impls/plex/plexcreate.c

#define PETSCDM_DLL
#include <petsc-private/dmpleximpl.h>    /*I   "petscdmplex.h"   I*/
#include <petscdmda.h>
#include <petscsf.h>

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateDoublet"
/*@
  DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.

  Collective on MPI_Comm

  Input Parameters:
+ comm - The communicator for the DM object
. dim - The spatial dimension
. simplex - Flag for simplicial cells, otherwise they are tensor product cells
. interpolate - Flag to create intermediate mesh pieces (edges, faces)
. refinementUniform - Flag for uniform parallel refinement
- refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell

  Output Parameter:
. dm  - The DM object

  Level: beginner

.keywords: DM, create
.seealso: DMSetType(), DMCreate()
@*/
PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscBool refinementUniform, PetscReal refinementLimit, DM *newdm)
{
  DM             dm;
  PetscInt       p;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
  ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(dm, dim);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  switch (dim) {
  case 2:
    if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
    else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
    break;
  case 3:
    if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
    else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
    break;
  default:
    SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
  }
  if (rank) {
    PetscInt numPoints[2] = {0, 0};
    ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
  } else {
    switch (dim) {
    case 2:
      if (simplex) {
        PetscInt    numPoints[2]        = {4, 2};
        PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
        PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
        PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
        PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
        PetscInt    markerPoints[8]     = {2, 1, 3, 1, 4, 1, 5, 1};

        ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
        for (p = 0; p < 4; ++p) {ierr = DMPlexSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
      } else {
        PetscInt    numPoints[2]        = {6, 2};
        PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
        PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
        PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
        PetscScalar vertexCoords[12]    = {-1.0, -0.5,  0.0, -0.5,  0.0, 0.5,  -1.0, 0.5,  1.0, -0.5,  1.0, 0.5};

        ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
      }
      break;
    case 3:
      if (simplex) {
        PetscInt    numPoints[2]        = {5, 2};
        PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
        PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
        PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
        PetscScalar vertexCoords[15]    = {-1.0, 0.0, 0.0,  0.0, -1.0, 0.0,  0.0, 0.0, 1.0,  0.0, 1.0, 0.0,  1.0, 0.0, 0.0};
        PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};

        ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
        for (p = 0; p < 5; ++p) {ierr = DMPlexSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
      } else {
        PetscInt    numPoints[2]         = {12, 2};
        PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
        PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
        PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
        PetscScalar vertexCoords[36]     = {-1.0, -0.5, -0.5,  -1.0,  0.5, -0.5,  0.0,  0.5, -0.5,   0.0, -0.5, -0.5,
                                            -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
                                             1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};

        ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
      }
      break;
    default:
      SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
    }
  }
  *newdm = dm;
  if (refinementLimit > 0.0) {
    DM rdm;
    const char *name;

    ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
    ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
    ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
    ierr = DMDestroy(newdm);CHKERRQ(ierr);
    *newdm = rdm;
  }
  if (interpolate) {
    DM idm;
    const char *name;

    ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject)    idm,  name);CHKERRQ(ierr);
    ierr = DMPlexCopyCoordinates(*newdm, idm);CHKERRQ(ierr);
    ierr = DMPlexCopyLabels(*newdm, idm);CHKERRQ(ierr);
    ierr = DMDestroy(newdm);CHKERRQ(ierr);
    *newdm = idm;
  }
  {
    DM refinedMesh     = NULL;
    DM distributedMesh = NULL;

    /* Distribute mesh over processes */
    ierr = DMPlexDistribute(*newdm, NULL, 0, NULL, &distributedMesh);CHKERRQ(ierr);
    if (distributedMesh) {
      ierr = DMDestroy(newdm);CHKERRQ(ierr);
      *newdm = distributedMesh;
    }
    if (refinementUniform) {
      ierr = DMPlexSetRefinementUniform(*newdm, refinementUniform);CHKERRQ(ierr);
      ierr = DMRefine(*newdm, comm, &refinedMesh);CHKERRQ(ierr);
      if (refinedMesh) {
        ierr = DMDestroy(newdm);CHKERRQ(ierr);
        *newdm = refinedMesh;
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSquareBoundary"
/*@
  DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.

