Date: 2022-03-31T04:47:31+00:00

Actual source code: plexgeometry.c

      1: #include <petsc/private/dmpleximpl.h>
      2: #include <petsc/private/petscfeimpl.h>
      3: #include <petscblaslapack.h>
      4: #include <petsctime.h>

      6: /*@
      7:   DMPlexFindVertices - Try to find DAG points based on their coordinates.

      9:   Not Collective (provided DMGetCoordinatesLocalSetUp() has been called already)

     11:   Input Parameters:
     12: + dm - The DMPlex object
     13: . coordinates - The Vec of coordinates of the sought points
     14: - eps - The tolerance or PETSC_DEFAULT

     16:   Output Parameters:
     17: . points - The IS of found DAG points or -1

     19:   Level: intermediate

     21:   Notes:
     22:   The length of Vec coordinates must be npoints * dim where dim is the spatial dimension returned by DMGetCoordinateDim() and npoints is the number of sought points.

     24:   The output IS is living on PETSC_COMM_SELF and its length is npoints.
     25:   Each rank does the search independently.
     26:   If this rank's local DMPlex portion contains the DAG point corresponding to the i-th tuple of coordinates, the i-th entry of the output IS is set to that DAG point, otherwise to -1.

     28:   The output IS must be destroyed by user.

     30:   The tolerance is interpreted as the maximum Euclidean (L2) distance of the sought point from the specified coordinates.

     32:   Complexity of this function is currently O(mn) with m number of vertices to find and n number of vertices in the local mesh. This could probably be improved if needed.

     34: .seealso: DMPlexCreate(), DMGetCoordinatesLocal()
     35: @*/
     36: PetscErrorCode DMPlexFindVertices(DM dm, Vec coordinates, PetscReal eps, IS *points)
     37: {
     38:   PetscInt          c, cdim, i, j, o, p, vStart, vEnd;
     39:   PetscInt          npoints;
     40:   const PetscScalar *coord;
     41:   Vec               allCoordsVec;
     42:   const PetscScalar *allCoords;
     43:   PetscInt          *dagPoints;

     45:   if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
     46:   DMGetCoordinateDim(dm, &cdim);
     47:   {
     48:     PetscInt n;

     50:     VecGetLocalSize(coordinates, &n);
     52:     npoints = n / cdim;
     53:   }
     54:   DMGetCoordinatesLocal(dm, &allCoordsVec);
     55:   VecGetArrayRead(allCoordsVec, &allCoords);
     56:   VecGetArrayRead(coordinates, &coord);
     57:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
     58:   if (PetscDefined(USE_DEBUG)) {
     59:     /* check coordinate section is consistent with DM dimension */
     60:     PetscSection      cs;
     61:     PetscInt          ndof;

     63:     DMGetCoordinateSection(dm, &cs);
     64:     for (p = vStart; p < vEnd; p++) {
     65:       PetscSectionGetDof(cs, p, &ndof);
     67:     }
     68:   }
     69:   PetscMalloc1(npoints, &dagPoints);
     70:   if (eps == 0.0) {
     71:     for (i=0,j=0; i < npoints; i++,j+=cdim) {
     72:       dagPoints[i] = -1;
     73:       for (p = vStart,o=0; p < vEnd; p++,o+=cdim) {
     74:         for (c = 0; c < cdim; c++) {
     75:           if (coord[j+c] != allCoords[o+c]) break;
     76:         }
     77:         if (c == cdim) {
     78:           dagPoints[i] = p;
     79:           break;
     80:         }
     81:       }
     82:     }
     83:   } else {
     84:     for (i=0,j=0; i < npoints; i++,j+=cdim) {
     85:       PetscReal         norm;

     87:       dagPoints[i] = -1;
     88:       for (p = vStart,o=0; p < vEnd; p++,o+=cdim) {
     89:         norm = 0.0;
     90:         for (c = 0; c < cdim; c++) {
     91:           norm += PetscRealPart(PetscSqr(coord[j+c] - allCoords[o+c]));
     92:         }
     93:         norm = PetscSqrtReal(norm);
     94:         if (norm <= eps) {
     95:           dagPoints[i] = p;
     96:           break;
     97:         }
     98:       }
     99:     }
    100:   }
    101:   VecRestoreArrayRead(allCoordsVec, &allCoords);
    102:   VecRestoreArrayRead(coordinates, &coord);
    103:   ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points);
    104:   return 0;
    105: }

    107: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
    108: {
    109:   const PetscReal p0_x  = segmentA[0*2+0];
    110:   const PetscReal p0_y  = segmentA[0*2+1];
    111:   const PetscReal p1_x  = segmentA[1*2+0];
    112:   const PetscReal p1_y  = segmentA[1*2+1];
    113:   const PetscReal p2_x  = segmentB[0*2+0];
    114:   const PetscReal p2_y  = segmentB[0*2+1];
    115:   const PetscReal p3_x  = segmentB[1*2+0];
    116:   const PetscReal p3_y  = segmentB[1*2+1];
    117:   const PetscReal s1_x  = p1_x - p0_x;
    118:   const PetscReal s1_y  = p1_y - p0_y;
    119:   const PetscReal s2_x  = p3_x - p2_x;
    120:   const PetscReal s2_y  = p3_y - p2_y;
    121:   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);

    123:   *hasIntersection = PETSC_FALSE;
    124:   /* Non-parallel lines */
    125:   if (denom != 0.0) {
    126:     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
    127:     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;

    129:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
    130:       *hasIntersection = PETSC_TRUE;
    131:       if (intersection) {
    132:         intersection[0] = p0_x + (t * s1_x);
    133:         intersection[1] = p0_y + (t * s1_y);
    134:       }
    135:     }
    136:   }
    137:   return 0;
    138: }

    140: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
    141: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
    142: {
    143:   const PetscReal p0_x  = segmentA[0*3+0];
    144:   const PetscReal p0_y  = segmentA[0*3+1];
    145:   const PetscReal p0_z  = segmentA[0*3+2];
    146:   const PetscReal p1_x  = segmentA[1*3+0];
    147:   const PetscReal p1_y  = segmentA[1*3+1];
    148:   const PetscReal p1_z  = segmentA[1*3+2];
    149:   const PetscReal q0_x  = segmentB[0*3+0];
    150:   const PetscReal q0_y  = segmentB[0*3+1];
    151:   const PetscReal q0_z  = segmentB[0*3+2];
    152:   const PetscReal q1_x  = segmentB[1*3+0];
    153:   const PetscReal q1_y  = segmentB[1*3+1];
    154:   const PetscReal q1_z  = segmentB[1*3+2];
    155:   const PetscReal r0_x  = segmentC[0*3+0];
    156:   const PetscReal r0_y  = segmentC[0*3+1];
    157:   const PetscReal r0_z  = segmentC[0*3+2];
    158:   const PetscReal r1_x  = segmentC[1*3+0];
    159:   const PetscReal r1_y  = segmentC[1*3+1];
    160:   const PetscReal r1_z  = segmentC[1*3+2];
    161:   const PetscReal s0_x  = p1_x - p0_x;
    162:   const PetscReal s0_y  = p1_y - p0_y;
    163:   const PetscReal s0_z  = p1_z - p0_z;
    164:   const PetscReal s1_x  = q1_x - q0_x;
    165:   const PetscReal s1_y  = q1_y - q0_y;
    166:   const PetscReal s1_z  = q1_z - q0_z;
    167:   const PetscReal s2_x  = r1_x - r0_x;
    168:   const PetscReal s2_y  = r1_y - r0_y;
    169:   const PetscReal s2_z  = r1_z - r0_z;
    170:   const PetscReal s3_x  = s1_y*s2_z - s1_z*s2_y; /* s1 x s2 */
    171:   const PetscReal s3_y  = s1_z*s2_x - s1_x*s2_z;
    172:   const PetscReal s3_z  = s1_x*s2_y - s1_y*s2_x;
    173:   const PetscReal s4_x  = s0_y*s2_z - s0_z*s2_y; /* s0 x s2 */
    174:   const PetscReal s4_y  = s0_z*s2_x - s0_x*s2_z;
    175:   const PetscReal s4_z  = s0_x*s2_y - s0_y*s2_x;
    176:   const PetscReal s5_x  = s1_y*s0_z - s1_z*s0_y; /* s1 x s0 */
    177:   const PetscReal s5_y  = s1_z*s0_x - s1_x*s0_z;
    178:   const PetscReal s5_z  = s1_x*s0_y - s1_y*s0_x;
    179:   const PetscReal denom = -(s0_x*s3_x + s0_y*s3_y + s0_z*s3_z); /* -s0 . (s1 x s2) */

    181:   *hasIntersection = PETSC_FALSE;
    182:   /* Line not parallel to plane */
    183:   if (denom != 0.0) {
    184:     const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
    185:     const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
    186:     const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;

    188:     if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
    189:       *hasIntersection = PETSC_TRUE;
    190:       if (intersection) {
    191:         intersection[0] = p0_x + (t * s0_x);
    192:         intersection[1] = p0_y + (t * s0_y);
    193:         intersection[2] = p0_z + (t * s0_z);
    194:       }
    195:     }
    196:   }
    197:   return 0;
    198: }

    200: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    201: {
    202:   const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
    203:   const PetscReal x   = PetscRealPart(point[0]);
    204:   PetscReal       v0, J, invJ, detJ;
    205:   PetscReal       xi;

    207:   DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ);
    208:   xi   = invJ*(x - v0);

    210:   if ((xi >= -eps) && (xi <= 2.+eps)) *cell = c;
    211:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    212:   return 0;
    213: }

    215: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    216: {
    217:   const PetscInt  embedDim = 2;
    218:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    219:   PetscReal       x        = PetscRealPart(point[0]);
    220:   PetscReal       y        = PetscRealPart(point[1]);
    221:   PetscReal       v0[2], J[4], invJ[4], detJ;
    222:   PetscReal       xi, eta;

    224:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    225:   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
    226:   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);

    228:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
    229:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    230:   return 0;
    231: }

    233: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
    234: {
    235:   const PetscInt  embedDim = 2;
    236:   PetscReal       x        = PetscRealPart(point[0]);
    237:   PetscReal       y        = PetscRealPart(point[1]);
    238:   PetscReal       v0[2], J[4], invJ[4], detJ;
    239:   PetscReal       xi, eta, r;

    241:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    242:   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
    243:   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);

    245:   xi  = PetscMax(xi,  0.0);
    246:   eta = PetscMax(eta, 0.0);
    247:   if (xi + eta > 2.0) {
    248:     r    = (xi + eta)/2.0;
    249:     xi  /= r;
    250:     eta /= r;
    251:   }
    252:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
    253:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
    254:   return 0;
    255: }

    257: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    258: {
    259:   PetscSection       coordSection;
    260:   Vec             coordsLocal;
    261:   PetscScalar    *coords = NULL;
    262:   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
    263:   PetscReal       x         = PetscRealPart(point[0]);
    264:   PetscReal       y         = PetscRealPart(point[1]);
    265:   PetscInt        crossings = 0, f;

    267:   DMGetCoordinatesLocal(dm, &coordsLocal);
    268:   DMGetCoordinateSection(dm, &coordSection);
    269:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    270:   for (f = 0; f < 4; ++f) {
    271:     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
    272:     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
    273:     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
    274:     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
    275:     PetscReal slope = (y_j - y_i) / (x_j - x_i);
    276:     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
    277:     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
    278:     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
    279:     if ((cond1 || cond2)  && above) ++crossings;
    280:   }
    281:   if (crossings % 2) *cell = c;
    282:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    283:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    284:   return 0;
    285: }

    287: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    288: {
    289:   const PetscInt  embedDim = 3;
    290:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    291:   PetscReal       v0[3], J[9], invJ[9], detJ;
    292:   PetscReal       x = PetscRealPart(point[0]);
    293:   PetscReal       y = PetscRealPart(point[1]);
    294:   PetscReal       z = PetscRealPart(point[2]);
    295:   PetscReal       xi, eta, zeta;

    297:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    298:   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
    299:   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
    300:   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);

    302:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0+eps)) *cell = c;
    303:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    304:   return 0;
    305: }

    307: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    308: {
    309:   PetscSection   coordSection;
    310:   Vec            coordsLocal;
    311:   PetscScalar   *coords = NULL;
    312:   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
    313:                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
    314:   PetscBool      found = PETSC_TRUE;
    315:   PetscInt       f;

    317:   DMGetCoordinatesLocal(dm, &coordsLocal);
    318:   DMGetCoordinateSection(dm, &coordSection);
    319:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    320:   for (f = 0; f < 6; ++f) {
    321:     /* Check the point is under plane */
    322:     /*   Get face normal */
    323:     PetscReal v_i[3];
    324:     PetscReal v_j[3];
    325:     PetscReal normal[3];
    326:     PetscReal pp[3];
    327:     PetscReal dot;

    329:     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
    330:     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
    331:     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
    332:     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
    333:     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
    334:     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
    335:     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
    336:     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
    337:     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
    338:     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
    339:     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
    340:     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
    341:     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];

    343:     /* Check that projected point is in face (2D location problem) */
    344:     if (dot < 0.0) {
    345:       found = PETSC_FALSE;
    346:       break;
    347:     }
    348:   }
    349:   if (found) *cell = c;
    350:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    351:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    352:   return 0;
    353: }

    355: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
    356: {
    357:   PetscInt d;

    359:   box->dim = dim;
    360:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
    361:   return 0;
    362: }

    364: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    365: {
    366:   PetscMalloc1(1, box);
    367:   PetscGridHashInitialize_Internal(*box, dim, point);
    368:   return 0;
    369: }

    371: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
    372: {
    373:   PetscInt d;

    375:   for (d = 0; d < box->dim; ++d) {
    376:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    377:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    378:   }
    379:   return 0;
    380: }

    382: /*
    383:   PetscGridHashSetGrid - Divide the grid into boxes

    385:   Not collective

    387:   Input Parameters:
    388: + box - The grid hash object
    389: . n   - The number of boxes in each dimension, or PETSC_DETERMINE
    390: - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE

    392:   Level: developer

    394: .seealso: PetscGridHashCreate()
    395: */
    396: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
    397: {
    398:   PetscInt d;

    400:   for (d = 0; d < box->dim; ++d) {
    401:     box->extent[d] = box->upper[d] - box->lower[d];
    402:     if (n[d] == PETSC_DETERMINE) {
    403:       box->h[d] = h[d];
    404:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
    405:     } else {
    406:       box->n[d] = n[d];
    407:       box->h[d] = box->extent[d]/n[d];
    408:     }
    409:   }
    410:   return 0;
    411: }

    413: /*
    414:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

    416:   Not collective

    418:   Input Parameters:
    419: + box       - The grid hash object
    420: . numPoints - The number of input points
    421: - points    - The input point coordinates

    423:   Output Parameters:
    424: + dboxes    - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
    425: - boxes     - An array of numPoints integers expressing the enclosing box as single number, or NULL

