Actual source code: plexcreate.c
petsc-3.15.0 2021-03-30
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      1: #define PETSCDM_DLL
      2: #include <petsc/private/dmpleximpl.h>
      3: #include <petsc/private/hashseti.h>
      4: #include <petscsf.h>

      6: PetscLogEvent DMPLEX_CreateFromFile, DMPLEX_BuildFromCellList, DMPLEX_BuildCoordinatesFromCellList;

      8: /*@
      9:   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.

     11:   Collective

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

     20:   Output Parameter:
     21: . dm - The DM object

     23:   Level: beginner

     25: .seealso: DMSetType(), DMCreate()
     26: @*/
     27: PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscReal refinementLimit, DM *newdm)
     28: {
     29:   DM             dm;
     30:   PetscMPIInt    rank;

     34:   DMCreate(comm, &dm);
     35:   DMSetType(dm, DMPLEX);
     36:   DMSetDimension(dm, dim);
     37:   MPI_Comm_rank(comm, &rank);
     38:   switch (dim) {
     39:   case 2:
     40:     if (simplex) {PetscObjectSetName((PetscObject) dm, "triangular");}
     41:     else         {PetscObjectSetName((PetscObject) dm, "quadrilateral");}
     42:     break;
     43:   case 3:
     44:     if (simplex) {PetscObjectSetName((PetscObject) dm, "tetrahedral");}
     45:     else         {PetscObjectSetName((PetscObject) dm, "hexahedral");}
     46:     break;
     47:   default:
     48:     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
     49:   }
     50:   if (rank) {
     51:     PetscInt numPoints[2] = {0, 0};
     52:     DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);
     53:   } else {
     54:     switch (dim) {
     55:     case 2:
     56:       if (simplex) {
     57:         PetscInt    numPoints[2]        = {4, 2};
     58:         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
     59:         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
     60:         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
     61:         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};

     63:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     64:       } else {
     65:         PetscInt    numPoints[2]        = {6, 2};
     66:         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
     67:         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
     68:         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
     69:         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};

     71:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     72:       }
     73:       break;
     74:     case 3:
     75:       if (simplex) {
     76:         PetscInt    numPoints[2]        = {5, 2};
     77:         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
     78:         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
     79:         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
     80:         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};

     82:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     83:       } else {
     84:         PetscInt    numPoints[2]         = {12, 2};
     85:         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
     86:         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
     87:         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
     88:         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,
     89:                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
     90:                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};

     92:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     93:       }
     94:       break;
     95:     default:
     96:       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
     97:     }
     98:   }
     99:   *newdm = dm;
    100:   if (refinementLimit > 0.0) {
    101:     DM rdm;
    102:     const char *name;

    104:     DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);
    105:     DMPlexSetRefinementLimit(*newdm, refinementLimit);
    106:     DMRefine(*newdm, comm, &rdm);
    107:     PetscObjectGetName((PetscObject) *newdm, &name);
    108:     PetscObjectSetName((PetscObject)    rdm,  name);
    109:     DMDestroy(newdm);
    110:     *newdm = rdm;
    111:   }
    112:   if (interpolate) {
    113:     DM idm;

    115:     DMPlexInterpolate(*newdm, &idm);
    116:     DMDestroy(newdm);
    117:     *newdm = idm;
    118:   }
    119:   return(0);
    120: }

    122: /*@
    123:   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.

    125:   Collective

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

    133:   Output Parameter:
    134: . dm  - The DM object

    136:   Note: Here is the numbering returned for 2 cells in each direction:
    137: $ 18--5-17--4--16
    138: $  |     |     |
    139: $  6    10     3
    140: $  |     |     |
    141: $ 19-11-20--9--15
    142: $  |     |     |
    143: $  7     8     2
    144: $  |     |     |
    145: $ 12--0-13--1--14

    147:   Level: beginner

    149: .seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
    150: @*/
    151: PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
    152: {
    153:   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
    154:   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
    155:   PetscInt       markerTop      = 1;
    156:   PetscInt       markerBottom   = 1;
    157:   PetscInt       markerRight    = 1;
    158:   PetscInt       markerLeft     = 1;
    159:   PetscBool      markerSeparate = PETSC_FALSE;
    160:   Vec            coordinates;
    161:   PetscSection   coordSection;
    162:   PetscScalar    *coords;
    163:   PetscInt       coordSize;
    164:   PetscMPIInt    rank;
    165:   PetscInt       v, vx, vy;

    169:   PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);
    170:   if (markerSeparate) {
    171:     markerTop    = 3;
    172:     markerBottom = 1;
    173:     markerRight  = 2;
    174:     markerLeft   = 4;
    175:   }
    176:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    177:   if (!rank) {
    178:     PetscInt e, ex, ey;

    180:     DMPlexSetChart(dm, 0, numEdges+numVertices);
    181:     for (e = 0; e < numEdges; ++e) {
    182:       DMPlexSetConeSize(dm, e, 2);
    183:     }
    184:     DMSetUp(dm); /* Allocate space for cones */
    185:     for (vx = 0; vx <= edges[0]; vx++) {
    186:       for (ey = 0; ey < edges[1]; ey++) {
    187:         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
    188:         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
    189:         PetscInt cone[2];

    191:         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
    192:         DMPlexSetCone(dm, edge, cone);
    193:         if (vx == edges[0]) {
    194:           DMSetLabelValue(dm, "marker", edge,    markerRight);
    195:           DMSetLabelValue(dm, "marker", cone[0], markerRight);
    196:           if (ey == edges[1]-1) {
    197:             DMSetLabelValue(dm, "marker", cone[1], markerRight);
    198:             DMSetLabelValue(dm, "Face Sets", cone[1], markerRight);
    199:           }
    200:         } else if (vx == 0) {
    201:           DMSetLabelValue(dm, "marker", edge,    markerLeft);
    202:           DMSetLabelValue(dm, "marker", cone[0], markerLeft);
    203:           if (ey == edges[1]-1) {
    204:             DMSetLabelValue(dm, "marker", cone[1], markerLeft);
    205:             DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft);
    206:           }
    207:         }
    208:       }
    209:     }
    210:     for (vy = 0; vy <= edges[1]; vy++) {
    211:       for (ex = 0; ex < edges[0]; ex++) {
    212:         PetscInt edge   = vy*edges[0]     + ex;
    213:         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
    214:         PetscInt cone[2];

    216:         cone[0] = vertex; cone[1] = vertex+1;
    217:         DMPlexSetCone(dm, edge, cone);
    218:         if (vy == edges[1]) {
    219:           DMSetLabelValue(dm, "marker", edge,    markerTop);
    220:           DMSetLabelValue(dm, "marker", cone[0], markerTop);
    221:           if (ex == edges[0]-1) {
    222:             DMSetLabelValue(dm, "marker", cone[1], markerTop);
    223:             DMSetLabelValue(dm, "Face Sets", cone[1], markerTop);
    224:           }
    225:         } else if (vy == 0) {
    226:           DMSetLabelValue(dm, "marker", edge,    markerBottom);
    227:           DMSetLabelValue(dm, "marker", cone[0], markerBottom);
    228:           if (ex == edges[0]-1) {
    229:             DMSetLabelValue(dm, "marker", cone[1], markerBottom);
    230:             DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom);
    231:           }
    232:         }
    233:       }
    234:     }
    235:   }
    236:   DMPlexSymmetrize(dm);
    237:   DMPlexStratify(dm);
    238:   /* Build coordinates */
    239:   DMSetCoordinateDim(dm, 2);
    240:   DMGetCoordinateSection(dm, &coordSection);
    241:   PetscSectionSetNumFields(coordSection, 1);
    242:   PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);
    243:   PetscSectionSetFieldComponents(coordSection, 0, 2);
    244:   for (v = numEdges; v < numEdges+numVertices; ++v) {
    245:     PetscSectionSetDof(coordSection, v, 2);
    246:     PetscSectionSetFieldDof(coordSection, v, 0, 2);
    247:   }
    248:   PetscSectionSetUp(coordSection);
    249:   PetscSectionGetStorageSize(coordSection, &coordSize);
    250:   VecCreate(PETSC_COMM_SELF, &coordinates);
    251:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    252:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    253:   VecSetBlockSize(coordinates, 2);
    254:   VecSetType(coordinates,VECSTANDARD);
    255:   VecGetArray(coordinates, &coords);
    256:   for (vy = 0; vy <= edges[1]; ++vy) {
    257:     for (vx = 0; vx <= edges[0]; ++vx) {
    258:       coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
    259:       coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
    260:     }
    261:   }
    262:   VecRestoreArray(coordinates, &coords);
    263:   DMSetCoordinatesLocal(dm, coordinates);
    264:   VecDestroy(&coordinates);
    265:   return(0);
    266: }

    268: /*@
    269:   DMPlexCreateCubeBoundary - Creates a 2D mesh that is the boundary of a cubic lattice.

    271:   Collective

    273:   Input Parameters:
    274: + comm  - The communicator for the DM object
    275: . lower - The lower left front corner coordinates
    276: . upper - The upper right back corner coordinates
    277: - faces - The number of faces in each direction (the same as the number of cells)

    279:   Output Parameter:
    280: . dm  - The DM object

    282:   Level: beginner

    284: .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
    285: @*/
    286: PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
    287: {
    288:   PetscInt       vertices[3], numVertices;
    289:   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
    290:   Vec            coordinates;
    291:   PetscSection   coordSection;
    292:   PetscScalar    *coords;
    293:   PetscInt       coordSize;
    294:   PetscMPIInt    rank;
    295:   PetscInt       v, vx, vy, vz;
    296:   PetscInt       voffset, iface=0, cone[4];

    300:   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");
    301:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    302:   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
    303:   numVertices = vertices[0]*vertices[1]*vertices[2];
    304:   if (!rank) {
    305:     PetscInt f;

    307:     DMPlexSetChart(dm, 0, numFaces+numVertices);
    308:     for (f = 0; f < numFaces; ++f) {
    309:       DMPlexSetConeSize(dm, f, 4);
    310:     }
    311:     DMSetUp(dm); /* Allocate space for cones */

    313:     /* Side 0 (Top) */
    314:     for (vy = 0; vy < faces[1]; vy++) {
    315:       for (vx = 0; vx < faces[0]; vx++) {
    316:         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
    317:         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
    318:         DMPlexSetCone(dm, iface, cone);
    319:         DMSetLabelValue(dm, "marker", iface, 1);
    320:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    321:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    322:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    323:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);
    324:         iface++;
    325:       }
    326:     }

    328:     /* Side 1 (Bottom) */
    329:     for (vy = 0; vy < faces[1]; vy++) {
    330:       for (vx = 0; vx < faces[0]; vx++) {
    331:         voffset = numFaces + vy*(faces[0]+1) + vx;
    332:         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
    333:         DMPlexSetCone(dm, iface, cone);
    334:         DMSetLabelValue(dm, "marker", iface, 1);
    335:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    336:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    337:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    338:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);
    339:         iface++;
    340:       }
    341:     }

    343:     /* Side 2 (Front) */
    344:     for (vz = 0; vz < faces[2]; vz++) {
    345:       for (vx = 0; vx < faces[0]; vx++) {
    346:         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
    347:         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
    348:         DMPlexSetCone(dm, iface, cone);
    349:         DMSetLabelValue(dm, "marker", iface, 1);
    350:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    351:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    352:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);
    353:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);
    354:         iface++;
    355:       }
    356:     }

    358:     /* Side 3 (Back) */
    359:     for (vz = 0; vz < faces[2]; vz++) {
    360:       for (vx = 0; vx < faces[0]; vx++) {
    361:         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
    362:         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
    363:         cone[2] = voffset+1; cone[3] = voffset;
    364:         DMPlexSetCone(dm, iface, cone);
    365:         DMSetLabelValue(dm, "marker", iface, 1);
    366:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    367:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    368:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);
    369:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);
    370:         iface++;
    371:       }
    372:     }

    374:     /* Side 4 (Left) */
    375:     for (vz = 0; vz < faces[2]; vz++) {
    376:       for (vy = 0; vy < faces[1]; vy++) {
    377:         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
    378:         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
    379:         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
    380:         DMPlexSetCone(dm, iface, cone);
    381:         DMSetLabelValue(dm, "marker", iface, 1);
    382:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    383:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    384:         DMSetLabelValue(dm, "marker", voffset+vertices[1]+0, 1);
    385:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);
    386:         iface++;
    387:       }
    388:     }

    390:     /* Side 5 (Right) */
    391:     for (vz = 0; vz < faces[2]; vz++) {
    392:       for (vy = 0; vy < faces[1]; vy++) {
    393:         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
    394:         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
    395:         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
    396:         DMPlexSetCone(dm, iface, cone);
    397:         DMSetLabelValue(dm, "marker", iface, 1);
    398:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    399:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    400:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);
    401:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);
    402:         iface++;
    403:       }
    404:     }
    405:   }
    406:   DMPlexSymmetrize(dm);
    407:   DMPlexStratify(dm);
    408:   /* Build coordinates */
    409:   DMSetCoordinateDim(dm, 3);
    410:   DMGetCoordinateSection(dm, &coordSection);
    411:   PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);
    412:   for (v = numFaces; v < numFaces+numVertices; ++v) {
    413:     PetscSectionSetDof(coordSection, v, 3);
    414:   }
    415:   PetscSectionSetUp(coordSection);
    416:   PetscSectionGetStorageSize(coordSection, &coordSize);
    417:   VecCreate(PETSC_COMM_SELF, &coordinates);
    418:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    419:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    420:   VecSetBlockSize(coordinates, 3);
    421:   VecSetType(coordinates,VECSTANDARD);
    422:   VecGetArray(coordinates, &coords);
    423:   for (vz = 0; vz <= faces[2]; ++vz) {
    424:     for (vy = 0; vy <= faces[1]; ++vy) {
    425:       for (vx = 0; vx <= faces[0]; ++vx) {
    426:         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
    427:         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
    428:         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
    429:       }
    430:     }
    431:   }
    432:   VecRestoreArray(coordinates, &coords);
    433:   DMSetCoordinatesLocal(dm, coordinates);
    434:   VecDestroy(&coordinates);
    435:   return(0);
    436: }

    438: static PetscErrorCode DMPlexCreateLineMesh_Internal(MPI_Comm comm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd,DM *dm)
    439: {
    440:   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
    441:   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
    442:   PetscScalar    *vertexCoords;
    443:   PetscReal      L,maxCell;
    444:   PetscBool      markerSeparate = PETSC_FALSE;
    445:   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
    446:   PetscInt       markerRight = 1, faceMarkerRight = 2;
    447:   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
    448:   PetscMPIInt    rank;

    454:   DMCreate(comm,dm);
    455:   DMSetType(*dm,DMPLEX);
    456:   DMSetDimension(*dm,1);
    457:   DMCreateLabel(*dm,"marker");
    458:   DMCreateLabel(*dm,"Face Sets");

    460:   MPI_Comm_rank(comm,&rank);
    461:   if (!rank) numCells = segments;
    462:   if (!rank) numVerts = segments + (wrap ? 0 : 1);

    464:   numPoints[0] = numVerts ; numPoints[1] = numCells;
    465:   PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);
    466:   PetscArrayzero(coneOrientations,numCells+numVerts);
    467:   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
    468:   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
    469:   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
    470:   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
    471:   DMPlexCreateFromDAG(*dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);
    472:   PetscFree4(coneSize,cones,coneOrientations,vertexCoords);

    474:   PetscOptionsGetBool(((PetscObject)*dm)->options,((PetscObject)*dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);
    475:   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
    476:   if (!wrap && !rank) {
    477:     DMPlexGetHeightStratum(*dm,1,&fStart,&fEnd);
    478:     DMSetLabelValue(*dm,"marker",fStart,markerLeft);
    479:     DMSetLabelValue(*dm,"marker",fEnd-1,markerRight);
    480:     DMSetLabelValue(*dm,"Face Sets",fStart,faceMarkerLeft);
    481:     DMSetLabelValue(*dm,"Face Sets",fEnd-1,faceMarkerRight);
    482:   }
    483:   if (wrap) {
    484:     L       = upper - lower;
    485:     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
    486:     DMSetPeriodicity(*dm,PETSC_TRUE,&maxCell,&L,&bd);
    487:   }
    488:   DMPlexSetRefinementUniform(*dm, PETSC_TRUE);
    489:   return(0);
    490: }

    492: static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
    493: {
    494:   DM             boundary;
    495:   PetscInt       i;

    500:   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
    501:   DMCreate(comm, &boundary);
    503:   DMSetType(boundary, DMPLEX);
    504:   DMSetDimension(boundary, dim-1);
    505:   DMSetCoordinateDim(boundary, dim);
    506:   switch (dim) {
    507:   case 2: DMPlexCreateSquareBoundary(boundary, lower, upper, faces);break;
    508:   case 3: DMPlexCreateCubeBoundary(boundary, lower, upper, faces);break;
    509:   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %D", dim);
    510:   }
    511:   DMPlexGenerate(boundary, NULL, interpolate, dm);
    512:   DMDestroy(&boundary);
    513:   return(0);
    514: }

    516: static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
    517: {
    518:   DMLabel        cutLabel = NULL;
    519:   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
    520:   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
    521:   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
    522:   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
    523:   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
    524:   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
    525:   PetscInt       dim;
    526:   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
    527:   PetscMPIInt    rank;

    531:   DMGetDimension(dm,&dim);
    532:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    533:   DMCreateLabel(dm,"marker");
    534:   DMCreateLabel(dm,"Face Sets");
    535:   PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);
    536:   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
    537:       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
    538:       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {

    540:     if (cutMarker) {DMCreateLabel(dm, "periodic_cut"); DMGetLabel(dm, "periodic_cut", &cutLabel);}
    541:   }
    542:   switch (dim) {
    543:   case 2:
    544:     faceMarkerTop    = 3;
    545:     faceMarkerBottom = 1;
    546:     faceMarkerRight  = 2;
    547:     faceMarkerLeft   = 4;
    548:     break;
    549:   case 3:
    550:     faceMarkerBottom = 1;
    551:     faceMarkerTop    = 2;
    552:     faceMarkerFront  = 3;
    553:     faceMarkerBack   = 4;
    554:     faceMarkerRight  = 5;
    555:     faceMarkerLeft   = 6;
    556:     break;
    557:   default:
    558:     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %D not supported",dim);
    559:   }
    560:   PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);
    561:   if (markerSeparate) {
    562:     markerBottom = faceMarkerBottom;
    563:     markerTop    = faceMarkerTop;
    564:     markerFront  = faceMarkerFront;
    565:     markerBack   = faceMarkerBack;
    566:     markerRight  = faceMarkerRight;
    567:     markerLeft   = faceMarkerLeft;
    568:   }
    569:   {
    570:     const PetscInt numXEdges    = !rank ? edges[0] : 0;
    571:     const PetscInt numYEdges    = !rank ? edges[1] : 0;
    572:     const PetscInt numZEdges    = !rank ? edges[2] : 0;
    573:     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
    574:     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
    575:     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
    576:     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
    577:     const PetscInt numXFaces    = numYEdges*numZEdges;
    578:     const PetscInt numYFaces    = numXEdges*numZEdges;
    579:     const PetscInt numZFaces    = numXEdges*numYEdges;
    580:     const PetscInt numTotXFaces = numXVertices*numXFaces;
    581:     const PetscInt numTotYFaces = numYVertices*numYFaces;
    582:     const PetscInt numTotZFaces = numZVertices*numZFaces;
    583:     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
    584:     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
    585:     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
    586:     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
    587:     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
    588:     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
    589:     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
    590:     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
    591:     const PetscInt firstYFace   = firstXFace + numTotXFaces;
    592:     const PetscInt firstZFace   = firstYFace + numTotYFaces;
    593:     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
    594:     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
    595:     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
    596:     Vec            coordinates;
    597:     PetscSection   coordSection;
    598:     PetscScalar   *coords;
    599:     PetscInt       coordSize;
    600:     PetscInt       v, vx, vy, vz;
    601:     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;

    603:     DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);
    604:     for (c = 0; c < numCells; c++) {
    605:       DMPlexSetConeSize(dm, c, 6);
    606:     }
    607:     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
    608:       DMPlexSetConeSize(dm, f, 4);
    609:     }
    610:     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
    611:       DMPlexSetConeSize(dm, e, 2);
    612:     }
    613:     DMSetUp(dm); /* Allocate space for cones */
    614:     /* Build cells */
    615:     for (fz = 0; fz < numZEdges; ++fz) {
    616:       for (fy = 0; fy < numYEdges; ++fy) {
    617:         for (fx = 0; fx < numXEdges; ++fx) {
    618:           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
    619:           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
    620:           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
    621:           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
    622:           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
    623:           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
    624:           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
    625:                             /* B,  T,  F,  K,  R,  L */
    626:           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
    627:           PetscInt cone[6];

    629:           /* no boundary twisting in 3D */
    630:           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
    631:           DMPlexSetCone(dm, cell, cone);
    632:           DMPlexSetConeOrientation(dm, cell, ornt);
    633:           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, cell, 2);}
    634:           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, cell, 2);}
    635:           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, cell, 2);}
    636:         }
    637:       }
    638:     }
    639:     /* Build x faces */
    640:     for (fz = 0; fz < numZEdges; ++fz) {
    641:       for (fy = 0; fy < numYEdges; ++fy) {
    642:         for (fx = 0; fx < numXVertices; ++fx) {
    643:           PetscInt face    = firstXFace + (fz*numYEdges+fy)     *numXVertices+fx;
    644:           PetscInt edgeL   = firstZEdge + (fy                   *numXVertices+fx)*numZEdges + fz;
    645:           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
    646:           PetscInt edgeB   = firstYEdge + (fz                   *numXVertices+fx)*numYEdges + fy;
    647:           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
    648:           PetscInt ornt[4] = {0, 0, -2, -2};
    649:           PetscInt cone[4];

    651:           if (dim == 3) {
    652:             /* markers */
    653:             if (bdX != DM_BOUNDARY_PERIODIC) {
    654:               if (fx == numXVertices-1) {
    655:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);
    656:                 DMSetLabelValue(dm, "marker", face, markerRight);
    657:               }
    658:               else if (fx == 0) {
    659:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);
    660:                 DMSetLabelValue(dm, "marker", face, markerLeft);
    661:               }
    662:             }
    663:           }
    664:           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
    665:           DMPlexSetCone(dm, face, cone);
    666:           DMPlexSetConeOrientation(dm, face, ornt);
    667:         }
    668:       }
    669:     }
    670:     /* Build y faces */
    671:     for (fz = 0; fz < numZEdges; ++fz) {
    672:       for (fx = 0; fx < numXEdges; ++fx) {
    673:         for (fy = 0; fy < numYVertices; ++fy) {
    674:           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
    675:           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx)*numZEdges + fz;
    676:           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
    677:           PetscInt edgeB   = firstXEdge + (fz                   *numYVertices+fy)*numXEdges + fx;
    678:           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
    679:           PetscInt ornt[4] = {0, 0, -2, -2};
    680:           PetscInt cone[4];

    682:           if (dim == 3) {
    683:             /* markers */
    684:             if (bdY != DM_BOUNDARY_PERIODIC) {
    685:               if (fy == numYVertices-1) {
    686:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);
    687:                 DMSetLabelValue(dm, "marker", face, markerBack);
    688:               }
    689:               else if (fy == 0) {
    690:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);
    691:                 DMSetLabelValue(dm, "marker", face, markerFront);
    692:               }
    693:             }
    694:           }
    695:           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
    696:           DMPlexSetCone(dm, face, cone);
    697:           DMPlexSetConeOrientation(dm, face, ornt);
    698:         }
    699:       }
    700:     }
    701:     /* Build z faces */
    702:     for (fy = 0; fy < numYEdges; ++fy) {
    703:       for (fx = 0; fx < numXEdges; ++fx) {
    704:         for (fz = 0; fz < numZVertices; fz++) {
    705:           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
    706:           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx)*numYEdges + fy;
    707:           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
    708:           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy)*numXEdges + fx;
    709:           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
    710:           PetscInt ornt[4] = {0, 0, -2, -2};
    711:           PetscInt cone[4];

    713:           if (dim == 2) {
    714:             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
    715:             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
    716:             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, face, 2);}
    717:             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, face, 2);}
    718:           } else {
    719:             /* markers */
    720:             if (bdZ != DM_BOUNDARY_PERIODIC) {
    721:               if (fz == numZVertices-1) {
    722:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);
    723:                 DMSetLabelValue(dm, "marker", face, markerTop);
    724:               }
    725:               else if (fz == 0) {
    726:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);
    727:                 DMSetLabelValue(dm, "marker", face, markerBottom);
    728:               }
    729:             }
    730:           }
    731:           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
    732:           DMPlexSetCone(dm, face, cone);
    733:           DMPlexSetConeOrientation(dm, face, ornt);
    734:         }
    735:       }
    736:     }
    737:     /* Build Z edges*/
    738:     for (vy = 0; vy < numYVertices; vy++) {
    739:       for (vx = 0; vx < numXVertices; vx++) {
    740:         for (ez = 0; ez < numZEdges; ez++) {
    741:           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
    742:           const PetscInt vertexB = firstVertex + (ez                   *numYVertices+vy)*numXVertices + vx;
    743:           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
    744:           PetscInt       cone[2];

    746:           if (dim == 3) {
    747:             if (bdX != DM_BOUNDARY_PERIODIC) {
    748:               if (vx == numXVertices-1) {
    749:                 DMSetLabelValue(dm, "marker", edge, markerRight);
    750:               }
    751:               else if (vx == 0) {
    752:                 DMSetLabelValue(dm, "marker", edge, markerLeft);
    753:               }
    754:             }
    755:             if (bdY != DM_BOUNDARY_PERIODIC) {
    756:               if (vy == numYVertices-1) {
    757:                 DMSetLabelValue(dm, "marker", edge, markerBack);
    758:               }
    759:               else if (vy == 0) {
    760:                 DMSetLabelValue(dm, "marker", edge, markerFront);
    761:               }
    762:             }
    763:           }
    764:           cone[0] = vertexB; cone[1] = vertexT;
    765:           DMPlexSetCone(dm, edge, cone);
    766:         }
    767:       }
    768:     }
    769:     /* Build Y edges*/
    770:     for (vz = 0; vz < numZVertices; vz++) {
    771:       for (vx = 0; vx < numXVertices; vx++) {
    772:         for (ey = 0; ey < numYEdges; ey++) {
    773:           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
    774:           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
    775:           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
    776:           const PetscInt vertexK = firstVertex + nextv;
    777:           PetscInt       cone[2];

    779:           cone[0] = vertexF; cone[1] = vertexK;
    780:           DMPlexSetCone(dm, edge, cone);
    781:           if (dim == 2) {
    782:             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
    783:               if (vx == numXVertices-1) {
    784:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);
    785:                 DMSetLabelValue(dm, "marker", edge,    markerRight);
    786:                 DMSetLabelValue(dm, "marker", cone[0], markerRight);
    787:                 if (ey == numYEdges-1) {
    788:                   DMSetLabelValue(dm, "marker", cone[1], markerRight);
    789:                 }
    790:               } else if (vx == 0) {
    791:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);
    792:                 DMSetLabelValue(dm, "marker", edge,    markerLeft);
    793:                 DMSetLabelValue(dm, "marker", cone[0], markerLeft);
    794:                 if (ey == numYEdges-1) {
    795:                   DMSetLabelValue(dm, "marker", cone[1], markerLeft);
    796:                 }
    797:               }
    798:             } else {
    799:               if (vx == 0 && cutLabel) {
    800:                 DMLabelSetValue(cutLabel, edge,    1);
    801:                 DMLabelSetValue(cutLabel, cone[0], 1);
    802:                 if (ey == numYEdges-1) {
    803:                   DMLabelSetValue(cutLabel, cone[1], 1);
    804:                 }
    805:               }
    806:             }
    807:           } else {
    808:             if (bdX != DM_BOUNDARY_PERIODIC) {
    809:               if (vx == numXVertices-1) {
    810:                 DMSetLabelValue(dm, "marker", edge, markerRight);
    811:               } else if (vx == 0) {
    812:                 DMSetLabelValue(dm, "marker", edge, markerLeft);
    813:               }
    814:             }
    815:             if (bdZ != DM_BOUNDARY_PERIODIC) {
    816:               if (vz == numZVertices-1) {
    817:                 DMSetLabelValue(dm, "marker", edge, markerTop);
    818:               } else if (vz == 0) {
    819:                 DMSetLabelValue(dm, "marker", edge, markerBottom);
    820:               }
    821:             }
    822:           }
    823:         }
    824:       }
    825:     }
    826:     /* Build X edges*/
    827:     for (vz = 0; vz < numZVertices; vz++) {
    828:       for (vy = 0; vy < numYVertices; vy++) {
    829:         for (ex = 0; ex < numXEdges; ex++) {
    830:           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
    831:           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
    832:           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
    833:           const PetscInt vertexR = firstVertex + nextv;
    834:           PetscInt       cone[2];

    836:           cone[0] = vertexL; cone[1] = vertexR;
    837:           DMPlexSetCone(dm, edge, cone);
    838:           if (dim == 2) {
    839:             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
    840:               if (vy == numYVertices-1) {
    841:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);
    842:                 DMSetLabelValue(dm, "marker", edge,    markerTop);
    843:                 DMSetLabelValue(dm, "marker", cone[0], markerTop);
    844:                 if (ex == numXEdges-1) {
    845:                   DMSetLabelValue(dm, "marker", cone[1], markerTop);
    846:                 }
    847:               } else if (vy == 0) {
    848:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);
    849:                 DMSetLabelValue(dm, "marker", edge,    markerBottom);
    850:                 DMSetLabelValue(dm, "marker", cone[0], markerBottom);
    851:                 if (ex == numXEdges-1) {
    852:                   DMSetLabelValue(dm, "marker", cone[1], markerBottom);
    853:                 }
    854:               }
    855:             } else {
    856:               if (vy == 0 && cutLabel) {
    857:                 DMLabelSetValue(cutLabel, edge,    1);
    858:                 DMLabelSetValue(cutLabel, cone[0], 1);
    859:                 if (ex == numXEdges-1) {
    860:                   DMLabelSetValue(cutLabel, cone[1], 1);
    861:                 }
    862:               }
    863:             }
    864:           } else {
    865:             if (bdY != DM_BOUNDARY_PERIODIC) {
    866:               if (vy == numYVertices-1) {
    867:                 DMSetLabelValue(dm, "marker", edge, markerBack);
    868:               }
    869:               else if (vy == 0) {
    870:                 DMSetLabelValue(dm, "marker", edge, markerFront);
    871:               }
    872:             }
    873:             if (bdZ != DM_BOUNDARY_PERIODIC) {
    874:               if (vz == numZVertices-1) {
    875:                 DMSetLabelValue(dm, "marker", edge, markerTop);
    876:               }
    877:               else if (vz == 0) {
    878:                 DMSetLabelValue(dm, "marker", edge, markerBottom);
    879:               }
    880:             }
    881:           }
    882:         }
    883:       }
    884:     }
    885:     DMPlexSymmetrize(dm);
    886:     DMPlexStratify(dm);
    887:     /* Build coordinates */
    888:     DMGetCoordinateSection(dm, &coordSection);
    889:     PetscSectionSetNumFields(coordSection, 1);
    890:     PetscSectionSetFieldComponents(coordSection, 0, dim);
    891:     PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);
    892:     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
    893:       PetscSectionSetDof(coordSection, v, dim);
    894:       PetscSectionSetFieldDof(coordSection, v, 0, dim);
    895:     }
    896:     PetscSectionSetUp(coordSection);
    897:     PetscSectionGetStorageSize(coordSection, &coordSize);
    898:     VecCreate(PETSC_COMM_SELF, &coordinates);
    899:     PetscObjectSetName((PetscObject) coordinates, "coordinates");
    900:     VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    901:     VecSetBlockSize(coordinates, dim);
    902:     VecSetType(coordinates,VECSTANDARD);
    903:     VecGetArray(coordinates, &coords);
    904:     for (vz = 0; vz < numZVertices; ++vz) {
    905:       for (vy = 0; vy < numYVertices; ++vy) {
    906:         for (vx = 0; vx < numXVertices; ++vx) {
    907:           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
    908:           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
    909:           if (dim == 3) {
    910:             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
    911:           }
    912:         }
    913:       }
    914:     }
    915:     VecRestoreArray(coordinates, &coords);
    916:     DMSetCoordinatesLocal(dm, coordinates);
    917:     VecDestroy(&coordinates);
    918:   }
    919:   return(0);
    920: }

    922: static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
    923: {
    924:   PetscInt       i;

    929:   DMCreate(comm, dm);
    931:   DMSetType(*dm, DMPLEX);
    932:   DMSetDimension(*dm, dim);
    933:   switch (dim) {
    934:   case 2: {DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], DM_BOUNDARY_NONE);break;}
    935:   case 3: {DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], periodicity[2]);break;}
    936:   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %D", dim);
    937:   }
    938:   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
    939:       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
    940:       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
    941:     PetscReal L[3];
    942:     PetscReal maxCell[3];

    944:     for (i = 0; i < dim; i++) {
    945:       L[i]       = upper[i] - lower[i];
    946:       maxCell[i] = 1.1 * (L[i] / PetscMax(1,faces[i]));
    947:     }
    948:     DMSetPeriodicity(*dm,PETSC_TRUE,maxCell,L,periodicity);
    949:   }
    950:   if (!interpolate) {
    951:     DM udm;

    953:     DMPlexUninterpolate(*dm, &udm);
    954:     DMPlexCopyCoordinates(*dm, udm);
    955:     DMDestroy(dm);
    956:     *dm  = udm;
    957:   }
    958:   DMPlexSetRefinementUniform(*dm, PETSC_TRUE);
    959:   return(0);
    960: }

    962: /*@C
    963:   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).

    965:   Collective

    967:   Input Parameters:
    968: + comm        - The communicator for the DM object
    969: . dim         - The spatial dimension
    970: . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
    971: . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
    972: . lower       - The lower left corner, or NULL for (0, 0, 0)
    973: . upper       - The upper right corner, or NULL for (1, 1, 1)
    974: . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
    975: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    977:   Output Parameter:
    978: . dm  - The DM object

    980:   Options Database Keys:
    981:   These options override the hard-wired input values.
    982: + -dm_plex_box_dim <dim>          - Set the topological dimension
    983: . -dm_plex_box_simplex <bool>     - PETSC_TRUE for simplex elements, PETSC_FALSE for tensor elements
    984: . -dm_plex_box_lower <x,y,z>      - Specify lower-left-bottom coordinates for the box
    985: . -dm_plex_box_upper <x,y,z>      - Specify upper-right-top coordinates for the box
    986: . -dm_plex_box_faces <m,n,p>      - Number of faces in each linear direction
    987: . -dm_plex_box_bd <bx,by,bz>      - Specify the DMBoundaryType for each direction
    988: - -dm_plex_box_interpolate <bool> - PETSC_TRUE turns on topological interpolation (creating edges and faces)

    990:   Notes:
    991:   The options database keys above take lists of length d in d dimensions.

