xref: /petsc/src/dm/impls/da/da2.c (revision bcda9346efad4e5ba2d553af84eb238771ba1e25)

#include <petsc/private/dmdaimpl.h> /*I   "petscdmda.h"   I*/
#include <petscdraw.h>

static PetscErrorCode DMView_DA_2d(DM da, PetscViewer viewer)
{
  PetscMPIInt rank;
  PetscBool   isascii, isdraw, isglvis, isbinary;
  DM_DA      *dd = (DM_DA *)da->data;
#if defined(PETSC_HAVE_MATLAB)
  PetscBool ismatlab;
#endif

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)da), &rank));

  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERGLVIS, &isglvis));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
#if defined(PETSC_HAVE_MATLAB)
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERMATLAB, &ismatlab));
#endif
  if (isascii) {
    PetscViewerFormat format;

    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_LOAD_BALANCE) {
      PetscInt      i, nmax = 0, nmin = PETSC_INT_MAX, navg = 0, *nz, nzlocal;
      DMDALocalInfo info;
      PetscMPIInt   size;
      PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)da), &size));
      PetscCall(DMDAGetLocalInfo(da, &info));
      nzlocal = info.xm * info.ym;
      PetscCall(PetscMalloc1(size, &nz));
      PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)da)));
      for (i = 0; i < size; i++) {
        nmax = PetscMax(nmax, nz[i]);
        nmin = PetscMin(nmin, nz[i]);
        navg += nz[i];
      }
      PetscCall(PetscFree(nz));
      navg = navg / size;
      PetscCall(PetscViewerASCIIPrintf(viewer, "  Load Balance - Grid Points: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
      PetscFunctionReturn(PETSC_SUCCESS);
    }
    if (format != PETSC_VIEWER_ASCII_GLVIS) {
      DMDALocalInfo info;
      PetscCall(DMDAGetLocalInfo(da, &info));
      PetscCall(PetscViewerASCIIPushSynchronized(viewer));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Processor [%d] M %" PetscInt_FMT " N %" PetscInt_FMT " m %" PetscInt_FMT " n %" PetscInt_FMT " w %" PetscInt_FMT " s %" PetscInt_FMT "\n", rank, dd->M, dd->N, dd->m, dd->n, dd->w, dd->s));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "X range of indices: %" PetscInt_FMT " %" PetscInt_FMT ", Y range of indices: %" PetscInt_FMT " %" PetscInt_FMT "\n", info.xs, info.xs + info.xm, info.ys, info.ys + info.ym));
      PetscCall(PetscViewerFlush(viewer));
      PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    } else if (format == PETSC_VIEWER_ASCII_GLVIS) PetscCall(DMView_DA_GLVis(da, viewer));
  } else if (isdraw) {
    PetscDraw       draw;
    double          ymin = -1 * dd->s - 1, ymax = dd->N + dd->s;
    double          xmin = -1 * dd->s - 1, xmax = dd->M + dd->s;
    double          x, y;
    PetscInt        base;
    const PetscInt *idx;
    char            node[10];
    PetscBool       isnull;

    PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    PetscCall(PetscDrawIsNull(draw, &isnull));
    if (isnull) PetscFunctionReturn(PETSC_SUCCESS);

    PetscCall(PetscDrawCheckResizedWindow(draw));
    PetscCall(PetscDrawClear(draw));
    PetscCall(PetscDrawSetCoordinates(draw, xmin, ymin, xmax, ymax));

    PetscDrawCollectiveBegin(draw);
    /* first processor draw all node lines */
    if (rank == 0) {
      ymin = 0.0;
      ymax = dd->N - 1;
      for (xmin = 0; xmin < dd->M; xmin++) PetscCall(PetscDrawLine(draw, xmin, ymin, xmin, ymax, PETSC_DRAW_BLACK));
      xmin = 0.0;
      xmax = dd->M - 1;
      for (ymin = 0; ymin < dd->N; ymin++) PetscCall(PetscDrawLine(draw, xmin, ymin, xmax, ymin, PETSC_DRAW_BLACK));
    }
    PetscDrawCollectiveEnd(draw);
    PetscCall(PetscDrawFlush(draw));
    PetscCall(PetscDrawPause(draw));