  Collective on MPI_Comm

  Input Parameters:
+ comm  - The communicator for the DM object
. lower - The lower left corner coordinates
. upper - The upper right corner coordinates
- edges - The number of cells in each direction

  Output Parameter:
. dm  - The DM object

  Note: Here is the numbering returned for 2 cells in each direction:
$ 18--5-17--4--16
$  |     |     |
$  6    10     3
$  |     |     |
$ 19-11-20--9--15
$  |     |     |
$  7     8     2
$  |     |     |
$ 12--0-13--1--14

  Level: beginner

.keywords: DM, create
.seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
@*/
PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
{
  PetscInt       numVertices    = (edges[0]+1)*(edges[1]+1);
  PetscInt       numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
  PetscInt       markerTop      = 1;
  PetscInt       markerBottom   = 1;
  PetscInt       markerRight    = 1;
  PetscInt       markerLeft     = 1;
  PetscBool      markerSeparate = PETSC_FALSE;
  Vec            coordinates;
  PetscSection   coordSection;
  PetscScalar    *coords;
  PetscInt       coordSize;
  PetscMPIInt    rank;
  PetscInt       v, vx, vy;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsGetBool(((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
  if (markerSeparate) {
    markerTop    = 1;
    markerBottom = 0;
    markerRight  = 0;
    markerLeft   = 0;
  }
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
  if (!rank) {
    PetscInt e, ex, ey;

    ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
    for (e = 0; e < numEdges; ++e) {
      ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
    }
    ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
    for (vx = 0; vx <= edges[0]; vx++) {
      for (ey = 0; ey < edges[1]; ey++) {
        PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
        PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
        PetscInt cone[2];

        cone[0] = vertex; cone[1] = vertex+edges[0]+1;
        ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
        if (vx == edges[0]) {
          ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
          ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
          if (ey == edges[1]-1) {
            ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
          }
        } else if (vx == 0) {
          ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
          ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
          if (ey == edges[1]-1) {
            ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
          }
        }
      }
    }
    for (vy = 0; vy <= edges[1]; vy++) {
      for (ex = 0; ex < edges[0]; ex++) {
        PetscInt edge   = vy*edges[0]     + ex;
        PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
        PetscInt cone[2];

        cone[0] = vertex; cone[1] = vertex+1;
        ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
        if (vy == edges[1]) {
          ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
          ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
          if (ex == edges[0]-1) {
            ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
          }
        } else if (vy == 0) {
          ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
          ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
          if (ex == edges[0]-1) {
            ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
          }
        }
      }
    }
  }
  ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
  ierr = DMPlexStratify(dm);CHKERRQ(ierr);
  /* Build coordinates */
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);CHKERRQ(ierr);
  for (v = numEdges; v < numEdges+numVertices; ++v) {
    ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
  ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
  ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  for (vy = 0; vy <= edges[1]; ++vy) {
    for (vx = 0; vx <= edges[0]; ++vx) {
      coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
      coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
    }
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
  ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateCubeBoundary"
/*@
  DMPlexCreateCubeBoundary - Creates a 2D mesh the is the boundary of a cubic lattice.

  Collective on MPI_Comm

  Input Parameters:
+ comm  - The communicator for the DM object
. lower - The lower left front corner coordinates
. upper - The upper right back corner coordinates
- edges - The number of cells in each direction

  Output Parameter:
. dm  - The DM object

  Level: beginner

.keywords: DM, create
.seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
@*/
PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
{
  PetscInt       numVertices = (faces[0]+1)*(faces[1]+1)*(faces[2]+1);
  PetscInt       numFaces    = 6;
  Vec            coordinates;
  PetscSection   coordSection;
  PetscScalar    *coords;
  PetscInt       coordSize;
  PetscMPIInt    rank;
  PetscInt       v, vx, vy, vz;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if ((faces[0] < 1) || (faces[1] < 1) || (faces[2] < 1)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
  if ((faces[0] > 1) || (faces[1] > 1) || (faces[2] > 1)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Currently can't handle more than 1 face per side");
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
  if (!rank) {
    PetscInt f;

    ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
    for (f = 0; f < numFaces; ++f) {
      ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
    }
    ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
    for (v = 0; v < numFaces+numVertices; ++v) {
      ierr = DMPlexSetLabelValue(dm, "marker", v, 1);CHKERRQ(ierr);
    }
    { /* Side 0 (Front) */
      PetscInt cone[4];
      cone[0] = numFaces+4; cone[1] = numFaces+5; cone[2] = numFaces+7; cone[3] = numFaces+6;
      ierr    = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
    }
    { /* Side 1 (Back) */
      PetscInt cone[4];
      cone[0] = numFaces+1; cone[1] = numFaces+0; cone[2] = numFaces+2; cone[3] = numFaces+3;
      ierr    = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
    }
    { /* Side 2 (Bottom) */
      PetscInt cone[4];
      cone[0] = numFaces+0; cone[1] = numFaces+1; cone[2] = numFaces+5; cone[3] = numFaces+4;
      ierr    = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
    }
    { /* Side 3 (Top) */
      PetscInt cone[4];
      cone[0] = numFaces+6; cone[1] = numFaces+7; cone[2] = numFaces+3; cone[3] = numFaces+2;
      ierr    = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
    }
    { /* Side 4 (Left) */
      PetscInt cone[4];
      cone[0] = numFaces+0; cone[1] = numFaces+4; cone[2] = numFaces+6; cone[3] = numFaces+2;
      ierr    = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
    }
    { /* Side 5 (Right) */
      PetscInt cone[4];
      cone[0] = numFaces+5; cone[1] = numFaces+1; cone[2] = numFaces+3; cone[3] = numFaces+7;
      ierr    = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
    }
  }
  ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
  ierr = DMPlexStratify(dm);CHKERRQ(ierr);
  /* Build coordinates */
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
  for (v = numFaces; v < numFaces+numVertices; ++v) {
    ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
  ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
  ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  for (vz = 0; vz <= faces[2]; ++vz) {
    for (vy = 0; vy <= faces[1]; ++vy) {
      for (vx = 0; vx <= faces[0]; ++vx) {
        coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
        coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
        coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
      }
    }
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
  ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSquareMesh"
/*@
  DMPlexCreateSquareMesh - Creates a 2D mesh for a square lattice.

  Collective on MPI_Comm

  Input Parameters:
+ comm  - The communicator for the DM object
. lower - The lower left corner coordinates
. upper - The upper right corner coordinates
. edges - The number of cells in each direction
. bdX   - The boundary type for the X direction
- bdY   - The boundary type for the Y direction

  Output Parameter:
. dm  - The DM object

  Note: Here is the numbering returned for 2 cells in each direction:
$ 22--8-23--9--24
$  |     |     |
$ 13  2 14  3  15
$  |     |     |
$ 19--6-20--7--21
$  |     |     |
$ 10  0 11  1 12
$  |     |     |
$ 16--4-17--5--18

  Level: beginner

.keywords: DM, create
.seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
@*/
PetscErrorCode DMPlexCreateSquareMesh(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY)
{
  PetscInt       markerTop      = 1;
  PetscInt       markerBottom   = 1;
  PetscInt       markerRight    = 1;
  PetscInt       markerLeft     = 1;
  PetscBool      markerSeparate = PETSC_FALSE;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
  if (markerSeparate) {
    markerTop    = 3;
    markerBottom = 1;
    markerRight  = 2;
    markerLeft   = 4;
  }
  {
    const PetscInt numXEdges    = !rank ? edges[0]   : 0;
    const PetscInt numYEdges    = !rank ? edges[1]   : 0;
    const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
    const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
    const PetscInt numTotXEdges = numXEdges*numYVertices;
    const PetscInt numTotYEdges = numYEdges*numXVertices;
    const PetscInt numVertices  = numXVertices*numYVertices;
    const PetscInt numEdges     = numTotXEdges + numTotYEdges;
    const PetscInt numFaces     = numXEdges*numYEdges;
    const PetscInt firstVertex  = numFaces;
    const PetscInt firstXEdge   = numFaces + numVertices;
    const PetscInt firstYEdge   = numFaces + numVertices + numTotXEdges;
    Vec            coordinates;
    PetscSection   coordSection;
    PetscScalar   *coords;
    PetscInt       coordSize;
    PetscInt       v, vx, vy;
    PetscInt       f, fx, fy, e, ex, ey;