    427:   Level: developer

    429: .seealso: PetscGridHashCreate()
    430: */
    431: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
    432: {
    433:   const PetscReal *lower = box->lower;
    434:   const PetscReal *upper = box->upper;
    435:   const PetscReal *h     = box->h;
    436:   const PetscInt  *n     = box->n;
    437:   const PetscInt   dim   = box->dim;
    438:   PetscInt         d, p;

    440:   for (p = 0; p < numPoints; ++p) {
    441:     for (d = 0; d < dim; ++d) {
    442:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

    444:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    445:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
    447:                                              p, (double) PetscRealPart(points[p*dim+0]), dim > 1 ? (double) PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? (double) PetscRealPart(points[p*dim+2]) : 0.0);
    448:       dboxes[p*dim+d] = dbox;
    449:     }
    450:     if (boxes) for (d = dim-2, boxes[p] = dboxes[p*dim+dim-1]; d >= 0; --d) boxes[p] = boxes[p]*n[d] + dboxes[p*dim+d];
    451:   }
    452:   return 0;
    453: }

    455: /*
    456:  PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

    458:  Not collective

    460:   Input Parameters:
    461: + box       - The grid hash object
    462: . numPoints - The number of input points
    463: - points    - The input point coordinates

    465:   Output Parameters:
    466: + dboxes    - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
    467: . boxes     - An array of numPoints integers expressing the enclosing box as single number, or NULL
    468: - found     - Flag indicating if point was located within a box

    470:   Level: developer

    472: .seealso: PetscGridHashGetEnclosingBox()
    473: */
    474: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[],PetscBool *found)
    475: {
    476:   const PetscReal *lower = box->lower;
    477:   const PetscReal *upper = box->upper;
    478:   const PetscReal *h     = box->h;
    479:   const PetscInt  *n     = box->n;
    480:   const PetscInt   dim   = box->dim;
    481:   PetscInt         d, p;

    483:   *found = PETSC_FALSE;
    484:   for (p = 0; p < numPoints; ++p) {
    485:     for (d = 0; d < dim; ++d) {
    486:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

    488:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    489:       if (dbox < 0 || dbox >= n[d]) {
    490:         return 0;
    491:       }
    492:       dboxes[p*dim+d] = dbox;
    493:     }
    494:     if (boxes) for (d = dim-2, boxes[p] = dboxes[p*dim+dim-1]; d >= 0; --d) boxes[p] = boxes[p]*n[d] + dboxes[p*dim+d];
    495:   }
    496:   *found = PETSC_TRUE;
    497:   return 0;
    498: }

    500: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    501: {
    502:   if (*box) {
    503:     PetscSectionDestroy(&(*box)->cellSection);
    504:     ISDestroy(&(*box)->cells);
    505:     DMLabelDestroy(&(*box)->cellsSparse);
    506:   }
    507:   PetscFree(*box);
    508:   return 0;
    509: }

    511: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
    512: {
    513:   DMPolytopeType ct;

    515:   DMPlexGetCellType(dm, cellStart, &ct);
    516:   switch (ct) {
    517:     case DM_POLYTOPE_SEGMENT:
    518:     DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell);break;
    519:     case DM_POLYTOPE_TRIANGLE:
    520:     DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);break;
    521:     case DM_POLYTOPE_QUADRILATERAL:
    522:     DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell);break;
    523:     case DM_POLYTOPE_TETRAHEDRON:
    524:     DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);break;
    525:     case DM_POLYTOPE_HEXAHEDRON:
    526:     DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);break;
    527:     default: SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %D with type %s", cellStart, DMPolytopeTypes[ct]);
    528:   }
    529:   return 0;
    530: }

    532: /*
    533:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
    534: */
    535: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
    536: {
    537:   DMPolytopeType ct;

    539:   DMPlexGetCellType(dm, cell, &ct);
    540:   switch (ct) {
    541:     case DM_POLYTOPE_TRIANGLE:
    542:     DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);break;
    543: #if 0
    544:     case DM_POLYTOPE_QUADRILATERAL:
    545:     DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);break;
    546:     case DM_POLYTOPE_TETRAHEDRON:
    547:     DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);break;
    548:     case DM_POLYTOPE_HEXAHEDRON:
    549:     DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);break;
    550: #endif
    551:     default: SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    552:   }
    553:   return 0;
    554: }

    556: /*
    557:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex

    559:   Collective on dm

    561:   Input Parameter:
    562: . dm - The Plex

    564:   Output Parameter:
    565: . localBox - The grid hash object

    567:   Level: developer

    569: .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
    570: */
    571: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
    572: {
    573:   const PetscInt     debug = 0;
    574:   MPI_Comm           comm;
    575:   PetscGridHash      lbox;
    576:   Vec                coordinates;
    577:   PetscSection       coordSection;
    578:   Vec                coordsLocal;
    579:   const PetscScalar *coords;
    580:   PetscScalar       *edgeCoords;
    581:   PetscInt          *dboxes, *boxes;
    582:   PetscInt           n[3] = {2, 2, 2};
    583:   PetscInt           dim, N, maxConeSize, cStart, cEnd, c, eStart, eEnd, i;
    584:   PetscBool          flg;

    586:   PetscObjectGetComm((PetscObject) dm, &comm);
    587:   DMGetCoordinatesLocal(dm, &coordinates);
    588:   DMGetCoordinateDim(dm, &dim);
    589:   DMPlexGetMaxSizes(dm, &maxConeSize, NULL);
    590:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    591:   VecGetLocalSize(coordinates, &N);
    592:   VecGetArrayRead(coordinates, &coords);
    593:   PetscGridHashCreate(comm, dim, coords, &lbox);
    594:   for (i = 0; i < N; i += dim) PetscGridHashEnlarge(lbox, &coords[i]);
    595:   VecRestoreArrayRead(coordinates, &coords);
    596:   c    = dim;
    597:   PetscOptionsGetIntArray(NULL, ((PetscObject) dm)->prefix, "-dm_plex_hash_box_faces", n, &c, &flg);
    598:   if (flg) {for (i = c; i < dim; ++i) n[i] = n[c-1];}
    599:   else     {for (i = 0; i < dim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal) (cEnd - cStart), 1.0/dim) * 0.8));}
    600:   PetscGridHashSetGrid(lbox, n, NULL);
    601: #if 0
    602:   /* Could define a custom reduction to merge these */
    603:   MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);
    604:   MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);
    605: #endif
    606:   /* Is there a reason to snap the local bounding box to a division of the global box? */
    607:   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
    608:   /* Create label */
    609:   DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);
    610:   if (dim < 2) eStart = eEnd = -1;
    611:   DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse);
    612:   DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);
    613:   /* Compute boxes which overlap each cell: https://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
    614:   DMGetCoordinatesLocal(dm, &coordsLocal);
    615:   DMGetCoordinateSection(dm, &coordSection);
    616:   PetscCalloc3(16 * dim, &dboxes, 16, &boxes, PetscPowInt(maxConeSize, dim) * dim, &edgeCoords);
    617:   for (c = cStart; c < cEnd; ++c) {
    618:     const PetscReal *h       = lbox->h;
    619:     PetscScalar     *ccoords = NULL;
    620:     PetscInt         csize   = 0;
    621:     PetscInt        *closure = NULL;
    622:     PetscInt         Ncl, cl, Ne = 0;
    623:     PetscScalar      point[3];
    624:     PetscInt         dlim[6], d, e, i, j, k;

    626:     /* Get all edges in cell */
    627:     DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure);
    628:     for (cl = 0; cl < Ncl*2; ++cl) {
    629:       if ((closure[cl] >= eStart) && (closure[cl] < eEnd)) {
    630:         PetscScalar *ecoords = &edgeCoords[Ne*dim*2];
    631:         PetscInt     ecsize  = dim*2;

    633:         DMPlexVecGetClosure(dm, coordSection, coordsLocal, closure[cl], &ecsize, &ecoords);
    635:         ++Ne;
    636:       }
    637:     }
    638:     DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure);
    639:     /* Find boxes enclosing each vertex */
    640:     DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);
    641:     PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);
    642:     /* Mark cells containing the vertices */
    643:     for (e = 0; e < csize/dim; ++e) {
    644:       if (debug) PetscPrintf(PETSC_COMM_SELF, "Cell %D has vertex in box %D (%D, %D, %D)\n", c, boxes[e], dboxes[e*dim+0], dim > 1 ? dboxes[e*dim+1] : -1, dim > 2 ? dboxes[e*dim+2] : -1);
    645:       DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);
    646:     }
    647:     /* Get grid of boxes containing these */
    648:     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
    649:     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
    650:     for (e = 1; e < dim+1; ++e) {
    651:       for (d = 0; d < dim; ++d) {
    652:         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
    653:         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
    654:       }
    655:     }
    656:     /* Check for intersection of box with cell */
    657:     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
    658:       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
    659:         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
    660:           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
    661:           PetscScalar    cpoint[3];
    662:           PetscInt       cell, edge, ii, jj, kk;

    664:           if (debug) PetscPrintf(PETSC_COMM_SELF, "Box %D: (%.2g, %.2g, %.2g) -- (%.2g, %.2g, %.2g)\n", box, point[0], point[1], point[2], point[0] + h[0], point[1] + h[1], point[2] + h[2]);
    665:           /* Check whether cell contains any vertex of this subbox TODO vectorize this */
    666:           for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
    667:             for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
    668:               for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {

    670:                 DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);
    671:                 if (cell >= 0) {
    672:                   if (debug) PetscPrintf(PETSC_COMM_SELF, "  Cell %D contains vertex (%.2g, %.2g, %.2g) of box %D\n", c, cpoint[0], cpoint[1], cpoint[2], box);
    673:                   DMLabelSetValue(lbox->cellsSparse, c, box);
    674:                   jj = kk = 2;
    675:                   break;
    676:                 }
    677:               }
    678:             }
    679:           }
    680:           /* Check whether cell edge intersects any face of these subboxes TODO vectorize this */
    681:           for (edge = 0; edge < Ne; ++edge) {
    682:             PetscReal segA[6] = {0.,0.,0.,0.,0.,0.};
    683:             PetscReal segB[6] = {0.,0.,0.,0.,0.,0.};
    684:             PetscReal segC[6] = {0.,0.,0.,0.,0.,0.};

    687:             for (d = 0; d < dim*2; ++d) segA[d] = PetscRealPart(edgeCoords[edge*dim*2+d]);
    688:             /* 1D: (x) -- (x+h)               0 -- 1
    689:                2D: (x,   y)   -- (x,   y+h)   (0, 0) -- (0, 1)
    690:                    (x+h, y)   -- (x+h, y+h)   (1, 0) -- (1, 1)
    691:                    (x,   y)   -- (x+h, y)     (0, 0) -- (1, 0)
    692:                    (x,   y+h) -- (x+h, y+h)   (0, 1) -- (1, 1)
    693:                3D: (x,   y,   z)   -- (x,   y+h, z),   (x,   y,   z)   -- (x,   y,   z+h) (0, 0, 0) -- (0, 1, 0), (0, 0, 0) -- (0, 0, 1)
    694:                    (x+h, y,   z)   -- (x+h, y+h, z),   (x+h, y,   z)   -- (x+h, y,   z+h) (1, 0, 0) -- (1, 1, 0), (1, 0, 0) -- (1, 0, 1)
    695:                    (x,   y,   z)   -- (x+h, y,   z),   (x,   y,   z)   -- (x,   y,   z+h) (0, 0, 0) -- (1, 0, 0), (0, 0, 0) -- (0, 0, 1)
    696:                    (x,   y+h, z)   -- (x+h, y+h, z),   (x,   y+h, z)   -- (x,   y+h, z+h) (0, 1, 0) -- (1, 1, 0), (0, 1, 0) -- (0, 1, 1)
    697:                    (x,   y,   z)   -- (x+h, y,   z),   (x,   y,   z)   -- (x,   y+h, z)   (0, 0, 0) -- (1, 0, 0), (0, 0, 0) -- (0, 1, 0)
    698:                    (x,   y,   z+h) -- (x+h, y,   z+h), (x,   y,   z+h) -- (x,   y+h, z+h) (0, 0, 1) -- (1, 0, 1), (0, 0, 1) -- (0, 1, 1)
    699:              */
    700:             /* Loop over faces with normal in direction d */
    701:             for (d = 0; d < dim; ++d) {
    702:               PetscBool intersects = PETSC_FALSE;
    703:               PetscInt  e = (d+1)%dim;
    704:               PetscInt  f = (d+2)%dim;

    706:               /* There are two faces in each dimension */
    707:               for (ii = 0; ii < 2; ++ii) {
    708:                 segB[d]     = PetscRealPart(point[d] + ii*h[d]);
    709:                 segB[dim+d] = PetscRealPart(point[d] + ii*h[d]);
    710:                 segC[d]     = PetscRealPart(point[d] + ii*h[d]);
    711:                 segC[dim+d] = PetscRealPart(point[d] + ii*h[d]);
    712:                 if (dim > 1) {
    713:                   segB[e]     = PetscRealPart(point[e] + 0*h[e]);
    714:                   segB[dim+e] = PetscRealPart(point[e] + 1*h[e]);
    715:                   segC[e]     = PetscRealPart(point[e] + 0*h[e]);
    716:                   segC[dim+e] = PetscRealPart(point[e] + 0*h[e]);
    717:                 }
    718:                 if (dim > 2) {
    719:                   segB[f]     = PetscRealPart(point[f] + 0*h[f]);
    720:                   segB[dim+f] = PetscRealPart(point[f] + 0*h[f]);
    721:                   segC[f]     = PetscRealPart(point[f] + 0*h[f]);
    722:                   segC[dim+f] = PetscRealPart(point[f] + 1*h[f]);
    723:                 }
    724:                 if (dim == 2) {
    725:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
    726:                 } else if (dim == 3) {
    727:                   DMPlexGetLinePlaneIntersection_3D_Internal(segA, segB, segC, NULL, &intersects);
    728:                 }
    729:                 if (intersects) {
    730:                   if (debug) PetscPrintf(PETSC_COMM_SELF, "  Cell %D edge %D (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g) intersects box %D, face (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g) (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g)\n", c, edge, segA[0], segA[1], segA[2], segA[3], segA[4], segA[5], box, segB[0], segB[1], segB[2], segB[3], segB[4], segB[5], segC[0], segC[1], segC[2], segC[3], segC[4], segC[5]);
    731:                   DMLabelSetValue(lbox->cellsSparse, c, box); edge = Ne; break;
    732:                 }
    733:               }
    734:             }
    735:           }
    736:         }
    737:       }
    738:     }
    739:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
    740:   }
    741:   PetscFree3(dboxes, boxes, edgeCoords);
    742:   if (debug) DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF);
    743:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
    744:   DMLabelDestroy(&lbox->cellsSparse);
    745:   *localBox = lbox;
    746:   return 0;
    747: }