    PetscDrawCollectiveBegin(draw);
    /* draw my box */
    xmin = dd->xs / dd->w;
    xmax = (dd->xe - 1) / dd->w;
    ymin = dd->ys;
    ymax = dd->ye - 1;
    PetscCall(PetscDrawLine(draw, xmin, ymin, xmax, ymin, PETSC_DRAW_RED));
    PetscCall(PetscDrawLine(draw, xmin, ymin, xmin, ymax, PETSC_DRAW_RED));
    PetscCall(PetscDrawLine(draw, xmin, ymax, xmax, ymax, PETSC_DRAW_RED));
    PetscCall(PetscDrawLine(draw, xmax, ymin, xmax, ymax, PETSC_DRAW_RED));
    /* put in numbers */
    base = (dd->base) / dd->w;
    for (y = ymin; y <= ymax; y++) {
      for (x = xmin; x <= xmax; x++) {
        PetscCall(PetscSNPrintf(node, sizeof(node), "%" PetscInt_FMT, base++));
        PetscCall(PetscDrawString(draw, x, y, PETSC_DRAW_BLACK, node));
      }
    }
    PetscDrawCollectiveEnd(draw);
    PetscCall(PetscDrawFlush(draw));
    PetscCall(PetscDrawPause(draw));

    PetscDrawCollectiveBegin(draw);
    /* overlay ghost numbers, useful for error checking */
    PetscCall(ISLocalToGlobalMappingGetBlockIndices(da->ltogmap, &idx));
    base = 0;
    xmin = dd->Xs;
    xmax = dd->Xe;
    ymin = dd->Ys;
    ymax = dd->Ye;
    for (y = ymin; y < ymax; y++) {
      for (x = xmin; x < xmax; x++) {
        if ((base % dd->w) == 0) {
          PetscCall(PetscSNPrintf(node, sizeof(node), "%d", (int)(idx[base / dd->w])));
          PetscCall(PetscDrawString(draw, x / dd->w, y, PETSC_DRAW_BLUE, node));
        }
        base++;
      }
    }
    PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap, &idx));
    PetscDrawCollectiveEnd(draw);
    PetscCall(PetscDrawFlush(draw));
    PetscCall(PetscDrawPause(draw));
    PetscCall(PetscDrawSave(draw));
  } else if (isglvis) {
    PetscCall(DMView_DA_GLVis(da, viewer));
  } else if (isbinary) {
    PetscCall(DMView_DA_Binary(da, viewer));
#if defined(PETSC_HAVE_MATLAB)
  } else if (ismatlab) {
    PetscCall(DMView_DA_Matlab(da, viewer));
#endif
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if defined(new)
/*
  DMDAGetDiagonal_MFFD - Gets the diagonal for a matrix-free matrix where local
    function lives on a DMDA

        y ~= (F(u + ha) - F(u))/h,
  where F = nonlinear function, as set by SNESSetFunction()
        u = current iterate
        h = difference interval
*/
PetscErrorCode DMDAGetDiagonal_MFFD(DM da, Vec U, Vec a)
{
  PetscScalar   h, *aa, *ww, v;
  PetscReal     epsilon = PETSC_SQRT_MACHINE_EPSILON, umin = 100.0 * PETSC_SQRT_MACHINE_EPSILON;
  PetscInt      gI, nI;
  MatStencil    stencil;
  DMDALocalInfo info;

  PetscFunctionBegin;
  PetscCall((*ctx->func)(0, U, a, ctx->funcctx));
  PetscCall((*ctx->funcisetbase)(U, ctx->funcctx));

  PetscCall(VecGetArray(U, &ww));
  PetscCall(VecGetArray(a, &aa));

  nI = 0;
  h  = ww[gI];
  if (h == 0.0) h = 1.0;
  if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
  else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
  h *= epsilon;

  ww[gI] += h;
  PetscCall((*ctx->funci)(i, w, &v, ctx->funcctx));
  aa[nI] = (v - aa[nI]) / h;
  ww[gI] -= h;
  nI++;

  PetscCall(VecRestoreArray(U, &ww));
  PetscCall(VecRestoreArray(a, &aa));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

