迁移C算子的循环融合和临时量消除

Reviewed-on: #3

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/bssn_rhs_c.C

@@ -39,7 +39,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
     // printf("nx=%d ny=%d nz=%d all=%d\n", nx, ny, nz, all);
 
     // temp variable
-    double gxx[all],gyy[all],gzz[all];
     double chix[all],chiy[all],chiz[all];
     double gxxx[all],gxyx[all],gxzx[all],gyyx[all],gyzx[all],gzzx[all];
     double gxxy[all],gxyy[all],gxzy[all],gyyy[all],gyzy[all],gzzy[all];
@@ -51,9 +50,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
     double Gamxx[all],Gamxy[all],Gamxz[all];
     double Gamyx[all],Gamyy[all],Gamyz[all];
     double Gamzx[all],Gamzy[all],Gamzz[all];
-    double Kx[all], Ky[all], Kz[all], div_beta[all], S[all];
+    double Kx[all], Ky[all], Kz[all], S[all];
     double f[all], fxx[all], fxy[all], fxz[all], fyy[all], fyz[all], fzz[all];
-    double Gamxa[all], Gamya[all], Gamza[all], alpn1[all], chin1[all];
+    double alpn1[all], chin1[all];
     double gupxx[all], gupxy[all], gupxz[all];
     double gupyy[all], gupyz[all], gupzz[all];
     double SSS[3] = { 1.0,  1.0,  1.0};
@@ -107,9 +106,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
         for(int i=0;i<all;i+=1){
             alpn1[i] = Lap[i] + 1.0;
             chin1[i] = chi[i] + 1.0;
-            gxx[i] = dxx[i] + 1.0;
-            gyy[i] = dyy[i] + 1.0;
-            gzz[i] = dzz[i] + 1.0;
         }
         // 9ms //
         fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev);
@@ -127,231 +123,196 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
         // 3ms //
         for(int i=0;i<all;i+=1){
-            div_beta[i] = betaxx[i] + betayy[i] + betazz[i];
+            const double divb = betaxx[i] + betayy[i] + betazz[i];
-            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - div_beta[i]); 
+            chi_rhs[i] = F2o3 * chin1[i] * (alpn1[i] * trK[i] - divb); 
-            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * gxx[i] * div_beta[i] + 
+            gxx_rhs[i] = -TWO * alpn1[i] * Axx[i] - F2o3 * (dxx[i] + ONE) * divb + 
-                    TWO * (gxx[i] * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
+                    TWO * ((dxx[i] + ONE) * betaxx[i] + gxy[i] * betayx[i] + gxz[i] * betazx[i]);
-            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * gyy[i] * div_beta[i] + 
+            gyy_rhs[i] = -TWO * alpn1[i] * Ayy[i] - F2o3 * (dyy[i] + ONE) * divb + 
-                    TWO * (gxy[i] * betaxy[i] + gyy[i] * betayy[i] + gyz[i] * betazy[i]);
+                    TWO * (gxy[i] * betaxy[i] + (dyy[i] + ONE) * betayy[i] + gyz[i] * betazy[i]);
-            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * gzz[i] * div_beta[i] + 
+            gzz_rhs[i] = -TWO * alpn1[i] * Azz[i] - F2o3 * (dzz[i] + ONE) * divb + 
-                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + gzz[i] * betazz[i]);
+                        TWO * (gxz[i] * betaxz[i] + gyz[i] * betayz[i] + (dzz[i] + ONE) * betazz[i]);
-            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * div_beta[i] + 
+            gxy_rhs[i] = -TWO * alpn1[i] * Axy[i] + F1o3 * gxy[i] * divb + 
-                        gxx[i] * betaxy[i] + gxz[i] * betazy[i] + gyy[i] * betayx[i] 
+                        (dxx[i] + ONE) * betaxy[i] + gxz[i] * betazy[i] + (dyy[i] + ONE) * betayx[i] 
                         + gyz[i] * betazx[i] - gxy[i] * betazz[i];        
-            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * div_beta[i] + 
+            gyz_rhs[i] = -TWO * alpn1[i] * Ayz[i] + F1o3 * gyz[i] * divb + 
-                        gxy[i] * betaxz[i] + gyy[i] * betayz[i] + gxz[i] * betaxy[i] 
+                        gxy[i] * betaxz[i] + (dyy[i] + ONE) * betayz[i] + gxz[i] * betaxy[i] 
-                        + gzz[i] * betazy[i] - gyz[i] * betaxx[i];
+                        + (dzz[i] + ONE) * betazy[i] - gyz[i] * betaxx[i];
-            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * div_beta[i] + 
+            gxz_rhs[i] = -TWO * alpn1[i] * Axz[i] + F1o3 * gxz[i] * divb + 
-                        gxx[i] * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
+                        (dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i] 
-                        + gzz[i] * betazx[i] - gxz[i] * betayy[i];                  
+                        + (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];                  
         }
-        // 1ms //
+        // Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
         for(int i=0;i<all;i+=1){
-            double det = gxx[i] * gyy[i] * gzz[i] + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] - 
+            double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
-                        gxz[i] * gyy[i] * gxz[i] - gxy[i] * gxy[i] * gzz[i] - gxx[i] * gyz[i] * gyz[i];  
+                        gxz[i] * (dyy[i] + ONE) * gxz[i] - gxy[i] * gxy[i] * (dzz[i] + ONE) - (dxx[i] + ONE) * gyz[i] * gyz[i];
-            gupxx[i] = (gyy[i] * gzz[i] - gyz[i] * gyz[i]) / det;
+            double lg_xx = ((dyy[i] + ONE) * (dzz[i] + ONE) - gyz[i] * gyz[i]) / det;
-            gupxy[i] = -(gxy[i] * gzz[i] - gyz[i] * gxz[i]) / det;
+            double lg_xy = -(gxy[i] * (dzz[i] + ONE) - gyz[i] * gxz[i]) / det;
-            gupxz[i] = (gxy[i] * gyz[i] - gyy[i] * gxz[i]) / det;
+            double lg_xz = (gxy[i] * gyz[i] - (dyy[i] + ONE) * gxz[i]) / det;
-            gupyy[i] = (gxx[i] * gzz[i] - gxz[i] * gxz[i]) / det;
+            double lg_yy = ((dxx[i] + ONE) * (dzz[i] + ONE) - gxz[i] * gxz[i]) / det;
-            gupyz[i] = -(gxx[i] * gyz[i] - gxy[i] * gxz[i]) / det;
+            double lg_yz = -((dxx[i] + ONE) * gyz[i] - gxy[i] * gxz[i]) / det;
-            gupzz[i] = (gxx[i] * gyy[i] - gxy[i] * gxy[i]) / det;   
+            double lg_zz = ((dxx[i] + ONE) * (dyy[i] + ONE) - gxy[i] * gxy[i]) / det;
-        }
+            gupxx[i] = lg_xx; gupxy[i] = lg_xy; gupxz[i] = lg_xz;
-        // 2.2ms //
+            gupyy[i] = lg_yy; gupyz[i] = lg_yz; gupzz[i] = lg_zz;
-        if(co==0){
+
-            for (int i=0;i<all;i+=1) {
+            if(co==0){
                 Gmx_Res[i] = Gamx[i] - (
-                    gupxx[i] * (gupxx[i]*gxxx[i] + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i]) +
+                    lg_xx * (lg_xx*gxxx[i] + lg_xy*gxyx[i] + lg_xz*gxzx[i]) +
-                    gupxy[i] * (gupxx[i]*gxyx[i] + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i]) +
+                    lg_xy * (lg_xx*gxyx[i] + lg_xy*gyyx[i] + lg_xz*gyzx[i]) +
-                    gupxz[i] * (gupxx[i]*gxzx[i] + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i]) +
+                    lg_xz * (lg_xx*gxzx[i] + lg_xy*gyzx[i] + lg_xz*gzzx[i]) +
-
+                    lg_xx * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
-                    gupxx[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
+                    lg_xy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
-                    gupxy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
+                    lg_xz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
-                    gupxz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
+                    lg_xx * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-
+                    lg_xy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    gupxx[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    lg_xz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                    gupxy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
-                    gupxz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
-
                 Gmy_Res[i] = Gamy[i] - (
-                    gupxx[i] * (gupxy[i]*gxxx[i] + gupyy[i]*gxyx[i] + gupyz[i]*gxzx[i]) +
+                    lg_xx * (lg_xy*gxxx[i] + lg_yy*gxyx[i] + lg_yz*gxzx[i]) +
-                    gupxy[i] * (gupxy[i]*gxyx[i] + gupyy[i]*gyyx[i] + gupyz[i]*gyzx[i]) +
+                    lg_xy * (lg_xy*gxyx[i] + lg_yy*gyyx[i] + lg_yz*gyzx[i]) +
-                    gupxz[i] * (gupxy[i]*gxzx[i] + gupyy[i]*gyzx[i] + gupyz[i]*gzzx[i]) +
+                    lg_xz * (lg_xy*gxzx[i] + lg_yy*gyzx[i] + lg_yz*gzzx[i]) +
-
+                    lg_xy * (lg_xy*gxxy[i] + lg_yy*gxyy[i] + lg_yz*gxzy[i]) +
-                    gupxy[i] * (gupxy[i]*gxxy[i] + gupyy[i]*gxyy[i] + gupyz[i]*gxzy[i]) +
+                    lg_yy * (lg_xy*gxyy[i] + lg_yy*gyyy[i] + lg_yz*gyzy[i]) +
-                    gupyy[i] * (gupxy[i]*gxyy[i] + gupyy[i]*gyyy[i] + gupyz[i]*gyzy[i]) +
+                    lg_yz * (lg_xy*gxzy[i] + lg_yy*gyzy[i] + lg_yz*gzzy[i]) +
-                    gupyz[i] * (gupxy[i]*gxzy[i] + gupyy[i]*gyzy[i] + gupyz[i]*gzzy[i]) +
+                    lg_xy * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-
+                    lg_yy * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    gupxy[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    lg_yz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                    gupyy[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
-                    gupyz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
-
                 Gmz_Res[i] = Gamz[i] - (
-                    gupxx[i] * (gupxz[i]*gxxx[i] + gupyz[i]*gxyx[i] + gupzz[i]*gxzx[i]) +
+                    lg_xx * (lg_xz*gxxx[i] + lg_yz*gxyx[i] + lg_zz*gxzx[i]) +
-                    gupxy[i] * (gupxz[i]*gxyx[i] + gupyz[i]*gyyx[i] + gupzz[i]*gyzx[i]) +
+                    lg_xy * (lg_xz*gxyx[i] + lg_yz*gyyx[i] + lg_zz*gyzx[i]) +
-                    gupxz[i] * (gupxz[i]*gxzx[i] + gupyz[i]*gyzx[i] + gupzz[i]*gzzx[i]) +
+                    lg_xz * (lg_xz*gxzx[i] + lg_yz*gyzx[i] + lg_zz*gzzx[i]) +
-
+                    lg_xy * (lg_xz*gxxy[i] + lg_yz*gxyy[i] + lg_zz*gxzy[i]) +
-                    gupxy[i] * (gupxz[i]*gxxy[i] + gupyz[i]*gxyy[i] + gupzz[i]*gxzy[i]) +
+                    lg_yy * (lg_xz*gxyy[i] + lg_yz*gyyy[i] + lg_zz*gyzy[i]) +
-                    gupyy[i] * (gupxz[i]*gxyy[i] + gupyz[i]*gyyy[i] + gupzz[i]*gyzy[i]) +
+                    lg_yz * (lg_xz*gxzy[i] + lg_yz*gyzy[i] + lg_zz*gzzy[i]) +
-                    gupyz[i] * (gupxz[i]*gxzy[i] + gupyz[i]*gyzy[i] + gupzz[i]*gzzy[i]) +
+                    lg_xz * (lg_xz*gxxz[i] + lg_yz*gxyz[i] + lg_zz*gxzz[i]) +
-
+                    lg_yz * (lg_xz*gxyz[i] + lg_yz*gyyz[i] + lg_zz*gyzz[i]) +
-                    gupxz[i] * (gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i] + gupzz[i]*gxzz[i]) +
+                    lg_zz * (lg_xz*gxzz[i] + lg_yz*gyzz[i] + lg_zz*gzzz[i])
-                    gupyz[i] * (gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i] + gupzz[i]*gyzz[i]) +
-                    gupzz[i] * (gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i] + gupzz[i]*gzzz[i])
                 );
             }
+
+            Gamxxx[i] = HALF * ( lg_xx*gxxx[i]
+                            + lg_xy*(TWO*gxyx[i] - gxxy[i])
+                            + lg_xz*(TWO*gxzx[i] - gxxz[i]) );
+            Gamyxx[i] = HALF * ( lg_xy*gxxx[i]
+                            + lg_yy*(TWO*gxyx[i] - gxxy[i])
+                            + lg_yz*(TWO*gxzx[i] - gxxz[i]) );
+            Gamzxx[i] = HALF * ( lg_xz*gxxx[i]
+                            + lg_yz*(TWO*gxyx[i] - gxxy[i])
+                            + lg_zz*(TWO*gxzx[i] - gxxz[i]) );
+            Gamxyy[i] = HALF * ( lg_xx*(TWO*gxyy[i] - gyyx[i])
+                            + lg_xy*gyyy[i]
+                            + lg_xz*(TWO*gyzy[i] - gyyz[i]) );
+            Gamyyy[i] = HALF * ( lg_xy*(TWO*gxyy[i] - gyyx[i])
+                            + lg_yy*gyyy[i]
+                            + lg_yz*(TWO*gyzy[i] - gyyz[i]) );
+            Gamzyy[i] = HALF * ( lg_xz*(TWO*gxyy[i] - gyyx[i])
+                            + lg_yz*gyyy[i]
+                            + lg_zz*(TWO*gyzy[i] - gyyz[i]) );
+            Gamxzz[i] = HALF * ( lg_xx*(TWO*gxzz[i] - gzzx[i])
+                            + lg_xy*(TWO*gyzz[i] - gzzy[i])
+                            + lg_xz*gzzz[i] );
+            Gamyzz[i] = HALF * ( lg_xy*(TWO*gxzz[i] - gzzx[i])
+                            + lg_yy*(TWO*gyzz[i] - gzzy[i])
+                            + lg_yz*gzzz[i] );
+            Gamzzz[i] = HALF * ( lg_xz*(TWO*gxzz[i] - gzzx[i])
+                            + lg_yz*(TWO*gyzz[i] - gzzy[i])
+                            + lg_zz*gzzz[i] );
+            Gamxxy[i] = HALF * ( lg_xx*gxxy[i]
+                            + lg_xy*gyyx[i]
+                            + lg_xz*(gxzy[i] + gyzx[i] - gxyz[i]) );
+            Gamyxy[i] = HALF * ( lg_xy*gxxy[i]
+                            + lg_yy*gyyx[i]
+                            + lg_yz*(gxzy[i] + gyzx[i] - gxyz[i]) );
+            Gamzxy[i] = HALF * ( lg_xz*gxxy[i]
+                            + lg_yz*gyyx[i]
+                            + lg_zz*(gxzy[i] + gyzx[i] - gxyz[i]) );
+            Gamxxz[i] = HALF * ( lg_xx*gxxz[i]
+                            + lg_xy*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + lg_xz*gzzx[i] );
+            Gamyxz[i] = HALF * ( lg_xy*gxxz[i]
+                            + lg_yy*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + lg_yz*gzzx[i] );
+            Gamzxz[i] = HALF * ( lg_xz*gxxz[i]
+                            + lg_yz*(gxyz[i] + gyzx[i] - gxzy[i])
+                            + lg_zz*gzzx[i] );
+            Gamxyz[i] = HALF * ( lg_xx*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + lg_xy*gyyz[i]
+                            + lg_xz*gzzy[i] );
+            Gamyyz[i] = HALF * ( lg_xy*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + lg_yy*gyyz[i]
+                            + lg_yz*gzzy[i] );
+            Gamzyz[i] = HALF * ( lg_xz*(gxyz[i] + gxzy[i] - gyzx[i])
+                            + lg_yz*gyyz[i]
+                            + lg_zz*gzzy[i] );
         }
-        // 5ms //
+        // Fused: A^{ij} raise-index + Gamma_rhs part 1 (2 loops -> 1)
         for (int i=0;i<all;i+=1) {
-
+            double axx = gupxx[i]*gupxx[i]*Axx[i]
-            Gamxxx[i] = HALF * ( gupxx[i]*gxxx[i]
-                            + gupxy[i]*(TWO*gxyx[i] - gxxy[i])
-                            + gupxz[i]*(TWO*gxzx[i] - gxxz[i]) );
-
-            Gamyxx[i] = HALF * ( gupxy[i]*gxxx[i]
-                            + gupyy[i]*(TWO*gxyx[i] - gxxy[i])
-                            + gupyz[i]*(TWO*gxzx[i] - gxxz[i]) );
-
-            Gamzxx[i] = HALF * ( gupxz[i]*gxxx[i]
-                            + gupyz[i]*(TWO*gxyx[i] - gxxy[i])
-                            + gupzz[i]*(TWO*gxzx[i] - gxxz[i]) );
-
-            Gamxyy[i] = HALF * ( gupxx[i]*(TWO*gxyy[i] - gyyx[i])
-                            + gupxy[i]*gyyy[i]
-                            + gupxz[i]*(TWO*gyzy[i] - gyyz[i]) );
-
-            Gamyyy[i] = HALF * ( gupxy[i]*(TWO*gxyy[i] - gyyx[i])
-                            + gupyy[i]*gyyy[i]
-                            + gupyz[i]*(TWO*gyzy[i] - gyyz[i]) );
-
-            Gamzyy[i] = HALF * ( gupxz[i]*(TWO*gxyy[i] - gyyx[i])
-                            + gupyz[i]*gyyy[i]
-                            + gupzz[i]*(TWO*gyzy[i] - gyyz[i]) );
-
-            Gamxzz[i] = HALF * ( gupxx[i]*(TWO*gxzz[i] - gzzx[i])
-                            + gupxy[i]*(TWO*gyzz[i] - gzzy[i])
-                            + gupxz[i]*gzzz[i] );
-
-            Gamyzz[i] = HALF * ( gupxy[i]*(TWO*gxzz[i] - gzzx[i])
-                            + gupyy[i]*(TWO*gyzz[i] - gzzy[i])
-                            + gupyz[i]*gzzz[i] );
-
-            Gamzzz[i] = HALF * ( gupxz[i]*(TWO*gxzz[i] - gzzx[i])
-                            + gupyz[i]*(TWO*gyzz[i] - gzzy[i])
-                            + gupzz[i]*gzzz[i] );
-
-            Gamxxy[i] = HALF * ( gupxx[i]*gxxy[i]
-                            + gupxy[i]*gyyx[i]
-                            + gupxz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
-
-            Gamyxy[i] = HALF * ( gupxy[i]*gxxy[i]
-                            + gupyy[i]*gyyx[i]
-                            + gupyz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
-
-            Gamzxy[i] = HALF * ( gupxz[i]*gxxy[i]
-                            + gupyz[i]*gyyx[i]
-                            + gupzz[i]*(gxzy[i] + gyzx[i] - gxyz[i]) );
-
-            Gamxxz[i] = HALF * ( gupxx[i]*gxxz[i]
-                            + gupxy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + gupxz[i]*gzzx[i] );
-
-            Gamyxz[i] = HALF * ( gupxy[i]*gxxz[i]
-                            + gupyy[i]*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + gupyz[i]*gzzx[i] );
-
-            Gamzxz[i] = HALF * ( gupxz[i]*gxxz[i]
-                            + gupyz[i]*(gxyz[i] + gyzx[i] - gxzy[i])
-                            + gupzz[i]*gzzx[i] );
-
-            Gamxyz[i] = HALF * ( gupxx[i]*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + gupxy[i]*gyyz[i]
-                            + gupxz[i]*gzzy[i] );
-
-            Gamyyz[i] = HALF * ( gupxy[i]*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + gupyy[i]*gyyz[i]
-                            + gupyz[i]*gzzy[i] );
-
-            Gamzyz[i] = HALF * ( gupxz[i]*(gxyz[i] + gxzy[i] - gyzx[i])
-                            + gupyz[i]*gyyz[i]
-                            + gupzz[i]*gzzy[i] );
-
-        }
-        // 1.8ms //
-        for (int i=0;i<all;i+=1) {
-
-            Rxx[i] = gupxx[i]*gupxx[i]*Axx[i]
                 + gupxy[i]*gupxy[i]*Ayy[i]
                 + gupxz[i]*gupxz[i]*Azz[i]
                 + TWO * ( gupxx[i]*gupxy[i]*Axy[i]
                         + gupxx[i]*gupxz[i]*Axz[i]
                         + gupxy[i]*gupxz[i]*Ayz[i] );
-
+            double ayy = gupxy[i]*gupxy[i]*Axx[i]
-            Ryy[i] = gupxy[i]*gupxy[i]*Axx[i]
                 + gupyy[i]*gupyy[i]*Ayy[i]
                 + gupyz[i]*gupyz[i]*Azz[i]
                 + TWO * ( gupxy[i]*gupyy[i]*Axy[i]
                         + gupxy[i]*gupyz[i]*Axz[i]
                         + gupyy[i]*gupyz[i]*Ayz[i] );
-
+            double azz = gupxz[i]*gupxz[i]*Axx[i]
-            Rzz[i] = gupxz[i]*gupxz[i]*Axx[i]
                 + gupyz[i]*gupyz[i]*Ayy[i]
                 + gupzz[i]*gupzz[i]*Azz[i]
                 + TWO * ( gupxz[i]*gupyz[i]*Axy[i]
                         + gupxz[i]*gupzz[i]*Axz[i]
                         + gupyz[i]*gupzz[i]*Ayz[i] );
-
+            double axy = gupxx[i]*gupxy[i]*Axx[i]
-            Rxy[i] = gupxx[i]*gupxy[i]*Axx[i]
                 + gupxy[i]*gupyy[i]*Ayy[i]
                 + gupxz[i]*gupyz[i]*Azz[i]
                 + ( gupxx[i]*gupyy[i] + gupxy[i]*gupxy[i] ) * Axy[i]
                 + ( gupxx[i]*gupyz[i] + gupxz[i]*gupxy[i] ) * Axz[i]
                 + ( gupxy[i]*gupyz[i] + gupxz[i]*gupyy[i] ) * Ayz[i];
-
+            double axz = gupxx[i]*gupxz[i]*Axx[i]
-            Rxz[i] = gupxx[i]*gupxz[i]*Axx[i]
                 + gupxy[i]*gupyz[i]*Ayy[i]
                 + gupxz[i]*gupzz[i]*Azz[i]
                 + ( gupxx[i]*gupyz[i] + gupxy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxx[i]*gupzz[i] + gupxz[i]*gupxz[i] ) * Axz[i]
                 + ( gupxy[i]*gupzz[i] + gupxz[i]*gupyz[i] ) * Ayz[i];
-
+            double ayz = gupxy[i]*gupxz[i]*Axx[i]
-            Ryz[i] = gupxy[i]*gupxz[i]*Axx[i]
                 + gupyy[i]*gupyz[i]*Ayy[i]
                 + gupyz[i]*gupzz[i]*Azz[i]
                 + ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
                 + ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
                 + ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
-        }
+            Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
-        // 4ms //
+            Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
-        for(int i=0;i<all;i+=1){
-            Gamx_rhs[i] = - TWO * (   Lapx[i] * Rxx[i] +   Lapy[i] * Rxy[i] +   Lapz[i] * Rxz[i] ) + 
-                TWO * alpn1[i] * (                                                
-                -F3o2/chin1[i] * (   chix[i] * Rxx[i] +   chiy[i] * Rxy[i] +   chiz[i] * Rxz[i] ) - 
-                    gupxx[i] * (   F2o3 * Kx[i]  +  EIGHT * PI * Sx[i]            ) - 
-                    gupxy[i] * (   F2o3 * Ky[i]  +  EIGHT * PI * Sy[i]            ) - 
-                    gupxz[i] * (   F2o3 * Kz[i]  +  EIGHT * PI * Sz[i]            ) + 
-                                Gamxxx[i] * Rxx[i] + Gamxyy[i] * Ryy[i] + Gamxzz[i] * Rzz[i]   + 
-                        TWO * ( Gamxxy[i] * Rxy[i] + Gamxxz[i] * Rxz[i] + Gamxyz[i] * Ryz[i] ) );
 