    993:   Here is the numbering returned for 2 faces in each direction for tensor cells:
    994: $ 10---17---11---18----12
    995: $  |         |         |
    996: $  |         |         |
    997: $ 20    2   22    3    24
    998: $  |         |         |
    999: $  |         |         |
    1000: $  7---15----8---16----9
    1001: $  |         |         |
    1002: $  |         |         |
    1003: $ 19    0   21    1   23
    1004: $  |         |         |
    1005: $  |         |         |
    1006: $  4---13----5---14----6

    1008: and for simplicial cells

    1010: $ 14----8---15----9----16
    1011: $  |\     5  |\      7 |
    1012: $  | \       | \       |
    1013: $ 13   2    14    3    15
    1014: $  | 4   \   | 6   \   |
    1015: $  |       \ |       \ |
    1016: $ 11----6---12----7----13
    1017: $  |\        |\        |
    1018: $  | \    1  | \     3 |
    1019: $ 10   0    11    1    12
    1020: $  | 0   \   | 2   \   |
    1021: $  |       \ |       \ |
    1022: $  8----4----9----5----10

    1024:   Level: beginner

    1026: .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
    1027: @*/
    1028: PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
    1029: {
    1030:   PetscInt       fac[3] = {0, 0, 0};
    1031:   PetscReal      low[3] = {0, 0, 0};
    1032:   PetscReal      upp[3] = {1, 1, 1};
    1033:   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
    1034:   PetscInt       i, n;
    1035:   PetscBool      flg;

    1039:   PetscOptionsGetInt(NULL, NULL, "-dm_plex_box_dim", &dim, &flg);
    1040:   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
    1041:   PetscOptionsGetBool(NULL, NULL, "-dm_plex_box_simplex", &simplex, &flg);
    1042:   n    = dim;
    1043:   PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", fac, &n, &flg);
    1044:   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (flg && i < n ? fac[i] : (dim == 1 ? 1 : 4-dim));
    1045:   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
    1046:   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
    1047:   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
    1048:   /* Allow bounds to be specified from the command line */
    1049:   n    = 3;
    1050:   PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_lower", low, &n, &flg);
    1051:   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
    1052:   n    = 3;
    1053:   PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_upper", upp, &n, &flg);
    1054:   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
    1055:   n    = 3;
    1056:   PetscOptionsGetEnumArray(NULL, NULL, "-dm_plex_box_bd", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);
    1057:   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
    1058:   PetscOptionsGetBool(NULL, NULL, "-dm_plex_box_interpolate", &interpolate, &flg);

    1060:   if (dim == 1)      {DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);}
    1061:   else if (simplex)  {DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);}
    1062:   else               {DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);}
    1063:   return(0);
    1064: }

    1066: /*@
    1067:   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.

    1069:   Collective

    1071:   Input Parameters:
    1072: + comm        - The communicator for the DM object
    1073: . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
    1074: . lower       - The lower left corner, or NULL for (0, 0, 0)
    1075: . upper       - The upper right corner, or NULL for (1, 1, 1)
    1076: . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
    1077: . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
    1078: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    1080:   Output Parameter:
    1081: . dm  - The DM object

    1083:   Level: beginner

    1085: .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMPlexExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1086: @*/
    1087: PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
    1088: {
    1089:   DM             bdm, botdm;
    1090:   PetscInt       i;
    1091:   PetscInt       fac[3] = {0, 0, 0};
    1092:   PetscReal      low[3] = {0, 0, 0};
    1093:   PetscReal      upp[3] = {1, 1, 1};
    1094:   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};

    1098:   for (i = 0; i < 3; ++i) fac[i] = faces ? (faces[i] > 0 ? faces[i] : 1) : 1;
    1099:   if (lower) for (i = 0; i < 3; ++i) low[i] = lower[i];
    1100:   if (upper) for (i = 0; i < 3; ++i) upp[i] = upper[i];
    1101:   if (periodicity) for (i = 0; i < 3; ++i) bdt[i] = periodicity[i];
    1102:   for (i = 0; i < 3; ++i) if (bdt[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity not yet supported");

    1104:   DMCreate(comm, &bdm);
    1105:   DMSetType(bdm, DMPLEX);
    1106:   DMSetDimension(bdm, 1);
    1107:   DMSetCoordinateDim(bdm, 2);
    1108:   DMPlexCreateSquareBoundary(bdm, low, upp, fac);
    1109:   DMPlexGenerate(bdm, NULL, PETSC_FALSE, &botdm);
    1110:   DMDestroy(&bdm);
    1111:   DMPlexExtrude(botdm, fac[2], upp[2] - low[2], orderHeight, NULL, interpolate, dm);
    1112:   if (low[2] != 0.0) {
    1113:     Vec         v;
    1114:     PetscScalar *x;
    1115:     PetscInt    cDim, n;

    1117:     DMGetCoordinatesLocal(*dm, &v);
    1118:     VecGetBlockSize(v, &cDim);
    1119:     VecGetLocalSize(v, &n);
    1120:     VecGetArray(v, &x);
    1121:     x   += cDim;
    1122:     for (i=0; i<n; i+=cDim) x[i] += low[2];
    1123:     VecRestoreArray(v,&x);
    1124:     DMSetCoordinatesLocal(*dm, v);
    1125:   }
    1126:   DMDestroy(&botdm);
    1127:   return(0);
    1128: }

    1130: /*@C
    1131:   DMPlexExtrude - Creates a (d+1)-D mesh by extruding a d-D mesh in the normal direction using prismatic cells.

    1133:   Collective on idm

    1135:   Input Parameters:
    1136: + idm         - The mesh to be extruded
    1137: . layers      - The number of layers, or PETSC_DETERMINE to use the default
    1138: . height      - The total height of the extrusion, or PETSC_DETERMINE to use the default
    1139: . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
    1140: . extNormal   - The normal direction in which the mesh should be extruded, or NULL to extrude using the surface normal
    1141: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    1143:   Output Parameter:
    1144: . dm  - The DM object

    1146:   Notes:
    1147:   The mesh created has prismatic cells, and the vertex ordering in the cone of the cell is that of the tensor prismatic cells. Not currently supported in Fortran.

    1149:   Options Database Keys:
    1150: +   -dm_plex_extrude_layers <k> - Sets the number of layers k
    1151: .   -dm_plex_extrude_height <h> - Sets the total height of the extrusion
    1152: .   -dm_plex_extrude_heights <h0,h1,...> - Sets the height of each layer
    1153: .   -dm_plex_extrude_order_height - If true, order cells by height first
    1154: -   -dm_plex_extrude_normal <n0,...,nd> - Sets the normal vector along which to extrude

    1156:   Level: advanced

    1158: .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMSetType(), DMCreate()
    1159: @*/
    1160: PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool orderHeight, const PetscReal extNormal[], PetscBool interpolate, DM* dm)
    1161: {
    1162:   PetscScalar       *coordsB;
    1163:   const PetscScalar *coordsA;
    1164:   PetscReal         *normals = NULL, *heights = NULL;
    1165:   PetscReal         clNormal[3];
    1166:   Vec               coordinatesA, coordinatesB;
    1167:   PetscSection      coordSectionA, coordSectionB;
    1168:   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone, nl;
    1169:   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
    1170:   const char       *prefix;
    1171:   PetscBool         haveCLNormal, flg;
    1172:   PetscErrorCode    ierr;

    1179:   DMGetDimension(idm, &dim);
    1180:   DMGetCoordinateDim(idm, &cDim);
    1181:   cDimB = cDim == dim ? cDim+1 : cDim;
    1182:   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);

    1184:   PetscObjectGetOptionsPrefix((PetscObject) idm, &prefix);
    1185:   if (layers < 0) layers = 1;
    1186:   PetscOptionsGetInt(NULL, prefix, "-dm_plex_extrude_layers", &layers, NULL);
    1187:   if (layers <= 0) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Number of layers %D must be positive", layers);
    1188:   if (height < 0.) height = 1.;
    1189:   PetscOptionsGetReal(NULL, prefix, "-dm_plex_extrude_height", &height, NULL);
    1190:   if (height <= 0.) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Height of layers %g must be positive", (double) height);
    1191:   PetscMalloc1(layers, &heights);
    1192:   nl   = layers;
    1193:   PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_heights", heights, &nl, &flg);
    1194:   if (flg) {
    1195:     if (!nl) SETERRQ(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Must give at least one height for -dm_plex_extrude_heights");
    1196:     for (l = nl; l < layers; ++l) heights[l] = heights[l-1];
    1197:     for (l = 0; l < layers; ++l) if (heights[l] <= 0.) SETERRQ2(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Height %g of layers %D must be positive", (double) heights[l], l);
    1198:   } else {
    1199:     for (l = 0; l < layers; ++l) heights[l] = height/layers;
    1200:   }
    1201:   PetscOptionsGetBool(NULL, prefix, "-dm_plex_extrude_order_height", &orderHeight, NULL);
    1202:   c = 3;
    1203:   PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_normal", clNormal, &c, &haveCLNormal);
    1204:   if (haveCLNormal && c != cDimB) SETERRQ2(PetscObjectComm((PetscObject)idm), PETSC_ERR_ARG_SIZ, "Input normal has size %D != %D extruded coordinate dimension", c, cDimB);

    1206:   DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);
    1207:   DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);
    1208:   numCells = (cEnd - cStart)*layers;
    1209:   numVertices = (vEnd - vStart)*(layers+1);
    1210:   DMCreate(PetscObjectComm((PetscObject)idm), dm);
    1211:   DMSetType(*dm, DMPLEX);
    1212:   DMSetDimension(*dm, dim+1);
    1213:   DMPlexSetChart(*dm, 0, numCells+numVertices);
    1214:   /* Must create the celltype label here so that we do not automatically try to compute the types */
    1215:   DMCreateLabel(*dm, "celltype");
    1216:   for (c = cStart, cellV = 0; c < cEnd; ++c) {
    1217:     DMPolytopeType ct, nct;
    1218:     PetscInt      *closure = NULL;
    1219:     PetscInt       closureSize, numCorners = 0;

    1221:     DMPlexGetCellType(idm, c, &ct);
    1222:     switch (ct) {
    1223:       case DM_POLYTOPE_SEGMENT:       nct = DM_POLYTOPE_SEG_PRISM_TENSOR;break;
    1224:       case DM_POLYTOPE_TRIANGLE:      nct = DM_POLYTOPE_TRI_PRISM_TENSOR;break;
    1225:       case DM_POLYTOPE_QUADRILATERAL: nct = DM_POLYTOPE_QUAD_PRISM_TENSOR;break;
    1226:       default: nct = DM_POLYTOPE_UNKNOWN;
    1227:     }
    1228:     DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1229:     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
    1230:     DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1231:     for (l = 0; l < layers; ++l) {
    1232:       const PetscInt cell = orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart;

    1234:       DMPlexSetConeSize(*dm, cell, 2*numCorners);
    1235:       DMPlexSetCellType(*dm, cell, nct);
    1236:     }
    1237:     cellV = PetscMax(numCorners,cellV);
    1238:   }
    1239:   DMSetUp(*dm);

    1241:   if (dim != cDim && !(extNormal || haveCLNormal)) {PetscCalloc1(cDim*(vEnd - vStart), &normals);}
    1242:   PetscMalloc1(3*cellV,&newCone);
    1243:   for (c = cStart; c < cEnd; ++c) {
    1244:     PetscInt *closure = NULL;
    1245:     PetscInt closureSize, numCorners = 0, l;
    1246:     PetscReal normal[3] = {0, 0, 0};

    1248:     if (normals) {DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);}
    1249:     DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1250:     for (v = 0; v < closureSize*2; v += 2) {
    1251:       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
    1252:         PetscInt d;

    1254:         newCone[numCorners++] = closure[v] - vStart;
    1255:         if (normals) {for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d];}
    1256:       }
    1257:     }
    1258:     DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1259:     for (l = 0; l < layers; ++l) {
    1260:       PetscInt i;

    1262:       for (i = 0; i < numCorners; ++i) {
    1263:         newCone[  numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
    1264:         newCone[2*numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
    1265:       }
    1266:       DMPlexSetCone(*dm, orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);
    1267:     }
    1268:   }
    1269:   DMPlexSymmetrize(*dm);
    1270:   DMPlexStratify(*dm);
    1271:   PetscFree(newCone);

    1273:   DMGetCoordinateSection(*dm, &coordSectionB);
    1274:   PetscSectionSetNumFields(coordSectionB, 1);
    1275:   PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);
    1276:   PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);
    1277:   for (v = numCells; v < numCells+numVertices; ++v) {
    1278:     PetscSectionSetDof(coordSectionB, v, cDimB);
    1279:     PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);
    1280:     DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);
    1281:   }
    1282:   PetscSectionSetUp(coordSectionB);
    1283:   PetscSectionGetStorageSize(coordSectionB, &coordSize);
    1284:   VecCreate(PETSC_COMM_SELF, &coordinatesB);
    1285:   PetscObjectSetName((PetscObject) coordinatesB, "coordinates");
    1286:   VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);
    1287:   VecSetBlockSize(coordinatesB, cDimB);
    1288:   VecSetType(coordinatesB,VECSTANDARD);

    1290:   DMGetCoordinateSection(idm, &coordSectionA);
    1291:   DMGetCoordinatesLocal(idm, &coordinatesA);
    1292:   VecGetArray(coordinatesB, &coordsB);
    1293:   VecGetArrayRead(coordinatesA, &coordsA);
    1294:   for (v = vStart; v < vEnd; ++v) {
    1295:     const PetscScalar *cptr;
    1296:     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
    1297:     PetscReal         normal[3];
    1298:     PetscReal         norm;
    1299:     PetscInt          offA, d, cDimA = cDim;

    1301:     if (normals)           {for (d = 0; d < cDimB; ++d) normal[d] = normals[cDimB*(v - vStart)+d];}
    1302:     else if (haveCLNormal) {for (d = 0; d < cDimB; ++d) normal[d] = clNormal[d];}
    1303:     else if (extNormal)    {for (d = 0; d < cDimB; ++d) normal[d] = extNormal[d];}
    1304:     else if (cDimB == 2)   {for (d = 0; d < cDimB; ++d) normal[d] = ones2[d];}
    1305:     else if (cDimB == 3)   {for (d = 0; d < cDimB; ++d) normal[d] = ones3[d];}
    1306:     else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unable to determine normal for extrusion");
    1307:     for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
    1308:     for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);

    1310:     PetscSectionGetOffset(coordSectionA, v, &offA);
    1311:     cptr = coordsA + offA;
    1312:     for (l = 0; l <= layers; ++l) {
    1313:       PetscInt offB, d, newV;

    1315:       newV = orderHeight ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
    1316:       PetscSectionGetOffset(coordSectionB, newV, &offB);
    1317:       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
    1318:       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*heights[l-1] : 0.0; }
    1319:       cptr    = coordsB + offB;
    1320:       cDimA   = cDimB;
    1321:     }
    1322:   }
    1323:   VecRestoreArrayRead(coordinatesA, &coordsA);
    1324:   VecRestoreArray(coordinatesB, &coordsB);
    1325:   DMSetCoordinatesLocal(*dm, coordinatesB);
    1326:   VecDestroy(&coordinatesB);
    1327:   PetscFree(normals);
    1328:   PetscFree(heights);
    1329:   if (interpolate) {
    1330:     DM idm;

    1332:     DMPlexInterpolate(*dm, &idm);
    1333:     DMPlexCopyCoordinates(*dm, idm);
    1334:     DMDestroy(dm);
    1335:     *dm  = idm;
    1336:   }
    1337:   return(0);
    1338: }

    1340: /*@C
    1341:   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.

    1343:   Logically Collective on dm

    1345:   Input Parameters:
    1346: + dm - the DM context
    1347: - prefix - the prefix to prepend to all option names

    1349:   Notes:
    1350:   A hyphen (-) must NOT be given at the beginning of the prefix name.
    1351:   The first character of all runtime options is AUTOMATICALLY the hyphen.

    1353:   Level: advanced

    1355: .seealso: SNESSetFromOptions()
    1356: @*/
    1357: PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
    1358: {
    1359:   DM_Plex       *mesh = (DM_Plex *) dm->data;

    1364:   PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);
    1365:   PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);
    1366:   return(0);
    1367: }

    1369: /*@
    1370:   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.