PetscErrorCode DMSetUp_DA_2D(DM da)
{
  DM_DA          *dd = (DM_DA *)da->data;
  const PetscInt  M  = dd->M;
  const PetscInt  N  = dd->N;
  PetscMPIInt     m, n;
  const PetscInt  dof          = dd->w;
  const PetscInt  s            = dd->s;
  DMBoundaryType  bx           = dd->bx;
  DMBoundaryType  by           = dd->by;
  DMDAStencilType stencil_type = dd->stencil_type;
  PetscInt       *lx           = dd->lx;
  PetscInt       *ly           = dd->ly;
  MPI_Comm        comm;
  PetscMPIInt     rank, size, n0, n1, n2, n3, n5, n6, n7, n8;
  PetscInt        xs, xe, ys, ye, x, y, Xs, Xe, Ys, Ye, IXs, IXe, IYs, IYe;
  PetscInt        up, down, left, right, i, *idx, nn;
  PetscInt        xbase, *bases, *ldims, j, x_t, y_t, s_t, base, count;
  PetscInt        s_x, s_y; /* s proportionalized to w */
  PetscMPIInt     sn0 = 0, sn2 = 0, sn6 = 0, sn8 = 0;
  Vec             local, global;
  VecScatter      gtol;
  IS              to, from;

  PetscFunctionBegin;
  PetscCheck(stencil_type != DMDA_STENCIL_BOX || (bx != DM_BOUNDARY_MIRROR && by != DM_BOUNDARY_MIRROR), PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Mirror boundary and box stencil");
  PetscCall(PetscObjectGetComm((PetscObject)da, &comm));
#if !defined(PETSC_USE_64BIT_INDICES)
  PetscCheck(((PetscInt64)M) * ((PetscInt64)N) * ((PetscInt64)dof) <= (PetscInt64)PETSC_MPI_INT_MAX, comm, PETSC_ERR_INT_OVERFLOW, "Mesh of %" PetscInt_FMT " by %" PetscInt_FMT " by %" PetscInt_FMT " (dof) is too large for 32-bit indices", M, N, dof);
#endif
  PetscCall(PetscMPIIntCast(dd->m, &m));
  PetscCall(PetscMPIIntCast(dd->n, &n));

  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCallMPI(MPI_Comm_rank(comm, &rank));

  dd->p = 1;
  if (m != PETSC_DECIDE) {
    PetscCheck(m >= 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "Non-positive number of processors in X direction: %d", m);
    PetscCheck(m <= size, comm, PETSC_ERR_ARG_OUTOFRANGE, "Too many processors in X direction: %d %d", m, size);
  }
  if (n != PETSC_DECIDE) {
    PetscCheck(n >= 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "Non-positive number of processors in Y direction: %d", n);
    PetscCheck(n <= size, comm, PETSC_ERR_ARG_OUTOFRANGE, "Too many processors in Y direction: %d %d", n, size);
  }

  if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
    if (n != PETSC_DECIDE) {
      m = size / n;
    } else if (m != PETSC_DECIDE) {
      n = size / m;
    } else {
      /* try for squarish distribution */
      m = (PetscMPIInt)(0.5 + PetscSqrtReal(((PetscReal)M) * ((PetscReal)size) / ((PetscReal)N)));
      if (!m) m = 1;
      while (m > 0) {
        n = size / m;
        if (m * n == size) break;
        m--;
      }
      if (M > N && m < n) {
        PetscMPIInt _m = m;
        m              = n;
        n              = _m;
      }
    }
    PetscCheck(m * n == size, comm, PETSC_ERR_PLIB, "Unable to create partition, check the size of the communicator and input m and n ");
  } else PetscCheck(m * n == size, comm, PETSC_ERR_ARG_OUTOFRANGE, "Given Bad partition");

  PetscCheck(M >= m, comm, PETSC_ERR_ARG_OUTOFRANGE, "Partition in x direction is too fine! %" PetscInt_FMT " %d", M, m);
  PetscCheck(N >= n, comm, PETSC_ERR_ARG_OUTOFRANGE, "Partition in y direction is too fine! %" PetscInt_FMT " %d", N, n);

  /*
     Determine locally owned region
     xs is the first local node number, x is the number of local nodes
  */
  if (!lx) {
    PetscCall(PetscMalloc1(m, &dd->lx));
    lx = dd->lx;
    for (i = 0; i < m; i++) lx[i] = M / m + ((M % m) > i);
  }
  x  = lx[rank % m];
  xs = 0;
  for (i = 0; i < (rank % m); i++) xs += lx[i];
  if (PetscDefined(USE_DEBUG)) {
    left = xs;
    for (i = (rank % m); i < m; i++) left += lx[i];
    PetscCheck(left == M, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Sum of lx across processors not equal to M: %" PetscInt_FMT " %" PetscInt_FMT, left, M);
  }

