Date: 2021-03-03T22:26:49+00:00

Actual source code: plexcreate.c
petsc-3.14.5 2021-03-03
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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: . refinementUniform - Flag for uniform parallel refinement
     19: - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell

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

     24:   Level: beginner

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

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

     66:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     67:         for (p = 0; p < 4; ++p) {DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);}
     68:       } else {
     69:         PetscInt    numPoints[2]        = {6, 2};
     70:         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
     71:         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
     72:         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
     73:         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};

     75:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     76:       }
     77:       break;
     78:     case 3:
     79:       if (simplex) {
     80:         PetscInt    numPoints[2]        = {5, 2};
     81:         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
     82:         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
     83:         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
     84:         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};
     85:         PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};

     87:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     88:         for (p = 0; p < 5; ++p) {DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);}
     89:       } else {
     90:         PetscInt    numPoints[2]         = {12, 2};
     91:         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
     92:         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
     93:         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
     94:         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,
     95:                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
     96:                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};

     98:         DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
     99:       }
    100:       break;
    101:     default:
    102:       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
    103:     }
    104:   }
    105:   *newdm = dm;
    106:   if (refinementLimit > 0.0) {
    107:     DM rdm;
    108:     const char *name;

    110:     DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);
    111:     DMPlexSetRefinementLimit(*newdm, refinementLimit);
    112:     DMRefine(*newdm, comm, &rdm);
    113:     PetscObjectGetName((PetscObject) *newdm, &name);
    114:     PetscObjectSetName((PetscObject)    rdm,  name);
    115:     DMDestroy(newdm);
    116:     *newdm = rdm;
    117:   }
    118:   if (interpolate) {
    119:     DM idm;

    121:     DMPlexInterpolate(*newdm, &idm);
    122:     DMDestroy(newdm);
    123:     *newdm = idm;
    124:   }
    125:   {
    126:     DM refinedMesh     = NULL;
    127:     DM distributedMesh = NULL;

    129:     /* Distribute mesh over processes */
    130:     DMPlexDistribute(*newdm, 0, NULL, &distributedMesh);
    131:     if (distributedMesh) {
    132:       DMDestroy(newdm);
    133:       *newdm = distributedMesh;
    134:     }
    135:     if (refinementUniform) {
    136:       DMPlexSetRefinementUniform(*newdm, refinementUniform);
    137:       DMRefine(*newdm, comm, &refinedMesh);
    138:       if (refinedMesh) {
    139:         DMDestroy(newdm);
    140:         *newdm = refinedMesh;
    141:       }
    142:     }
    143:   }
    144:   return(0);
    145: }

    147: /*@
    148:   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.

    150:   Collective

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

    158:   Output Parameter:
    159: . dm  - The DM object

    161:   Note: Here is the numbering returned for 2 cells in each direction:
    162: $ 18--5-17--4--16
    163: $  |     |     |
    164: $  6    10     3
    165: $  |     |     |
    166: $ 19-11-20--9--15
    167: $  |     |     |
    168: $  7     8     2
    169: $  |     |     |
    170: $ 12--0-13--1--14

    172:   Level: beginner

    174: .seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
    175: @*/
    176: PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
    177: {
    178:   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
    179:   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
    180:   PetscInt       markerTop      = 1;
    181:   PetscInt       markerBottom   = 1;
    182:   PetscInt       markerRight    = 1;
    183:   PetscInt       markerLeft     = 1;
    184:   PetscBool      markerSeparate = PETSC_FALSE;
    185:   Vec            coordinates;
    186:   PetscSection   coordSection;
    187:   PetscScalar    *coords;
    188:   PetscInt       coordSize;
    189:   PetscMPIInt    rank;
    190:   PetscInt       v, vx, vy;

    194:   PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);
    195:   if (markerSeparate) {
    196:     markerTop    = 3;
    197:     markerBottom = 1;
    198:     markerRight  = 2;
    199:     markerLeft   = 4;
    200:   }
    201:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    202:   if (!rank) {
    203:     PetscInt e, ex, ey;

    205:     DMPlexSetChart(dm, 0, numEdges+numVertices);
    206:     for (e = 0; e < numEdges; ++e) {
    207:       DMPlexSetConeSize(dm, e, 2);
    208:     }
    209:     DMSetUp(dm); /* Allocate space for cones */
    210:     for (vx = 0; vx <= edges[0]; vx++) {
    211:       for (ey = 0; ey < edges[1]; ey++) {
    212:         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
    213:         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
    214:         PetscInt cone[2];

    216:         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
    217:         DMPlexSetCone(dm, edge, cone);
    218:         if (vx == edges[0]) {
    219:           DMSetLabelValue(dm, "marker", edge,    markerRight);
    220:           DMSetLabelValue(dm, "marker", cone[0], markerRight);
    221:           if (ey == edges[1]-1) {
    222:             DMSetLabelValue(dm, "marker", cone[1], markerRight);
    223:             DMSetLabelValue(dm, "Face Sets", cone[1], markerRight);
    224:           }
    225:         } else if (vx == 0) {
    226:           DMSetLabelValue(dm, "marker", edge,    markerLeft);
    227:           DMSetLabelValue(dm, "marker", cone[0], markerLeft);
    228:           if (ey == edges[1]-1) {
    229:             DMSetLabelValue(dm, "marker", cone[1], markerLeft);
    230:             DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft);
    231:           }
    232:         }
    233:       }
    234:     }
    235:     for (vy = 0; vy <= edges[1]; vy++) {
    236:       for (ex = 0; ex < edges[0]; ex++) {
    237:         PetscInt edge   = vy*edges[0]     + ex;
    238:         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
    239:         PetscInt cone[2];

    241:         cone[0] = vertex; cone[1] = vertex+1;
    242:         DMPlexSetCone(dm, edge, cone);
    243:         if (vy == edges[1]) {
    244:           DMSetLabelValue(dm, "marker", edge,    markerTop);
    245:           DMSetLabelValue(dm, "marker", cone[0], markerTop);
    246:           if (ex == edges[0]-1) {
    247:             DMSetLabelValue(dm, "marker", cone[1], markerTop);
    248:             DMSetLabelValue(dm, "Face Sets", cone[1], markerTop);
    249:           }
    250:         } else if (vy == 0) {
    251:           DMSetLabelValue(dm, "marker", edge,    markerBottom);
    252:           DMSetLabelValue(dm, "marker", cone[0], markerBottom);
    253:           if (ex == edges[0]-1) {
    254:             DMSetLabelValue(dm, "marker", cone[1], markerBottom);
    255:             DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom);
    256:           }
    257:         }
    258:       }
    259:     }
    260:   }
    261:   DMPlexSymmetrize(dm);
    262:   DMPlexStratify(dm);
    263:   /* Build coordinates */
    264:   DMSetCoordinateDim(dm, 2);
    265:   DMGetCoordinateSection(dm, &coordSection);
    266:   PetscSectionSetNumFields(coordSection, 1);
    267:   PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);
    268:   PetscSectionSetFieldComponents(coordSection, 0, 2);
    269:   for (v = numEdges; v < numEdges+numVertices; ++v) {
    270:     PetscSectionSetDof(coordSection, v, 2);
    271:     PetscSectionSetFieldDof(coordSection, v, 0, 2);
    272:   }
    273:   PetscSectionSetUp(coordSection);
    274:   PetscSectionGetStorageSize(coordSection, &coordSize);
    275:   VecCreate(PETSC_COMM_SELF, &coordinates);
    276:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    277:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    278:   VecSetBlockSize(coordinates, 2);
    279:   VecSetType(coordinates,VECSTANDARD);
    280:   VecGetArray(coordinates, &coords);
    281:   for (vy = 0; vy <= edges[1]; ++vy) {
    282:     for (vx = 0; vx <= edges[0]; ++vx) {
    283:       coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
    284:       coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
    285:     }
    286:   }
    287:   VecRestoreArray(coordinates, &coords);
    288:   DMSetCoordinatesLocal(dm, coordinates);
    289:   VecDestroy(&coordinates);
    290:   return(0);
    291: }

    293: /*@
    294:   DMPlexCreateCubeBoundary - Creates a 2D mesh that is the boundary of a cubic lattice.

    296:   Collective

    298:   Input Parameters:
    299: + comm  - The communicator for the DM object
    300: . lower - The lower left front corner coordinates
    301: . upper - The upper right back corner coordinates
    302: - faces - The number of faces in each direction (the same as the number of cells)

    304:   Output Parameter:
    305: . dm  - The DM object

    307:   Level: beginner

    309: .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
    310: @*/
    311: PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
    312: {
    313:   PetscInt       vertices[3], numVertices;
    314:   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
    315:   Vec            coordinates;
    316:   PetscSection   coordSection;
    317:   PetscScalar    *coords;
    318:   PetscInt       coordSize;
    319:   PetscMPIInt    rank;
    320:   PetscInt       v, vx, vy, vz;
    321:   PetscInt       voffset, iface=0, cone[4];

    325:   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");
    326:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    327:   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
    328:   numVertices = vertices[0]*vertices[1]*vertices[2];
    329:   if (!rank) {
    330:     PetscInt f;

    332:     DMPlexSetChart(dm, 0, numFaces+numVertices);
    333:     for (f = 0; f < numFaces; ++f) {
    334:       DMPlexSetConeSize(dm, f, 4);
    335:     }
    336:     DMSetUp(dm); /* Allocate space for cones */

    338:     /* Side 0 (Top) */
    339:     for (vy = 0; vy < faces[1]; vy++) {
    340:       for (vx = 0; vx < faces[0]; vx++) {
    341:         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
    342:         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
    343:         DMPlexSetCone(dm, iface, cone);
    344:         DMSetLabelValue(dm, "marker", iface, 1);
    345:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    346:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    347:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    348:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);
    349:         iface++;
    350:       }
    351:     }

    353:     /* Side 1 (Bottom) */
    354:     for (vy = 0; vy < faces[1]; vy++) {
    355:       for (vx = 0; vx < faces[0]; vx++) {
    356:         voffset = numFaces + vy*(faces[0]+1) + vx;
    357:         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
    358:         DMPlexSetCone(dm, iface, cone);
    359:         DMSetLabelValue(dm, "marker", iface, 1);
    360:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    361:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    362:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    363:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);
    364:         iface++;
    365:       }
    366:     }

    368:     /* Side 2 (Front) */
    369:     for (vz = 0; vz < faces[2]; vz++) {
    370:       for (vx = 0; vx < faces[0]; vx++) {
    371:         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
    372:         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
    373:         DMPlexSetCone(dm, iface, cone);
    374:         DMSetLabelValue(dm, "marker", iface, 1);
    375:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    376:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    377:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);
    378:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);
    379:         iface++;
    380:       }
    381:     }

    383:     /* Side 3 (Back) */
    384:     for (vz = 0; vz < faces[2]; vz++) {
    385:       for (vx = 0; vx < faces[0]; vx++) {
    386:         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
    387:         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
    388:         cone[2] = voffset+1; cone[3] = voffset;
    389:         DMPlexSetCone(dm, iface, cone);
    390:         DMSetLabelValue(dm, "marker", iface, 1);
    391:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    392:         DMSetLabelValue(dm, "marker", voffset+1, 1);
    393:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);
    394:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);
    395:         iface++;
    396:       }
    397:     }

    399:     /* Side 4 (Left) */
    400:     for (vz = 0; vz < faces[2]; vz++) {
    401:       for (vy = 0; vy < faces[1]; vy++) {
    402:         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
    403:         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
    404:         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
    405:         DMPlexSetCone(dm, iface, cone);
    406:         DMSetLabelValue(dm, "marker", iface, 1);
    407:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    408:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    409:         DMSetLabelValue(dm, "marker", voffset+vertices[1]+0, 1);
    410:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);
    411:         iface++;
    412:       }
    413:     }

    415:     /* Side 5 (Right) */
    416:     for (vz = 0; vz < faces[2]; vz++) {
    417:       for (vy = 0; vy < faces[1]; vy++) {
    418:         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
    419:         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
    420:         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
    421:         DMPlexSetCone(dm, iface, cone);
    422:         DMSetLabelValue(dm, "marker", iface, 1);
    423:         DMSetLabelValue(dm, "marker", voffset+0, 1);
    424:         DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);
    425:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);
    426:         DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);
    427:         iface++;
    428:       }
    429:     }
    430:   }
    431:   DMPlexSymmetrize(dm);
    432:   DMPlexStratify(dm);
    433:   /* Build coordinates */
    434:   DMSetCoordinateDim(dm, 3);
    435:   DMGetCoordinateSection(dm, &coordSection);
    436:   PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);
    437:   for (v = numFaces; v < numFaces+numVertices; ++v) {
    438:     PetscSectionSetDof(coordSection, v, 3);
    439:   }
    440:   PetscSectionSetUp(coordSection);
    441:   PetscSectionGetStorageSize(coordSection, &coordSize);
    442:   VecCreate(PETSC_COMM_SELF, &coordinates);
    443:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    444:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    445:   VecSetBlockSize(coordinates, 3);
    446:   VecSetType(coordinates,VECSTANDARD);
    447:   VecGetArray(coordinates, &coords);
    448:   for (vz = 0; vz <= faces[2]; ++vz) {
    449:     for (vy = 0; vy <= faces[1]; ++vy) {
    450:       for (vx = 0; vx <= faces[0]; ++vx) {
    451:         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
    452:         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
    453:         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
    454:       }
    455:     }
    456:   }
    457:   VecRestoreArray(coordinates, &coords);
    458:   DMSetCoordinatesLocal(dm, coordinates);
    459:   VecDestroy(&coordinates);
    460:   return(0);
    461: }

    463: static PetscErrorCode DMPlexCreateLineMesh_Internal(MPI_Comm comm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd,DM *dm)
    464: {
    465:   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
    466:   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
    467:   PetscScalar    *vertexCoords;
    468:   PetscReal      L,maxCell;
    469:   PetscBool      markerSeparate = PETSC_FALSE;
    470:   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
    471:   PetscInt       markerRight = 1, faceMarkerRight = 2;
    472:   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
    473:   PetscMPIInt    rank;

    479:   DMCreate(comm,dm);
    480:   DMSetType(*dm,DMPLEX);
    481:   DMSetDimension(*dm,1);
    482:   DMCreateLabel(*dm,"marker");
    483:   DMCreateLabel(*dm,"Face Sets");

    485:   MPI_Comm_rank(comm,&rank);
    486:   if (!rank) numCells = segments;
    487:   if (!rank) numVerts = segments + (wrap ? 0 : 1);

    489:   numPoints[0] = numVerts ; numPoints[1] = numCells;
    490:   PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);
    491:   PetscArrayzero(coneOrientations,numCells+numVerts);
    492:   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
    493:   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
    494:   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
    495:   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
    496:   DMPlexCreateFromDAG(*dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);
    497:   PetscFree4(coneSize,cones,coneOrientations,vertexCoords);

    499:   PetscOptionsGetBool(((PetscObject)*dm)->options,((PetscObject)*dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);
    500:   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
    501:   if (!wrap && !rank) {
    502:     DMPlexGetHeightStratum(*dm,1,&fStart,&fEnd);
    503:     DMSetLabelValue(*dm,"marker",fStart,markerLeft);
    504:     DMSetLabelValue(*dm,"marker",fEnd-1,markerRight);
    505:     DMSetLabelValue(*dm,"Face Sets",fStart,faceMarkerLeft);
    506:     DMSetLabelValue(*dm,"Face Sets",fEnd-1,faceMarkerRight);
    507:   }
    508:   if (wrap) {
    509:     L       = upper - lower;
    510:     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
    511:     DMSetPeriodicity(*dm,PETSC_TRUE,&maxCell,&L,&bd);
    512:   }
    513:   return(0);
    514: }

    516: 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)
    517: {
    518:   DM             boundary;
    519:   PetscInt       i;

    524:   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
    525:   DMCreate(comm, &boundary);
    527:   DMSetType(boundary, DMPLEX);
    528:   DMSetDimension(boundary, dim-1);
    529:   DMSetCoordinateDim(boundary, dim);
    530:   switch (dim) {
    531:   case 2: DMPlexCreateSquareBoundary(boundary, lower, upper, faces);break;
    532:   case 3: DMPlexCreateCubeBoundary(boundary, lower, upper, faces);break;
    533:   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %D", dim);
    534:   }
    535:   DMPlexGenerate(boundary, NULL, interpolate, dm);
    536:   DMDestroy(&boundary);
    537:   return(0);
    538: }

    540: static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
    541: {
    542:   DMLabel        cutLabel = NULL;
    543:   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
    544:   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
    545:   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
    546:   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
    547:   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
    548:   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
    549:   PetscInt       dim;
    550:   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
    551:   PetscMPIInt    rank;

    555:   DMGetDimension(dm,&dim);
    556:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    557:   DMCreateLabel(dm,"marker");
    558:   DMCreateLabel(dm,"Face Sets");
    559:   PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);
    560:   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
    561:       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
    562:       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {

    564:     if (cutMarker) {DMCreateLabel(dm, "periodic_cut"); DMGetLabel(dm, "periodic_cut", &cutLabel);}
    565:   }
    566:   switch (dim) {
    567:   case 2:
    568:     faceMarkerTop    = 3;
    569:     faceMarkerBottom = 1;
    570:     faceMarkerRight  = 2;
    571:     faceMarkerLeft   = 4;
    572:     break;
    573:   case 3:
    574:     faceMarkerBottom = 1;
    575:     faceMarkerTop    = 2;
    576:     faceMarkerFront  = 3;
    577:     faceMarkerBack   = 4;
    578:     faceMarkerRight  = 5;
    579:     faceMarkerLeft   = 6;
    580:     break;
    581:   default:
    582:     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %D not supported",dim);
    583:   }
    584:   PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);
    585:   if (markerSeparate) {
    586:     markerBottom = faceMarkerBottom;
    587:     markerTop    = faceMarkerTop;
    588:     markerFront  = faceMarkerFront;
    589:     markerBack   = faceMarkerBack;
    590:     markerRight  = faceMarkerRight;
    591:     markerLeft   = faceMarkerLeft;
    592:   }
    593:   {
    594:     const PetscInt numXEdges    = !rank ? edges[0] : 0;
    595:     const PetscInt numYEdges    = !rank ? edges[1] : 0;
    596:     const PetscInt numZEdges    = !rank ? edges[2] : 0;
    597:     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
    598:     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
    599:     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
    600:     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
    601:     const PetscInt numXFaces    = numYEdges*numZEdges;
    602:     const PetscInt numYFaces    = numXEdges*numZEdges;
    603:     const PetscInt numZFaces    = numXEdges*numYEdges;
    604:     const PetscInt numTotXFaces = numXVertices*numXFaces;
    605:     const PetscInt numTotYFaces = numYVertices*numYFaces;
    606:     const PetscInt numTotZFaces = numZVertices*numZFaces;
    607:     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
    608:     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
    609:     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
    610:     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
    611:     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
    612:     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
    613:     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
    614:     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
    615:     const PetscInt firstYFace   = firstXFace + numTotXFaces;
    616:     const PetscInt firstZFace   = firstYFace + numTotYFaces;
    617:     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
    618:     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
    619:     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
    620:     Vec            coordinates;
    621:     PetscSection   coordSection;
    622:     PetscScalar   *coords;
    623:     PetscInt       coordSize;
    624:     PetscInt       v, vx, vy, vz;
    625:     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;

    627:     DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);
    628:     for (c = 0; c < numCells; c++) {
    629:       DMPlexSetConeSize(dm, c, 6);
    630:     }
    631:     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
    632:       DMPlexSetConeSize(dm, f, 4);
    633:     }
    634:     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
    635:       DMPlexSetConeSize(dm, e, 2);
    636:     }
    637:     DMSetUp(dm); /* Allocate space for cones */
    638:     /* Build cells */
    639:     for (fz = 0; fz < numZEdges; ++fz) {
    640:       for (fy = 0; fy < numYEdges; ++fy) {
    641:         for (fx = 0; fx < numXEdges; ++fx) {
    642:           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
    643:           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
    644:           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
    645:           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
    646:           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
    647:           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
    648:           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
    649:                             /* B,  T,  F,  K,  R,  L */
    650:           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
    651:           PetscInt cone[6];

    653:           /* no boundary twisting in 3D */
    654:           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
    655:           DMPlexSetCone(dm, cell, cone);
    656:           DMPlexSetConeOrientation(dm, cell, ornt);
    657:           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, cell, 2);}
    658:           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, cell, 2);}
    659:           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, cell, 2);}
    660:         }
    661:       }
    662:     }
    663:     /* Build x faces */
    664:     for (fz = 0; fz < numZEdges; ++fz) {
    665:       for (fy = 0; fy < numYEdges; ++fy) {
    666:         for (fx = 0; fx < numXVertices; ++fx) {
    667:           PetscInt face    = firstXFace + (fz*numYEdges+fy)     *numXVertices+fx;
    668:           PetscInt edgeL   = firstZEdge + (fy                   *numXVertices+fx)*numZEdges + fz;
    669:           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
    670:           PetscInt edgeB   = firstYEdge + (fz                   *numXVertices+fx)*numYEdges + fy;
    671:           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
    672:           PetscInt ornt[4] = {0, 0, -2, -2};
    673:           PetscInt cone[4];

    675:           if (dim == 3) {
    676:             /* markers */
    677:             if (bdX != DM_BOUNDARY_PERIODIC) {
    678:               if (fx == numXVertices-1) {
    679:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);
    680:                 DMSetLabelValue(dm, "marker", face, markerRight);
    681:               }
    682:               else if (fx == 0) {
    683:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);
    684:                 DMSetLabelValue(dm, "marker", face, markerLeft);
    685:               }
    686:             }
    687:           }
    688:           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
    689:           DMPlexSetCone(dm, face, cone);
    690:           DMPlexSetConeOrientation(dm, face, ornt);
    691:         }
    692:       }
    693:     }
    694:     /* Build y faces */
    695:     for (fz = 0; fz < numZEdges; ++fz) {
    696:       for (fx = 0; fx < numXEdges; ++fx) {
    697:         for (fy = 0; fy < numYVertices; ++fy) {
    698:           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
    699:           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx)*numZEdges + fz;
    700:           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
    701:           PetscInt edgeB   = firstXEdge + (fz                   *numYVertices+fy)*numXEdges + fx;
    702:           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
    703:           PetscInt ornt[4] = {0, 0, -2, -2};
    704:           PetscInt cone[4];

    706:           if (dim == 3) {
    707:             /* markers */
    708:             if (bdY != DM_BOUNDARY_PERIODIC) {
    709:               if (fy == numYVertices-1) {
    710:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);
    711:                 DMSetLabelValue(dm, "marker", face, markerBack);
    712:               }
    713:               else if (fy == 0) {
    714:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);
    715:                 DMSetLabelValue(dm, "marker", face, markerFront);
    716:               }
    717:             }
    718:           }
    719:           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
    720:           DMPlexSetCone(dm, face, cone);
    721:           DMPlexSetConeOrientation(dm, face, ornt);
    722:         }
    723:       }
    724:     }
    725:     /* Build z faces */
    726:     for (fy = 0; fy < numYEdges; ++fy) {
    727:       for (fx = 0; fx < numXEdges; ++fx) {
    728:         for (fz = 0; fz < numZVertices; fz++) {
    729:           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
    730:           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx)*numYEdges + fy;
    731:           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
    732:           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy)*numXEdges + fx;
    733:           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
    734:           PetscInt ornt[4] = {0, 0, -2, -2};
    735:           PetscInt cone[4];

    737:           if (dim == 2) {
    738:             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
    739:             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
    740:             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, face, 2);}
    741:             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {DMLabelSetValue(cutLabel, face, 2);}
    742:           } else {
    743:             /* markers */
    744:             if (bdZ != DM_BOUNDARY_PERIODIC) {
    745:               if (fz == numZVertices-1) {
    746:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);
    747:                 DMSetLabelValue(dm, "marker", face, markerTop);
    748:               }
    749:               else if (fz == 0) {
    750:                 DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);
    751:                 DMSetLabelValue(dm, "marker", face, markerBottom);
    752:               }
    753:             }
    754:           }
    755:           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
    756:           DMPlexSetCone(dm, face, cone);
    757:           DMPlexSetConeOrientation(dm, face, ornt);
    758:         }
    759:       }
    760:     }
    761:     /* Build Z edges*/
    762:     for (vy = 0; vy < numYVertices; vy++) {
    763:       for (vx = 0; vx < numXVertices; vx++) {
    764:         for (ez = 0; ez < numZEdges; ez++) {
    765:           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
    766:           const PetscInt vertexB = firstVertex + (ez                   *numYVertices+vy)*numXVertices + vx;
    767:           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
    768:           PetscInt       cone[2];

    770:           if (dim == 3) {
    771:             if (bdX != DM_BOUNDARY_PERIODIC) {
    772:               if (vx == numXVertices-1) {
    773:                 DMSetLabelValue(dm, "marker", edge, markerRight);
    774:               }
    775:               else if (vx == 0) {
    776:                 DMSetLabelValue(dm, "marker", edge, markerLeft);
    777:               }
    778:             }
    779:             if (bdY != DM_BOUNDARY_PERIODIC) {
    780:               if (vy == numYVertices-1) {
    781:                 DMSetLabelValue(dm, "marker", edge, markerBack);
    782:               }
    783:               else if (vy == 0) {
    784:                 DMSetLabelValue(dm, "marker", edge, markerFront);
    785:               }
    786:             }
    787:           }
    788:           cone[0] = vertexB; cone[1] = vertexT;
    789:           DMPlexSetCone(dm, edge, cone);
    790:         }
    791:       }
    792:     }
    793:     /* Build Y edges*/
    794:     for (vz = 0; vz < numZVertices; vz++) {
    795:       for (vx = 0; vx < numXVertices; vx++) {
    796:         for (ey = 0; ey < numYEdges; ey++) {
    797:           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
    798:           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
    799:           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
    800:           const PetscInt vertexK = firstVertex + nextv;
    801:           PetscInt       cone[2];

    803:           cone[0] = vertexF; cone[1] = vertexK;
    804:           DMPlexSetCone(dm, edge, cone);
    805:           if (dim == 2) {
    806:             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
    807:               if (vx == numXVertices-1) {
    808:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);
    809:                 DMSetLabelValue(dm, "marker", edge,    markerRight);
    810:                 DMSetLabelValue(dm, "marker", cone[0], markerRight);
    811:                 if (ey == numYEdges-1) {
    812:                   DMSetLabelValue(dm, "marker", cone[1], markerRight);
    813:                 }
    814:               } else if (vx == 0) {
    815:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);
    816:                 DMSetLabelValue(dm, "marker", edge,    markerLeft);
    817:                 DMSetLabelValue(dm, "marker", cone[0], markerLeft);
    818:                 if (ey == numYEdges-1) {
    819:                   DMSetLabelValue(dm, "marker", cone[1], markerLeft);
    820:                 }
    821:               }
    822:             } else {
    823:               if (vx == 0 && cutLabel) {
    824:                 DMLabelSetValue(cutLabel, edge,    1);
    825:                 DMLabelSetValue(cutLabel, cone[0], 1);
    826:                 if (ey == numYEdges-1) {
    827:                   DMLabelSetValue(cutLabel, cone[1], 1);
    828:                 }
    829:               }
    830:             }
    831:           } else {
    832:             if (bdX != DM_BOUNDARY_PERIODIC) {
    833:               if (vx == numXVertices-1) {
    834:                 DMSetLabelValue(dm, "marker", edge, markerRight);
    835:               } else if (vx == 0) {
    836:                 DMSetLabelValue(dm, "marker", edge, markerLeft);
    837:               }
    838:             }
    839:             if (bdZ != DM_BOUNDARY_PERIODIC) {
    840:               if (vz == numZVertices-1) {
    841:                 DMSetLabelValue(dm, "marker", edge, markerTop);
    842:               } else if (vz == 0) {
    843:                 DMSetLabelValue(dm, "marker", edge, markerBottom);
    844:               }
    845:             }
    846:           }
    847:         }
    848:       }
    849:     }
    850:     /* Build X edges*/
    851:     for (vz = 0; vz < numZVertices; vz++) {
    852:       for (vy = 0; vy < numYVertices; vy++) {
    853:         for (ex = 0; ex < numXEdges; ex++) {
    854:           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
    855:           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
    856:           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
    857:           const PetscInt vertexR = firstVertex + nextv;
    858:           PetscInt       cone[2];

    860:           cone[0] = vertexL; cone[1] = vertexR;
    861:           DMPlexSetCone(dm, edge, cone);
    862:           if (dim == 2) {
    863:             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
    864:               if (vy == numYVertices-1) {
    865:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);
    866:                 DMSetLabelValue(dm, "marker", edge,    markerTop);
    867:                 DMSetLabelValue(dm, "marker", cone[0], markerTop);
    868:                 if (ex == numXEdges-1) {
    869:                   DMSetLabelValue(dm, "marker", cone[1], markerTop);
    870:                 }
    871:               } else if (vy == 0) {
    872:                 DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);
    873:                 DMSetLabelValue(dm, "marker", edge,    markerBottom);
    874:                 DMSetLabelValue(dm, "marker", cone[0], markerBottom);
    875:                 if (ex == numXEdges-1) {
    876:                   DMSetLabelValue(dm, "marker", cone[1], markerBottom);
    877:                 }
    878:               }
    879:             } else {
    880:               if (vy == 0 && cutLabel) {
    881:                 DMLabelSetValue(cutLabel, edge,    1);
    882:                 DMLabelSetValue(cutLabel, cone[0], 1);
    883:                 if (ex == numXEdges-1) {
    884:                   DMLabelSetValue(cutLabel, cone[1], 1);
    885:                 }
    886:               }
    887:             }
    888:           } else {
    889:             if (bdY != DM_BOUNDARY_PERIODIC) {
    890:               if (vy == numYVertices-1) {
    891:                 DMSetLabelValue(dm, "marker", edge, markerBack);
    892:               }
    893:               else if (vy == 0) {
    894:                 DMSetLabelValue(dm, "marker", edge, markerFront);
    895:               }
    896:             }
    897:             if (bdZ != DM_BOUNDARY_PERIODIC) {
    898:               if (vz == numZVertices-1) {
    899:                 DMSetLabelValue(dm, "marker", edge, markerTop);
    900:               }
    901:               else if (vz == 0) {
    902:                 DMSetLabelValue(dm, "marker", edge, markerBottom);
    903:               }
    904:             }
    905:           }
    906:         }
    907:       }
    908:     }
    909:     DMPlexSymmetrize(dm);
    910:     DMPlexStratify(dm);
    911:     /* Build coordinates */
    912:     DMGetCoordinateSection(dm, &coordSection);
    913:     PetscSectionSetNumFields(coordSection, 1);
    914:     PetscSectionSetFieldComponents(coordSection, 0, dim);
    915:     PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);
    916:     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
    917:       PetscSectionSetDof(coordSection, v, dim);
    918:       PetscSectionSetFieldDof(coordSection, v, 0, dim);
    919:     }
    920:     PetscSectionSetUp(coordSection);
    921:     PetscSectionGetStorageSize(coordSection, &coordSize);
    922:     VecCreate(PETSC_COMM_SELF, &coordinates);
    923:     PetscObjectSetName((PetscObject) coordinates, "coordinates");
    924:     VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    925:     VecSetBlockSize(coordinates, dim);
    926:     VecSetType(coordinates,VECSTANDARD);
    927:     VecGetArray(coordinates, &coords);
    928:     for (vz = 0; vz < numZVertices; ++vz) {
    929:       for (vy = 0; vy < numYVertices; ++vy) {
    930:         for (vx = 0; vx < numXVertices; ++vx) {
    931:           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
    932:           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
    933:           if (dim == 3) {
    934:             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
    935:           }
    936:         }
    937:       }
    938:     }
    939:     VecRestoreArray(coordinates, &coords);
    940:     DMSetCoordinatesLocal(dm, coordinates);
    941:     VecDestroy(&coordinates);
    942:   }
    943:   return(0);
    944: }

    946: 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)
    947: {
    948:   PetscInt       i;

    953:   DMCreate(comm, dm);
    955:   DMSetType(*dm, DMPLEX);
    956:   DMSetDimension(*dm, dim);
    957:   switch (dim) {
    958:   case 2: {DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], DM_BOUNDARY_NONE);break;}
    959:   case 3: {DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], periodicity[2]);break;}
    960:   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %D", dim);
    961:   }
    962:   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
    963:       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
    964:       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
    965:     PetscReal L[3];
    966:     PetscReal maxCell[3];

    968:     for (i = 0; i < dim; i++) {
    969:       L[i]       = upper[i] - lower[i];
    970:       maxCell[i] = 1.1 * (L[i] / PetscMax(1,faces[i]));
    971:     }
    972:     DMSetPeriodicity(*dm,PETSC_TRUE,maxCell,L,periodicity);
    973:   }
    974:   if (!interpolate) {
    975:     DM udm;

    977:     DMPlexUninterpolate(*dm, &udm);
    978:     DMPlexCopyCoordinates(*dm, udm);
    979:     DMDestroy(dm);
    980:     *dm  = udm;
    981:   }
    982:   return(0);
    983: }

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

    988:   Collective

    990:   Input Parameters:
    991: + comm        - The communicator for the DM object
    992: . dim         - The spatial dimension
    993: . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
    994: . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
    995: . lower       - The lower left corner, or NULL for (0, 0, 0)
    996: . upper       - The upper right corner, or NULL for (1, 1, 1)
    997: . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
    998: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    1000:   Output Parameter:
    1001: . dm  - The DM object

    1003:   Options Database Keys:
    1004:   These options override the hard-wired input values.
    1005: + -dm_plex_box_dim <dim>          - Set the topological dimension
    1006: . -dm_plex_box_simplex <bool>     - PETSC_TRUE for simplex elements, PETSC_FALSE for tensor elements
    1007: . -dm_plex_box_lower <x,y,z>      - Specify lower-left-bottom coordinates for the box
    1008: . -dm_plex_box_upper <x,y,z>      - Specify upper-right-top coordinates for the box
    1009: . -dm_plex_box_faces <m,n,p>      - Number of faces in each linear direction
    1010: . -dm_plex_box_bd <bx,by,bz>      - Specify the DMBoundaryType for each direction
    1011: - -dm_plex_box_interpolate <bool> - PETSC_TRUE turns on topological interpolation (creating edges and faces)

    1013:   Notes:
    1014:   The options database keys above take lists of length d in d dimensions.