    749: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
    750: {
    751:   const PetscInt  debug = 0;
    752:   DM_Plex        *mesh = (DM_Plex *) dm->data;
    753:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
    754:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
    755:   PetscInt        dim, cStart, cEnd, numCells, c, d;
    756:   const PetscInt *boxCells;
    757:   PetscSFNode    *cells;
    758:   PetscScalar    *a;
    759:   PetscMPIInt     result;
    760:   PetscLogDouble  t0,t1;
    761:   PetscReal       gmin[3],gmax[3];
    762:   PetscInt        terminating_query_type[] = { 0, 0, 0 };

    764:   PetscLogEventBegin(DMPLEX_LocatePoints,0,0,0,0);
    765:   PetscTime(&t0);
    767:   DMGetCoordinateDim(dm, &dim);
    768:   VecGetBlockSize(v, &bs);
    769:   MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);
    772:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    773:   VecGetLocalSize(v, &numPoints);
    774:   VecGetArray(v, &a);
    775:   numPoints /= bs;
    776:   {
    777:     const PetscSFNode *sf_cells;

    779:     PetscSFGetGraph(cellSF,NULL,NULL,NULL,&sf_cells);
    780:     if (sf_cells) {
    781:       PetscInfo(dm,"[DMLocatePoints_Plex] Re-using existing StarForest node list\n");
    782:       cells = (PetscSFNode*)sf_cells;
    783:       reuse = PETSC_TRUE;
    784:     } else {
    785:       PetscInfo(dm,"[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n");
    786:       PetscMalloc1(numPoints, &cells);
    787:       /* initialize cells if created */
    788:       for (p=0; p<numPoints; p++) {
    789:         cells[p].rank  = 0;
    790:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    791:       }
    792:     }
    793:   }
    794:   /* define domain bounding box */
    795:   {
    796:     Vec coorglobal;

    798:     DMGetCoordinates(dm,&coorglobal);
    799:     VecStrideMaxAll(coorglobal,NULL,gmax);
    800:     VecStrideMinAll(coorglobal,NULL,gmin);
    801:   }
    802:   if (hash) {
    803:     if (!mesh->lbox) {PetscInfo(dm, "Initializing grid hashing"));PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox);}
    804:     /* Designate the local box for each point */
    805:     /* Send points to correct process */
    806:     /* Search cells that lie in each subbox */
    807:     /*   Should we bin points before doing search? */
    808:     ISGetIndices(mesh->lbox->cells, &boxCells);
    809:   }
    810:   for (p = 0, numFound = 0; p < numPoints; ++p) {
    811:     const PetscScalar *point = &a[p*bs];
    812:     PetscInt           dbin[3] = {-1,-1,-1}, bin, cell = -1, cellOffset;
    813:     PetscBool          point_outside_domain = PETSC_FALSE;

    815:     /* check bounding box of domain */
    816:     for (d=0; d<dim; d++) {
    817:       if (PetscRealPart(point[d]) < gmin[d]) { point_outside_domain = PETSC_TRUE; break; }
    818:       if (PetscRealPart(point[d]) > gmax[d]) { point_outside_domain = PETSC_TRUE; break; }
    819:     }
    820:     if (point_outside_domain) {
    821:       cells[p].rank = 0;
    822:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    823:       terminating_query_type[0]++;
    824:       continue;
    825:     }

    827:     /* check initial values in cells[].index - abort early if found */
    828:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    829:       c = cells[p].index;
    830:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    831:       DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    832:       if (cell >= 0) {
    833:         cells[p].rank = 0;
    834:         cells[p].index = cell;
    835:         numFound++;
    836:       }
    837:     }
    838:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    839:       terminating_query_type[1]++;
    840:       continue;
    841:     }

    843:     if (hash) {
    844:       PetscBool found_box;

    846:       if (debug) PetscPrintf(PETSC_COMM_SELF, "Checking point %D (%.2g, %.2g, %.2g)\n", p, point[0], point[1], point[2]);
    847:       /* allow for case that point is outside box - abort early */
    848:       PetscGridHashGetEnclosingBoxQuery(mesh->lbox, 1, point, dbin, &bin,&found_box);
    849:       if (found_box) {
    850:         if (debug) PetscPrintf(PETSC_COMM_SELF, "  Found point in box %D (%D, %D, %D)\n", bin, dbin[0], dbin[1], dbin[2]);
    851:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
    852:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    853:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    854:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    855:           if (debug) PetscPrintf(PETSC_COMM_SELF, "    Checking for point in cell %D\n", boxCells[c]);
    856:           DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);
    857:           if (cell >= 0) {
    858:             if (debug) PetscPrintf(PETSC_COMM_SELF, "      FOUND in cell %D\n", cell);
    859:             cells[p].rank = 0;
    860:             cells[p].index = cell;
    861:             numFound++;
    862:             terminating_query_type[2]++;
    863:             break;
    864:           }
    865:         }
    866:       }
    867:     } else {
    868:       for (c = cStart; c < cEnd; ++c) {
    869:         DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    870:         if (cell >= 0) {
    871:           cells[p].rank = 0;
    872:           cells[p].index = cell;
    873:           numFound++;
    874:           terminating_query_type[2]++;
    875:           break;
    876:         }
    877:       }
    878:     }
    879:   }
    880:   if (hash) ISRestoreIndices(mesh->lbox->cells, &boxCells);
    881:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
    882:     for (p = 0; p < numPoints; p++) {
    883:       const PetscScalar *point = &a[p*bs];
    884:       PetscReal          cpoint[3], diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
    885:       PetscInt           dbin[3] = {-1,-1,-1}, bin, cellOffset, d, bestc = -1;

    887:       if (cells[p].index < 0) {
    888:         PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);
    889:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    890:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    891:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    892:           DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);
    893:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
    894:           dist = DMPlex_NormD_Internal(dim, diff);
    895:           if (dist < distMax) {
    896:             for (d = 0; d < dim; ++d) best[d] = cpoint[d];
    897:             bestc = boxCells[c];
    898:             distMax = dist;
    899:           }
    900:         }
    901:         if (distMax < PETSC_MAX_REAL) {
    902:           ++numFound;
    903:           cells[p].rank  = 0;
    904:           cells[p].index = bestc;
    905:           for (d = 0; d < dim; ++d) a[p*bs+d] = best[d];
    906:         }
    907:       }
    908:     }
    909:   }
    910:   /* This code is only be relevant when interfaced to parallel point location */
    911:   /* Check for highest numbered proc that claims a point (do we care?) */
    912:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
    913:     PetscMalloc1(numFound,&found);
    914:     for (p = 0, numFound = 0; p < numPoints; p++) {
    915:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
    916:         if (numFound < p) {
    917:           cells[numFound] = cells[p];
    918:         }
    919:         found[numFound++] = p;
    920:       }
    921:     }
    922:   }
    923:   VecRestoreArray(v, &a);
    924:   if (!reuse) {
    925:     PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);
    926:   }
    927:   PetscTime(&t1);
    928:   if (hash) {
    929:     PetscInfo(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside initial cell] : %D [hash]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
    930:   } else {
    931:     PetscInfo(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside initial cell] : %D [brute-force]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
    932:   }
    933:   PetscInfo(dm,"[DMLocatePoints_Plex] npoints %D : time(rank0) %1.2e (sec): points/sec %1.4e\n",numPoints,t1-t0,(double)((double)numPoints/(t1-t0)));
    934:   PetscLogEventEnd(DMPLEX_LocatePoints,0,0,0,0);
    935:   return 0;
    936: }

    938: /*@C
    939:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

    941:   Not collective

    943:   Input/Output Parameter:
    944: . coords - The coordinates of a segment, on output the new y-coordinate, and 0 for x

    946:   Output Parameter:
    947: . R - The rotation which accomplishes the projection

    949:   Level: developer

    951: .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
    952: @*/
    953: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
    954: {
    955:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
    956:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
    957:   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;

    959:   R[0] = c; R[1] = -s;
    960:   R[2] = s; R[3] =  c;
    961:   coords[0] = 0.0;
    962:   coords[1] = r;
    963:   return 0;
    964: }

    966: /*@C
    967:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

    969:   Not collective

    971:   Input/Output Parameter:
    972: . coords - The coordinates of a segment; on output, the new y-coordinate, and 0 for x and z

    974:   Output Parameter:
    975: . R - The rotation which accomplishes the projection

    977:   Note: This uses the basis completion described by Frisvad in http://www.imm.dtu.dk/~jerf/papers/abstracts/onb.html, DOI:10.1080/2165347X.2012.689606

    979:   Level: developer

    981: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
    982: @*/
    983: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
    984: {
    985:   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
    986:   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
    987:   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
    988:   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
    989:   PetscReal      rinv = 1. / r;

    991:   x *= rinv; y *= rinv; z *= rinv;
    992:   if (x > 0.) {
    993:     PetscReal inv1pX   = 1./ (1. + x);

    995:     R[0] = x; R[1] = -y;              R[2] = -z;
    996:     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
    997:     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
    998:   }
    999:   else {
    1000:     PetscReal inv1mX   = 1./ (1. - x);

    1002:     R[0] = x; R[1] = z;               R[2] = y;
    1003:     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
    1004:     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
    1005:   }
    1006:   coords[0] = 0.0;
    1007:   coords[1] = r;
    1008:   return 0;
    1009: }

    1011: /*@
    1012:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
    1013:     plane.  The normal is defined by positive orientation of the first 3 points.

    1015:   Not collective

    1017:   Input Parameter:
    1018: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

    1020:   Input/Output Parameter:
    1021: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
    1022:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

    1024:   Output Parameter:
    1025: . R - 3x3 row-major rotation matrix whose columns are the tangent basis [t1, t2, n].  Multiplying by R^T transforms from original frame to tangent frame.

    1027:   Level: developer

    1029: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
    1030: @*/
    1031: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    1032: {
    1033:   PetscReal x1[3], x2[3], n[3], c[3], norm;
    1034:   const PetscInt dim = 3;
    1035:   PetscInt       d, p;

    1037:   /* 0) Calculate normal vector */
    1038:   for (d = 0; d < dim; ++d) {
    1039:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
    1040:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
    1041:   }
    1042:   // n = x1 \otimes x2
    1043:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
    1044:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
    1045:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
    1046:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    1047:   for (d = 0; d < dim; d++) n[d] /= norm;
    1048:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
    1049:   for (d = 0; d < dim; d++) x1[d] /= norm;
    1050:   // x2 = n \otimes x1
    1051:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
    1052:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
    1053:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
    1054:   for (d=0; d<dim; d++) {
    1055:     R[d * dim + 0] = x1[d];
    1056:     R[d * dim + 1] = x2[d];
    1057:     R[d * dim + 2] = n[d];
    1058:     c[d] = PetscRealPart(coords[0*dim + d]);
    1059:   }
    1060:   for (p=0; p<coordSize/dim; p++) {
    1061:     PetscReal y[3];
    1062:     for (d=0; d<dim; d++) y[d] = PetscRealPart(coords[p*dim + d]) - c[d];
    1063:     for (d=0; d<2; d++) coords[p*2+d] = R[0*dim + d] * y[0] + R[1*dim + d] * y[1] + R[2*dim + d] * y[2];
    1064:   }
    1065:   return 0;
    1066: }

    1068: PETSC_UNUSED
    1069: static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    1070: {
    1071:   /* Signed volume is 1/2 the determinant

    1073:    |  1  1  1 |
    1074:    | x0 x1 x2 |
    1075:    | y0 y1 y2 |

    1077:      but if x0,y0 is the origin, we have

    1079:    | x1 x2 |
    1080:    | y1 y2 |
    1081:   */
    1082:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    1083:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    1084:   PetscReal       M[4], detM;
    1085:   M[0] = x1; M[1] = x2;
    1086:   M[2] = y1; M[3] = y2;
    1087:   DMPlex_Det2D_Internal(&detM, M);
    1088:   *vol = 0.5*detM;
    1089:   (void)PetscLogFlops(5.0);
    1090: }

    1092: PETSC_UNUSED
    1093: static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    1094: {
    1095:   /* Signed volume is 1/6th of the determinant

    1097:    |  1  1  1  1 |
    1098:    | x0 x1 x2 x3 |
    1099:    | y0 y1 y2 y3 |
    1100:    | z0 z1 z2 z3 |

    1102:      but if x0,y0,z0 is the origin, we have

    1104:    | x1 x2 x3 |
    1105:    | y1 y2 y3 |
    1106:    | z1 z2 z3 |
    1107:   */
    1108:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
    1109:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
    1110:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    1111:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1112:   PetscReal       M[9], detM;
    1113:   M[0] = x1; M[1] = x2; M[2] = x3;
    1114:   M[3] = y1; M[4] = y2; M[5] = y3;
    1115:   M[6] = z1; M[7] = z2; M[8] = z3;
    1116:   DMPlex_Det3D_Internal(&detM, M);
    1117:   *vol = -onesixth*detM;
    1118:   (void)PetscLogFlops(10.0);
    1119: }

    1121: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1122: {
    1123:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1124:   DMPlex_Det3D_Internal(vol, coords);
    1125:   *vol *= -onesixth;
    1126: }

    1128: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1129: {
    1130:   PetscSection   coordSection;
    1131:   Vec            coordinates;
    1132:   const PetscScalar *coords;
    1133:   PetscInt       dim, d, off;

    1135:   DMGetCoordinatesLocal(dm, &coordinates);
    1136:   DMGetCoordinateSection(dm, &coordSection);
    1137:   PetscSectionGetDof(coordSection,e,&dim);
    1138:   if (!dim) return 0;
    1139:   PetscSectionGetOffset(coordSection,e,&off);
    1140:   VecGetArrayRead(coordinates,&coords);
    1141:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
    1142:   VecRestoreArrayRead(coordinates,&coords);
    1143:   *detJ = 1.;
    1144:   if (J) {
    1145:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1146:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1147:     if (invJ) {
    1148:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1149:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1150:     }
    1151:   }
    1152:   return 0;
    1153: }

    1155: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1156: {
    1157:   PetscSection   coordSection;
    1158:   Vec            coordinates;
    1159:   PetscScalar   *coords = NULL;
    1160:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

    1162:   DMGetCoordinatesLocal(dm, &coordinates);
    1163:   DMGetCoordinateSection(dm, &coordSection);
    1164:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1165:   if (e >= pStart && e < pEnd) PetscSectionGetDof(coordSection,e,&numSelfCoords);
    1166:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1167:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1169:   *detJ = 0.0;
    1170:   if (numCoords == 6) {
    1171:     const PetscInt dim = 3;
    1172:     PetscReal      R[9], J0;

    1174:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1175:     DMPlexComputeProjection3Dto1D(coords, R);
    1176:     if (J)    {
    1177:       J0   = 0.5*PetscRealPart(coords[1]);
    1178:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
    1179:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
    1180:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
    1181:       DMPlex_Det3D_Internal(detJ, J);
    1182:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1183:     }
    1184:   } else if (numCoords == 4) {
    1185:     const PetscInt dim = 2;
    1186:     PetscReal      R[4], J0;