    ierr = DMPlexSetChart(dm, 0, numFaces+numEdges+numVertices);CHKERRQ(ierr);
    for (f = 0; f < numFaces; ++f) {
      ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
    }
    for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
      ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
    }
    ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
    /* Build faces */
    for (fy = 0; fy < numYEdges; fy++) {
      for (fx = 0; fx < numXEdges; fx++) {
        const PetscInt face    = fy*numXEdges + fx;
        const PetscInt edgeL   = firstYEdge +   fx                 *numYEdges + fy;
        const PetscInt edgeR   = firstYEdge + ((fx+1)%numXVertices)*numYEdges + fy;
        const PetscInt edgeB   = firstXEdge +   fy                 *numXEdges + fx;
        const PetscInt edgeT   = firstXEdge + ((fy+1)%numYVertices)*numXEdges + fx;
        const PetscInt ornt[4] = {0, 0, -2, -2};
        PetscInt       cone[4];

        cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
        ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
        ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
      }
    }
    /* Build Y edges*/
    for (vx = 0; vx < numXVertices; vx++) {
      for (ey = 0; ey < numYEdges; ey++) {
        const PetscInt nextv   = (bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : ((ey+1)%numYVertices)*numXVertices + vx;
        const PetscInt edge    = firstYEdge  + vx*numYEdges + ey;
        const PetscInt vertexB = firstVertex + ey*numXVertices + vx;
        const PetscInt vertexT = firstVertex + nextv;
        PetscInt       cone[2];

        cone[0] = vertexB; cone[1] = vertexT;
        ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
        if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
          if (vx == numXVertices-1) {
            ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
            ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
            if (ey == numYEdges-1) {
              ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
            }
          } else if (vx == 0) {
            ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
            ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
            if (ey == numYEdges-1) {
              ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
            }
          }
        }
      }
    }
    /* Build X edges*/
    for (vy = 0; vy < numYVertices; vy++) {
      for (ex = 0; ex < numXEdges; ex++) {
        const PetscInt nextv   = (bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : vy*numXVertices + (ex+1)%numXVertices;
        const PetscInt edge    = firstXEdge  + vy*numXEdges + ex;
        const PetscInt vertexL = firstVertex + vy*numXVertices + ex;
        const PetscInt vertexR = firstVertex + nextv;
        PetscInt       cone[2];

        cone[0] = vertexL; cone[1] = vertexR;
        ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
        if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
          if (vy == numYVertices-1) {
            ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
            ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
            if (ex == numXEdges-1) {
              ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
            }
          } else if (vy == 0) {
            ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
            ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
            if (ex == numXEdges-1) {
              ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
            }
          }
        }
      }
    }
    ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
    ierr = DMPlexStratify(dm);CHKERRQ(ierr);
    /* Build coordinates */
    ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
    for (v = firstVertex; v < firstVertex+numVertices; ++v) {
      ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
    ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
    ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
    for (vy = 0; vy < numYVertices; ++vy) {
      for (vx = 0; vx < numXVertices; ++vx) {
        coords[(vy*numXVertices+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
        coords[(vy*numXVertices+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
      }
    }
    ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
    ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateBoxMesh"
/*@
  DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices.

  Collective on MPI_Comm

  Input Parameters:
+ comm - The communicator for the DM object
. dim - The spatial dimension
- interpolate - Flag to create intermediate mesh pieces (edges, faces)

  Output Parameter:
. dm  - The DM object

  Level: beginner

.keywords: DM, create
.seealso: DMPlexCreateHexBoxMesh(), DMSetType(), DMCreate()
@*/
PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool interpolate, DM *dm)
{
  DM             boundary;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(dm, 4);
  ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
  PetscValidLogicalCollectiveInt(boundary,dim,2);
  ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(boundary, dim-1);CHKERRQ(ierr);
  switch (dim) {
  case 2:
  {
    PetscReal lower[2] = {0.0, 0.0};
    PetscReal upper[2] = {1.0, 1.0};
    PetscInt  edges[2] = {2, 2};

    ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, edges);CHKERRQ(ierr);
    break;
  }
  case 3:
  {
    PetscReal lower[3] = {0.0, 0.0, 0.0};
    PetscReal upper[3] = {1.0, 1.0, 1.0};
    PetscInt  faces[3] = {1, 1, 1};

    ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);
    break;
  }
  default:
    SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
  }
  ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
  ierr = DMDestroy(&boundary);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateHexBoxMesh"
/*@
  DMPlexCreateHexBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using hexahedra.