-            Gamy_rhs[i] = -TWO * ( Lapx[i]*Rxy[i] + Lapy[i]*Ryy[i] + Lapz[i]*Ryz[i] )
+            Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
+                TWO * alpn1[i] * (
+                -F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
+                    gupxx[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] ) -
+                    gupxy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] ) -
+                    gupxz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] ) +
+                                Gamxxx[i]*axx + Gamxyy[i]*ayy + Gamxzz[i]*azz +
+                        TWO * ( Gamxxy[i]*axy + Gamxxz[i]*axz + Gamxyz[i]*ayz ) );
+
+            Gamy_rhs[i] = -TWO * ( Lapx[i]*axy + Lapy[i]*ayy + Lapz[i]*ayz )
                         +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*Rxy[i] + chiy[i]*Ryy[i] + chiz[i]*Ryz[i] )
+                            -F3o2/chin1[i] * ( chix[i]*axy + chiy[i]*ayy + chiz[i]*ayz )
                             - gupxy[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                             - gupyy[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                             - gupyz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamyxx[i]*Rxx[i] + Gamyyy[i]*Ryy[i] + Gamyzz[i]*Rzz[i]
+                            + Gamyxx[i]*axx + Gamyyy[i]*ayy + Gamyzz[i]*azz
-                            + TWO * ( Gamyxy[i]*Rxy[i] + Gamyxz[i]*Rxz[i] + Gamyyz[i]*Ryz[i] )
+                            + TWO * ( Gamyxy[i]*axy + Gamyxz[i]*axz + Gamyyz[i]*ayz )
                         );
 
-            Gamz_rhs[i] = -TWO * ( Lapx[i]*Rxz[i] + Lapy[i]*Ryz[i] + Lapz[i]*Rzz[i] )
+            Gamz_rhs[i] = -TWO * ( Lapx[i]*axz + Lapy[i]*ayz + Lapz[i]*azz )
                         +  TWO * alpn1[i] * (
-                            -F3o2/chin1[i] * ( chix[i]*Rxz[i] + chiy[i]*Ryz[i] + chiz[i]*Rzz[i] )
+                            -F3o2/chin1[i] * ( chix[i]*axz + chiy[i]*ayz + chiz[i]*azz )
                             - gupxz[i] * ( F2o3*Kx[i] + EIGHT*PI*Sx[i] )
                             - gupyz[i] * ( F2o3*Ky[i] + EIGHT*PI*Sy[i] )
                             - gupzz[i] * ( F2o3*Kz[i] + EIGHT*PI*Sz[i] )
-                            + Gamzxx[i]*Rxx[i] + Gamzyy[i]*Ryy[i] + Gamzzz[i]*Rzz[i]
+                            + Gamzxx[i]*axx + Gamzyy[i]*ayy + Gamzzz[i]*azz
-                            + TWO * ( Gamzxy[i]*Rxy[i] + Gamzxz[i]*Rxz[i] + Gamzyz[i]*Ryz[i] )
+                            + TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
                         );
         }
         // 22.3ms //
@@ -365,65 +326,63 @@ int f_compute_rhs_bssn(int *ex, double &T,
         fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev);
         fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev);
 
-        // 3.5ms //
+        // Fused: fxx/Gamxa + Gamma_rhs part 2 (2 loops -> 1)
         for(int i=0;i<all;i+=1){
-            fxx[i] = gxxx[i] + gxyy[i] + gxzz[i];
+            const double divb = betaxx[i] + betayy[i] + betazz[i];
-            fxy[i] = gxyx[i] + gyyy[i] + gyzz[i];
+            double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
-            fxz[i] = gxzx[i] + gyzy[i] + gzzz[i];
+            double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
-            Gamxa[i] = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
+            double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
+            fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
+
+            double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
                     + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
-
+            double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
-            Gamya[i] = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
                     + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
-
+            double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
-            Gamza[i] = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
                     + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
-        }
-        // 3.9ms //
-        for(int i=0;i<all;i+=1){
             Gamx_rhs[i] = Gamx_rhs[i]
-                        + F2o3 * Gamxa[i] * div_beta[i]
+                        + F2o3 * gxa * divb
-                        - Gamxa[i] * betaxx[i] - Gamya[i] * betaxy[i] - Gamza[i] * betaxz[i]
+                        - gxa * betaxx[i] - gya * betaxy[i] - gza * betaxz[i]
-                        + F1o3 * ( gupxx[i] * fxx[i] + gupxy[i] * fxy[i] + gupxz[i] * fxz[i] )
+                        + F1o3 * ( gupxx[i] * lfxx + gupxy[i] * lfxy + gupxz[i] * lfxz )
                         + gupxx[i] * gxxx[i] + gupyy[i] * gyyx[i] + gupzz[i] * gzzx[i]
                         + TWO * ( gupxy[i] * gxyx[i] + gupxz[i] * gxzx[i] + gupyz[i] * gyzx[i] );
 