    1188:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1189:     DMPlexComputeProjection2Dto1D(coords, R);
    1190:     if (J)    {
    1191:       J0   = 0.5*PetscRealPart(coords[1]);
    1192:       J[0] = R[0]*J0; J[1] = R[1];
    1193:       J[2] = R[2]*J0; J[3] = R[3];
    1194:       DMPlex_Det2D_Internal(detJ, J);
    1195:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1196:     }
    1197:   } else if (numCoords == 2) {
    1198:     const PetscInt dim = 1;

    1200:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1201:     if (J)    {
    1202:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1203:       *detJ = J[0];
    1204:       PetscLogFlops(2.0);
    1205:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
    1206:     }
    1207:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
    1208:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1209:   return 0;
    1210: }

    1212: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1213: {
    1214:   PetscSection   coordSection;
    1215:   Vec            coordinates;
    1216:   PetscScalar   *coords = NULL;
    1217:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1219:   DMGetCoordinatesLocal(dm, &coordinates);
    1220:   DMGetCoordinateSection(dm, &coordSection);
    1221:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1222:   if (e >= pStart && e < pEnd) PetscSectionGetDof(coordSection,e,&numSelfCoords);
    1223:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1224:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1225:   *detJ = 0.0;
    1226:   if (numCoords == 9) {
    1227:     const PetscInt dim = 3;
    1228:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1230:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1231:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1232:     if (J)    {
    1233:       const PetscInt pdim = 2;

    1235:       for (d = 0; d < pdim; d++) {
    1236:         for (f = 0; f < pdim; f++) {
    1237:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1238:         }
    1239:       }
    1240:       PetscLogFlops(8.0);
    1241:       DMPlex_Det3D_Internal(detJ, J0);
    1242:       for (d = 0; d < dim; d++) {
    1243:         for (f = 0; f < dim; f++) {
    1244:           J[d*dim+f] = 0.0;
    1245:           for (g = 0; g < dim; g++) {
    1246:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1247:           }
    1248:         }
    1249:       }
    1250:       PetscLogFlops(18.0);
    1251:     }
    1252:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1253:   } else if (numCoords == 6) {
    1254:     const PetscInt dim = 2;

    1256:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1257:     if (J)    {
    1258:       for (d = 0; d < dim; d++) {
    1259:         for (f = 0; f < dim; f++) {
    1260:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1261:         }
    1262:       }
    1263:       PetscLogFlops(8.0);
    1264:       DMPlex_Det2D_Internal(detJ, J);
    1265:     }
    1266:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1267:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
    1268:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1269:   return 0;
    1270: }

    1272: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1273: {
    1274:   PetscSection   coordSection;
    1275:   Vec            coordinates;
    1276:   PetscScalar   *coords = NULL;
    1277:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1279:   DMGetCoordinatesLocal(dm, &coordinates);
    1280:   DMGetCoordinateSection(dm, &coordSection);
    1281:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1282:   if (e >= pStart && e < pEnd) PetscSectionGetDof(coordSection,e,&numSelfCoords);
    1283:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1284:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1285:   if (!Nq) {
    1286:     PetscInt vorder[4] = {0, 1, 2, 3};

    1288:     if (isTensor) {vorder[2] = 3; vorder[3] = 2;}
    1289:     *detJ = 0.0;
    1290:     if (numCoords == 12) {
    1291:       const PetscInt dim = 3;
    1292:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1294:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1295:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1296:       if (J)    {
    1297:         const PetscInt pdim = 2;

    1299:         for (d = 0; d < pdim; d++) {
    1300:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*pdim+d]) - PetscRealPart(coords[vorder[0]*pdim+d]));
    1301:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[2]*pdim+d]) - PetscRealPart(coords[vorder[1]*pdim+d]));
    1302:         }
    1303:         PetscLogFlops(8.0);
    1304:         DMPlex_Det3D_Internal(detJ, J0);
    1305:         for (d = 0; d < dim; d++) {
    1306:           for (f = 0; f < dim; f++) {
    1307:             J[d*dim+f] = 0.0;
    1308:             for (g = 0; g < dim; g++) {
    1309:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1310:             }
    1311:           }
    1312:         }
    1313:         PetscLogFlops(18.0);
    1314:       }
    1315:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1316:     } else if (numCoords == 8) {
    1317:       const PetscInt dim = 2;

    1319:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1320:       if (J)    {
    1321:         for (d = 0; d < dim; d++) {
    1322:           J[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1323:           J[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[3]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1324:         }
    1325:         PetscLogFlops(8.0);
    1326:         DMPlex_Det2D_Internal(detJ, J);
    1327:       }
    1328:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1329:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1330:   } else {
    1331:     const PetscInt Nv = 4;
    1332:     const PetscInt dimR = 2;
    1333:     PetscInt  zToPlex[4] = {0, 1, 3, 2};
    1334:     PetscReal zOrder[12];
    1335:     PetscReal zCoeff[12];
    1336:     PetscInt  i, j, k, l, dim;

    1338:     if (isTensor) {zToPlex[2] = 2; zToPlex[3] = 3;}
    1339:     if (numCoords == 12) {
    1340:       dim = 3;
    1341:     } else if (numCoords == 8) {
    1342:       dim = 2;
    1343:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1344:     for (i = 0; i < Nv; i++) {
    1345:       PetscInt zi = zToPlex[i];

    1347:       for (j = 0; j < dim; j++) {
    1348:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1349:       }
    1350:     }
    1351:     for (j = 0; j < dim; j++) {
    1352:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
    1353:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
    1354:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
    1355:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
    1356:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
    1357:       */
    1358:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1359:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1360:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1361:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1362:     }
    1363:     for (i = 0; i < Nq; i++) {
    1364:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    1366:       if (v) {
    1367:         PetscReal extPoint[4];

    1369:         extPoint[0] = 1.;
    1370:         extPoint[1] = xi;
    1371:         extPoint[2] = eta;
    1372:         extPoint[3] = xi * eta;
    1373:         for (j = 0; j < dim; j++) {
    1374:           PetscReal val = 0.;

    1376:           for (k = 0; k < Nv; k++) {
    1377:             val += extPoint[k] * zCoeff[dim * k + j];
    1378:           }
    1379:           v[i * dim + j] = val;
    1380:         }
    1381:       }
    1382:       if (J) {
    1383:         PetscReal extJ[8];

    1385:         extJ[0] = 0.;
    1386:         extJ[1] = 0.;
    1387:         extJ[2] = 1.;
    1388:         extJ[3] = 0.;
    1389:         extJ[4] = 0.;
    1390:         extJ[5] = 1.;
    1391:         extJ[6] = eta;
    1392:         extJ[7] = xi;
    1393:         for (j = 0; j < dim; j++) {
    1394:           for (k = 0; k < dimR; k++) {
    1395:             PetscReal val = 0.;

    1397:             for (l = 0; l < Nv; l++) {
    1398:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1399:             }
    1400:             J[i * dim * dim + dim * j + k] = val;
    1401:           }
    1402:         }
    1403:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    1404:           PetscReal x, y, z;
    1405:           PetscReal *iJ = &J[i * dim * dim];
    1406:           PetscReal norm;

    1408:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    1409:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    1410:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    1411:           norm = PetscSqrtReal(x * x + y * y + z * z);
    1412:           iJ[2] = x / norm;
    1413:           iJ[5] = y / norm;
    1414:           iJ[8] = z / norm;
    1415:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1416:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1417:         } else {
    1418:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    1419:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1420:         }
    1421:       }
    1422:     }
    1423:   }
    1424:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1425:   return 0;
    1426: }

    1428: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1429: {
    1430:   PetscSection   coordSection;
    1431:   Vec            coordinates;
    1432:   PetscScalar   *coords = NULL;
    1433:   const PetscInt dim = 3;
    1434:   PetscInt       d;

    1436:   DMGetCoordinatesLocal(dm, &coordinates);
    1437:   DMGetCoordinateSection(dm, &coordSection);
    1438:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1439:   *detJ = 0.0;
    1440:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1441:   if (J)    {
    1442:     for (d = 0; d < dim; d++) {
    1443:       /* I orient with outward face normals */
    1444:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1445:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1446:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1447:     }
    1448:     PetscLogFlops(18.0);
    1449:     DMPlex_Det3D_Internal(detJ, J);
    1450:   }
    1451:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1452:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1453:   return 0;
    1454: }

    1456: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1457: {
    1458:   PetscSection   coordSection;
    1459:   Vec            coordinates;
    1460:   PetscScalar   *coords = NULL;
    1461:   const PetscInt dim = 3;
    1462:   PetscInt       d;

    1464:   DMGetCoordinatesLocal(dm, &coordinates);
    1465:   DMGetCoordinateSection(dm, &coordSection);
    1466:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1467:   if (!Nq) {
    1468:     *detJ = 0.0;
    1469:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1470:     if (J)    {
    1471:       for (d = 0; d < dim; d++) {
    1472:         J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1473:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1474:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1475:       }
    1476:       PetscLogFlops(18.0);
    1477:       DMPlex_Det3D_Internal(detJ, J);
    1478:     }
    1479:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1480:   } else {
    1481:     const PetscInt Nv = 8;
    1482:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    1483:     const PetscInt dim = 3;
    1484:     const PetscInt dimR = 3;
    1485:     PetscReal zOrder[24];
    1486:     PetscReal zCoeff[24];
    1487:     PetscInt  i, j, k, l;

    1489:     for (i = 0; i < Nv; i++) {
    1490:       PetscInt zi = zToPlex[i];

    1492:       for (j = 0; j < dim; j++) {
    1493:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1494:       }
    1495:     }
    1496:     for (j = 0; j < dim; j++) {
    1497:       zCoeff[dim * 0 + j] = 0.125 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1498:       zCoeff[dim * 1 + j] = 0.125 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1499:       zCoeff[dim * 2 + j] = 0.125 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1500:       zCoeff[dim * 3 + j] = 0.125 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1501:       zCoeff[dim * 4 + j] = 0.125 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1502:       zCoeff[dim * 5 + j] = 0.125 * (+ zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1503:       zCoeff[dim * 6 + j] = 0.125 * (+ zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1504:       zCoeff[dim * 7 + j] = 0.125 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
    1505:     }
    1506:     for (i = 0; i < Nq; i++) {
    1507:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    1509:       if (v) {
    1510:         PetscReal extPoint[8];

    1512:         extPoint[0] = 1.;
    1513:         extPoint[1] = xi;
    1514:         extPoint[2] = eta;
    1515:         extPoint[3] = xi * eta;
    1516:         extPoint[4] = theta;
    1517:         extPoint[5] = theta * xi;
    1518:         extPoint[6] = theta * eta;
    1519:         extPoint[7] = theta * eta * xi;
    1520:         for (j = 0; j < dim; j++) {
    1521:           PetscReal val = 0.;

    1523:           for (k = 0; k < Nv; k++) {
    1524:             val += extPoint[k] * zCoeff[dim * k + j];
    1525:           }
    1526:           v[i * dim + j] = val;
    1527:         }
    1528:       }
    1529:       if (J) {
    1530:         PetscReal extJ[24];

    1532:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
    1533:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
    1534:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
    1535:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
    1536:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
    1537:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
    1538:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
    1539:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

    1541:         for (j = 0; j < dim; j++) {
    1542:           for (k = 0; k < dimR; k++) {
    1543:             PetscReal val = 0.;

    1545:             for (l = 0; l < Nv; l++) {
    1546:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1547:             }
    1548:             J[i * dim * dim + dim * j + k] = val;
    1549:           }
    1550:         }
    1551:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1552:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1553:       }
    1554:     }
    1555:   }
    1556:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1557:   return 0;
    1558: }

    1560: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1561: {
    1562:   PetscSection   coordSection;
    1563:   Vec            coordinates;
    1564:   PetscScalar   *coords = NULL;
    1565:   const PetscInt dim = 3;
    1566:   PetscInt       d;

    1568:   DMGetCoordinatesLocal(dm, &coordinates);
    1569:   DMGetCoordinateSection(dm, &coordSection);
    1570:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1571:   if (!Nq) {
    1572:     /* Assume that the map to the reference is affine */
    1573:     *detJ = 0.0;
    1574:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1575:     if (J)    {
    1576:       for (d = 0; d < dim; d++) {
    1577:         J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1578:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1579:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1580:       }
    1581:       PetscLogFlops(18.0);
    1582:       DMPlex_Det3D_Internal(detJ, J);
    1583:     }
    1584:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1585:   } else {
    1586:     const PetscInt dim  = 3;
    1587:     const PetscInt dimR = 3;
    1588:     const PetscInt Nv   = 6;
    1589:     PetscReal verts[18];
    1590:     PetscReal coeff[18];
    1591:     PetscInt  i, j, k, l;

    1593:     for (i = 0; i < Nv; ++i) for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
    1594:     for (j = 0; j < dim; ++j) {
    1595:       /* Check for triangle,
    1596:            phi^0 = -1/2 (xi + eta)  chi^0 = delta(-1, -1)   x(xi) = \sum_k x_k phi^k(xi) = \sum_k chi^k(x) phi^k(xi)
    1597:            phi^1 =  1/2 (1 + xi)    chi^1 = delta( 1, -1)   y(xi) = \sum_k y_k phi^k(xi) = \sum_k chi^k(y) phi^k(xi)
    1598:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

    1600:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
    1601:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
    1602:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

    1604:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
    1605:                                  | -1  1 -1 | | phi_1 | =
    1606:                                  \ -1 -1  1 / \ phi_2 /

    1608:           Check phi^0: 1/2 (phi^0 chi^1 + phi^0 chi^2 + phi^0 chi^0 - phi^0 chi^1 + phi^0 chi^0 - phi^0 chi^2) = phi^0 chi^0
    1609:       */
    1610:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
    1611:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
    1612:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
    1613:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
    1614:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
    1615:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
    1616:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
    1617:            1/4 /  0  1  1  0  1  1 \
    1618:                | -1  1  0 -1  0  1 |
    1619:                | -1  0  1 -1  1  0 |
    1620:                |  0 -1 -1  0  1  1 |
    1621:                |  1  0 -1 -1  1  0 |
    1622:                \  1 -1  0 -1  0  1 /
    1623:       */
    1624:       coeff[dim * 0 + j] = (1./4.) * (                      verts[dim * 1 + j] + verts[dim * 2 + j]                      + verts[dim * 4 + j] + verts[dim * 5 + j]);
    1625:       coeff[dim * 1 + j] = (1./4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j]                      - verts[dim * 3 + j]                      + verts[dim * 5 + j]);
    1626:       coeff[dim * 2 + j] = (1./4.) * (-verts[dim * 0 + j]                      + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
    1627:       coeff[dim * 3 + j] = (1./4.) * (                    - verts[dim * 1 + j] - verts[dim * 2 + j]                      + verts[dim * 4 + j] + verts[dim * 5 + j]);
    1628:       coeff[dim * 4 + j] = (1./4.) * ( verts[dim * 0 + j]                      - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
    1629:       coeff[dim * 5 + j] = (1./4.) * ( verts[dim * 0 + j] - verts[dim * 1 + j]                      - verts[dim * 3 + j]                      + verts[dim * 5 + j]);
    1630:       /* For reference prism:
    1631:       {0, 0, 0}
    1632:       {0, 1, 0}
    1633:       {1, 0, 0}
    1634:       {0, 0, 1}
    1635:       {0, 0, 0}
    1636:       {0, 0, 0}
    1637:       */
    1638:     }
    1639:     for (i = 0; i < Nq; ++i) {
    1640:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