    1016:   Here is the numbering returned for 2 faces in each direction for tensor cells:
    1017: $ 10---17---11---18----12
    1018: $  |         |         |
    1019: $  |         |         |
    1020: $ 20    2   22    3    24
    1021: $  |         |         |
    1022: $  |         |         |
    1023: $  7---15----8---16----9
    1024: $  |         |         |
    1025: $  |         |         |
    1026: $ 19    0   21    1   23
    1027: $  |         |         |
    1028: $  |         |         |
    1029: $  4---13----5---14----6

    1031: and for simplicial cells

    1033: $ 14----8---15----9----16
    1034: $  |\     5  |\      7 |
    1035: $  | \       | \       |
    1036: $ 13   2    14    3    15
    1037: $  | 4   \   | 6   \   |
    1038: $  |       \ |       \ |
    1039: $ 11----6---12----7----13
    1040: $  |\        |\        |
    1041: $  | \    1  | \     3 |
    1042: $ 10   0    11    1    12
    1043: $  | 0   \   | 2   \   |
    1044: $  |       \ |       \ |
    1045: $  8----4----9----5----10

    1047:   Level: beginner

    1049: .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
    1050: @*/
    1051: 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)
    1052: {
    1053:   PetscInt       fac[3] = {0, 0, 0};
    1054:   PetscReal      low[3] = {0, 0, 0};
    1055:   PetscReal      upp[3] = {1, 1, 1};
    1056:   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
    1057:   PetscInt       i, n;
    1058:   PetscBool      flg;

    1062:   PetscOptionsGetInt(NULL, NULL, "-dm_plex_box_dim", &dim, &flg);
    1063:   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
    1064:   PetscOptionsGetBool(NULL, NULL, "-dm_plex_box_simplex", &simplex, &flg);
    1065:   n    = dim;
    1066:   PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", fac, &n, &flg);
    1067:   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (flg && i < n ? fac[i] : (dim == 1 ? 1 : 4-dim));
    1068:   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
    1069:   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
    1070:   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
    1071:   /* Allow bounds to be specified from the command line */
    1072:   n    = 3;
    1073:   PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_lower", low, &n, &flg);
    1074:   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
    1075:   n    = 3;
    1076:   PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_upper", upp, &n, &flg);
    1077:   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
    1078:   n    = 3;
    1079:   PetscOptionsGetEnumArray(NULL, NULL, "-dm_plex_box_bd", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);
    1080:   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
    1081:   PetscOptionsGetBool(NULL, NULL, "-dm_plex_box_interpolate", &interpolate, &flg);

    1083:   if (dim == 1)      {DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);}
    1084:   else if (simplex)  {DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);}
    1085:   else               {DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);}
    1086:   return(0);
    1087: }

    1089: /*@
    1090:   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.

    1092:   Collective

    1094:   Input Parameters:
    1095: + comm        - The communicator for the DM object
    1096: . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
    1097: . lower       - The lower left corner, or NULL for (0, 0, 0)
    1098: . upper       - The upper right corner, or NULL for (1, 1, 1)
    1099: . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
    1100: . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
    1101: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    1103:   Output Parameter:
    1104: . dm  - The DM object

    1106:   Level: beginner

    1108: .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMPlexExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1109: @*/
    1110: PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
    1111: {
    1112:   DM             bdm, botdm;
    1113:   PetscInt       i;
    1114:   PetscInt       fac[3] = {0, 0, 0};
    1115:   PetscReal      low[3] = {0, 0, 0};
    1116:   PetscReal      upp[3] = {1, 1, 1};
    1117:   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};

    1121:   for (i = 0; i < 3; ++i) fac[i] = faces ? (faces[i] > 0 ? faces[i] : 1) : 1;
    1122:   if (lower) for (i = 0; i < 3; ++i) low[i] = lower[i];
    1123:   if (upper) for (i = 0; i < 3; ++i) upp[i] = upper[i];
    1124:   if (periodicity) for (i = 0; i < 3; ++i) bdt[i] = periodicity[i];
    1125:   for (i = 0; i < 3; ++i) if (bdt[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity not yet supported");

    1127:   DMCreate(comm, &bdm);
    1128:   DMSetType(bdm, DMPLEX);
    1129:   DMSetDimension(bdm, 1);
    1130:   DMSetCoordinateDim(bdm, 2);
    1131:   DMPlexCreateSquareBoundary(bdm, low, upp, fac);
    1132:   DMPlexGenerate(bdm, NULL, PETSC_FALSE, &botdm);
    1133:   DMDestroy(&bdm);
    1134:   DMPlexExtrude(botdm, fac[2], upp[2] - low[2], orderHeight, NULL, interpolate, dm);
    1135:   if (low[2] != 0.0) {
    1136:     Vec         v;
    1137:     PetscScalar *x;
    1138:     PetscInt    cDim, n;

    1140:     DMGetCoordinatesLocal(*dm, &v);
    1141:     VecGetBlockSize(v, &cDim);
    1142:     VecGetLocalSize(v, &n);
    1143:     VecGetArray(v, &x);
    1144:     x   += cDim;
    1145:     for (i=0; i<n; i+=cDim) x[i] += low[2];
    1146:     VecRestoreArray(v,&x);
    1147:     DMSetCoordinatesLocal(*dm, v);
    1148:   }
    1149:   DMDestroy(&botdm);
    1150:   return(0);
    1151: }

    1153: /*@C
    1154:   DMPlexExtrude - Creates a (d+1)-D mesh by extruding a d-D mesh in the normal direction using prismatic cells.

    1156:   Collective on idm

    1158:   Input Parameters:
    1159: + idm         - The mesh to be extruded
    1160: . layers      - The number of layers, or PETSC_DETERMINE to use the default
    1161: . height      - The total height of the extrusion, or PETSC_DETERMINE to use the default
    1162: . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
    1163: . extNormal   - The normal direction in which the mesh should be extruded, or NULL to extrude using the surface normal
    1164: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    1166:   Output Parameter:
    1167: . dm  - The DM object

    1169:   Notes:
    1170:   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.

    1172:   Options Database Keys:
    1173: +   -dm_plex_extrude_layers <k> - Sets the number of layers k
    1174: .   -dm_plex_extrude_height <h> - Sets the total height of the extrusion
    1175: .   -dm_plex_extrude_heights <h0,h1,...> - Sets the height of each layer
    1176: .   -dm_plex_extrude_order_height - If true, order cells by height first
    1177: -   -dm_plex_extrude_normal <n0,...,nd> - Sets the normal vector along which to extrude

    1179:   Level: advanced

    1181: .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMSetType(), DMCreate()
    1182: @*/
    1183: PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool orderHeight, const PetscReal extNormal[], PetscBool interpolate, DM* dm)
    1184: {
    1185:   PetscScalar       *coordsB;
    1186:   const PetscScalar *coordsA;
    1187:   PetscReal         *normals = NULL, *heights = NULL;
    1188:   PetscReal         clNormal[3];
    1189:   Vec               coordinatesA, coordinatesB;
    1190:   PetscSection      coordSectionA, coordSectionB;
    1191:   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone, nl;
    1192:   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
    1193:   const char       *prefix;
    1194:   PetscBool         haveCLNormal, flg;
    1195:   PetscErrorCode    ierr;

    1202:   DMGetDimension(idm, &dim);
    1203:   DMGetCoordinateDim(idm, &cDim);
    1204:   cDimB = cDim == dim ? cDim+1 : cDim;
    1205:   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);

    1207:   PetscObjectGetOptionsPrefix((PetscObject) idm, &prefix);
    1208:   if (layers < 0) layers = 1;
    1209:   PetscOptionsGetInt(NULL, prefix, "-dm_plex_extrude_layers", &layers, NULL);
    1210:   if (layers <= 0) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Number of layers %D must be positive", layers);
    1211:   if (height < 0.) height = 1.;
    1212:   PetscOptionsGetReal(NULL, prefix, "-dm_plex_extrude_height", &height, NULL);
    1213:   if (height <= 0.) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Height of layers %g must be positive", (double) height);
    1214:   PetscMalloc1(layers, &heights);
    1215:   nl   = layers;
    1216:   PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_heights", heights, &nl, &flg);
    1217:   if (flg) {
    1218:     if (!nl) SETERRQ(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Must give at least one height for -dm_plex_extrude_heights");
    1219:     for (l = nl; l < layers; ++l) heights[l] = heights[l-1];
    1220:     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);
    1221:   } else {
    1222:     for (l = 0; l < layers; ++l) heights[l] = height/layers;
    1223:   }
    1224:   PetscOptionsGetBool(NULL, prefix, "-dm_plex_extrude_order_height", &orderHeight, NULL);
    1225:   c = 3;
    1226:   PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_normal", clNormal, &c, &haveCLNormal);
    1227:   if (haveCLNormal && c != cDimB) SETERRQ2(PetscObjectComm((PetscObject)idm), PETSC_ERR_ARG_SIZ, "Input normal has size %D != %D extruded coordinate dimension", c, cDimB);

    1229:   DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);
    1230:   DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);
    1231:   numCells = (cEnd - cStart)*layers;
    1232:   numVertices = (vEnd - vStart)*(layers+1);
    1233:   DMCreate(PetscObjectComm((PetscObject)idm), dm);
    1234:   DMSetType(*dm, DMPLEX);
    1235:   DMSetDimension(*dm, dim+1);
    1236:   DMPlexSetChart(*dm, 0, numCells+numVertices);
    1237:   /* Must create the celltype label here so that we do not automatically try to compute the types */
    1238:   DMCreateLabel(*dm, "celltype");
    1239:   for (c = cStart, cellV = 0; c < cEnd; ++c) {
    1240:     DMPolytopeType ct, nct;
    1241:     PetscInt      *closure = NULL;
    1242:     PetscInt       closureSize, numCorners = 0;

    1244:     DMPlexGetCellType(idm, c, &ct);
    1245:     switch (ct) {
    1246:       case DM_POLYTOPE_SEGMENT:       nct = DM_POLYTOPE_SEG_PRISM_TENSOR;break;
    1247:       case DM_POLYTOPE_TRIANGLE:      nct = DM_POLYTOPE_TRI_PRISM_TENSOR;break;
    1248:       case DM_POLYTOPE_QUADRILATERAL: nct = DM_POLYTOPE_QUAD_PRISM_TENSOR;break;
    1249:       default: nct = DM_POLYTOPE_UNKNOWN;
    1250:     }
    1251:     DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1252:     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
    1253:     DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1254:     for (l = 0; l < layers; ++l) {
    1255:       const PetscInt cell = orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart;

    1257:       DMPlexSetConeSize(*dm, cell, 2*numCorners);
    1258:       DMPlexSetCellType(*dm, cell, nct);
    1259:     }
    1260:     cellV = PetscMax(numCorners,cellV);
    1261:   }
    1262:   DMSetUp(*dm);

    1264:   if (dim != cDim && !(extNormal || haveCLNormal)) {PetscCalloc1(cDim*(vEnd - vStart), &normals);}
    1265:   PetscMalloc1(3*cellV,&newCone);
    1266:   for (c = cStart; c < cEnd; ++c) {
    1267:     PetscInt *closure = NULL;
    1268:     PetscInt closureSize, numCorners = 0, l;
    1269:     PetscReal normal[3] = {0, 0, 0};

    1271:     if (normals) {DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);}
    1272:     DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1273:     for (v = 0; v < closureSize*2; v += 2) {
    1274:       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
    1275:         PetscInt d;

    1277:         newCone[numCorners++] = closure[v] - vStart;
    1278:         if (normals) {for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d];}
    1279:       }
    1280:     }
    1281:     DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);
    1282:     for (l = 0; l < layers; ++l) {
    1283:       PetscInt i;

    1285:       for (i = 0; i < numCorners; ++i) {
    1286:         newCone[  numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
    1287:         newCone[2*numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
    1288:       }
    1289:       DMPlexSetCone(*dm, orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);
    1290:     }
    1291:   }
    1292:   DMPlexSymmetrize(*dm);
    1293:   DMPlexStratify(*dm);
    1294:   PetscFree(newCone);

    1296:   DMGetCoordinateSection(*dm, &coordSectionB);
    1297:   PetscSectionSetNumFields(coordSectionB, 1);
    1298:   PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);
    1299:   PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);
    1300:   for (v = numCells; v < numCells+numVertices; ++v) {
    1301:     PetscSectionSetDof(coordSectionB, v, cDimB);
    1302:     PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);
    1303:     DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);
    1304:   }
    1305:   PetscSectionSetUp(coordSectionB);
    1306:   PetscSectionGetStorageSize(coordSectionB, &coordSize);
    1307:   VecCreate(PETSC_COMM_SELF, &coordinatesB);
    1308:   PetscObjectSetName((PetscObject) coordinatesB, "coordinates");
    1309:   VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);
    1310:   VecSetBlockSize(coordinatesB, cDimB);
    1311:   VecSetType(coordinatesB,VECSTANDARD);

    1313:   DMGetCoordinateSection(idm, &coordSectionA);
    1314:   DMGetCoordinatesLocal(idm, &coordinatesA);
    1315:   VecGetArray(coordinatesB, &coordsB);
    1316:   VecGetArrayRead(coordinatesA, &coordsA);
    1317:   for (v = vStart; v < vEnd; ++v) {
    1318:     const PetscScalar *cptr;
    1319:     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
    1320:     PetscReal         normal[3];
    1321:     PetscReal         norm;
    1322:     PetscInt          offA, d, cDimA = cDim;

    1324:     if (normals)           {for (d = 0; d < cDimB; ++d) normal[d] = normals[cDimB*(v - vStart)+d];}
    1325:     else if (haveCLNormal) {for (d = 0; d < cDimB; ++d) normal[d] = clNormal[d];}
    1326:     else if (extNormal)    {for (d = 0; d < cDimB; ++d) normal[d] = extNormal[d];}
    1327:     else if (cDimB == 2)   {for (d = 0; d < cDimB; ++d) normal[d] = ones2[d];}
    1328:     else if (cDimB == 3)   {for (d = 0; d < cDimB; ++d) normal[d] = ones3[d];}
    1329:     else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unable to determine normal for extrusion");
    1330:     for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
    1331:     for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);

    1333:     PetscSectionGetOffset(coordSectionA, v, &offA);
    1334:     cptr = coordsA + offA;
    1335:     for (l = 0; l <= layers; ++l) {
    1336:       PetscInt offB, d, newV;

    1338:       newV = orderHeight ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
    1339:       PetscSectionGetOffset(coordSectionB, newV, &offB);
    1340:       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
    1341:       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*heights[l-1] : 0.0; }
    1342:       cptr    = coordsB + offB;
    1343:       cDimA   = cDimB;
    1344:     }
    1345:   }
    1346:   VecRestoreArrayRead(coordinatesA, &coordsA);
    1347:   VecRestoreArray(coordinatesB, &coordsB);
    1348:   DMSetCoordinatesLocal(*dm, coordinatesB);
    1349:   VecDestroy(&coordinatesB);
    1350:   PetscFree(normals);
    1351:   PetscFree(heights);
    1352:   if (interpolate) {
    1353:     DM idm;

    1355:     DMPlexInterpolate(*dm, &idm);
    1356:     DMPlexCopyCoordinates(*dm, idm);
    1357:     DMDestroy(dm);
    1358:     *dm  = idm;
    1359:   }
    1360:   return(0);
    1361: }

    1363: /*@C
    1364:   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.

    1366:   Logically Collective on dm

    1368:   Input Parameters:
    1369: + dm - the DM context
    1370: - prefix - the prefix to prepend to all option names

    1372:   Notes:
    1373:   A hyphen (-) must NOT be given at the beginning of the prefix name.
    1374:   The first character of all runtime options is AUTOMATICALLY the hyphen.

    1376:   Level: advanced

    1378: .seealso: SNESSetFromOptions()
    1379: @*/
    1380: PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
    1381: {
    1382:   DM_Plex       *mesh = (DM_Plex *) dm->data;

    1387:   PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);
    1388:   PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);
    1389:   return(0);
    1390: }

    1392: /*@
    1393:   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.

