Date: 2025-03-28T21:10:45+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: const char *const DMPlexCoordMaps[] = {"none", "shear", "flare", "annulus", "shell", "unknown", "DMPlexCoordMap", "DM_COORD_MAP_", NULL};

      8: /*@
      9:   DMPlexFindVertices - Try to find DAG points based on their coordinates.

     11:   Not Collective (provided `DMGetCoordinatesLocalSetUp()` has been already called)

     13:   Input Parameters:
     14: + dm          - The `DMPLEX` object
     15: . coordinates - The `Vec` of coordinates of the sought points
     16: - eps         - The tolerance or `PETSC_DEFAULT`

     18:   Output Parameter:
     19: . points - The `IS` of found DAG points or -1

     21:   Level: intermediate

     23:   Notes:
     24:   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.

     26:   The output `IS` is living on `PETSC_COMM_SELF` and its length is npoints.
     27:   Each rank does the search independently.
     28:   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.

     30:   The output `IS` must be destroyed by user.

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

     34:   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.

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

     47:   PetscFunctionBegin;
     48:   if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
     49:   PetscCall(DMGetCoordinateDim(dm, &cdim));
     50:   {
     51:     PetscInt n;

     53:     PetscCall(VecGetLocalSize(coordinates, &n));
     54:     PetscCheck(n % cdim == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Given coordinates Vec has local length %" PetscInt_FMT " not divisible by coordinate dimension %" PetscInt_FMT " of given DM", n, cdim);
     55:     npoints = n / cdim;
     56:   }
     57:   PetscCall(DMGetCoordinatesLocal(dm, &allCoordsVec));
     58:   PetscCall(VecGetArrayRead(allCoordsVec, &allCoords));
     59:   PetscCall(VecGetArrayRead(coordinates, &coord));
     60:   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
     61:   if (PetscDefined(USE_DEBUG)) {
     62:     /* check coordinate section is consistent with DM dimension */
     63:     PetscSection cs;
     64:     PetscInt     ndof;

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

     90:       dagPoints[i] = -1;
     91:       for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
     92:         norm = 0.0;
     93:         for (c = 0; c < cdim; c++) norm += PetscRealPart(PetscSqr(coord[j + c] - allCoords[o + c]));
     94:         norm = PetscSqrtReal(norm);
     95:         if (norm <= eps) {
     96:           dagPoints[i] = p;
     97:           break;
     98:         }
     99:       }
    100:     }
    101:   }
    102:   PetscCall(VecRestoreArrayRead(allCoordsVec, &allCoords));
    103:   PetscCall(VecRestoreArrayRead(coordinates, &coord));
    104:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points));
    105:   PetscFunctionReturn(PETSC_SUCCESS);
    106: }

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

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

    132:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
    133:       *hasIntersection = PETSC_TRUE;
    134:       if (intersection) {
    135:         intersection[0] = p0_x + (t * s1_x);
    136:         intersection[1] = p0_y + (t * s1_y);
    137:       }
    138:     }
    139:   }
    140:   PetscFunctionReturn(PETSC_SUCCESS);
    141: }

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

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

    192:     if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
    193:       *hasIntersection = PETSC_TRUE;
    194:       if (intersection) {
    195:         intersection[0] = p0_x + (t * s0_x);
    196:         intersection[1] = p0_y + (t * s0_y);
    197:         intersection[2] = p0_z + (t * s0_z);
    198:       }
    199:     }
    200:   }
    201:   PetscFunctionReturn(PETSC_SUCCESS);
    202: }
    203: #endif

    205: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Coords_Internal(DM dm, PetscInt dim, PetscInt cdim, const PetscScalar coords[], const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
    206: {
    207:   PetscReal d[4]; // distance of vertices to the plane
    208:   PetscReal dp;   // distance from origin to the plane
    209:   PetscInt  n = 0;

    211:   PetscFunctionBegin;
    212:   if (pos) *pos = PETSC_FALSE;
    213:   if (Nint) *Nint = 0;
    214:   if (PetscDefined(USE_DEBUG)) {
    215:     PetscReal mag = DMPlex_NormD_Internal(cdim, normal);
    216:     PetscCheck(PetscAbsReal(mag - (PetscReal)1.0) < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Normal vector is not normalized: %g", (double)mag);
    217:   }

    219:   dp = DMPlex_DotRealD_Internal(cdim, normal, p);
    220:   for (PetscInt v = 0; v < dim + 1; ++v) {
    221:     // d[v] is positive, zero, or negative if vertex i is above, on, or below the plane
    222: #if defined(PETSC_USE_COMPLEX)
    223:     PetscReal c[4];
    224:     for (PetscInt i = 0; i < cdim; ++i) c[i] = PetscRealPart(coords[v * cdim + i]);
    225:     d[v] = DMPlex_DotRealD_Internal(cdim, normal, c);
    226: #else
    227:     d[v] = DMPlex_DotRealD_Internal(cdim, normal, &coords[v * cdim]);
    228: #endif
    229:     d[v] -= dp;
    230:   }

    232:   // If all d are positive or negative, no intersection
    233:   {
    234:     PetscInt v;
    235:     for (v = 0; v < dim + 1; ++v)
    236:       if (d[v] >= 0.) break;
    237:     if (v == dim + 1) PetscFunctionReturn(PETSC_SUCCESS);
    238:     for (v = 0; v < dim + 1; ++v)
    239:       if (d[v] <= 0.) break;
    240:     if (v == dim + 1) {
    241:       if (pos) *pos = PETSC_TRUE;
    242:       PetscFunctionReturn(PETSC_SUCCESS);
    243:     }
    244:   }

    246:   for (PetscInt v = 0; v < dim + 1; ++v) {
    247:     // Points with zero distance are automatically added to the list.
    248:     if (PetscAbsReal(d[v]) < PETSC_MACHINE_EPSILON) {
    249:       for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = PetscRealPart(coords[v * cdim + i]);
    250:       ++n;
    251:     } else {
    252:       // For each point with nonzero distance, seek another point with opposite sign
    253:       // and higher index, and compute the intersection of the line between those
    254:       // points and the plane.
    255:       for (PetscInt w = v + 1; w < dim + 1; ++w) {
    256:         if (d[v] * d[w] < 0.) {
    257:           PetscReal inv_dist = 1. / (d[v] - d[w]);
    258:           for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = (d[v] * PetscRealPart(coords[w * cdim + i]) - d[w] * PetscRealPart(coords[v * cdim + i])) * inv_dist;
    259:           ++n;
    260:         }
    261:       }
    262:     }
    263:   }
    264:   // TODO order output points if there are 4
    265:   *Nint = n;
    266:   PetscFunctionReturn(PETSC_SUCCESS);
    267: }

    269: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
    270: {
    271:   const PetscScalar *array;
    272:   PetscScalar       *coords = NULL;
    273:   PetscInt           numCoords;
    274:   PetscBool          isDG;
    275:   PetscInt           cdim;

    277:   PetscFunctionBegin;
    278:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    279:   PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
    280:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    281:   PetscCheck(numCoords == dim * (dim + 1), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Tetrahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * (dim + 1), numCoords);
    282:   PetscCall(PetscArrayzero(intPoints, dim * (dim + 1)));

    284:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, coords, p, normal, pos, Nint, intPoints));

    286:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    287:   PetscFunctionReturn(PETSC_SUCCESS);
    288: }

    290: static PetscErrorCode DMPlexGetPlaneQuadIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
    291: {
    292:   const PetscScalar *array;
    293:   PetscScalar       *coords = NULL;
    294:   PetscInt           numCoords;
    295:   PetscBool          isDG;
    296:   PetscInt           cdim;
    297:   PetscScalar        tcoords[6] = {0., 0., 0., 0., 0., 0.};
    298:   const PetscInt     vertsA[3]  = {0, 1, 3};
    299:   const PetscInt     vertsB[3]  = {1, 2, 3};
    300:   PetscInt           NintA, NintB;

    302:   PetscFunctionBegin;
    303:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    304:   PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
    305:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    306:   PetscCheck(numCoords == dim * 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 4, numCoords);
    307:   PetscCall(PetscArrayzero(intPoints, dim * 4));

    309:   for (PetscInt v = 0; v < 3; ++v)
    310:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
    311:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, intPoints));
    312:   for (PetscInt v = 0; v < 3; ++v)
    313:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
    314:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[NintA * cdim]));
    315:   *Nint = NintA + NintB;

    317:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    318:   PetscFunctionReturn(PETSC_SUCCESS);
    319: }

    321: static PetscErrorCode DMPlexGetPlaneHexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
    322: {
    323:   const PetscScalar *array;
    324:   PetscScalar       *coords = NULL;
    325:   PetscInt           numCoords;
    326:   PetscBool          isDG;
    327:   PetscInt           cdim;
    328:   PetscScalar        tcoords[12] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
    329:   // We split using the (2, 4) main diagonal, so all tets contain those vertices
    330:   const PetscInt vertsA[4] = {0, 1, 2, 4};
    331:   const PetscInt vertsB[4] = {0, 2, 3, 4};
    332:   const PetscInt vertsC[4] = {1, 7, 2, 4};
    333:   const PetscInt vertsD[4] = {2, 7, 6, 4};
    334:   const PetscInt vertsE[4] = {3, 5, 4, 2};
    335:   const PetscInt vertsF[4] = {4, 5, 6, 2};
    336:   PetscInt       NintA, NintB, NintC, NintD, NintE, NintF, Nsum = 0;

    338:   PetscFunctionBegin;
    339:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    340:   PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
    341:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    342:   PetscCheck(numCoords == dim * 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Hexahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 8, numCoords);
    343:   PetscCall(PetscArrayzero(intPoints, dim * 18));

    345:   for (PetscInt v = 0; v < 4; ++v)
    346:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
    347:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, &intPoints[Nsum * cdim]));
    348:   Nsum += NintA;
    349:   for (PetscInt v = 0; v < 4; ++v)
    350:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
    351:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[Nsum * cdim]));
    352:   Nsum += NintB;
    353:   for (PetscInt v = 0; v < 4; ++v)
    354:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsC[v] * cdim + d];
    355:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintC, &intPoints[Nsum * cdim]));
    356:   Nsum += NintC;
    357:   for (PetscInt v = 0; v < 4; ++v)
    358:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsD[v] * cdim + d];
    359:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintD, &intPoints[Nsum * cdim]));
    360:   Nsum += NintD;
    361:   for (PetscInt v = 0; v < 4; ++v)
    362:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsE[v] * cdim + d];
    363:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintE, &intPoints[Nsum * cdim]));
    364:   Nsum += NintE;
    365:   for (PetscInt v = 0; v < 4; ++v)
    366:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsF[v] * cdim + d];
    367:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintF, &intPoints[Nsum * cdim]));
    368:   Nsum += NintF;
    369:   *Nint = Nsum;

    371:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    372:   PetscFunctionReturn(PETSC_SUCCESS);
    373: }

    375: /*
    376:   DMPlexGetPlaneCellIntersection_Internal - Finds the intersection of a plane with a cell

    378:   Not collective

    380:   Input Parameters:
    381: + dm     - the DM
    382: . c      - the mesh point
    383: . p      - a point on the plane.
    384: - normal - a normal vector to the plane, must be normalized

    386:   Output Parameters:
    387: . pos       - `PETSC_TRUE` is the cell is on the positive side of the plane, `PETSC_FALSE` on the negative side
    388: + Nint      - the number of intersection points, in [0, 4]
    389: - intPoints - the coordinates of the intersection points, should be length at least 12

    391:   Note: The `pos` argument is only meaningful if the number of intersections is 0. The algorithmic idea comes from https://github.com/chrisk314/tet-plane-intersection.

    393:   Level: developer

    395: .seealso:
    396: @*/
    397: static PetscErrorCode DMPlexGetPlaneCellIntersection_Internal(DM dm, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
    398: {
    399:   DMPolytopeType ct;

    401:   PetscFunctionBegin;
    402:   PetscCall(DMPlexGetCellType(dm, c, &ct));
    403:   switch (ct) {
    404:   case DM_POLYTOPE_SEGMENT:
    405:   case DM_POLYTOPE_TRIANGLE:
    406:   case DM_POLYTOPE_TETRAHEDRON:
    407:     PetscCall(DMPlexGetPlaneSimplexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
    408:     break;
    409:   case DM_POLYTOPE_QUADRILATERAL:
    410:     PetscCall(DMPlexGetPlaneQuadIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
    411:     break;
    412:   case DM_POLYTOPE_HEXAHEDRON:
    413:     PetscCall(DMPlexGetPlaneHexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
    414:     break;
    415:   default:
    416:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No plane intersection for cell %" PetscInt_FMT " with type %s", c, DMPolytopeTypes[ct]);
    417:   }
    418:   PetscFunctionReturn(PETSC_SUCCESS);
    419: }

    421: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    422: {
    423:   const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
    424:   const PetscReal x   = PetscRealPart(point[0]);
    425:   PetscReal       v0, J, invJ, detJ;
    426:   PetscReal       xi;

    428:   PetscFunctionBegin;
    429:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ));
    430:   xi = invJ * (x - v0);

    432:   if ((xi >= -eps) && (xi <= 2. + eps)) *cell = c;
    433:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    434:   PetscFunctionReturn(PETSC_SUCCESS);
    435: }

    437: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    438: {
    439:   const PetscInt  embedDim = 2;
    440:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    441:   PetscReal       x        = PetscRealPart(point[0]);
    442:   PetscReal       y        = PetscRealPart(point[1]);
    443:   PetscReal       v0[2], J[4], invJ[4], detJ;
    444:   PetscReal       xi, eta;

    446:   PetscFunctionBegin;
    447:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
    448:   xi  = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
    449:   eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);

    451:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0 + eps)) *cell = c;
    452:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    453:   PetscFunctionReturn(PETSC_SUCCESS);
    454: }