  Collective on MPI_Comm

  Input Parameters:
+ comm  - The communicator for the DM object
. dim   - The spatial dimension
. periodicX - The boundary type for the X direction
. periodicY - The boundary type for the Y direction
. periodicZ - The boundary type for the Z direction
- cells - The number of cells in each direction

  Output Parameter:
. dm  - The DM object

  Level: beginner

.keywords: DM, create
.seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
@*/
PetscErrorCode DMPlexCreateHexBoxMesh(MPI_Comm comm, PetscInt dim, const PetscInt cells[], DMBoundaryType periodicX, DMBoundaryType periodicY, DMBoundaryType periodicZ, DM *dm)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(dm, 4);
  ierr = DMCreate(comm, dm);CHKERRQ(ierr);
  PetscValidLogicalCollectiveInt(*dm,dim,2);
  ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(*dm, dim);CHKERRQ(ierr);
  switch (dim) {
  case 2:
  {
    PetscReal lower[2] = {0.0, 0.0};
    PetscReal upper[2] = {1.0, 1.0};

    ierr = DMPlexCreateSquareMesh(*dm, lower, upper, cells, periodicX, periodicY);CHKERRQ(ierr);
    break;
  }
#if 0
  case 3:
  {
    PetscReal lower[3] = {0.0, 0.0, 0.0};
    PetscReal upper[3] = {1.0, 1.0, 1.0};

    ierr = DMPlexCreateCubeMesh(boundary, lower, upper, cells, periodicX, periodicY, periodicZ);CHKERRQ(ierr);
    break;
  }
#endif
  default:
    SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
  }
  PetscFunctionReturn(0);
}

/* External function declarations here */
extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
extern PetscErrorCode DMRefine_Plex(DM dm, MPI_Comm comm, DM *dmRefined);
extern PetscErrorCode DMCoarsen_Plex(DM dm, MPI_Comm comm, DM *dmCoarsened);
extern PetscErrorCode DMRefineHierarchy_Plex(DM dm, PetscInt nlevels, DM dmRefined[]);
extern PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
extern PetscErrorCode DMSetUp_Plex(DM dm);
extern PetscErrorCode DMDestroy_Plex(DM dm);
extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, PetscInt fields[], IS *is, DM *subdm);
extern PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, IS *cellIS);

#undef __FUNCT__
#define __FUNCT__ "DMPlexReplace_Static"
/* Replace dm with the contents of dmNew
   - Share the DM_Plex structure
   - Share the coordinates
*/
static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
{
  PetscSection   coordSection;
  Vec            coords;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinateSection(dmNew, &coordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
  ierr = DMSetCoordinateSection(dm, coordSection);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
  ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
  dm->data = dmNew->data;
  ((DM_Plex *) dmNew->data)->refct++;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSwap_Static"
/* Swap dm with the contents of dmNew
   - Swap the DM_Plex structure
   - Swap the coordinates
*/
static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
{
  DM             coordDMA, coordDMB;
  Vec            coordsA,  coordsB;
  void          *tmp;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
  ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
  ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
  ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
  ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
  ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);

  ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
  ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
  ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
  tmp       = dmA->data;
  dmA->data = dmB->data;
  dmB->data = tmp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMSetFromOptions_Plex"
PetscErrorCode  DMSetFromOptions_Plex(DM dm)
{
  DM_Plex       *mesh   = (DM_Plex*) dm->data;
  PetscInt       refine = 0, r;
  PetscBool      isHierarchy;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscOptionsHead("DMPlex Options");CHKERRQ(ierr);
  /* Handle DMPlex refinement */
  ierr = PetscOptionsInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy);CHKERRQ(ierr);
  ierr = DMPlexSetRefinementUniform(dm, refine ? PETSC_TRUE : PETSC_FALSE);CHKERRQ(ierr);
  if (refine && isHierarchy) {
    DM *dms;

    ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
    ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
    /* Total hack since we do not pass in a pointer */
    ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
    if (refine == 1) {
      ierr = DMPlexSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
    } else {
      ierr = DMPlexSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
      ierr = DMPlexSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
    }
    /* Free DMs */
    for (r = 0; r < refine; ++r) {ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);}
    ierr = PetscFree(dms);CHKERRQ(ierr);
  } else {
    for (r = 0; r < refine; ++r) {
      DM refinedMesh;

      ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
      /* Total hack since we do not pass in a pointer */
      ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
      ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
    }
  }
  /* Handle associated vectors */
  /* Handle viewing */
  ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMView", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMView", 0, &mesh->printFEM, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMView", PETSC_FALSE, &mesh->printTol, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateGlobalVector_Plex"
static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
  /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
  ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void))VecView_Plex);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateLocalVector_Plex"
static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
  ierr = VecSetOperation(*vec, VECOP_VIEW, (void(*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInitialize_Plex"
PetscErrorCode DMInitialize_Plex(DM dm)
{
  PetscFunctionBegin;
  dm->ops->view                            = DMView_Plex;
  dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
  dm->ops->clone                           = DMClone_Plex;
  dm->ops->setup                           = DMSetUp_Plex;
  dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
  dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
  dm->ops->getlocaltoglobalmapping         = NULL;
  dm->ops->getlocaltoglobalmappingblock    = NULL;
  dm->ops->createfieldis                   = NULL;
  dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
  dm->ops->getcoloring                     = NULL;
  dm->ops->creatematrix                    = DMCreateMatrix_Plex;
  dm->ops->createinterpolation             = 0;
  dm->ops->getaggregates                   = 0;
  dm->ops->getinjection                    = 0;
  dm->ops->refine                          = DMRefine_Plex;
  dm->ops->coarsen                         = DMCoarsen_Plex;
  dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
  dm->ops->coarsenhierarchy                = NULL;
  dm->ops->globaltolocalbegin              = NULL;
  dm->ops->globaltolocalend                = NULL;
  dm->ops->localtoglobalbegin              = NULL;
  dm->ops->localtoglobalend                = NULL;
  dm->ops->destroy                         = DMDestroy_Plex;
  dm->ops->createsubdm                     = DMCreateSubDM_Plex;
  dm->ops->locatepoints                    = DMLocatePoints_Plex;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMClone_Plex"
PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
{
  DM_Plex        *mesh = (DM_Plex *) dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  mesh->refct++;
  (*newdm)->data = mesh;
  ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
  ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
  DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
                    In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
                    specified by a PetscSection object. Ownership in the global representation is determined by
                    ownership of the underlying DMPlex points. This is specified by another PetscSection object.

  Level: intermediate

.seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
M*/

#undef __FUNCT__
#define __FUNCT__ "DMCreate_Plex"
PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
{
  DM_Plex        *mesh;
  PetscInt       unit, d;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
  dm->data = mesh;

  mesh->refct             = 1;
  mesh->dim               = 0;
  ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
  mesh->maxConeSize       = 0;
  mesh->cones             = NULL;
  mesh->coneOrientations  = NULL;
  ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
  mesh->maxSupportSize    = 0;
  mesh->supports          = NULL;
  mesh->refinementUniform = PETSC_TRUE;
  mesh->refinementLimit   = -1.0;

  mesh->facesTmp = NULL;

  mesh->subpointMap = NULL;

  for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;

  mesh->labels              = NULL;
  mesh->depthLabel          = NULL;
  mesh->globalVertexNumbers = NULL;
  mesh->globalCellNumbers   = NULL;
  for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
  mesh->vtkCellHeight     = 0;
  mesh->preallocCenterDim = -1;

  mesh->printSetValues = PETSC_FALSE;
  mesh->printFEM       = 0;
  mesh->printTol       = 1.0e-10;

  ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreate"
/*@
  DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.