    1395:   Collective

    1397:   Input Parameters:
    1398: + comm      - The communicator for the DM object
    1399: . numRefine - The number of regular refinements to the basic 5 cell structure
    1400: - periodicZ - The boundary type for the Z direction

    1402:   Output Parameter:
    1403: . dm  - The DM object

    1405:   Options Database Keys:
    1406: These options override the hard-wired input values.
    1407: + -dm_plex_hex_cyl_refine <r> - Refine the sylinder r times
    1408: - -dm_plex_hex_cyl_bd <bz>    - Specify the DMBoundaryType in the z-direction

    1410:   Note:
    1411:   Here is the output numbering looking from the bottom of the cylinder:
    1412: $       17-----14
    1413: $        |     |
    1414: $        |  2  |
    1415: $        |     |
    1416: $ 17-----8-----7-----14
    1417: $  |     |     |     |
    1418: $  |  3  |  0  |  1  |
    1419: $  |     |     |     |
    1420: $ 19-----5-----6-----13
    1421: $        |     |
    1422: $        |  4  |
    1423: $        |     |
    1424: $       19-----13
    1425: $
    1426: $ and up through the top
    1427: $
    1428: $       18-----16
    1429: $        |     |
    1430: $        |  2  |
    1431: $        |     |
    1432: $ 18----10----11-----16
    1433: $  |     |     |     |
    1434: $  |  3  |  0  |  1  |
    1435: $  |     |     |     |
    1436: $ 20-----9----12-----15
    1437: $        |     |
    1438: $        |  4  |
    1439: $        |     |
    1440: $       20-----15

    1442:   Level: beginner

    1444: .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1445: @*/
    1446: PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
    1447: {
    1448:   const PetscInt dim = 3;
    1449:   PetscInt       numCells, numVertices, r;
    1450:   PetscMPIInt    rank;

    1455:   MPI_Comm_rank(comm, &rank);
    1456:   PetscOptionsGetInt(NULL, NULL, "-dm_plex_hex_cyl_refine", &numRefine, NULL);
    1457:   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
    1458:   PetscOptionsGetEnum(NULL, NULL, "-dm_plex_box_bd", DMBoundaryTypes, (PetscEnum *) &periodicZ, NULL);
    1459:   DMCreate(comm, dm);
    1460:   DMSetType(*dm, DMPLEX);
    1461:   DMSetDimension(*dm, dim);
    1462:   /* Create topology */
    1463:   {
    1464:     PetscInt cone[8], c;

    1466:     numCells    = !rank ?  5 : 0;
    1467:     numVertices = !rank ? 16 : 0;
    1468:     if (periodicZ == DM_BOUNDARY_PERIODIC) {
    1469:       numCells   *= 3;
    1470:       numVertices = !rank ? 24 : 0;
    1471:     }
    1472:     DMPlexSetChart(*dm, 0, numCells+numVertices);
    1473:     for (c = 0; c < numCells; c++) {DMPlexSetConeSize(*dm, c, 8);}
    1474:     DMSetUp(*dm);
    1475:     if (!rank) {
    1476:       if (periodicZ == DM_BOUNDARY_PERIODIC) {
    1477:         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
    1478:         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
    1479:         DMPlexSetCone(*dm, 0, cone);
    1480:         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
    1481:         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
    1482:         DMPlexSetCone(*dm, 1, cone);
    1483:         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
    1484:         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
    1485:         DMPlexSetCone(*dm, 2, cone);
    1486:         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
    1487:         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
    1488:         DMPlexSetCone(*dm, 3, cone);
    1489:         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
    1490:         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
    1491:         DMPlexSetCone(*dm, 4, cone);

    1493:         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
    1494:         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
    1495:         DMPlexSetCone(*dm, 5, cone);
    1496:         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
    1497:         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
    1498:         DMPlexSetCone(*dm, 6, cone);
    1499:         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
    1500:         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
    1501:         DMPlexSetCone(*dm, 7, cone);
    1502:         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
    1503:         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
    1504:         DMPlexSetCone(*dm, 8, cone);
    1505:         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
    1506:         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
    1507:         DMPlexSetCone(*dm, 9, cone);

    1509:         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
    1510:         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
    1511:         DMPlexSetCone(*dm, 10, cone);
    1512:         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
    1513:         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
    1514:         DMPlexSetCone(*dm, 11, cone);
    1515:         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
    1516:         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
    1517:         DMPlexSetCone(*dm, 12, cone);
    1518:         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
    1519:         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
    1520:         DMPlexSetCone(*dm, 13, cone);
    1521:         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
    1522:         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
    1523:         DMPlexSetCone(*dm, 14, cone);
    1524:       } else {
    1525:         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
    1526:         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
    1527:         DMPlexSetCone(*dm, 0, cone);
    1528:         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
    1529:         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
    1530:         DMPlexSetCone(*dm, 1, cone);
    1531:         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
    1532:         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
    1533:         DMPlexSetCone(*dm, 2, cone);
    1534:         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
    1535:         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
    1536:         DMPlexSetCone(*dm, 3, cone);
    1537:         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
    1538:         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
    1539:         DMPlexSetCone(*dm, 4, cone);
    1540:       }
    1541:     }
    1542:     DMPlexSymmetrize(*dm);
    1543:     DMPlexStratify(*dm);
    1544:   }
    1545:   /* Interpolate */
    1546:   {
    1547:     DM idm;

    1549:     DMPlexInterpolate(*dm, &idm);
    1550:     DMDestroy(dm);
    1551:     *dm  = idm;
    1552:   }
    1553:   /* Create cube geometry */
    1554:   {
    1555:     Vec             coordinates;
    1556:     PetscSection    coordSection;
    1557:     PetscScalar    *coords;
    1558:     PetscInt        coordSize, v;
    1559:     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
    1560:     const PetscReal ds2 = dis/2.0;

    1562:     /* Build coordinates */
    1563:     DMGetCoordinateSection(*dm, &coordSection);
    1564:     PetscSectionSetNumFields(coordSection, 1);
    1565:     PetscSectionSetFieldComponents(coordSection, 0, dim);
    1566:     PetscSectionSetChart(coordSection, numCells, numCells+numVertices);
    1567:     for (v = numCells; v < numCells+numVertices; ++v) {
    1568:       PetscSectionSetDof(coordSection, v, dim);
    1569:       PetscSectionSetFieldDof(coordSection, v, 0, dim);
    1570:     }
    1571:     PetscSectionSetUp(coordSection);
    1572:     PetscSectionGetStorageSize(coordSection, &coordSize);
    1573:     VecCreate(PETSC_COMM_SELF, &coordinates);
    1574:     PetscObjectSetName((PetscObject) coordinates, "coordinates");
    1575:     VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    1576:     VecSetBlockSize(coordinates, dim);
    1577:     VecSetType(coordinates,VECSTANDARD);
    1578:     VecGetArray(coordinates, &coords);
    1579:     if (!rank) {
    1580:       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
    1581:       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
    1582:       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
    1583:       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
    1584:       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
    1585:       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
    1586:       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
    1587:       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
    1588:       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
    1589:       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
    1590:       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
    1591:       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
    1592:       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
    1593:       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
    1594:       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
    1595:       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
    1596:       if (periodicZ == DM_BOUNDARY_PERIODIC) {
    1597:         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
    1598:         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
    1599:         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
    1600:         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
    1601:         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
    1602:         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
    1603:         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
    1604:         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
    1605:       }
    1606:     }
    1607:     VecRestoreArray(coordinates, &coords);
    1608:     DMSetCoordinatesLocal(*dm, coordinates);
    1609:     VecDestroy(&coordinates);
    1610:   }
    1611:   /* Create periodicity */
    1612:   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
    1613:     PetscReal      L[3];
    1614:     PetscReal      maxCell[3];
    1615:     DMBoundaryType bdType[3];
    1616:     PetscReal      lower[3] = {0.0, 0.0, 0.0};
    1617:     PetscReal      upper[3] = {1.0, 1.0, 1.5};
    1618:     PetscInt       i, numZCells = 3;

    1620:     bdType[0] = DM_BOUNDARY_NONE;
    1621:     bdType[1] = DM_BOUNDARY_NONE;
    1622:     bdType[2] = periodicZ;
    1623:     for (i = 0; i < dim; i++) {
    1624:       L[i]       = upper[i] - lower[i];
    1625:       maxCell[i] = 1.1 * (L[i] / numZCells);
    1626:     }
    1627:     DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);
    1628:   }
    1629:   /* Refine topology */
    1630:   for (r = 0; r < numRefine; ++r) {
    1631:     DM rdm = NULL;

    1633:     DMRefine(*dm, comm, &rdm);
    1634:     DMDestroy(dm);
    1635:     *dm  = rdm;
    1636:   }
    1637:   /* Remap geometry to cylinder
    1638:        Interior square: Linear interpolation is correct
    1639:        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
    1640:        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance

    1642:          phi     = arctan(y/x)
    1643:          d_close = sqrt(1/8 + 1/4 sin^2(phi))
    1644:          d_far   = sqrt(1/2 + sin^2(phi))

    1646:        so we remap them using

    1648:          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
    1649:          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)

    1651:        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
    1652:   */
    1653:   {
    1654:     Vec           coordinates;
    1655:     PetscSection  coordSection;
    1656:     PetscScalar  *coords;
    1657:     PetscInt      vStart, vEnd, v;
    1658:     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
    1659:     const PetscReal ds2 = 0.5*dis;

    1661:     DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);
    1662:     DMGetCoordinateSection(*dm, &coordSection);
    1663:     DMGetCoordinatesLocal(*dm, &coordinates);
    1664:     VecGetArray(coordinates, &coords);
    1665:     for (v = vStart; v < vEnd; ++v) {
    1666:       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
    1667:       PetscInt  off;

    1669:       PetscSectionGetOffset(coordSection, v, &off);
    1670:       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
    1671:       x    = PetscRealPart(coords[off]);
    1672:       y    = PetscRealPart(coords[off+1]);
    1673:       phi  = PetscAtan2Real(y, x);
    1674:       sinp = PetscSinReal(phi);
    1675:       cosp = PetscCosReal(phi);
    1676:       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
    1677:         dc = PetscAbsReal(ds2/sinp);
    1678:         df = PetscAbsReal(dis/sinp);
    1679:         xc = ds2*x/PetscAbsReal(y);
    1680:         yc = ds2*PetscSignReal(y);
    1681:       } else {
    1682:         dc = PetscAbsReal(ds2/cosp);
    1683:         df = PetscAbsReal(dis/cosp);
    1684:         xc = ds2*PetscSignReal(x);
    1685:         yc = ds2*y/PetscAbsReal(x);
    1686:       }
    1687:       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
    1688:       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
    1689:     }
    1690:     VecRestoreArray(coordinates, &coords);
    1691:     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
    1692:       DMLocalizeCoordinates(*dm);
    1693:     }
    1694:   }
    1695:   return(0);
    1696: }

    1698: /*@
    1699:   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.

    1701:   Collective

    1703:   Input Parameters:
    1704: + comm - The communicator for the DM object
    1705: . n    - The number of wedges around the origin
    1706: - interpolate - Create edges and faces

    1708:   Output Parameter:
    1709: . dm  - The DM object

    1711:   Level: beginner

    1713: .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1714: @*/
    1715: PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
    1716: {
    1717:   const PetscInt dim = 3;
    1718:   PetscInt       numCells, numVertices, v;
    1719:   PetscMPIInt    rank;

    1724:   MPI_Comm_rank(comm, &rank);
    1725:   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
    1726:   DMCreate(comm, dm);
    1727:   DMSetType(*dm, DMPLEX);
    1728:   DMSetDimension(*dm, dim);
    1729:   /* Must create the celltype label here so that we do not automatically try to compute the types */
    1730:   DMCreateLabel(*dm, "celltype");
    1731:   /* Create topology */
    1732:   {
    1733:     PetscInt cone[6], c;

    1735:     numCells    = !rank ?        n : 0;
    1736:     numVertices = !rank ?  2*(n+1) : 0;
    1737:     DMPlexSetChart(*dm, 0, numCells+numVertices);
    1738:     for (c = 0; c < numCells; c++) {DMPlexSetConeSize(*dm, c, 6);}
    1739:     DMSetUp(*dm);
    1740:     for (c = 0; c < numCells; c++) {
    1741:       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
    1742:       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
    1743:       DMPlexSetCone(*dm, c, cone);
    1744:       DMPlexSetCellType(*dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);
    1745:     }
    1746:     DMPlexSymmetrize(*dm);
    1747:     DMPlexStratify(*dm);
    1748:   }
    1749:   for (v = numCells; v < numCells+numVertices; ++v) {
    1750:     DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);
    1751:   }
    1752:   /* Interpolate */
    1753:   if (interpolate) {
    1754:     DM idm;

    1756:     DMPlexInterpolate(*dm, &idm);
    1757:     DMDestroy(dm);
    1758:     *dm  = idm;
    1759:   }
    1760:   /* Create cylinder geometry */
    1761:   {
    1762:     Vec          coordinates;
    1763:     PetscSection coordSection;
    1764:     PetscScalar *coords;
    1765:     PetscInt     coordSize, c;

    1767:     /* Build coordinates */
    1768:     DMGetCoordinateSection(*dm, &coordSection);
    1769:     PetscSectionSetNumFields(coordSection, 1);
    1770:     PetscSectionSetFieldComponents(coordSection, 0, dim);
    1771:     PetscSectionSetChart(coordSection, numCells, numCells+numVertices);
    1772:     for (v = numCells; v < numCells+numVertices; ++v) {
    1773:       PetscSectionSetDof(coordSection, v, dim);
    1774:       PetscSectionSetFieldDof(coordSection, v, 0, dim);
    1775:     }
    1776:     PetscSectionSetUp(coordSection);
    1777:     PetscSectionGetStorageSize(coordSection, &coordSize);
    1778:     VecCreate(PETSC_COMM_SELF, &coordinates);
    1779:     PetscObjectSetName((PetscObject) coordinates, "coordinates");
    1780:     VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    1781:     VecSetBlockSize(coordinates, dim);
    1782:     VecSetType(coordinates,VECSTANDARD);
    1783:     VecGetArray(coordinates, &coords);
    1784:     for (c = 0; c < numCells; c++) {
    1785:       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;
    1786:       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;
    1787:     }
    1788:     if (!rank) {
    1789:       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
    1790:       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
    1791:     }
    1792:     VecRestoreArray(coordinates, &coords);
    1793:     DMSetCoordinatesLocal(*dm, coordinates);
    1794:     VecDestroy(&coordinates);
    1795:   }
    1796:   return(0);
    1797: }

    1799: PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
    1800: {
    1801:   PetscReal prod = 0.0;
    1802:   PetscInt  i;
    1803:   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
    1804:   return PetscSqrtReal(prod);
    1805: }
    1806: PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
    1807: {
    1808:   PetscReal prod = 0.0;
    1809:   PetscInt  i;
    1810:   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
    1811:   return prod;
    1812: }

    1814: /* The first constant is the sphere radius */
    1815: static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    1816:                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    1817:                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    1818:                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    1819: {
    1820:   PetscReal r = PetscRealPart(constants[0]);
    1821:   PetscReal norm2 = 0.0, fac;
    1822:   PetscInt  n = uOff[1] - uOff[0], d;

    1824:   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
    1825:   fac = r/PetscSqrtReal(norm2);
    1826:   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
    1827: }

    1829: /*@
    1830:   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.

    1832:   Collective

    1834:   Input Parameters:
    1835: + comm    - The communicator for the DM object
    1836: . dim     - The dimension
    1837: . simplex - Use simplices, or tensor product cells
    1838: - R       - The radius

    1840:   Output Parameter:
    1841: . dm  - The DM object

    1843:   Level: beginner

    1845: .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    1846: @*/
    1847: PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
    1848: {
    1849:   const PetscInt  embedDim = dim+1;
    1850:   PetscSection    coordSection;
    1851:   Vec             coordinates;
    1852:   PetscScalar    *coords;
    1853:   PetscReal      *coordsIn;
    1854:   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
    1855:   PetscMPIInt     rank;
    1856:   PetscErrorCode  ierr;

    1860:   DMCreate(comm, dm);
    1861:   DMSetType(*dm, DMPLEX);
    1862:   DMSetDimension(*dm, dim);
    1863:   DMSetCoordinateDim(*dm, dim+1);
    1864:   MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);
    1865:   switch (dim) {
    1866:   case 2:
    1867:     if (simplex) {
    1868:       DM              idm;
    1869:       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
    1870:       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
    1871:       const PetscInt  degree    = 5;
    1872:       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
    1873:       PetscInt        s[3]      = {1, 1, 1};
    1874:       PetscInt        cone[3];
    1875:       PetscInt       *graph, p, i, j, k;

    1877:       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
    1878:       numCells    = !rank ? 20 : 0;
    1879:       numVerts    = !rank ? 12 : 0;
    1880:       firstVertex = numCells;
    1881:       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of

    1883:            (0, \pm 1/\phi+1, \pm \phi/\phi+1)

    1885:          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
    1886:          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
    1887:       */
    1888:       /* Construct vertices */
    1889:       PetscCalloc1(numVerts * embedDim, &coordsIn);
    1890:       if (!rank) {
    1891:         for (p = 0, i = 0; p < embedDim; ++p) {
    1892:           for (s[1] = -1; s[1] < 2; s[1] += 2) {
    1893:             for (s[2] = -1; s[2] < 2; s[2] += 2) {
    1894:               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
    1895:               ++i;
    1896:             }
    1897:           }
    1898:         }
    1899:       }
    1900:       /* Construct graph */
    1901:       PetscCalloc1(numVerts * numVerts, &graph);
    1902:       for (i = 0; i < numVerts; ++i) {
    1903:         for (j = 0, k = 0; j < numVerts; ++j) {
    1904:           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
    1905:         }
    1906:         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
    1907:       }
    1908:       /* Build Topology */
    1909:       DMPlexSetChart(*dm, 0, numCells+numVerts);
    1910:       for (c = 0; c < numCells; c++) {
    1911:         DMPlexSetConeSize(*dm, c, embedDim);
    1912:       }
    1913:       DMSetUp(*dm); /* Allocate space for cones */
    1914:       /* Cells */
    1915:       for (i = 0, c = 0; i < numVerts; ++i) {
    1916:         for (j = 0; j < i; ++j) {
    1917:           for (k = 0; k < j; ++k) {
    1918:             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
    1919:               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
    1920:               /* Check orientation */
    1921:               {
    1922:                 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}}};
    1923:                 PetscReal normal[3];
    1924:                 PetscInt  e, f;