    1372:   Collective

    1374:   Input Parameters:
    1375: + comm      - The communicator for the DM object
    1376: . numRefine - The number of regular refinements to the basic 5 cell structure
    1377: - periodicZ - The boundary type for the Z direction

    1379:   Output Parameter:
    1380: . dm  - The DM object

    1382:   Options Database Keys:
    1383: These options override the hard-wired input values.
    1384: + -dm_plex_hex_cyl_refine <r> - Refine the sylinder r times
    1385: - -dm_plex_hex_cyl_bd <bz>    - Specify the DMBoundaryType in the z-direction

    1387:   Note:
    1388:   Here is the output numbering looking from the bottom of the cylinder:
    1389: $       17-----14
    1390: $        |     |
    1391: $        |  2  |
    1392: $        |     |
    1393: $ 17-----8-----7-----14
    1394: $  |     |     |     |
    1395: $  |  3  |  0  |  1  |
    1396: $  |     |     |     |
    1397: $ 19-----5-----6-----13
    1398: $        |     |
    1399: $        |  4  |
    1400: $        |     |
    1401: $       19-----13
    1402: $
    1403: $ and up through the top
    1404: $
    1405: $       18-----16
    1406: $        |     |
    1407: $        |  2  |
    1408: $        |     |
    1409: $ 18----10----11-----16
    1410: $  |     |     |     |
    1411: $  |  3  |  0  |  1  |
    1412: $  |     |     |     |
    1413: $ 20-----9----12-----15
    1414: $        |     |
    1415: $        |  4  |
    1416: $        |     |
    1417: $       20-----15

    1419:   Level: beginner

    1421: .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1422: @*/
    1423: PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
    1424: {
    1425:   const PetscInt dim = 3;
    1426:   PetscInt       numCells, numVertices, r;
    1427:   PetscMPIInt    rank;

    1432:   MPI_Comm_rank(comm, &rank);
    1433:   PetscOptionsGetInt(NULL, NULL, "-dm_plex_hex_cyl_refine", &numRefine, NULL);
    1434:   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
    1435:   PetscOptionsGetEnum(NULL, NULL, "-dm_plex_box_bd", DMBoundaryTypes, (PetscEnum *) &periodicZ, NULL);
    1436:   DMCreate(comm, dm);
    1437:   DMSetType(*dm, DMPLEX);
    1438:   DMSetDimension(*dm, dim);
    1439:   /* Create topology */
    1440:   {
    1441:     PetscInt cone[8], c;

    1443:     numCells    = !rank ?  5 : 0;
    1444:     numVertices = !rank ? 16 : 0;
    1445:     if (periodicZ == DM_BOUNDARY_PERIODIC) {
    1446:       numCells   *= 3;
    1447:       numVertices = !rank ? 24 : 0;
    1448:     }
    1449:     DMPlexSetChart(*dm, 0, numCells+numVertices);
    1450:     for (c = 0; c < numCells; c++) {DMPlexSetConeSize(*dm, c, 8);}
    1451:     DMSetUp(*dm);
    1452:     if (!rank) {
    1453:       if (periodicZ == DM_BOUNDARY_PERIODIC) {
    1454:         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
    1455:         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
    1456:         DMPlexSetCone(*dm, 0, cone);
    1457:         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
    1458:         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
    1459:         DMPlexSetCone(*dm, 1, cone);
    1460:         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
    1461:         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
    1462:         DMPlexSetCone(*dm, 2, cone);
    1463:         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
    1464:         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
    1465:         DMPlexSetCone(*dm, 3, cone);
    1466:         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
    1467:         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
    1468:         DMPlexSetCone(*dm, 4, cone);

    1470:         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
    1471:         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
    1472:         DMPlexSetCone(*dm, 5, cone);
    1473:         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
    1474:         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
    1475:         DMPlexSetCone(*dm, 6, cone);
    1476:         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
    1477:         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
    1478:         DMPlexSetCone(*dm, 7, cone);
    1479:         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
    1480:         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
    1481:         DMPlexSetCone(*dm, 8, cone);
    1482:         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
    1483:         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
    1484:         DMPlexSetCone(*dm, 9, cone);

    1486:         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
    1487:         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
    1488:         DMPlexSetCone(*dm, 10, cone);
    1489:         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
    1490:         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
    1491:         DMPlexSetCone(*dm, 11, cone);
    1492:         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
    1493:         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
    1494:         DMPlexSetCone(*dm, 12, cone);
    1495:         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
    1496:         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
    1497:         DMPlexSetCone(*dm, 13, cone);
    1498:         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
    1499:         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
    1500:         DMPlexSetCone(*dm, 14, cone);
    1501:       } else {
    1502:         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
    1503:         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
    1504:         DMPlexSetCone(*dm, 0, cone);
    1505:         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
    1506:         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
    1507:         DMPlexSetCone(*dm, 1, cone);
    1508:         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
    1509:         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
    1510:         DMPlexSetCone(*dm, 2, cone);
    1511:         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
    1512:         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
    1513:         DMPlexSetCone(*dm, 3, cone);
    1514:         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
    1515:         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
    1516:         DMPlexSetCone(*dm, 4, cone);
    1517:       }
    1518:     }
    1519:     DMPlexSymmetrize(*dm);
    1520:     DMPlexStratify(*dm);
    1521:   }
    1522:   /* Interpolate */
    1523:   {
    1524:     DM idm;

    1526:     DMPlexInterpolate(*dm, &idm);
    1527:     DMDestroy(dm);
    1528:     *dm  = idm;
    1529:   }
    1530:   /* Create cube geometry */
    1531:   {
    1532:     Vec             coordinates;
    1533:     PetscSection    coordSection;
    1534:     PetscScalar    *coords;
    1535:     PetscInt        coordSize, v;
    1536:     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
    1537:     const PetscReal ds2 = dis/2.0;

    1539:     /* Build coordinates */
    1540:     DMGetCoordinateSection(*dm, &coordSection);
    1541:     PetscSectionSetNumFields(coordSection, 1);
    1542:     PetscSectionSetFieldComponents(coordSection, 0, dim);
    1543:     PetscSectionSetChart(coordSection, numCells, numCells+numVertices);
    1544:     for (v = numCells; v < numCells+numVertices; ++v) {
    1545:       PetscSectionSetDof(coordSection, v, dim);
    1546:       PetscSectionSetFieldDof(coordSection, v, 0, dim);
    1547:     }
    1548:     PetscSectionSetUp(coordSection);
    1549:     PetscSectionGetStorageSize(coordSection, &coordSize);
    1550:     VecCreate(PETSC_COMM_SELF, &coordinates);
    1551:     PetscObjectSetName((PetscObject) coordinates, "coordinates");
    1552:     VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    1553:     VecSetBlockSize(coordinates, dim);
    1554:     VecSetType(coordinates,VECSTANDARD);
    1555:     VecGetArray(coordinates, &coords);
    1556:     if (!rank) {
    1557:       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
    1558:       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
    1559:       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
    1560:       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
    1561:       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
    1562:       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
    1563:       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
    1564:       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
    1565:       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
    1566:       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
    1567:       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
    1568:       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
    1569:       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
    1570:       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
    1571:       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
    1572:       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
    1573:       if (periodicZ == DM_BOUNDARY_PERIODIC) {
    1574:         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
    1575:         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
    1576:         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
    1577:         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
    1578:         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
    1579:         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
    1580:         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
    1581:         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
    1582:       }
    1583:     }
    1584:     VecRestoreArray(coordinates, &coords);
    1585:     DMSetCoordinatesLocal(*dm, coordinates);
    1586:     VecDestroy(&coordinates);
    1587:   }
    1588:   /* Create periodicity */
    1589:   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
    1590:     PetscReal      L[3];
    1591:     PetscReal      maxCell[3];
    1592:     DMBoundaryType bdType[3];
    1593:     PetscReal      lower[3] = {0.0, 0.0, 0.0};
    1594:     PetscReal      upper[3] = {1.0, 1.0, 1.5};
    1595:     PetscInt       i, numZCells = 3;

    1597:     bdType[0] = DM_BOUNDARY_NONE;
    1598:     bdType[1] = DM_BOUNDARY_NONE;
    1599:     bdType[2] = periodicZ;
    1600:     for (i = 0; i < dim; i++) {
    1601:       L[i]       = upper[i] - lower[i];
    1602:       maxCell[i] = 1.1 * (L[i] / numZCells);
    1603:     }
    1604:     DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);
    1605:   }
    1606:   /* Refine topology */
    1607:   for (r = 0; r < numRefine; ++r) {
    1608:     DM rdm = NULL;

    1610:     DMRefine(*dm, comm, &rdm);
    1611:     DMDestroy(dm);
    1612:     *dm  = rdm;
    1613:   }
    1614:   /* Remap geometry to cylinder
    1615:        Interior square: Linear interpolation is correct
    1616:        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
    1617:        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance

    1619:          phi     = arctan(y/x)
    1620:          d_close = sqrt(1/8 + 1/4 sin^2(phi))
    1621:          d_far   = sqrt(1/2 + sin^2(phi))

    1623:        so we remap them using

    1625:          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
    1626:          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)

    1628:        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
    1629:   */
    1630:   {
    1631:     Vec           coordinates;
    1632:     PetscSection  coordSection;
    1633:     PetscScalar  *coords;
    1634:     PetscInt      vStart, vEnd, v;
    1635:     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
    1636:     const PetscReal ds2 = 0.5*dis;

    1638:     DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);
    1639:     DMGetCoordinateSection(*dm, &coordSection);
    1640:     DMGetCoordinatesLocal(*dm, &coordinates);
    1641:     VecGetArray(coordinates, &coords);
    1642:     for (v = vStart; v < vEnd; ++v) {
    1643:       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
    1644:       PetscInt  off;

    1646:       PetscSectionGetOffset(coordSection, v, &off);
    1647:       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
    1648:       x    = PetscRealPart(coords[off]);
    1649:       y    = PetscRealPart(coords[off+1]);
    1650:       phi  = PetscAtan2Real(y, x);
    1651:       sinp = PetscSinReal(phi);
    1652:       cosp = PetscCosReal(phi);
    1653:       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
    1654:         dc = PetscAbsReal(ds2/sinp);
    1655:         df = PetscAbsReal(dis/sinp);
    1656:         xc = ds2*x/PetscAbsReal(y);
    1657:         yc = ds2*PetscSignReal(y);
    1658:       } else {
    1659:         dc = PetscAbsReal(ds2/cosp);
    1660:         df = PetscAbsReal(dis/cosp);
    1661:         xc = ds2*PetscSignReal(x);
    1662:         yc = ds2*y/PetscAbsReal(x);
    1663:       }
    1664:       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
    1665:       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
    1666:     }
    1667:     VecRestoreArray(coordinates, &coords);
    1668:     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
    1669:       DMLocalizeCoordinates(*dm);
    1670:     }
    1671:   }
    1672:   return(0);
    1673: }

    1675: /*@
    1676:   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.

    1678:   Collective

    1680:   Input Parameters:
    1681: + comm - The communicator for the DM object
    1682: . n    - The number of wedges around the origin
    1683: - interpolate - Create edges and faces

    1685:   Output Parameter:
    1686: . dm  - The DM object

    1688:   Level: beginner

    1690: .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1691: @*/
    1692: PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
    1693: {
    1694:   const PetscInt dim = 3;
    1695:   PetscInt       numCells, numVertices, v;
    1696:   PetscMPIInt    rank;

    1701:   MPI_Comm_rank(comm, &rank);
    1702:   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
    1703:   DMCreate(comm, dm);
    1704:   DMSetType(*dm, DMPLEX);
    1705:   DMSetDimension(*dm, dim);
    1706:   /* Must create the celltype label here so that we do not automatically try to compute the types */
    1707:   DMCreateLabel(*dm, "celltype");
    1708:   /* Create topology */
    1709:   {
    1710:     PetscInt cone[6], c;

    1712:     numCells    = !rank ?        n : 0;
    1713:     numVertices = !rank ?  2*(n+1) : 0;
    1714:     DMPlexSetChart(*dm, 0, numCells+numVertices);
    1715:     for (c = 0; c < numCells; c++) {DMPlexSetConeSize(*dm, c, 6);}
    1716:     DMSetUp(*dm);
    1717:     for (c = 0; c < numCells; c++) {
    1718:       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
    1719:       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
    1720:       DMPlexSetCone(*dm, c, cone);
    1721:       DMPlexSetCellType(*dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);
    1722:     }
    1723:     DMPlexSymmetrize(*dm);
    1724:     DMPlexStratify(*dm);
    1725:   }
    1726:   for (v = numCells; v < numCells+numVertices; ++v) {
    1727:     DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);
    1728:   }
    1729:   /* Interpolate */
    1730:   if (interpolate) {
    1731:     DM idm;

    1733:     DMPlexInterpolate(*dm, &idm);
    1734:     DMDestroy(dm);
    1735:     *dm  = idm;
    1736:   }
    1737:   /* Create cylinder geometry */
    1738:   {
    1739:     Vec          coordinates;
    1740:     PetscSection coordSection;
    1741:     PetscScalar *coords;
    1742:     PetscInt     coordSize, c;

    1744:     /* Build coordinates */
    1745:     DMGetCoordinateSection(*dm, &coordSection);
    1746:     PetscSectionSetNumFields(coordSection, 1);
    1747:     PetscSectionSetFieldComponents(coordSection, 0, dim);
    1748:     PetscSectionSetChart(coordSection, numCells, numCells+numVertices);
    1749:     for (v = numCells; v < numCells+numVertices; ++v) {
    1750:       PetscSectionSetDof(coordSection, v, dim);
    1751:       PetscSectionSetFieldDof(coordSection, v, 0, dim);
    1752:     }
    1753:     PetscSectionSetUp(coordSection);
    1754:     PetscSectionGetStorageSize(coordSection, &coordSize);
    1755:     VecCreate(PETSC_COMM_SELF, &coordinates);
    1756:     PetscObjectSetName((PetscObject) coordinates, "coordinates");
    1757:     VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    1758:     VecSetBlockSize(coordinates, dim);
    1759:     VecSetType(coordinates,VECSTANDARD);
    1760:     VecGetArray(coordinates, &coords);
    1761:     for (c = 0; c < numCells; c++) {
    1762:       coords[(c+0*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+2] = 1.0;
    1763:       coords[(c+1*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+2] = 0.0;
    1764:     }
    1765:     if (!rank) {
    1766:       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
    1767:       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
    1768:     }
    1769:     VecRestoreArray(coordinates, &coords);
    1770:     DMSetCoordinatesLocal(*dm, coordinates);
    1771:     VecDestroy(&coordinates);
    1772:   }
    1773:   return(0);
    1774: }

    1776: PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
    1777: {
    1778:   PetscReal prod = 0.0;
    1779:   PetscInt  i;
    1780:   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
    1781:   return PetscSqrtReal(prod);
    1782: }
    1783: PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
    1784: {
    1785:   PetscReal prod = 0.0;
    1786:   PetscInt  i;
    1787:   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
    1788:   return prod;
    1789: }

    1791: /* The first constant is the sphere radius */
    1792: static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    1793:                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    1794:                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    1795:                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    1796: {
    1797:   PetscReal r = PetscRealPart(constants[0]);
    1798:   PetscReal norm2 = 0.0, fac;
    1799:   PetscInt  n = uOff[1] - uOff[0], d;

    1801:   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
    1802:   fac = r/PetscSqrtReal(norm2);
    1803:   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
    1804: }

    1806: /*@
    1807:   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.

    1809:   Collective

    1811:   Input Parameters:
    1812: + comm    - The communicator for the DM object
    1813: . dim     - The dimension
    1814: . simplex - Use simplices, or tensor product cells
    1815: - R       - The radius

    1817:   Output Parameter:
    1818: . dm  - The DM object

    1820:   Level: beginner

    1822: .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1823: @*/
    1824: PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
    1825: {
    1826:   const PetscInt  embedDim = dim+1;
    1827:   PetscSection    coordSection;
    1828:   Vec             coordinates;
    1829:   PetscScalar    *coords;
    1830:   PetscReal      *coordsIn;
    1831:   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
    1832:   PetscMPIInt     rank;
    1833:   PetscErrorCode  ierr;

    1837:   DMCreate(comm, dm);
    1838:   DMSetType(*dm, DMPLEX);
    1839:   DMSetDimension(*dm, dim);
    1840:   DMSetCoordinateDim(*dm, dim+1);
    1841:   MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);
    1842:   switch (dim) {
    1843:   case 2:
    1844:     if (simplex) {
    1845:       DM              idm;
    1846:       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
    1847:       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
    1848:       const PetscInt  degree    = 5;
    1849:       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
    1850:       PetscInt        s[3]      = {1, 1, 1};
    1851:       PetscInt        cone[3];
    1852:       PetscInt       *graph, p, i, j, k;

    1854:       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
    1855:       numCells    = !rank ? 20 : 0;
    1856:       numVerts    = !rank ? 12 : 0;
    1857:       firstVertex = numCells;
    1858:       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of

    1860:            (0, \pm 1/\phi+1, \pm \phi/\phi+1)

    1862:          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
    1863:          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
    1864:       */
    1865:       /* Construct vertices */
    1866:       PetscCalloc1(numVerts * embedDim, &coordsIn);
    1867:       if (!rank) {
    1868:         for (p = 0, i = 0; p < embedDim; ++p) {
    1869:           for (s[1] = -1; s[1] < 2; s[1] += 2) {
    1870:             for (s[2] = -1; s[2] < 2; s[2] += 2) {
    1871:               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
    1872:               ++i;
    1873:             }
    1874:           }
    1875:         }
    1876:       }
    1877:       /* Construct graph */
    1878:       PetscCalloc1(numVerts * numVerts, &graph);
    1879:       for (i = 0; i < numVerts; ++i) {
    1880:         for (j = 0, k = 0; j < numVerts; ++j) {
    1881:           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
    1882:         }
    1883:         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
    1884:       }
    1885:       /* Build Topology */
    1886:       DMPlexSetChart(*dm, 0, numCells+numVerts);
    1887:       for (c = 0; c < numCells; c++) {
    1888:         DMPlexSetConeSize(*dm, c, embedDim);
    1889:       }
    1890:       DMSetUp(*dm); /* Allocate space for cones */
    1891:       /* Cells */
    1892:       for (i = 0, c = 0; i < numVerts; ++i) {
    1893:         for (j = 0; j < i; ++j) {
    1894:           for (k = 0; k < j; ++k) {
    1895:             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
    1896:               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
    1897:               /* Check orientation */
    1898:               {
    1899:                 const PetscInt epsilon[3][3][3] = {{{0, 0, 0}, {0, 0, 1}, {0, -1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, 0, 0}}, {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}}};
    1900:                 PetscReal normal[3];
    1901:                 PetscInt  e, f;

    1903:                 for (d = 0; d < embedDim; ++d) {
    1904:                   normal[d] = 0.0;
    1905:                   for (e = 0; e < embedDim; ++e) {
    1906:                     for (f = 0; f < embedDim; ++f) {
    1907:                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
    1908:                     }
    1909:                   }
    1910:                 }
    1911:                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
    1912:               }
    1913:               DMPlexSetCone(*dm, c++, cone);
    1914:             }
    1915:           }
    1916:         }
    1917:       }
    1918:       DMPlexSymmetrize(*dm);
    1919:       DMPlexStratify(*dm);
    1920:       PetscFree(graph);
    1921:       /* Interpolate mesh */
    1922:       DMPlexInterpolate(*dm, &idm);
    1923:       DMDestroy(dm);
    1924:       *dm  = idm;
    1925:     } else {
    1926:       /*
    1927:         12-21--13
    1928:          |     |
    1929:         25  4  24
    1930:          |     |
    1931:   12-25--9-16--8-24--13
    1932:    |     |     |     |
    1933:   23  5 17  0 15  3  22
    1934:    |     |     |     |
    1935:   10-20--6-14--7-19--11
    1936:          |     |
    1937:         20  1  19
    1938:          |     |
    1939:         10-18--11
    1940:          |     |
    1941:         23  2  22
    1942:          |     |
    1943:         12-21--13
    1944:        */
    1945:       PetscInt cone[4], ornt[4];