    1642:       if (v) {
    1643:         PetscReal extPoint[6];
    1644:         PetscInt  c;

    1646:         extPoint[0] = 1.;
    1647:         extPoint[1] = eta;
    1648:         extPoint[2] = xi;
    1649:         extPoint[3] = zeta;
    1650:         extPoint[4] = xi * zeta;
    1651:         extPoint[5] = eta * zeta;
    1652:         for (c = 0; c < dim; ++c) {
    1653:           PetscReal val = 0.;

    1655:           for (k = 0; k < Nv; ++k) {
    1656:             val += extPoint[k] * coeff[k*dim + c];
    1657:           }
    1658:           v[i*dim + c] = val;
    1659:         }
    1660:       }
    1661:       if (J) {
    1662:         PetscReal extJ[18];

    1664:         extJ[0]  = 0.  ; extJ[1]  = 0.  ; extJ[2]  = 0. ;
    1665:         extJ[3]  = 0.  ; extJ[4]  = 1.  ; extJ[5]  = 0. ;
    1666:         extJ[6]  = 1.  ; extJ[7]  = 0.  ; extJ[8]  = 0. ;
    1667:         extJ[9]  = 0.  ; extJ[10] = 0.  ; extJ[11] = 1. ;
    1668:         extJ[12] = zeta; extJ[13] = 0.  ; extJ[14] = xi ;
    1669:         extJ[15] = 0.  ; extJ[16] = zeta; extJ[17] = eta;

    1671:         for (j = 0; j < dim; j++) {
    1672:           for (k = 0; k < dimR; k++) {
    1673:             PetscReal val = 0.;

    1675:             for (l = 0; l < Nv; l++) {
    1676:               val += coeff[dim * l + j] * extJ[dimR * l + k];
    1677:             }
    1678:             J[i * dim * dim + dim * j + k] = val;
    1679:           }
    1680:         }
    1681:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1682:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1683:       }
    1684:     }
    1685:   }
    1686:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1687:   return 0;
    1688: }

    1690: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1691: {
    1692:   DMPolytopeType  ct;
    1693:   PetscInt        depth, dim, coordDim, coneSize, i;
    1694:   PetscInt        Nq = 0;
    1695:   const PetscReal *points = NULL;
    1696:   DMLabel         depthLabel;
    1697:   PetscReal       xi0[3] = {-1.,-1.,-1.}, v0[3], J0[9], detJ0;
    1698:   PetscBool       isAffine = PETSC_TRUE;

    1700:   DMPlexGetDepth(dm, &depth);
    1701:   DMPlexGetConeSize(dm, cell, &coneSize);
    1702:   DMPlexGetDepthLabel(dm, &depthLabel);
    1703:   DMLabelGetValue(depthLabel, cell, &dim);
    1704:   if (depth == 1 && dim == 1) {
    1705:     DMGetDimension(dm, &dim);
    1706:   }
    1707:   DMGetCoordinateDim(dm, &coordDim);
    1709:   if (quad) PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);
    1710:   DMPlexGetCellType(dm, cell, &ct);
    1711:   switch (ct) {
    1712:     case DM_POLYTOPE_POINT:
    1713:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1714:     isAffine = PETSC_FALSE;
    1715:     break;
    1716:     case DM_POLYTOPE_SEGMENT:
    1717:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1718:     if (Nq) DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
    1719:     else    DMPlexComputeLineGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);
    1720:     break;
    1721:     case DM_POLYTOPE_TRIANGLE:
    1722:     if (Nq) DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
    1723:     else    DMPlexComputeTriangleGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);
    1724:     break;
    1725:     case DM_POLYTOPE_QUADRILATERAL:
    1726:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ);
    1727:     isAffine = PETSC_FALSE;
    1728:     break;
    1729:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1730:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ);
    1731:     isAffine = PETSC_FALSE;
    1732:     break;
    1733:     case DM_POLYTOPE_TETRAHEDRON:
    1734:     if (Nq) DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
    1735:     else    DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);
    1736:     break;
    1737:     case DM_POLYTOPE_HEXAHEDRON:
    1738:     DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1739:     isAffine = PETSC_FALSE;
    1740:     break;
    1741:     case DM_POLYTOPE_TRI_PRISM:
    1742:     DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1743:     isAffine = PETSC_FALSE;
    1744:     break;
    1745:     default: SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[PetscMax(0, PetscMin(ct, DM_NUM_POLYTOPES))]);
    1746:   }
    1747:   if (isAffine && Nq) {
    1748:     if (v) {
    1749:       for (i = 0; i < Nq; i++) {
    1750:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    1751:       }
    1752:     }
    1753:     if (detJ) {
    1754:       for (i = 0; i < Nq; i++) {
    1755:         detJ[i] = detJ0;
    1756:       }
    1757:     }
    1758:     if (J) {
    1759:       PetscInt k;

    1761:       for (i = 0, k = 0; i < Nq; i++) {
    1762:         PetscInt j;

    1764:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1765:           J[k] = J0[j];
    1766:         }
    1767:       }
    1768:     }
    1769:     if (invJ) {
    1770:       PetscInt k;
    1771:       switch (coordDim) {
    1772:       case 0:
    1773:         break;
    1774:       case 1:
    1775:         invJ[0] = 1./J0[0];
    1776:         break;
    1777:       case 2:
    1778:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    1779:         break;
    1780:       case 3:
    1781:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    1782:         break;
    1783:       }
    1784:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    1785:         PetscInt j;

    1787:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1788:           invJ[k] = invJ[j];
    1789:         }
    1790:       }
    1791:     }
    1792:   }
    1793:   return 0;
    1794: }

    1796: /*@C
    1797:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    1799:   Collective on dm

    1801:   Input Parameters:
    1802: + dm   - the DM
    1803: - cell - the cell

    1805:   Output Parameters:
    1806: + v0   - the translation part of this affine transform
    1807: . J    - the Jacobian of the transform from the reference element
    1808: . invJ - the inverse of the Jacobian
    1809: - detJ - the Jacobian determinant

    1811:   Level: advanced

    1813:   Fortran Notes:
    1814:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1815:   include petsc.h90 in your code.

    1817: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
    1818: @*/
    1819: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1820: {
    1821:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
    1822:   return 0;
    1823: }

    1825: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1826: {
    1827:   PetscQuadrature   feQuad;
    1828:   PetscSection      coordSection;
    1829:   Vec               coordinates;
    1830:   PetscScalar      *coords = NULL;
    1831:   const PetscReal  *quadPoints;
    1832:   PetscTabulation T;
    1833:   PetscInt          dim, cdim, pdim, qdim, Nq, numCoords, q;

    1835:   DMGetCoordinatesLocal(dm, &coordinates);
    1836:   DMGetCoordinateSection(dm, &coordSection);
    1837:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1838:   DMGetDimension(dm, &dim);
    1839:   DMGetCoordinateDim(dm, &cdim);
    1840:   if (!quad) { /* use the first point of the first functional of the dual space */
    1841:     PetscDualSpace dsp;

    1843:     PetscFEGetDualSpace(fe, &dsp);
    1844:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
    1845:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1846:     Nq = 1;
    1847:   } else {
    1848:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1849:   }
    1850:   PetscFEGetDimension(fe, &pdim);
    1851:   PetscFEGetQuadrature(fe, &feQuad);
    1852:   if (feQuad == quad) {
    1853:     PetscFEGetCellTabulation(fe, J ? 1 : 0, &T);
    1855:   } else {
    1856:     PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T);
    1857:   }
    1859:   {
    1860:     const PetscReal *basis    = T->T[0];
    1861:     const PetscReal *basisDer = T->T[1];
    1862:     PetscReal        detJt;

    1864: #if defined(PETSC_USE_DEBUG)
    1869: #endif
    1870:     if (v) {
    1871:       PetscArrayzero(v, Nq*cdim);
    1872:       for (q = 0; q < Nq; ++q) {
    1873:         PetscInt i, k;

    1875:         for (k = 0; k < pdim; ++k) {
    1876:           const PetscInt vertex = k/cdim;
    1877:           for (i = 0; i < cdim; ++i) {
    1878:             v[q*cdim + i] += basis[(q*pdim + k)*cdim + i] * PetscRealPart(coords[vertex*cdim + i]);
    1879:           }
    1880:         }
    1881:         PetscLogFlops(2.0*pdim*cdim);
    1882:       }
    1883:     }
    1884:     if (J) {
    1885:       PetscArrayzero(J, Nq*cdim*cdim);
    1886:       for (q = 0; q < Nq; ++q) {
    1887:         PetscInt i, j, k, c, r;

    1889:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    1890:         for (k = 0; k < pdim; ++k) {
    1891:           const PetscInt vertex = k/cdim;
    1892:           for (j = 0; j < dim; ++j) {
    1893:             for (i = 0; i < cdim; ++i) {
    1894:               J[(q*cdim + i)*cdim + j] += basisDer[((q*pdim + k)*cdim + i)*dim + j] * PetscRealPart(coords[vertex*cdim + i]);
    1895:             }
    1896:           }
    1897:         }
    1898:         PetscLogFlops(2.0*pdim*dim*cdim);
    1899:         if (cdim > dim) {
    1900:           for (c = dim; c < cdim; ++c)
    1901:             for (r = 0; r < cdim; ++r)
    1902:               J[r*cdim+c] = r == c ? 1.0 : 0.0;
    1903:         }
    1904:         if (!detJ && !invJ) continue;
    1905:         detJt = 0.;
    1906:         switch (cdim) {
    1907:         case 3:
    1908:           DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
    1909:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1910:           break;
    1911:         case 2:
    1912:           DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
    1913:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1914:           break;
    1915:         case 1:
    1916:           detJt = J[q*cdim*dim];
    1917:           if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
    1918:         }
    1919:         if (detJ) detJ[q] = detJt;
    1920:       }
    1922:   }
    1923:   if (feQuad != quad) PetscTabulationDestroy(&T);
    1924:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1925:   return 0;
    1926: }

    1928: /*@C
    1929:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    1931:   Collective on dm

    1933:   Input Parameters:
    1934: + dm   - the DM
    1935: . cell - the cell
    1936: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
    1937:          evaluated at the first vertex of the reference element

    1939:   Output Parameters:
    1940: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
    1941: . J    - the Jacobian of the transform from the reference element at each quadrature point
    1942: . invJ - the inverse of the Jacobian at each quadrature point
    1943: - detJ - the Jacobian determinant at each quadrature point

    1945:   Level: advanced

    1947:   Fortran Notes:
    1948:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1949:   include petsc.h90 in your code.

    1951: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1952: @*/
    1953: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1954: {
    1955:   DM             cdm;
    1956:   PetscFE        fe = NULL;

    1959:   DMGetCoordinateDM(dm, &cdm);
    1960:   if (cdm) {
    1961:     PetscClassId id;
    1962:     PetscInt     numFields;
    1963:     PetscDS      prob;
    1964:     PetscObject  disc;

    1966:     DMGetNumFields(cdm, &numFields);
    1967:     if (numFields) {
    1968:       DMGetDS(cdm, &prob);
    1969:       PetscDSGetDiscretization(prob,0,&disc);
    1970:       PetscObjectGetClassId(disc,&id);
    1971:       if (id == PETSCFE_CLASSID) {
    1972:         fe = (PetscFE) disc;
    1973:       }
    1974:     }
    1975:   }
    1976:   if (!fe) DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);
    1977:   else     DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);
    1978:   return 0;
    1979: }

    1981: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1982: {
    1983:   PetscSection        coordSection;
    1984:   Vec                 coordinates;
    1985:   const PetscScalar  *coords = NULL;
    1986:   PetscInt            d, dof, off;

    1988:   DMGetCoordinatesLocal(dm, &coordinates);
    1989:   DMGetCoordinateSection(dm, &coordSection);
    1990:   VecGetArrayRead(coordinates, &coords);

    1992:   /* for a point the centroid is just the coord */
    1993:   if (centroid) {
    1994:     PetscSectionGetDof(coordSection, cell, &dof);
    1995:     PetscSectionGetOffset(coordSection, cell, &off);
    1996:     for (d = 0; d < dof; d++){
    1997:       centroid[d] = PetscRealPart(coords[off + d]);
    1998:     }
    1999:   }
    2000:   if (normal) {
    2001:     const PetscInt *support, *cones;
    2002:     PetscInt        supportSize;
    2003:     PetscReal       norm, sign;

    2005:     /* compute the norm based upon the support centroids */
    2006:     DMPlexGetSupportSize(dm, cell, &supportSize);
    2007:     DMPlexGetSupport(dm, cell, &support);
    2008:     DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL);

    2010:     /* Take the normal from the centroid of the support to the vertex*/
    2011:     PetscSectionGetDof(coordSection, cell, &dof);
    2012:     PetscSectionGetOffset(coordSection, cell, &off);
    2013:     for (d = 0; d < dof; d++){
    2014:       normal[d] -= PetscRealPart(coords[off + d]);
    2015:     }

    2017:     /* Determine the sign of the normal based upon its location in the support */
    2018:     DMPlexGetCone(dm, support[0], &cones);
    2019:     sign = cones[0] == cell ? 1.0 : -1.0;

    2021:     norm = DMPlex_NormD_Internal(dim, normal);
    2022:     for (d = 0; d < dim; ++d) normal[d] /= (norm*sign);
    2023:   }
    2024:   if (vol) {
    2025:     *vol = 1.0;
    2026:   }
    2027:   VecRestoreArrayRead(coordinates, &coords);
    2028:   return 0;
    2029: }

    2031: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2032: {
    2033:   PetscSection   coordSection;
    2034:   Vec            coordinates;
    2035:   PetscScalar   *coords = NULL;
    2036:   PetscScalar    tmp[2];
    2037:   PetscInt       coordSize, d;

    2039:   DMGetCoordinatesLocal(dm, &coordinates);
    2040:   DMGetCoordinateSection(dm, &coordSection);
    2041:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    2042:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
    2043:   if (centroid) {
    2044:     for (d = 0; d < dim; ++d) centroid[d] = 0.5*PetscRealPart(coords[d] + tmp[d]);
    2045:   }
    2046:   if (normal) {
    2047:     PetscReal norm;

    2050:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
    2051:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
    2052:     norm       = DMPlex_NormD_Internal(dim, normal);
    2053:     for (d = 0; d < dim; ++d) normal[d] /= norm;
    2054:   }
    2055:   if (vol) {
    2056:     *vol = 0.0;
    2057:     for (d = 0; d < dim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - tmp[d]));
    2058:     *vol = PetscSqrtReal(*vol);
    2059:   }
    2060:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    2061:   return 0;
    2062: }