    1926:                 for (d = 0; d < embedDim; ++d) {
    1927:                   normal[d] = 0.0;
    1928:                   for (e = 0; e < embedDim; ++e) {
    1929:                     for (f = 0; f < embedDim; ++f) {
    1930:                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
    1931:                     }
    1932:                   }
    1933:                 }
    1934:                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
    1935:               }
    1936:               DMPlexSetCone(*dm, c++, cone);
    1937:             }
    1938:           }
    1939:         }
    1940:       }
    1941:       DMPlexSymmetrize(*dm);
    1942:       DMPlexStratify(*dm);
    1943:       PetscFree(graph);
    1944:       /* Interpolate mesh */
    1945:       DMPlexInterpolate(*dm, &idm);
    1946:       DMDestroy(dm);
    1947:       *dm  = idm;
    1948:     } else {
    1949:       /*
    1950:         12-21--13
    1951:          |     |
    1952:         25  4  24
    1953:          |     |
    1954:   12-25--9-16--8-24--13
    1955:    |     |     |     |
    1956:   23  5 17  0 15  3  22
    1957:    |     |     |     |
    1958:   10-20--6-14--7-19--11
    1959:          |     |
    1960:         20  1  19
    1961:          |     |
    1962:         10-18--11
    1963:          |     |
    1964:         23  2  22
    1965:          |     |
    1966:         12-21--13
    1967:        */
    1968:       PetscInt cone[4], ornt[4];

    1970:       numCells    = !rank ?  6 : 0;
    1971:       numEdges    = !rank ? 12 : 0;
    1972:       numVerts    = !rank ?  8 : 0;
    1973:       firstVertex = numCells;
    1974:       firstEdge   = numCells + numVerts;
    1975:       /* Build Topology */
    1976:       DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);
    1977:       for (c = 0; c < numCells; c++) {
    1978:         DMPlexSetConeSize(*dm, c, 4);
    1979:       }
    1980:       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
    1981:         DMPlexSetConeSize(*dm, e, 2);
    1982:       }
    1983:       DMSetUp(*dm); /* Allocate space for cones */
    1984:       if (!rank) {
    1985:         /* Cell 0 */
    1986:         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
    1987:         DMPlexSetCone(*dm, 0, cone);
    1988:         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
    1989:         DMPlexSetConeOrientation(*dm, 0, ornt);
    1990:         /* Cell 1 */
    1991:         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
    1992:         DMPlexSetCone(*dm, 1, cone);
    1993:         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
    1994:         DMPlexSetConeOrientation(*dm, 1, ornt);
    1995:         /* Cell 2 */
    1996:         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
    1997:         DMPlexSetCone(*dm, 2, cone);
    1998:         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
    1999:         DMPlexSetConeOrientation(*dm, 2, ornt);
    2000:         /* Cell 3 */
    2001:         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
    2002:         DMPlexSetCone(*dm, 3, cone);
    2003:         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
    2004:         DMPlexSetConeOrientation(*dm, 3, ornt);
    2005:         /* Cell 4 */
    2006:         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
    2007:         DMPlexSetCone(*dm, 4, cone);
    2008:         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
    2009:         DMPlexSetConeOrientation(*dm, 4, ornt);
    2010:         /* Cell 5 */
    2011:         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
    2012:         DMPlexSetCone(*dm, 5, cone);
    2013:         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
    2014:         DMPlexSetConeOrientation(*dm, 5, ornt);
    2015:         /* Edges */
    2016:         cone[0] =  6; cone[1] =  7;
    2017:         DMPlexSetCone(*dm, 14, cone);
    2018:         cone[0] =  7; cone[1] =  8;
    2019:         DMPlexSetCone(*dm, 15, cone);
    2020:         cone[0] =  8; cone[1] =  9;
    2021:         DMPlexSetCone(*dm, 16, cone);
    2022:         cone[0] =  9; cone[1] =  6;
    2023:         DMPlexSetCone(*dm, 17, cone);
    2024:         cone[0] = 10; cone[1] = 11;
    2025:         DMPlexSetCone(*dm, 18, cone);
    2026:         cone[0] = 11; cone[1] =  7;
    2027:         DMPlexSetCone(*dm, 19, cone);
    2028:         cone[0] =  6; cone[1] = 10;
    2029:         DMPlexSetCone(*dm, 20, cone);
    2030:         cone[0] = 12; cone[1] = 13;
    2031:         DMPlexSetCone(*dm, 21, cone);
    2032:         cone[0] = 13; cone[1] = 11;
    2033:         DMPlexSetCone(*dm, 22, cone);
    2034:         cone[0] = 10; cone[1] = 12;
    2035:         DMPlexSetCone(*dm, 23, cone);
    2036:         cone[0] = 13; cone[1] =  8;
    2037:         DMPlexSetCone(*dm, 24, cone);
    2038:         cone[0] = 12; cone[1] =  9;
    2039:         DMPlexSetCone(*dm, 25, cone);
    2040:       }
    2041:       DMPlexSymmetrize(*dm);
    2042:       DMPlexStratify(*dm);
    2043:       /* Build coordinates */
    2044:       PetscCalloc1(numVerts * embedDim, &coordsIn);
    2045:       if (!rank) {
    2046:         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
    2047:         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
    2048:         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
    2049:         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
    2050:         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
    2051:         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
    2052:         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
    2053:         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
    2054:       }
    2055:     }
    2056:     break;
    2057:   case 3:
    2058:     if (simplex) {
    2059:       DM              idm;
    2060:       const PetscReal edgeLen         = 1.0/PETSC_PHI;
    2061:       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
    2062:       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
    2063:       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
    2064:       const PetscInt  degree          = 12;
    2065:       PetscInt        s[4]            = {1, 1, 1};
    2066:       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},
    2067:                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
    2068:       PetscInt        cone[4];
    2069:       PetscInt       *graph, p, i, j, k, l;

    2071:       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
    2072:       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
    2073:       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
    2074:       numCells    = !rank ? 600 : 0;
    2075:       numVerts    = !rank ? 120 : 0;
    2076:       firstVertex = numCells;
    2077:       /* Use the 600-cell, which for a unit sphere has coordinates which are

    2079:            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
    2080:                (\pm 1,    0,       0,      0)  all cyclic permutations   8
    2081:            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96

    2083:          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
    2084:          length is then given by 1/\phi = 0.61803.

    2086:          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
    2087:          http://mathworld.wolfram.com/600-Cell.html
    2088:       */
    2089:       /* Construct vertices */
    2090:       PetscCalloc1(numVerts * embedDim, &coordsIn);
    2091:       i    = 0;
    2092:       if (!rank) {
    2093:         for (s[0] = -1; s[0] < 2; s[0] += 2) {
    2094:           for (s[1] = -1; s[1] < 2; s[1] += 2) {
    2095:             for (s[2] = -1; s[2] < 2; s[2] += 2) {
    2096:               for (s[3] = -1; s[3] < 2; s[3] += 2) {
    2097:                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
    2098:                 ++i;
    2099:               }
    2100:             }
    2101:           }
    2102:         }
    2103:         for (p = 0; p < embedDim; ++p) {
    2104:           s[1] = s[2] = s[3] = 1;
    2105:           for (s[0] = -1; s[0] < 2; s[0] += 2) {
    2106:             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
    2107:             ++i;
    2108:           }
    2109:         }
    2110:         for (p = 0; p < 12; ++p) {
    2111:           s[3] = 1;
    2112:           for (s[0] = -1; s[0] < 2; s[0] += 2) {
    2113:             for (s[1] = -1; s[1] < 2; s[1] += 2) {
    2114:               for (s[2] = -1; s[2] < 2; s[2] += 2) {
    2115:                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
    2116:                 ++i;
    2117:               }
    2118:             }
    2119:           }
    2120:         }
    2121:       }
    2122:       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
    2123:       /* Construct graph */
    2124:       PetscCalloc1(numVerts * numVerts, &graph);
    2125:       for (i = 0; i < numVerts; ++i) {
    2126:         for (j = 0, k = 0; j < numVerts; ++j) {
    2127:           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
    2128:         }
    2129:         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
    2130:       }
    2131:       /* Build Topology */
    2132:       DMPlexSetChart(*dm, 0, numCells+numVerts);
    2133:       for (c = 0; c < numCells; c++) {
    2134:         DMPlexSetConeSize(*dm, c, embedDim);
    2135:       }
    2136:       DMSetUp(*dm); /* Allocate space for cones */
    2137:       /* Cells */
    2138:       if (!rank) {
    2139:         for (i = 0, c = 0; i < numVerts; ++i) {
    2140:           for (j = 0; j < i; ++j) {
    2141:             for (k = 0; k < j; ++k) {
    2142:               for (l = 0; l < k; ++l) {
    2143:                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
    2144:                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
    2145:                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
    2146:                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
    2147:                   {
    2148:                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2149:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
    2150:                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
    2151:                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},

    2153:                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
    2154:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2155:                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
    2156:                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},

    2158:                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
    2159:                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
    2160:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2161:                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},

    2163:                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
    2164:                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
    2165:                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
    2166:                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
    2167:                     PetscReal normal[4];
    2168:                     PetscInt  e, f, g;

    2170:                     for (d = 0; d < embedDim; ++d) {
    2171:                       normal[d] = 0.0;
    2172:                       for (e = 0; e < embedDim; ++e) {
    2173:                         for (f = 0; f < embedDim; ++f) {
    2174:                           for (g = 0; g < embedDim; ++g) {
    2175:                             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]);
    2176:                           }
    2177:                         }
    2178:                       }
    2179:                     }
    2180:                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
    2181:                   }
    2182:                   DMPlexSetCone(*dm, c++, cone);
    2183:                 }
    2184:               }
    2185:             }
    2186:           }
    2187:         }
    2188:       }
    2189:       DMPlexSymmetrize(*dm);
    2190:       DMPlexStratify(*dm);
    2191:       PetscFree(graph);
    2192:       /* Interpolate mesh */
    2193:       DMPlexInterpolate(*dm, &idm);
    2194:       DMDestroy(dm);
    2195:       *dm  = idm;
    2196:       break;
    2197:     }
    2198:   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
    2199:   }
    2200:   /* Create coordinates */
    2201:   DMGetCoordinateSection(*dm, &coordSection);
    2202:   PetscSectionSetNumFields(coordSection, 1);
    2203:   PetscSectionSetFieldComponents(coordSection, 0, embedDim);
    2204:   PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);
    2205:   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
    2206:     PetscSectionSetDof(coordSection, v, embedDim);
    2207:     PetscSectionSetFieldDof(coordSection, v, 0, embedDim);
    2208:   }
    2209:   PetscSectionSetUp(coordSection);
    2210:   PetscSectionGetStorageSize(coordSection, &coordSize);
    2211:   VecCreate(PETSC_COMM_SELF, &coordinates);
    2212:   VecSetBlockSize(coordinates, embedDim);
    2213:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    2214:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    2215:   VecSetType(coordinates,VECSTANDARD);
    2216:   VecGetArray(coordinates, &coords);
    2217:   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
    2218:   VecRestoreArray(coordinates, &coords);
    2219:   DMSetCoordinatesLocal(*dm, coordinates);
    2220:   VecDestroy(&coordinates);
    2221:   PetscFree(coordsIn);
    2222:   /* Create coordinate function space */
    2223:   {
    2224:     DM          cdm;
    2225:     PetscDS     cds;
    2226:     PetscFE     fe;
    2227:     PetscScalar radius = R;
    2228:     PetscInt    dT, dE;

    2230:     DMGetCoordinateDM(*dm, &cdm);
    2231:     DMGetDimension(*dm, &dT);
    2232:     DMGetCoordinateDim(*dm, &dE);
    2233:     PetscFECreateLagrange(PETSC_COMM_SELF, dT, dE, simplex, 1, -1, &fe);
    2234:     DMSetField(cdm, 0, NULL, (PetscObject) fe);
    2235:     PetscFEDestroy(&fe);
    2236:     DMCreateDS(cdm);

    2238:     DMGetDS(cdm, &cds);
    2239:     PetscDSSetConstants(cds, 1, &radius);
    2240:   }
    2241:   ((DM_Plex *) (*dm)->data)->coordFunc = snapToSphere;
    2242:   return(0);
    2243: }

    2245: /*@
    2246:   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.

    2248:   Collective

    2250:   Input Parameters:
    2251: + comm  - The communicator for the DM object
    2252: . dim   - The dimension
    2253: - R     - The radius

    2255:   Output Parameter:
    2256: . dm  - The DM object

    2258:   Options Database Keys:
    2259: - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry

    2261:   Level: beginner

    2263: .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
    2264: @*/
    2265: PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
    2266: {
    2267:   DM             sdm;
    2268:   DMLabel        bdlabel;

    2272:   DMPlexCreateSphereMesh(comm, dim-1, PETSC_TRUE, R, &sdm);
    2273:   PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");
    2274:   DMSetFromOptions(sdm);
    2275:   DMPlexGenerate(sdm, NULL, PETSC_TRUE, dm);
    2276:   DMDestroy(&sdm);
    2277:   DMCreateLabel(*dm, "marker");
    2278:   DMGetLabel(*dm, "marker", &bdlabel);
    2279:   DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);
    2280:   DMPlexLabelComplete(*dm, bdlabel);
    2281:   return(0);
    2282: }

    2284: /* External function declarations here */
    2285: extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
    2286: extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
    2287: extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
    2288: extern PetscErrorCode DMCreateLocalSection_Plex(DM dm);
    2289: extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
    2290: extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
    2291: extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
    2292: extern PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field);
    2293: PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
    2294: extern PetscErrorCode DMSetUp_Plex(DM dm);
    2295: extern PetscErrorCode DMDestroy_Plex(DM dm);
    2296: extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
    2297: extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
    2298: extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
    2299: extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
    2300: static PetscErrorCode DMInitialize_Plex(DM dm);

    2302: /* Replace dm with the contents of dmNew
    2303:    - Share the DM_Plex structure
    2304:    - Share the coordinates
    2305:    - Share the SF
    2306: */
    2307: static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
    2308: {
    2309:   PetscSF               sf;
    2310:   DM                    coordDM, coarseDM;
    2311:   DMField               coordField;
    2312:   Vec                   coords;
    2313:   PetscBool             isper;
    2314:   const PetscReal      *maxCell, *L;
    2315:   const DMBoundaryType *bd;
    2316:   PetscErrorCode        ierr;

    2319:   DMGetPointSF(dmNew, &sf);
    2320:   DMSetPointSF(dm, sf);
    2321:   DMGetCoordinateDM(dmNew, &coordDM);
    2322:   DMGetCoordinatesLocal(dmNew, &coords);
    2323:   DMGetCoordinateField(dmNew, &coordField);
    2324:   DMSetCoordinateDM(dm, coordDM);
    2325:   DMSetCoordinatesLocal(dm, coords);
    2326:   DMSetCoordinateField(dm, coordField);
    2327:   DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);
    2328:   DMSetPeriodicity(dmNew, isper, maxCell, L, bd);
    2329:   DMDestroy_Plex(dm);
    2330:   DMInitialize_Plex(dm);
    2331:   dm->data = dmNew->data;
    2332:   ((DM_Plex *) dmNew->data)->refct++;
    2333:   DMDestroyLabelLinkList_Internal(dm);
    2334:   DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE);
    2335:   DMGetCoarseDM(dmNew,&coarseDM);
    2336:   DMSetCoarseDM(dm,coarseDM);
    2337:   return(0);
    2338: }

    2340: /* Swap dm with the contents of dmNew
    2341:    - Swap the DM_Plex structure
    2342:    - Swap the coordinates
    2343:    - Swap the point PetscSF
    2344: */
    2345: static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
    2346: {
    2347:   DM              coordDMA, coordDMB;
    2348:   Vec             coordsA,  coordsB;
    2349:   PetscSF         sfA,      sfB;
    2350:   void            *tmp;
    2351:   DMLabelLink     listTmp;
    2352:   DMLabel         depthTmp;
    2353:   PetscInt        tmpI;
    2354:   PetscErrorCode  ierr;

    2357:   DMGetPointSF(dmA, &sfA);
    2358:   DMGetPointSF(dmB, &sfB);
    2359:   PetscObjectReference((PetscObject) sfA);
    2360:   DMSetPointSF(dmA, sfB);
    2361:   DMSetPointSF(dmB, sfA);
    2362:   PetscObjectDereference((PetscObject) sfA);

    2364:   DMGetCoordinateDM(dmA, &coordDMA);
    2365:   DMGetCoordinateDM(dmB, &coordDMB);
    2366:   PetscObjectReference((PetscObject) coordDMA);
    2367:   DMSetCoordinateDM(dmA, coordDMB);
    2368:   DMSetCoordinateDM(dmB, coordDMA);
    2369:   PetscObjectDereference((PetscObject) coordDMA);

    2371:   DMGetCoordinatesLocal(dmA, &coordsA);
    2372:   DMGetCoordinatesLocal(dmB, &coordsB);
    2373:   PetscObjectReference((PetscObject) coordsA);
    2374:   DMSetCoordinatesLocal(dmA, coordsB);
    2375:   DMSetCoordinatesLocal(dmB, coordsA);
    2376:   PetscObjectDereference((PetscObject) coordsA);

    2378:   tmp       = dmA->data;
    2379:   dmA->data = dmB->data;
    2380:   dmB->data = tmp;
    2381:   listTmp   = dmA->labels;
    2382:   dmA->labels = dmB->labels;
    2383:   dmB->labels = listTmp;
    2384:   depthTmp  = dmA->depthLabel;
    2385:   dmA->depthLabel = dmB->depthLabel;
    2386:   dmB->depthLabel = depthTmp;
    2387:   depthTmp  = dmA->celltypeLabel;
    2388:   dmA->celltypeLabel = dmB->celltypeLabel;
    2389:   dmB->celltypeLabel = depthTmp;
    2390:   tmpI         = dmA->levelup;
    2391:   dmA->levelup = dmB->levelup;
    2392:   dmB->levelup = tmpI;
    2393:   return(0);
    2394: }