    456: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
    457: {
    458:   const PetscInt embedDim = 2;
    459:   PetscReal      x        = PetscRealPart(point[0]);
    460:   PetscReal      y        = PetscRealPart(point[1]);
    461:   PetscReal      v0[2], J[4], invJ[4], detJ;
    462:   PetscReal      xi, eta, r;

    464:   PetscFunctionBegin;
    465:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
    466:   xi  = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
    467:   eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);

    469:   xi  = PetscMax(xi, 0.0);
    470:   eta = PetscMax(eta, 0.0);
    471:   if (xi + eta > 2.0) {
    472:     r = (xi + eta) / 2.0;
    473:     xi /= r;
    474:     eta /= r;
    475:   }
    476:   cpoint[0] = J[0 * embedDim + 0] * xi + J[0 * embedDim + 1] * eta + v0[0];
    477:   cpoint[1] = J[1 * embedDim + 0] * xi + J[1 * embedDim + 1] * eta + v0[1];
    478:   PetscFunctionReturn(PETSC_SUCCESS);
    479: }

    481: // This is the ray-casting, or even-odd algorithm: https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule
    482: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    483: {
    484:   const PetscScalar *array;
    485:   PetscScalar       *coords    = NULL;
    486:   const PetscInt     faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
    487:   PetscReal          x         = PetscRealPart(point[0]);
    488:   PetscReal          y         = PetscRealPart(point[1]);
    489:   PetscInt           crossings = 0, numCoords, f;
    490:   PetscBool          isDG;

    492:   PetscFunctionBegin;
    493:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    494:   PetscCheck(numCoords == 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
    495:   for (f = 0; f < 4; ++f) {
    496:     PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 0]);
    497:     PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 1]);
    498:     PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 0]);
    499:     PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 1]);

    501:     if ((x == x_j) && (y == y_j)) {
    502:       // point is a corner
    503:       crossings = 1;
    504:       break;
    505:     }
    506:     if ((y_j > y) != (y_i > y)) {
    507:       PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
    508:       if (slope == 0) {
    509:         // point is a corner
    510:         crossings = 1;
    511:         break;
    512:       }
    513:       if ((slope < 0) != (y_i < y_j)) ++crossings;
    514:     }
    515:   }
    516:   if (crossings % 2) *cell = c;
    517:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    518:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    519:   PetscFunctionReturn(PETSC_SUCCESS);
    520: }

    522: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    523: {
    524:   const PetscInt  embedDim = 3;
    525:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    526:   PetscReal       v0[3], J[9], invJ[9], detJ;
    527:   PetscReal       x = PetscRealPart(point[0]);
    528:   PetscReal       y = PetscRealPart(point[1]);
    529:   PetscReal       z = PetscRealPart(point[2]);
    530:   PetscReal       xi, eta, zeta;

    532:   PetscFunctionBegin;
    533:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
    534:   xi   = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
    535:   eta  = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
    536:   zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);

    538:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
    539:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    540:   PetscFunctionReturn(PETSC_SUCCESS);
    541: }

    543: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    544: {
    545:   const PetscScalar *array;
    546:   PetscScalar       *coords    = NULL;
    547:   const PetscInt     faces[24] = {0, 3, 2, 1, 5, 4, 7, 6, 3, 0, 4, 5, 1, 2, 6, 7, 3, 5, 6, 2, 0, 1, 7, 4};
    548:   PetscBool          found     = PETSC_TRUE;
    549:   PetscInt           numCoords, f;
    550:   PetscBool          isDG;

    552:   PetscFunctionBegin;
    553:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    554:   PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
    555:   for (f = 0; f < 6; ++f) {
    556:     /* Check the point is under plane */
    557:     /*   Get face normal */
    558:     PetscReal v_i[3];
    559:     PetscReal v_j[3];
    560:     PetscReal normal[3];
    561:     PetscReal pp[3];
    562:     PetscReal dot;

    564:     v_i[0]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
    565:     v_i[1]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
    566:     v_i[2]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
    567:     v_j[0]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
    568:     v_j[1]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
    569:     v_j[2]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
    570:     normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
    571:     normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
    572:     normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
    573:     pp[0]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
    574:     pp[1]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
    575:     pp[2]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
    576:     dot       = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];

    578:     /* Check that projected point is in face (2D location problem) */
    579:     if (dot < 0.0) {
    580:       found = PETSC_FALSE;
    581:       break;
    582:     }
    583:   }
    584:   if (found) *cell = c;
    585:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    586:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    587:   PetscFunctionReturn(PETSC_SUCCESS);
    588: }

    590: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
    591: {
    592:   PetscInt d;

    594:   PetscFunctionBegin;
    595:   box->dim = dim;
    596:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
    597:   PetscFunctionReturn(PETSC_SUCCESS);
    598: }

    600: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    601: {
    602:   PetscFunctionBegin;
    603:   PetscCall(PetscCalloc1(1, box));
    604:   PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
    605:   PetscFunctionReturn(PETSC_SUCCESS);
    606: }

    608: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
    609: {
    610:   PetscInt d;

    612:   PetscFunctionBegin;
    613:   for (d = 0; d < box->dim; ++d) {
    614:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    615:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    616:   }
    617:   PetscFunctionReturn(PETSC_SUCCESS);
    618: }

    620: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
    621: {
    622:   Vec                coordinates;
    623:   const PetscScalar *a;
    624:   PetscInt           cdim, cStart, cEnd;

    626:   PetscFunctionBegin;
    627:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    628:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    629:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));

    631:   PetscCall(VecGetArrayRead(coordinates, &a));
    632:   PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
    633:   PetscCall(VecRestoreArrayRead(coordinates, &a));
    634:   for (PetscInt c = cStart; c < cEnd; ++c) {
    635:     const PetscScalar *array;
    636:     PetscScalar       *coords = NULL;
    637:     PetscInt           numCoords;
    638:     PetscBool          isDG;

    640:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    641:     for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
    642:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    643:   }
    644:   PetscFunctionReturn(PETSC_SUCCESS);
    645: }

    647: /*@C
    648:   PetscGridHashSetGrid - Divide the grid into boxes

    650:   Not Collective

    652:   Input Parameters:
    653: + box - The grid hash object
    654: . n   - The number of boxes in each dimension, may use `PETSC_DETERMINE` for the entries
    655: - h   - The box size in each dimension, only used if n[d] == `PETSC_DETERMINE`, if not needed you can pass in `NULL`

    657:   Level: developer

    659: .seealso: `DMPLEX`, `PetscGridHashCreate()`
    660: @*/
    661: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
    662: {
    663:   PetscInt d;

    665:   PetscFunctionBegin;
    666:   PetscAssertPointer(n, 2);
    667:   if (h) PetscAssertPointer(h, 3);
    668:   for (d = 0; d < box->dim; ++d) {
    669:     box->extent[d] = box->upper[d] - box->lower[d];
    670:     if (n[d] == PETSC_DETERMINE) {
    671:       PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
    672:       box->h[d] = h[d];
    673:       box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
    674:     } else {
    675:       box->n[d] = n[d];
    676:       box->h[d] = box->extent[d] / n[d];
    677:     }
    678:   }
    679:   PetscFunctionReturn(PETSC_SUCCESS);
    680: }

    682: /*@C
    683:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

    685:   Not Collective

    687:   Input Parameters:
    688: + box       - The grid hash object
    689: . numPoints - The number of input points
    690: - points    - The input point coordinates

    692:   Output Parameters:
    693: + dboxes - An array of `numPoints` x `dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
    694: - boxes  - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`

    696:   Level: developer

    698:   Note:
    699:   This only guarantees that a box contains a point, not that a cell does.

    701: .seealso: `DMPLEX`, `PetscGridHashCreate()`
    702: @*/
    703: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
    704: {
    705:   const PetscReal *lower = box->lower;
    706:   const PetscReal *upper = box->upper;
    707:   const PetscReal *h     = box->h;
    708:   const PetscInt  *n     = box->n;
    709:   const PetscInt   dim   = box->dim;
    710:   PetscInt         d, p;

    712:   PetscFunctionBegin;
    713:   for (p = 0; p < numPoints; ++p) {
    714:     for (d = 0; d < dim; ++d) {
    715:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

    717:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
    718:       if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
    719:       PetscCheck(dbox >= 0 && dbox < n[d], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %" PetscInt_FMT " (%g, %g, %g) is outside of our bounding box (%g, %g, %g) - (%g, %g, %g)", 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, (double)lower[0], (double)lower[1], (double)lower[2], (double)upper[0], (double)upper[1], (double)upper[2]);
    720:       dboxes[p * dim + d] = dbox;
    721:     }
    722:     if (boxes)
    723:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
    724:   }
    725:   PetscFunctionReturn(PETSC_SUCCESS);
    726: }

    728: /*
    729:   PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

    731:   Not Collective

    733:   Input Parameters:
    734: + box         - The grid hash object
    735: . cellSection - The PetscSection mapping cells to boxes
    736: . numPoints   - The number of input points
    737: - points      - The input point coordinates

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

    744:   Level: developer

    746:   Note:
    747:   This does an additional check that a cell actually contains the point, and found is `PETSC_FALSE` if no cell does. Thus, this function requires that `cellSection` is already constructed.

    749: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
    750: */
    751: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
    752: {
    753:   const PetscReal *lower = box->lower;
    754:   const PetscReal *upper = box->upper;
    755:   const PetscReal *h     = box->h;
    756:   const PetscInt  *n     = box->n;
    757:   const PetscInt   dim   = box->dim;
    758:   PetscInt         bStart, bEnd, d, p;

    760:   PetscFunctionBegin;
    762:   *found = PETSC_FALSE;
    763:   PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
    764:   for (p = 0; p < numPoints; ++p) {
    765:     for (d = 0; d < dim; ++d) {
    766:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

    768:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
    769:       if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
    770:       dboxes[p * dim + d] = dbox;
    771:     }
    772:     if (boxes)
    773:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
    774:     // It is possible for a box to overlap no grid cells
    775:     if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
    776:   }
    777:   *found = PETSC_TRUE;
    778:   PetscFunctionReturn(PETSC_SUCCESS);
    779: }

    781: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    782: {
    783:   PetscFunctionBegin;
    784:   if (*box) {
    785:     PetscCall(PetscSectionDestroy(&(*box)->cellSection));
    786:     PetscCall(ISDestroy(&(*box)->cells));
    787:     PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
    788:   }
    789:   PetscCall(PetscFree(*box));
    790:   PetscFunctionReturn(PETSC_SUCCESS);
    791: }

    793: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
    794: {
    795:   DMPolytopeType ct;

    797:   PetscFunctionBegin;
    798:   PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
    799:   switch (ct) {
    800:   case DM_POLYTOPE_SEGMENT:
    801:     PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
    802:     break;
    803:   case DM_POLYTOPE_TRIANGLE:
    804:     PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
    805:     break;
    806:   case DM_POLYTOPE_QUADRILATERAL:
    807:     PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
    808:     break;
    809:   case DM_POLYTOPE_TETRAHEDRON:
    810:     PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
    811:     break;
    812:   case DM_POLYTOPE_HEXAHEDRON:
    813:     PetscCall(DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell));
    814:     break;
    815:   default:
    816:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
    817:   }
    818:   PetscFunctionReturn(PETSC_SUCCESS);
    819: }

    821: /*
    822:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
    823: */
    824: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
    825: {
    826:   DMPolytopeType ct;

    828:   PetscFunctionBegin;
    829:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    830:   switch (ct) {
    831:   case DM_POLYTOPE_TRIANGLE:
    832:     PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
    833:     break;
    834: #if 0
    835:     case DM_POLYTOPE_QUADRILATERAL:
    836:     PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
    837:     case DM_POLYTOPE_TETRAHEDRON:
    838:     PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
    839:     case DM_POLYTOPE_HEXAHEDRON:
    840:     PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
    841: #endif
    842:   default:
    843:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
    844:   }
    845:   PetscFunctionReturn(PETSC_SUCCESS);
    846: }

    848: /*
    849:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`

    851:   Collective

    853:   Input Parameter:
    854: . dm - The `DMPLEX`

    856:   Output Parameter:
    857: . localBox - The grid hash object

    859:   Level: developer

    861:   Notes:
    862:   How do we determine all boxes intersecting a given cell?

    864:   1) Get convex body enclosing cell. We will use a box called the box-hull.

    866:   2) Get smallest brick of boxes enclosing the box-hull

    868:   3) Each box is composed of 6 planes, 3 lower and 3 upper. We loop over dimensions, and
    869:      for each new plane determine whether the cell is on the negative side, positive side, or intersects it.