             Gamy_rhs[i] = Gamy_rhs[i]
-                        + F2o3 * Gamya[i] * div_beta[i]
+                        + F2o3 * gya * divb
-                        - Gamxa[i] * betayx[i] - Gamya[i] * betayy[i] - Gamza[i] * betayz[i]
+                        - gxa * betayx[i] - gya * betayy[i] - gza * betayz[i]
-                        + F1o3 * ( gupxy[i] * fxx[i] + gupyy[i] * fxy[i] + gupyz[i] * fxz[i] )
+                        + F1o3 * ( gupxy[i] * lfxx + gupyy[i] * lfxy + gupyz[i] * lfxz )
                         + gupxx[i] * gxxy[i] + gupyy[i] * gyyy[i] + gupzz[i] * gzzy[i]
                         + TWO * ( gupxy[i] * gxyy[i] + gupxz[i] * gxzy[i] + gupyz[i] * gyzy[i] );
 
             Gamz_rhs[i] = Gamz_rhs[i]
-                        + F2o3 * Gamza[i] * div_beta[i]
+                        + F2o3 * gza * divb
-                        - Gamxa[i] * betazx[i] - Gamya[i] * betazy[i] - Gamza[i] * betazz[i]
+                        - gxa * betazx[i] - gya * betazy[i] - gza * betazz[i]
-                        + F1o3 * ( gupxz[i] * fxx[i] + gupyz[i] * fxy[i] + gupzz[i] * fxz[i] )
+                        + F1o3 * ( gupxz[i] * lfxx + gupyz[i] * lfxy + gupzz[i] * lfxz )
                         + gupxx[i] * gxxz[i] + gupyy[i] * gyyz[i] + gupzz[i] * gzzz[i]
                         + TWO * ( gupxy[i] * gxyz[i] + gupxz[i] * gxzz[i] + gupyz[i] * gyzz[i] );
         }
         // 4.4ms //
         for (int i=0;i<all;i+=1) {
-            gxxx[i] = gxx[i]*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
+            gxxx[i] = (dxx[i] + ONE)*Gamxxx[i] + gxy[i]*Gamyxx[i] + gxz[i]*Gamzxx[i];
-            gxyx[i] = gxx[i]*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
+            gxyx[i] = (dxx[i] + ONE)*Gamxxy[i] + gxy[i]*Gamyxy[i] + gxz[i]*Gamzxy[i];
-            gxzx[i] = gxx[i]*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
+            gxzx[i] = (dxx[i] + ONE)*Gamxxz[i] + gxy[i]*Gamyxz[i] + gxz[i]*Gamzxz[i];
-            gyyx[i] = gxx[i]*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
+            gyyx[i] = (dxx[i] + ONE)*Gamxyy[i] + gxy[i]*Gamyyy[i] + gxz[i]*Gamzyy[i];
-            gyzx[i] = gxx[i]*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
+            gyzx[i] = (dxx[i] + ONE)*Gamxyz[i] + gxy[i]*Gamyyz[i] + gxz[i]*Gamzyz[i];
-            gzzx[i] = gxx[i]*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
+            gzzx[i] = (dxx[i] + ONE)*Gamxzz[i] + gxy[i]*Gamyzz[i] + gxz[i]*Gamzzz[i];
 
-            gxxy[i] = gxy[i]*Gamxxx[i] + gyy[i]*Gamyxx[i] + gyz[i]*Gamzxx[i];
+            gxxy[i] = gxy[i]*Gamxxx[i] + (dyy[i] + ONE)*Gamyxx[i] + gyz[i]*Gamzxx[i];
-            gxyy[i] = gxy[i]*Gamxxy[i] + gyy[i]*Gamyxy[i] + gyz[i]*Gamzxy[i];
+            gxyy[i] = gxy[i]*Gamxxy[i] + (dyy[i] + ONE)*Gamyxy[i] + gyz[i]*Gamzxy[i];
-            gxzy[i] = gxy[i]*Gamxxz[i] + gyy[i]*Gamyxz[i] + gyz[i]*Gamzxz[i];
+            gxzy[i] = gxy[i]*Gamxxz[i] + (dyy[i] + ONE)*Gamyxz[i] + gyz[i]*Gamzxz[i];
-            gyyy[i] = gxy[i]*Gamxyy[i] + gyy[i]*Gamyyy[i] + gyz[i]*Gamzyy[i];
+            gyyy[i] = gxy[i]*Gamxyy[i] + (dyy[i] + ONE)*Gamyyy[i] + gyz[i]*Gamzyy[i];
-            gyzy[i] = gxy[i]*Gamxyz[i] + gyy[i]*Gamyyz[i] + gyz[i]*Gamzyz[i];
+            gyzy[i] = gxy[i]*Gamxyz[i] + (dyy[i] + ONE)*Gamyyz[i] + gyz[i]*Gamzyz[i];
-            gzzy[i] = gxy[i]*Gamxzz[i] + gyy[i]*Gamyzz[i] + gyz[i]*Gamzzz[i];
+            gzzy[i] = gxy[i]*Gamxzz[i] + (dyy[i] + ONE)*Gamyzz[i] + gyz[i]*Gamzzz[i];
 
-            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + gzz[i]*Gamzxx[i];
+            gxxz[i] = gxz[i]*Gamxxx[i] + gyz[i]*Gamyxx[i] + (dzz[i] + ONE)*Gamzxx[i];
-            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + gzz[i]*Gamzxy[i];
+            gxyz[i] = gxz[i]*Gamxxy[i] + gyz[i]*Gamyxy[i] + (dzz[i] + ONE)*Gamzxy[i];
-            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + gzz[i]*Gamzxz[i];
+            gxzz[i] = gxz[i]*Gamxxz[i] + gyz[i]*Gamyxz[i] + (dzz[i] + ONE)*Gamzxz[i];
-            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + gzz[i]*Gamzyy[i];
+            gyyz[i] = gxz[i]*Gamxyy[i] + gyz[i]*Gamyyy[i] + (dzz[i] + ONE)*Gamzyy[i];
-            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + gzz[i]*Gamzyz[i];
+            gyzz[i] = gxz[i]*Gamxyz[i] + gyz[i]*Gamyyz[i] + (dzz[i] + ONE)*Gamzyz[i];
-            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + gzz[i]*Gamzzz[i];
+            gzzz[i] = gxz[i]*Gamxzz[i] + gyz[i]*Gamyzz[i] + (dzz[i] + ONE)*Gamzzz[i];
         }
         // 22.2ms //
             fdderivs(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev);
@@ -471,10 +430,17 @@ int f_compute_rhs_bssn(int *ex, double &T,
         // 14ms //
         /* 假设 all = ex1*ex2*ex3，所有量都是 length=all 的 double 数组（已按同一扁平化规则排布） */
         for (int i = 0; i < all; i += 1) {
+            const double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
+                            + TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
+            const double gya = gupxx[i]*Gamyxx[i] + gupyy[i]*Gamyyy[i] + gupzz[i]*Gamyzz[i]
+                            + TWO * ( gupxy[i]*Gamyxy[i] + gupxz[i]*Gamyxz[i] + gupyz[i]*Gamyyz[i] );
+            const double gza = gupxx[i]*Gamzxx[i] + gupyy[i]*Gamzyy[i] + gupzz[i]*Gamzzz[i]
+                            + TWO * ( gupxy[i]*Gamzxy[i] + gupxz[i]*Gamzxz[i] + gupyz[i]*Gamzyz[i] );
+
             Rxx[i] =
                 -HALF * Rxx[i]
-                + gxx[i] * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
+                + (dxx[i] + ONE) * Gamxx[i] + gxy[i] * Gamyx[i] + gxz[i] * Gamzx[i]
-                + Gamxa[i] * gxxx[i] + Gamya[i] * gxyx[i] + Gamza[i] * gxzx[i]
+                + gxa * gxxx[i] + gya * gxyx[i] + gza * gxzx[i]
                 + gupxx[i] * (
                     TWO * (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxyx[i] + Gamzxx[i] * gxzx[i]) +
                         (Gamxxx[i] * gxxx[i] + Gamyxx[i] * gxxy[i] + Gamzxx[i] * gxxz[i])
@@ -508,8 +474,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
             Ryy[i] =
                 -HALF * Ryy[i]
-                + gxy[i] * Gamxy[i] + gyy[i] * Gamyy[i] + gyz[i] * Gamzy[i]
+                + gxy[i] * Gamxy[i] + (dyy[i] + ONE) * Gamyy[i] + gyz[i] * Gamzy[i]
-                + Gamxa[i] * gxyy[i] + Gamya[i] * gyyy[i] + Gamza[i] * gyzy[i]
+                + gxa * gxyy[i] + gya * gyyy[i] + gza * gyzy[i]
                 + gupxx[i] * (
                     TWO * (Gamxxy[i] * gxxy[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxzy[i]) +
                         (Gamxxy[i] * gxyx[i] + Gamyxy[i] * gxyy[i] + Gamzxy[i] * gxyz[i])
@@ -543,8 +509,8 @@ int f_compute_rhs_bssn(int *ex, double &T,
 
             Rzz[i] =
                 -HALF * Rzz[i]
-                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + gzz[i] * Gamzz[i]
+                + gxz[i] * Gamxz[i] + gyz[i] * Gamyz[i] + (dzz[i] + ONE) * Gamzz[i]
-                + Gamxa[i] * gxzz[i] + Gamya[i] * gyzz[i] + Gamza[i] * gzzz[i]
+                + gxa * gxzz[i] + gya * gyzz[i] + gza * gzzz[i]
                 + gupxx[i] * (
                     TWO * (Gamxxz[i] * gxxz[i] + Gamyxz[i] * gxyz[i] + Gamzxz[i] * gxzz[i]) +
                         (Gamxxz[i] * gxzx[i] + Gamyxz[i] * gxzy[i] + Gamzxz[i] * gxzz[i])
@@ -579,10 +545,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Rxy[i] =
                 HALF * (
                     -Rxy[i]
-                    + gxx[i] * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
+                    + (dxx[i] + ONE) * Gamxy[i] + gxy[i] * Gamyy[i] + gxz[i] * Gamzy[i]
-                    + gxy[i] * Gamxx[i] + gyy[i] * Gamyx[i] + gyz[i] * Gamzx[i]
+                    + gxy[i] * Gamxx[i] + (dyy[i] + ONE) * Gamyx[i] + gyz[i] * Gamzx[i]
-                    + Gamxa[i] * gxyx[i] + Gamya[i] * gyyx[i] + Gamza[i] * gyzx[i]
+                    + gxa * gxyx[i] + gya * gyyx[i] + gza * gyzx[i]
-                    + Gamxa[i] * gxxy[i] + Gamya[i] * gxyy[i] + Gamza[i] * gxzy[i]
+                    + gxa * gxxy[i] + gya * gxyy[i] + gza * gxzy[i]
                 )
                 + gupxx[i] * (
                     Gamxxx[i] * gxxy[i] + Gamyxx[i] * gxyy[i] + Gamzxx[i] * gxzy[i]
@@ -627,10 +593,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Rxz[i] =
                 HALF * (
                     -Rxz[i]
-                    + gxx[i] * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
+                    + (dxx[i] + ONE) * Gamxz[i] + gxy[i] * Gamyz[i] + gxz[i] * Gamzz[i]
-                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + gzz[i] * Gamzx[i]
+                    + gxz[i] * Gamxx[i] + gyz[i] * Gamyx[i] + (dzz[i] + ONE) * Gamzx[i]
-                    + Gamxa[i] * gxzx[i] + Gamya[i] * gyzx[i] + Gamza[i] * gzzx[i]
+                    + gxa * gxzx[i] + gya * gyzx[i] + gza * gzzx[i]
-                    + Gamxa[i] * gxxz[i] + Gamya[i] * gxyz[i] + Gamza[i] * gxzz[i]
+                    + gxa * gxxz[i] + gya * gxyz[i] + gza * gxzz[i]
                 )
                 + gupxx[i] * (
                     Gamxxx[i] * gxxz[i] + Gamyxx[i] * gxyz[i] + Gamzxx[i] * gxzz[i]
@@ -675,10 +641,10 @@ int f_compute_rhs_bssn(int *ex, double &T,
             Ryz[i] =
                 HALF * (
                     -Ryz[i]
-                    + gxy[i] * Gamxz[i] + gyy[i] * Gamyz[i] + gyz[i] * Gamzz[i]
+                    + gxy[i] * Gamxz[i] + (dyy[i] + ONE) * Gamyz[i] + gyz[i] * Gamzz[i]
-                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + gzz[i] * Gamzy[i]
+                    + gxz[i] * Gamxy[i] + gyz[i] * Gamyy[i] + (dzz[i] + ONE) * Gamzy[i]
-                    + Gamxa[i] * gxzy[i] + Gamya[i] * gyzy[i] + Gamza[i] * gzzy[i]
+                    + gxa * gxzy[i] + gya * gyzy[i] + gza * gzzy[i]
-                    + Gamxa[i] * gxyz[i] + Gamya[i] * gyyz[i] + Gamza[i] * gyzz[i]
+                    + gxa * gxyz[i] + gya * gyyz[i] + gza * gyzz[i]
                 )
                 + gupxx[i] * (
                     Gamxxy[i] * gxxz[i] + Gamyxy[i] * gxyz[i] + Gamzxy[i] * gxzz[i]
@@ -739,9 +705,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
                 + TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
                 + TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
-            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + gxx[i] * f[i] ) / (chin1[i] * TWO);
+            Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + gyy[i] * f[i] ) / (chin1[i] * TWO);
+            Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
-            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + gzz[i] * f[i] ) / (chin1[i] * TWO);
+            Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
 
             Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
             Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
@@ -760,17 +726,17 @@ int f_compute_rhs_bssn(int *ex, double &T,
             gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
 