    2396: PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
    2397: {
    2398:   DM_Plex       *mesh = (DM_Plex*) dm->data;
    2399:   PetscBool      flg;

    2403:   /* Handle viewing */
    2404:   PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);
    2405:   PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);
    2406:   PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);
    2407:   PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);
    2408:   DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);
    2409:   if (flg) {PetscLogDefaultBegin();}
    2410:   /* Point Location */
    2411:   PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);
    2412:   /* Partitioning and distribution */
    2413:   PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);
    2414:   /* Generation and remeshing */
    2415:   PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);
    2416:   /* Projection behavior */
    2417:   PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);
    2418:   PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);
    2419:   PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "ex40.c", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);
    2420:   /* Checking structure */
    2421:   {
    2422:     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;

    2424:     PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);
    2425:     PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);
    2426:     if (all || (flg && flg2)) {DMPlexCheckSymmetry(dm);}
    2427:     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);
    2428:     if (all || (flg && flg2)) {DMPlexCheckSkeleton(dm, 0);}
    2429:     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);
    2430:     if (all || (flg && flg2)) {DMPlexCheckFaces(dm, 0);}
    2431:     PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);
    2432:     if (all || (flg && flg2)) {DMPlexCheckGeometry(dm);}
    2433:     PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);
    2434:     if (all || (flg && flg2)) {DMPlexCheckPointSF(dm);}
    2435:     PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2);
    2436:     if (all || (flg && flg2)) {DMPlexCheckInterfaceCones(dm);}
    2437:     PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);
    2438:     if (flg && flg2) {DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);}
    2439:   }

    2441:   PetscPartitionerSetFromOptions(mesh->partitioner);
    2442:   return(0);
    2443: }

    2445: static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
    2446: {
    2447:   PetscReal      volume = -1.0;
    2448:   PetscInt       prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0;
    2449:   PetscBool      uniformOrig, uniform = PETSC_TRUE, distribute = PETSC_FALSE, isHierarchy, flg;

    2454:   PetscOptionsHead(PetscOptionsObject,"DMPlex Options");
    2455:   /* Handle DMPlex refinement before distribution */
    2456:   DMPlexGetRefinementUniform(dm, &uniformOrig);
    2457:   PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);
    2458:   if (flg) {DMPlexSetRefinementUniform(dm, uniform);}
    2459:   PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);
    2460:   if (flg) {DMPlexSetRefinementLimit(dm, volume);}
    2461:   PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);
    2462:   for (r = 0; r < prerefine; ++r) {
    2463:     DM             rdm;
    2464:     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;

    2466:     DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2467:     DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);
    2468:     /* Total hack since we do not pass in a pointer */
    2469:     DMPlexReplace_Static(dm, rdm);
    2470:     DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2471:     if (coordFunc) {
    2472:       DMPlexRemapGeometry(dm, 0.0, coordFunc);
    2473:       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
    2474:     }
    2475:     DMDestroy(&rdm);
    2476:   }
    2477:   DMPlexSetRefinementUniform(dm, uniformOrig);
    2478:   /* Handle DMPlex distribution */
    2479:   PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);
    2480:   PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);
    2481:   if (distribute) {
    2482:     DM               pdm = NULL;
    2483:     PetscPartitioner part;

    2485:     DMPlexGetPartitioner(dm, &part);
    2486:     PetscPartitionerSetFromOptions(part);
    2487:     DMPlexDistribute(dm, overlap, NULL, &pdm);
    2488:     if (pdm) {
    2489:       DMPlexReplace_Static(dm, pdm);
    2490:       DMDestroy(&pdm);
    2491:     }
    2492:   }
    2493:   /* Handle DMPlex refinement */
    2494:   PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);
    2495:   PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);
    2496:   if (refine) {DMPlexSetRefinementUniform(dm, PETSC_TRUE);}
    2497:   if (refine && isHierarchy) {
    2498:     DM *dms, coarseDM;

    2500:     DMGetCoarseDM(dm, &coarseDM);
    2501:     PetscObjectReference((PetscObject)coarseDM);
    2502:     PetscMalloc1(refine,&dms);
    2503:     DMRefineHierarchy(dm, refine, dms);
    2504:     /* Total hack since we do not pass in a pointer */
    2505:     DMPlexSwap_Static(dm, dms[refine-1]);
    2506:     if (refine == 1) {
    2507:       DMSetCoarseDM(dm, dms[0]);
    2508:       DMPlexSetRegularRefinement(dm, PETSC_TRUE);
    2509:     } else {
    2510:       DMSetCoarseDM(dm, dms[refine-2]);
    2511:       DMPlexSetRegularRefinement(dm, PETSC_TRUE);
    2512:       DMSetCoarseDM(dms[0], dms[refine-1]);
    2513:       DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);
    2514:     }
    2515:     DMSetCoarseDM(dms[refine-1], coarseDM);
    2516:     PetscObjectDereference((PetscObject)coarseDM);
    2517:     /* Free DMs */
    2518:     for (r = 0; r < refine; ++r) {
    2519:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);
    2520:       DMDestroy(&dms[r]);
    2521:     }
    2522:     PetscFree(dms);
    2523:   } else {
    2524:     for (r = 0; r < refine; ++r) {
    2525:       DM refinedMesh;
    2526:       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;

    2528:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2529:       DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);
    2530:       /* Total hack since we do not pass in a pointer */
    2531:       DMPlexReplace_Static(dm, refinedMesh);
    2532:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2533:       if (coordFunc) {
    2534:         DMPlexRemapGeometry(dm, 0.0, coordFunc);
    2535:         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
    2536:       }
    2537:       DMDestroy(&refinedMesh);
    2538:     }
    2539:   }
    2540:   /* Handle DMPlex coarsening */
    2541:   PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);
    2542:   PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);
    2543:   if (coarsen && isHierarchy) {
    2544:     DM *dms;

    2546:     PetscMalloc1(coarsen, &dms);
    2547:     DMCoarsenHierarchy(dm, coarsen, dms);
    2548:     /* Free DMs */
    2549:     for (r = 0; r < coarsen; ++r) {
    2550:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);
    2551:       DMDestroy(&dms[r]);
    2552:     }
    2553:     PetscFree(dms);
    2554:   } else {
    2555:     for (r = 0; r < coarsen; ++r) {
    2556:       DM coarseMesh;

    2558:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2559:       DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);
    2560:       /* Total hack since we do not pass in a pointer */
    2561:       DMPlexReplace_Static(dm, coarseMesh);
    2562:       DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2563:       DMDestroy(&coarseMesh);
    2564:     }
    2565:   }
    2566:   /* Handle */
    2567:   DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);
    2568:   PetscOptionsTail();
    2569:   return(0);
    2570: }

    2572: static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
    2573: {

    2577:   DMCreateGlobalVector_Section_Private(dm,vec);
    2578:   /* VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM); */
    2579:   VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);
    2580:   VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);
    2581:   VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);
    2582:   VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);
    2583:   return(0);
    2584: }

    2586: static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
    2587: {

    2591:   DMCreateLocalVector_Section_Private(dm,vec);
    2592:   VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);
    2593:   VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);
    2594:   return(0);
    2595: }

    2597: static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
    2598: {
    2599:   PetscInt       depth, d;

    2603:   DMPlexGetDepth(dm, &depth);
    2604:   if (depth == 1) {
    2605:     DMGetDimension(dm, &d);
    2606:     if (dim == 0)      {DMPlexGetDepthStratum(dm, dim, pStart, pEnd);}
    2607:     else if (dim == d) {DMPlexGetDepthStratum(dm, 1, pStart, pEnd);}
    2608:     else               {*pStart = 0; *pEnd = 0;}
    2609:   } else {
    2610:     DMPlexGetDepthStratum(dm, dim, pStart, pEnd);
    2611:   }
    2612:   return(0);
    2613: }

    2615: static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
    2616: {
    2617:   PetscSF           sf;
    2618:   PetscInt          niranks, njranks, n;
    2619:   const PetscMPIInt *iranks, *jranks;
    2620:   DM_Plex           *data = (DM_Plex*) dm->data;
    2621:   PetscErrorCode    ierr;

    2624:   DMGetPointSF(dm, &sf);
    2625:   if (!data->neighbors) {
    2626:     PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);
    2627:     PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);
    2628:     PetscMalloc1(njranks + niranks + 1, &data->neighbors);
    2629:     PetscArraycpy(data->neighbors + 1, jranks, njranks);
    2630:     PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);
    2631:     n = njranks + niranks;
    2632:     PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);
    2633:     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
    2634:     PetscMPIIntCast(n, data->neighbors);
    2635:   }
    2636:   if (nranks) *nranks = data->neighbors[0];
    2637:   if (ranks) {
    2638:     if (data->neighbors[0]) *ranks = data->neighbors + 1;
    2639:     else                    *ranks = NULL;
    2640:   }
    2641:   return(0);
    2642: }

    2644: static PetscErrorCode DMInitialize_Plex(DM dm)
    2645: {

    2649:   dm->ops->view                            = DMView_Plex;
    2650:   dm->ops->load                            = DMLoad_Plex;
    2651:   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
    2652:   dm->ops->clone                           = DMClone_Plex;
    2653:   dm->ops->setup                           = DMSetUp_Plex;
    2654:   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
    2655:   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
    2656:   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
    2657:   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
    2658:   dm->ops->getlocaltoglobalmapping         = NULL;
    2659:   dm->ops->createfieldis                   = NULL;
    2660:   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
    2661:   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
    2662:   dm->ops->getcoloring                     = NULL;
    2663:   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
    2664:   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
    2665:   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
    2666:   dm->ops->createinjection                 = DMCreateInjection_Plex;
    2667:   dm->ops->refine                          = DMRefine_Plex;
    2668:   dm->ops->coarsen                         = DMCoarsen_Plex;
    2669:   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
    2670:   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
    2671:   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
    2672:   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
    2673:   dm->ops->globaltolocalbegin              = NULL;
    2674:   dm->ops->globaltolocalend                = NULL;
    2675:   dm->ops->localtoglobalbegin              = NULL;
    2676:   dm->ops->localtoglobalend                = NULL;
    2677:   dm->ops->destroy                         = DMDestroy_Plex;
    2678:   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
    2679:   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
    2680:   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
    2681:   dm->ops->locatepoints                    = DMLocatePoints_Plex;
    2682:   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
    2683:   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
    2684:   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
    2685:   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
    2686:   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
    2687:   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
    2688:   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
    2689:   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
    2690:   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
    2691:   PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);
    2692:   PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);
    2693:   PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);
    2694:   PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);
    2695:   PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);
    2696:   return(0);
    2697: }

    2699: PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
    2700: {
    2701:   DM_Plex        *mesh = (DM_Plex *) dm->data;

    2705:   mesh->refct++;
    2706:   (*newdm)->data = mesh;
    2707:   PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);
    2708:   DMInitialize_Plex(*newdm);
    2709:   return(0);
    2710: }

    2712: /*MC
    2713:   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
    2714:                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
    2715:                     specified by a PetscSection object. Ownership in the global representation is determined by
    2716:                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.

    2718:   Options Database Keys:
    2719: + -dm_refine_pre                     - Refine mesh before distribution
    2720: + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
    2721: + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
    2722: . -dm_distribute                     - Distribute mesh across processes
    2723: . -dm_distribute_overlap             - Number of cells to overlap for distribution
    2724: . -dm_refine                         - Refine mesh after distribution
    2725: . -dm_plex_hash_location             - Use grid hashing for point location
    2726: . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
    2727: . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
    2728: . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
    2729: . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
    2730: . -dm_plex_check_all                 - Perform all shecks below
    2731: . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
    2732: . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
    2733: . -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
    2734: . -dm_plex_check_geometry            - Check that cells have positive volume
    2735: . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
    2736: . -dm_plex_view_scale <num>          - Scale the TikZ
    2737: - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices

    2740:   Level: intermediate

    2742: .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
    2743: M*/

    2745: PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
    2746: {
    2747:   DM_Plex       *mesh;
    2748:   PetscInt       unit;

    2753:   PetscNewLog(dm,&mesh);
    2754:   dm->dim  = 0;
    2755:   dm->data = mesh;

    2757:   mesh->refct             = 1;
    2758:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);
    2759:   mesh->maxConeSize       = 0;
    2760:   mesh->cones             = NULL;
    2761:   mesh->coneOrientations  = NULL;
    2762:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);
    2763:   mesh->maxSupportSize    = 0;
    2764:   mesh->supports          = NULL;
    2765:   mesh->refinementUniform = PETSC_TRUE;
    2766:   mesh->refinementLimit   = -1.0;
    2767:   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
    2768:   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;

    2770:   mesh->facesTmp = NULL;

    2772:   mesh->tetgenOpts   = NULL;
    2773:   mesh->triangleOpts = NULL;
    2774:   PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);
    2775:   mesh->remeshBd     = PETSC_FALSE;

    2777:   mesh->subpointMap = NULL;

    2779:   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;

    2781:   mesh->regularRefinement   = PETSC_FALSE;
    2782:   mesh->depthState          = -1;
    2783:   mesh->celltypeState       = -1;
    2784:   mesh->globalVertexNumbers = NULL;
    2785:   mesh->globalCellNumbers   = NULL;
    2786:   mesh->anchorSection       = NULL;
    2787:   mesh->anchorIS            = NULL;
    2788:   mesh->createanchors       = NULL;
    2789:   mesh->computeanchormatrix = NULL;
    2790:   mesh->parentSection       = NULL;
    2791:   mesh->parents             = NULL;
    2792:   mesh->childIDs            = NULL;
    2793:   mesh->childSection        = NULL;
    2794:   mesh->children            = NULL;
    2795:   mesh->referenceTree       = NULL;
    2796:   mesh->getchildsymmetry    = NULL;
    2797:   mesh->vtkCellHeight       = 0;
    2798:   mesh->useAnchors          = PETSC_FALSE;

    2800:   mesh->maxProjectionHeight = 0;

    2802:   mesh->neighbors           = NULL;

    2804:   mesh->printSetValues = PETSC_FALSE;
    2805:   mesh->printFEM       = 0;
    2806:   mesh->printTol       = 1.0e-10;

    2808:   DMInitialize_Plex(dm);
    2809:   return(0);
    2810: }

    2812: /*@
    2813:   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.

    2815:   Collective

    2817:   Input Parameter:
    2818: . comm - The communicator for the DMPlex object

    2820:   Output Parameter:
    2821: . mesh  - The DMPlex object

    2823:   Level: beginner

    2825: @*/
    2826: PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
    2827: {

    2832:   DMCreate(comm, mesh);
    2833:   DMSetType(*mesh, DMPLEX);
    2834:   return(0);
    2835: }

    2837: /*@C
    2838:   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)

    2840:   Input Parameters:
    2841: + dm - The DM
    2842: . numCells - The number of cells owned by this process
    2843: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    2844: . NVertices - The global number of vertices, or PETSC_DECIDE
    2845: . numCorners - The number of vertices for each cell
    2846: - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell

    2848:   Output Parameter:
    2849: . vertexSF - (Optional) SF describing complete vertex ownership

    2851:   Notes:
    2852:   Two triangles sharing a face
    2853: $
    2854: $        2
    2855: $      / | \
    2856: $     /  |  \
    2857: $    /   |   \
    2858: $   0  0 | 1  3
    2859: $    \   |   /
    2860: $     \  |  /
    2861: $      \ | /
    2862: $        1
    2863: would have input
    2864: $  numCells = 2, numVertices = 4
    2865: $  cells = [0 1 2  1 3 2]
    2866: $
    2867: which would result in the DMPlex
    2868: $
    2869: $        4
    2870: $      / | \
    2871: $     /  |  \
    2872: $    /   |   \
    2873: $   2  0 | 1  5
    2874: $    \   |   /
    2875: $     \  |  /
    2876: $      \ | /
    2877: $        3

    2879:   Vertices are implicitly numbered consecutively 0,...,NVertices.
    2880:   Each rank owns a chunk of numVertices consecutive vertices.
    2881:   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
    2882:   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
    2883:   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.

    2885:   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.

    2887:   Not currently supported in Fortran.