    871:      a) If the cell is on the negative side of the lower planes, it is not in the box

    873:      b) If the cell is on the positive side of the upper planes, it is not in the box

    875:      c) If there is no intersection, it is in the box

    877:      d) If any intersection point is within the box limits, it is in the box

    879: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
    880: */
    881: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
    882: {
    883:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
    884:   PetscGridHash   lbox;
    885:   PetscSF         sf;
    886:   const PetscInt *leaves;
    887:   PetscInt       *dboxes, *boxes;
    888:   PetscInt        cdim, cStart, cEnd, Nl = -1;
    889:   PetscBool       flg;

    891:   PetscFunctionBegin;
    892:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    893:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
    894:   PetscCall(DMPlexCreateGridHash(dm, &lbox));
    895:   {
    896:     PetscInt n[3], d;

    898:     PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
    899:     if (flg) {
    900:       for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
    901:     } else {
    902:       for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
    903:     }
    904:     PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
    905:     if (debug)
    906:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "GridHash:\n  (%g, %g, %g) -- (%g, %g, %g)\n  n %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n  h %g %g %g\n", (double)lbox->lower[0], (double)lbox->lower[1], cdim > 2 ? (double)lbox->lower[2] : 0.,
    907:                             (double)lbox->upper[0], (double)lbox->upper[1], cdim > 2 ? (double)lbox->upper[2] : 0, n[0], n[1], cdim > 2 ? n[2] : 0, (double)lbox->h[0], (double)lbox->h[1], cdim > 2 ? (double)lbox->h[2] : 0.));
    908:   }

    910:   PetscCall(DMGetPointSF(dm, &sf));
    911:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
    912:   Nl = PetscMax(Nl, 0);
    913:   PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));

    915:   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
    916:   PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
    917:   for (PetscInt c = cStart; c < cEnd; ++c) {
    918:     PetscReal          intPoints[6 * 6 * 6 * 3];
    919:     const PetscScalar *array;
    920:     PetscScalar       *coords            = NULL;
    921:     const PetscReal   *h                 = lbox->h;
    922:     PetscReal          normal[9]         = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
    923:     PetscReal         *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
    924:     PetscReal         *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
    925:     PetscReal          lp[3], up[3], *tmp;
    926:     PetscInt           numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
    927:     PetscBool          isDG, lower[3], upper[3];

    929:     PetscCall(PetscFindInt(c, Nl, leaves, &idx));
    930:     if (idx >= 0) continue;
    931:     // Get grid of boxes containing the cell
    932:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    933:     PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
    934:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    935:     for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
    936:     for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
    937:     for (PetscInt e = 1; e < numCoords / cdim; ++e) {
    938:       for (PetscInt d = 0; d < cdim; ++d) {
    939:         dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
    940:         dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
    941:       }
    942:     }
    943:     if (debug > 4) {
    944:       for (PetscInt d = 0; d < cdim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " direction %" PetscInt_FMT " box limits %" PetscInt_FMT "--%" PetscInt_FMT "\n", c, d, dlim[d * 2 + 0], dlim[d * 2 + 1]));
    945:     }
    946:     // Initialize with lower planes for first box
    947:     for (PetscInt d = 0; d < cdim; ++d) {
    948:       lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
    949:       up[d] = lp[d] + h[d];
    950:     }
    951:     for (PetscInt d = 0; d < cdim; ++d) {
    952:       PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
    953:       if (debug > 4) {
    954:         if (!lowerInt[d])
    955:           PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) does not intersect %s\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lower[d] ? "positive" : "negative"));
    956:         else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lowerInt[d]));
    957:       }
    958:     }
    959:     // Loop over grid
    960:     for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
    961:       if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
    962:       if (cdim > 2 && debug > 4) {
    963:         if (!upperInt[2]) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[2] ? "positive" : "negative"));
    964:         else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[2]));
    965:       }
    966:       for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
    967:         if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
    968:         if (cdim > 1 && debug > 4) {
    969:           if (!upperInt[1])
    970:             PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[1] ? "positive" : "negative"));
    971:           else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[1]));
    972:         }
    973:         for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
    974:           const PetscInt box    = (k * lbox->n[1] + j) * lbox->n[0] + i;
    975:           PetscBool      excNeg = PETSC_TRUE;
    976:           PetscBool      excPos = PETSC_TRUE;
    977:           PetscInt       NlInt  = 0;
    978:           PetscInt       NuInt  = 0;

    980:           PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
    981:           if (debug > 4) {
    982:             if (!upperInt[0])
    983:               PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[0] ? "positive" : "negative"));
    984:             else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[0]));
    985:           }
    986:           for (PetscInt d = 0; d < cdim; ++d) {
    987:             NlInt += lowerInt[d];
    988:             NuInt += upperInt[d];
    989:           }
    990:           // If there is no intersection...
    991:           if (!NlInt && !NuInt) {
    992:             // If the cell is on the negative side of the lower planes, it is not in the box
    993:             for (PetscInt d = 0; d < cdim; ++d)
    994:               if (lower[d]) {
    995:                 excNeg = PETSC_FALSE;
    996:                 break;
    997:               }
    998:             // If the cell is on the positive side of the upper planes, it is not in the box
    999:             for (PetscInt d = 0; d < cdim; ++d)
    1000:               if (!upper[d]) {
    1001:                 excPos = PETSC_FALSE;
    1002:                 break;
    1003:               }
    1004:             if (excNeg || excPos) {
    1005:               if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
    1006:               if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
    1007:               continue;
    1008:             }
    1009:             // Otherwise it is in the box
    1010:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
    1011:             PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1012:             continue;
    1013:           }
    1014:           /*
    1015:             If any intersection point is within the box limits, it is in the box
    1016:             We need to have tolerances here since intersection point calculations can introduce errors
    1017:             Initialize a count to track which planes have intersection outside the box.
    1018:             if two adjacent planes have intersection points upper and lower all outside the box, look
    1019:             first at if another plane has intersection points outside the box, if so, it is inside the cell
    1020:             look next if no intersection points exist on the other planes, and check if the planes are on the
    1021:             outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
    1022:           */
    1023:           PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
    1024:           for (PetscInt plane = 0; plane < cdim; ++plane) {
    1025:             for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
    1026:               PetscInt d;

    1028:               for (d = 0; d < cdim; ++d) {
    1029:                 if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
    1030:                   if (lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) outsideCount[d]++; // The lower point is to the left of this box, and we count it
    1031:                   break;
    1032:                 }
    1033:               }
    1034:               if (d == cdim) {
    1035:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
    1036:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1037:                 goto end;
    1038:               }
    1039:             }
    1040:             for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
    1041:               PetscInt d;

    1043:               for (d = 0; d < cdim; ++d) {
    1044:                 if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
    1045:                   if (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL)) outsideCount[cdim + d]++; // The upper point is to the right of this box, and we count it
    1046:                   break;
    1047:                 }
    1048:               }
    1049:               if (d == cdim) {
    1050:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
    1051:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1052:                 goto end;
    1053:               }
    1054:             }
    1055:           }
    1056:           /*
    1057:              Check the planes with intersections
    1058:              in 2D, check if the square falls in the middle of a cell
    1059:              ie all four planes have intersection points outside of the box
    1060:              You do not want to be doing this, because it means your grid hashing is finer than your grid,
    1061:              but we should still support it I guess
    1062:           */
    1063:           if (cdim == 2) {
    1064:             PetscInt nIntersects = 0;
    1065:             for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
    1066:             // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
    1067:             if (nIntersects == 8) {
    1068:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1069:               goto end;
    1070:             }
    1071:           }
    1072:           /*
    1073:              In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
    1074:              we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
    1075:              If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
    1076:           */
    1077:           if (cdim == 3) {
    1078:             PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
    1079:             // Find two adjacent planes with at least 3 intersection points in the upper and lower
    1080:             // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
    1081:             for (PetscInt d = 0; d < cdim; ++d)
    1082:               if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
    1083:                 faces[d]++;
    1084:                 checkInternalFace++;
    1085:               }
    1086:             if (checkInternalFace == 3) {
    1087:               // All planes have 3 intersection points, add it.
    1088:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1089:               goto end;
    1090:             }
    1091:             // Gross, figure out which adjacent faces have at least 3 points
    1092:             PetscInt nonIntersectingFace = -1;
    1093:             if (faces[0] == faces[1]) nonIntersectingFace = 2;
    1094:             if (faces[0] == faces[2]) nonIntersectingFace = 1;
    1095:             if (faces[1] == faces[2]) nonIntersectingFace = 0;
    1096:             if (nonIntersectingFace >= 0) {
    1097:               for (PetscInt plane = 0; plane < cdim; ++plane) {
    1098:                 if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
    1099:                 // If we have 2 adjacent sides with pyramids of intersection outside of them, and there is a point between the end caps at all, it must be between the two non intersecting ends, and the box is inside the cell.
    1100:                 for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
    1101:                   if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
    1102:                 }
    1103:                 for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
    1104:                   if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
    1105:                 }
    1106:                 goto end;
    1107:               }
    1108:               // The points are within the bonds of the non intersecting planes, add it.
    1109:             setpoint:
    1110:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1111:               goto end;
    1112:             }
    1113:           }
    1114:         end:
    1115:           lower[0]          = upper[0];
    1116:           lowerInt[0]       = upperInt[0];
    1117:           tmp               = lowerIntPoints[0];
    1118:           lowerIntPoints[0] = upperIntPoints[0];
    1119:           upperIntPoints[0] = tmp;
    1120:         }
    1121:         lp[0]             = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
    1122:         up[0]             = lp[0] + h[0];
    1123:         lower[1]          = upper[1];
    1124:         lowerInt[1]       = upperInt[1];
    1125:         tmp               = lowerIntPoints[1];
    1126:         lowerIntPoints[1] = upperIntPoints[1];
    1127:         upperIntPoints[1] = tmp;
    1128:       }
    1129:       lp[1]             = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
    1130:       up[1]             = lp[1] + h[1];
    1131:       lower[2]          = upper[2];
    1132:       lowerInt[2]       = upperInt[2];
    1133:       tmp               = lowerIntPoints[2];
    1134:       lowerIntPoints[2] = upperIntPoints[2];
    1135:       upperIntPoints[2] = tmp;
    1136:     }
    1137:   }
    1138:   PetscCall(PetscFree2(dboxes, boxes));

    1140:   if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
    1141:   PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
    1142:   PetscCall(DMLabelDestroy(&lbox->cellsSparse));
    1143:   *localBox = lbox;
    1144:   PetscFunctionReturn(PETSC_SUCCESS);
    1145: }

    1147: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
    1148: {
    1149:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
    1150:   DM_Plex        *mesh  = (DM_Plex *)dm->data;
    1151:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
    1152:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
    1153:   PetscInt        dim, Nl = 0, cStart, cEnd, numCells, c, d;
    1154:   PetscSF         sf;
    1155:   const PetscInt *leaves;
    1156:   const PetscInt *boxCells;
    1157:   PetscSFNode    *cells;
    1158:   PetscScalar    *a;
    1159:   PetscMPIInt     result;
    1160:   PetscLogDouble  t0, t1;
    1161:   PetscReal       gmin[3], gmax[3];
    1162:   PetscInt        terminating_query_type[] = {0, 0, 0};
    1163:   PetscMPIInt     rank;

    1165:   PetscFunctionBegin;
    1166:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
    1167:   PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
    1168:   PetscCall(PetscTime(&t0));
    1169:   PetscCheck(ltype != DM_POINTLOCATION_NEAREST || hash, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing. Use -dm_plex_hash_location to enable it.");
    1170:   PetscCall(DMGetCoordinateDim(dm, &dim));
    1171:   PetscCall(VecGetBlockSize(v, &bs));
    1172:   PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
    1173:   PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
    1174:   PetscCheck(bs == dim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, dim);
    1175:   PetscCall(DMGetCoordinatesLocalSetUp(dm));
    1176:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
    1177:   PetscCall(DMGetPointSF(dm, &sf));
    1178:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
    1179:   Nl = PetscMax(Nl, 0);
    1180:   PetscCall(VecGetLocalSize(v, &numPoints));
    1181:   PetscCall(VecGetArray(v, &a));
    1182:   numPoints /= bs;
    1183:   {
    1184:     const PetscSFNode *sf_cells;

    1186:     PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
    1187:     if (sf_cells) {
    1188:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
    1189:       cells = (PetscSFNode *)sf_cells;
    1190:       reuse = PETSC_TRUE;
    1191:     } else {
    1192:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
    1193:       PetscCall(PetscMalloc1(numPoints, &cells));
    1194:       /* initialize cells if created */
    1195:       for (p = 0; p < numPoints; p++) {
    1196:         cells[p].rank  = 0;
    1197:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    1198:       }
    1199:     }
    1200:   }
    1201:   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
    1202:   if (hash) {
    1203:     if (!mesh->lbox) {
    1204:       PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
    1205:       PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
    1206:     }
    1207:     /* Designate the local box for each point */
    1208:     /* Send points to correct process */
    1209:     /* Search cells that lie in each subbox */
    1210:     /*   Should we bin points before doing search? */
    1211:     PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
    1212:   }
    1213:   for (p = 0, numFound = 0; p < numPoints; ++p) {
    1214:     const PetscScalar *point   = &a[p * bs];
    1215:     PetscInt           dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
    1216:     PetscBool          point_outside_domain = PETSC_FALSE;

    1218:     /* check bounding box of domain */
    1219:     for (d = 0; d < dim; d++) {
    1220:       if (PetscRealPart(point[d]) < gmin[d]) {
    1221:         point_outside_domain = PETSC_TRUE;
    1222:         break;
    1223:       }
    1224:       if (PetscRealPart(point[d]) > gmax[d]) {
    1225:         point_outside_domain = PETSC_TRUE;
    1226:         break;
    1227:       }
    1228:     }
    1229:     if (point_outside_domain) {
    1230:       cells[p].rank  = 0;
    1231:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    1232:       terminating_query_type[0]++;
    1233:       continue;
    1234:     }

    1236:     /* check initial values in cells[].index - abort early if found */
    1237:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    1238:       c              = cells[p].index;
    1239:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    1240:       PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
    1241:       if (cell >= 0) {
    1242:         cells[p].rank  = 0;
    1243:         cells[p].index = cell;
    1244:         numFound++;
    1245:       }
    1246:     }
    1247:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    1248:       terminating_query_type[1]++;
    1249:       continue;
    1250:     }

    1252:     if (hash) {
    1253:       PetscBool found_box;

    1255:       if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]Checking point %" PetscInt_FMT " (%.2g, %.2g, %.2g)\n", rank, p, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), dim > 2 ? (double)PetscRealPart(point[2]) : 0.));
    1256:       /* allow for case that point is outside box - abort early */
    1257:       PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
    1258:       if (found_box) {
    1259:         if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]  Found point in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", rank, bin, dbin[0], dbin[1], dim > 2 ? dbin[2] : 0));
    1260:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
    1261:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
    1262:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
    1263:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    1264:           if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]    Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
    1265:           PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell));
    1266:           if (cell >= 0) {
    1267:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]      FOUND in cell %" PetscInt_FMT "\n", rank, cell));
    1268:             cells[p].rank  = 0;
    1269:             cells[p].index = cell;
    1270:             numFound++;
    1271:             terminating_query_type[2]++;
    1272:             break;
    1273:           }
    1274:         }
    1275:       }
    1276:     } else {
    1277:       for (c = cStart; c < cEnd; ++c) {
    1278:         PetscInt idx;

