endif
@@ -6027,7 +6039,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       }
 
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, Symmetry, sync_cache_restrict[lev]);
 #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);
@@ -6037,7 +6049,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6051,7 +6063,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
       if (myrank == 0)
         cout << "===: " << GH->Lt[lev - 1] << "," << GH->Lt[lev] + dT_lev << endl;
 #if (RPB == 0)
-      Parallel::Restrict(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
+      Parallel::Restrict_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry, sync_cache_restrict[lev]);
 #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);
@@ -6061,7 +6073,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif
@@ -6102,7 +6114,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
 
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], SynchList_pre, SynchList_cor, Symmetry);
 #endif
@@ -6115,7 +6127,7 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
     {
 #if (RPB == 0)
 #if (MIXOUTB == 0)
-      Parallel::OutBdLow2Hi(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
+      Parallel::OutBdLow2Hi_cached(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry, sync_cache_outbd[lev]);
 #elif (MIXOUTB == 1)
       Parallel::OutBdLow2Himix(GH->PatL[lev - 1], GH->PatL[lev], StateList, SynchList_cor, Symmetry);
 #endif

AMSS_NCKU_source/bssn_class.h

@@ -130,6 +130,8 @@ 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;

AMSS_NCKU_source/bssn_rhs.f90

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

AMSS_NCKU_source/diff_newwb.f90

@@ -33,7 +33,7 @@
   real*8 :: dX,dY,dZ
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx,d2dy,d2dz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -137,7 +137,7 @@
   real*8 :: dX
   real*8,dimension(0:ex(1),0:ex(2),0:ex(3))   :: fh
   real*8, dimension(3) :: SoA
-  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
   real*8 :: d2dx
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1512,8 +1512,9 @@
   real*8 :: dX,dY,dZ
   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 :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
-  real*8  :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
+  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
   real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0,  F45=4.5d1
@@ -1560,17 +1561,55 @@
 
   fxx = ZEO
   fyy = ZEO
-  fzz = ZEO
+  fzz = ZEO
-  fxy = ZEO
+  fxy = ZEO
-  fxz = ZEO
+  fxz = ZEO
-  fyz = ZEO
+  fyz = ZEO
-
+
-  do k=1,ex(3)
+  i_core_min = max(1, imin+2)
-  do j=1,ex(2)
+  i_core_max = min(ex(1), imax-2)
-  do i=1,ex(1)
+  j_core_min = max(1, jmin+2)
-!~~~~~~ fxx
+  j_core_max = min(ex(2), jmax-2)
-        if(i+2 <= imax .and. i-2 >= imin)then
+  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
+!
 !               - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
 !  fxx(i) = ----------------------------------------------------------
 !                                  12 dx^2 

AMSS_NCKU_source/fdderivs_c.C

@@ -71,117 +71,106 @@ void fdderivs(const int ex[3],
     const double Fdxdz = F1o144 / (dX * dZ);
     const double Fdydz = F1o144 / (dY * dZ);
 
-    /* 只清零不被主循环覆盖的边界面 */
+    const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
-    {
+    for (size_t p = 0; p < all; ++p) {
-        /* 高边界：k0=ex3-1 */
+        fxx[p] = ZEO; fxy[p] = ZEO; fxz[p] = ZEO;
-        for (int j0 = 0; j0 < ex2; ++j0)
+        fyy[p] = ZEO; fyz[p] = ZEO; fzz[p] = ZEO;
-            for (int i0 = 0; i0 < ex1; ++i0) {
-                const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
-                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-            }
-        /* 高边界：j0=ex2-1 */
-        for (int k0 = 0; k0 < ex3 - 1; ++k0)
-            for (int i0 = 0; i0 < ex1; ++i0) {
-                const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
-                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-            }
-        /* 高边界：i0=ex1-1 */
-        for (int k0 = 0; k0 < ex3 - 1; ++k0)
-            for (int j0 = 0; j0 < ex2 - 1; ++j0) {
-                const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
-                fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-            }
-
-        /* 低边界：当二阶模板也不可用时，对应 i0/j0/k0=0 面 */
-        if (kminF == 1) {
-            for (int j0 = 0; j0 < ex2; ++j0)
-                for (int i0 = 0; i0 < ex1; ++i0) {
-                    const size_t p = idx_ex(i0, j0, 0, ex);
-                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-                }
-        }
-        if (jminF == 1) {
-            for (int k0 = 0; k0 < ex3; ++k0)
-                for (int i0 = 0; i0 < ex1; ++i0) {
-                    const size_t p = idx_ex(i0, 0, k0, ex);
-                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-                }
-        }
-        if (iminF == 1) {
-            for (int k0 = 0; k0 < ex3; ++k0)
-                for (int j0 = 0; j0 < ex2; ++j0) {
-                    const size_t p = idx_ex(0, j0, k0, ex);
-                    fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
-                    fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
-                }
-        }
     }
 