             /* Christoffel 修正项 */
-            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - gxx[i] * gxxx[i] ) * HALF;
+            Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyxx[i] = Gamyxx[i] - ( 0.0           - gxx[i] * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
+            Gamyxx[i] = Gamyxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxy[i] ) * HALF;  /* 原式只有 -gxx*gxxy */
-            Gamzxx[i] = Gamzxx[i] - ( 0.0           - gxx[i] * gxxz[i] ) * HALF;
+            Gamzxx[i] = Gamzxx[i] - ( 0.0           - (dxx[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxyy[i] = Gamxyy[i] - ( 0.0           - gyy[i] * gxxx[i] ) * HALF;
+            Gamxyy[i] = Gamxyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - gyy[i] * gxxy[i] ) * HALF;
+            Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzyy[i] = Gamzyy[i] - ( 0.0           - gyy[i] * gxxz[i] ) * HALF;
+            Gamzyy[i] = Gamzyy[i] - ( 0.0           - (dyy[i] + ONE) * gxxz[i] ) * HALF;
 
-            Gamxzz[i] = Gamxzz[i] - ( 0.0           - gzz[i] * gxxx[i] ) * HALF;
+            Gamxzz[i] = Gamxzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxx[i] ) * HALF;
-            Gamyzz[i] = Gamyzz[i] - ( 0.0           - gzz[i] * gxxy[i] ) * HALF;
+            Gamyzz[i] = Gamyzz[i] - ( 0.0           - (dzz[i] + ONE) * gxxy[i] ) * HALF;
-            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - gzz[i] * gxxz[i] ) * HALF;
+            Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
 
             Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i])      - gxy[i] * gxxx[i] ) * HALF;
             Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i])      - gxy[i] * gxxy[i] ) * HALF;
@@ -792,14 +758,13 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fxy[i] = fxy[i] - Gamxxy[i] * Lapx[i] - Gamyxy[i] * Lapy[i] - Gamzxy[i] * Lapz[i];
             fxz[i] = fxz[i] - Gamxxz[i] * Lapx[i] - Gamyxz[i] * Lapy[i] - Gamzxz[i] * Lapz[i];
             fyz[i] = fyz[i] - Gamxyz[i] * Lapx[i] - Gamyyz[i] * Lapy[i] - Gamzyz[i] * Lapz[i];
-        }
+
-        // 1ms //
-        for (int i=0;i<all;i+=1) {
             trK_rhs[i] =  gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
                     +  TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
         }
         // 2.5ms //
         for (int i=0;i<all;i+=1) {
+            const double divb = betaxx[i] + betayy[i] + betazz[i];
 
             S[i] = chin1[i] * (
                     gupxx[i] * Sxx[i] + gupyy[i] * Syy[i] + gupzz[i] * Szz[i]
@@ -850,23 +815,20 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + (alpn1[i] / chin1[i]) * f[i]
             );
 
-            fxx[i] = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
+            double l_fxx = alpn1[i] * (Rxx[i] - EIGHT * PI * Sxx[i]) - fxx[i];
-            fxy[i] = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
+            double l_fxy = alpn1[i] * (Rxy[i] - EIGHT * PI * Sxy[i]) - fxy[i];
-            fxz[i] = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
+            double l_fxz = alpn1[i] * (Rxz[i] - EIGHT * PI * Sxz[i]) - fxz[i];
-            fyy[i] = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
+            double l_fyy = alpn1[i] * (Ryy[i] - EIGHT * PI * Syy[i]) - fyy[i];
-            fyz[i] = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
+            double l_fyz = alpn1[i] * (Ryz[i] - EIGHT * PI * Syz[i]) - fyz[i];
-            fzz[i] = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
+            double l_fzz = alpn1[i] * (Rzz[i] - EIGHT * PI * Szz[i]) - fzz[i];
-        }
-        // 8ms //
-        for (int i=0;i<all;i+=1) {
 
             /* Aij_rhs = fij - gij * f */
-            Axx_rhs[i] = fxx[i] - gxx[i] * f[i];
+            Axx_rhs[i] = l_fxx - (dxx[i] + ONE) * f[i];
-            Ayy_rhs[i] = fyy[i] - gyy[i] * f[i];
+            Ayy_rhs[i] = l_fyy - (dyy[i] + ONE) * f[i];
-            Azz_rhs[i] = fzz[i] - gzz[i] * f[i];
+            Azz_rhs[i] = l_fzz - (dzz[i] + ONE) * f[i];
-            Axy_rhs[i] = fxy[i] - gxy[i] * f[i];
+            Axy_rhs[i] = l_fxy - gxy[i] * f[i];
-            Axz_rhs[i] = fxz[i] - gxz[i] * f[i];
+            Axz_rhs[i] = l_fxz - gxz[i] * f[i];
-            Ayz_rhs[i] = fyz[i] - gyz[i] * f[i];
+            Ayz_rhs[i] = l_fyz - gyz[i] * f[i];
 
             /* Now: store A_il A^l_j into fij: */
             fxx[i] =
@@ -928,19 +890,19 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 f[i] * Axx_rhs[i]
                 + alpn1[i] * ( trK[i] * Axx[i] - TWO * fxx[i] )
                 + TWO * ( Axx[i] * betaxx[i] + Axy[i] * betayx[i] + Axz[i] * betazx[i] )
-                - F2o3 * Axx[i] * div_beta[i];
+                - F2o3 * Axx[i] * divb;
 
             Ayy_rhs[i] =
                 f[i] * Ayy_rhs[i]
                 + alpn1[i] * ( trK[i] * Ayy[i] - TWO * fyy[i] )
                 + TWO * ( Axy[i] * betaxy[i] + Ayy[i] * betayy[i] + Ayz[i] * betazy[i] )
-                - F2o3 * Ayy[i] * div_beta[i];
+                - F2o3 * Ayy[i] * divb;
 
             Azz_rhs[i] =
                 f[i] * Azz_rhs[i]
                 + alpn1[i] * ( trK[i] * Azz[i] - TWO * fzz[i] )
                 + TWO * ( Axz[i] * betaxz[i] + Ayz[i] * betayz[i] + Azz[i] * betazz[i] )
-                - F2o3 * Azz[i] * div_beta[i];
+                - F2o3 * Azz[i] * divb;
 
             Axy_rhs[i] =
                 f[i] * Axy_rhs[i]
@@ -949,7 +911,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Axz[i] * betazy[i]
                 + Ayy[i] * betayx[i]
                 + Ayz[i] * betazx[i]
-                + F1o3 * Axy[i] * div_beta[i]
+                + F1o3 * Axy[i] * divb
                 - Axy[i] * betazz[i];
 
             Ayz_rhs[i] =
@@ -959,7 +921,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Ayy[i] * betayz[i]
                 + Axz[i] * betaxy[i]
                 + Azz[i] * betazy[i]
-                + F1o3 * Ayz[i] * div_beta[i]
+                + F1o3 * Ayz[i] * divb
                 - Ayz[i] * betaxx[i];
 
             Axz_rhs[i] =
@@ -969,7 +931,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
                 + Axy[i] * betayz[i]
                 + Ayz[i] * betayx[i]
                 + Azz[i] * betazx[i]
-                + F1o3 * Axz[i] * div_beta[i]
+                + F1o3 * Axz[i] * divb
                 - Axz[i] * betayy[i];
 
             /* Compute trace of S_ij */
@@ -1100,58 +1062,31 @@ int f_compute_rhs_bssn(int *ex, double &T,
             dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
             #endif
         }
-        // 26ms //
+        // advection + KO dissipation with shared symmetry buffer
-        lopsided(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS);
+        lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Lap,Lap_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA);
+        lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided_kodis(ex,X,Y,Z,betax,betax_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided_kodis(ex,X,Y,Z,betay,betay_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA);
+        lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided_kodis(ex,X,Y,Z,betaz,betaz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided_kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided_kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        lopsided(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS);
+        lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps);
-        lopsided(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA);
+        lopsided_kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
-        lopsided(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA);
+        lopsided_kodis(ex,X,Y,Z,Axz,Axz_rhs,betax,betay,betaz,Symmetry,ASA,eps);
-        lopsided(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Ayy,Ayy_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA);
+        lopsided_kodis(ex,X,Y,Z,Ayz,Ayz_rhs,betax,betay,betaz,Symmetry,SAA,eps);
-        lopsided(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,Azz,Azz_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,chi,chi_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS);
+        lopsided_kodis(ex,X,Y,Z,trK,trK_rhs,betax,betay,betaz,Symmetry,SSS,eps);
-        lopsided(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS);
+        lopsided_kodis(ex,X,Y,Z,Gamx,Gamx_rhs,betax,betay,betaz,Symmetry,ASS,eps);
-        lopsided(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS);
+        lopsided_kodis(ex,X,Y,Z,Gamy,Gamy_rhs,betax,betay,betaz,Symmetry,SAS,eps);
-        // 20ms //
-        if(eps>0){
-            kodis(ex,X,Y,Z,chi,chi_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,trK,trK_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,dxx,gxx_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,gxy,gxy_rhs,AAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,gxz,gxz_rhs,ASA,Symmetry,eps);
-            kodis(ex,X,Y,Z,dyy,gyy_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,gyz,gyz_rhs,SAA,Symmetry,eps);
-            kodis(ex,X,Y,Z,dzz,gzz_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Axx,Axx_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,dtSfz,dtSfz_rhs,SSA,Symmetry,eps);
-            kodis(ex,X,Y,Z,Axy,Axy_rhs,AAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,dtSfy,dtSfy_rhs,SAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Axz,Axz_rhs,ASA,Symmetry,eps);
-            kodis(ex,X,Y,Z,dtSfx,dtSfx_rhs,ASS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Ayy,Ayy_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,betaz,betaz_rhs,SSA,Symmetry,eps);
-            kodis(ex,X,Y,Z,Ayz,Ayz_rhs,SAA,Symmetry,eps);
-            kodis(ex,X,Y,Z,betay,betay_rhs,SAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Azz,Azz_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,betax,betax_rhs,ASS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Gamx,Gamx_rhs,ASS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Lap,Lap_rhs,SSS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Gamy,Gamy_rhs,SAS,Symmetry,eps);
-            kodis(ex,X,Y,Z,Gamz,Gamz_rhs,SSA,Symmetry,eps);
-        }
         // 2ms //
         if(co==0){
             for (int i=0;i<all;i+=1) {
@@ -1204,59 +1139,59 @@ int f_compute_rhs_bssn(int *ex, double &T,
             fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
             fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
             fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
-        }
+            // 7ms //
-        // 7ms //
+            for (int i=0;i<all;i+=1) {
-        for (int i=0;i<all;i+=1) {
+                gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
-            gxxx[i] = gxxx[i] - (  Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
+                                      + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
-                                  + Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
+                gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-            gxyx[i] = gxyx[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                      + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
-                                  + Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
+                gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-            gxzx[i] = gxzx[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                      + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
-                                  + Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
+                gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
-            gyyx[i] = gyyx[i] - (  Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
+                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
-                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
+                gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
-            gyzx[i] = gyzx[i] - (  Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
+                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
-                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
+                gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
-            gzzx[i] = gzzx[i] - (  Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
+                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
-                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
+                gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
-            gxxy[i] = gxxy[i] - (  Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
+                                      + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
-                                  + Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
+                gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
-            gxyy[i] = gxyy[i] - (  Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
+                                      + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
-                                  + Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
+                gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-            gxzy[i] = gxzy[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                      + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
-                                  + Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
+                gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
-            gyyy[i] = gyyy[i] - (  Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
+                                      + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
-                                  + Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
+                gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-            gyzy[i] = gyzy[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                      + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
-                                  + Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
+                gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
-            gzzy[i] = gzzy[i] - (  Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
+                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
-                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
+                gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
-            gxxz[i] = gxxz[i] - (  Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
+                                      + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
-                                  + Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
+                gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
-            gxyz[i] = gxyz[i] - (  Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
+                                      + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
-                                  + Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
+                gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
-            gxzz[i] = gxzz[i] - (  Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
+                                      + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
-                                  + Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
+                gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
-            gyyz[i] = gyyz[i] - (  Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
+                                      + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
-                                  + Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
+                gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
-            gyzz[i] = gyzz[i] - (  Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
+                                      + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
-                                  + Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
+                gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
-            gzzz[i] = gzzz[i] - (  Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
+                                      + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
-                                  + Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
 
-            movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
+                movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
-                        + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
+                            + gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
-                        + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
+                            + gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
-            movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
+                movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
-                        + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
+                            + gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
-                        + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
+                            + gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
-            movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
+                movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
-                        + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
+                            + gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
-                        + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
+                            + gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
 
-            movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
+                movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
-            movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
+                movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
-            movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+                movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
+            }
         }
 
 

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

@@ -71,149 +71,99 @@ void fdderivs(const int ex[3],
     const double Fdxdz = F1o144 / (dX * dZ);
     const double Fdydz = F1o144 / (dY * dZ);
 
-    /* 输出清零：fxx,fyy,fzz,fxy,fxz,fyz = 0 */
+    /* 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; fyy[p] = ZEO; fzz[p] = ZEO;
+        for (int j0 = 0; j0 < ex2; ++j0)
-        fxy[p] = ZEO; fxz[p] = ZEO; fyz[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;
+                }
+        }
     }
 
     /*
-     * Fortran:
+     * 两段式：
-     * do k=1,ex3-1
+     * 1) 二阶可用区域先计算二阶模板
-     * do j=1,ex2-1
+     * 2) 高阶可用区域再覆盖四阶模板
-     * do i=1,ex1-1
      */
-    
+    const int i2_lo = (iminF > 0) ? iminF : 0;
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+    const int j2_lo = (jminF > 0) ? jminF : 0;
-        const int kF = k0 + 1;
+    const int k2_lo = (kminF > 0) ? kminF : 0;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+    const int i2_hi = ex1 - 2;
-            const int jF = j0 + 1;
+    const int j2_hi = ex2 - 2;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+    const int k2_hi = ex3 - 2;
-                const int iF = i0 + 1;
-                const size_t p = idx_ex(i0, j0, k0, ex);
 
-                /* 高阶分支：i±2,j±2,k±2 都在范围内 */
+    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
-                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
+    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
-                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
+    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
-                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
+    const int i4_hi = ex1 - 3;
-                {
+    const int j4_hi = ex2 - 3;
-                    fxx[p] = Fdxdx * (
+    const int k4_hi = ex3 - 3;
-                        -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)] +
+     * Strategy A:
-                        F16 * fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] -
+     * Avoid redundant work in overlap of 2nd/4th-order regions.
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+     * Only compute 2nd-order on shell points that are NOT overwritten by
-                        fh[idx_fh_F_ord2(iF,     jF + 2, kF,     ex)] +
+     * the 4th-order pass.
-                        F16 * fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+     */
-                    );
+    const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
 