    1280:         PetscCall(PetscFindInt(c, Nl, leaves, &idx));
    1281:         if (idx >= 0) continue;
    1282:         PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
    1283:         if (cell >= 0) {
    1284:           cells[p].rank  = 0;
    1285:           cells[p].index = cell;
    1286:           numFound++;
    1287:           terminating_query_type[2]++;
    1288:           break;
    1289:         }
    1290:       }
    1291:     }
    1292:   }
    1293:   if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
    1294:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
    1295:     for (p = 0; p < numPoints; p++) {
    1296:       const PetscScalar *point     = &a[p * bs];
    1297:       PetscReal          cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
    1298:       PetscInt           dbin[3] = {-1, -1, -1}, bin, cellOffset, d, bestc = -1;

    1300:       if (cells[p].index < 0) {
    1301:         PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
    1302:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
    1303:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
    1304:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    1305:           PetscCall(DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint));
    1306:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
    1307:           dist = DMPlex_NormD_Internal(dim, diff);
    1308:           if (dist < distMax) {
    1309:             for (d = 0; d < dim; ++d) best[d] = cpoint[d];
    1310:             bestc   = boxCells[c];
    1311:             distMax = dist;
    1312:           }
    1313:         }
    1314:         if (distMax < PETSC_MAX_REAL) {
    1315:           ++numFound;
    1316:           cells[p].rank  = 0;
    1317:           cells[p].index = bestc;
    1318:           for (d = 0; d < dim; ++d) a[p * bs + d] = best[d];
    1319:         }
    1320:       }
    1321:     }
    1322:   }
    1323:   /* This code is only be relevant when interfaced to parallel point location */
    1324:   /* Check for highest numbered proc that claims a point (do we care?) */
    1325:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
    1326:     PetscCall(PetscMalloc1(numFound, &found));
    1327:     for (p = 0, numFound = 0; p < numPoints; p++) {
    1328:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
    1329:         if (numFound < p) cells[numFound] = cells[p];
    1330:         found[numFound++] = p;
    1331:       }
    1332:     }
    1333:   }
    1334:   PetscCall(VecRestoreArray(v, &a));
    1335:   if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
    1336:   PetscCall(PetscTime(&t1));
    1337:   if (hash) {
    1338:     PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [hash]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
    1339:   } else {
    1340:     PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [brute-force]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
    1341:   }
    1342:   PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, (double)((double)numPoints / (t1 - t0))));
    1343:   PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
    1344:   PetscFunctionReturn(PETSC_SUCCESS);
    1345: }

    1347: /*@
    1348:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

    1350:   Not Collective

    1352:   Input/Output Parameter:
    1353: . coords - The coordinates of a segment, on output the new y-coordinate, and 0 for x, an array of size 4, last two entries are unchanged

    1355:   Output Parameter:
    1356: . R - The rotation which accomplishes the projection, array of size 4

    1358:   Level: developer

    1360: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
    1361: @*/
    1362: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
    1363: {
    1364:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
    1365:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
    1366:   const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;

    1368:   PetscFunctionBegin;
    1369:   R[0]      = c;
    1370:   R[1]      = -s;
    1371:   R[2]      = s;
    1372:   R[3]      = c;
    1373:   coords[0] = 0.0;
    1374:   coords[1] = r;
    1375:   PetscFunctionReturn(PETSC_SUCCESS);
    1376: }

    1378: /*@
    1379:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

    1381:   Not Collective

    1383:   Input/Output Parameter:
    1384: . coords - The coordinates of a segment; on output, the new y-coordinate, and 0 for x and z, an array of size 6, the other entries are unchanged

    1386:   Output Parameter:
    1387: . R - The rotation which accomplishes the projection, an array of size 9

    1389:   Level: developer

    1391:   Note:
    1392:   This uses the basis completion described by Frisvad {cite}`frisvad2012building`

    1394: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
    1395: @*/
    1396: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
    1397: {
    1398:   PetscReal x    = PetscRealPart(coords[3] - coords[0]);
    1399:   PetscReal y    = PetscRealPart(coords[4] - coords[1]);
    1400:   PetscReal z    = PetscRealPart(coords[5] - coords[2]);
    1401:   PetscReal r    = PetscSqrtReal(x * x + y * y + z * z);
    1402:   PetscReal rinv = 1. / r;

    1404:   PetscFunctionBegin;
    1405:   x *= rinv;
    1406:   y *= rinv;
    1407:   z *= rinv;
    1408:   if (x > 0.) {
    1409:     PetscReal inv1pX = 1. / (1. + x);

    1411:     R[0] = x;
    1412:     R[1] = -y;
    1413:     R[2] = -z;
    1414:     R[3] = y;
    1415:     R[4] = 1. - y * y * inv1pX;
    1416:     R[5] = -y * z * inv1pX;
    1417:     R[6] = z;
    1418:     R[7] = -y * z * inv1pX;
    1419:     R[8] = 1. - z * z * inv1pX;
    1420:   } else {
    1421:     PetscReal inv1mX = 1. / (1. - x);

    1423:     R[0] = x;
    1424:     R[1] = z;
    1425:     R[2] = y;
    1426:     R[3] = y;
    1427:     R[4] = -y * z * inv1mX;
    1428:     R[5] = 1. - y * y * inv1mX;
    1429:     R[6] = z;
    1430:     R[7] = 1. - z * z * inv1mX;
    1431:     R[8] = -y * z * inv1mX;
    1432:   }
    1433:   coords[0] = 0.0;
    1434:   coords[1] = r;
    1435:   coords[2] = 0.0;
    1436:   PetscFunctionReturn(PETSC_SUCCESS);
    1437: }

    1439: /*@
    1440:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
    1441:   plane.  The normal is defined by positive orientation of the first 3 points.

    1443:   Not Collective

    1445:   Input Parameter:
    1446: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

    1448:   Input/Output Parameter:
    1449: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
    1450:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

    1452:   Output Parameter:
    1453: . 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.

    1455:   Level: developer

    1457: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
    1458: @*/
    1459: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    1460: {
    1461:   PetscReal      x1[3], x2[3], n[3], c[3], norm;
    1462:   const PetscInt dim = 3;
    1463:   PetscInt       d, p;

    1465:   PetscFunctionBegin;
    1466:   /* 0) Calculate normal vector */
    1467:   for (d = 0; d < dim; ++d) {
    1468:     x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
    1469:     x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
    1470:   }
    1471:   // n = x1 \otimes x2
    1472:   n[0] = x1[1] * x2[2] - x1[2] * x2[1];
    1473:   n[1] = x1[2] * x2[0] - x1[0] * x2[2];
    1474:   n[2] = x1[0] * x2[1] - x1[1] * x2[0];
    1475:   norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
    1476:   for (d = 0; d < dim; d++) n[d] /= norm;
    1477:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
    1478:   for (d = 0; d < dim; d++) x1[d] /= norm;
    1479:   // x2 = n \otimes x1
    1480:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
    1481:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
    1482:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
    1483:   for (d = 0; d < dim; d++) {
    1484:     R[d * dim + 0] = x1[d];
    1485:     R[d * dim + 1] = x2[d];
    1486:     R[d * dim + 2] = n[d];
    1487:     c[d]           = PetscRealPart(coords[0 * dim + d]);
    1488:   }
    1489:   for (p = 0; p < coordSize / dim; p++) {
    1490:     PetscReal y[3];
    1491:     for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
    1492:     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];
    1493:   }
    1494:   PetscFunctionReturn(PETSC_SUCCESS);
    1495: }

    1497: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    1498: {
    1499:   /* Signed volume is 1/2 the determinant

    1501:    |  1  1  1 |
    1502:    | x0 x1 x2 |
    1503:    | y0 y1 y2 |

    1505:      but if x0,y0 is the origin, we have

    1507:    | x1 x2 |
    1508:    | y1 y2 |
    1509:   */
    1510:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    1511:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    1512:   PetscReal       M[4], detM;
    1513:   M[0] = x1;
    1514:   M[1] = x2;
    1515:   M[2] = y1;
    1516:   M[3] = y2;
    1517:   DMPlex_Det2D_Internal(&detM, M);
    1518:   *vol = 0.5 * detM;
    1519:   (void)PetscLogFlops(5.0);
    1520: }

    1522: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    1523: {
    1524:   /* Signed volume is 1/6th of the determinant

    1526:    |  1  1  1  1 |
    1527:    | x0 x1 x2 x3 |
    1528:    | y0 y1 y2 y3 |
    1529:    | z0 z1 z2 z3 |

    1531:      but if x0,y0,z0 is the origin, we have

    1533:    | x1 x2 x3 |
    1534:    | y1 y2 y3 |
    1535:    | z1 z2 z3 |
    1536:   */
    1537:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
    1538:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
    1539:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    1540:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
    1541:   PetscReal       M[9], detM;
    1542:   M[0] = x1;
    1543:   M[1] = x2;
    1544:   M[2] = x3;
    1545:   M[3] = y1;
    1546:   M[4] = y2;
    1547:   M[5] = y3;
    1548:   M[6] = z1;
    1549:   M[7] = z2;
    1550:   M[8] = z3;
    1551:   DMPlex_Det3D_Internal(&detM, M);
    1552:   *vol = -onesixth * detM;
    1553:   (void)PetscLogFlops(10.0);
    1554: }

    1556: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1557: {
    1558:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
    1559:   DMPlex_Det3D_Internal(vol, coords);
    1560:   *vol *= -onesixth;
    1561: }

    1563: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1564: {
    1565:   PetscSection       coordSection;
    1566:   Vec                coordinates;
    1567:   const PetscScalar *coords;
    1568:   PetscInt           dim, d, off;

    1570:   PetscFunctionBegin;
    1571:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    1572:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
    1573:   PetscCall(PetscSectionGetDof(coordSection, e, &dim));
    1574:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
    1575:   PetscCall(PetscSectionGetOffset(coordSection, e, &off));
    1576:   PetscCall(VecGetArrayRead(coordinates, &coords));
    1577:   if (v0) {
    1578:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
    1579:   }
    1580:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
    1581:   *detJ = 1.;
    1582:   if (J) {
    1583:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1584:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1585:     if (invJ) {
    1586:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1587:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1588:     }
    1589:   }
    1590:   PetscFunctionReturn(PETSC_SUCCESS);
    1591: }

    1593: /*@C
    1594:   DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity

    1596:   Not Collective

    1598:   Input Parameters:
    1599: + dm   - The `DMPLEX`
    1600: - cell - The cell number

    1602:   Output Parameters:
    1603: + isDG   - Using cellwise coordinates
    1604: . Nc     - The number of coordinates
    1605: . array  - The coordinate array
    1606: - coords - The cell coordinates

    1608:   Level: developer

    1610: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
    1611: @*/
    1612: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
    1613: {
    1614:   DM                 cdm;
    1615:   Vec                coordinates;
    1616:   PetscSection       cs;
    1617:   const PetscScalar *ccoords;
    1618:   PetscInt           pStart, pEnd;

    1620:   PetscFunctionBeginHot;
    1621:   *isDG   = PETSC_FALSE;
    1622:   *Nc     = 0;
    1623:   *array  = NULL;
    1624:   *coords = NULL;
    1625:   /* Check for cellwise coordinates */
    1626:   PetscCall(DMGetCellCoordinateSection(dm, &cs));
    1627:   if (!cs) goto cg;
    1628:   /* Check that the cell exists in the cellwise section */
    1629:   PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
    1630:   if (cell < pStart || cell >= pEnd) goto cg;
    1631:   /* Check for cellwise coordinates for this cell */
    1632:   PetscCall(PetscSectionGetDof(cs, cell, Nc));
    1633:   if (!*Nc) goto cg;
    1634:   /* Check for cellwise coordinates */
    1635:   PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
    1636:   if (!coordinates) goto cg;
    1637:   /* Get cellwise coordinates */
    1638:   PetscCall(DMGetCellCoordinateDM(dm, &cdm));
    1639:   PetscCall(VecGetArrayRead(coordinates, array));
    1640:   PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
    1641:   PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
    1642:   PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
    1643:   PetscCall(VecRestoreArrayRead(coordinates, array));
    1644:   *isDG = PETSC_TRUE;
    1645:   PetscFunctionReturn(PETSC_SUCCESS);
    1646: cg:
    1647:   /* Use continuous coordinates */
    1648:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    1649:   PetscCall(DMGetCoordinateSection(dm, &cs));
    1650:   PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
    1651:   PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
    1652:   PetscFunctionReturn(PETSC_SUCCESS);
    1653: }

    1655: /*@C
    1656:   DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity

    1658:   Not Collective

    1660:   Input Parameters:
    1661: + dm   - The `DMPLEX`
    1662: - cell - The cell number

    1664:   Output Parameters:
    1665: + isDG   - Using cellwise coordinates
    1666: . Nc     - The number of coordinates
    1667: . array  - The coordinate array
    1668: - coords - The cell coordinates

    1670:   Level: developer

    1672: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
    1673: @*/
    1674: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
    1675: {
    1676:   DM           cdm;
    1677:   PetscSection cs;
    1678:   Vec          coordinates;

    1680:   PetscFunctionBeginHot;
    1681:   if (*isDG) {
    1682:     PetscCall(DMGetCellCoordinateDM(dm, &cdm));
    1683:     PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
    1684:   } else {
    1685:     PetscCall(DMGetCoordinateDM(dm, &cdm));
    1686:     PetscCall(DMGetCoordinateSection(dm, &cs));
    1687:     PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
    1688:     PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, (PetscScalar **)coords));
    1689:   }
    1690:   PetscFunctionReturn(PETSC_SUCCESS);
    1691: }