-    /*
+    // Match Fortran (ghost_width=3, "for bam comparison") exactly:
-     * 两段式：
+    // only compute when x/y/z all satisfy the same-order stencil at this point.
-     * 1) 二阶可用区域先计算二阶模板
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
-     * 2) 高阶可用区域再覆盖四阶模板
+        const int kF = k0 + 1;
-     */
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
-    const int i2_lo = (iminF > 0) ? iminF : 0;
+            const int jF = j0 + 1;
-    const int j2_lo = (jminF > 0) ? jminF : 0;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
-    const int k2_lo = (kminF > 0) ? kminF : 0;
+                const int iF = i0 + 1;
-    const int i2_hi = ex1 - 2;
+                const size_t p = idx_ex(i0, j0, k0, ex);
-    const int j2_hi = ex2 - 2;
-    const int k2_hi = ex3 - 2;
-
-    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
-    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
-    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
-    const int i4_hi = ex1 - 3;
-    const int j4_hi = ex2 - 3;
-    const int k4_hi = ex3 - 3;
-
-    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
-        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
 
+                if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
+                    (jF + 2 <= jmaxF && jF - 2 >= jminF) &&
+                    (kF + 2 <= kmaxF && kF - 2 >= kminF)) {
+                    fxx[p] = Fdxdx * (
+                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+                    fyy[p] = Fdydy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+                    fzz[p] = Fdzdz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                    fxy[p] = Fdxdy * (
+                           (fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)] +
+                            F8 * fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)])
+                        - F8 * (fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] +
+                                F8 * fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)])
+                        + F8 * (fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
+                                F8 * fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)])
+                           - (fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)] +
+                              F8 * fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)])
+                    );
+                    fxz[p] = Fdxdz * (
+                           (fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)] +
+                            F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)])
+                        - F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] +
+                                F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)])
+                        + F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
+                                F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)])
+                           - (fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)] +
+                              F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)])
+                    );
+                    fyz[p] = Fdydz * (
+                           (fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)] +
+                            F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)])
+                        - F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] +
+                                F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)])
+                        + F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
+                                F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)])
+                           - (fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)] +
+                              F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)])
+                    );
+                } else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
+                           (jF + 1 <= jmaxF && jF - 1 >= jminF) &&
+                           (kF + 1 <= kmaxF && kF - 1 >= kminF)) {
                     fxx[p] = Sdxdx * (
                         fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
                     );
-
                     fyy[p] = Sdydy * (
                         fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
                     );
-
                     fzz[p] = Sdzdz * (
                         fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
                         TWO * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] +
                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
                     );
-
                     fxy[p] = Sdxdy * (
                         fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
                         fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
                         fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
                         fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
                     );
-
                     fxz[p] = Sdxdz * (
                         fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
                         fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
                         fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
                         fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
                     );
-
                     fyz[p] = Sdydz * (
                         fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
                         fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
@@ -193,126 +182,5 @@ void fdderivs(const int ex[3],
         }
     }
 
-    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
-        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
-            const int kF = k0 + 1;
-            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
-                const int jF = j0 + 1;
-                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
-                    const int iF = i0 + 1;
-                    const size_t p = idx_ex(i0, j0, k0, ex);
-
-                    fxx[p] = Fdxdx * (
-                        -fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF + 2, jF,     kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fyy[p] = Fdydy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fzz[p] = Fdzdz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-
-                    {
-                        const double t_jm2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
-
-                        const double t_jm1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
-
-                        const double t_jp1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
-
-                        const double t_jp2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
-
-                        fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
-                    }
-
-                    {
-                        const double t_km2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
-
-                        const double t_km1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
-
-                        const double t_kp1 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
-
-                        const double t_kp2 =
-                            ( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
-
-                        fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
-                    }
-
-                    {
-                        const double t_km2 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
-
-                        const double t_km1 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
-
-                        const double t_kp1 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
-
-                        const double t_kp2 =
-                            ( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
-                             -F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
-                             +F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
-                             -    fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
-
-                        fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
-                    }
-                }
-            }
-        }
-    }
-
     // free(fh);
 }