    1947:       numCells    = !rank ?  6 : 0;
    1948:       numEdges    = !rank ? 12 : 0;
    1949:       numVerts    = !rank ?  8 : 0;
    1950:       firstVertex = numCells;
    1951:       firstEdge   = numCells + numVerts;
    1952:       /* Build Topology */
    1953:       DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);
    1954:       for (c = 0; c < numCells; c++) {
    1955:         DMPlexSetConeSize(*dm, c, 4);
    1956:       }
    1957:       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
    1958:         DMPlexSetConeSize(*dm, e, 2);
    1959:       }
    1960:       DMSetUp(*dm); /* Allocate space for cones */
    1961:       if (!rank) {
    1962:         /* Cell 0 */
    1963:         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
    1964:         DMPlexSetCone(*dm, 0, cone);
    1965:         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
    1966:         DMPlexSetConeOrientation(*dm, 0, ornt);
    1967:         /* Cell 1 */
    1968:         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
    1969:         DMPlexSetCone(*dm, 1, cone);
    1970:         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
    1971:         DMPlexSetConeOrientation(*dm, 1, ornt);
    1972:         /* Cell 2 */
    1973:         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
    1974:         DMPlexSetCone(*dm, 2, cone);
    1975:         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
    1976:         DMPlexSetConeOrientation(*dm, 2, ornt);
    1977:         /* Cell 3 */
    1978:         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
    1979:         DMPlexSetCone(*dm, 3, cone);
    1980:         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
    1981:         DMPlexSetConeOrientation(*dm, 3, ornt);
    1982:         /* Cell 4 */
    1983:         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
    1984:         DMPlexSetCone(*dm, 4, cone);
    1985:         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
    1986:         DMPlexSetConeOrientation(*dm, 4, ornt);
    1987:         /* Cell 5 */
    1988:         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
    1989:         DMPlexSetCone(*dm, 5, cone);
    1990:         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
    1991:         DMPlexSetConeOrientation(*dm, 5, ornt);
    1992:         /* Edges */
    1993:         cone[0] =  6; cone[1] =  7;
    1994:         DMPlexSetCone(*dm, 14, cone);
    1995:         cone[0] =  7; cone[1] =  8;
    1996:         DMPlexSetCone(*dm, 15, cone);
    1997:         cone[0] =  8; cone[1] =  9;
    1998:         DMPlexSetCone(*dm, 16, cone);
    1999:         cone[0] =  9; cone[1] =  6;
    2000:         DMPlexSetCone(*dm, 17, cone);
    2001:         cone[0] = 10; cone[1] = 11;
    2002:         DMPlexSetCone(*dm, 18, cone);
    2003:         cone[0] = 11; cone[1] =  7;
    2004:         DMPlexSetCone(*dm, 19, cone);
    2005:         cone[0] =  6; cone[1] = 10;
    2006:         DMPlexSetCone(*dm, 20, cone);
    2007:         cone[0] = 12; cone[1] = 13;
    2008:         DMPlexSetCone(*dm, 21, cone);
    2009:         cone[0] = 13; cone[1] = 11;
    2010:         DMPlexSetCone(*dm, 22, cone);
    2011:         cone[0] = 10; cone[1] = 12;
    2012:         DMPlexSetCone(*dm, 23, cone);
    2013:         cone[0] = 13; cone[1] =  8;
    2014:         DMPlexSetCone(*dm, 24, cone);
    2015:         cone[0] = 12; cone[1] =  9;
    2016:         DMPlexSetCone(*dm, 25, cone);
    2017:       }
    2018:       DMPlexSymmetrize(*dm);
    2019:       DMPlexStratify(*dm);
    2020:       /* Build coordinates */
    2021:       PetscCalloc1(numVerts * embedDim, &coordsIn);
    2022:       if (!rank) {
    2023:         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
    2024:         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
    2025:         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
    2026:         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
    2027:         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
    2028:         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
    2029:         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
    2030:         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
    2031:       }
    2032:     }
    2033:     break;
    2034:   case 3:
    2035:     if (simplex) {
    2036:       DM              idm;
    2037:       const PetscReal edgeLen         = 1.0/PETSC_PHI;
    2038:       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
    2039:       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
    2040:       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
    2041:       const PetscInt  degree          = 12;
    2042:       PetscInt        s[4]            = {1, 1, 1};
    2043:       PetscInt        evenPerm[12][4] = {{0, 1, 2, 3}, {0, 2, 3, 1}, {0, 3, 1, 2}, {1, 0, 3, 2}, {1, 2, 0, 3}, {1, 3, 2, 0},
    2044:                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
    2045:       PetscInt        cone[4];
    2046:       PetscInt       *graph, p, i, j, k, l;

    2048:       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
    2049:       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
    2050:       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
    2051:       numCells    = !rank ? 600 : 0;
    2052:       numVerts    = !rank ? 120 : 0;
    2053:       firstVertex = numCells;
    2054:       /* Use the 600-cell, which for a unit sphere has coordinates which are

    2056:            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
    2057:                (\pm 1,    0,       0,      0)  all cyclic permutations   8
    2058:            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96

    2060:          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
    2061:          length is then given by 1/\phi = 0.61803.

    2063:          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
    2064:          http://mathworld.wolfram.com/600-Cell.html
    2065:       */
    2066:       /* Construct vertices */
    2067:       PetscCalloc1(numVerts * embedDim, &coordsIn);
    2068:       i    = 0;
    2069:       if (!rank) {
    2070:         for (s[0] = -1; s[0] < 2; s[0] += 2) {
    2071:           for (s[1] = -1; s[1] < 2; s[1] += 2) {
    2072:             for (s[2] = -1; s[2] < 2; s[2] += 2) {
    2073:               for (s[3] = -1; s[3] < 2; s[3] += 2) {
    2074:                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
    2075:                 ++i;
    2076:               }
    2077:             }
    2078:           }
    2079:         }
    2080:         for (p = 0; p < embedDim; ++p) {
    2081:           s[1] = s[2] = s[3] = 1;
    2082:           for (s[0] = -1; s[0] < 2; s[0] += 2) {
    2083:             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
    2084:             ++i;
    2085:           }
    2086:         }
    2087:         for (p = 0; p < 12; ++p) {
    2088:           s[3] = 1;
    2089:           for (s[0] = -1; s[0] < 2; s[0] += 2) {
    2090:             for (s[1] = -1; s[1] < 2; s[1] += 2) {
    2091:               for (s[2] = -1; s[2] < 2; s[2] += 2) {
    2092:                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
    2093:                 ++i;
    2094:               }
    2095:             }
    2096:           }
    2097:         }
    2098:       }
    2099:       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
    2100:       /* Construct graph */
    2101:       PetscCalloc1(numVerts * numVerts, &graph);
    2102:       for (i = 0; i < numVerts; ++i) {
    2103:         for (j = 0, k = 0; j < numVerts; ++j) {
    2104:           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
    2105:         }
    2106:         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
    2107:       }
    2108:       /* Build Topology */
    2109:       DMPlexSetChart(*dm, 0, numCells+numVerts);
    2110:       for (c = 0; c < numCells; c++) {
    2111:         DMPlexSetConeSize(*dm, c, embedDim);
    2112:       }
    2113:       DMSetUp(*dm); /* Allocate space for cones */
    2114:       /* Cells */
    2115:       if (!rank) {
    2116:         for (i = 0, c = 0; i < numVerts; ++i) {
    2117:           for (j = 0; j < i; ++j) {
    2118:             for (k = 0; k < j; ++k) {
    2119:               for (l = 0; l < k; ++l) {
    2120:                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
    2121:                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
    2122:                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
    2123:                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
    2124:                   {
    2125:                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2126:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
    2127:                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
    2128:                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},

    2130:                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
    2131:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2132:                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
    2133:                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},

    2135:                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
    2136:                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
    2137:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2138:                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},

    2140:                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
    2141:                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
    2142:                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2143:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
    2144:                     PetscReal normal[4];
    2145:                     PetscInt  e, f, g;

    2147:                     for (d = 0; d < embedDim; ++d) {
    2148:                       normal[d] = 0.0;
    2149:                       for (e = 0; e < embedDim; ++e) {
    2150:                         for (f = 0; f < embedDim; ++f) {
    2151:                           for (g = 0; g < embedDim; ++g) {
    2152:                             normal[d] += epsilon[d][e][f][g]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f])*(coordsIn[l*embedDim+f] - coordsIn[i*embedDim+f]);
    2153:                           }
    2154:                         }
    2155:                       }
    2156:                     }
    2157:                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
    2158:                   }
    2159:                   DMPlexSetCone(*dm, c++, cone);
    2160:                 }
    2161:               }
    2162:             }
    2163:           }
    2164:         }
    2165:       }
    2166:       DMPlexSymmetrize(*dm);
    2167:       DMPlexStratify(*dm);
    2168:       PetscFree(graph);
    2169:       /* Interpolate mesh */
    2170:       DMPlexInterpolate(*dm, &idm);
    2171:       DMDestroy(dm);
    2172:       *dm  = idm;
    2173:       break;
    2174:     }
    2175:   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
    2176:   }
    2177:   /* Create coordinates */
    2178:   DMGetCoordinateSection(*dm, &coordSection);
    2179:   PetscSectionSetNumFields(coordSection, 1);
    2180:   PetscSectionSetFieldComponents(coordSection, 0, embedDim);
    2181:   PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);
    2182:   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
    2183:     PetscSectionSetDof(coordSection, v, embedDim);
    2184:     PetscSectionSetFieldDof(coordSection, v, 0, embedDim);
    2185:   }
    2186:   PetscSectionSetUp(coordSection);
    2187:   PetscSectionGetStorageSize(coordSection, &coordSize);
    2188:   VecCreate(PETSC_COMM_SELF, &coordinates);
    2189:   VecSetBlockSize(coordinates, embedDim);
    2190:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    2191:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    2192:   VecSetType(coordinates,VECSTANDARD);
    2193:   VecGetArray(coordinates, &coords);
    2194:   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
    2195:   VecRestoreArray(coordinates, &coords);
    2196:   DMSetCoordinatesLocal(*dm, coordinates);
    2197:   VecDestroy(&coordinates);
    2198:   PetscFree(coordsIn);
    2199:   /* Create coordinate function space */
    2200:   {
    2201:     DM          cdm;
    2202:     PetscDS     cds;
    2203:     PetscFE     fe;
    2204:     PetscScalar radius = R;
    2205:     PetscInt    dT, dE;

    2207:     DMGetCoordinateDM(*dm, &cdm);
    2208:     DMGetDimension(*dm, &dT);
    2209:     DMGetCoordinateDim(*dm, &dE);
    2210:     PetscFECreateLagrange(PETSC_COMM_SELF, dT, dE, simplex, 1, -1, &fe);
    2211:     DMSetField(cdm, 0, NULL, (PetscObject) fe);
    2212:     PetscFEDestroy(&fe);
    2213:     DMCreateDS(cdm);

    2215:     DMGetDS(cdm, &cds);
    2216:     PetscDSSetConstants(cds, 1, &radius);
    2217:   }
    2218:   ((DM_Plex *) (*dm)->data)->coordFunc = snapToSphere;
    2219:   return(0);
    2220: }

    2222: /*@
    2223:   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.

    2225:   Collective

    2227:   Input Parameters:
    2228: + comm  - The communicator for the DM object
    2229: . dim   - The dimension
    2230: - R     - The radius

    2232:   Output Parameter:
    2233: . dm  - The DM object

    2235:   Options Database Keys:
    2236: - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry

    2238:   Level: beginner

    2240: .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    2241: @*/
    2242: PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
    2243: {
    2244:   DM             sdm;
    2245:   DMLabel        bdlabel;

    2249:   DMPlexCreateSphereMesh(comm, dim-1, PETSC_TRUE, R, &sdm);
    2250:   PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");
    2251:   DMSetFromOptions(sdm);
    2252:   DMPlexGenerate(sdm, NULL, PETSC_TRUE, dm);
    2253:   DMDestroy(&sdm);
    2254:   DMCreateLabel(*dm, "marker");
    2255:   DMGetLabel(*dm, "marker", &bdlabel);
    2256:   DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);
    2257:   DMPlexLabelComplete(*dm, bdlabel);
    2258:   return(0);
    2259: }

    2261: /* External function declarations here */
    2262: extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
    2263: extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
    2264: extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
    2265: extern PetscErrorCode DMCreateLocalSection_Plex(DM dm);
    2266: extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
    2267: extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
    2268: extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
    2269: extern PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field);
    2270: PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
    2271: extern PetscErrorCode DMSetUp_Plex(DM dm);
    2272: extern PetscErrorCode DMDestroy_Plex(DM dm);
    2273: extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
    2274: extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
    2275: extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
    2276: extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
    2277: static PetscErrorCode DMInitialize_Plex(DM dm);

    2279: /* Replace dm with the contents of dmNew
    2280:    - Share the DM_Plex structure
    2281:    - Share the coordinates
    2282:    - Share the SF
    2283: */
    2284: static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
    2285: {
    2286:   PetscSF               sf;
    2287:   DM                    coordDM, coarseDM;
    2288:   Vec                   coords;
    2289:   PetscBool             isper;
    2290:   const PetscReal      *maxCell, *L;
    2291:   const DMBoundaryType *bd;
    2292:   PetscErrorCode        ierr;

    2295:   DMGetPointSF(dmNew, &sf);
    2296:   DMSetPointSF(dm, sf);
    2297:   DMGetCoordinateDM(dmNew, &coordDM);
    2298:   DMGetCoordinatesLocal(dmNew, &coords);
    2299:   DMSetCoordinateDM(dm, coordDM);
    2300:   DMSetCoordinatesLocal(dm, coords);
    2301:   /* Do not want to create the coordinate field if it does not already exist, so do not call DMGetCoordinateField() */
    2302:   DMFieldDestroy(&dm->coordinateField);
    2303:   dm->coordinateField = dmNew->coordinateField;
    2304:   DMGetPeriodicity(dmNew, &isper, &maxCell, &L, &bd);
    2305:   DMSetPeriodicity(dm, isper, maxCell, L, bd);
    2306:   DMDestroy_Plex(dm);
    2307:   DMInitialize_Plex(dm);
    2308:   dm->data = dmNew->data;
    2309:   ((DM_Plex *) dmNew->data)->refct++;
    2310:   DMDestroyLabelLinkList_Internal(dm);
    2311:   DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE);
    2312:   DMGetCoarseDM(dmNew,&coarseDM);
    2313:   DMSetCoarseDM(dm,coarseDM);
    2314:   return(0);
    2315: }

    2317: /* Swap dm with the contents of dmNew
    2318:    - Swap the DM_Plex structure
    2319:    - Swap the coordinates
    2320:    - Swap the point PetscSF
    2321: */
    2322: static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
    2323: {
    2324:   DM              coordDMA, coordDMB;
    2325:   Vec             coordsA,  coordsB;
    2326:   PetscSF         sfA,      sfB;
    2327:   DMField         fieldTmp;
    2328:   void            *tmp;
    2329:   DMLabelLink     listTmp;
    2330:   DMLabel         depthTmp;
    2331:   PetscInt        tmpI;
    2332:   PetscErrorCode  ierr;

    2335:   DMGetPointSF(dmA, &sfA);
    2336:   DMGetPointSF(dmB, &sfB);
    2337:   PetscObjectReference((PetscObject) sfA);
    2338:   DMSetPointSF(dmA, sfB);
    2339:   DMSetPointSF(dmB, sfA);
    2340:   PetscObjectDereference((PetscObject) sfA);

    2342:   DMGetCoordinateDM(dmA, &coordDMA);
    2343:   DMGetCoordinateDM(dmB, &coordDMB);
    2344:   PetscObjectReference((PetscObject) coordDMA);
    2345:   DMSetCoordinateDM(dmA, coordDMB);
    2346:   DMSetCoordinateDM(dmB, coordDMA);
    2347:   PetscObjectDereference((PetscObject) coordDMA);

    2349:   DMGetCoordinatesLocal(dmA, &coordsA);
    2350:   DMGetCoordinatesLocal(dmB, &coordsB);
    2351:   PetscObjectReference((PetscObject) coordsA);
    2352:   DMSetCoordinatesLocal(dmA, coordsB);
    2353:   DMSetCoordinatesLocal(dmB, coordsA);
    2354:   PetscObjectDereference((PetscObject) coordsA);

    2356:   fieldTmp             = dmA->coordinateField;
    2357:   dmA->coordinateField = dmB->coordinateField;
    2358:   dmB->coordinateField = fieldTmp;
    2359:   tmp       = dmA->data;
    2360:   dmA->data = dmB->data;
    2361:   dmB->data = tmp;
    2362:   listTmp   = dmA->labels;
    2363:   dmA->labels = dmB->labels;
    2364:   dmB->labels = listTmp;
    2365:   depthTmp  = dmA->depthLabel;
    2366:   dmA->depthLabel = dmB->depthLabel;
    2367:   dmB->depthLabel = depthTmp;
    2368:   depthTmp  = dmA->celltypeLabel;
    2369:   dmA->celltypeLabel = dmB->celltypeLabel;
    2370:   dmB->celltypeLabel = depthTmp;
    2371:   tmpI         = dmA->levelup;
    2372:   dmA->levelup = dmB->levelup;
    2373:   dmB->levelup = tmpI;
    2374:   return(0);
    2375: }

    2377: PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
    2378: {
    2379:   DM_Plex       *mesh = (DM_Plex*) dm->data;
    2380:   PetscBool      flg;