    2889:   Level: advanced

    2891: .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
    2892: @*/
    2893: PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
    2894: {
    2895:   PetscSF         sfPoint, sfVert;
    2896:   PetscLayout     vLayout;
    2897:   PetscSFNode    *vertexLocal, *vertexOwner, *remoteVertex;
    2898:   PetscInt        numVerticesAdj, *verticesAdj, numVerticesGhost = 0, *localVertex, *cones, c, p, v, g, dim;
    2899:   PetscMPIInt     rank, size;
    2900:   PetscErrorCode  ierr;

    2904:   PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);
    2905:   MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);
    2906:   MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);
    2907:   DMGetDimension(dm, &dim);
    2908:   /* Get/check global number of vertices */
    2909:   {
    2910:     PetscInt NVerticesInCells, i;
    2911:     const PetscInt len = numCells * numCorners;

    2913:     /* NVerticesInCells = max(cells) + 1 */
    2914:     NVerticesInCells = PETSC_MIN_INT;
    2915:     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
    2916:     ++NVerticesInCells;
    2917:     MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));

    2919:     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
    2920:     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);
    2921:   }
    2922:   /* Partition vertices */
    2923:   PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);
    2924:   PetscLayoutSetLocalSize(vLayout, numVertices);
    2925:   PetscLayoutSetSize(vLayout, NVertices);
    2926:   PetscLayoutSetBlockSize(vLayout, 1);
    2927:   PetscLayoutSetUp(vLayout);
    2928:   /* Count locally unique vertices */
    2929:   {
    2930:     PetscHSetI vhash;
    2931:     PetscInt off = 0;

    2933:     PetscHSetICreate(&vhash);
    2934:     for (c = 0; c < numCells; ++c) {
    2935:       for (p = 0; p < numCorners; ++p) {
    2936:         PetscHSetIAdd(vhash, cells[c*numCorners+p]);
    2937:       }
    2938:     }
    2939:     PetscHSetIGetSize(vhash, &numVerticesAdj);
    2940:     PetscMalloc1(numVerticesAdj, &verticesAdj);
    2941:     PetscHSetIGetElems(vhash, &off, verticesAdj);
    2942:     PetscHSetIDestroy(&vhash);
    2943:     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
    2944:   }
    2945:   PetscSortInt(numVerticesAdj, verticesAdj);
    2946:   /* Create cones */
    2947:   DMPlexSetChart(dm, 0, numCells+numVerticesAdj);
    2948:   for (c = 0; c < numCells; ++c) {DMPlexSetConeSize(dm, c, numCorners);}
    2949:   DMSetUp(dm);
    2950:   DMPlexGetCones(dm,&cones);
    2951:   for (c = 0; c < numCells; ++c) {
    2952:     for (p = 0; p < numCorners; ++p) {
    2953:       const PetscInt gv = cells[c*numCorners+p];
    2954:       PetscInt       lv;

    2956:       /* Positions within verticesAdj form 0-based local vertex numbering;
    2957:          we need to shift it by numCells to get correct DAG points (cells go first) */
    2958:       PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);
    2959:       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
    2960:       cones[c*numCorners+p] = lv+numCells;
    2961:     }
    2962:   }
    2963:   /* Create SF for vertices */
    2964:   PetscSFCreate(PetscObjectComm((PetscObject)dm), &sfVert);
    2965:   PetscObjectSetName((PetscObject) sfVert, "Vertex Ownership SF");
    2966:   PetscSFSetFromOptions(sfVert);
    2967:   PetscSFSetGraphLayout(sfVert, vLayout, numVerticesAdj, NULL, PETSC_OWN_POINTER, verticesAdj);
    2968:   PetscFree(verticesAdj);
    2969:   /* Build pointSF */
    2970:   PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);
    2971:   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
    2972:   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
    2973:   PetscSFReduceBegin(sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);
    2974:   PetscSFReduceEnd(sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);
    2975:   for (v = 0; v < numVertices;    ++v) if (vertexOwner[v].rank < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Global vertex %D was unclaimed", v + vLayout->rstart);
    2976:   PetscSFBcastBegin(sfVert, MPIU_2INT, vertexOwner, vertexLocal);
    2977:   PetscSFBcastEnd(sfVert, MPIU_2INT, vertexOwner, vertexLocal);
    2978:   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
    2979:   PetscMalloc1(numVerticesGhost, &localVertex);
    2980:   PetscMalloc1(numVerticesGhost, &remoteVertex);
    2981:   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
    2982:     if (vertexLocal[v].rank != rank) {
    2983:       localVertex[g]        = v+numCells;
    2984:       remoteVertex[g].index = vertexLocal[v].index;
    2985:       remoteVertex[g].rank  = vertexLocal[v].rank;
    2986:       ++g;
    2987:     }
    2988:   }
    2989:   PetscFree2(vertexLocal, vertexOwner);
    2990:   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
    2991:   DMGetPointSF(dm, &sfPoint);
    2992:   PetscObjectSetName((PetscObject) sfPoint, "point SF");
    2993:   PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);
    2994:   PetscLayoutDestroy(&vLayout);
    2995:   /* Fill in the rest of the topology structure */
    2996:   DMPlexSymmetrize(dm);
    2997:   DMPlexStratify(dm);
    2998:   PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);
    2999:   if (vertexSF) *vertexSF = sfVert;
    3000:   else {PetscSFDestroy(&sfVert);}
    3001:   return(0);
    3002: }

    3004: /*@C
    3005:   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)

    3007:   Input Parameters:
    3008: + dm - The DM
    3009: . spaceDim - The spatial dimension used for coordinates
    3010: . sfVert - SF describing complete vertex ownership
    3011: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3013:   Level: advanced

    3015:   Notes:
    3016:   Not currently supported in Fortran.

    3018: .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
    3019: @*/
    3020: PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
    3021: {
    3022:   PetscSection   coordSection;
    3023:   Vec            coordinates;
    3024:   PetscScalar   *coords;
    3025:   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;

    3029:   PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3030:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3031:   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
    3032:   DMSetCoordinateDim(dm, spaceDim);
    3033:   PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);
    3034:   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);
    3035:   DMGetCoordinateSection(dm, &coordSection);
    3036:   PetscSectionSetNumFields(coordSection, 1);
    3037:   PetscSectionSetFieldComponents(coordSection, 0, spaceDim);
    3038:   PetscSectionSetChart(coordSection, vStart, vEnd);
    3039:   for (v = vStart; v < vEnd; ++v) {
    3040:     PetscSectionSetDof(coordSection, v, spaceDim);
    3041:     PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);
    3042:   }
    3043:   PetscSectionSetUp(coordSection);
    3044:   PetscSectionGetStorageSize(coordSection, &coordSize);
    3045:   VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);
    3046:   VecSetBlockSize(coordinates, spaceDim);
    3047:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3048:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    3049:   VecSetType(coordinates,VECSTANDARD);
    3050:   VecGetArray(coordinates, &coords);
    3051:   {
    3052:     MPI_Datatype coordtype;

    3054:     /* Need a temp buffer for coords if we have complex/single */
    3055:     MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);
    3056:     MPI_Type_commit(&coordtype);
    3057: #if defined(PETSC_USE_COMPLEX)
    3058:     {
    3059:     PetscScalar *svertexCoords;
    3060:     PetscInt    i;
    3061:     PetscMalloc1(numVertices*spaceDim,&svertexCoords);
    3062:     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
    3063:     PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);
    3064:     PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);
    3065:     PetscFree(svertexCoords);
    3066:     }
    3067: #else
    3068:     PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);
    3069:     PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);
    3070: #endif
    3071:     MPI_Type_free(&coordtype);
    3072:   }
    3073:   VecRestoreArray(coordinates, &coords);
    3074:   DMSetCoordinatesLocal(dm, coordinates);
    3075:   VecDestroy(&coordinates);
    3076:   PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3077:   return(0);
    3078: }

    3080: /*@
    3081:   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)

    3083:   Input Parameters:
    3084: + comm - The communicator
    3085: . dim - The topological dimension of the mesh
    3086: . numCells - The number of cells owned by this process
    3087: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    3088: . NVertices - The global number of vertices, or PETSC_DECIDE
    3089: . numCorners - The number of vertices for each cell
    3090: . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
    3091: . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
    3092: . spaceDim - The spatial dimension used for coordinates
    3093: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3095:   Output Parameter:
    3096: + dm - The DM
    3097: - vertexSF - (Optional) SF describing complete vertex ownership

    3099:   Notes:
    3100:   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
    3101:   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()

    3103:   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
    3104:   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.

    3106:   Level: intermediate

    3108: .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
    3109: @*/
    3110: 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)
    3111: {
    3112:   PetscSF        sfVert;

    3116:   DMCreate(comm, dm);
    3117:   DMSetType(*dm, DMPLEX);
    3120:   DMSetDimension(*dm, dim);
    3121:   DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);
    3122:   if (interpolate) {
    3123:     DM idm;

    3125:     DMPlexInterpolate(*dm, &idm);
    3126:     DMDestroy(dm);
    3127:     *dm  = idm;
    3128:   }
    3129:   DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);
    3130:   if (vertexSF) *vertexSF = sfVert;
    3131:   else {PetscSFDestroy(&sfVert);}
    3132:   return(0);
    3133: }

    3136: /*@
    3137:   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()

    3139:   Level: deprecated

    3141: .seealso: DMPlexCreateFromCellListParallelPetsc()
    3142: @*/
    3143: 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)
    3144: {
    3146:   PetscInt       i;
    3147:   PetscInt       *pintCells;

    3150:   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));
    3151:   if (sizeof(int) == sizeof(PetscInt)) {
    3152:     pintCells = (PetscInt *) cells;
    3153:   } else {
    3154:     PetscMalloc1(numCells*numCorners, &pintCells);
    3155:     for (i = 0; i < numCells*numCorners; i++) {
    3156:       pintCells[i] = (PetscInt) cells[i];
    3157:     }
    3158:   }
    3159:   DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);
    3160:   if (sizeof(int) != sizeof(PetscInt)) {
    3161:     PetscFree(pintCells);
    3162:   }
    3163:   return(0);
    3164: }

    3166: /*@C
    3167:   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)

    3169:   Input Parameters:
    3170: + dm - The DM
    3171: . numCells - The number of cells owned by this process
    3172: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    3173: . numCorners - The number of vertices for each cell
    3174: - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell

    3176:   Level: advanced

    3178:   Notes:
    3179:   Two triangles sharing a face
    3180: $
    3181: $        2
    3182: $      / | \
    3183: $     /  |  \
    3184: $    /   |   \
    3185: $   0  0 | 1  3
    3186: $    \   |   /
    3187: $     \  |  /
    3188: $      \ | /
    3189: $        1
    3190: would have input
    3191: $  numCells = 2, numVertices = 4
    3192: $  cells = [0 1 2  1 3 2]
    3193: $
    3194: which would result in the DMPlex
    3195: $
    3196: $        4
    3197: $      / | \
    3198: $     /  |  \
    3199: $    /   |   \
    3200: $   2  0 | 1  5
    3201: $    \   |   /
    3202: $     \  |  /
    3203: $      \ | /
    3204: $        3

    3206:   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.

    3208:   Not currently supported in Fortran.

    3210: .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
    3211: @*/
    3212: PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
    3213: {
    3214:   PetscInt      *cones, c, p, dim;

    3218:   PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);
    3219:   DMGetDimension(dm, &dim);
    3220:   /* Get/check global number of vertices */
    3221:   {
    3222:     PetscInt NVerticesInCells, i;
    3223:     const PetscInt len = numCells * numCorners;

    3225:     /* NVerticesInCells = max(cells) + 1 */
    3226:     NVerticesInCells = PETSC_MIN_INT;
    3227:     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
    3228:     ++NVerticesInCells;

    3230:     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
    3231:     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);
    3232:   }
    3233:   DMPlexSetChart(dm, 0, numCells+numVertices);
    3234:   for (c = 0; c < numCells; ++c) {
    3235:     DMPlexSetConeSize(dm, c, numCorners);
    3236:   }
    3237:   DMSetUp(dm);
    3238:   DMPlexGetCones(dm,&cones);
    3239:   for (c = 0; c < numCells; ++c) {
    3240:     for (p = 0; p < numCorners; ++p) {
    3241:       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
    3242:     }
    3243:   }
    3244:   DMPlexSymmetrize(dm);
    3245:   DMPlexStratify(dm);
    3246:   PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);
    3247:   return(0);
    3248: }

    3250: /*@C
    3251:   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)

    3253:   Input Parameters:
    3254: + dm - The DM
    3255: . spaceDim - The spatial dimension used for coordinates
    3256: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3258:   Level: advanced

    3260:   Notes:
    3261:   Not currently supported in Fortran.

    3263: .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
    3264: @*/
    3265: PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
    3266: {
    3267:   PetscSection   coordSection;
    3268:   Vec            coordinates;
    3269:   DM             cdm;
    3270:   PetscScalar   *coords;
    3271:   PetscInt       v, vStart, vEnd, d;

    3275:   PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3276:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3277:   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
    3278:   DMSetCoordinateDim(dm, spaceDim);
    3279:   DMGetCoordinateSection(dm, &coordSection);
    3280:   PetscSectionSetNumFields(coordSection, 1);
    3281:   PetscSectionSetFieldComponents(coordSection, 0, spaceDim);
    3282:   PetscSectionSetChart(coordSection, vStart, vEnd);
    3283:   for (v = vStart; v < vEnd; ++v) {
    3284:     PetscSectionSetDof(coordSection, v, spaceDim);
    3285:     PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);
    3286:   }
    3287:   PetscSectionSetUp(coordSection);

    3289:   DMGetCoordinateDM(dm, &cdm);
    3290:   DMCreateLocalVector(cdm, &coordinates);
    3291:   VecSetBlockSize(coordinates, spaceDim);
    3292:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3293:   VecGetArrayWrite(coordinates, &coords);
    3294:   for (v = 0; v < vEnd-vStart; ++v) {
    3295:     for (d = 0; d < spaceDim; ++d) {
    3296:       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
    3297:     }
    3298:   }
    3299:   VecRestoreArrayWrite(coordinates, &coords);
    3300:   DMSetCoordinatesLocal(dm, coordinates);
    3301:   VecDestroy(&coordinates);
    3302:   PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);
    3303:   return(0);
    3304: }

    3306: /*@
    3307:   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output)

    3309:   Input Parameters:
    3310: + comm - The communicator
    3311: . dim - The topological dimension of the mesh
    3312: . numCells - The number of cells
    3313: . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
    3314: . numCorners - The number of vertices for each cell
    3315: . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
    3316: . cells - An array of numCells*numCorners numbers, the vertices for each cell
    3317: . spaceDim - The spatial dimension used for coordinates
    3318: - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex

    3320:   Output Parameter:
    3321: . dm - The DM

    3323:   Notes:
    3324:   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
    3325:   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()

    3327:   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
    3328:   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.

    3330:   Level: intermediate

    3332: .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
    3333: @*/
    3334: 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)
    3335: {

    3339:   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.");
    3340:   DMCreate(comm, dm);
    3341:   DMSetType(*dm, DMPLEX);
    3342:   DMSetDimension(*dm, dim);
    3343:   DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);
    3344:   if (interpolate) {
    3345:     DM idm;

    3347:     DMPlexInterpolate(*dm, &idm);
    3348:     DMDestroy(dm);
    3349:     *dm  = idm;
    3350:   }
    3351:   DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);
    3352:   return(0);
    3353: }

    3355: /*@
    3356:   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()

    3358:   Level: deprecated

    3360: .seealso: DMPlexCreateFromCellListPetsc()
    3361: @*/
    3362: 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)
    3363: {
    3365:   PetscInt       i;
    3366:   PetscInt       *pintCells;
    3367:   PetscReal      *prealVC;

    3370:   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));
    3371:   if (sizeof(int) == sizeof(PetscInt)) {
    3372:     pintCells = (PetscInt *) cells;
    3373:   } else {
    3374:     PetscMalloc1(numCells*numCorners, &pintCells);
    3375:     for (i = 0; i < numCells*numCorners; i++) {
    3376:       pintCells[i] = (PetscInt) cells[i];
    3377:     }
    3378:   }
    3379:   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));
    3380:   if (sizeof(double) == sizeof(PetscReal)) {
    3381:     prealVC = (PetscReal *) vertexCoords;
    3382:   } else {
    3383:     PetscMalloc1(numVertices*spaceDim, &prealVC);
    3384:     for (i = 0; i < numVertices*spaceDim; i++) {
    3385:       prealVC[i] = (PetscReal) vertexCoords[i];
    3386:     }
    3387:   }
    3388:   DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);
    3389:   if (sizeof(int) != sizeof(PetscInt)) {
    3390:     PetscFree(pintCells);
    3391:   }
    3392:   if (sizeof(double) != sizeof(PetscReal)) {
    3393:     PetscFree(prealVC);
    3394:   }
    3395:   return(0);
    3396: }

    3398: /*@
    3399:   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM

    3401:   Input Parameters:
    3402: + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
    3403: . depth - The depth of the DAG
    3404: . numPoints - Array of size depth + 1 containing the number of points at each depth
    3405: . coneSize - The cone size of each point
    3406: . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
    3407: . coneOrientations - The orientation of each cone point
    3408: - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()

    3410:   Output Parameter:
    3411: . dm - The DM

    3413:   Note: Two triangles sharing a face would have input
    3414: $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
    3415: $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
    3416: $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
    3417: $
    3418: which would result in the DMPlex
    3419: $
    3420: $        4
    3421: $      / | \
    3422: $     /  |  \
    3423: $    /   |   \
    3424: $   2  0 | 1  5
    3425: $    \   |   /
    3426: $     \  |  /
    3427: $      \ | /
    3428: $        3
    3429: $
    3430: $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()

    3432:   Level: advanced

    3434: .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
    3435: @*/
    3436: PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
    3437: {
    3438:   Vec            coordinates;
    3439:   PetscSection   coordSection;
    3440:   PetscScalar    *coords;
    3441:   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;

    3445:   DMGetDimension(dm, &dim);
    3446:   DMGetCoordinateDim(dm, &dimEmbed);
    3447:   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
    3448:   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
    3449:   DMPlexSetChart(dm, pStart, pEnd);
    3450:   for (p = pStart; p < pEnd; ++p) {
    3451:     DMPlexSetConeSize(dm, p, coneSize[p-pStart]);
    3452:     if (firstVertex < 0 && !coneSize[p - pStart]) {
    3453:       firstVertex = p - pStart;
    3454:     }
    3455:   }
    3456:   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
    3457:   DMSetUp(dm); /* Allocate space for cones */
    3458:   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
    3459:     DMPlexSetCone(dm, p, &cones[off]);
    3460:     DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);
    3461:   }
    3462:   DMPlexSymmetrize(dm);
    3463:   DMPlexStratify(dm);
    3464:   /* Build coordinates */
    3465:   DMGetCoordinateSection(dm, &coordSection);
    3466:   PetscSectionSetNumFields(coordSection, 1);
    3467:   PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);
    3468:   PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);
    3469:   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
    3470:     PetscSectionSetDof(coordSection, v, dimEmbed);
    3471:     PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);
    3472:   }
    3473:   PetscSectionSetUp(coordSection);
    3474:   PetscSectionGetStorageSize(coordSection, &coordSize);
    3475:   VecCreate(PETSC_COMM_SELF, &coordinates);
    3476:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3477:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    3478:   VecSetBlockSize(coordinates, dimEmbed);
    3479:   VecSetType(coordinates,VECSTANDARD);
    3480:   VecGetArray(coordinates, &coords);
    3481:   for (v = 0; v < numPoints[0]; ++v) {
    3482:     PetscInt off;

    3484:     PetscSectionGetOffset(coordSection, v+firstVertex, &off);
    3485:     for (d = 0; d < dimEmbed; ++d) {
    3486:       coords[off+d] = vertexCoords[v*dimEmbed+d];
    3487:     }
    3488:   }
    3489:   VecRestoreArray(coordinates, &coords);
    3490:   DMSetCoordinatesLocal(dm, coordinates);
    3491:   VecDestroy(&coordinates);
    3492:   return(0);
    3493: }

    3495: /*@C
    3496:   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.