    1693: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1694: {
    1695:   const PetscScalar *array;
    1696:   PetscScalar       *coords = NULL;
    1697:   PetscInt           numCoords, d;
    1698:   PetscBool          isDG;

    1700:   PetscFunctionBegin;
    1701:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1702:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1703:   *detJ = 0.0;
    1704:   if (numCoords == 6) {
    1705:     const PetscInt dim = 3;
    1706:     PetscReal      R[9], J0;

    1708:     if (v0) {
    1709:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1710:     }
    1711:     PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
    1712:     if (J) {
    1713:       J0   = 0.5 * PetscRealPart(coords[1]);
    1714:       J[0] = R[0] * J0;
    1715:       J[1] = R[1];
    1716:       J[2] = R[2];
    1717:       J[3] = R[3] * J0;
    1718:       J[4] = R[4];
    1719:       J[5] = R[5];
    1720:       J[6] = R[6] * J0;
    1721:       J[7] = R[7];
    1722:       J[8] = R[8];
    1723:       DMPlex_Det3D_Internal(detJ, J);
    1724:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1725:     }
    1726:   } else if (numCoords == 4) {
    1727:     const PetscInt dim = 2;
    1728:     PetscReal      R[4], J0;

    1730:     if (v0) {
    1731:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1732:     }
    1733:     PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
    1734:     if (J) {
    1735:       J0   = 0.5 * PetscRealPart(coords[1]);
    1736:       J[0] = R[0] * J0;
    1737:       J[1] = R[1];
    1738:       J[2] = R[2] * J0;
    1739:       J[3] = R[3];
    1740:       DMPlex_Det2D_Internal(detJ, J);
    1741:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
    1742:     }
    1743:   } else if (numCoords == 2) {
    1744:     const PetscInt dim = 1;

    1746:     if (v0) {
    1747:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1748:     }
    1749:     if (J) {
    1750:       J[0]  = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1751:       *detJ = J[0];
    1752:       PetscCall(PetscLogFlops(2.0));
    1753:       if (invJ) {
    1754:         invJ[0] = 1.0 / J[0];
    1755:         PetscCall(PetscLogFlops(1.0));
    1756:       }
    1757:     }
    1758:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for segment %" PetscInt_FMT " is %" PetscInt_FMT " != 2 or 4 or 6", e, numCoords);
    1759:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1760:   PetscFunctionReturn(PETSC_SUCCESS);
    1761: }

    1763: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1764: {
    1765:   const PetscScalar *array;
    1766:   PetscScalar       *coords = NULL;
    1767:   PetscInt           numCoords, d;
    1768:   PetscBool          isDG;

    1770:   PetscFunctionBegin;
    1771:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1772:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1773:   *detJ = 0.0;
    1774:   if (numCoords == 9) {
    1775:     const PetscInt dim = 3;
    1776:     PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

    1778:     if (v0) {
    1779:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1780:     }
    1781:     PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
    1782:     if (J) {
    1783:       const PetscInt pdim = 2;

    1785:       for (d = 0; d < pdim; d++) {
    1786:         for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
    1787:       }
    1788:       PetscCall(PetscLogFlops(8.0));
    1789:       DMPlex_Det3D_Internal(detJ, J0);
    1790:       for (d = 0; d < dim; d++) {
    1791:         for (PetscInt f = 0; f < dim; f++) {
    1792:           J[d * dim + f] = 0.0;
    1793:           for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
    1794:         }
    1795:       }
    1796:       PetscCall(PetscLogFlops(18.0));
    1797:     }
    1798:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1799:   } else if (numCoords == 6) {
    1800:     const PetscInt dim = 2;

    1802:     if (v0) {
    1803:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1804:     }
    1805:     if (J) {
    1806:       for (d = 0; d < dim; d++) {
    1807:         for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    1808:       }
    1809:       PetscCall(PetscLogFlops(8.0));
    1810:       DMPlex_Det2D_Internal(detJ, J);
    1811:     }
    1812:     if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
    1813:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
    1814:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1815:   PetscFunctionReturn(PETSC_SUCCESS);
    1816: }

    1818: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1819: {
    1820:   const PetscScalar *array;
    1821:   PetscScalar       *coords = NULL;
    1822:   PetscInt           numCoords, d;
    1823:   PetscBool          isDG;

    1825:   PetscFunctionBegin;
    1826:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1827:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1828:   if (!Nq) {
    1829:     PetscInt vorder[4] = {0, 1, 2, 3};

    1831:     if (isTensor) {
    1832:       vorder[2] = 3;
    1833:       vorder[3] = 2;
    1834:     }
    1835:     *detJ = 0.0;
    1836:     if (numCoords == 12) {
    1837:       const PetscInt dim = 3;
    1838:       PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

    1840:       if (v) {
    1841:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    1842:       }
    1843:       PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
    1844:       if (J) {
    1845:         const PetscInt pdim = 2;

    1847:         for (d = 0; d < pdim; d++) {
    1848:           J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
    1849:           J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
    1850:         }
    1851:         PetscCall(PetscLogFlops(8.0));
    1852:         DMPlex_Det3D_Internal(detJ, J0);
    1853:         for (d = 0; d < dim; d++) {
    1854:           for (PetscInt f = 0; f < dim; f++) {
    1855:             J[d * dim + f] = 0.0;
    1856:             for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
    1857:           }
    1858:         }
    1859:         PetscCall(PetscLogFlops(18.0));
    1860:       }
    1861:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1862:     } else if (numCoords == 8) {
    1863:       const PetscInt dim = 2;

    1865:       if (v) {
    1866:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    1867:       }
    1868:       if (J) {
    1869:         for (d = 0; d < dim; d++) {
    1870:           J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
    1871:           J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
    1872:         }
    1873:         PetscCall(PetscLogFlops(8.0));
    1874:         DMPlex_Det2D_Internal(detJ, J);
    1875:       }
    1876:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
    1877:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
    1878:   } else {
    1879:     const PetscInt Nv         = 4;
    1880:     const PetscInt dimR       = 2;
    1881:     PetscInt       zToPlex[4] = {0, 1, 3, 2};
    1882:     PetscReal      zOrder[12];
    1883:     PetscReal      zCoeff[12];
    1884:     PetscInt       i, j, k, l, dim;

    1886:     if (isTensor) {
    1887:       zToPlex[2] = 2;
    1888:       zToPlex[3] = 3;
    1889:     }
    1890:     if (numCoords == 12) {
    1891:       dim = 3;
    1892:     } else if (numCoords == 8) {
    1893:       dim = 2;
    1894:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
    1895:     for (i = 0; i < Nv; i++) {
    1896:       PetscInt zi = zToPlex[i];

    1898:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1899:     }
    1900:     for (j = 0; j < dim; j++) {
    1901:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
    1902:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
    1903:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
    1904:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
    1905:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
    1906:       */
    1907:       zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1908:       zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1909:       zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1910:       zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1911:     }
    1912:     for (i = 0; i < Nq; i++) {
    1913:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    1915:       if (v) {
    1916:         PetscReal extPoint[4];

    1918:         extPoint[0] = 1.;
    1919:         extPoint[1] = xi;
    1920:         extPoint[2] = eta;
    1921:         extPoint[3] = xi * eta;
    1922:         for (j = 0; j < dim; j++) {
    1923:           PetscReal val = 0.;

    1925:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
    1926:           v[i * dim + j] = val;
    1927:         }
    1928:       }
    1929:       if (J) {
    1930:         PetscReal extJ[8];

    1932:         extJ[0] = 0.;
    1933:         extJ[1] = 0.;
    1934:         extJ[2] = 1.;
    1935:         extJ[3] = 0.;
    1936:         extJ[4] = 0.;
    1937:         extJ[5] = 1.;
    1938:         extJ[6] = eta;
    1939:         extJ[7] = xi;
    1940:         for (j = 0; j < dim; j++) {
    1941:           for (k = 0; k < dimR; k++) {
    1942:             PetscReal val = 0.;

    1944:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1945:             J[i * dim * dim + dim * j + k] = val;
    1946:           }
    1947:         }
    1948:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    1949:           PetscReal  x, y, z;
    1950:           PetscReal *iJ = &J[i * dim * dim];
    1951:           PetscReal  norm;

    1953:           x     = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    1954:           y     = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    1955:           z     = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    1956:           norm  = PetscSqrtReal(x * x + y * y + z * z);
    1957:           iJ[2] = x / norm;
    1958:           iJ[5] = y / norm;
    1959:           iJ[8] = z / norm;
    1960:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1961:           if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    1962:         } else {
    1963:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    1964:           if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    1965:         }
    1966:       }
    1967:     }
    1968:   }
    1969:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1970:   PetscFunctionReturn(PETSC_SUCCESS);
    1971: }

    1973: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1974: {
    1975:   const PetscScalar *array;
    1976:   PetscScalar       *coords = NULL;
    1977:   const PetscInt     dim    = 3;
    1978:   PetscInt           numCoords, d;
    1979:   PetscBool          isDG;

    1981:   PetscFunctionBegin;
    1982:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1983:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1984:   *detJ = 0.0;
    1985:   if (v0) {
    1986:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1987:   }
    1988:   if (J) {
    1989:     for (d = 0; d < dim; d++) {
    1990:       /* I orient with outward face normals */
    1991:       J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    1992:       J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    1993:       J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    1994:     }
    1995:     PetscCall(PetscLogFlops(18.0));
    1996:     DMPlex_Det3D_Internal(detJ, J);
    1997:   }
    1998:   if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1999:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2000:   PetscFunctionReturn(PETSC_SUCCESS);
    2001: }

    2003: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2004: {
    2005:   const PetscScalar *array;
    2006:   PetscScalar       *coords = NULL;
    2007:   const PetscInt     dim    = 3;
    2008:   PetscInt           numCoords, d;
    2009:   PetscBool          isDG;

    2011:   PetscFunctionBegin;
    2012:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2013:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    2014:   if (!Nq) {
    2015:     *detJ = 0.0;
    2016:     if (v) {
    2017:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    2018:     }
    2019:     if (J) {
    2020:       for (d = 0; d < dim; d++) {
    2021:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2022:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2023:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2024:       }
    2025:       PetscCall(PetscLogFlops(18.0));
    2026:       DMPlex_Det3D_Internal(detJ, J);
    2027:     }
    2028:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    2029:   } else {
    2030:     const PetscInt Nv         = 8;
    2031:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    2032:     const PetscInt dim        = 3;
    2033:     const PetscInt dimR       = 3;
    2034:     PetscReal      zOrder[24];
    2035:     PetscReal      zCoeff[24];
    2036:     PetscInt       i, j, k, l;

    2038:     for (i = 0; i < Nv; i++) {
    2039:       PetscInt zi = zToPlex[i];

    2041:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    2042:     }
    2043:     for (j = 0; j < dim; j++) {
    2044:       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]);
    2045:       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]);
    2046:       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]);
    2047:       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]);
    2048:       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]);
    2049:       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]);
    2050:       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]);
    2051:       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]);
    2052:     }
    2053:     for (i = 0; i < Nq; i++) {
    2054:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    2056:       if (v) {
    2057:         PetscReal extPoint[8];

    2059:         extPoint[0] = 1.;
    2060:         extPoint[1] = xi;
    2061:         extPoint[2] = eta;
    2062:         extPoint[3] = xi * eta;
    2063:         extPoint[4] = theta;
    2064:         extPoint[5] = theta * xi;
    2065:         extPoint[6] = theta * eta;
    2066:         extPoint[7] = theta * eta * xi;
    2067:         for (j = 0; j < dim; j++) {
    2068:           PetscReal val = 0.;

    2070:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
    2071:           v[i * dim + j] = val;
    2072:         }
    2073:       }
    2074:       if (J) {
    2075:         PetscReal extJ[24];

    2077:         extJ[0]  = 0.;
    2078:         extJ[1]  = 0.;
    2079:         extJ[2]  = 0.;
    2080:         extJ[3]  = 1.;
    2081:         extJ[4]  = 0.;
    2082:         extJ[5]  = 0.;
    2083:         extJ[6]  = 0.;
    2084:         extJ[7]  = 1.;
    2085:         extJ[8]  = 0.;
    2086:         extJ[9]  = eta;
    2087:         extJ[10] = xi;
    2088:         extJ[11] = 0.;
    2089:         extJ[12] = 0.;
    2090:         extJ[13] = 0.;
    2091:         extJ[14] = 1.;
    2092:         extJ[15] = theta;
    2093:         extJ[16] = 0.;
    2094:         extJ[17] = xi;
    2095:         extJ[18] = 0.;
    2096:         extJ[19] = theta;
    2097:         extJ[20] = eta;
    2098:         extJ[21] = theta * eta;
    2099:         extJ[22] = theta * xi;
    2100:         extJ[23] = eta * xi;

    2102:         for (j = 0; j < dim; j++) {
    2103:           for (k = 0; k < dimR; k++) {
    2104:             PetscReal val = 0.;

    2106:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    2107:             J[i * dim * dim + dim * j + k] = val;
    2108:           }
    2109:         }
    2110:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    2111:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    2112:       }
    2113:     }
    2114:   }
    2115:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2116:   PetscFunctionReturn(PETSC_SUCCESS);
    2117: }

    2119: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2120: {
    2121:   const PetscScalar *array;
    2122:   PetscScalar       *coords = NULL;
    2123:   const PetscInt     dim    = 3;
    2124:   PetscInt           numCoords, d;
    2125:   PetscBool          isDG;