  /*
     Determine locally owned region
     ys is the first local node number, y is the number of local nodes
  */
  if (!ly) {
    PetscCall(PetscMalloc1(n, &dd->ly));
    ly = dd->ly;
    for (i = 0; i < n; i++) ly[i] = N / n + ((N % n) > i);
  }
  y  = ly[rank / m];
  ys = 0;
  for (i = 0; i < (rank / m); i++) ys += ly[i];
  if (PetscDefined(USE_DEBUG)) {
    left = ys;
    for (i = (rank / m); i < n; i++) left += ly[i];
    PetscCheck(left == N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Sum of ly across processors not equal to N: %" PetscInt_FMT " %" PetscInt_FMT, left, N);
  }

  /*
   check if the scatter requires more than one process neighbor or wraps around
   the domain more than once
  */
  PetscCheck((x >= s) || ((m <= 1) && (bx != DM_BOUNDARY_PERIODIC)), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local x-width of domain x %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT, x, s);
  PetscCheck((y >= s) || ((n <= 1) && (by != DM_BOUNDARY_PERIODIC)), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local y-width of domain y %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT, y, s);
  PetscCheck((x > s) || (bx != DM_BOUNDARY_MIRROR), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local x-width of domain x %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT " with mirror", x, s);
  PetscCheck((y > s) || (by != DM_BOUNDARY_MIRROR), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local y-width of domain y %" PetscInt_FMT " is smaller than stencil width s %" PetscInt_FMT " with mirror", y, s);
  xe = xs + x;
  ye = ys + y;

  /* determine ghost region (Xs) and region scattered into (IXs)  */
  if (xs - s > 0) {
    Xs  = xs - s;
    IXs = xs - s;
  } else {
    if (bx) {
      Xs = xs - s;
    } else {
      Xs = 0;
    }
    IXs = 0;
  }
  if (xe + s <= M) {
    Xe  = xe + s;
    IXe = xe + s;
  } else {
    if (bx) {
      Xs = xs - s;
      Xe = xe + s;
    } else {
      Xe = M;
    }
    IXe = M;
  }

  if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
    IXs = xs - s;
    IXe = xe + s;
    Xs  = xs - s;
    Xe  = xe + s;
  }

  if (ys - s > 0) {
    Ys  = ys - s;
    IYs = ys - s;
  } else {
    if (by) {
      Ys = ys - s;
    } else {
      Ys = 0;
    }
    IYs = 0;
  }
  if (ye + s <= N) {
    Ye  = ye + s;
    IYe = ye + s;
  } else {
    if (by) {
      Ye = ye + s;
    } else {
      Ye = N;
    }
    IYe = N;
  }

  if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
    IYs = ys - s;
    IYe = ye + s;
    Ys  = ys - s;
    Ye  = ye + s;
  }

  /* stencil length in each direction */
  s_x = s;
  s_y = s;

  /* determine starting point of each processor */
  nn = x * y;
  PetscCall(PetscMalloc2(size + 1, &bases, size, &ldims));
  PetscCallMPI(MPI_Allgather(&nn, 1, MPIU_INT, ldims, 1, MPIU_INT, comm));
  bases[0] = 0;
  for (i = 1; i <= size; i++) bases[i] = ldims[i - 1];
  for (i = 1; i <= size; i++) bases[i] += bases[i - 1];
  base = bases[rank] * dof;

  /* allocate the base parallel and sequential vectors */
  dd->Nlocal = x * y * dof;
  PetscCall(VecCreateMPIWithArray(comm, dof, dd->Nlocal, PETSC_DECIDE, NULL, &global));
  dd->nlocal = (Xe - Xs) * (Ye - Ys) * dof;
  PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, dof, dd->nlocal, NULL, &local));

  /* generate global to local vector scatter and local to global mapping*/

  /* global to local must include ghost points within the domain,
     but not ghost points outside the domain that aren't periodic */
  PetscCall(PetscMalloc1((IXe - IXs) * (IYe - IYs), &idx));
  if (stencil_type == DMDA_STENCIL_BOX) {
    left  = IXs - Xs;
    right = left + (IXe - IXs);
    down  = IYs - Ys;
    up    = down + (IYe - IYs);
    count = 0;
    for (i = down; i < up; i++) {
      for (j = left; j < right; j++) idx[count++] = j + i * (Xe - Xs);
    }
    PetscCall(ISCreateBlock(comm, dof, count, idx, PETSC_OWN_POINTER, &to));