    2384:   /* Handle viewing */
    2385:   PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);
    2386:   PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);
    2387:   PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);
    2388:   PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);
    2389:   DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);
    2390:   if (flg) {PetscLogDefaultBegin();}
    2391:   /* Point Location */
    2392:   PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);
    2393:   /* Partitioning and distribution */
    2394:   PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);
    2395:   /* Generation and remeshing */
    2396:   PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);
    2397:   /* Projection behavior */
    2398:   PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);
    2399:   PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);
    2400:   PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "ex40.c", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);
    2401:   /* Checking structure */
    2402:   {
    2403:     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;

    2405:     PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);
    2406:     PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);
    2407:     if (all || (flg && flg2)) {DMPlexCheckSymmetry(dm);}
    2408:     PetscOptionsBool("-dm_plex_check_skeleton", "Check that each cell has the correct number of vertices (only for homogeneous simplex or tensor meshes)", "DMPlexCheckSkeleton", PETSC_FALSE, &flg, &flg2);
    2409:     if (all || (flg && flg2)) {DMPlexCheckSkeleton(dm, 0);}
    2410:     PetscOptionsBool("-dm_plex_check_faces", "Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type", "DMPlexCheckFaces", PETSC_FALSE, &flg, &flg2);
    2411:     if (all || (flg && flg2)) {DMPlexCheckFaces(dm, 0);}
    2412:     PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);
    2413:     if (all || (flg && flg2)) {DMPlexCheckGeometry(dm);}
    2414:     PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);
    2415:     if (all || (flg && flg2)) {DMPlexCheckPointSF(dm);}
    2416:     PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2);
    2417:     if (all || (flg && flg2)) {DMPlexCheckInterfaceCones(dm);}
    2418:     PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);
    2419:     if (flg && flg2) {DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);}
    2420:   }

    2422:   PetscPartitionerSetFromOptions(mesh->partitioner);
    2423:   return(0);
    2424: }

    2426: static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
    2427: {
    2428:   PetscReal      volume = -1.0;
    2429:   PetscInt       prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0;
    2430:   PetscBool      uniformOrig, uniform = PETSC_TRUE, distribute = PETSC_FALSE, isHierarchy, flg;

    2435:   PetscOptionsHead(PetscOptionsObject,"DMPlex Options");
    2436:   /* Handle DMPlex refinement before distribution */
    2437:   DMPlexGetRefinementUniform(dm, &uniformOrig);
    2438:   PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);
    2439:   if (flg) {DMPlexSetRefinementUniform(dm, uniform);}
    2440:   PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);
    2441:   if (flg) {DMPlexSetRefinementLimit(dm, volume);}
    2442:   PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);
    2443:   for (r = 0; r < prerefine; ++r) {
    2444:     DM             rdm;
    2445:     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;

    2447:     DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2448:     DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);
    2449:     /* Total hack since we do not pass in a pointer */
    2450:     DMPlexReplace_Static(dm, rdm);
    2451:     DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2452:     if (coordFunc) {
    2453:       DMPlexRemapGeometry(dm, 0.0, coordFunc);
    2454:       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
    2455:     }
    2456:     DMDestroy(&rdm);
    2457:   }
    2458:   DMPlexSetRefinementUniform(dm, uniformOrig);
    2459:   /* Handle DMPlex distribution */
    2460:   PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);
    2461:   PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);
    2462:   if (distribute) {
    2463:     DM               pdm = NULL;
    2464:     PetscPartitioner part;

    2466:     DMPlexGetPartitioner(dm, &part);
    2467:     PetscPartitionerSetFromOptions(part);
    2468:     DMPlexDistribute(dm, overlap, NULL, &pdm);
    2469:     if (pdm) {
    2470:       DMPlexReplace_Static(dm, pdm);
    2471:       DMDestroy(&pdm);
    2472:     }
    2473:   }
    2474:   /* Handle DMPlex refinement */
    2475:   PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);
    2476:   PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);
    2477:   if (refine) {DMPlexSetRefinementUniform(dm, PETSC_TRUE);}
    2478:   if (refine && isHierarchy) {
    2479:     DM *dms, coarseDM;

    2481:     DMGetCoarseDM(dm, &coarseDM);
    2482:     PetscObjectReference((PetscObject)coarseDM);
    2483:     PetscMalloc1(refine,&dms);
    2484:     DMRefineHierarchy(dm, refine, dms);
    2485:     /* Total hack since we do not pass in a pointer */
    2486:     DMPlexSwap_Static(dm, dms[refine-1]);
    2487:     if (refine == 1) {
    2488:       DMSetCoarseDM(dm, dms[0]);
    2489:       DMPlexSetRegularRefinement(dm, PETSC_TRUE);
    2490:     } else {
    2491:       DMSetCoarseDM(dm, dms[refine-2]);
    2492:       DMPlexSetRegularRefinement(dm, PETSC_TRUE);
    2493:       DMSetCoarseDM(dms[0], dms[refine-1]);
    2494:       DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);
    2495:     }
    2496:     DMSetCoarseDM(dms[refine-1], coarseDM);
    2497:     PetscObjectDereference((PetscObject)coarseDM);
    2498:     /* Free DMs */
    2499:     for (r = 0; r < refine; ++r) {
    2500:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);
    2501:       DMDestroy(&dms[r]);
    2502:     }
    2503:     PetscFree(dms);
    2504:   } else {
    2505:     for (r = 0; r < refine; ++r) {
    2506:       DM refinedMesh;
    2507:       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;

    2509:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2510:       DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);
    2511:       /* Total hack since we do not pass in a pointer */
    2512:       DMPlexReplace_Static(dm, refinedMesh);
    2513:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2514:       if (coordFunc) {
    2515:         DMPlexRemapGeometry(dm, 0.0, coordFunc);
    2516:         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
    2517:       }
    2518:       DMDestroy(&refinedMesh);
    2519:     }
    2520:   }
    2521:   /* Handle DMPlex coarsening */
    2522:   PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);
    2523:   PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);
    2524:   if (coarsen && isHierarchy) {
    2525:     DM *dms;

    2527:     PetscMalloc1(coarsen, &dms);
    2528:     DMCoarsenHierarchy(dm, coarsen, dms);
    2529:     /* Free DMs */
    2530:     for (r = 0; r < coarsen; ++r) {
    2531:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);
    2532:       DMDestroy(&dms[r]);
    2533:     }
    2534:     PetscFree(dms);
    2535:   } else {
    2536:     for (r = 0; r < coarsen; ++r) {
    2537:       DM coarseMesh;

    2539:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2540:       DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);
    2541:       /* Total hack since we do not pass in a pointer */
    2542:       DMPlexReplace_Static(dm, coarseMesh);
    2543:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2544:       DMDestroy(&coarseMesh);
    2545:     }
    2546:   }
    2547:   /* Handle */
    2548:   DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2549:   PetscOptionsTail();
    2550:   return(0);
    2551: }

    2553: static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
    2554: {

    2558:   DMCreateGlobalVector_Section_Private(dm,vec);
    2559:   /* VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM); */
    2560:   VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);
    2561:   VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);
    2562:   VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);
    2563:   VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);
    2564:   return(0);
    2565: }

    2567: static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
    2568: {

    2572:   DMCreateLocalVector_Section_Private(dm,vec);
    2573:   VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);
    2574:   VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);
    2575:   return(0);
    2576: }

    2578: static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
    2579: {
    2580:   PetscInt       depth, d;

    2584:   DMPlexGetDepth(dm, &depth);
    2585:   if (depth == 1) {
    2586:     DMGetDimension(dm, &d);
    2587:     if (dim == 0)      {DMPlexGetDepthStratum(dm, dim, pStart, pEnd);}
    2588:     else if (dim == d) {DMPlexGetDepthStratum(dm, 1, pStart, pEnd);}
    2589:     else               {*pStart = 0; *pEnd = 0;}
    2590:   } else {
    2591:     DMPlexGetDepthStratum(dm, dim, pStart, pEnd);
    2592:   }
    2593:   return(0);
    2594: }

    2596: static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
    2597: {
    2598:   PetscSF           sf;
    2599:   PetscInt          niranks, njranks, n;
    2600:   const PetscMPIInt *iranks, *jranks;
    2601:   DM_Plex           *data = (DM_Plex*) dm->data;
    2602:   PetscErrorCode    ierr;

    2605:   DMGetPointSF(dm, &sf);
    2606:   if (!data->neighbors) {
    2607:     PetscSFSetUp(sf);
    2608:     PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);
    2609:     PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);
    2610:     PetscMalloc1(njranks + niranks + 1, &data->neighbors);
    2611:     PetscArraycpy(data->neighbors + 1, jranks, njranks);
    2612:     PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);
    2613:     n = njranks + niranks;
    2614:     PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);
    2615:     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
    2616:     PetscMPIIntCast(n, data->neighbors);
    2617:   }
    2618:   if (nranks) *nranks = data->neighbors[0];
    2619:   if (ranks) {
    2620:     if (data->neighbors[0]) *ranks = data->neighbors + 1;
    2621:     else                    *ranks = NULL;
    2622:   }
    2623:   return(0);
    2624: }

    2626: PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);

    2628: static PetscErrorCode DMInitialize_Plex(DM dm)
    2629: {

    2633:   dm->ops->view                            = DMView_Plex;
    2634:   dm->ops->load                            = DMLoad_Plex;
    2635:   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
    2636:   dm->ops->clone                           = DMClone_Plex;
    2637:   dm->ops->setup                           = DMSetUp_Plex;
    2638:   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
    2639:   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
    2640:   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
    2641:   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
    2642:   dm->ops->getlocaltoglobalmapping         = NULL;
    2643:   dm->ops->createfieldis                   = NULL;
    2644:   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
    2645:   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
    2646:   dm->ops->getcoloring                     = NULL;
    2647:   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
    2648:   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
    2649:   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
    2650:   dm->ops->createinjection                 = DMCreateInjection_Plex;
    2651:   dm->ops->refine                          = DMRefine_Plex;
    2652:   dm->ops->coarsen                         = DMCoarsen_Plex;
    2653:   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
    2654:   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
    2655:   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
    2656:   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
    2657:   dm->ops->globaltolocalbegin              = NULL;
    2658:   dm->ops->globaltolocalend                = NULL;
    2659:   dm->ops->localtoglobalbegin              = NULL;
    2660:   dm->ops->localtoglobalend                = NULL;
    2661:   dm->ops->destroy                         = DMDestroy_Plex;
    2662:   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
    2663:   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
    2664:   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
    2665:   dm->ops->locatepoints                    = DMLocatePoints_Plex;
    2666:   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
    2667:   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
    2668:   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
    2669:   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
    2670:   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
    2671:   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
    2672:   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
    2673:   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
    2674:   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
    2675:   PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);
    2676:   PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);
    2677:   PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);
    2678:   PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);
    2679:   PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);
    2680:   PetscObjectComposeFunction((PetscObject)dm,"DMInterpolateSolution_C",DMInterpolateSolution_Plex);
    2681:   return(0);
    2682: }

    2684: PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
    2685: {
    2686:   DM_Plex        *mesh = (DM_Plex *) dm->data;

    2690:   mesh->refct++;
    2691:   (*newdm)->data = mesh;
    2692:   PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);
    2693:   DMInitialize_Plex(*newdm);
    2694:   return(0);
    2695: }

    2697: /*MC
    2698:   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
    2699:                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
    2700:                     specified by a PetscSection object. Ownership in the global representation is determined by
    2701:                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.

    2703:   Options Database Keys:
    2704: + -dm_refine_pre                     - Refine mesh before distribution
    2705: + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
    2706: + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
    2707: . -dm_distribute                     - Distribute mesh across processes
    2708: . -dm_distribute_overlap             - Number of cells to overlap for distribution
    2709: . -dm_refine                         - Refine mesh after distribution
    2710: . -dm_plex_hash_location             - Use grid hashing for point location
    2711: . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
    2712: . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
    2713: . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
    2714: . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
    2715: . -dm_plex_check_all                 - Perform all shecks below
    2716: . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
    2717: . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
    2718: . -dm_plex_check_faces <celltype>    - Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type
    2719: . -dm_plex_check_geometry            - Check that cells have positive volume
    2720: . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
    2721: . -dm_plex_view_scale <num>          - Scale the TikZ
    2722: - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices

    2725:   Level: intermediate

    2727: .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
    2728: M*/

    2730: PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
    2731: {
    2732:   DM_Plex       *mesh;
    2733:   PetscInt       unit;

    2738:   PetscNewLog(dm,&mesh);
    2739:   dm->dim  = 0;
    2740:   dm->data = mesh;

    2742:   mesh->refct             = 1;
    2743:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);
    2744:   mesh->maxConeSize       = 0;
    2745:   mesh->cones             = NULL;
    2746:   mesh->coneOrientations  = NULL;
    2747:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);
    2748:   mesh->maxSupportSize    = 0;
    2749:   mesh->supports          = NULL;
    2750:   mesh->refinementUniform = PETSC_TRUE;
    2751:   mesh->refinementLimit   = -1.0;
    2752:   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
    2753:   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;

    2755:   mesh->facesTmp = NULL;

    2757:   mesh->tetgenOpts   = NULL;
    2758:   mesh->triangleOpts = NULL;
    2759:   PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);
    2760:   mesh->remeshBd     = PETSC_FALSE;

    2762:   mesh->subpointMap = NULL;

    2764:   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;

    2766:   mesh->regularRefinement   = PETSC_FALSE;
    2767:   mesh->depthState          = -1;
    2768:   mesh->celltypeState       = -1;
    2769:   mesh->globalVertexNumbers = NULL;
    2770:   mesh->globalCellNumbers   = NULL;
    2771:   mesh->anchorSection       = NULL;
    2772:   mesh->anchorIS            = NULL;
    2773:   mesh->createanchors       = NULL;
    2774:   mesh->computeanchormatrix = NULL;
    2775:   mesh->parentSection       = NULL;
    2776:   mesh->parents             = NULL;
    2777:   mesh->childIDs            = NULL;
    2778:   mesh->childSection        = NULL;
    2779:   mesh->children            = NULL;
    2780:   mesh->referenceTree       = NULL;
    2781:   mesh->getchildsymmetry    = NULL;
    2782:   mesh->vtkCellHeight       = 0;
    2783:   mesh->useAnchors          = PETSC_FALSE;

    2785:   mesh->maxProjectionHeight = 0;

    2787:   mesh->neighbors           = NULL;

    2789:   mesh->printSetValues = PETSC_FALSE;
    2790:   mesh->printFEM       = 0;
    2791:   mesh->printTol       = 1.0e-10;

    2793:   DMInitialize_Plex(dm);
    2794:   return(0);
    2795: }

    2797: /*@
    2798:   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.

    2800:   Collective

    2802:   Input Parameter:
    2803: . comm - The communicator for the DMPlex object

    2805:   Output Parameter:
    2806: . mesh  - The DMPlex object

    2808:   Level: beginner

    2810: @*/
    2811: PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
    2812: {

    2817:   DMCreate(comm, mesh);
    2818:   DMSetType(*mesh, DMPLEX);
    2819:   return(0);
    2820: }

    2822: /*@C
    2823:   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)

    2825:   Input Parameters:
    2826: + dm - The DM
    2827: . numCells - The number of cells owned by this process
    2828: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    2829: . NVertices - The global number of vertices, or PETSC_DECIDE
    2830: . numCorners - The number of vertices for each cell
    2831: - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell

    2833:   Output Parameter:
    2834: . vertexSF - (Optional) SF describing complete vertex ownership

    2836:   Notes:
    2837:   Two triangles sharing a face
    2838: $
    2839: $        2
    2840: $      / | \
    2841: $     /  |  \
    2842: $    /   |   \
    2843: $   0  0 | 1  3
    2844: $    \   |   /
    2845: $     \  |  /
    2846: $      \ | /
    2847: $        1
    2848: would have input
    2849: $  numCells = 2, numVertices = 4
    2850: $  cells = [0 1 2  1 3 2]
    2851: $
    2852: which would result in the DMPlex
    2853: $
    2854: $        4
    2855: $      / | \
    2856: $     /  |  \
    2857: $    /   |   \
    2858: $   2  0 | 1  5
    2859: $    \   |   /
    2860: $     \  |  /
    2861: $      \ | /
    2862: $        3

    2864:   Vertices are implicitly numbered consecutively 0,...,NVertices.
    2865:   Each rank owns a chunk of numVertices consecutive vertices.
    2866:   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
    2867:   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
    2868:   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.

    2870:   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.

    2872:   Not currently supported in Fortran.