    2064: /* Centroid_i = (\sum_n A_n Cn_i) / A */
    2065: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2066: {
    2067:   DMPolytopeType ct;
    2068:   PetscSection   coordSection;
    2069:   Vec            coordinates;
    2070:   PetscScalar   *coords = NULL;
    2071:   PetscInt       fv[4] = {0, 1, 2, 3};
    2072:   PetscInt       cdim, coordSize, numCorners, p, d;

    2074:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2075:   DMPlexGetCellType(dm, cell, &ct);
    2076:   switch (ct) {
    2077:     case DM_POLYTOPE_SEG_PRISM_TENSOR: fv[2] = 3; fv[3] = 2;break;
    2078:     default: break;
    2079:   }
    2080:   DMGetCoordinatesLocal(dm, &coordinates);
    2081:   DMPlexGetConeSize(dm, cell, &numCorners);
    2082:   DMGetCoordinateSection(dm, &coordSection);
    2083:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    2084:   DMGetCoordinateDim(dm, &cdim);
    2085:   {
    2086:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

    2088:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
    2089:     for (p = 0; p < numCorners-2; ++p) {
    2090:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
    2091:       for (d = 0; d < cdim; d++) {
    2092:         e0[d] = PetscRealPart(coords[cdim*fv[p+1]+d]) - origin[d];
    2093:         e1[d] = PetscRealPart(coords[cdim*fv[p+2]+d]) - origin[d];
    2094:       }
    2095:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
    2096:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
    2097:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
    2098:       const PetscReal a  = PetscSqrtReal(dx*dx + dy*dy + dz*dz);

    2100:       n[0] += dx;
    2101:       n[1] += dy;
    2102:       n[2] += dz;
    2103:       for (d = 0; d < cdim; d++) {
    2104:         c[d] += a * PetscRealPart(origin[d] + coords[cdim*fv[p+1]+d] + coords[cdim*fv[p+2]+d]) / 3.;
    2105:       }
    2106:     }
    2107:     norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    2108:     n[0] /= norm;
    2109:     n[1] /= norm;
    2110:     n[2] /= norm;
    2111:     c[0] /= norm;
    2112:     c[1] /= norm;
    2113:     c[2] /= norm;
    2114:     if (vol) *vol = 0.5*norm;
    2115:     if (centroid) for (d = 0; d < cdim; ++d) centroid[d] = c[d];
    2116:     if (normal) for (d = 0; d < cdim; ++d) normal[d] = n[d];
    2117:   }
    2118:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    2119:   return 0;
    2120: }

    2122: /* Centroid_i = (\sum_n V_n Cn_i) / V */
    2123: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2124: {
    2125:   DMPolytopeType  ct;
    2126:   PetscSection    coordSection;
    2127:   Vec             coordinates;
    2128:   PetscScalar    *coords = NULL;
    2129:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3], origin[3];
    2130:   const PetscInt *faces, *facesO;
    2131:   PetscBool       isHybrid = PETSC_FALSE;
    2132:   PetscInt        numFaces, f, coordSize, p, d;

    2135:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2136:   DMPlexGetCellType(dm, cell, &ct);
    2137:   switch (ct) {
    2138:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2139:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2140:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    2141:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    2142:       isHybrid = PETSC_TRUE;
    2143:     default: break;
    2144:   }

    2146:   DMGetCoordinatesLocal(dm, &coordinates);
    2147:   DMGetCoordinateSection(dm, &coordSection);

    2149:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    2150:   DMPlexGetConeSize(dm, cell, &numFaces);
    2151:   DMPlexGetCone(dm, cell, &faces);
    2152:   DMPlexGetConeOrientation(dm, cell, &facesO);
    2153:   for (f = 0; f < numFaces; ++f) {
    2154:     PetscBool      flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
    2155:     DMPolytopeType ct;

    2157:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    2158:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
    2159:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
    2160:     // so that all tetrahedra have positive volume.
    2161:     if (f == 0) for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
    2162:     DMPlexGetCellType(dm, faces[f], &ct);
    2163:     switch (ct) {
    2164:     case DM_POLYTOPE_TRIANGLE:
    2165:       for (d = 0; d < dim; ++d) {
    2166:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]) - origin[d];
    2167:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]) - origin[d];
    2168:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]) - origin[d];
    2169:       }
    2170:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2171:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    2172:       vsum += vtmp;
    2173:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
    2174:         for (d = 0; d < dim; ++d) {
    2175:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    2176:         }
    2177:       }
    2178:       break;
    2179:     case DM_POLYTOPE_QUADRILATERAL:
    2180:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2181:     {
    2182:       PetscInt fv[4] = {0, 1, 2, 3};

    2184:       /* Side faces for hybrid cells are are stored as tensor products */
    2185:       if (isHybrid && f > 1) {fv[2] = 3; fv[3] = 2;}
    2186:       /* DO FOR PYRAMID */
    2187:       /* First tet */
    2188:       for (d = 0; d < dim; ++d) {
    2189:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[0]*dim+d]) - origin[d];
    2190:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[1]*dim+d]) - origin[d];
    2191:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]) - origin[d];
    2192:       }
    2193:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2194:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    2195:       vsum += vtmp;
    2196:       if (centroid) {
    2197:         for (d = 0; d < dim; ++d) {
    2198:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    2199:         }
    2200:       }
    2201:       /* Second tet */
    2202:       for (d = 0; d < dim; ++d) {
    2203:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[1]*dim+d]) - origin[d];
    2204:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[2]*dim+d]) - origin[d];
    2205:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]) - origin[d];
    2206:       }
    2207:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2208:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    2209:       vsum += vtmp;
    2210:       if (centroid) {
    2211:         for (d = 0; d < dim; ++d) {
    2212:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    2213:         }
    2214:       }
    2215:       break;
    2216:     }
    2217:     default:
    2218:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %D of type %s", faces[f], DMPolytopeTypes[ct]);
    2219:     }
    2220:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    2221:   }
    2222:   if (vol)     *vol = PetscAbsReal(vsum);
    2223:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
    2224:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum*4) + origin[d];
    2225: ;
    2226:   return 0;
    2227: }

    2229: /*@C
    2230:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    2232:   Collective on dm

    2234:   Input Parameters:
    2235: + dm   - the DM
    2236: - cell - the cell

    2238:   Output Parameters:
    2239: + volume   - the cell volume
    2240: . centroid - the cell centroid
    2241: - normal - the cell normal, if appropriate

    2243:   Level: advanced

    2245:   Fortran Notes:
    2246:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    2247:   include petsc.h90 in your code.

    2249: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    2250: @*/
    2251: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2252: {
    2253:   PetscInt       depth, dim;

    2255:   DMPlexGetDepth(dm, &depth);
    2256:   DMGetDimension(dm, &dim);
    2258:   DMPlexGetPointDepth(dm, cell, &depth);
    2259:   switch (depth) {
    2260:   case 0:
    2261:     DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal);
    2262:     break;
    2263:   case 1:
    2264:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
    2265:     break;
    2266:   case 2:
    2267:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
    2268:     break;
    2269:   case 3:
    2270:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
    2271:     break;
    2272:   default:
    2273:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
    2274:   }
    2275:   return 0;
    2276: }

    2278: /*@
    2279:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

    2281:   Collective on dm

    2283:   Input Parameter:
    2284: . dm - The DMPlex

    2286:   Output Parameter:
    2287: . cellgeom - A vector with the cell geometry data for each cell

    2289:   Level: beginner

    2291: @*/
    2292: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
    2293: {
    2294:   DM             dmCell;
    2295:   Vec            coordinates;
    2296:   PetscSection   coordSection, sectionCell;
    2297:   PetscScalar   *cgeom;
    2298:   PetscInt       cStart, cEnd, c;

    2300:   DMClone(dm, &dmCell);
    2301:   DMGetCoordinateSection(dm, &coordSection);
    2302:   DMGetCoordinatesLocal(dm, &coordinates);
    2303:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2304:   DMSetCoordinatesLocal(dmCell, coordinates);
    2305:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2306:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    2307:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2308:   /* TODO This needs to be multiplied by Nq for non-affine */
    2309:   for (c = cStart; c < cEnd; ++c) PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));
    2310:   PetscSectionSetUp(sectionCell);
    2311:   DMSetLocalSection(dmCell, sectionCell);
    2312:   PetscSectionDestroy(&sectionCell);
    2313:   DMCreateLocalVector(dmCell, cellgeom);
    2314:   VecGetArray(*cellgeom, &cgeom);
    2315:   for (c = cStart; c < cEnd; ++c) {
    2316:     PetscFEGeom *cg;

    2318:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2319:     PetscArrayzero(cg, 1);
    2320:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
    2322:   }
    2323:   return 0;
    2324: }

    2326: /*@
    2327:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2329:   Input Parameter:
    2330: . dm - The DM

    2332:   Output Parameters:
    2333: + cellgeom - A Vec of PetscFVCellGeom data
    2334: - facegeom - A Vec of PetscFVFaceGeom data

    2336:   Level: developer

    2338: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
    2339: @*/
    2340: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2341: {
    2342:   DM             dmFace, dmCell;
    2343:   DMLabel        ghostLabel;
    2344:   PetscSection   sectionFace, sectionCell;
    2345:   PetscSection   coordSection;
    2346:   Vec            coordinates;
    2347:   PetscScalar   *fgeom, *cgeom;
    2348:   PetscReal      minradius, gminradius;
    2349:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2351:   DMGetDimension(dm, &dim);
    2352:   DMGetCoordinateSection(dm, &coordSection);
    2353:   DMGetCoordinatesLocal(dm, &coordinates);
    2354:   /* Make cell centroids and volumes */
    2355:   DMClone(dm, &dmCell);
    2356:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2357:   DMSetCoordinatesLocal(dmCell, coordinates);
    2358:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2359:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2360:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2361:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2362:   for (c = cStart; c < cEnd; ++c) PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));
    2363:   PetscSectionSetUp(sectionCell);
    2364:   DMSetLocalSection(dmCell, sectionCell);
    2365:   PetscSectionDestroy(&sectionCell);
    2366:   DMCreateLocalVector(dmCell, cellgeom);
    2367:   if (cEndInterior < 0) cEndInterior = cEnd;
    2368:   VecGetArray(*cellgeom, &cgeom);
    2369:   for (c = cStart; c < cEndInterior; ++c) {
    2370:     PetscFVCellGeom *cg;

    2372:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2373:     PetscArrayzero(cg, 1);
    2374:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
    2375:   }
    2376:   /* Compute face normals and minimum cell radius */
    2377:   DMClone(dm, &dmFace);
    2378:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
    2379:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2380:   PetscSectionSetChart(sectionFace, fStart, fEnd);
    2381:   for (f = fStart; f < fEnd; ++f) PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));
    2382:   PetscSectionSetUp(sectionFace);
    2383:   DMSetLocalSection(dmFace, sectionFace);
    2384:   PetscSectionDestroy(&sectionFace);
    2385:   DMCreateLocalVector(dmFace, facegeom);
    2386:   VecGetArray(*facegeom, &fgeom);
    2387:   DMGetLabel(dm, "ghost", &ghostLabel);
    2388:   minradius = PETSC_MAX_REAL;
    2389:   for (f = fStart; f < fEnd; ++f) {
    2390:     PetscFVFaceGeom *fg;
    2391:     PetscReal        area;
    2392:     const PetscInt  *cells;
    2393:     PetscInt         ncells, ghost = -1, d, numChildren;

    2395:     if (ghostLabel) DMLabelGetValue(ghostLabel, f, &ghost);
    2396:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
    2397:     DMPlexGetSupport(dm, f, &cells);
    2398:     DMPlexGetSupportSize(dm, f, &ncells);
    2399:     /* It is possible to get a face with no support when using partition overlap */
    2400:     if (!ncells || ghost >= 0 || numChildren) continue;
    2401:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
    2402:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
    2403:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    2404:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    2405:     {
    2406:       PetscFVCellGeom *cL, *cR;
    2407:       PetscReal       *lcentroid, *rcentroid;
    2408:       PetscReal        l[3], r[3], v[3];

    2410:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
    2411:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    2412:       if (ncells > 1) {
    2413:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
    2414:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    2415:       }
    2416:       else {
    2417:         rcentroid = fg->centroid;
    2418:       }
    2419:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
    2420:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
    2421:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    2422:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    2423:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    2424:       }
    2425:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    2428:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
    2429:       }
    2430:       if (cells[0] < cEndInterior) {
    2431:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    2432:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2433:       }
    2434:       if (ncells > 1 && cells[1] < cEndInterior) {
    2435:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    2436:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2437:       }
    2438:     }
    2439:   }
    2440:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
    2441:   DMPlexSetMinRadius(dm, gminradius);
    2442:   /* Compute centroids of ghost cells */
    2443:   for (c = cEndInterior; c < cEnd; ++c) {
    2444:     PetscFVFaceGeom *fg;
    2445:     const PetscInt  *cone,    *support;
    2446:     PetscInt         coneSize, supportSize, s;

    2448:     DMPlexGetConeSize(dmCell, c, &coneSize);
    2450:     DMPlexGetCone(dmCell, c, &cone);
    2451:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
    2453:     DMPlexGetSupport(dmCell, cone[0], &support);
    2454:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
    2455:     for (s = 0; s < 2; ++s) {
    2456:       /* Reflect ghost centroid across plane of face */
    2457:       if (support[s] == c) {
    2458:         PetscFVCellGeom       *ci;
    2459:         PetscFVCellGeom       *cg;
    2460:         PetscReal              c2f[3], a;

    2462:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
    2463:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    2464:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    2465:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
    2466:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
    2467:         cg->volume = ci->volume;
    2468:       }
    2469:     }
    2470:   }
    2471:   VecRestoreArray(*facegeom, &fgeom);
    2472:   VecRestoreArray(*cellgeom, &cgeom);
    2473:   DMDestroy(&dmCell);
    2474:   DMDestroy(&dmFace);
    2475:   return 0;
    2476: }

    2478: /*@C
    2479:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    2481:   Not collective

    2483:   Input Parameter:
    2484: . dm - the DM

    2486:   Output Parameter:
    2487: . minradius - the minimum cell radius

    2489:   Level: developer

    2491: .seealso: DMGetCoordinates()
    2492: @*/
    2493: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    2494: {
    2497:   *minradius = ((DM_Plex*) dm->data)->minradius;
    2498:   return 0;
    2499: }

    2501: /*@C
    2502:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    2504:   Logically collective

    2506:   Input Parameters:
    2507: + dm - the DM
    2508: - minradius - the minimum cell radius

    2510:   Level: developer

    2512: .seealso: DMSetCoordinates()
    2513: @*/
    2514: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    2515: {
    2517:   ((DM_Plex*) dm->data)->minradius = minradius;
    2518:   return 0;
    2519: }