  } else {
    /* must drop into cross shape region */
    /*       ---------|
            |  top    |
         |---         ---| up
         |   middle      |
         |               |
         ----         ---- down
            | bottom  |
            -----------
         Xs xs        xe Xe */
    left  = xs - Xs;
    right = left + x;
    down  = ys - Ys;
    up    = down + y;
    count = 0;
    /* bottom */
    for (i = (IYs - Ys); i < down; i++) {
      for (j = left; j < right; j++) idx[count++] = j + i * (Xe - Xs);
    }
    /* middle */
    for (i = down; i < up; i++) {
      for (j = (IXs - Xs); j < (IXe - Xs); j++) idx[count++] = j + i * (Xe - Xs);
    }
    /* top */
    for (i = up; i < up + IYe - ye; i++) {
      for (j = left; j < right; j++) idx[count++] = j + i * (Xe - Xs);
    }
    PetscCall(ISCreateBlock(comm, dof, count, idx, PETSC_OWN_POINTER, &to));
  }

  /* determine who lies on each side of us stored in    n6 n7 n8
                                                        n3    n5
                                                        n0 n1 n2
  */

  /* Assume the Non-Periodic Case */
  n1 = rank - m;
  if (rank % m) {
    n0 = n1 - 1;
  } else {
    n0 = -1;
  }
  if ((rank + 1) % m) {
    n2 = n1 + 1;
    n5 = rank + 1;
    n8 = rank + m + 1;
    if (n8 >= m * n) n8 = -1;
  } else {
    n2 = -1;
    n5 = -1;
    n8 = -1;
  }
  if (rank % m) {
    n3 = rank - 1;
    n6 = n3 + m;
    if (n6 >= m * n) n6 = -1;
  } else {
    n3 = -1;
    n6 = -1;
  }
  n7 = rank + m;
  if (n7 >= m * n) n7 = -1;

  if (bx == DM_BOUNDARY_PERIODIC && by == DM_BOUNDARY_PERIODIC) {
    /* Modify for Periodic Cases */
    /* Handle all four corners */
    if ((n6 < 0) && (n7 < 0) && (n3 < 0)) n6 = m - 1;
    if ((n8 < 0) && (n7 < 0) && (n5 < 0)) n8 = 0;
    if ((n2 < 0) && (n5 < 0) && (n1 < 0)) n2 = size - m;
    if ((n0 < 0) && (n3 < 0) && (n1 < 0)) n0 = size - 1;

    /* Handle Top and Bottom Sides */
    if (n1 < 0) n1 = rank + m * (n - 1);
    if (n7 < 0) n7 = rank - m * (n - 1);
    if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    if ((n3 >= 0) && (n6 < 0)) n6 = (rank % m) - 1;
    if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    if ((n5 >= 0) && (n8 < 0)) n8 = (rank % m) + 1;

    /* Handle Left and Right Sides */
    if (n3 < 0) n3 = rank + (m - 1);
    if (n5 < 0) n5 = rank - (m - 1);
    if ((n1 >= 0) && (n0 < 0)) n0 = rank - 1;
    if ((n1 >= 0) && (n2 < 0)) n2 = rank - 2 * m + 1;
    if ((n7 >= 0) && (n6 < 0)) n6 = rank + 2 * m - 1;
    if ((n7 >= 0) && (n8 < 0)) n8 = rank + 1;
  } else if (by == DM_BOUNDARY_PERIODIC) { /* Handle Top and Bottom Sides */
    if (n1 < 0) n1 = rank + m * (n - 1);
    if (n7 < 0) n7 = rank - m * (n - 1);
    if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    if ((n3 >= 0) && (n6 < 0)) n6 = (rank % m) - 1;
    if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    if ((n5 >= 0) && (n8 < 0)) n8 = (rank % m) + 1;
  } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
    if (n3 < 0) n3 = rank + (m - 1);
    if (n5 < 0) n5 = rank - (m - 1);
    if ((n1 >= 0) && (n0 < 0)) n0 = rank - 1;
    if ((n1 >= 0) && (n2 < 0)) n2 = rank - 2 * m + 1;
    if ((n7 >= 0) && (n6 < 0)) n6 = rank + 2 * m - 1;
    if ((n7 >= 0) && (n8 < 0)) n8 = rank + 1;
  }