    2127:   PetscFunctionBegin;
    2128:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2129:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    2130:   if (!Nq) {
    2131:     /* Assume that the map to the reference is affine */
    2132:     *detJ = 0.0;
    2133:     if (v) {
    2134:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    2135:     }
    2136:     if (J) {
    2137:       for (d = 0; d < dim; d++) {
    2138:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2139:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2140:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2141:       }
    2142:       PetscCall(PetscLogFlops(18.0));
    2143:       DMPlex_Det3D_Internal(detJ, J);
    2144:     }
    2145:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    2146:   } else {
    2147:     const PetscInt dim  = 3;
    2148:     const PetscInt dimR = 3;
    2149:     const PetscInt Nv   = 6;
    2150:     PetscReal      verts[18];
    2151:     PetscReal      coeff[18];
    2152:     PetscInt       i, j, k, l;

    2154:     for (i = 0; i < Nv; ++i)
    2155:       for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
    2156:     for (j = 0; j < dim; ++j) {
    2157:       /* Check for triangle,
    2158:            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)
    2159:            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)
    2160:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

    2162:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
    2163:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
    2164:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

    2166:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
    2167:                                  | -1  1 -1 | | phi_1 | =
    2168:                                  \ -1 -1  1 / \ phi_2 /

    2170:           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
    2171:       */
    2172:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
    2173:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
    2174:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
    2175:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
    2176:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
    2177:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
    2178:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
    2179:            1/4 /  0  1  1  0  1  1 \
    2180:                | -1  1  0 -1  0  1 |
    2181:                | -1  0  1 -1  1  0 |
    2182:                |  0 -1 -1  0  1  1 |
    2183:                |  1  0 -1 -1  1  0 |
    2184:                \  1 -1  0 -1  0  1 /
    2185:       */
    2186:       coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
    2187:       coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
    2188:       coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
    2189:       coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
    2190:       coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
    2191:       coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
    2192:       /* For reference prism:
    2193:       {0, 0, 0}
    2194:       {0, 1, 0}
    2195:       {1, 0, 0}
    2196:       {0, 0, 1}
    2197:       {0, 0, 0}
    2198:       {0, 0, 0}
    2199:       */
    2200:     }
    2201:     for (i = 0; i < Nq; ++i) {
    2202:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

    2204:       if (v) {
    2205:         PetscReal extPoint[6];
    2206:         PetscInt  c;

    2208:         extPoint[0] = 1.;
    2209:         extPoint[1] = eta;
    2210:         extPoint[2] = xi;
    2211:         extPoint[3] = zeta;
    2212:         extPoint[4] = xi * zeta;
    2213:         extPoint[5] = eta * zeta;
    2214:         for (c = 0; c < dim; ++c) {
    2215:           PetscReal val = 0.;

    2217:           for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
    2218:           v[i * dim + c] = val;
    2219:         }
    2220:       }
    2221:       if (J) {
    2222:         PetscReal extJ[18];

    2224:         extJ[0]  = 0.;
    2225:         extJ[1]  = 0.;
    2226:         extJ[2]  = 0.;
    2227:         extJ[3]  = 0.;
    2228:         extJ[4]  = 1.;
    2229:         extJ[5]  = 0.;
    2230:         extJ[6]  = 1.;
    2231:         extJ[7]  = 0.;
    2232:         extJ[8]  = 0.;
    2233:         extJ[9]  = 0.;
    2234:         extJ[10] = 0.;
    2235:         extJ[11] = 1.;
    2236:         extJ[12] = zeta;
    2237:         extJ[13] = 0.;
    2238:         extJ[14] = xi;
    2239:         extJ[15] = 0.;
    2240:         extJ[16] = zeta;
    2241:         extJ[17] = eta;

    2243:         for (j = 0; j < dim; j++) {
    2244:           for (k = 0; k < dimR; k++) {
    2245:             PetscReal val = 0.;

    2247:             for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
    2248:             J[i * dim * dim + dim * j + k] = val;
    2249:           }
    2250:         }
    2251:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    2252:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    2253:       }
    2254:     }
    2255:   }
    2256:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2257:   PetscFunctionReturn(PETSC_SUCCESS);
    2258: }

    2260: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    2261: {
    2262:   DMPolytopeType   ct;
    2263:   PetscInt         depth, dim, coordDim, coneSize, i;
    2264:   PetscInt         Nq     = 0;
    2265:   const PetscReal *points = NULL;
    2266:   DMLabel          depthLabel;
    2267:   PetscReal        xi0[3]   = {-1., -1., -1.}, v0[3], J0[9], detJ0;
    2268:   PetscBool        isAffine = PETSC_TRUE;

    2270:   PetscFunctionBegin;
    2271:   PetscCall(DMPlexGetDepth(dm, &depth));
    2272:   PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
    2273:   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
    2274:   PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
    2275:   if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
    2276:   PetscCall(DMGetCoordinateDim(dm, &coordDim));
    2277:   PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
    2278:   if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
    2279:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    2280:   switch (ct) {
    2281:   case DM_POLYTOPE_POINT:
    2282:     PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2283:     isAffine = PETSC_FALSE;
    2284:     break;
    2285:   case DM_POLYTOPE_SEGMENT:
    2286:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2287:     if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
    2288:     else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2289:     break;
    2290:   case DM_POLYTOPE_TRIANGLE:
    2291:     if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
    2292:     else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2293:     break;
    2294:   case DM_POLYTOPE_QUADRILATERAL:
    2295:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
    2296:     isAffine = PETSC_FALSE;
    2297:     break;
    2298:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2299:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
    2300:     isAffine = PETSC_FALSE;
    2301:     break;
    2302:   case DM_POLYTOPE_TETRAHEDRON:
    2303:     if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
    2304:     else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2305:     break;
    2306:   case DM_POLYTOPE_HEXAHEDRON:
    2307:     PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
    2308:     isAffine = PETSC_FALSE;
    2309:     break;
    2310:   case DM_POLYTOPE_TRI_PRISM:
    2311:     PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
    2312:     isAffine = PETSC_FALSE;
    2313:     break;
    2314:   default:
    2315:     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))]);
    2316:   }
    2317:   if (isAffine && Nq) {
    2318:     if (v) {
    2319:       for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    2320:     }
    2321:     if (detJ) {
    2322:       for (i = 0; i < Nq; i++) detJ[i] = detJ0;
    2323:     }
    2324:     if (J) {
    2325:       PetscInt k;

    2327:       for (i = 0, k = 0; i < Nq; i++) {
    2328:         PetscInt j;

    2330:         for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
    2331:       }
    2332:     }
    2333:     if (invJ) {
    2334:       PetscInt k;
    2335:       switch (coordDim) {
    2336:       case 0:
    2337:         break;
    2338:       case 1:
    2339:         invJ[0] = 1. / J0[0];
    2340:         break;
    2341:       case 2:
    2342:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    2343:         break;
    2344:       case 3:
    2345:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    2346:         break;
    2347:       }
    2348:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    2349:         PetscInt j;

    2351:         for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
    2352:       }
    2353:     }
    2354:   }
    2355:   PetscFunctionReturn(PETSC_SUCCESS);
    2356: }

    2358: /*@C
    2359:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    2361:   Collective

    2363:   Input Parameters:
    2364: + dm   - the `DMPLEX`
    2365: - cell - the cell

    2367:   Output Parameters:
    2368: + v0   - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
    2369: . J    - the Jacobian of the transform from the reference element
    2370: . invJ - the inverse of the Jacobian
    2371: - detJ - the Jacobian determinant

    2373:   Level: advanced

    2375: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
    2376: @*/
    2377: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    2378: {
    2379:   PetscFunctionBegin;
    2380:   PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
    2381:   PetscFunctionReturn(PETSC_SUCCESS);
    2382: }

    2384: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2385: {
    2386:   const PetscScalar *array;
    2387:   PetscScalar       *coords = NULL;
    2388:   PetscInt           numCoords;
    2389:   PetscBool          isDG;
    2390:   PetscQuadrature    feQuad;
    2391:   const PetscReal   *quadPoints;
    2392:   PetscTabulation    T;
    2393:   PetscInt           dim, cdim, pdim, qdim, Nq, q;

    2395:   PetscFunctionBegin;
    2396:   PetscCall(DMGetDimension(dm, &dim));
    2397:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2398:   PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
    2399:   if (!quad) { /* use the first point of the first functional of the dual space */
    2400:     PetscDualSpace dsp;

    2402:     PetscCall(PetscFEGetDualSpace(fe, &dsp));
    2403:     PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
    2404:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
    2405:     Nq = 1;
    2406:   } else {
    2407:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
    2408:   }
    2409:   PetscCall(PetscFEGetDimension(fe, &pdim));
    2410:   PetscCall(PetscFEGetQuadrature(fe, &feQuad));
    2411:   if (feQuad == quad) {
    2412:     PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
    2413:     PetscCheck(numCoords == pdim * cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "There are %" PetscInt_FMT " coordinates for point %" PetscInt_FMT " != %" PetscInt_FMT "*%" PetscInt_FMT, numCoords, point, pdim, cdim);
    2414:   } else {
    2415:     PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
    2416:   }
    2417:   PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
    2418:   {
    2419:     const PetscReal *basis    = T->T[0];
    2420:     const PetscReal *basisDer = T->T[1];
    2421:     PetscReal        detJt;

    2423:     PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
    2424:     PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
    2425:     PetscAssert(dim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->Nc);
    2426:     PetscAssert(cdim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->cdim);
    2427:     if (v) {
    2428:       PetscCall(PetscArrayzero(v, Nq * cdim));
    2429:       for (q = 0; q < Nq; ++q) {
    2430:         PetscInt i, k;

    2432:         for (k = 0; k < pdim; ++k) {
    2433:           const PetscInt vertex = k / cdim;
    2434:           for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
    2435:         }
    2436:         PetscCall(PetscLogFlops(2.0 * pdim * cdim));
    2437:       }
    2438:     }
    2439:     if (J) {
    2440:       PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
    2441:       for (q = 0; q < Nq; ++q) {
    2442:         PetscInt i, j, k, c, r;

    2444:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    2445:         for (k = 0; k < pdim; ++k) {
    2446:           const PetscInt vertex = k / cdim;
    2447:           for (j = 0; j < dim; ++j) {
    2448:             for (i = 0; i < cdim; ++i) J[(q * cdim + i) * cdim + j] += basisDer[((q * pdim + k) * cdim + i) * dim + j] * PetscRealPart(coords[vertex * cdim + i]);
    2449:           }
    2450:         }
    2451:         PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
    2452:         if (cdim > dim) {
    2453:           for (c = dim; c < cdim; ++c)
    2454:             for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
    2455:         }
    2456:         if (!detJ && !invJ) continue;
    2457:         detJt = 0.;
    2458:         switch (cdim) {
    2459:         case 3:
    2460:           DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
    2461:           if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
    2462:           break;
    2463:         case 2:
    2464:           DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
    2465:           if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
    2466:           break;
    2467:         case 1:
    2468:           detJt = J[q * cdim * dim];
    2469:           if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
    2470:         }
    2471:         if (detJ) detJ[q] = detJt;
    2472:       }
    2473:     } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
    2474:   }
    2475:   if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
    2476:   PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
    2477:   PetscFunctionReturn(PETSC_SUCCESS);
    2478: }

    2480: /*@C
    2481:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    2483:   Collective

    2485:   Input Parameters:
    2486: + dm   - the `DMPLEX`
    2487: . cell - the cell
    2488: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If `quad` is `NULL`, geometry will be
    2489:          evaluated at the first vertex of the reference element

    2491:   Output Parameters:
    2492: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
    2493: . J    - the Jacobian of the transform from the reference element at each quadrature point
    2494: . invJ - the inverse of the Jacobian at each quadrature point
    2495: - detJ - the Jacobian determinant at each quadrature point

    2497:   Level: advanced

    2499: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
    2500: @*/
    2501: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    2502: {
    2503:   DM      cdm;
    2504:   PetscFE fe = NULL;

    2506:   PetscFunctionBegin;
    2507:   PetscAssertPointer(detJ, 7);
    2508:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    2509:   if (cdm) {
    2510:     PetscClassId id;
    2511:     PetscInt     numFields;
    2512:     PetscDS      prob;
    2513:     PetscObject  disc;

    2515:     PetscCall(DMGetNumFields(cdm, &numFields));
    2516:     if (numFields) {
    2517:       PetscCall(DMGetDS(cdm, &prob));
    2518:       PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
    2519:       PetscCall(PetscObjectGetClassId(disc, &id));
    2520:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
    2521:     }
    2522:   }
    2523:   if (!fe) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
    2524:   else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
    2525:   PetscFunctionReturn(PETSC_SUCCESS);
    2526: }

    2528: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2529: {
    2530:   PetscSection       coordSection;
    2531:   Vec                coordinates;
    2532:   const PetscScalar *coords = NULL;
    2533:   PetscInt           d, dof, off;

    2535:   PetscFunctionBegin;
    2536:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    2537:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
    2538:   PetscCall(VecGetArrayRead(coordinates, &coords));

    2540:   /* for a point the centroid is just the coord */
    2541:   if (centroid) {
    2542:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
    2543:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
    2544:     for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
    2545:   }
    2546:   if (normal) {
    2547:     const PetscInt *support, *cones;
    2548:     PetscInt        supportSize;
    2549:     PetscReal       norm, sign;

    2551:     /* compute the norm based upon the support centroids */
    2552:     PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
    2553:     PetscCall(DMPlexGetSupport(dm, cell, &support));
    2554:     PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));

    2556:     /* Take the normal from the centroid of the support to the vertex*/
    2557:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
    2558:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
    2559:     for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);

    2561:     /* Determine the sign of the normal based upon its location in the support */
    2562:     PetscCall(DMPlexGetCone(dm, support[0], &cones));
    2563:     sign = cones[0] == cell ? 1.0 : -1.0;

    2565:     norm = DMPlex_NormD_Internal(dim, normal);
    2566:     for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
    2567:   }
    2568:   if (vol) *vol = 1.0;
    2569:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
    2570:   PetscFunctionReturn(PETSC_SUCCESS);
    2571: }