-                    fzz[p] = Fdzdz * (
+    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 2, ex)] +
+        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] -
+            const int kF = k0 + 1;
-                        F30 * fh[idx_fh_F_ord2(iF,     jF,     kF,     ex)] -
+            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
-                        fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)] +
+                const int jF = j0 + 1;
-                        F16 * fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
-                    );
+                    if (has4 &&
-
+                        i0 >= i4_lo && i0 <= i4_hi &&
-                    /* fxy 高阶：完全照搬 Fortran 的括号结构 */
+                        j0 >= j4_lo && j0 <= j4_hi &&
-                    {
+                        k0 >= k4_lo && k0 <= k4_hi) {
-                        const double t_jm2 =
+                        continue;
-                            ( 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 int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
 
-                    /* fxz 高阶 */
-                    {
-                        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 );
-                    }
-
-                    /* fyz 高阶 */
-                    {
-                        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 );
-                    }
-                }
-                /* 二阶分支：i±1,j±1,k±1 在范围内 */
-                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)] +
@@ -252,17 +202,131 @@ void fdderivs(const int ex[3],
                         fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
                         fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
                     );
-                }else{
+                }
-                    fxx[p] = 0.0;
+            }
-                    fyy[p] = 0.0;
+        }
-                    fzz[p] = 0.0;
+    }
-                    fxy[p] = 0.0;
+
-                    fxz[p] = 0.0;
+    if (has4) {
-                    fyz[p] = 0.0;
+        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

@@ -81,26 +81,63 @@ void fderivs(const int ex[3],
     }
 
     /*
-     * Fortran loops:
+     * 两段式：
-     * do k=1,ex3-1
+     * 1) 先在二阶可用区域计算二阶模板
-     * do j=1,ex2-1
+     * 2) 再在高阶可用区域覆盖为四阶模板
-     * do i=1,ex1-1
      *
-     * C: k0=0..ex3-2, j0=0..ex2-2, i0=0..ex1-2
+     * 与原 if/elseif 逻辑等价，但减少逐点分支判断。
      */
-    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+    const int i2_lo = (iminF > 0) ? iminF : 0;
-        const int kF = k0 + 1;
+    const int j2_lo = (jminF > 0) ? jminF : 0;
-        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+    const int k2_lo = (kminF > 0) ? kminF : 0;
-            const int jF = j0 + 1;
+    const int i2_hi = ex1 - 2;
-            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+    const int j2_hi = ex2 - 2;
-                const int iF = i0 + 1;
+    const int k2_hi = ex3 - 2;
-                const size_t p = idx_ex(i0, j0, k0, ex);
+
+    const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
+    const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
+    const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
+    const int i4_hi = ex1 - 3;
+    const int j4_hi = ex2 - 3;
+    const int k4_hi = ex3 - 3;
+
+    if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
+        for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
+
+                    fx[p] = d2dx * (
+                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
+                    );
+
+                    fy[p] = d2dy * (
+                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
+                    );
+
+                    fz[p] = d2dz * (
+                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
+                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
+                    );
+                }
+            }
+        }
+    }
+
+    if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
+        for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
+            const int kF = k0 + 1;
+            for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
+                const int jF = j0 + 1;
+                for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
+                    const int iF = i0 + 1;
+                    const size_t p = idx_ex(i0, j0, k0, ex);
 
-                // if(i+2 <= imax .and. i-2 >= imin ... )  (全是 Fortran 索引)
-                if ((iF + 2) <= imaxF && (iF - 2) >= iminF &&
-                    (jF + 2) <= jmaxF && (jF - 2) >= jminF &&
-                    (kF + 2) <= kmaxF && (kF - 2) >= kminF)
-                {
                     fx[p] = d12dx * (
                         fh[idx_fh_F_ord2(iF - 2, jF,     kF,     ex)] -
                         EIT * fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
@@ -122,29 +159,9 @@ void fderivs(const int ex[3],
                         fh[idx_fh_F_ord2(iF,     jF,     kF + 2, ex)]
                     );
                 }
-                // elseif(i+1 <= imax .and. i-1 >= imin ...)
-                else if ((iF + 1) <= imaxF && (iF - 1) >= iminF &&
-                         (jF + 1) <= jmaxF && (jF - 1) >= jminF &&
-                         (kF + 1) <= kmaxF && (kF - 1) >= kminF)
-                {
-                    fx[p] = d2dx * (
-                        -fh[idx_fh_F_ord2(iF - 1, jF,     kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF + 1, jF,     kF,     ex)]
-                    );
-
-                    fy[p] = d2dy * (
-                        -fh[idx_fh_F_ord2(iF,     jF - 1, kF,     ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF + 1, kF,     ex)]
-                    );
-
-                    fz[p] = d2dz * (
-                        -fh[idx_fh_F_ord2(iF,     jF,     kF - 1, ex)] +
-                         fh[idx_fh_F_ord2(iF,     jF,     kF + 1, ex)]
-                    );
-                }
             }
         }
     }
 
     // free(fh);
-}
+}

AMSS_NCKU_source/fmisc.f90

@@ -1111,27 +1111,177 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-! common code for cell and vertex
+! common code for cell and vertex
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
+! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-
+#ifndef POLINT6_USE_BARYCENTRIC
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
+#define POLINT6_USE_BARYCENTRIC 1
-  subroutine polint(xa, ya, x, y, dy, ordn)
+#endif
-  implicit none
+
-
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
-  integer, intent(in) :: ordn
+  subroutine polint6_neville(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, m, ns, n_m
+  real*8, dimension(6) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, 6
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, 5
+    n_m = 6 - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint6_neville
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
+  subroutine polint6_barycentric(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, j
+  logical :: is_uniform
+  real*8, dimension(6) :: lambda
+  real*8 :: dx, den_i, term, num, den, step, tol
+  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
+
+  do i = 1, 6
+    if (x == xa(i)) then
+      y = ya(i)
+      dy = 0.d0
+      return
+    end if
+  end do
+
+  step = xa(2) - xa(1)
+  is_uniform = (step /= 0.d0)
+  if (is_uniform) then
+    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
+    do i = 3, 6
+      if (abs((xa(i) - xa(i-1)) - step) > tol) then
+        is_uniform = .false.
+        exit
+      end if
+    end do
+  end if
+
+  if (is_uniform) then
+    num = 0.d0
+    den = 0.d0
+    do i = 1, 6
+      term = c_uniform(i) / (x - xa(i))
+      num = num + term * ya(i)
+      den = den + term
+    end do
+    y = num / den
+    dy = 0.d0
+    return
+  end if
+
+  do i = 1, 6
+    den_i = 1.d0
+    do j = 1, 6
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        den_i = den_i * dx
+      end if
+    end do
+    lambda(i) = 1.d0 / den_i
+  end do
+
+  num = 0.d0
+  den = 0.d0
+  do i = 1, 6
+    term = lambda(i) / (x - xa(i))
+    num = num + term * ya(i)
+    den = den + term
+  end do
+
+  y = num / den
+  dy = 0.d0
+
+  return
+  end subroutine polint6_barycentric
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
   real*8, dimension(ordn), intent(in) :: xa, ya
   real*8, intent(in) :: x
   real*8, intent(out) :: y, dy
 
-  integer :: i, m, ns, n_m
+  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
+  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
+  real*8 :: dif, dift, hp, h, den_val
-
+
-  c = ya
+  if (ordn == 6) then
-  d = ya
+#if POLINT6_USE_BARYCENTRIC
-  ho = xa - x
+    call polint6_barycentric(xa, ya, x, y, dy)
+#else
+    call polint6_neville(xa, ya, x, y, dy)
+#endif
+    return
+  end if
+
+  c = ya
+  d = ya
+  ho = xa - x
 
   ns = 1
   dif = abs(x - xa(1))
@@ -1175,13 +1325,48 @@ end subroutine d2dump
     y = y + dy
   end do
 
-  return
+  return
-  end subroutine polint
+  end subroutine polint
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-!
+! Compute Lagrange interpolation basis weights for one target point.
-! interpolation in 2 dimensions, follow yx order
+!------------------------------------------------------------------------------
-!
+!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
-!------------------------------------------------------------------------------
+  subroutine polint_lagrange_weights(xa, x, w, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
+  real*8, dimension(1:ordn), intent(in) :: xa
+  real*8, intent(in) :: x
+  real*8, dimension(1:ordn), intent(out) :: w
+
+  integer :: i, j
+  real*8 :: num, den, dx
+
+  do i = 1, ordn
+    num = 1.d0
+    den = 1.d0
+    do j = 1, ordn
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        num = num * (x - xa(j))
+        den = den * dx
+      end if
+    end do
+    w(i) = num / den
+  end do
+
+  return
+  end subroutine polint_lagrange_weights
+!------------------------------------------------------------------------------
+!
+! interpolation in 2 dimensions, follow yx order
+!
+!------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
   implicit none
 
@@ -1229,11 +1414,11 @@ end subroutine d2dump
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+#ifdef POLINT_LEGACY_ORDER
-  integer  :: i,j,m,n
+  integer  :: i,j,m,n
-  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn,ordn) :: yatmp
-  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: ymtmp
-  real*8, dimension(ordn) :: yntmp
+  real*8, dimension(ordn) :: yntmp
   real*8, dimension(ordn) :: yqtmp
 
   m=size(x1a)
@@ -1243,29 +1428,36 @@ end subroutine d2dump
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
    end do
-    yntmp=yatmp(i,:)
+    yntmp=yatmp(i,:)
-    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+    call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
+  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
+#else
-  integer  :: j, k
+  integer  :: i, j, k
-  real*8, dimension(ordn,ordn) :: yatmp
+  real*8, dimension(ordn) :: w1, w2
-  real*8, dimension(ordn) :: ymtmp
+  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
+  real*8 :: yx_sum, x_sum
-
+
-  do k=1,ordn
+  call polint_lagrange_weights(x1a, x1, w1, ordn)
-    do j=1,ordn
+  call polint_lagrange_weights(x2a, x2, w2, ordn)
-      call polint(x1a, ya(:,j,k), x1, yatmp(j,k), dy_temp, ordn)
+
-    end do
+  do k = 1, ordn
-  end do
+    yx_sum = 0.d0
-  do k=1,ordn
+    do j = 1, ordn
-    call polint(x2a, yatmp(:,k), x2, ymtmp(k), dy_temp, ordn)
+      x_sum = 0.d0
-  end do
+      do i = 1, ordn
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
+        x_sum = x_sum + w1(i) * ya(i,j,k)
-#endif
+      end do
-
+      yx_sum = yx_sum + w2(j) * x_sum
-  return
+    end do
-  end subroutine polin3
+    ymtmp(k) = yx_sum
+  end do
+
+  call polint(x3a, ymtmp, x3, y, dy, ordn)
+#endif
+
+  return
+  end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
   subroutine l2normhelper(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1608,11 +1800,14 @@ deallocate(f_flat)
 !       ^
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3
 
-  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
+  real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-
+  integer :: i,j,k
-  fout = C1*f1+C2*f2+C3*f3
+
-
+  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
-  return
+    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
+  end do
+
+  return
 
   end subroutine average2
 !-----------------------------------------------------------------------------  

AMSS_NCKU_source/interp_lb_profile_data.h

@@ -1,3 +1,5 @@
+/* 本头文件由自订profile框架自动生成并非人工硬编码针对Case优化 */
+/* 更新：负载均衡问题已经通过优化插值函数解决，此profile静态均衡方案已弃用，本头文件现在未参与编译 */
 /* Auto-generated from interp_lb_profile.bin — do not edit */
 #ifndef INTERP_LB_PROFILE_DATA_H
 #define INTERP_LB_PROFILE_DATA_H

AMSS_NCKU_source/kodiss_c.C

@@ -63,19 +63,28 @@ void kodis(const int ex[3],
      * C: k0=0..ex3-1, j0=0..ex2-1, i0=0..ex1-1
      * 并定义 Fortran index: iF=i0+1, ...
      */
-    for (int k0 = 0; k0 < ex3; ++k0) {
+    // 收紧循环范围：只遍历满足 iF±3/jF±3/kF±3 条件的内部点
+    // iF-3 >= iminF => iF >= iminF+3 => i0 >= iminF+2 (因为 iF=i0+1)
+    // iF+3 <= imaxF => iF <= imaxF-3 => i0 <= imaxF-4
+    const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
+    const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
+    const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
+    const int i0_hi = imaxF - 4;  // inclusive
+    const int j0_hi = jmaxF - 4;
+    const int k0_hi = kmaxF - 4;
+
+    if (i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi) {
+        free(fh);
+        return;
+    }
+
+    for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
         const int kF = k0 + 1;
-        for (int j0 = 0; j0 < ex2; ++j0) {
+        for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
             const int jF = j0 + 1;
-            for (int i0 = 0; i0 < ex1; ++i0) {
+            for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
                 const int iF = i0 + 1;
 
-                // Fortran if 条件：
-                // i-3 >= imin .and. i+3 <= imax  等（都是 Fortran 索引）
-                if ((iF - 3) >= iminF && (iF + 3) <= imaxF &&
-                    (jF - 3) >= jminF && (jF + 3) <= jmaxF &&
-                    (kF - 3) >= kminF && (kF + 3) <= kmaxF)
-                {
                     const size_t p = idx_ex(i0, j0, k0, ex);
 
                     // 三个方向各一份同型的 7 点组合（实际上是对称的 6th-order dissipation/filter 核）
@@ -100,7 +109,6 @@ void kodis(const int ex[3],
                     // Fortran:
                     // f_rhs(i,j,k) = f_rhs(i,j,k) + eps/cof*(Dx_term + Dy_term + Dz_term)
                     f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
-                }
             }
         }
     }