    2521: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2522: {
    2523:   DMLabel        ghostLabel;
    2524:   PetscScalar   *dx, *grad, **gref;
    2525:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    2527:   DMGetDimension(dm, &dim);
    2528:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2529:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2530:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
    2531:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
    2532:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2533:   DMGetLabel(dm, "ghost", &ghostLabel);
    2534:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2535:   for (c = cStart; c < cEndInterior; c++) {
    2536:     const PetscInt        *faces;
    2537:     PetscInt               numFaces, usedFaces, f, d;
    2538:     PetscFVCellGeom        *cg;
    2539:     PetscBool              boundary;
    2540:     PetscInt               ghost;

    2542:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
    2543:     DMLabelGetValue(ghostLabel, c, &ghost);
    2544:     if (ghost >= 0) continue;

    2546:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2547:     DMPlexGetConeSize(dm, c, &numFaces);
    2548:     DMPlexGetCone(dm, c, &faces);
    2550:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2551:       PetscFVCellGeom       *cg1;
    2552:       PetscFVFaceGeom       *fg;
    2553:       const PetscInt        *fcells;
    2554:       PetscInt               ncell, side;

    2556:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2557:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2558:       if ((ghost >= 0) || boundary) continue;
    2559:       DMPlexGetSupport(dm, faces[f], &fcells);
    2560:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    2561:       ncell = fcells[!side];    /* the neighbor */
    2562:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
    2563:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2564:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2565:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2566:     }
    2568:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
    2569:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2570:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2571:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2572:       if ((ghost >= 0) || boundary) continue;
    2573:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
    2574:       ++usedFaces;
    2575:     }
    2576:   }
    2577:   PetscFree3(dx, grad, gref);
    2578:   return 0;
    2579: }

    2581: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2582: {
    2583:   DMLabel        ghostLabel;
    2584:   PetscScalar   *dx, *grad, **gref;
    2585:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    2586:   PetscSection   neighSec;
    2587:   PetscInt     (*neighbors)[2];
    2588:   PetscInt      *counter;

    2590:   DMGetDimension(dm, &dim);
    2591:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2592:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2593:   if (cEndInterior < 0) cEndInterior = cEnd;
    2594:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
    2595:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
    2596:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2597:   DMGetLabel(dm, "ghost", &ghostLabel);
    2598:   for (f = fStart; f < fEnd; f++) {
    2599:     const PetscInt        *fcells;
    2600:     PetscBool              boundary;
    2601:     PetscInt               ghost = -1;
    2602:     PetscInt               numChildren, numCells, c;

    2604:     if (ghostLabel) DMLabelGetValue(ghostLabel, f, &ghost);
    2605:     DMIsBoundaryPoint(dm, f, &boundary);
    2606:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2607:     if ((ghost >= 0) || boundary || numChildren) continue;
    2608:     DMPlexGetSupportSize(dm, f, &numCells);
    2609:     if (numCells == 2) {
    2610:       DMPlexGetSupport(dm, f, &fcells);
    2611:       for (c = 0; c < 2; c++) {
    2612:         PetscInt cell = fcells[c];

    2614:         if (cell >= cStart && cell < cEndInterior) {
    2615:           PetscSectionAddDof(neighSec,cell,1);
    2616:         }
    2617:       }
    2618:     }
    2619:   }
    2620:   PetscSectionSetUp(neighSec);
    2621:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
    2622:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2623:   nStart = 0;
    2624:   PetscSectionGetStorageSize(neighSec,&nEnd);
    2625:   PetscMalloc1((nEnd-nStart),&neighbors);
    2626:   PetscCalloc1((cEndInterior-cStart),&counter);
    2627:   for (f = fStart; f < fEnd; f++) {
    2628:     const PetscInt        *fcells;
    2629:     PetscBool              boundary;
    2630:     PetscInt               ghost = -1;
    2631:     PetscInt               numChildren, numCells, c;

    2633:     if (ghostLabel) DMLabelGetValue(ghostLabel, f, &ghost);
    2634:     DMIsBoundaryPoint(dm, f, &boundary);
    2635:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2636:     if ((ghost >= 0) || boundary || numChildren) continue;
    2637:     DMPlexGetSupportSize(dm, f, &numCells);
    2638:     if (numCells == 2) {
    2639:       DMPlexGetSupport(dm, f, &fcells);
    2640:       for (c = 0; c < 2; c++) {
    2641:         PetscInt cell = fcells[c], off;

    2643:         if (cell >= cStart && cell < cEndInterior) {
    2644:           PetscSectionGetOffset(neighSec,cell,&off);
    2645:           off += counter[cell - cStart]++;
    2646:           neighbors[off][0] = f;
    2647:           neighbors[off][1] = fcells[1 - c];
    2648:         }
    2649:       }
    2650:     }
    2651:   }
    2652:   PetscFree(counter);
    2653:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2654:   for (c = cStart; c < cEndInterior; c++) {
    2655:     PetscInt               numFaces, f, d, off, ghost = -1;
    2656:     PetscFVCellGeom        *cg;

    2658:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2659:     PetscSectionGetDof(neighSec, c, &numFaces);
    2660:     PetscSectionGetOffset(neighSec, c, &off);

    2662:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
    2663:     if (ghostLabel) DMLabelGetValue(ghostLabel, c, &ghost);
    2664:     if (ghost >= 0) continue;

    2667:     for (f = 0; f < numFaces; ++f) {
    2668:       PetscFVCellGeom       *cg1;
    2669:       PetscFVFaceGeom       *fg;
    2670:       const PetscInt        *fcells;
    2671:       PetscInt               ncell, side, nface;

    2673:       nface = neighbors[off + f][0];
    2674:       ncell = neighbors[off + f][1];
    2675:       DMPlexGetSupport(dm,nface,&fcells);
    2676:       side  = (c != fcells[0]);
    2677:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
    2678:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2679:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2680:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2681:     }
    2682:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
    2683:     for (f = 0; f < numFaces; ++f) {
    2684:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
    2685:     }
    2686:   }
    2687:   PetscFree3(dx, grad, gref);
    2688:   PetscSectionDestroy(&neighSec);
    2689:   PetscFree(neighbors);
    2690:   return 0;
    2691: }

    2693: /*@
    2694:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    2696:   Collective on dm

    2698:   Input Parameters:
    2699: + dm  - The DM
    2700: . fvm - The PetscFV
    2701: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

    2703:   Input/Output Parameter:
    2704: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM(); on output
    2705:                  the geometric factors for gradient calculation are inserted

    2707:   Output Parameter:
    2708: . dmGrad - The DM describing the layout of gradient data

    2710:   Level: developer

    2712: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
    2713: @*/
    2714: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    2715: {
    2716:   DM             dmFace, dmCell;
    2717:   PetscScalar   *fgeom, *cgeom;
    2718:   PetscSection   sectionGrad, parentSection;
    2719:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

    2721:   DMGetDimension(dm, &dim);
    2722:   PetscFVGetNumComponents(fvm, &pdim);
    2723:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2724:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2725:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    2726:   VecGetDM(faceGeometry, &dmFace);
    2727:   VecGetDM(cellGeometry, &dmCell);
    2728:   VecGetArray(faceGeometry, &fgeom);
    2729:   VecGetArray(cellGeometry, &cgeom);
    2730:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
    2731:   if (!parentSection) {
    2732:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2733:   } else {
    2734:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2735:   }
    2736:   VecRestoreArray(faceGeometry, &fgeom);
    2737:   VecRestoreArray(cellGeometry, &cgeom);
    2738:   /* Create storage for gradients */
    2739:   DMClone(dm, dmGrad);
    2740:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
    2741:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
    2742:   for (c = cStart; c < cEnd; ++c) PetscSectionSetDof(sectionGrad, c, pdim*dim);
    2743:   PetscSectionSetUp(sectionGrad);
    2744:   DMSetLocalSection(*dmGrad, sectionGrad);
    2745:   PetscSectionDestroy(&sectionGrad);
    2746:   return 0;
    2747: }

    2749: /*@
    2750:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    2752:   Collective on dm

    2754:   Input Parameters:
    2755: + dm  - The DM
    2756: - fv  - The PetscFV

    2758:   Output Parameters:
    2759: + cellGeometry - The cell geometry
    2760: . faceGeometry - The face geometry
    2761: - gradDM       - The gradient matrices

    2763:   Level: developer

    2765: .seealso: DMPlexComputeGeometryFVM()
    2766: @*/
    2767: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    2768: {
    2769:   PetscObject    cellgeomobj, facegeomobj;

    2771:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2772:   if (!cellgeomobj) {
    2773:     Vec cellgeomInt, facegeomInt;

    2775:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
    2776:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
    2777:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
    2778:     VecDestroy(&cellgeomInt);
    2779:     VecDestroy(&facegeomInt);
    2780:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2781:   }
    2782:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
    2783:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
    2784:   if (facegeom) *facegeom = (Vec) facegeomobj;
    2785:   if (gradDM) {
    2786:     PetscObject gradobj;
    2787:     PetscBool   computeGradients;

    2789:     PetscFVGetComputeGradients(fv,&computeGradients);
    2790:     if (!computeGradients) {
    2791:       *gradDM = NULL;
    2792:       return 0;
    2793:     }
    2794:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2795:     if (!gradobj) {
    2796:       DM dmGradInt;

    2798:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
    2799:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
    2800:       DMDestroy(&dmGradInt);
    2801:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2802:     }
    2803:     *gradDM = (DM) gradobj;
    2804:   }
    2805:   return 0;
    2806: }

    2808: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
    2809: {
    2810:   PetscInt l, m;

    2813:   if (dimC == dimR && dimR <= 3) {
    2814:     /* invert Jacobian, multiply */
    2815:     PetscScalar det, idet;

    2817:     switch (dimR) {
    2818:     case 1:
    2819:       invJ[0] = 1./ J[0];
    2820:       break;
    2821:     case 2:
    2822:       det = J[0] * J[3] - J[1] * J[2];
    2823:       idet = 1./det;
    2824:       invJ[0] =  J[3] * idet;
    2825:       invJ[1] = -J[1] * idet;
    2826:       invJ[2] = -J[2] * idet;
    2827:       invJ[3] =  J[0] * idet;
    2828:       break;
    2829:     case 3:
    2830:       {
    2831:         invJ[0] = J[4] * J[8] - J[5] * J[7];
    2832:         invJ[1] = J[2] * J[7] - J[1] * J[8];
    2833:         invJ[2] = J[1] * J[5] - J[2] * J[4];
    2834:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    2835:         idet = 1./det;
    2836:         invJ[0] *= idet;
    2837:         invJ[1] *= idet;
    2838:         invJ[2] *= idet;
    2839:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
    2840:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
    2841:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
    2842:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
    2843:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
    2844:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
    2845:       }
    2846:       break;
    2847:     }
    2848:     for (l = 0; l < dimR; l++) {
    2849:       for (m = 0; m < dimC; m++) {
    2850:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    2851:       }
    2852:     }
    2853:   } else {
    2854: #if defined(PETSC_USE_COMPLEX)
    2855:     char transpose = 'C';
    2856: #else
    2857:     char transpose = 'T';
    2858: #endif
    2859:     PetscBLASInt m = dimR;
    2860:     PetscBLASInt n = dimC;
    2861:     PetscBLASInt one = 1;
    2862:     PetscBLASInt worksize = dimR * dimC, info;

    2864:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

    2866:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));

    2869:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
    2870:   }
    2871:   return 0;
    2872: }

    2874: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2875: {
    2876:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    2877:   PetscScalar    *coordsScalar = NULL;
    2878:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    2879:   PetscScalar    *J, *invJ, *work;

    2882:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2884:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2885:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2886:   cellCoords = &cellData[0];
    2887:   cellCoeffs = &cellData[coordSize];
    2888:   extJ       = &cellData[2 * coordSize];
    2889:   resNeg     = &cellData[2 * coordSize + dimR];
    2890:   invJ       = &J[dimR * dimC];
    2891:   work       = &J[2 * dimR * dimC];
    2892:   if (dimR == 2) {
    2893:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2895:     for (i = 0; i < 4; i++) {
    2896:       PetscInt plexI = zToPlex[i];

    2898:       for (j = 0; j < dimC; j++) {
    2899:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2900:       }
    2901:     }
    2902:   } else if (dimR == 3) {
    2903:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2905:     for (i = 0; i < 8; i++) {
    2906:       PetscInt plexI = zToPlex[i];

    2908:       for (j = 0; j < dimC; j++) {
    2909:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2910:       }
    2911:     }
    2912:   } else {
    2913:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2914:   }
    2915:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2916:   for (i = 0; i < dimR; i++) {
    2917:     PetscReal *swap;

    2919:     for (j = 0; j < (numV / 2); j++) {
    2920:       for (k = 0; k < dimC; k++) {
    2921:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2922:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2923:       }
    2924:     }

    2926:     if (i < dimR - 1) {
    2927:       swap = cellCoeffs;
    2928:       cellCoeffs = cellCoords;
    2929:       cellCoords = swap;
    2930:     }
    2931:   }
    2932:   PetscArrayzero(refCoords,numPoints * dimR);
    2933:   for (j = 0; j < numPoints; j++) {
    2934:     for (i = 0; i < maxIts; i++) {
    2935:       PetscReal *guess = &refCoords[dimR * j];

    2937:       /* compute -residual and Jacobian */
    2938:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
    2939:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
    2940:       for (k = 0; k < numV; k++) {
    2941:         PetscReal extCoord = 1.;
    2942:         for (l = 0; l < dimR; l++) {
    2943:           PetscReal coord = guess[l];
    2944:           PetscInt  dep   = (k & (1 << l)) >> l;

    2946:           extCoord *= dep * coord + !dep;
    2947:           extJ[l] = dep;

    2949:           for (m = 0; m < dimR; m++) {
    2950:             PetscReal coord = guess[m];
    2951:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    2952:             PetscReal mult  = dep * coord + !dep;

    2954:             extJ[l] *= mult;
    2955:           }
    2956:         }
    2957:         for (l = 0; l < dimC; l++) {
    2958:           PetscReal coeff = cellCoeffs[dimC * k + l];

    2960:           resNeg[l] -= coeff * extCoord;
    2961:           for (m = 0; m < dimR; m++) {
    2962:             J[dimR * l + m] += coeff * extJ[m];
    2963:           }
    2964:         }
    2965:       }
    2966:       if (0 && PetscDefined(USE_DEBUG)) {
    2967:         PetscReal maxAbs = 0.;

    2969:         for (l = 0; l < dimC; l++) {
    2970:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2971:         }
    2972:         PetscInfo(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2973:       }

    2975:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
    2976:     }
    2977:   }
    2978:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2979:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2980:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2981:   return 0;
    2982: }

    2984: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2985: {
    2986:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
    2987:   PetscScalar    *coordsScalar = NULL;
    2988:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

    2991:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2993:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2994:   cellCoords = &cellData[0];
    2995:   cellCoeffs = &cellData[coordSize];
    2996:   if (dimR == 2) {
    2997:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2999:     for (i = 0; i < 4; i++) {
    3000:       PetscInt plexI = zToPlex[i];