  Collective on MPI_Comm

  Input Parameter:
. comm - The communicator for the DMPlex object

  Output Parameter:
. mesh  - The DMPlex object

  Level: beginner

.keywords: DMPlex, create
@*/
PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(mesh,2);
  ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
  ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexBuildFromCellList_Private"
/*
  This takes as input the common mesh generator output, a list of the vertices for each cell
*/
PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
{
  PetscInt      *cone, c, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
  for (c = 0; c < numCells; ++c) {
    ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
  }
  ierr = DMSetUp(dm);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
  for (c = 0; c < numCells; ++c) {
    for (p = 0; p < numCorners; ++p) {
      cone[p] = cells[c*numCorners+p]+numCells;
    }
    ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
  }
  ierr = DMRestoreWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
  ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
  ierr = DMPlexStratify(dm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexBuildCoordinates_Private"
/*
  This takes as input the coordinates for each vertex
*/
PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
{
  PetscSection   coordSection;
  Vec            coordinates;
  PetscScalar   *coords;
  PetscInt       coordSize, v, d;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
  ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
  for (v = numCells; v < numCells+numVertices; ++v) {
    ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
  ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
  ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  for (v = 0; v < numVertices; ++v) {
    for (d = 0; d < spaceDim; ++d) {
      coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
    }
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
  ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateFromCellList"
/*@C
  DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM

  Input Parameters:
+ comm - The communicator
. dim - The topological dimension of the mesh
. numCells - The number of cells
. numVertices - The number of vertices
. numCorners - The number of vertices for each cell
. interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
. cells - An array of numCells*numCorners numbers, the vertices for each cell
. spaceDim - The spatial dimension used for coordinates
- vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

  Output Parameter:
. dm - The DM

  Note: Two triangles sharing a face
$
$        2
$      / | \
$     /  |  \
$    /   |   \
$   0  0 | 1  3
$    \   |   /
$     \  |  /
$      \ | /
$        1
would have input
$  numCells = 2, numVertices = 4
$  cells = [0 1 2  1 3 2]
$
which would result in the DMPlex
$
$        4
$      / | \
$     /  |  \
$    /   |   \
$   2  0 | 1  5
$    \   |   /
$     \  |  /
$      \ | /
$        3

  Level: beginner

.seealso: DMPlexCreateFromDAG(), DMPlexCreate()
@*/
PetscErrorCode DMPlexCreateFromCellList(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const int cells[], PetscInt spaceDim, const double vertexCoords[], DM *dm)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMCreate(comm, dm);CHKERRQ(ierr);
  ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(*dm, dim);CHKERRQ(ierr);
  ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
  if (interpolate) {
    DM idm;

    ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
    ierr = DMDestroy(dm);CHKERRQ(ierr);
    *dm  = idm;
  }
  ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateFromDAG"
/*@
  DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM

  Input Parameters:
+ dm - The empty DM object, usually from DMCreate() and DMPlexSetDimension()
. depth - The depth of the DAG
. numPoints - The number of points at each depth
. coneSize - The cone size of each point
. cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
. coneOrientations - The orientation of each cone point
- vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex

  Output Parameter:
. dm - The DM

  Note: Two triangles sharing a face would have input
$  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
$  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
$ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
$
which would result in the DMPlex
$
$        4
$      / | \
$     /  |  \
$    /   |   \
$   2  0 | 1  5
$    \   |   /
$     \  |  /
$      \ | /
$        3
$
$ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()

  Level: advanced

.seealso: DMPlexCreateFromCellList(), DMPlexCreate()
@*/
PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
{
  Vec            coordinates;
  PetscSection   coordSection;
  PetscScalar    *coords;
  PetscInt       coordSize, firstVertex = numPoints[depth], pStart = 0, pEnd = 0, p, v, dim, d, off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
  ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
  }
  ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
  for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
    ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
    ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
  }
  ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
  ierr = DMPlexStratify(dm);CHKERRQ(ierr);
  /* Build coordinates */
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
  ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
  for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
    ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
  ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
  ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  for (v = 0; v < numPoints[0]; ++v) {
    PetscInt off;

    ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
    for (d = 0; d < dim; ++d) {
      coords[off+d] = vertexCoords[v*dim+d];
    }
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
  ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}