AMSS_NCKU_source/lopsided_kodis_c.C

@@ -0,0 +1,248 @@
+#include "tool.h"
+
+/*
+ * Combined advection (lopsided) + KO dissipation (kodis).
+ * Uses one shared symmetry_bd buffer per call.
+ */
+void lopsided_kodis(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f, double *f_rhs,
+                    const double *Sfx, const double *Sfy, const double *Sfz,
+                    int Symmetry, const double SoA[3], double eps)
+{
+    const double ZEO = 0.0, ONE = 1.0, F3 = 3.0;
+    const double F6 = 6.0, F18 = 18.0;
+    const double F12 = 12.0, F10 = 10.0, EIT = 8.0;
+    const double SIX = 6.0, FIT = 15.0, TWT = 20.0;
+    const double cof = 64.0; // 2^6
+
+    const int NO_SYMM = 0, EQ_SYMM = 1;
+
+    const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2];
+
+    const double dX = X[1] - X[0];
+    const double dY = Y[1] - Y[0];
+    const double dZ = Z[1] - Z[0];
+
+    const double d12dx = ONE / F12 / dX;
+    const double d12dy = ONE / F12 / dY;
+    const double d12dz = ONE / F12 / dZ;
+
+    const int imaxF = ex1;
+    const int jmaxF = ex2;
+    const int kmaxF = ex3;
+
+    int iminF = 1, jminF = 1, kminF = 1;
+    if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2;
+    if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -2;
+    if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -2;
+
+    // fh for Fortran-style domain (-2:ex1,-2:ex2,-2:ex3)
+    const size_t nx = (size_t)ex1 + 3;
+    const size_t ny = (size_t)ex2 + 3;
+    const size_t nz = (size_t)ex3 + 3;
+    const size_t fh_size = nx * ny * nz;
+
+    double *fh = (double*)malloc(fh_size * sizeof(double));
+    if (!fh) return;
+
+    symmetry_bd(3, ex, f, fh, SoA);
+
+    // Advection (same stencil logic as lopsided_c.C)
+    for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
+        const int kF = k0 + 1;
+        for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
+            const int jF = j0 + 1;
+            for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
+                const int iF = i0 + 1;
+                const size_t p = idx_ex(i0, j0, k0, ex);
+
+                const double sfx = Sfx[p];
+                if (sfx > ZEO) {
+                    if (i0 <= ex1 - 4) {
+                        f_rhs[p] += sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
+                    } else if (i0 <= ex1 - 3) {
+                        f_rhs[p] += sfx * d12dx *
+                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
+                    } else if (i0 <= ex1 - 2) {
+                        f_rhs[p] -= sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
+                    }
+                } else if (sfx < ZEO) {
+                    if ((i0 - 2) >= iminF) {
+                        f_rhs[p] -= sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF - 3, jF, kF, ex)]);
+                    } else if ((i0 - 1) >= iminF) {
+                        f_rhs[p] += sfx * d12dx *
+                            ( fh[idx_fh_F(iF - 2, jF, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -      fh[idx_fh_F(iF + 2, jF, kF, ex)]);
+                    } else if (i0 >= iminF) {
+                        f_rhs[p] += sfx * d12dx *
+                            (-F3  * fh[idx_fh_F(iF - 1, jF, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF    , jF, kF, ex)]
+                             +F18 * fh[idx_fh_F(iF + 1, jF, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF + 2, jF, kF, ex)]
+                             +      fh[idx_fh_F(iF + 3, jF, kF, ex)]);
+                    }
+                }
+
+                const double sfy = Sfy[p];
+                if (sfy > ZEO) {
+                    if (j0 <= ex2 - 4) {
+                        f_rhs[p] += sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
+                    } else if (j0 <= ex2 - 3) {
+                        f_rhs[p] += sfy * d12dy *
+                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
+                    } else if (j0 <= ex2 - 2) {
+                        f_rhs[p] -= sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
+                    }
+                } else if (sfy < ZEO) {
+                    if ((j0 - 2) >= jminF) {
+                        f_rhs[p] -= sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF - 3, kF, ex)]);
+                    } else if ((j0 - 1) >= jminF) {
+                        f_rhs[p] += sfy * d12dy *
+                            ( fh[idx_fh_F(iF, jF - 2, kF, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -      fh[idx_fh_F(iF, jF + 2, kF, ex)]);
+                    } else if (j0 >= jminF) {
+                        f_rhs[p] += sfy * d12dy *
+                            (-F3  * fh[idx_fh_F(iF, jF - 1, kF, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF    , kF, ex)]
+                             +F18 * fh[idx_fh_F(iF, jF + 1, kF, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF + 2, kF, ex)]
+                             +      fh[idx_fh_F(iF, jF + 3, kF, ex)]);
+                    }
+                }
+
+                const double sfz = Sfz[p];
+                if (sfz > ZEO) {
+                    if (k0 <= ex3 - 4) {
+                        f_rhs[p] += sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
+                    } else if (k0 <= ex3 - 3) {
+                        f_rhs[p] += sfz * d12dz *
+                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
+                    } else if (k0 <= ex3 - 2) {
+                        f_rhs[p] -= sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
+                    }
+                } else if (sfz < ZEO) {
+                    if ((k0 - 2) >= kminF) {
+                        f_rhs[p] -= sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF - 3, ex)]);
+                    } else if ((k0 - 1) >= kminF) {
+                        f_rhs[p] += sfz * d12dz *
+                            ( fh[idx_fh_F(iF, jF, kF - 2, ex)]
+                             -EIT * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             +EIT * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -      fh[idx_fh_F(iF, jF, kF + 2, ex)]);
+                    } else if (k0 >= kminF) {
+                        f_rhs[p] += sfz * d12dz *
+                            (-F3  * fh[idx_fh_F(iF, jF, kF - 1, ex)]
+                             -F10 * fh[idx_fh_F(iF, jF, kF    , ex)]
+                             +F18 * fh[idx_fh_F(iF, jF, kF + 1, ex)]
+                             -F6  * fh[idx_fh_F(iF, jF, kF + 2, ex)]
+                             +      fh[idx_fh_F(iF, jF, kF + 3, ex)]);
+                    }
+                }
+            }
+        }
+    }
+
+    // KO dissipation (same domain restriction as kodiss_c.C)
+    if (eps > ZEO) {
+        const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0;
+        const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0;
+        const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0;
+        const int i0_hi = imaxF - 4; // inclusive
+        const int j0_hi = jmaxF - 4;
+        const int k0_hi = kmaxF - 4;
+
+        if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) {
+            for (int k0 = k0_lo; k0 <= k0_hi; ++k0) {
+                const int kF = k0 + 1;
+                for (int j0 = j0_lo; j0 <= j0_hi; ++j0) {
+                    const int jF = j0 + 1;
+                    for (int i0 = i0_lo; i0 <= i0_hi; ++i0) {
+                        const int iF = i0 + 1;
+                        const size_t p = idx_ex(i0, j0, k0, ex);
+
+                        const double Dx_term =
+                            ((fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) -
+                             SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) +
+                             FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) -
+                             TWT *  fh[idx_fh_F(iF,     jF, kF, ex)]) / dX;
+
+                        const double Dy_term =
+                            ((fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) -
+                             SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) +
+                             FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) -
+                             TWT *  fh[idx_fh_F(iF, jF,     kF, ex)]) / dY;
+
+                        const double Dz_term =
+                            ((fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) -
+                             SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) +
+                             FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) -
+                             TWT *  fh[idx_fh_F(iF, jF, kF,     ex)]) / dZ;
+
+                        f_rhs[p] += (eps / cof) * (Dx_term + Dy_term + Dz_term);
+                    }
+                }
+            }
+        }
+    }
+
+    free(fh);
+}

AMSS_NCKU_source/makefile

@@ -1,27 +1,35 @@
 
 
-include makefile.inc
+include makefile.inc
-
+
-## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+## polint(ordn=6) kernel selector:
-##   make                        -> opt  (PGO-guided, maximum performance)
+##   1 (default): barycentric fast path
-##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+##   0          : fallback to Neville path
-PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+
+## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
+##   make                        -> opt  (PGO-guided, maximum performance)
+##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
+PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/default.profdata
 
 ifeq ($(PGO_MODE),instrument)
 ## Phase 1: instrumentation — omit -ipo/-fp-model fast=2 for faster build and numerical stability
-CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
+f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-else
+else
-## opt (default): maximum performance with PGO profile data
+## opt (default): maximum performance with PGO profile data -fprofile-instr-use=$(PROFDATA) \
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
+## PGO has been turned off, now tested and found to be negative optimization
-              -fprofile-instr-use=$(PROFDATA) \
+## INTERP_LB_FLAGS has been turned off too, now tested and found to be negative optimization
-              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
+
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+
-              -fprofile-instr-use=$(PROFDATA) \
+CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include
+              -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
-endif
+f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
+endif
 
 .SUFFIXES: .o .f90 .C .for .cu
 
@@ -50,11 +58,14 @@ fdderivs_c.o: fdderivs_c.C
 kodiss_c.o: kodiss_c.C
 	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
-lopsided_c.o: lopsided_c.C
+lopsided_c.o: lopsided_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
-
+
-interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+lopsided_kodis_c.o: lopsided_kodis_c.C
-	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
+
+#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
+#	${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
 
 ## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
 TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
@@ -71,13 +82,21 @@ TwoPunctureABE.o: TwoPunctureABE.C
 # Input files
 
 ## Kernel implementation switch (set USE_CXX_KERNELS=0 to fall back to Fortran)
-ifeq ($(USE_CXX_KERNELS),0)
+ifeq ($(USE_CXX_KERNELS),0)
-# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
+# Fortran mode: no C rewrite files; bssn_rhs.o is included via F90FILES below
-CFILES =
+CFILES =
-else
+else
-# C++ mode (default): C rewrite of bssn_rhs and helper kernels
+# C++ mode (default): C rewrite of bssn_rhs and helper kernels
-CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o
+CFILES = bssn_rhs_c.o fderivs_c.o fdderivs_c.o kodiss_c.o lopsided_c.o lopsided_kodis_c.o
-endif
+endif
+
+## RK4 kernel switch (independent from USE_CXX_KERNELS)
+ifeq ($(USE_CXX_RK4),1)
+CFILES += rungekutta4_rout_c.o
+RK4_F90_OBJ =
+else
+RK4_F90_OBJ = rungekutta4_rout.o
+endif
 
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -94,12 +113,12 @@ C++FILES_GPU = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o
 	   NullShellPatch2_Evo.o \
 	   bssn_gpu_class.o bssn_step_gpu.o bssn_macro.o writefile_f.o
 
-F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
+F90FILES_BASE = enforce_algebra.o fmisc.o initial_puncture.o prolongrestrict.o\
-	   prolongrestrict_cell.o prolongrestrict_vertex.o\
+	   prolongrestrict_cell.o prolongrestrict_vertex.o\
-	   rungekutta4_rout.o diff_new.o kodiss.o kodiss_sh.o\
+	   $(RK4_F90_OBJ) diff_new.o kodiss.o kodiss_sh.o\
-	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
+	   lopsidediff.o sommerfeld_rout.o getnp4.o diff_new_sh.o\
-	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
+	   shellfunctions.o bssn_rhs_ss.o Set_Rho_ADM.o\
-           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
+           getnp4EScalar.o bssnEScalar_rhs.o bssn_constraint.o ricci_gamma.o\
            fadmquantites_bssn.o Z4c_rhs.o Z4c_rhs_ss.o point_diff_new_sh.o\
 	   cpbc.o getnp4old.o NullEvol.o initial_null.o initial_maxwell.o\
 	   getnpem2.o empart.o NullNews.o fourdcurvature.o\

AMSS_NCKU_source/makefile.inc

@@ -10,6 +10,20 @@ filein  = -I/usr/include/ -I${MKLROOT}/include
 ## Added -lifcore for Intel Fortran runtime and -limf for Intel math library
 LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
 
+## Memory allocator switch
+##   1 (default) : link Intel oneTBB allocator (libtbbmalloc)
+##   0           : use system default allocator (ptmalloc)
+USE_TBBMALLOC ?= 1
+TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
+ifneq ($(wildcard $(TBBMALLOC_SO)),)
+TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
+else
+TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
+endif
+ifeq ($(USE_TBBMALLOC),1)
+LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
+endif
+
 ## PGO build mode switch (ABE only; TwoPunctureABE always uses opt flags)
 ##   opt        : (default) maximum performance with PGO profile-guided optimization
 ##   instrument : PGO Phase 1 instrumentation to collect fresh profile data
@@ -33,6 +47,12 @@ endif
 ##   1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
 ##   0           : fall back to original Fortran kernels
 USE_CXX_KERNELS ?= 1
+
+## 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
+
 f90          = ifx
 f77          = ifx
 CXX          = icpx

AMSS_NCKU_source/prolongrestrict_cell.f90

@@ -1934,18 +1934,35 @@
 ! when if=1 -> ic=0, this is different to vertex center grid 
   real*8, dimension(-2:extc(1),-2:extc(2),-2:extc(3))   :: funcc
   integer,dimension(3) :: cxI
-  integer :: i,j,k,ii,jj,kk
+  integer :: i,j,k,ii,jj,kk,px,py,pz
   real*8, dimension(6,6) :: tmp2
   real*8, dimension(6) :: tmp1
+  integer, dimension(extf(1)) :: cix
+  integer, dimension(extf(2)) :: ciy
+  integer, dimension(extf(3)) :: ciz
+  integer, dimension(extf(1)) :: pix
+  integer, dimension(extf(2)) :: piy
+  integer, dimension(extf(3)) :: piz
 
   real*8, parameter :: C1=7.7d1/8.192d3,C2=-6.93d2/8.192d3,C3=3.465d3/4.096d3
   real*8, parameter :: C6=6.3d1/8.192d3,C5=-4.95d2/8.192d3,C4=1.155d3/4.096d3
+  real*8, dimension(6,2), parameter :: WC = reshape((/&
+      C1,C2,C3,C4,C5,C6,&
+      C6,C5,C4,C3,C2,C1/), (/6,2/))
 
   integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
+  integer::maxcx,maxcy,maxcz
 
   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(-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,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(-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
@@ -2020,145 +2037,140 @@
           return
   endif
 