  PetscCall(PetscMalloc1(9, &dd->neighbors));

  dd->neighbors[0] = n0;
  dd->neighbors[1] = n1;
  dd->neighbors[2] = n2;
  dd->neighbors[3] = n3;
  dd->neighbors[4] = rank;
  dd->neighbors[5] = n5;
  dd->neighbors[6] = n6;
  dd->neighbors[7] = n7;
  dd->neighbors[8] = n8;

  if (stencil_type == DMDA_STENCIL_STAR) {
    /* save corner processor numbers */
    sn0 = n0;
    sn2 = n2;
    sn6 = n6;
    sn8 = n8;
    n0 = n2 = n6 = n8 = -1;
  }

  PetscCall(PetscMalloc1((Xe - Xs) * (Ye - Ys), &idx));

  nn    = 0;
  xbase = bases[rank];
  for (i = 1; i <= s_y; i++) {
    if (n0 >= 0) { /* left below */
      x_t = lx[n0 % m];
      y_t = ly[n0 / m];
      s_t = bases[n0] + x_t * y_t - (s_y - i) * x_t - s_x;
      for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
    }

    if (n1 >= 0) { /* directly below */
      x_t = x;
      y_t = ly[n1 / m];
      s_t = bases[n1] + x_t * y_t - (s_y + 1 - i) * x_t;
      for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
    } else if (by == DM_BOUNDARY_MIRROR) {
      for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (s_y - i + 1) + j;
    }

    if (n2 >= 0) { /* right below */
      x_t = lx[n2 % m];
      y_t = ly[n2 / m];
      s_t = bases[n2] + x_t * y_t - (s_y + 1 - i) * x_t;
      for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
    }
  }

  for (i = 0; i < y; i++) {
    if (n3 >= 0) { /* directly left */
      x_t = lx[n3 % m];
      /* y_t = y; */
      s_t = bases[n3] + (i + 1) * x_t - s_x;
      for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
    } else if (bx == DM_BOUNDARY_MIRROR) {
      for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * i + s_x - j;
    }

    for (j = 0; j < x; j++) idx[nn++] = xbase++; /* interior */

    if (n5 >= 0) { /* directly right */
      x_t = lx[n5 % m];
      /* y_t = y; */
      s_t = bases[n5] + (i)*x_t;
      for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
    } else if (bx == DM_BOUNDARY_MIRROR) {
      for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * (i + 1) - 2 - j;
    }
  }

  for (i = 1; i <= s_y; i++) {
    if (n6 >= 0) { /* left above */
      x_t = lx[n6 % m];
      /* y_t = ly[n6 / m]; */
      s_t = bases[n6] + (i)*x_t - s_x;
      for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
    }

    if (n7 >= 0) { /* directly above */
      x_t = x;
      /* y_t = ly[n7 / m]; */
      s_t = bases[n7] + (i - 1) * x_t;
      for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
    } else if (by == DM_BOUNDARY_MIRROR) {
      for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (y - i - 1) + j;
    }

    if (n8 >= 0) { /* right above */
      x_t = lx[n8 % m];
      /* y_t = ly[n8 / m]; */
      s_t = bases[n8] + (i - 1) * x_t;
      for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
    }
  }

  PetscCall(ISCreateBlock(comm, dof, nn, idx, PETSC_USE_POINTER, &from));
  PetscCall(VecScatterCreate(global, from, local, to, &gtol));
  PetscCall(ISDestroy(&to));
  PetscCall(ISDestroy(&from));

  if (stencil_type == DMDA_STENCIL_STAR) {
    n0 = sn0;
    n2 = sn2;
    n6 = sn6;
    n8 = sn8;
  }

  if ((stencil_type == DMDA_STENCIL_STAR) || (bx && bx != DM_BOUNDARY_PERIODIC) || (by && by != DM_BOUNDARY_PERIODIC)) {
    /*
        Recompute the local to global mappings, this time keeping the
      information about the cross corner processor numbers and any ghosted
      but not periodic indices.
    */
    nn    = 0;
    xbase = bases[rank];
    for (i = 1; i <= s_y; i++) {
      if (n0 >= 0) { /* left below */
        x_t = lx[n0 % m];
        y_t = ly[n0 / m];
        s_t = bases[n0] + x_t * y_t - (s_y - i) * x_t - s_x;
        for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
      } else if (xs - Xs > 0 && ys - Ys > 0) {
        for (j = 0; j < s_x; j++) idx[nn++] = -1;
      }
      if (n1 >= 0) { /* directly below */
        x_t = x;
        y_t = ly[n1 / m];
        s_t = bases[n1] + x_t * y_t - (s_y + 1 - i) * x_t;
        for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
      } else if (ys - Ys > 0) {
        if (by == DM_BOUNDARY_MIRROR) {
          for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (s_y - i + 1) + j;
        } else {
          for (j = 0; j < x; j++) idx[nn++] = -1;
        }
      }
      if (n2 >= 0) { /* right below */
        x_t = lx[n2 % m];
        y_t = ly[n2 / m];
        s_t = bases[n2] + x_t * y_t - (s_y + 1 - i) * x_t;
        for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
      } else if (Xe - xe > 0 && ys - Ys > 0) {
        for (j = 0; j < s_x; j++) idx[nn++] = -1;
      }
    }