    3002:       for (j = 0; j < dimC; j++) {
    3003:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3004:       }
    3005:     }
    3006:   } else if (dimR == 3) {
    3007:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    3009:     for (i = 0; i < 8; i++) {
    3010:       PetscInt plexI = zToPlex[i];

    3012:       for (j = 0; j < dimC; j++) {
    3013:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3014:       }
    3015:     }
    3016:   } else {
    3017:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    3018:   }
    3019:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    3020:   for (i = 0; i < dimR; i++) {
    3021:     PetscReal *swap;

    3023:     for (j = 0; j < (numV / 2); j++) {
    3024:       for (k = 0; k < dimC; k++) {
    3025:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    3026:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    3027:       }
    3028:     }

    3030:     if (i < dimR - 1) {
    3031:       swap = cellCoeffs;
    3032:       cellCoeffs = cellCoords;
    3033:       cellCoords = swap;
    3034:     }
    3035:   }
    3036:   PetscArrayzero(realCoords,numPoints * dimC);
    3037:   for (j = 0; j < numPoints; j++) {
    3038:     const PetscReal *guess  = &refCoords[dimR * j];
    3039:     PetscReal       *mapped = &realCoords[dimC * j];

    3041:     for (k = 0; k < numV; k++) {
    3042:       PetscReal extCoord = 1.;
    3043:       for (l = 0; l < dimR; l++) {
    3044:         PetscReal coord = guess[l];
    3045:         PetscInt  dep   = (k & (1 << l)) >> l;

    3047:         extCoord *= dep * coord + !dep;
    3048:       }
    3049:       for (l = 0; l < dimC; l++) {
    3050:         PetscReal coeff = cellCoeffs[dimC * k + l];

    3052:         mapped[l] += coeff * extCoord;
    3053:       }
    3054:     }
    3055:   }
    3056:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    3057:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    3058:   return 0;
    3059: }

    3061: /* TODO: TOBY please fix this for Nc > 1 */
    3062: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    3063: {
    3064:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
    3065:   PetscScalar    *nodes = NULL;
    3066:   PetscReal      *invV, *modes;
    3067:   PetscReal      *B, *D, *resNeg;
    3068:   PetscScalar    *J, *invJ, *work;

    3070:   PetscFEGetDimension(fe, &pdim);
    3071:   PetscFEGetNumComponents(fe, &numComp);
    3073:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3074:   /* convert nodes to values in the stable evaluation basis */
    3075:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    3076:   invV = fe->invV;
    3077:   for (i = 0; i < pdim; ++i) {
    3078:     modes[i] = 0.;
    3079:     for (j = 0; j < pdim; ++j) {
    3080:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3081:     }
    3082:   }
    3083:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    3084:   D      = &B[pdim*Nc];
    3085:   resNeg = &D[pdim*Nc * dimR];
    3086:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    3087:   invJ = &J[Nc * dimR];
    3088:   work = &invJ[Nc * dimR];
    3089:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
    3090:   for (j = 0; j < numPoints; j++) {
    3091:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    3092:       PetscReal *guess = &refCoords[j * dimR];
    3093:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
    3094:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
    3095:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
    3096:       for (k = 0; k < pdim; k++) {
    3097:         for (l = 0; l < Nc; l++) {
    3098:           resNeg[l] -= modes[k] * B[k * Nc + l];
    3099:           for (m = 0; m < dimR; m++) {
    3100:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    3101:           }
    3102:         }
    3103:       }
    3104:       if (0 && PetscDefined(USE_DEBUG)) {
    3105:         PetscReal maxAbs = 0.;

    3107:         for (l = 0; l < Nc; l++) {
    3108:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    3109:         }
    3110:         PetscInfo(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    3111:       }
    3112:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
    3113:     }
    3114:   }
    3115:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    3116:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    3117:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    3118:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3119:   return 0;
    3120: }

    3122: /* TODO: TOBY please fix this for Nc > 1 */
    3123: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    3124: {
    3125:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
    3126:   PetscScalar    *nodes = NULL;
    3127:   PetscReal      *invV, *modes;
    3128:   PetscReal      *B;

    3130:   PetscFEGetDimension(fe, &pdim);
    3131:   PetscFEGetNumComponents(fe, &numComp);
    3133:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3134:   /* convert nodes to values in the stable evaluation basis */
    3135:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    3136:   invV = fe->invV;
    3137:   for (i = 0; i < pdim; ++i) {
    3138:     modes[i] = 0.;
    3139:     for (j = 0; j < pdim; ++j) {
    3140:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3141:     }
    3142:   }
    3143:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    3144:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
    3145:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
    3146:   for (j = 0; j < numPoints; j++) {
    3147:     PetscReal *mapped = &realCoords[j * Nc];

    3149:     for (k = 0; k < pdim; k++) {
    3150:       for (l = 0; l < Nc; l++) {
    3151:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    3152:       }
    3153:     }
    3154:   }
    3155:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    3156:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    3157:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3158:   return 0;
    3159: }

    3161: /*@
    3162:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
    3163:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
    3164:   extend uniquely outside the reference cell (e.g, most non-affine maps)

    3166:   Not collective

    3168:   Input Parameters:
    3169: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    3170:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3171:                as a multilinear map for tensor-product elements
    3172: . cell       - the cell whose map is used.
    3173: . numPoints  - the number of points to locate
    3174: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    3176:   Output Parameters:
    3177: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    3179:   Level: intermediate

    3181: .seealso: DMPlexReferenceToCoordinates()
    3182: @*/
    3183: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    3184: {
    3185:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    3186:   DM             coordDM = NULL;
    3187:   Vec            coords;
    3188:   PetscFE        fe = NULL;

    3191:   DMGetDimension(dm,&dimR);
    3192:   DMGetCoordinateDim(dm,&dimC);
    3193:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return 0;
    3194:   DMPlexGetDepth(dm,&depth);
    3195:   DMGetCoordinatesLocal(dm,&coords);
    3196:   DMGetCoordinateDM(dm,&coordDM);
    3197:   if (coordDM) {
    3198:     PetscInt coordFields;

    3200:     DMGetNumFields(coordDM,&coordFields);
    3201:     if (coordFields) {
    3202:       PetscClassId id;
    3203:       PetscObject  disc;

    3205:       DMGetField(coordDM,0,NULL,&disc);
    3206:       PetscObjectGetClassId(disc,&id);
    3207:       if (id == PETSCFE_CLASSID) {
    3208:         fe = (PetscFE) disc;
    3209:       }
    3210:     }
    3211:   }
    3212:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3214:   if (!fe) { /* implicit discretization: affine or multilinear */
    3215:     PetscInt  coneSize;
    3216:     PetscBool isSimplex, isTensor;

    3218:     DMPlexGetConeSize(dm,cell,&coneSize);
    3219:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3220:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3221:     if (isSimplex) {
    3222:       PetscReal detJ, *v0, *J, *invJ;

    3224:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3225:       J    = &v0[dimC];
    3226:       invJ = &J[dimC * dimC];
    3227:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
    3228:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    3229:         const PetscReal x0[3] = {-1.,-1.,-1.};

    3231:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    3232:       }
    3233:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3234:     } else if (isTensor) {
    3235:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    3236:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3237:   } else {
    3238:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    3239:   }
    3240:   return 0;
    3241: }

    3243: /*@
    3244:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

    3246:   Not collective

    3248:   Input Parameters:
    3249: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    3250:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3251:                as a multilinear map for tensor-product elements
    3252: . cell       - the cell whose map is used.
    3253: . numPoints  - the number of points to locate
    3254: - refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    3256:   Output Parameters:
    3257: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    3259:    Level: intermediate

    3261: .seealso: DMPlexCoordinatesToReference()
    3262: @*/
    3263: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    3264: {
    3265:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    3266:   DM             coordDM = NULL;
    3267:   Vec            coords;
    3268:   PetscFE        fe = NULL;

    3271:   DMGetDimension(dm,&dimR);
    3272:   DMGetCoordinateDim(dm,&dimC);
    3273:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return 0;
    3274:   DMPlexGetDepth(dm,&depth);
    3275:   DMGetCoordinatesLocal(dm,&coords);
    3276:   DMGetCoordinateDM(dm,&coordDM);
    3277:   if (coordDM) {
    3278:     PetscInt coordFields;

    3280:     DMGetNumFields(coordDM,&coordFields);
    3281:     if (coordFields) {
    3282:       PetscClassId id;
    3283:       PetscObject  disc;

    3285:       DMGetField(coordDM,0,NULL,&disc);
    3286:       PetscObjectGetClassId(disc,&id);
    3287:       if (id == PETSCFE_CLASSID) {
    3288:         fe = (PetscFE) disc;
    3289:       }
    3290:     }
    3291:   }
    3292:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3294:   if (!fe) { /* implicit discretization: affine or multilinear */
    3295:     PetscInt  coneSize;
    3296:     PetscBool isSimplex, isTensor;

    3298:     DMPlexGetConeSize(dm,cell,&coneSize);
    3299:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3300:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3301:     if (isSimplex) {
    3302:       PetscReal detJ, *v0, *J;

    3304:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3305:       J    = &v0[dimC];
    3306:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
    3307:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3308:         const PetscReal xi0[3] = {-1.,-1.,-1.};

    3310:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3311:       }
    3312:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3313:     } else if (isTensor) {
    3314:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3315:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3316:   } else {
    3317:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3318:   }
    3319:   return 0;
    3320: }

    3322: /*@C
    3323:   DMPlexRemapGeometry - This function maps the original DM coordinates to new coordinates.

    3325:   Not collective

    3327:   Input Parameters:
    3328: + dm      - The DM
    3329: . time    - The time
    3330: - func    - The function transforming current coordinates to new coordaintes

    3332:    Calling sequence of func:
    3333: $    func(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3334: $         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3335: $         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3336: $         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]);

    3338: +  dim          - The spatial dimension
    3339: .  Nf           - The number of input fields (here 1)
    3340: .  NfAux        - The number of input auxiliary fields
    3341: .  uOff         - The offset of the coordinates in u[] (here 0)
    3342: .  uOff_x       - The offset of the coordinates in u_x[] (here 0)
    3343: .  u            - The coordinate values at this point in space
    3344: .  u_t          - The coordinate time derivative at this point in space (here NULL)
    3345: .  u_x          - The coordinate derivatives at this point in space
    3346: .  aOff         - The offset of each auxiliary field in u[]
    3347: .  aOff_x       - The offset of each auxiliary field in u_x[]
    3348: .  a            - The auxiliary field values at this point in space
    3349: .  a_t          - The auxiliary field time derivative at this point in space (or NULL)
    3350: .  a_x          - The auxiliary field derivatives at this point in space
    3351: .  t            - The current time
    3352: .  x            - The coordinates of this point (here not used)
    3353: .  numConstants - The number of constants
    3354: .  constants    - The value of each constant
    3355: -  f            - The new coordinates at this point in space

    3357:   Level: intermediate

    3359: .seealso: DMGetCoordinates(), DMGetCoordinatesLocal(), DMGetCoordinateDM(), DMProjectFieldLocal(), DMProjectFieldLabelLocal()
    3360: @*/
    3361: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time,
    3362:                                    void (*func)(PetscInt, PetscInt, PetscInt,
    3363:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3364:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3365:                                                 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))
    3366: {
    3367:   DM             cdm;
    3368:   DMField        cf;
    3369:   Vec            lCoords, tmpCoords;

    3371:   DMGetCoordinateDM(dm, &cdm);
    3372:   DMGetCoordinatesLocal(dm, &lCoords);
    3373:   DMGetLocalVector(cdm, &tmpCoords);
    3374:   VecCopy(lCoords, tmpCoords);
    3375:   /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
    3376:   DMGetCoordinateField(dm, &cf);
    3377:   cdm->coordinateField = cf;
    3378:   DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords);
    3379:   cdm->coordinateField = NULL;
    3380:   DMRestoreLocalVector(cdm, &tmpCoords);
    3381:   DMSetCoordinatesLocal(dm, lCoords);
    3382:   return 0;
    3383: }

    3385: /* Shear applies the transformation, assuming we fix z,
    3386:   / 1  0  m_0 \
    3387:   | 0  1  m_1 |
    3388:   \ 0  0   1  /
    3389: */
    3390: static void f0_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3391:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3392:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3393:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
    3394: {
    3395:   const PetscInt Nc = uOff[1]-uOff[0];
    3396:   const PetscInt ax = (PetscInt) PetscRealPart(constants[0]);
    3397:   PetscInt       c;

    3399:   for (c = 0; c < Nc; ++c) {
    3400:     coords[c] = u[c] + constants[c+1]*u[ax];
    3401:   }
    3402: }

    3404: /*@C
    3405:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

    3407:   Not collective

    3409:   Input Parameters:
    3410: + dm          - The DM
    3411: . direction   - The shear coordinate direction, e.g. 0 is the x-axis
    3412: - multipliers - The multiplier m for each direction which is not the shear direction

    3414:   Level: intermediate

    3416: .seealso: DMPlexRemapGeometry()
    3417: @*/
    3418: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
    3419: {
    3420:   DM             cdm;
    3421:   PetscDS        cds;
    3422:   PetscObject    obj;
    3423:   PetscClassId   id;
    3424:   PetscScalar   *moduli;
    3425:   const PetscInt dir = (PetscInt) direction;
    3426:   PetscInt       dE, d, e;

    3428:   DMGetCoordinateDM(dm, &cdm);
    3429:   DMGetCoordinateDim(dm, &dE);
    3430:   PetscMalloc1(dE+1, &moduli);
    3431:   moduli[0] = dir;
    3432:   for (d = 0, e = 0; d < dE; ++d) moduli[d+1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
    3433:   DMGetDS(cdm, &cds);
    3434:   PetscDSGetDiscretization(cds, 0, &obj);
    3435:   PetscObjectGetClassId(obj, &id);
    3436:   if (id != PETSCFE_CLASSID) {
    3437:     Vec           lCoords;
    3438:     PetscSection  cSection;
    3439:     PetscScalar  *coords;
    3440:     PetscInt      vStart, vEnd, v;

    3442:     DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3443:     DMGetCoordinateSection(dm, &cSection);
    3444:     DMGetCoordinatesLocal(dm, &lCoords);
    3445:     VecGetArray(lCoords, &coords);
    3446:     for (v = vStart; v < vEnd; ++v) {
    3447:       PetscReal ds;
    3448:       PetscInt  off, c;

    3450:       PetscSectionGetOffset(cSection, v, &off);
    3451:       ds   = PetscRealPart(coords[off+dir]);
    3452:       for (c = 0; c < dE; ++c) coords[off+c] += moduli[c]*ds;
    3453:     }
    3454:     VecRestoreArray(lCoords, &coords);
    3455:   } else {
    3456:     PetscDSSetConstants(cds, dE+1, moduli);
    3457:     DMPlexRemapGeometry(dm, 0.0, f0_shear);
    3458:   }
    3459:   PetscFree(moduli);
    3460:   return 0;
    3461: }