    2874:   Level: advanced

    2876: .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
    2877: @*/
    2878: PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
    2879: {
    2880:   PetscSF         sfPoint;
    2881:   PetscLayout     layout;
    2882:   PetscInt        numVerticesAdj, *verticesAdj, *cones, c, p, dim;
    2883:   PetscMPIInt     rank, size;
    2884:   PetscErrorCode  ierr;

    2888:   PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);
    2889:   MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);
    2890:   MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);
    2891:   DMGetDimension(dm, &dim);
    2892:   /* Get/check global number of vertices */
    2893:   {
    2894:     PetscInt NVerticesInCells, i;
    2895:     const PetscInt len = numCells * numCorners;

    2897:     /* NVerticesInCells = max(cells) + 1 */
    2898:     NVerticesInCells = PETSC_MIN_INT;
    2899:     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
    2900:     ++NVerticesInCells;
    2901:     MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));

    2903:     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
    2904:     else if (NVertices != PETSC_DECIDE && NVertices < NVerticesInCells) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Specified global number of vertices %D must be greater than or equal to the number of vertices in cells %D",NVertices,NVerticesInCells);
    2905:   }
    2906:   /* Count locally unique vertices */
    2907:   {
    2908:     PetscHSetI vhash;
    2909:     PetscInt off = 0;

    2911:     PetscHSetICreate(&vhash);
    2912:     for (c = 0; c < numCells; ++c) {
    2913:       for (p = 0; p < numCorners; ++p) {
    2914:         PetscHSetIAdd(vhash, cells[c*numCorners+p]);
    2915:       }
    2916:     }
    2917:     PetscHSetIGetSize(vhash, &numVerticesAdj);
    2918:     PetscMalloc1(numVerticesAdj, &verticesAdj);
    2919:     PetscHSetIGetElems(vhash, &off, verticesAdj);
    2920:     PetscHSetIDestroy(&vhash);
    2921:     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
    2922:   }
    2923:   PetscSortInt(numVerticesAdj, verticesAdj);
    2924:   /* Create cones */
    2925:   DMPlexSetChart(dm, 0, numCells+numVerticesAdj);
    2926:   for (c = 0; c < numCells; ++c) {DMPlexSetConeSize(dm, c, numCorners);}
    2927:   DMSetUp(dm);
    2928:   DMPlexGetCones(dm,&cones);
    2929:   for (c = 0; c < numCells; ++c) {
    2930:     for (p = 0; p < numCorners; ++p) {
    2931:       const PetscInt gv = cells[c*numCorners+p];
    2932:       PetscInt       lv;

    2934:       /* Positions within verticesAdj form 0-based local vertex numbering;
    2935:          we need to shift it by numCells to get correct DAG points (cells go first) */
    2936:       PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);
    2937:       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
    2938:       cones[c*numCorners+p] = lv+numCells;
    2939:     }
    2940:   }
    2941:   /* Build point sf */
    2942:   PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout);
    2943:   PetscLayoutSetSize(layout, NVertices);
    2944:   PetscLayoutSetLocalSize(layout, numVertices);
    2945:   PetscLayoutSetBlockSize(layout, 1);
    2946:   PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint);
    2947:   PetscLayoutDestroy(&layout);
    2948:   PetscFree(verticesAdj);
    2949:   PetscObjectSetName((PetscObject) sfPoint, "point SF");
    2950:   if (dm->sf) {
    2951:     const char *prefix;

    2953:     PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix);
    2954:     PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix);
    2955:   }
    2956:   DMSetPointSF(dm, sfPoint);
    2957:   PetscSFDestroy(&sfPoint);
    2958:   if (vertexSF) {PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF");}
    2959:   /* Fill in the rest of the topology structure */
    2960:   DMPlexSymmetrize(dm);
    2961:   DMPlexStratify(dm);
    2962:   PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);
    2963:   return(0);
    2964: }

    2966: /*@C
    2967:   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)

    2969:   Input Parameters:
    2970: + dm - The DM
    2971: . spaceDim - The spatial dimension used for coordinates
    2972: . sfVert - SF describing complete vertex ownership
    2973: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    2975:   Level: advanced

    2977:   Notes:
    2978:   Not currently supported in Fortran.

    2980: .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
    2981: @*/
    2982: PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
    2983: {
    2984:   PetscSection   coordSection;
    2985:   Vec            coordinates;
    2986:   PetscScalar   *coords;
    2987:   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;

    2991:   PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    2992:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    2993:   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
    2994:   DMSetCoordinateDim(dm, spaceDim);
    2995:   PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);
    2996:   if (vEnd - vStart != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Supplied sfVert has wrong number of leaves = %D != %D = vEnd - vStart",numVerticesAdj,vEnd - vStart);
    2997:   DMGetCoordinateSection(dm, &coordSection);
    2998:   PetscSectionSetNumFields(coordSection, 1);
    2999:   PetscSectionSetFieldComponents(coordSection, 0, spaceDim);
    3000:   PetscSectionSetChart(coordSection, vStart, vEnd);
    3001:   for (v = vStart; v < vEnd; ++v) {
    3002:     PetscSectionSetDof(coordSection, v, spaceDim);
    3003:     PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);
    3004:   }
    3005:   PetscSectionSetUp(coordSection);
    3006:   PetscSectionGetStorageSize(coordSection, &coordSize);
    3007:   VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);
    3008:   VecSetBlockSize(coordinates, spaceDim);
    3009:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3010:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    3011:   VecSetType(coordinates,VECSTANDARD);
    3012:   VecGetArray(coordinates, &coords);
    3013:   {
    3014:     MPI_Datatype coordtype;

    3016:     /* Need a temp buffer for coords if we have complex/single */
    3017:     MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);
    3018:     MPI_Type_commit(&coordtype);
    3019: #if defined(PETSC_USE_COMPLEX)
    3020:     {
    3021:     PetscScalar *svertexCoords;
    3022:     PetscInt    i;
    3023:     PetscMalloc1(numVertices*spaceDim,&svertexCoords);
    3024:     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
    3025:     PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);
    3026:     PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);
    3027:     PetscFree(svertexCoords);
    3028:     }
    3029: #else
    3030:     PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);
    3031:     PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);
    3032: #endif
    3033:     MPI_Type_free(&coordtype);
    3034:   }
    3035:   VecRestoreArray(coordinates, &coords);
    3036:   DMSetCoordinatesLocal(dm, coordinates);
    3037:   VecDestroy(&coordinates);
    3038:   PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3039:   return(0);
    3040: }

    3042: /*@
    3043:   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)

    3045:   Input Parameters:
    3046: + comm - The communicator
    3047: . dim - The topological dimension of the mesh
    3048: . numCells - The number of cells owned by this process
    3049: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    3050: . NVertices - The global number of vertices, or PETSC_DECIDE
    3051: . numCorners - The number of vertices for each cell
    3052: . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
    3053: . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
    3054: . spaceDim - The spatial dimension used for coordinates
    3055: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3057:   Output Parameter:
    3058: + dm - The DM
    3059: - vertexSF - (Optional) SF describing complete vertex ownership

    3061:   Notes:
    3062:   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
    3063:   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()

    3065:   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
    3066:   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.

    3068:   Level: intermediate

    3070: .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
    3071: @*/
    3072: PetscErrorCode DMPlexCreateFromCellListParallelPetsc(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, PetscBool interpolate, const PetscInt cells[], PetscInt spaceDim, const PetscReal vertexCoords[], PetscSF *vertexSF, DM *dm)
    3073: {
    3074:   PetscSF        sfVert;

    3078:   DMCreate(comm, dm);
    3079:   DMSetType(*dm, DMPLEX);
    3082:   DMSetDimension(*dm, dim);
    3083:   DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);
    3084:   if (interpolate) {
    3085:     DM idm;

    3087:     DMPlexInterpolate(*dm, &idm);
    3088:     DMDestroy(dm);
    3089:     *dm  = idm;
    3090:   }
    3091:   DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);
    3092:   if (vertexSF) *vertexSF = sfVert;
    3093:   else {PetscSFDestroy(&sfVert);}
    3094:   return(0);
    3095: }

    3098: /*@
    3099:   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()

    3101:   Level: deprecated

    3103: .seealso: DMPlexCreateFromCellListParallelPetsc()
    3104: @*/
    3105: PetscErrorCode DMPlexCreateFromCellListParallel(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const int cells[], PetscInt spaceDim, const PetscReal vertexCoords[], PetscSF *vertexSF, DM *dm)
    3106: {
    3108:   PetscInt       i;
    3109:   PetscInt       *pintCells;

    3112:   if (sizeof(int) > sizeof(PetscInt)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Size of int %zd greater than size of PetscInt %zd. Reconfigure PETSc --with-64-bit-indices=1", sizeof(int), sizeof(PetscInt));
    3113:   if (sizeof(int) == sizeof(PetscInt)) {
    3114:     pintCells = (PetscInt *) cells;
    3115:   } else {
    3116:     PetscMalloc1(numCells*numCorners, &pintCells);
    3117:     for (i = 0; i < numCells*numCorners; i++) {
    3118:       pintCells[i] = (PetscInt) cells[i];
    3119:     }
    3120:   }
    3121:   DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);
    3122:   if (sizeof(int) != sizeof(PetscInt)) {
    3123:     PetscFree(pintCells);
    3124:   }
    3125:   return(0);
    3126: }

    3128: /*@C
    3129:   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)

    3131:   Input Parameters:
    3132: + dm - The DM
    3133: . numCells - The number of cells owned by this process
    3134: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    3135: . numCorners - The number of vertices for each cell
    3136: - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell

    3138:   Level: advanced

    3140:   Notes:
    3141:   Two triangles sharing a face
    3142: $
    3143: $        2
    3144: $      / | \
    3145: $     /  |  \
    3146: $    /   |   \
    3147: $   0  0 | 1  3
    3148: $    \   |   /
    3149: $     \  |  /
    3150: $      \ | /
    3151: $        1
    3152: would have input
    3153: $  numCells = 2, numVertices = 4
    3154: $  cells = [0 1 2  1 3 2]
    3155: $
    3156: which would result in the DMPlex
    3157: $
    3158: $        4
    3159: $      / | \
    3160: $     /  |  \
    3161: $    /   |   \
    3162: $   2  0 | 1  5
    3163: $    \   |   /
    3164: $     \  |  /
    3165: $      \ | /
    3166: $        3

    3168:   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.

    3170:   Not currently supported in Fortran.

    3172: .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
    3173: @*/
    3174: PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
    3175: {
    3176:   PetscInt      *cones, c, p, dim;

    3180:   PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);
    3181:   DMGetDimension(dm, &dim);
    3182:   /* Get/check global number of vertices */
    3183:   {
    3184:     PetscInt NVerticesInCells, i;
    3185:     const PetscInt len = numCells * numCorners;

    3187:     /* NVerticesInCells = max(cells) + 1 */
    3188:     NVerticesInCells = PETSC_MIN_INT;
    3189:     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
    3190:     ++NVerticesInCells;

    3192:     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
    3193:     else if (numVertices < NVerticesInCells) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Specified number of vertices %D must be greater than or equal to the number of vertices in cells %D",numVertices,NVerticesInCells);
    3194:   }
    3195:   DMPlexSetChart(dm, 0, numCells+numVertices);
    3196:   for (c = 0; c < numCells; ++c) {
    3197:     DMPlexSetConeSize(dm, c, numCorners);
    3198:   }
    3199:   DMSetUp(dm);
    3200:   DMPlexGetCones(dm,&cones);
    3201:   for (c = 0; c < numCells; ++c) {
    3202:     for (p = 0; p < numCorners; ++p) {
    3203:       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
    3204:     }
    3205:   }
    3206:   DMPlexSymmetrize(dm);
    3207:   DMPlexStratify(dm);
    3208:   PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);
    3209:   return(0);
    3210: }

    3212: /*@C
    3213:   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)

    3215:   Input Parameters:
    3216: + dm - The DM
    3217: . spaceDim - The spatial dimension used for coordinates
    3218: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3220:   Level: advanced

    3222:   Notes:
    3223:   Not currently supported in Fortran.

    3225: .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
    3226: @*/
    3227: PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
    3228: {
    3229:   PetscSection   coordSection;
    3230:   Vec            coordinates;
    3231:   DM             cdm;
    3232:   PetscScalar   *coords;
    3233:   PetscInt       v, vStart, vEnd, d;

    3237:   PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3238:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3239:   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
    3240:   DMSetCoordinateDim(dm, spaceDim);
    3241:   DMGetCoordinateSection(dm, &coordSection);
    3242:   PetscSectionSetNumFields(coordSection, 1);
    3243:   PetscSectionSetFieldComponents(coordSection, 0, spaceDim);
    3244:   PetscSectionSetChart(coordSection, vStart, vEnd);
    3245:   for (v = vStart; v < vEnd; ++v) {
    3246:     PetscSectionSetDof(coordSection, v, spaceDim);
    3247:     PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);
    3248:   }
    3249:   PetscSectionSetUp(coordSection);

    3251:   DMGetCoordinateDM(dm, &cdm);
    3252:   DMCreateLocalVector(cdm, &coordinates);
    3253:   VecSetBlockSize(coordinates, spaceDim);
    3254:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3255:   VecGetArrayWrite(coordinates, &coords);
    3256:   for (v = 0; v < vEnd-vStart; ++v) {
    3257:     for (d = 0; d < spaceDim; ++d) {
    3258:       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
    3259:     }
    3260:   }
    3261:   VecRestoreArrayWrite(coordinates, &coords);
    3262:   DMSetCoordinatesLocal(dm, coordinates);
    3263:   VecDestroy(&coordinates);
    3264:   PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3265:   return(0);
    3266: }

    3268: /*@
    3269:   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output)

    3271:   Input Parameters:
    3272: + comm - The communicator
    3273: . dim - The topological dimension of the mesh
    3274: . numCells - The number of cells
    3275: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    3276: . numCorners - The number of vertices for each cell
    3277: . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
    3278: . cells - An array of numCells*numCorners numbers, the vertices for each cell
    3279: . spaceDim - The spatial dimension used for coordinates
    3280: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3282:   Output Parameter:
    3283: . dm - The DM

    3285:   Notes:
    3286:   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
    3287:   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()

    3289:   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
    3290:   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.

    3292:   Level: intermediate

    3294: .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
    3295: @*/
    3296: PetscErrorCode DMPlexCreateFromCellListPetsc(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const PetscInt cells[], PetscInt spaceDim, const PetscReal vertexCoords[], DM *dm)
    3297: {

    3301:   if (!dim) SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "This is not appropriate for 0-dimensional meshes. Consider either creating the DM using DMPlexCreateFromDAG(), by hand, or using DMSwarm.");
    3302:   DMCreate(comm, dm);
    3303:   DMSetType(*dm, DMPLEX);
    3304:   DMSetDimension(*dm, dim);
    3305:   DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);
    3306:   if (interpolate) {
    3307:     DM idm;

    3309:     DMPlexInterpolate(*dm, &idm);
    3310:     DMDestroy(dm);
    3311:     *dm  = idm;
    3312:   }
    3313:   DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);
    3314:   return(0);
    3315: }

    3317: /*@
    3318:   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()

    3320:   Level: deprecated

    3322: .seealso: DMPlexCreateFromCellListPetsc()
    3323: @*/
    3324: 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)
    3325: {
    3327:   PetscInt       i;
    3328:   PetscInt       *pintCells;
    3329:   PetscReal      *prealVC;

    3332:   if (sizeof(int) > sizeof(PetscInt)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Size of int %zd greater than size of PetscInt %zd. Reconfigure PETSc --with-64-bit-indices=1", sizeof(int), sizeof(PetscInt));
    3333:   if (sizeof(int) == sizeof(PetscInt)) {
    3334:     pintCells = (PetscInt *) cells;
    3335:   } else {
    3336:     PetscMalloc1(numCells*numCorners, &pintCells);
    3337:     for (i = 0; i < numCells*numCorners; i++) {
    3338:       pintCells[i] = (PetscInt) cells[i];
    3339:     }
    3340:   }
    3341:   if (sizeof(double) > sizeof(PetscReal)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Size of double %zd greater than size of PetscReal %zd. Reconfigure PETSc --with-precision=<higher precision>.", sizeof(double), sizeof(PetscReal));
    3342:   if (sizeof(double) == sizeof(PetscReal)) {
    3343:     prealVC = (PetscReal *) vertexCoords;
    3344:   } else {
    3345:     PetscMalloc1(numVertices*spaceDim, &prealVC);
    3346:     for (i = 0; i < numVertices*spaceDim; i++) {
    3347:       prealVC[i] = (PetscReal) vertexCoords[i];
    3348:     }
    3349:   }
    3350:   DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);
    3351:   if (sizeof(int) != sizeof(PetscInt)) {
    3352:     PetscFree(pintCells);
    3353:   }
    3354:   if (sizeof(double) != sizeof(PetscReal)) {
    3355:     PetscFree(prealVC);
    3356:   }
    3357:   return(0);
    3358: }

    3360: /*@
    3361:   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM

    3363:   Input Parameters:
    3364: + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
    3365: . depth - The depth of the DAG
    3366: . numPoints - Array of size depth + 1 containing the number of points at each depth
    3367: . coneSize - The cone size of each point
    3368: . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
    3369: . coneOrientations - The orientation of each cone point
    3370: - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()

    3372:   Output Parameter:
    3373: . dm - The DM

    3375:   Note: Two triangles sharing a face would have input
    3376: $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
    3377: $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
    3378: $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
    3379: $
    3380: which would result in the DMPlex
    3381: $
    3382: $        4
    3383: $      / | \
    3384: $     /  |  \
    3385: $    /   |   \
    3386: $   2  0 | 1  5
    3387: $    \   |   /
    3388: $     \  |  /
    3389: $      \ | /
    3390: $        3
    3391: $
    3392: $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()

    3394:   Level: advanced

    3396: .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
    3397: @*/
    3398: PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
    3399: {
    3400:   Vec            coordinates;
    3401:   PetscSection   coordSection;
    3402:   PetscScalar    *coords;
    3403:   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;

    3407:   DMGetDimension(dm, &dim);
    3408:   DMGetCoordinateDim(dm, &dimEmbed);
    3409:   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
    3410:   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
    3411:   DMPlexSetChart(dm, pStart, pEnd);
    3412:   for (p = pStart; p < pEnd; ++p) {
    3413:     DMPlexSetConeSize(dm, p, coneSize[p-pStart]);
    3414:     if (firstVertex < 0 && !coneSize[p - pStart]) {
    3415:       firstVertex = p - pStart;
    3416:     }
    3417:   }
    3418:   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
    3419:   DMSetUp(dm); /* Allocate space for cones */
    3420:   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
    3421:     DMPlexSetCone(dm, p, &cones[off]);
    3422:     DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);
    3423:   }
    3424:   DMPlexSymmetrize(dm);
    3425:   DMPlexStratify(dm);
    3426:   /* Build coordinates */
    3427:   DMGetCoordinateSection(dm, &coordSection);
    3428:   PetscSectionSetNumFields(coordSection, 1);
    3429:   PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);
    3430:   PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);
    3431:   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
    3432:     PetscSectionSetDof(coordSection, v, dimEmbed);
    3433:     PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);
    3434:   }
    3435:   PetscSectionSetUp(coordSection);
    3436:   PetscSectionGetStorageSize(coordSection, &coordSize);
    3437:   VecCreate(PETSC_COMM_SELF, &coordinates);
    3438:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3439:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    3440:   VecSetBlockSize(coordinates, dimEmbed);
    3441:   VecSetType(coordinates,VECSTANDARD);
    3442:   VecGetArray(coordinates, &coords);
    3443:   for (v = 0; v < numPoints[0]; ++v) {
    3444:     PetscInt off;

    3446:     PetscSectionGetOffset(coordSection, v+firstVertex, &off);
    3447:     for (d = 0; d < dimEmbed; ++d) {
    3448:       coords[off+d] = vertexCoords[v*dimEmbed+d];
    3449:     }
    3450:   }
    3451:   VecRestoreArray(coordinates, &coords);
    3452:   DMSetCoordinatesLocal(dm, coordinates);
    3453:   VecDestroy(&coordinates);
    3454:   return(0);
    3455: }

    3457: /*@C
    3458:   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.