    for (i = 0; i < y; i++) {
      if (n3 >= 0) { /* directly left */
        x_t = lx[n3 % m];
        /* y_t = y; */
        s_t = bases[n3] + (i + 1) * x_t - s_x;
        for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
      } else if (xs - Xs > 0) {
        if (bx == DM_BOUNDARY_MIRROR) {
          for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * i + s_x - j;
        } else {
          for (j = 0; j < s_x; j++) idx[nn++] = -1;
        }
      }

      for (j = 0; j < x; j++) idx[nn++] = xbase++; /* interior */

      if (n5 >= 0) { /* directly right */
        x_t = lx[n5 % m];
        /* y_t = y; */
        s_t = bases[n5] + (i)*x_t;
        for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
      } else if (Xe - xe > 0) {
        if (bx == DM_BOUNDARY_MIRROR) {
          for (j = 0; j < s_x; j++) idx[nn++] = bases[rank] + x * (i + 1) - 2 - j;
        } else {
          for (j = 0; j < s_x; j++) idx[nn++] = -1;
        }
      }
    }

    for (i = 1; i <= s_y; i++) {
      if (n6 >= 0) { /* left above */
        x_t = lx[n6 % m];
        /* y_t = ly[n6 / m]; */
        s_t = bases[n6] + (i)*x_t - s_x;
        for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
      } else if (xs - Xs > 0 && Ye - ye > 0) {
        for (j = 0; j < s_x; j++) idx[nn++] = -1;
      }
      if (n7 >= 0) { /* directly above */
        x_t = x;
        /* y_t = ly[n7 / m]; */
        s_t = bases[n7] + (i - 1) * x_t;
        for (j = 0; j < x_t; j++) idx[nn++] = s_t++;
      } else if (Ye - ye > 0) {
        if (by == DM_BOUNDARY_MIRROR) {
          for (j = 0; j < x; j++) idx[nn++] = bases[rank] + x * (y - i - 1) + j;
        } else {
          for (j = 0; j < x; j++) idx[nn++] = -1;
        }
      }
      if (n8 >= 0) { /* right above */
        x_t = lx[n8 % m];
        /* y_t = ly[n8 / m]; */
        s_t = bases[n8] + (i - 1) * x_t;
        for (j = 0; j < s_x; j++) idx[nn++] = s_t++;
      } else if (Xe - xe > 0 && Ye - ye > 0) {
        for (j = 0; j < s_x; j++) idx[nn++] = -1;
      }
    }
  }
  /*
     Set the local to global ordering in the global vector, this allows use
     of VecSetValuesLocal().
  */
  PetscCall(ISLocalToGlobalMappingCreate(comm, dof, nn, idx, PETSC_OWN_POINTER, &da->ltogmap));

  PetscCall(PetscFree2(bases, ldims));
  dd->m = m;
  dd->n = n;
  /* note PETSc expects xs/xe/Xs/Xe to be multiplied by #dofs in many places */
  dd->xs = xs * dof;
  dd->xe = xe * dof;
  dd->ys = ys;
  dd->ye = ye;
  dd->zs = 0;
  dd->ze = 1;
  dd->Xs = Xs * dof;
  dd->Xe = Xe * dof;
  dd->Ys = Ys;
  dd->Ye = Ye;
  dd->Zs = 0;
  dd->Ze = 1;

  PetscCall(VecDestroy(&local));
  PetscCall(VecDestroy(&global));

  dd->gtol      = gtol;
  dd->base      = base;
  da->ops->view = DMView_DA_2d;
  dd->ltol      = NULL;
  dd->ao        = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDACreate2d -  Creates an object that will manage the communication of two-dimensional
  regular array data that is distributed across one or more MPI processes.