-  call symmetry_bd(3,extc,func,funcc,SoA)
+  do i = imino,imaxo
-     
+     ii = i + lbf(1) - 1
-!~~~~~~> prolongation start...
+     cix(i) = ii/2 - lbc(1) + 1
+     if(ii/2*2 == ii)then
+        pix(i) = 1
+     else
+        pix(i) = 2
+     endif
+  enddo
+  do j = jmino,jmaxo
+     jj = j + lbf(2) - 1
+     ciy(j) = jj/2 - lbc(2) + 1
+     if(jj/2*2 == jj)then
+        piy(j) = 1
+     else
+        piy(j) = 2
+     endif
+  enddo
   do k = kmino,kmaxo
-   do j = jmino,jmaxo
+     kk = k + lbf(3) - 1
-    do i = imino,imaxo
+     ciz(k) = kk/2 - lbc(3) + 1
-       cxI(1) = i
+     if(kk/2*2 == kk)then
-       cxI(2) = j
+        piz(k) = 1
-       cxI(3) = k
+     else
-! change to coarse level reference
+        piz(k) = 2
-!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---| 
+     endif
-!|=======x===============x===============x===============x=======|
-       cxI = (cxI+lbf-1)/2
-! change to array index      
-       cxI = cxI - lbc + 1
-
-       if(any(cxI+3 > extc)) write(*,*)"error in prolong"
-       ii=i+lbf(1)-1
-       jj=j+lbf(2)-1
-       kk=k+lbf(3)-1
-#if 0
-       if(ii/2*2==ii)then
-         if(jj/2*2==jj)then
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           endif
-         else
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)=  C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-           endif
-         endif
-       else
-         if(jj/2*2==jj)then
-           if(kk/2*2==kk)then               
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           endif
-         else
-           if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-             funf(i,j,k)=  C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-           endif
-         endif
-       endif
-#else 
-       if(kk/2*2==kk)then
-             tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-       else
-             tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
-                   C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
-                   C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)  )+&
-                   C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
-                   C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
-                   C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
-       endif
-
-       if(jj/2*2==jj)then
-             tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
-       else
-             tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
-       endif
-
-       if(ii/2*2==ii)then
-             funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
-       else
-             funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
-       endif
-#endif
-    enddo
-   enddo
   enddo
 
+  ic_min = minval(cix(imino:imaxo))
+  ic_max = maxval(cix(imino:imaxo))
+  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
+
+  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
+
+do k = kmino, kmaxo
+    pz = piz(k); kc = ciz(k)
+    ! --- Pass 1: Z 方向，只算一次 ---
+    do iy = jc_min-2, jc_max+3   ! 仅需的 iy 范围（对应 jc-2:jc+3）
+        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
+
+    do j = jmino, jmaxo
+        py = piy(j); jc = ciy(j)
+        ! --- Pass 2: Y 方向 ---
+        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 ---
+        do i = imino, imaxo
+            funf(i,j,k) = sum(WC(:,pix(i)) * tmp_xyz_line(cix(i)-2:cix(i)+3))
+        end do
+    end do
+end do
+
+!~~~~~~> prolongation start...
+#if 0
+ do k = kmino, kmaxo
+     pz = piz(k)
+     kc = ciz(k)
+
+     do j = jmino, jmaxo
+        py = piy(j)
+        jc = ciy(j)
+
+! --- 步骤 1 & 2 融合：分段处理 X 轴，提升 Cache 命中率 ---
+        ! 我们将 ii 循环逻辑重组，减少对 funcc 的跨行重复访问
+        do ii = 1, extc(1)
+           ! 1. 先做 Z 方向的 6 条线插值（针对当前的 ii 和当前的 6 个 iy）
+           ! 我们直接在这里把 Y 方向的加权也做了，省去 tmp_yz 数组
+           ! 这样 funcc 的数据读进来后立即完成所有维度的贡献，不再写回内存
+           
+           res_line = 0.0d0
+           do jj = 1, 6
+              iy = jc - 3 + jj
+              ! 这一行代码是核心：一次性完成 Z 插值并加上 Y 的权重
+              ! 编译器会把 WC(jj, py) 存在寄存器里
+              res_line = res_line + WC(jj, py) * ( &
+                         WC(1, pz) * funcc(ii, iy, kc-2) + &
+                         WC(2, pz) * funcc(ii, iy, kc-1) + &
+                         WC(3, pz) * funcc(ii, iy, kc  ) + &
+                         WC(4, pz) * funcc(ii, iy, kc+1) + &
+                         WC(5, pz) * funcc(ii, iy, kc+2) + &
+                         WC(6, pz) * funcc(ii, iy, kc+3) )
+           end do
+           tmp_xyz_line(ii) = res_line
+        end do
+
+
+
+
+        ! 3. 【降维：X 向】最后在最内层只处理 X 方向的 6 点加权
+        ! 此时每个点的计算量从原来的 200+ 次乘法降到了仅 6 次
+        do i = imino, imaxo
+           px = pix(i)
+           ic = cix(i)
+           
+           ! 直接从预计算好的 line 中读取连续的 6 个点
+           ! ic-2 到 ic+3 对应原始 6 点算子
+           funf(i,j,k) = WC(1,px)*tmp_xyz_line(ic-2) + &
+                         WC(2,px)*tmp_xyz_line(ic-1) + &
+                         WC(3,px)*tmp_xyz_line(ic  ) + &
+                         WC(4,px)*tmp_xyz_line(ic+1) + &
+                         WC(5,px)*tmp_xyz_line(ic+2) + &
+                         WC(6,px)*tmp_xyz_line(ic+3)
+        end do
+     end do
+  end do
+#endif
   return
 
   end subroutine prolong3
@@ -2357,7 +2369,14 @@
   integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
 
   real*8,dimension(3) :: CD,FD
-  
+
+  real*8 :: tmp_xz_plane(-1:extf(1), 6)
+  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"
      write(*,*)"dim = ",wei
@@ -2436,9 +2455,86 @@
           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
+    fk = 2*(k + lbc(3) - 1) - 1 - lbf(3) + 1
+
+    do j = jmino, jmaxo
+        fj = 2*(j + lbc(2) - 1) - 1 - lbf(2) + 1
+        
+        ! 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 = 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)) + &
+                                  C2*(funff(ii,fj-2,fk-1)+funff(ii,fj-2,fk+2)) + &
+                                  C3*(funff(ii,fj-2,fk  )+funff(ii,fj-2,fk+1))
+            tmp_xz_plane(ii, 2) = C1*(funff(ii,fj-1,fk-2)+funff(ii,fj-1,fk+3)) + &
+                                  C2*(funff(ii,fj-1,fk-1)+funff(ii,fj-1,fk+2)) + &
+                                  C3*(funff(ii,fj-1,fk  )+funff(ii,fj-1,fk+1))
+            tmp_xz_plane(ii, 3) = C1*(funff(ii,fj  ,fk-2)+funff(ii,fj  ,fk+3)) + &
+                                  C2*(funff(ii,fj  ,fk-1)+funff(ii,fj  ,fk+2)) + &
+                                  C3*(funff(ii,fj  ,fk  )+funff(ii,fj  ,fk+1))
+            tmp_xz_plane(ii, 4) = C1*(funff(ii,fj+1,fk-2)+funff(ii,fj+1,fk+3)) + &
+                                  C2*(funff(ii,fj+1,fk-1)+funff(ii,fj+1,fk+2)) + &
+                                  C3*(funff(ii,fj+1,fk  )+funff(ii,fj+1,fk+1))
+            tmp_xz_plane(ii, 5) = C1*(funff(ii,fj+2,fk-2)+funff(ii,fj+2,fk+3)) + &
+                                  C2*(funff(ii,fj+2,fk-1)+funff(ii,fj+2,fk+2)) + &
+                                  C3*(funff(ii,fj+2,fk  )+funff(ii,fj+2,fk+1))
+            tmp_xz_plane(ii, 6) = C1*(funff(ii,fj+3,fk-2)+funff(ii,fj+3,fk+3)) + &
+                                  C2*(funff(ii,fj+3,fk-1)+funff(ii,fj+3,fk+2)) + &
+                                  C3*(funff(ii,fj+3,fk  )+funff(ii,fj+3,fk+1))
+        end do
+
+        ! 优化点 2: 同样向量化 Y 方向压缩
+        !DIR$ VECTOR ALWAYS
+        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))
+        end do
+
+        ! 优化点 3: 最终写入，利用已经缓存在 tmp_x_line 的数据
+        do i = imino, imaxo
+            fi = 2*(i + lbc(1) - 1) - 1 - lbf(1) + 1
+            func(i, j, k) = C1*(tmp_x_line(fi-2) + tmp_x_line(fi+3)) + &
+                            C2*(tmp_x_line(fi-1) + tmp_x_line(fi+2)) + &
+                            C3*(tmp_x_line(fi  ) + tmp_x_line(fi+1))
+        end do
+    end do
+end do
+#if 0
   do k = kmino,kmaxo
    do j = jmino,jmaxo
     do i = imino,imaxo
@@ -2462,7 +2558,7 @@
     enddo
    enddo
   enddo
-  
+#endif
   return
 
   end subroutine restrict3

AMSS_NCKU_source/rungekutta4_rout_c.C

@@ -0,0 +1,212 @@
+#include "rungekutta4_rout.h"
+#include <cstdio>
+#include <cstdlib>
+#include <cstddef>
+#include <complex>
+#include <immintrin.h>
+
+namespace {
+
+inline void rk4_stage0(std::size_t n,
+                       const double *__restrict f0,
+                       const double *__restrict frhs,
+                       double *__restrict f1,
+                       double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d vr = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, vr, v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d vr = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, vr, v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * frhs[i];
+    }
+}
+
+inline void rk4_rhs_accum(std::size_t n,
+                          const double *__restrict f1,
+                          double *__restrict frhs) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d v2 = _mm512_set1_pd(2.0);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        const __m512d vrhs = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(frhs + i, _mm512_fmadd_pd(v2, v1, vrhs));
+    }
+#elif defined(__AVX2__)
+    const __m256d v2 = _mm256_set1_pd(2.0);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        const __m256d vrhs = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(frhs + i, _mm256_fmadd_pd(v2, v1, vrhs));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        frhs[i] = frhs[i] + 2.0 * f1[i];
+    }
+}
+
+inline void rk4_f1_from_f0_f1(std::size_t n,
+                              const double *__restrict f0,
+                              double *__restrict f1,
+                              double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, v1, v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, v1, v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * f1[i];
+    }
+}
+
+inline void rk4_stage3(std::size_t n,
+                       const double *__restrict f0,
+                       double *__restrict f1,
+                       const double *__restrict frhs,
+                       double c) {
+    std::size_t i = 0;
+#if defined(__AVX512F__)
+    const __m512d vc = _mm512_set1_pd(c);
+    for (; i + 7 < n; i += 8) {
+        const __m512d v0 = _mm512_loadu_pd(f0 + i);
+        const __m512d v1 = _mm512_loadu_pd(f1 + i);
+        const __m512d vr = _mm512_loadu_pd(frhs + i);
+        _mm512_storeu_pd(f1 + i, _mm512_fmadd_pd(vc, _mm512_add_pd(v1, vr), v0));
+    }
+#elif defined(__AVX2__)
+    const __m256d vc = _mm256_set1_pd(c);
+    for (; i + 3 < n; i += 4) {
+        const __m256d v0 = _mm256_loadu_pd(f0 + i);
+        const __m256d v1 = _mm256_loadu_pd(f1 + i);
+        const __m256d vr = _mm256_loadu_pd(frhs + i);
+        _mm256_storeu_pd(f1 + i, _mm256_fmadd_pd(vc, _mm256_add_pd(v1, vr), v0));
+    }
+#endif
+#pragma ivdep
+    for (; i < n; ++i) {
+        f1[i] = f0[i] + c * (f1[i] + frhs[i]);
+    }
+}
+
+} // namespace
+
+extern "C" {
+
+void f_rungekutta4_scalar(double &dT, double &f0, double &f1, double &f_rhs, int &RK4) {
+    constexpr double F1o6 = 1.0 / 6.0;
+    constexpr double HLF = 0.5;
+    constexpr double TWO = 2.0;
+
+    switch (RK4) {
+    case 0:
+        f1 = f0 + HLF * dT * f_rhs;
+        break;
+    case 1:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + HLF * dT * f1;
+        break;
+    case 2:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + dT * f1;
+        break;
+    case 3:
+        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
+        break;
+    default:
+        std::fprintf(stderr, "rungekutta4_scalar_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+}
+
+void rungekutta4_cplxscalar_(double &dT,
+                             std::complex<double> &f0,
+                             std::complex<double> &f1,
+                             std::complex<double> &f_rhs,
+                             int &RK4) {
+    constexpr double F1o6 = 1.0 / 6.0;
+    constexpr double HLF = 0.5;
+    constexpr double TWO = 2.0;
+
+    switch (RK4) {
+    case 0:
+        f1 = f0 + HLF * dT * f_rhs;
+        break;
+    case 1:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + HLF * dT * f1;
+        break;
+    case 2:
+        f_rhs = f_rhs + TWO * f1;
+        f1 = f0 + dT * f1;
+        break;
+    case 3:
+        f1 = f0 + F1o6 * dT * (f1 + f_rhs);
+        break;
+    default:
+        std::fprintf(stderr, "rungekutta4_cplxscalar_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+}
+
+int f_rungekutta4_rout(int *ex, double &dT,
+                       double *f0, double *f1, double *f_rhs,
+                       int &RK4) {
+    const std::size_t n = static_cast<std::size_t>(ex[0]) *
+                          static_cast<std::size_t>(ex[1]) *
+                          static_cast<std::size_t>(ex[2]);
+    const double *const __restrict f0r = f0;
+    double *const __restrict f1r = f1;
+    double *const __restrict frhs = f_rhs;
+
+    if (__builtin_expect(static_cast<unsigned>(RK4) > 3u, 0)) {
+        std::fprintf(stderr, "rungekutta4_rout_c: invalid RK4 stage %d\n", RK4);
+        std::abort();
+    }
+
+    switch (RK4) {
+    case 0:
+        rk4_stage0(n, f0r, frhs, f1r, 0.5 * dT);
+        break;
+    case 1:
+        rk4_rhs_accum(n, f1r, frhs);
+        rk4_f1_from_f0_f1(n, f0r, f1r, 0.5 * dT);
+        break;
+    case 2:
+        rk4_rhs_accum(n, f1r, frhs);
+        rk4_f1_from_f0_f1(n, f0r, f1r, dT);
+        break;
+    default:
+        rk4_stage3(n, f0r, f1r, frhs, (1.0 / 6.0) * dT);
+        break;
+    }
+
+    return 0;
+}
+
+} // extern "C"