    2573: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2574: {
    2575:   const PetscScalar *array;
    2576:   PetscScalar       *coords = NULL;
    2577:   PetscInt           cdim, coordSize, d;
    2578:   PetscBool          isDG;

    2580:   PetscFunctionBegin;
    2581:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2582:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2583:   PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
    2584:   if (centroid) {
    2585:     for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
    2586:   }
    2587:   if (normal) {
    2588:     PetscReal norm;

    2590:     switch (cdim) {
    2591:     case 3:
    2592:       normal[2] = 0.; /* fall through */
    2593:     case 2:
    2594:       normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
    2595:       normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
    2596:       break;
    2597:     case 1:
    2598:       normal[0] = 1.0;
    2599:       break;
    2600:     default:
    2601:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
    2602:     }
    2603:     norm = DMPlex_NormD_Internal(cdim, normal);
    2604:     for (d = 0; d < cdim; ++d) normal[d] /= norm;
    2605:   }
    2606:   if (vol) {
    2607:     *vol = 0.0;
    2608:     for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
    2609:     *vol = PetscSqrtReal(*vol);
    2610:   }
    2611:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2612:   PetscFunctionReturn(PETSC_SUCCESS);
    2613: }

    2615: /* Centroid_i = (\sum_n A_n Cn_i) / A */
    2616: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2617: {
    2618:   DMPolytopeType     ct;
    2619:   const PetscScalar *array;
    2620:   PetscScalar       *coords = NULL;
    2621:   PetscInt           coordSize;
    2622:   PetscBool          isDG;
    2623:   PetscInt           fv[4] = {0, 1, 2, 3};
    2624:   PetscInt           cdim, numCorners, p, d;

    2626:   PetscFunctionBegin;
    2627:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2628:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    2629:   switch (ct) {
    2630:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2631:     fv[2] = 3;
    2632:     fv[3] = 2;
    2633:     break;
    2634:   default:
    2635:     break;
    2636:   }
    2637:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2638:   PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
    2639:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2640:   {
    2641:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

    2643:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
    2644:     for (p = 0; p < numCorners - 2; ++p) {
    2645:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
    2646:       for (d = 0; d < cdim; d++) {
    2647:         e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
    2648:         e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
    2649:       }
    2650:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
    2651:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
    2652:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
    2653:       const PetscReal a  = PetscSqrtReal(dx * dx + dy * dy + dz * dz);

    2655:       n[0] += dx;
    2656:       n[1] += dy;
    2657:       n[2] += dz;
    2658:       for (d = 0; d < cdim; d++) c[d] += a * PetscRealPart(origin[d] + coords[cdim * fv[p + 1] + d] + coords[cdim * fv[p + 2] + d]) / 3.;
    2659:     }
    2660:     norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
    2661:     // Allow zero volume cells
    2662:     if (norm != 0) {
    2663:       n[0] /= norm;
    2664:       n[1] /= norm;
    2665:       n[2] /= norm;
    2666:       c[0] /= norm;
    2667:       c[1] /= norm;
    2668:       c[2] /= norm;
    2669:     }
    2670:     if (vol) *vol = 0.5 * norm;
    2671:     if (centroid)
    2672:       for (d = 0; d < cdim; ++d) centroid[d] = c[d];
    2673:     if (normal)
    2674:       for (d = 0; d < cdim; ++d) normal[d] = n[d];
    2675:   }
    2676:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2677:   PetscFunctionReturn(PETSC_SUCCESS);
    2678: }

    2680: /* Centroid_i = (\sum_n V_n Cn_i) / V */
    2681: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2682: {
    2683:   DMPolytopeType        ct;
    2684:   const PetscScalar    *array;
    2685:   PetscScalar          *coords = NULL;
    2686:   PetscInt              coordSize;
    2687:   PetscBool             isDG;
    2688:   PetscReal             vsum      = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
    2689:   const PetscInt        order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
    2690:   const PetscInt       *cone, *faceSizes, *faces;
    2691:   const DMPolytopeType *faceTypes;
    2692:   PetscBool             isHybrid = PETSC_FALSE;
    2693:   PetscInt              numFaces, f, fOff = 0, p, d;

    2695:   PetscFunctionBegin;
    2696:   PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
    2697:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2698:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    2699:   switch (ct) {
    2700:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2701:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2702:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
    2703:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    2704:     isHybrid = PETSC_TRUE;
    2705:   default:
    2706:     break;
    2707:   }

    2709:   if (centroid)
    2710:     for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    2711:   PetscCall(DMPlexGetCone(dm, cell, &cone));

    2713:   // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
    2714:   PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
    2715:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2716:   for (f = 0; f < numFaces; ++f) {
    2717:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

    2719:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
    2720:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
    2721:     // so that all tetrahedra have positive volume.
    2722:     if (f == 0)
    2723:       for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
    2724:     switch (faceTypes[f]) {
    2725:     case DM_POLYTOPE_TRIANGLE:
    2726:       for (d = 0; d < dim; ++d) {
    2727:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
    2728:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
    2729:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
    2730:       }
    2731:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2732:       if (flip) vtmp = -vtmp;
    2733:       vsum += vtmp;
    2734:       if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
    2735:         for (d = 0; d < dim; ++d) {
    2736:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
    2737:         }
    2738:       }
    2739:       break;
    2740:     case DM_POLYTOPE_QUADRILATERAL:
    2741:     case DM_POLYTOPE_SEG_PRISM_TENSOR: {
    2742:       PetscInt fv[4] = {0, 1, 2, 3};

    2744:       /* Side faces for hybrid cells are stored as tensor products */
    2745:       if (isHybrid && f > 1) {
    2746:         fv[2] = 3;
    2747:         fv[3] = 2;
    2748:       }
    2749:       /* DO FOR PYRAMID */
    2750:       /* First tet */
    2751:       for (d = 0; d < dim; ++d) {
    2752:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
    2753:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
    2754:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
    2755:       }
    2756:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2757:       if (flip) vtmp = -vtmp;
    2758:       vsum += vtmp;
    2759:       if (centroid) {
    2760:         for (d = 0; d < dim; ++d) {
    2761:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
    2762:         }
    2763:       }
    2764:       /* Second tet */
    2765:       for (d = 0; d < dim; ++d) {
    2766:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
    2767:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
    2768:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
    2769:       }
    2770:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2771:       if (flip) vtmp = -vtmp;
    2772:       vsum += vtmp;
    2773:       if (centroid) {
    2774:         for (d = 0; d < dim; ++d) {
    2775:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
    2776:         }
    2777:       }
    2778:       break;
    2779:     }
    2780:     default:
    2781:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
    2782:     }
    2783:     fOff += faceSizes[f];
    2784:   }
    2785:   PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
    2786:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2787:   if (vol) *vol = PetscAbsReal(vsum);
    2788:   if (normal)
    2789:     for (d = 0; d < dim; ++d) normal[d] = 0.0;
    2790:   if (centroid)
    2791:     for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
    2792:   PetscFunctionReturn(PETSC_SUCCESS);
    2793: }

    2795: /*@C
    2796:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    2798:   Collective

    2800:   Input Parameters:
    2801: + dm   - the `DMPLEX`
    2802: - cell - the cell

    2804:   Output Parameters:
    2805: + vol      - the cell volume
    2806: . centroid - the cell centroid
    2807: - normal   - the cell normal, if appropriate

    2809:   Level: advanced

    2811: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
    2812: @*/
    2813: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2814: {
    2815:   PetscInt depth, dim;

    2817:   PetscFunctionBegin;
    2818:   PetscCall(DMPlexGetDepth(dm, &depth));
    2819:   PetscCall(DMGetDimension(dm, &dim));
    2820:   PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
    2821:   PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
    2822:   switch (depth) {
    2823:   case 0:
    2824:     PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
    2825:     break;
    2826:   case 1:
    2827:     PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
    2828:     break;
    2829:   case 2:
    2830:     PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
    2831:     break;
    2832:   case 3:
    2833:     PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
    2834:     break;
    2835:   default:
    2836:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
    2837:   }
    2838:   PetscFunctionReturn(PETSC_SUCCESS);
    2839: }

    2841: /*@
    2842:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2844:   Input Parameter:
    2845: . dm - The `DMPLEX`

    2847:   Output Parameters:
    2848: + cellgeom - A `Vec` of `PetscFVCellGeom` data
    2849: - facegeom - A `Vec` of `PetscFVFaceGeom` data

    2851:   Level: developer

    2853: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
    2854: @*/
    2855: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2856: {
    2857:   DM           dmFace, dmCell;
    2858:   DMLabel      ghostLabel;
    2859:   PetscSection sectionFace, sectionCell;
    2860:   PetscSection coordSection;
    2861:   Vec          coordinates;
    2862:   PetscScalar *fgeom, *cgeom;
    2863:   PetscReal    minradius, gminradius;
    2864:   PetscInt     dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2866:   PetscFunctionBegin;
    2867:   PetscCall(DMGetDimension(dm, &dim));
    2868:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
    2869:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    2870:   /* Make cell centroids and volumes */
    2871:   PetscCall(DMClone(dm, &dmCell));
    2872:   PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
    2873:   PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
    2874:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell));
    2875:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    2876:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    2877:   PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
    2878:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
    2879:   PetscCall(PetscSectionSetUp(sectionCell));
    2880:   PetscCall(DMSetLocalSection(dmCell, sectionCell));
    2881:   PetscCall(PetscSectionDestroy(&sectionCell));
    2882:   PetscCall(DMCreateLocalVector(dmCell, cellgeom));
    2883:   if (cEndInterior < 0) cEndInterior = cEnd;
    2884:   PetscCall(VecGetArray(*cellgeom, &cgeom));
    2885:   for (c = cStart; c < cEndInterior; ++c) {
    2886:     PetscFVCellGeom *cg;

    2888:     PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
    2889:     PetscCall(PetscArrayzero(cg, 1));
    2890:     PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
    2891:   }
    2892:   /* Compute face normals and minimum cell radius */
    2893:   PetscCall(DMClone(dm, &dmFace));
    2894:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionFace));
    2895:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
    2896:   PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
    2897:   for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
    2898:   PetscCall(PetscSectionSetUp(sectionFace));
    2899:   PetscCall(DMSetLocalSection(dmFace, sectionFace));
    2900:   PetscCall(PetscSectionDestroy(&sectionFace));
    2901:   PetscCall(DMCreateLocalVector(dmFace, facegeom));
    2902:   PetscCall(VecGetArray(*facegeom, &fgeom));
    2903:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
    2904:   minradius = PETSC_MAX_REAL;
    2905:   for (f = fStart; f < fEnd; ++f) {
    2906:     PetscFVFaceGeom *fg;
    2907:     PetscReal        area;
    2908:     const PetscInt  *cells;
    2909:     PetscInt         ncells, ghost = -1, d, numChildren;

    2911:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
    2912:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
    2913:     PetscCall(DMPlexGetSupport(dm, f, &cells));
    2914:     PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
    2915:     /* It is possible to get a face with no support when using partition overlap */
    2916:     if (!ncells || ghost >= 0 || numChildren) continue;
    2917:     PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
    2918:     PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
    2919:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    2920:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    2921:     {
    2922:       PetscFVCellGeom *cL, *cR;
    2923:       PetscReal       *lcentroid, *rcentroid;
    2924:       PetscReal        l[3], r[3], v[3];

    2926:       PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
    2927:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    2928:       if (ncells > 1) {
    2929:         PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
    2930:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    2931:       } else {
    2932:         rcentroid = fg->centroid;
    2933:       }
    2934:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
    2935:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
    2936:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    2937:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    2938:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    2939:       }
    2940:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    2941:         PetscCheck(dim != 2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed, normal (%g,%g) v (%g,%g)", f, (double)fg->normal[0], (double)fg->normal[1], (double)v[0], (double)v[1]);
    2942:         PetscCheck(dim != 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed, normal (%g,%g,%g) v (%g,%g,%g)", f, (double)fg->normal[0], (double)fg->normal[1], (double)fg->normal[2], (double)v[0], (double)v[1], (double)v[2]);
    2943:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
    2944:       }
    2945:       if (cells[0] < cEndInterior) {
    2946:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    2947:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2948:       }
    2949:       if (ncells > 1 && cells[1] < cEndInterior) {
    2950:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    2951:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2952:       }
    2953:     }
    2954:   }
    2955:   PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
    2956:   PetscCall(DMPlexSetMinRadius(dm, gminradius));
    2957:   /* Compute centroids of ghost cells */
    2958:   for (c = cEndInterior; c < cEnd; ++c) {
    2959:     PetscFVFaceGeom *fg;
    2960:     const PetscInt  *cone, *support;
    2961:     PetscInt         coneSize, supportSize, s;

    2963:     PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
    2964:     PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
    2965:     PetscCall(DMPlexGetCone(dmCell, c, &cone));
    2966:     PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
    2967:     PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
    2968:     PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
    2969:     PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
    2970:     for (s = 0; s < 2; ++s) {
    2971:       /* Reflect ghost centroid across plane of face */
    2972:       if (support[s] == c) {
    2973:         PetscFVCellGeom *ci;
    2974:         PetscFVCellGeom *cg;
    2975:         PetscReal        c2f[3], a;

    2977:         PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
    2978:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    2979:         a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    2980:         PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
    2981:         DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
    2982:         cg->volume = ci->volume;
    2983:       }
    2984:     }
    2985:   }
    2986:   PetscCall(VecRestoreArray(*facegeom, &fgeom));
    2987:   PetscCall(VecRestoreArray(*cellgeom, &cgeom));
    2988:   PetscCall(DMDestroy(&dmCell));
    2989:   PetscCall(DMDestroy(&dmFace));
    2990:   PetscFunctionReturn(PETSC_SUCCESS);
    2991: }

    2993: /*@
    2994:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    2996:   Not Collective