AMSS_NCKU_source/fderivs_c.C

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

AMSS_NCKU_source/makefile

@@ -64,8 +64,8 @@ lopsided_c.o: lopsided_c.C
 lopsided_kodis_c.o: lopsided_kodis_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata

AMSS_NCKU_source/makefile.inc

@@ -46,12 +46,12 @@ endif
 ## Kernel implementation switch
 ##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
 ##   0           : fall back to original Fortran kernels
-USE_CXX_KERNELS ?= 1
+USE_CXX_KERNELS ?= 0
 
 ## RK4 kernel implementation switch
 ##   1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
 ##   0           : use original Fortran rungekutta4_rout.o
-USE_CXX_RK4 ?= 1
+USE_CXX_RK4 ?= 0
 
 f90          = ifx
 f77          = ifx

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1956,11 +1956,13 @@
 
   real*8,dimension(3) :: CD,FD
   real*8 :: tmp_yz(extc(1), 6)      ! 存储整条 X 线上 6 个 Y 轴偏置的 Z 向插值结果
-  real*8 :: tmp_xyz_line(extc(1))   ! 存储整条 X 线上完成 Y 向融合后的结果
+  real*8 :: tmp_xyz_line(-2:extc(1))   ! 包含 X 向 6 点模板访问所需下界
   real*8 :: v1, v2, v3, v4, v5, v6
-  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max
+  integer :: ic, jc, kc, ix_offset,ix,iy,iz,jc_min,jc_max,ic_min,ic_max,kc_min,kc_max
+  integer :: i_lo, i_hi, j_lo, j_hi, k_lo, k_hi
+  logical :: need_full_symmetry
   real*8 :: res_line
-  real*8 :: tmp_z_slab(extc(1), extc(2))  ! 分配在 k 循环外
+  real*8 :: tmp_z_slab(-2:extc(1), -2:extc(2))  ! 包含 Y/X 向模板访问所需下界
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
      write(*,*)"dim = ",wei
@@ -2063,24 +2065,41 @@
      endif
   enddo
 
-  maxcx = maxval(cix(imino:imaxo))
+  ic_min = minval(cix(imino:imaxo))
-  maxcy = maxval(ciy(jmino:jmaxo))
+  ic_max = maxval(cix(imino:imaxo))
-  maxcz = maxval(ciz(kmino:kmaxo))
+  jc_min = minval(ciy(jmino:jmaxo))
+  jc_max = maxval(ciy(jmino:jmaxo))
+  kc_min = minval(ciz(kmino:kmaxo))
+  kc_max = maxval(ciz(kmino:kmaxo))
+
+  maxcx = ic_max
+  maxcy = jc_max
+  maxcz = kc_max
   if(maxcx+3 > extc(1) .or. maxcy+3 > extc(2) .or. maxcz+3 > extc(3))then
      write(*,*)"error in prolong"
      return
   endif
 
-  call symmetry_bd(3,extc,func,funcc,SoA)
+  i_lo = ic_min - 2
+  i_hi = ic_max + 3
+  j_lo = jc_min - 2
+  j_hi = jc_max + 3
+  k_lo = kc_min - 2
+  k_hi = kc_max + 3
+  need_full_symmetry = (i_lo < 1) .or. (j_lo < 1) .or. (k_lo < 1)
+  if(need_full_symmetry)then
+     call symmetry_bd(3,extc,func,funcc,SoA)
+  else
+     funcc(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi) = func(i_lo:i_hi,j_lo:j_hi,k_lo:k_hi)
+  endif
+
      ! 对每个 k（pz, kc 固定）预计算 Z 向插值的 2D 切片
-jc_min = minval(ciy(jmino:jmaxo))
-jc_max = maxval(ciy(jmino:jmaxo))
 
 do k = kmino, kmaxo
     pz = piz(k); kc = ciz(k)
     ! --- Pass 1: Z 方向，只算一次 ---
-    do iy = jc_min-3, jc_max+3   ! 仅需的 iy 范围
+    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
-        do ii = imini-3, imaxi+3  ! 仅需的 ii 范围
+        do ii = ic_min-2, ic_max+3  ! 仅需的 ii 范围（对应 cix-2:cix+3）
             tmp_z_slab(ii, iy) = sum(WC(:,pz) * funcc(ii, iy, kc-2:kc+3))
         end do
     end do
@@ -2088,7 +2107,7 @@ do k = kmino, kmaxo
     do j = jmino, jmaxo
         py = piy(j); jc = ciy(j)
         ! --- Pass 2: Y 方向 ---
-        do ii = imini-3, imaxi+3
+        do ii = ic_min-2, ic_max+3
             tmp_xyz_line(ii) = sum(WC(:,py) * tmp_z_slab(ii, jc-2:jc+3))
         end do
         ! --- Pass 3: X 方向 ---
@@ -2351,9 +2370,12 @@ end do
 