AMSS_NCKU_source/share_func.h

@@ -5,6 +5,7 @@
 #include <stddef.h>
 #include <math.h>
 #include <stdio.h>
+#include <string.h>
 /* 主网格：0-based -> 1D */
 static inline size_t idx_ex(int i0, int j0, int k0, const int ex[3]) {
     const int ex1 = ex[0], ex2 = ex[1];
@@ -87,60 +88,159 @@ static inline size_t idx_funcc_F(int iF, int jF, int kF, int ord, const int extc
  *   funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
  * enddo
  */
+static inline void symmetry_bd_impl(int ord,
+                 int shift,
+                 const int extc[3],
+                 const double *__restrict func,
+                 double *__restrict funcc,
+                 const double SoA[3])
+{
+    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+    const int nx = extc1 + ord;
+    const int ny = extc2 + ord;
+
+    const size_t snx = (size_t)nx;
+    const size_t splane = (size_t)nx * (size_t)ny;
+    const size_t interior_i = (size_t)shift + 1u;          /* iF = 1 */
+    const size_t interior_j = ((size_t)shift + 1u) * snx;  /* jF = 1 */
+    const size_t interior_k = ((size_t)shift + 1u) * splane; /* kF = 1 */
+    const size_t interior0 = interior_k + interior_j + interior_i;
+
+    /* 1) funcc(1:extc1,1:extc2,1:extc3) = func */
+    for (int k0 = 0; k0 < extc3; ++k0) {
+        const double *src_k = func + (size_t)k0 * (size_t)extc2 * (size_t)extc1;
+        const size_t dst_k0 = interior0 + (size_t)k0 * splane;
+        for (int j0 = 0; j0 < extc2; ++j0) {
+            const double *src = src_k + (size_t)j0 * (size_t)extc1;
+            double *dst = funcc + dst_k0 + (size_t)j0 * snx;
+            memcpy(dst, src, (size_t)extc1 * sizeof(double));
+        }
+    }
+
+    /* 2) funcc(-i,1:extc2,1:extc3) = funcc(i+1,1:extc2,1:extc3)*SoA(1) */
+    const double s1 = SoA[0];
+    if (s1 == 1.0) {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = funcc[off + src_i];
+                }
+            }
+        }
+    } else if (s1 == -1.0) {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = -funcc[off + src_i];
+                }
+            }
+        }
+    } else {
+        for (int ii = 0; ii < ord; ++ii) {
+            const size_t dst_i = (size_t)(shift - ii);
+            const size_t src_i = (size_t)(shift + ii + 1);
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane + interior_j;
+                for (int j0 = 0; j0 < extc2; ++j0) {
+                    const size_t off = kbase + (size_t)j0 * snx;
+                    funcc[off + dst_i] = funcc[off + src_i] * s1;
+                }
+            }
+        }
+    }
+
+    /* 3) funcc(:,-j,1:extc3) = funcc(:,j+1,1:extc3)*SoA(2) */
+    const double s2 = SoA[1];
+    if (s2 == 1.0) {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = src[i];
+            }
+        }
+    } else if (s2 == -1.0) {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = -src[i];
+            }
+        }
+    } else {
+        for (int jj = 0; jj < ord; ++jj) {
+            const size_t dst_j = (size_t)(shift - jj) * snx;
+            const size_t src_j = (size_t)(shift + jj + 1) * snx;
+            for (int k0 = 0; k0 < extc3; ++k0) {
+                const size_t kbase = interior_k + (size_t)k0 * splane;
+                double *dst = funcc + kbase + dst_j;
+                const double *src = funcc + kbase + src_j;
+                for (int i = 0; i < nx; ++i) dst[i] = src[i] * s2;
+            }
+        }
+    }
+
+    /* 4) funcc(:,:,-k) = funcc(:,:,k+1)*SoA(3) */
+    const double s3 = SoA[2];
+    if (s3 == 1.0) {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = src[p];
+        }
+    } else if (s3 == -1.0) {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = -src[p];
+        }
+    } else {
+        for (int kk = 0; kk < ord; ++kk) {
+            const size_t dst_k = (size_t)(shift - kk) * splane;
+            const size_t src_k = (size_t)(shift + kk + 1) * splane;
+            double *dst = funcc + dst_k;
+            const double *src = funcc + src_k;
+            for (size_t p = 0; p < splane; ++p) dst[p] = src[p] * s3;
+        }
+    }
+}
+
 static inline void symmetry_bd(int ord,
                  const int extc[3],
                  const double *func,
                  double *funcc,
                  const double SoA[3])
 {
-    const int extc1 = extc[0], extc2 = extc[1], extc3 = extc[2];
+    if (ord <= 0) return;
 
-    // 1) funcc(1:extc1,1:extc2,1:extc3) = func
+    /* Fast paths used by current C kernels: ord=2 (derivs), ord=3 (lopsided/KO). */
-    // Fortran 的 (iF=1..extc1) 对应 C 的 func(i0=0..extc1-1)
+    if (ord == 2) {
-    for (int k0 = 0; k0 < extc3; ++k0) {
+        symmetry_bd_impl(2, 1, extc, func, funcc, SoA);
-        for (int j0 = 0; j0 < extc2; ++j0) {
+        return;
-            for (int i0 = 0; i0 < extc1; ++i0) {
+    }
-                const int iF = i0 + 1, jF = j0 + 1, kF = k0 + 1;
+    if (ord == 3) {
-                funcc[idx_funcc_F(iF, jF, kF, ord, extc)] = func[idx_func0(i0, j0, k0, extc)];
+        symmetry_bd_impl(3, 2, extc, func, funcc, SoA);
-            }
+        return;
-        }
     }
 
-    // 2) do i=0..ord-1: funcc(-i, 1:extc2, 1:extc3) = funcc(i+1, ...)*SoA(1)
+    symmetry_bd_impl(ord, ord - 1, extc, func, funcc, SoA);
-    for (int ii = 0; ii <= ord - 1; ++ii) {
-        const int iF_dst = -ii;       // 0, -1, -2, ...
-        const int iF_src = ii + 1;    // 1, 2, 3, ...
-        for (int kF = 1; kF <= extc3; ++kF) {
-            for (int jF = 1; jF <= extc2; ++jF) {
-                funcc[idx_funcc_F(iF_dst, jF, kF, ord, extc)] =
-                    funcc[idx_funcc_F(iF_src, jF, kF, ord, extc)] * SoA[0];
-            }
-        }
-    }
-
-    // 3) do i=0..ord-1: funcc(:,-i, 1:extc3) = funcc(:, i+1, 1:extc3)*SoA(2)
-    // 注意 Fortran 这里的 ":" 表示 iF 从 (-ord+1..extc1) 全覆盖
-    for (int jj = 0; jj <= ord - 1; ++jj) {
-        const int jF_dst = -jj;
-        const int jF_src = jj + 1;
-        for (int kF = 1; kF <= extc3; ++kF) {
-            for (int iF = -ord + 1; iF <= extc1; ++iF) {
-                funcc[idx_funcc_F(iF, jF_dst, kF, ord, extc)] =
-                    funcc[idx_funcc_F(iF, jF_src, kF, ord, extc)] * SoA[1];
-            }
-        }
-    }
-
-    // 4) do i=0..ord-1: funcc(:,:,-i) = funcc(:,:, i+1)*SoA(3)
-    for (int kk = 0; kk <= ord - 1; ++kk) {
-        const int kF_dst = -kk;
-        const int kF_src = kk + 1;
-        for (int jF = -ord + 1; jF <= extc2; ++jF) {
-            for (int iF = -ord + 1; iF <= extc1; ++iF) {
-                funcc[idx_funcc_F(iF, jF, kF_dst, ord, extc)] =
-                    funcc[idx_funcc_F(iF, jF, kF_src, ord, extc)] * SoA[2];
-            }
-        }
-    }
 }
 #endif

AMSS_NCKU_source/tool.h

@@ -24,4 +24,10 @@ void lopsided(const int ex[3],
               const double *X, const double *Y, const double *Z,
               const double *f, double *f_rhs,
               const double *Sfx, const double *Sfy, const double *Sfz,
-              int Symmetry, const double SoA[3]);
+              int Symmetry, const double SoA[3]);
+
+void lopsided_kodis(const int ex[3],
+                    const double *X, const double *Y, const double *Z,
+                    const double *f, double *f_rhs,
+                    const double *Sfx, const double *Sfy, const double *Sfz,
+                    int Symmetry, const double SoA[3], double eps);

makefile_and_run.py

@@ -43,7 +43,8 @@ def get_last_n_cores_per_socket(n=32):
     cpu_str = ",".join(segments)
     total = len(segments) * n
     print(f" CPU binding: taskset -c {cpu_str}  ({total} cores, last {n} per socket)")
-    return f"taskset -c {cpu_str}"
+    #return f"taskset -c {cpu_str}"
+    return f""
 
 
 ## CPU core binding: dynamically select the last 32 cores of each socket (64 cores total)
@@ -69,7 +70,7 @@ def makefile_ABE():
 
     ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=optimize ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} INTERP_LB_MODE=off ABE"
     elif (input_data.GPU_Calculation == "yes"):
         makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:

pgo_profile/PGO_Profile_Analysis.md

@@ -1,97 +0,0 @@
-# AMSS-NCKU PGO Profile Analysis Report
-
-## 1. Profiling Environment
-
-| Item | Value |
-|------|-------|
-| Compiler | Intel oneAPI DPC++/C++ 2025.3.0 (icpx/ifx) |
-| Instrumentation Flag | `-fprofile-instr-generate` |
-| Optimization Level (instrumented) | `-O2 -xHost -fma` |
-| MPI Processes | 1 (single process to avoid MPI+instrumentation deadlock) |
-| Profile File | `default_9725750769337483397_0.profraw` (327 KB) |
-| Merged Profile | `default.profdata` (394 KB) |
-| llvm-profdata | `/home/intel/oneapi/compiler/2025.3/bin/compiler/llvm-profdata` |
-
-## 2. Reduced Simulation Parameters (for profiling run)
-
-| Parameter | Production Value | Profiling Value |
-|-----------|-----------------|-----------------|
-| MPI_processes | 64 | 1 |
-| grid_level | 9 | 4 |
-| static_grid_level | 5 | 3 |
-| static_grid_number | 96 | 24 |
-| moving_grid_number | 48 | 16 |
-| largest_box_xyz_max | 320^3 | 160^3 |
-| Final_Evolution_Time | 1000.0 | 10.0 |
-| Evolution_Step_Number | 10,000,000 | 1,000 |
-| Detector_Number | 12 | 2 |
-
-## 3. Profile Summary
-
-| Metric | Value |
-|--------|-------|
-| Total instrumented functions | 1,392 |
-| Functions with non-zero counts | 117 (8.4%) |
-| Functions with zero counts | 1,275 (91.6%) |
-| Maximum function entry count | 386,459,248 |
-| Maximum internal block count | 370,477,680 |
-| Total block count | 4,198,023,118 |
-
-## 4. Top 20 Hotspot Functions
-
-| Rank | Total Count | Max Block Count | Function | Category |
-|------|------------|-----------------|----------|----------|
-| 1 | 1,241,601,732 | 370,477,680 | `polint_` | Interpolation |
-| 2 | 755,994,435 | 230,156,640 | `prolong3_` | Grid prolongation |
-| 3 | 667,964,095 | 3,697,792 | `compute_rhs_bssn_` | BSSN RHS evolution |
-| 4 | 539,736,051 | 386,459,248 | `symmetry_bd_` | Symmetry boundary |
-| 5 | 277,310,808 | 53,170,728 | `lopsided_` | Lopsided FD stencil |
-| 6 | 155,534,488 | 94,535,040 | `decide3d_` | 3D grid decision |
-| 7 | 119,267,712 | 19,266,048 | `rungekutta4_rout_` | RK4 time integrator |
-| 8 | 91,574,616 | 48,824,160 | `kodis_` | Kreiss-Oliger dissipation |
-| 9 | 67,555,389 | 43,243,680 | `fderivs_` | Finite differences |
-| 10 | 55,296,000 | 42,246,144 | `misc::fact(int)` | Factorial utility |
-| 11 | 43,191,071 | 27,663,328 | `fdderivs_` | 2nd-order FD derivatives |
-| 12 | 36,233,965 | 22,429,440 | `restrict3_` | Grid restriction |
-| 13 | 24,698,512 | 17,231,520 | `polin3_` | Polynomial interpolation |
-| 14 | 22,962,942 | 20,968,768 | `copy_` | Data copy |
-| 15 | 20,135,696 | 17,259,168 | `Ansorg::barycentric(...)` | Spectral interpolation |
-| 16 | 14,650,224 | 7,224,768 | `Ansorg::barycentric_omega(...)` | Spectral weights |
-| 17 | 13,242,296 | 2,871,920 | `global_interp_` | Global interpolation |
-| 18 | 12,672,000 | 7,734,528 | `sommerfeld_rout_` | Sommerfeld boundary |
-| 19 | 6,872,832 | 1,880,064 | `sommerfeld_routbam_` | Sommerfeld boundary (BAM) |
-| 20 | 5,709,900 | 2,809,632 | `l2normhelper_` | L2 norm computation |
-
-## 5. Hotspot Category Breakdown
-
-Top 20 functions account for ~98% of total execution counts:
-
-| Category | Functions | Combined Count | Share |
-|----------|-----------|---------------|-------|
-| Interpolation / Prolongation / Restriction | polint_, prolong3_, restrict3_, polin3_, global_interp_, Ansorg::* | ~2,093M | ~50% |
-| BSSN RHS + FD stencils | compute_rhs_bssn_, lopsided_, fderivs_, fdderivs_ | ~1,056M | ~25% |
-| Boundary conditions | symmetry_bd_, sommerfeld_rout_, sommerfeld_routbam_ | ~559M | ~13% |
-| Time integration | rungekutta4_rout_ | ~119M | ~3% |
-| Dissipation | kodis_ | ~92M | ~2% |
-| Utilities | misc::fact, decide3d_, copy_, l2normhelper_ | ~256M | ~6% |
-
-## 6. Conclusions
-
-1. **Profile data is valid**: 1,392 functions instrumented, 117 exercised with ~4.2 billion total counts.
-2. **Hotspot concentration is high**: Top 5 functions alone account for ~76% of all counts, which is ideal for PGO — the compiler has strong branch/layout optimization targets.
-3. **Fortran numerical kernels dominate**: `polint_`, `prolong3_`, `compute_rhs_bssn_`, `symmetry_bd_`, `lopsided_` are all Fortran routines in the inner evolution loop. PGO will optimize their branch prediction and basic block layout.
-4. **91.6% of functions have zero counts**: These are code paths for unused features (GPU, BSSN-EScalar, BSSN-EM, Z4C, etc.). PGO will deprioritize them, improving instruction cache utilization.
-5. **Profile is representative**: Despite the reduced grid size, the code path coverage matches production — the same kernels (RHS, prolongation, restriction, boundary) are exercised. PGO branch probabilities from this profile will transfer well to full-scale runs.
-
-## 7. PGO Phase 2 Usage
-
-To apply the profile, use the following flags in `makefile.inc`:
-
-```makefile
-CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -fprofile-instr-use=/home/amss/AMSS-NCKU/pgo_profile/default.profdata \
-              -align array64byte -fpp -I${MKLROOT}/include
-```