  Collective

  Input Parameters:
+ comm         - MPI communicator
. bx           - type of ghost nodes the x array have. Use one of `DM_BOUNDARY_NONE`, `DM_BOUNDARY_GHOSTED`, `DM_BOUNDARY_PERIODIC`.
. by           - type of ghost nodes the y array have. Use one of `DM_BOUNDARY_NONE`, `DM_BOUNDARY_GHOSTED`, `DM_BOUNDARY_PERIODIC`.
. stencil_type - stencil type.  Use either `DMDA_STENCIL_BOX` or `DMDA_STENCIL_STAR`.
. M            - global dimension in x direction of the array
. N            - global dimension in y direction of the array
. m            - corresponding number of processors in x dimension (or `PETSC_DECIDE` to have calculated)
. n            - corresponding number of processors in y dimension (or `PETSC_DECIDE` to have calculated)
. dof          - number of degrees of freedom per node
. s            - stencil width
. lx           - arrays containing the number of nodes in each cell along the x coordinates, or `NULL`.
- ly           - arrays containing the number of nodes in each cell along the y coordinates, or `NULL`.

  Output Parameter:
. da - the resulting distributed array object

  Options Database Keys:
+ -dm_view              - Calls `DMView()` at the conclusion of `DMDACreate2d()`
. -da_grid_x <nx>       - number of grid points in x direction
. -da_grid_y <ny>       - number of grid points in y direction
. -da_processors_x <nx> - number of processors in x direction
. -da_processors_y <ny> - number of processors in y direction
. -da_bd_x <bx>         - boundary type in x direction
. -da_bd_y <by>         - boundary type in y direction
. -da_bd_all <bt>       - boundary type in all directions
. -da_refine_x <rx>     - refinement ratio in x direction
. -da_refine_y <ry>     - refinement ratio in y direction
- -da_refine <n>        - refine the `DMDA` n times before creating

  Level: beginner

  Notes:
  If `lx` or `ly` are non-null, these must be of length as `m` and `n`, and the corresponding
  `m` and `n` cannot be `PETSC_DECIDE`. The sum of the `lx` entries must be `M`, and the sum of
  the `ly` entries must be `N`.

  The stencil type `DMDA_STENCIL_STAR` with width 1 corresponds to the
  standard 5-pt stencil, while `DMDA_STENCIL_BOX` with width 1 denotes
  the standard 9-pt stencil.

  The array data itself is NOT stored in the `DMDA`, it is stored in `Vec` objects;
  The appropriate vector objects can be obtained with calls to `DMCreateGlobalVector()`
  and DMCreateLocalVector() and calls to `VecDuplicate()` if more are needed.

  You must call `DMSetUp()` after this call before using this `DM`.

  To use the options database to change values in the `DMDA` call `DMSetFromOptions()` after this call
  but before `DMSetUp()`.

.seealso: [](sec_struct), `DM`, `DMDA`, `DMDestroy()`, `DMView()`, `DMDACreate1d()`, `DMDACreate3d()`, `DMGlobalToLocalBegin()`, `DMDAGetRefinementFactor()`,
          `DMGlobalToLocalEnd()`, `DMLocalToGlobalBegin()`, `DMLocalToLocalBegin()`, `DMLocalToLocalEnd()`, `DMDASetRefinementFactor()`,
          `DMDAGetInfo()`, `DMCreateGlobalVector()`, `DMCreateLocalVector()`, `DMDACreateNaturalVector()`, `DMLoad()`, `DMDAGetOwnershipRanges()`,
          `DMStagCreate2d()`, `DMBoundaryType`
@*/
PetscErrorCode DMDACreate2d(MPI_Comm comm, DMBoundaryType bx, DMBoundaryType by, DMDAStencilType stencil_type, PetscInt M, PetscInt N, PetscInt m, PetscInt n, PetscInt dof, PetscInt s, const PetscInt lx[], const PetscInt ly[], DM *da)
{
  PetscFunctionBegin;
  PetscCall(DMDACreate(comm, da));
  PetscCall(DMSetDimension(*da, 2));
  PetscCall(DMDASetSizes(*da, M, N, 1));
  PetscCall(DMDASetNumProcs(*da, m, n, PETSC_DECIDE));
  PetscCall(DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE));
  PetscCall(DMDASetDof(*da, dof));
  PetscCall(DMDASetStencilType(*da, stencil_type));
  PetscCall(DMDASetStencilWidth(*da, s));
  PetscCall(DMDASetOwnershipRanges(*da, lx, ly, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}