   real*8,dimension(3) :: CD,FD
 
-  real*8 :: tmp_xz_plane(extf(1), 6) 
+  real*8 :: tmp_xz_plane(-1:extf(1), 6)
-  real*8 :: tmp_x_line(extf(1))
+  real*8 :: tmp_x_line(-1:extf(1))
   integer :: fi, fj, fk, ii, jj, kk
+  integer :: fi_min, fi_max, ii_lo, ii_hi
+  integer :: fj_min, fj_max, fk_min, fk_max, jj_lo, jj_hi, kk_lo, kk_hi
+  logical :: need_full_symmetry
 
   if(wei.ne.3)then
      write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
@@ -2433,7 +2455,34 @@ end do
           stop
   endif
 
-  call symmetry_bd(2,extf,funf,funff,SoA)
+  ! 仅计算 X 向最终写回所需的窗口：
+  ! func(i,j,k) 只访问 tmp_x_line(fi-2:fi+3)
+  fi_min = 2*(imino + lbc(1) - 1) - 1 - lbf(1) + 1
+  fi_max = 2*(imaxo + lbc(1) - 1) - 1 - lbf(1) + 1
+  fj_min = 2*(jmino + lbc(2) - 1) - 1 - lbf(2) + 1
+  fj_max = 2*(jmaxo + lbc(2) - 1) - 1 - lbf(2) + 1
+  fk_min = 2*(kmino + lbc(3) - 1) - 1 - lbf(3) + 1
+  fk_max = 2*(kmaxo + lbc(3) - 1) - 1 - lbf(3) + 1
+  ii_lo = fi_min - 2
+  ii_hi = fi_max + 3
+  jj_lo = fj_min - 2
+  jj_hi = fj_max + 3
+  kk_lo = fk_min - 2
+  kk_hi = fk_max + 3
+  if(ii_lo < -1 .or. ii_hi > extf(1) .or. &
+     jj_lo < -1 .or. jj_hi > extf(2) .or. &
+     kk_lo < -1 .or. kk_hi > extf(3))then
+      write(*,*)"restrict3: invalid stencil window"
+      write(*,*)"ii=",ii_lo,ii_hi," jj=",jj_lo,jj_hi," kk=",kk_lo,kk_hi
+      write(*,*)"extf=",extf
+      stop
+  endif
+  need_full_symmetry = (ii_lo < 1) .or. (jj_lo < 1) .or. (kk_lo < 1)
+  if(need_full_symmetry)then
+      call symmetry_bd(2,extf,funf,funff,SoA)
+  else
+      funff(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi) = funf(ii_lo:ii_hi,jj_lo:jj_hi,kk_lo:kk_hi)
+  endif
 
 !~~~~~~> restriction start...
 do k = kmino, kmaxo
@@ -2445,7 +2494,7 @@ do k = kmino, kmaxo
         ! 优化点 1: 显式展开 Z 方向计算，减少循环开销
         ! 确保 ii 循环是最内层且连续访问
         !DIR$ VECTOR ALWAYS
-        do ii = 1, extf(1)
+        do ii = ii_lo, ii_hi
             ! 预计算当前 j 对应的 6 行在 Z 方向的压缩结果
             ! 这里直接硬编码 jj 的偏移，彻底消除一层循环
             tmp_xz_plane(ii, 1) = C1*(funff(ii,fj-2,fk-2)+funff(ii,fj-2,fk+3)) + &
@@ -2470,7 +2519,7 @@ do k = kmino, kmaxo
 
         ! 优化点 2: 同样向量化 Y 方向压缩
         !DIR$ VECTOR ALWAYS
-        do ii = 1, extf(1)
+        do ii = ii_lo, ii_hi
             tmp_x_line(ii) = C1*(tmp_xz_plane(ii, 1) + tmp_xz_plane(ii, 6)) + &
                             C2*(tmp_xz_plane(ii, 2) + tmp_xz_plane(ii, 5)) + &
                             C3*(tmp_xz_plane(ii, 3) + tmp_xz_plane(ii, 4))