    3498: + comm        - The MPI communicator
    3499: . filename    - Name of the .dat file
    3500: - interpolate - Create faces and edges in the mesh

    3502:   Output Parameter:
    3503: . dm  - The DM object representing the mesh

    3505:   Note: The format is the simplest possible:
    3506: $ Ne
    3507: $ v0 v1 ... vk
    3508: $ Nv
    3509: $ x y z marker

    3511:   Level: beginner

    3513: .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
    3514: @*/
    3515: PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
    3516: {
    3517:   DMLabel         marker;
    3518:   PetscViewer     viewer;
    3519:   Vec             coordinates;
    3520:   PetscSection    coordSection;
    3521:   PetscScalar    *coords;
    3522:   char            line[PETSC_MAX_PATH_LEN];
    3523:   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
    3524:   PetscMPIInt     rank;
    3525:   int             snum, Nv, Nc;
    3526:   PetscErrorCode  ierr;

    3529:   MPI_Comm_rank(comm, &rank);
    3530:   PetscViewerCreate(comm, &viewer);
    3531:   PetscViewerSetType(viewer, PETSCVIEWERASCII);
    3532:   PetscViewerFileSetMode(viewer, FILE_MODE_READ);
    3533:   PetscViewerFileSetName(viewer, filename);
    3534:   if (!rank) {
    3535:     PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);
    3536:     snum = sscanf(line, "%d %d", &Nc, &Nv);
    3537:     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
    3538:   } else {
    3539:     Nc = Nv = 0;
    3540:   }
    3541:   DMCreate(comm, dm);
    3542:   DMSetType(*dm, DMPLEX);
    3543:   DMPlexSetChart(*dm, 0, Nc+Nv);
    3544:   DMSetDimension(*dm, dim);
    3545:   DMSetCoordinateDim(*dm, cdim);
    3546:   /* Read topology */
    3547:   if (!rank) {
    3548:     PetscInt cone[8], corners = 8;
    3549:     int      vbuf[8], v;

    3551:     for (c = 0; c < Nc; ++c) {DMPlexSetConeSize(*dm, c, corners);}
    3552:     DMSetUp(*dm);
    3553:     for (c = 0; c < Nc; ++c) {
    3554:       PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);
    3555:       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]);
    3556:       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
    3557:       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
    3558:       /* Hexahedra are inverted */
    3559:       {
    3560:         PetscInt tmp = cone[1];
    3561:         cone[1] = cone[3];
    3562:         cone[3] = tmp;
    3563:       }
    3564:       DMPlexSetCone(*dm, c, cone);
    3565:     }
    3566:   }
    3567:   DMPlexSymmetrize(*dm);
    3568:   DMPlexStratify(*dm);
    3569:   /* Read coordinates */
    3570:   DMGetCoordinateSection(*dm, &coordSection);
    3571:   PetscSectionSetNumFields(coordSection, 1);
    3572:   PetscSectionSetFieldComponents(coordSection, 0, cdim);
    3573:   PetscSectionSetChart(coordSection, Nc, Nc + Nv);
    3574:   for (v = Nc; v < Nc+Nv; ++v) {
    3575:     PetscSectionSetDof(coordSection, v, cdim);
    3576:     PetscSectionSetFieldDof(coordSection, v, 0, cdim);
    3577:   }
    3578:   PetscSectionSetUp(coordSection);
    3579:   PetscSectionGetStorageSize(coordSection, &coordSize);
    3580:   VecCreate(PETSC_COMM_SELF, &coordinates);
    3581:   PetscObjectSetName((PetscObject) coordinates, "coordinates");
    3582:   VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);
    3583:   VecSetBlockSize(coordinates, cdim);
    3584:   VecSetType(coordinates, VECSTANDARD);
    3585:   VecGetArray(coordinates, &coords);
    3586:   if (!rank) {
    3587:     double x[3];
    3588:     int    val;

    3590:     DMCreateLabel(*dm, "marker");
    3591:     DMGetLabel(*dm, "marker", &marker);
    3592:     for (v = 0; v < Nv; ++v) {
    3593:       PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);
    3594:       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
    3595:       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
    3596:       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
    3597:       if (val) {DMLabelSetValue(marker, v+Nc, val);}
    3598:     }
    3599:   }
    3600:   VecRestoreArray(coordinates, &coords);
    3601:   DMSetCoordinatesLocal(*dm, coordinates);
    3602:   VecDestroy(&coordinates);
    3603:   PetscViewerDestroy(&viewer);
    3604:   if (interpolate) {
    3605:     DM      idm;
    3606:     DMLabel bdlabel;

    3608:     DMPlexInterpolate(*dm, &idm);
    3609:     DMDestroy(dm);
    3610:     *dm  = idm;

    3612:     DMGetLabel(*dm, "marker", &bdlabel);
    3613:     DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);
    3614:     DMPlexLabelComplete(*dm, bdlabel);
    3615:   }
    3616:   return(0);
    3617: }

    3619: /*@C
    3620:   DMPlexCreateFromFile - This takes a filename and produces a DM

    3622:   Input Parameters:
    3623: + comm - The communicator
    3624: . filename - A file name
    3625: - interpolate - Flag to create intermediate mesh pieces (edges, faces)

    3627:   Output Parameter:
    3628: . dm - The DM

    3630:   Options Database Keys:
    3631: . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5

    3633:   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
    3634: $ -dm_plex_create_viewer_hdf5_collective

    3636:   Level: beginner

    3638: .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
    3639: @*/
    3640: PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
    3641: {
    3642:   const char    *extGmsh    = ".msh";
    3643:   const char    *extGmsh2   = ".msh2";
    3644:   const char    *extGmsh4   = ".msh4";
    3645:   const char    *extCGNS    = ".cgns";
    3646:   const char    *extExodus  = ".exo";
    3647:   const char    *extGenesis = ".gen";
    3648:   const char    *extFluent  = ".cas";
    3649:   const char    *extHDF5    = ".h5";
    3650:   const char    *extMed     = ".med";
    3651:   const char    *extPLY     = ".ply";
    3652:   const char    *extCV      = ".dat";
    3653:   size_t         len;
    3654:   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isCV;
    3655:   PetscMPIInt    rank;

    3661:   DMInitializePackage();
    3662:   PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);
    3663:   MPI_Comm_rank(comm, &rank);
    3664:   PetscStrlen(filename, &len);
    3665:   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
    3666:   PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);
    3667:   PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);
    3668:   PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);
    3669:   PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);
    3670:   PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);
    3671:   PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);
    3672:   PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);
    3673:   PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);
    3674:   PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);
    3675:   PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);
    3676:   PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);
    3677:   if (isGmsh || isGmsh2 || isGmsh4) {
    3678:     DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);
    3679:   } else if (isCGNS) {
    3680:     DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);
    3681:   } else if (isExodus || isGenesis) {
    3682:     DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);
    3683:   } else if (isFluent) {
    3684:     DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);
    3685:   } else if (isHDF5) {
    3686:     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
    3687:     PetscViewer viewer;

    3689:     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
    3690:     PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);
    3691:     PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);
    3692:     PetscViewerCreate(comm, &viewer);
    3693:     PetscViewerSetType(viewer, PETSCVIEWERHDF5);
    3694:     PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");
    3695:     PetscViewerSetFromOptions(viewer);
    3696:     PetscViewerFileSetMode(viewer, FILE_MODE_READ);
    3697:     PetscViewerFileSetName(viewer, filename);
    3698:     DMCreate(comm, dm);
    3699:     DMSetType(*dm, DMPLEX);
    3700:     if (load_hdf5_xdmf) {PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);}
    3701:     DMLoad(*dm, viewer);
    3702:     if (load_hdf5_xdmf) {PetscViewerPopFormat(viewer);}
    3703:     PetscViewerDestroy(&viewer);

    3705:     if (interpolate) {
    3706:       DM idm;

    3708:       DMPlexInterpolate(*dm, &idm);
    3709:       DMDestroy(dm);
    3710:       *dm  = idm;
    3711:     }
    3712:   } else if (isMed) {
    3713:     DMPlexCreateMedFromFile(comm, filename, interpolate, dm);
    3714:   } else if (isPLY) {
    3715:     DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);
    3716:   } else if (isCV) {
    3717:     DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);
    3718:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
    3719:   PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);
    3720:   return(0);
    3721: }

    3723: /*@
    3724:   DMPlexCreateReferenceCellByType - Create a DMPLEX with the appropriate FEM reference cell

    3726:   Collective

    3728:   Input Parameters:
    3729: + comm - The communicator
    3730: - ct   - The cell type of the reference cell

    3732:   Output Parameter:
    3733: . refdm - The reference cell

    3735:   Level: intermediate

    3737: .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
    3738: @*/
    3739: PetscErrorCode DMPlexCreateReferenceCellByType(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
    3740: {
    3741:   DM             rdm;
    3742:   Vec            coords;

    3746:   DMCreate(comm, &rdm);
    3747:   DMSetType(rdm, DMPLEX);
    3748:   switch (ct) {
    3749:     case DM_POLYTOPE_POINT:
    3750:     {
    3751:       PetscInt    numPoints[1]        = {1};
    3752:       PetscInt    coneSize[1]         = {0};
    3753:       PetscInt    cones[1]            = {0};
    3754:       PetscInt    coneOrientations[1] = {0};
    3755:       PetscScalar vertexCoords[1]     = {0.0};

    3757:       DMSetDimension(rdm, 0);
    3758:       DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3759:     }
    3760:     break;
    3761:     case DM_POLYTOPE_SEGMENT:
    3762:     {
    3763:       PetscInt    numPoints[2]        = {2, 1};
    3764:       PetscInt    coneSize[3]         = {2, 0, 0};
    3765:       PetscInt    cones[2]            = {1, 2};
    3766:       PetscInt    coneOrientations[2] = {0, 0};
    3767:       PetscScalar vertexCoords[2]     = {-1.0,  1.0};

    3769:       DMSetDimension(rdm, 1);
    3770:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3771:     }
    3772:     break;
    3773:     case DM_POLYTOPE_TRIANGLE:
    3774:     {
    3775:       PetscInt    numPoints[2]        = {3, 1};
    3776:       PetscInt    coneSize[4]         = {3, 0, 0, 0};
    3777:       PetscInt    cones[3]            = {1, 2, 3};
    3778:       PetscInt    coneOrientations[3] = {0, 0, 0};
    3779:       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};

    3781:       DMSetDimension(rdm, 2);
    3782:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3783:     }
    3784:     break;
    3785:     case DM_POLYTOPE_QUADRILATERAL:
    3786:     {
    3787:       PetscInt    numPoints[2]        = {4, 1};
    3788:       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
    3789:       PetscInt    cones[4]            = {1, 2, 3, 4};
    3790:       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
    3791:       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};

    3793:       DMSetDimension(rdm, 2);
    3794:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3795:     }
    3796:     break;
    3797:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    3798:     {
    3799:       PetscInt    numPoints[2]        = {4, 1};
    3800:       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
    3801:       PetscInt    cones[4]            = {1, 2, 3, 4};
    3802:       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
    3803:       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};

    3805:       DMSetDimension(rdm, 2);
    3806:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3807:     }
    3808:     break;
    3809:     case DM_POLYTOPE_TETRAHEDRON:
    3810:     {
    3811:       PetscInt    numPoints[2]        = {4, 1};
    3812:       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
    3813:       PetscInt    cones[4]            = {1, 3, 2, 4};
    3814:       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
    3815:       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};

    3817:       DMSetDimension(rdm, 3);
    3818:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3819:     }
    3820:     break;
    3821:     case DM_POLYTOPE_HEXAHEDRON:
    3822:     {
    3823:       PetscInt    numPoints[2]        = {8, 1};
    3824:       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
    3825:       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
    3826:       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
    3827:       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,
    3828:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};

    3830:       DMSetDimension(rdm, 3);
    3831:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3832:     }
    3833:     break;
    3834:     case DM_POLYTOPE_TRI_PRISM:
    3835:     {
    3836:       PetscInt    numPoints[2]        = {6, 1};
    3837:       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
    3838:       PetscInt    cones[6]            = {1, 3, 2, 4, 5, 6};
    3839:       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
    3840:       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
    3841:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};

    3843:       DMSetDimension(rdm, 3);
    3844:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3845:     }
    3846:     break;
    3847:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    3848:     {
    3849:       PetscInt    numPoints[2]        = {6, 1};
    3850:       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
    3851:       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
    3852:       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
    3853:       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
    3854:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};

    3856:       DMSetDimension(rdm, 3);
    3857:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3858:     }
    3859:     break;
    3860:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    3861:     {
    3862:       PetscInt    numPoints[2]        = {8, 1};
    3863:       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
    3864:       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
    3865:       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
    3866:       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,
    3867:                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};

    3869:       DMSetDimension(rdm, 3);
    3870:       DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);
    3871:     }
    3872:     break;
    3873:     default: SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
    3874:   }
    3875:   {
    3876:     PetscInt Nv, v;

    3878:     /* Must create the celltype label here so that we do not automatically try to compute the types */
    3879:     DMCreateLabel(rdm, "celltype");
    3880:     DMPlexSetCellType(rdm, 0, ct);
    3881:     DMPlexGetChart(rdm, NULL, &Nv);
    3882:     for (v = 1; v < Nv; ++v) {DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);}
    3883:   }
    3884:   DMPlexInterpolate(rdm, refdm);
    3885:   if (rdm->coordinateDM) {
    3886:     DM           ncdm;
    3887:     PetscSection cs;
    3888:     PetscInt     pEnd = -1;

    3890:     DMGetLocalSection(rdm->coordinateDM, &cs);
    3891:     if (cs) {PetscSectionGetChart(cs, NULL, &pEnd);}
    3892:     if (pEnd >= 0) {
    3893:       DMClone(*refdm, &ncdm);
    3894:       DMCopyDisc(rdm->coordinateDM, ncdm);
    3895:       DMSetLocalSection(ncdm, cs);
    3896:       DMSetCoordinateDM(*refdm, ncdm);
    3897:       DMDestroy(&ncdm);
    3898:     }
    3899:   }
    3900:   DMGetCoordinatesLocal(rdm, &coords);
    3901:   if (coords) {
    3902:     DMSetCoordinatesLocal(*refdm, coords);
    3903:   } else {
    3904:     DMGetCoordinates(rdm, &coords);
    3905:     if (coords) {DMSetCoordinates(*refdm, coords);}
    3906:   }
    3907:   DMDestroy(&rdm);
    3908:   return(0);
    3909: }

    3911: /*@
    3912:   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell

    3914:   Collective

    3916:   Input Parameters:
    3917: + comm    - The communicator
    3918: . dim     - The spatial dimension
    3919: - simplex - Flag for simplex, otherwise use a tensor-product cell

    3921:   Output Parameter:
    3922: . refdm - The reference cell

    3924:   Level: intermediate

    3926: .seealso: DMPlexCreateReferenceCellByType(), DMPlexCreateBoxMesh()
    3927: @*/
    3928: PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
    3929: {

    3933:   switch (dim) {
    3934:   case 0: DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_POINT, refdm);break;
    3935:   case 1: DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_SEGMENT, refdm);break;
    3936:   case 2:
    3937:     if (simplex) {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TRIANGLE, refdm);}
    3938:     else         {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_QUADRILATERAL, refdm);}
    3939:     break;
    3940:   case 3:
    3941:     if (simplex) {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TETRAHEDRON, refdm);}
    3942:     else         {DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_HEXAHEDRON, refdm);}
    3943:     break;
    3944:   default:
    3945:     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %D", dim);
    3946:   }
    3947:   return(0);
    3948: }