    3460: + comm        - The MPI communicator
    3461: . filename    - Name of the .dat file
    3462: - interpolate - Create faces and edges in the mesh

    3464:   Output Parameter:
    3465: . dm  - The DM object representing the mesh

    3467:   Note: The format is the simplest possible:
    3468: $ Ne
    3469: $ v0 v1 ... vk
    3470: $ Nv
    3471: $ x y z marker

    3473:   Level: beginner

    3475: .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
    3476: @*/
    3477: PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
    3478: {
    3479:   DMLabel         marker;
    3480:   PetscViewer     viewer;
    3481:   Vec             coordinates;
    3482:   PetscSection    coordSection;
    3483:   PetscScalar    *coords;
    3484:   char            line[PETSC_MAX_PATH_LEN];
    3485:   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
    3486:   PetscMPIInt     rank;
    3487:   int             snum, Nv, Nc;
    3488:   PetscErrorCode  ierr;

    3491:   MPI_Comm_rank(comm, &rank);
    3492:   PetscViewerCreate(comm, &viewer);
    3493:   PetscViewerSetType(viewer, PETSCVIEWERASCII);
    3494:   PetscViewerFileSetMode(viewer, FILE_MODE_READ);
    3495:   PetscViewerFileSetName(viewer, filename);
    3496:   if (!rank) {
    3497:     PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);
    3498:     snum = sscanf(line, "%d %d", &Nc, &Nv);
    3499:     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
    3500:   } else {
    3501:     Nc = Nv = 0;
    3502:   }
    3503:   DMCreate(comm, dm);
    3504:   DMSetType(*dm, DMPLEX);
    3505:   DMPlexSetChart(*dm, 0, Nc+Nv);
    3506:   DMSetDimension(*dm, dim);
    3507:   DMSetCoordinateDim(*dm, cdim);
    3508:   /* Read topology */
    3509:   if (!rank) {
    3510:     PetscInt cone[8], corners = 8;
    3511:     int      vbuf[8], v;

    3513:     for (c = 0; c < Nc; ++c) {DMPlexSetConeSize(*dm, c, corners);}
    3514:     DMSetUp(*dm);
    3515:     for (c = 0; c < Nc; ++c) {
    3516:       PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);
    3517:       snum = sscanf(line, "%d %d %d %d %d %d %d %d", &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);
    3518:       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
    3519:       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
    3520:       /* Hexahedra are inverted */
    3521:       {
    3522:         PetscInt tmp = cone[1];
    3523:         cone[1] = cone[3];
    3524:         cone[3] = tmp;
    3525:       }
    3526:       DMPlexSetCone(*dm, c, cone);
    3527:     }
    3528:   }
    3529:   DMPlexSymmetrize(*dm);
    3530:   DMPlexStratify(*dm);
    3531:   /* Read coordinates */
    3532:   DMGetCoordinateSection(*dm, &coordSection);
    3533:   PetscSectionSetNumFields(coordSection, 1);
    3534:   PetscSectionSetFieldComponents(coordSection, 0, cdim);
    3535:   PetscSectionSetChart(coordSection, Nc, Nc + Nv);
    3536:   for (v = Nc; v < Nc+Nv; ++v) {
    3537:     PetscSectionSetDof(coordSection, v, cdim);
    3538:     PetscSectionSetFieldDof(coordSection, v, 0, cdim);
    3539:   }
    3540:   PetscSectionSetUp(coordSection);
    3541:   PetscSectionGetStorageSize(coordSection, &coordSize);
    3542:   VecCreate(PETSC_COMM_SELF, &coordinates);
    3543:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3544:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    3545:   VecSetBlockSize(coordinates, cdim);
    3546:   VecSetType(coordinates, VECSTANDARD);
    3547:   VecGetArray(coordinates, &coords);
    3548:   if (!rank) {
    3549:     double x[3];
    3550:     int    val;

    3552:     DMCreateLabel(*dm, "marker");
    3553:     DMGetLabel(*dm, "marker", &marker);
    3554:     for (v = 0; v < Nv; ++v) {
    3555:       PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);
    3556:       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
    3557:       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
    3558:       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
    3559:       if (val) {DMLabelSetValue(marker, v+Nc, val);}
    3560:     }
    3561:   }
    3562:   VecRestoreArray(coordinates, &coords);
    3563:   DMSetCoordinatesLocal(*dm, coordinates);
    3564:   VecDestroy(&coordinates);
    3565:   PetscViewerDestroy(&viewer);
    3566:   if (interpolate) {
    3567:     DM      idm;
    3568:     DMLabel bdlabel;

    3570:     DMPlexInterpolate(*dm, &idm);
    3571:     DMDestroy(dm);
    3572:     *dm  = idm;

    3574:     DMGetLabel(*dm, "marker", &bdlabel);
    3575:     DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);
    3576:     DMPlexLabelComplete(*dm, bdlabel);
    3577:   }
    3578:   return(0);
    3579: }

    3581: /*@C
    3582:   DMPlexCreateFromFile - This takes a filename and produces a DM

    3584:   Input Parameters:
    3585: + comm - The communicator
    3586: . filename - A file name
    3587: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    3589:   Output Parameter:
    3590: . dm - The DM

    3592:   Options Database Keys:
    3593: . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5

    3595:   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
    3596: $ -dm_plex_create_viewer_hdf5_collective

    3598:   Level: beginner

    3600: .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
    3601: @*/
    3602: PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
    3603: {
    3604:   const char    *extGmsh    = ".msh";
    3605:   const char    *extGmsh2   = ".msh2";
    3606:   const char    *extGmsh4   = ".msh4";
    3607:   const char    *extCGNS    = ".cgns";
    3608:   const char    *extExodus  = ".exo";
    3609:   const char    *extGenesis = ".gen";
    3610:   const char    *extFluent  = ".cas";
    3611:   const char    *extHDF5    = ".h5";
    3612:   const char    *extMed     = ".med";
    3613:   const char    *extPLY     = ".ply";
    3614:   const char    *extEGADS   = ".egadslite";
    3615:   const char    *extCV      = ".dat";
    3616:   size_t         len;
    3617:   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADS, isCV;
    3618:   PetscMPIInt    rank;

    3624:   DMInitializePackage();
    3625:   PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);
    3626:   MPI_Comm_rank(comm, &rank);
    3627:   PetscStrlen(filename, &len);
    3628:   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
    3629:   PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);
    3630:   PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);
    3631:   PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);
    3632:   PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);
    3633:   PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);
    3634:   PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);
    3635:   PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);
    3636:   PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);
    3637:   PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);
    3638:   PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);
    3639:   PetscStrncmp(&filename[PetscMax(0,len-10)], extEGADS,   9, &isEGADS);
    3640:   PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);
    3641:   if (isGmsh || isGmsh2 || isGmsh4) {
    3642:     DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);
    3643:   } else if (isCGNS) {
    3644:     DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);
    3645:   } else if (isExodus || isGenesis) {
    3646:     DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);
    3647:   } else if (isFluent) {
    3648:     DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);
    3649:   } else if (isHDF5) {
    3650:     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
    3651:     PetscViewer viewer;

    3653:     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
    3654:     PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);
    3655:     PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);
    3656:     PetscViewerCreate(comm, &viewer);
    3657:     PetscViewerSetType(viewer, PETSCVIEWERHDF5);
    3658:     PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");
    3659:     PetscViewerSetFromOptions(viewer);
    3660:     PetscViewerFileSetMode(viewer, FILE_MODE_READ);
    3661:     PetscViewerFileSetName(viewer, filename);
    3662:     DMCreate(comm, dm);
    3663:     DMSetType(*dm, DMPLEX);
    3664:     if (load_hdf5_xdmf) {PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);}
    3665:     DMLoad(*dm, viewer);
    3666:     if (load_hdf5_xdmf) {PetscViewerPopFormat(viewer);}
    3667:     PetscViewerDestroy(&viewer);

    3669:     if (interpolate) {
    3670:       DM idm;

    3672:       DMPlexInterpolate(*dm, &idm);
    3673:       DMDestroy(dm);
    3674:       *dm  = idm;
    3675:     }
    3676:   } else if (isMed) {
    3677:     DMPlexCreateMedFromFile(comm, filename, interpolate, dm);
    3678:   } else if (isPLY) {
    3679:     DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);
    3680:   } else if (isEGADS) {
    3681:     DMPlexCreateEGADSFromFile(comm, filename, dm);
    3682:     if (!interpolate) {
    3683:       DM udm;

    3685:       DMPlexUninterpolate(*dm, &udm);
    3686:       DMDestroy(dm);
    3687:       *dm  = udm;
    3688:     }
    3689:   } else if (isCV) {
    3690:     DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);
    3691:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
    3692:   PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);
    3693:   return(0);
    3694: }

    3696: /*@
    3697:   DMPlexCreateReferenceCellByType - Create a DMPLEX with the appropriate FEM reference cell

    3699:   Collective

    3701:   Input Parameters:
    3702: + comm - The communicator
    3703: - ct   - The cell type of the reference cell

    3705:   Output Parameter:
    3706: . refdm - The reference cell

    3708:   Options Database Keys:
    3709: . -dm_plex_ref_type <ct> - Specify the celltyoe for the reference cell

    3711:   Level: intermediate

    3713: .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
    3714: @*/
    3715: PetscErrorCode DMPlexCreateReferenceCellByType(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
    3716: {
    3717:   DM             rdm;
    3718:   Vec            coords;

    3722:   PetscOptionsGetEnum(NULL, NULL, "-dm_plex_ref_type", DMPolytopeTypes, (PetscEnum *) &ct, NULL);
    3723:   DMCreate(comm, &rdm);
    3724:   DMSetType(rdm, DMPLEX);
    3725:   switch (ct) {
    3726:     case DM_POLYTOPE_POINT:
    3727:     {
    3728:       PetscInt    numPoints[1]        = {1};
    3729:       PetscInt    coneSize[1]         = {0};
    3730:       PetscInt    cones[1]            = {0};
    3731:       PetscInt    coneOrientations[1] = {0};
    3732:       PetscScalar vertexCoords[1]     = {0.0};

    3734:       DMSetDimension(rdm, 0);
    3735:       DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3736:     }
    3737:     break;
    3738:     case DM_POLYTOPE_SEGMENT:
    3739:     {
    3740:       PetscInt    numPoints[2]        = {2, 1};
    3741:       PetscInt    coneSize[3]         = {2, 0, 0};
    3742:       PetscInt    cones[2]            = {1, 2};
    3743:       PetscInt    coneOrientations[2] = {0, 0};
    3744:       PetscScalar vertexCoords[2]     = {-1.0,  1.0};

    3746:       DMSetDimension(rdm, 1);
    3747:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3748:     }
    3749:     break;
    3750:     case DM_POLYTOPE_TRIANGLE:
    3751:     {
    3752:       PetscInt    numPoints[2]        = {3, 1};
    3753:       PetscInt    coneSize[4]         = {3, 0, 0, 0};
    3754:       PetscInt    cones[3]            = {1, 2, 3};
    3755:       PetscInt    coneOrientations[3] = {0, 0, 0};
    3756:       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};

    3758:       DMSetDimension(rdm, 2);
    3759:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3760:     }
    3761:     break;
    3762:     case DM_POLYTOPE_QUADRILATERAL:
    3763:     {
    3764:       PetscInt    numPoints[2]        = {4, 1};
    3765:       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
    3766:       PetscInt    cones[4]            = {1, 2, 3, 4};
    3767:       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
    3768:       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};

    3770:       DMSetDimension(rdm, 2);
    3771:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3772:     }
    3773:     break;
    3774:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    3775:     {
    3776:       PetscInt    numPoints[2]        = {4, 1};
    3777:       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
    3778:       PetscInt    cones[4]            = {1, 2, 3, 4};
    3779:       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
    3780:       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};

    3782:       DMSetDimension(rdm, 2);
    3783:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3784:     }
    3785:     break;
    3786:     case DM_POLYTOPE_TETRAHEDRON:
    3787:     {
    3788:       PetscInt    numPoints[2]        = {4, 1};
    3789:       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
    3790:       PetscInt    cones[4]            = {1, 3, 2, 4};
    3791:       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
    3792:       PetscScalar vertexCoords[12]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,  -1.0, -1.0, 1.0};

    3794:       DMSetDimension(rdm, 3);
    3795:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3796:     }
    3797:     break;
    3798:     case DM_POLYTOPE_HEXAHEDRON:
    3799:     {
    3800:       PetscInt    numPoints[2]        = {8, 1};
    3801:       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
    3802:       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
    3803:       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
    3804:       PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  1.0, 1.0, -1.0,  -1.0, 1.0, -1.0,
    3805:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};

    3807:       DMSetDimension(rdm, 3);
    3808:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3809:     }
    3810:     break;
    3811:     case DM_POLYTOPE_TRI_PRISM:
    3812:     {
    3813:       PetscInt    numPoints[2]        = {6, 1};
    3814:       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
    3815:       PetscInt    cones[6]            = {1, 3, 2, 4, 5, 6};
    3816:       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
    3817:       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
    3818:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};

    3820:       DMSetDimension(rdm, 3);
    3821:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3822:     }
    3823:     break;
    3824:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    3825:     {
    3826:       PetscInt    numPoints[2]        = {6, 1};
    3827:       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
    3828:       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
    3829:       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
    3830:       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
    3831:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};

    3833:       DMSetDimension(rdm, 3);
    3834:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3835:     }
    3836:     break;
    3837:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    3838:     {
    3839:       PetscInt    numPoints[2]        = {8, 1};
    3840:       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
    3841:       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
    3842:       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
    3843:       PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  1.0, 1.0, -1.0,  -1.0, 1.0, -1.0,
    3844:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};

    3846:       DMSetDimension(rdm, 3);
    3847:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3848:     }
    3849:     break;
    3850:     case DM_POLYTOPE_PYRAMID:
    3851:     {
    3852:       PetscInt    numPoints[2]        = {5, 1};
    3853:       PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
    3854:       PetscInt    cones[5]            = {1, 4, 3, 2, 5};
    3855:       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
    3856:       PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  1.0, 1.0, -1.0,  -1.0, 1.0, -1.0,
    3857:                                           0.0,  0.0,  1.0};

    3859:       DMSetDimension(rdm, 3);
    3860:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3861:     }
    3862:     break;
    3863:     default: SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
    3864:   }
    3865:   {
    3866:     PetscInt Nv, v;

    3868:     /* Must create the celltype label here so that we do not automatically try to compute the types */
    3869:     DMCreateLabel(rdm, "celltype");
    3870:     DMPlexSetCellType(rdm, 0, ct);
    3871:     DMPlexGetChart(rdm, NULL, &Nv);
    3872:     for (v = 1; v < Nv; ++v) {DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);}
    3873:   }
    3874:   DMPlexInterpolate(rdm, refdm);
    3875:   if (rdm->coordinateDM) {
    3876:     DM           ncdm;
    3877:     PetscSection cs;
    3878:     PetscInt     pEnd = -1;

    3880:     DMGetLocalSection(rdm->coordinateDM, &cs);
    3881:     if (cs) {PetscSectionGetChart(cs, NULL, &pEnd);}
    3882:     if (pEnd >= 0) {
    3883:       DMClone(*refdm, &ncdm);
    3884:       DMCopyDisc(rdm->coordinateDM, ncdm);
    3885:       DMSetLocalSection(ncdm, cs);
    3886:       DMSetCoordinateDM(*refdm, ncdm);
    3887:       DMDestroy(&ncdm);
    3888:     }
    3889:   }
    3890:   DMGetCoordinatesLocal(rdm, &coords);
    3891:   if (coords) {
    3892:     DMSetCoordinatesLocal(*refdm, coords);
    3893:   } else {
    3894:     DMGetCoordinates(rdm, &coords);
    3895:     if (coords) {DMSetCoordinates(*refdm, coords);}
    3896:   }
    3897:   DMDestroy(&rdm);
    3898:   return(0);
    3899: }

    3901: /*@
    3902:   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell

    3904:   Collective

    3906:   Input Parameters:
    3907: + comm    - The communicator
    3908: . dim     - The spatial dimension
    3909: - simplex - Flag for simplex, otherwise use a tensor-product cell

    3911:   Output Parameter:
    3912: . refdm - The reference cell

    3914:   Level: intermediate

    3916: .seealso: DMPlexCreateReferenceCellByType(), DMPlexCreateBoxMesh()
    3917: @*/
    3918: PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
    3919: {

    3923:   switch (dim) {
    3924:   case 0: DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_POINT, refdm);break;
    3925:   case 1: DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_SEGMENT, refdm);break;
    3926:   case 2:
    3927:     if (simplex) {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TRIANGLE, refdm);}
    3928:     else         {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_QUADRILATERAL, refdm);}
    3929:     break;
    3930:   case 3:
    3931:     if (simplex) {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TETRAHEDRON, refdm);}
    3932:     else         {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_HEXAHEDRON, refdm);}
    3933:     break;
    3934:   default:
    3935:     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %D", dim);
    3936:   }
    3937:   return(0);
    3938: }