    2998:   Input Parameter:
    2999: . dm - the `DMPLEX`

    3001:   Output Parameter:
    3002: . minradius - the minimum cell radius

    3004:   Level: developer

    3006: .seealso: `DMPLEX`, `DMGetCoordinates()`
    3007: @*/
    3008: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    3009: {
    3010:   PetscFunctionBegin;
    3012:   PetscAssertPointer(minradius, 2);
    3013:   *minradius = ((DM_Plex *)dm->data)->minradius;
    3014:   PetscFunctionReturn(PETSC_SUCCESS);
    3015: }

    3017: /*@
    3018:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    3020:   Logically Collective

    3022:   Input Parameters:
    3023: + dm        - the `DMPLEX`
    3024: - minradius - the minimum cell radius

    3026:   Level: developer

    3028: .seealso: `DMPLEX`, `DMSetCoordinates()`
    3029: @*/
    3030: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    3031: {
    3032:   PetscFunctionBegin;
    3034:   ((DM_Plex *)dm->data)->minradius = minradius;
    3035:   PetscFunctionReturn(PETSC_SUCCESS);
    3036: }

    3038: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    3039: {
    3040:   DMLabel      ghostLabel;
    3041:   PetscScalar *dx, *grad, **gref;
    3042:   PetscInt     dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    3044:   PetscFunctionBegin;
    3045:   PetscCall(DMGetDimension(dm, &dim));
    3046:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    3047:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    3048:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
    3049:   PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
    3050:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
    3051:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
    3052:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
    3053:   for (c = cStart; c < cEndInterior; c++) {
    3054:     const PetscInt  *faces;
    3055:     PetscInt         numFaces, usedFaces, f, d;
    3056:     PetscFVCellGeom *cg;
    3057:     PetscBool        boundary;
    3058:     PetscInt         ghost;

    3060:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
    3061:     PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
    3062:     if (ghost >= 0) continue;

    3064:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
    3065:     PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
    3066:     PetscCall(DMPlexGetCone(dm, c, &faces));
    3067:     PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
    3068:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    3069:       PetscFVCellGeom *cg1;
    3070:       PetscFVFaceGeom *fg;
    3071:       const PetscInt  *fcells;
    3072:       PetscInt         ncell, side;

    3074:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
    3075:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
    3076:       if ((ghost >= 0) || boundary) continue;
    3077:       PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
    3078:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    3079:       ncell = fcells[!side];    /* the neighbor */
    3080:       PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
    3081:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
    3082:       for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
    3083:       gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
    3084:     }
    3085:     PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
    3086:     PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
    3087:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    3088:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
    3089:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
    3090:       if ((ghost >= 0) || boundary) continue;
    3091:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
    3092:       ++usedFaces;
    3093:     }
    3094:   }
    3095:   PetscCall(PetscFree3(dx, grad, gref));
    3096:   PetscFunctionReturn(PETSC_SUCCESS);
    3097: }

    3099: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    3100: {
    3101:   DMLabel      ghostLabel;
    3102:   PetscScalar *dx, *grad, **gref;
    3103:   PetscInt     dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    3104:   PetscSection neighSec;
    3105:   PetscInt(*neighbors)[2];
    3106:   PetscInt *counter;

    3108:   PetscFunctionBegin;
    3109:   PetscCall(DMGetDimension(dm, &dim));
    3110:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    3111:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    3112:   if (cEndInterior < 0) cEndInterior = cEnd;
    3113:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
    3114:   PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
    3115:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
    3116:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
    3117:   for (f = fStart; f < fEnd; f++) {
    3118:     const PetscInt *fcells;
    3119:     PetscBool       boundary;
    3120:     PetscInt        ghost = -1;
    3121:     PetscInt        numChildren, numCells, c;

    3123:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
    3124:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
    3125:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
    3126:     if ((ghost >= 0) || boundary || numChildren) continue;
    3127:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
    3128:     if (numCells == 2) {
    3129:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
    3130:       for (c = 0; c < 2; c++) {
    3131:         PetscInt cell = fcells[c];

    3133:         if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
    3134:       }
    3135:     }
    3136:   }
    3137:   PetscCall(PetscSectionSetUp(neighSec));
    3138:   PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
    3139:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
    3140:   nStart = 0;
    3141:   PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
    3142:   PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
    3143:   PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
    3144:   for (f = fStart; f < fEnd; f++) {
    3145:     const PetscInt *fcells;
    3146:     PetscBool       boundary;
    3147:     PetscInt        ghost = -1;
    3148:     PetscInt        numChildren, numCells, c;

    3150:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
    3151:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
    3152:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
    3153:     if ((ghost >= 0) || boundary || numChildren) continue;
    3154:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
    3155:     if (numCells == 2) {
    3156:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
    3157:       for (c = 0; c < 2; c++) {
    3158:         PetscInt cell = fcells[c], off;

    3160:         if (cell >= cStart && cell < cEndInterior) {
    3161:           PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
    3162:           off += counter[cell - cStart]++;
    3163:           neighbors[off][0] = f;
    3164:           neighbors[off][1] = fcells[1 - c];
    3165:         }
    3166:       }
    3167:     }
    3168:   }
    3169:   PetscCall(PetscFree(counter));
    3170:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
    3171:   for (c = cStart; c < cEndInterior; c++) {
    3172:     PetscInt         numFaces, f, d, off, ghost = -1;
    3173:     PetscFVCellGeom *cg;

    3175:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
    3176:     PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
    3177:     PetscCall(PetscSectionGetOffset(neighSec, c, &off));

    3179:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
    3180:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
    3181:     if (ghost >= 0) continue;

    3183:     PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
    3184:     for (f = 0; f < numFaces; ++f) {
    3185:       PetscFVCellGeom *cg1;
    3186:       PetscFVFaceGeom *fg;
    3187:       const PetscInt  *fcells;
    3188:       PetscInt         ncell, side, nface;

    3190:       nface = neighbors[off + f][0];
    3191:       ncell = neighbors[off + f][1];
    3192:       PetscCall(DMPlexGetSupport(dm, nface, &fcells));
    3193:       side = (c != fcells[0]);
    3194:       PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
    3195:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
    3196:       for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
    3197:       gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
    3198:     }
    3199:     PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
    3200:     for (f = 0; f < numFaces; ++f) {
    3201:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
    3202:     }
    3203:   }
    3204:   PetscCall(PetscFree3(dx, grad, gref));
    3205:   PetscCall(PetscSectionDestroy(&neighSec));
    3206:   PetscCall(PetscFree(neighbors));
    3207:   PetscFunctionReturn(PETSC_SUCCESS);
    3208: }

    3210: /*@
    3211:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    3213:   Collective

    3215:   Input Parameters:
    3216: + dm           - The `DMPLEX`
    3217: . fvm          - The `PetscFV`
    3218: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`

    3220:   Input/Output Parameter:
    3221: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
    3222:                  the geometric factors for gradient calculation are inserted

    3224:   Output Parameter:
    3225: . dmGrad - The `DM` describing the layout of gradient data

    3227:   Level: developer

    3229: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
    3230: @*/
    3231: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    3232: {
    3233:   DM           dmFace, dmCell;
    3234:   PetscScalar *fgeom, *cgeom;
    3235:   PetscSection sectionGrad, parentSection;
    3236:   PetscInt     dim, pdim, cStart, cEnd, cEndInterior, c;

    3238:   PetscFunctionBegin;
    3239:   PetscCall(DMGetDimension(dm, &dim));
    3240:   PetscCall(PetscFVGetNumComponents(fvm, &pdim));
    3241:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    3242:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    3243:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    3244:   PetscCall(VecGetDM(faceGeometry, &dmFace));
    3245:   PetscCall(VecGetDM(cellGeometry, &dmCell));
    3246:   PetscCall(VecGetArray(faceGeometry, &fgeom));
    3247:   PetscCall(VecGetArray(cellGeometry, &cgeom));
    3248:   PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
    3249:   if (!parentSection) {
    3250:     PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
    3251:   } else {
    3252:     PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
    3253:   }
    3254:   PetscCall(VecRestoreArray(faceGeometry, &fgeom));
    3255:   PetscCall(VecRestoreArray(cellGeometry, &cgeom));
    3256:   /* Create storage for gradients */
    3257:   PetscCall(DMClone(dm, dmGrad));
    3258:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionGrad));
    3259:   PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
    3260:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
    3261:   PetscCall(PetscSectionSetUp(sectionGrad));
    3262:   PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
    3263:   PetscCall(PetscSectionDestroy(&sectionGrad));
    3264:   PetscFunctionReturn(PETSC_SUCCESS);
    3265: }

    3267: /*@
    3268:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    3270:   Collective

    3272:   Input Parameters:
    3273: + dm - The `DM`
    3274: - fv - The `PetscFV`

    3276:   Output Parameters:
    3277: + cellgeom - The cell geometry
    3278: . facegeom - The face geometry
    3279: - gradDM   - The gradient matrices

    3281:   Level: developer

    3283: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
    3284: @*/
    3285: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    3286: {
    3287:   PetscObject cellgeomobj, facegeomobj;

    3289:   PetscFunctionBegin;
    3290:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
    3291:   if (!cellgeomobj) {
    3292:     Vec cellgeomInt, facegeomInt;

    3294:     PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
    3295:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
    3296:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
    3297:     PetscCall(VecDestroy(&cellgeomInt));
    3298:     PetscCall(VecDestroy(&facegeomInt));
    3299:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
    3300:   }
    3301:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
    3302:   if (cellgeom) *cellgeom = (Vec)cellgeomobj;
    3303:   if (facegeom) *facegeom = (Vec)facegeomobj;
    3304:   if (gradDM) {
    3305:     PetscObject gradobj;
    3306:     PetscBool   computeGradients;

    3308:     PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
    3309:     if (!computeGradients) {
    3310:       *gradDM = NULL;
    3311:       PetscFunctionReturn(PETSC_SUCCESS);
    3312:     }
    3313:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
    3314:     if (!gradobj) {
    3315:       DM dmGradInt;

    3317:       PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
    3318:       PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
    3319:       PetscCall(DMDestroy(&dmGradInt));
    3320:       PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
    3321:     }
    3322:     *gradDM = (DM)gradobj;
    3323:   }
    3324:   PetscFunctionReturn(PETSC_SUCCESS);
    3325: }

    3327: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
    3328: {
    3329:   PetscInt l, m;

    3331:   PetscFunctionBeginHot;
    3332:   if (dimC == dimR && dimR <= 3) {
    3333:     /* invert Jacobian, multiply */
    3334:     PetscScalar det, idet;

    3336:     switch (dimR) {
    3337:     case 1:
    3338:       invJ[0] = 1. / J[0];
    3339:       break;
    3340:     case 2:
    3341:       det     = J[0] * J[3] - J[1] * J[2];
    3342:       idet    = 1. / det;
    3343:       invJ[0] = J[3] * idet;
    3344:       invJ[1] = -J[1] * idet;
    3345:       invJ[2] = -J[2] * idet;
    3346:       invJ[3] = J[0] * idet;
    3347:       break;
    3348:     case 3: {
    3349:       invJ[0] = J[4] * J[8] - J[5] * J[7];
    3350:       invJ[1] = J[2] * J[7] - J[1] * J[8];
    3351:       invJ[2] = J[1] * J[5] - J[2] * J[4];
    3352:       det     = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    3353:       idet    = 1. / det;
    3354:       invJ[0] *= idet;
    3355:       invJ[1] *= idet;
    3356:       invJ[2] *= idet;
    3357:       invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
    3358:       invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
    3359:       invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
    3360:       invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
    3361:       invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
    3362:       invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
    3363:     } break;
    3364:     }
    3365:     for (l = 0; l < dimR; l++) {
    3366:       for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    3367:     }
    3368:   } else {
    3369: #if defined(PETSC_USE_COMPLEX)
    3370:     char transpose = 'C';
    3371: #else
    3372:     char transpose = 'T';
    3373: #endif
    3374:     PetscBLASInt m        = (PetscBLASInt)dimR;
    3375:     PetscBLASInt n        = (PetscBLASInt)dimC;
    3376:     PetscBLASInt one      = 1;
    3377:     PetscBLASInt worksize = (PetscBLASInt)(dimR * dimC), info;

    3379:     for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];

    3381:     PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
    3382:     PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");

    3384:     for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
    3385:   }
    3386:   PetscFunctionReturn(PETSC_SUCCESS);
    3387: }

    3389: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    3390: {
    3391:   PetscInt     coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    3392:   PetscScalar *coordsScalar = NULL;
    3393:   PetscReal   *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    3394:   PetscScalar *J, *invJ, *work;

    3396:   PetscFunctionBegin;
    3398:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3399:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
    3400:   PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
    3401:   PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
    3402:   cellCoords = &cellData[0];
    3403:   cellCoeffs = &cellData[coordSize];
    3404:   extJ       = &cellData[2 * coordSize];
    3405:   resNeg     = &cellData[2 * coordSize + dimR];
    3406:   invJ       = &J[dimR * dimC];
    3407:   work       = &J[2 * dimR * dimC];
    3408:   if (dimR == 2) {
    3409:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    3411:     for (i = 0; i < 4; i++) {
    3412:       PetscInt plexI = zToPlex[i];

    3414:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3415:     }
    3416:   } else if (dimR == 3) {
    3417:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    3419:     for (i = 0; i < 8; i++) {
    3420:       PetscInt plexI = zToPlex[i];

    3422:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3423:     }
    3424:   } else {
    3425:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
    3426:   }
    3427:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    3428:   for (i = 0; i < dimR; i++) {
    3429:     PetscReal *swap;

    3431:     for (j = 0; j < (numV / 2); j++) {
    3432:       for (k = 0; k < dimC; k++) {
    3433:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    3434:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    3435:       }
    3436:     }

    3438:     if (i < dimR - 1) {
    3439:       swap       = cellCoeffs;
    3440:       cellCoeffs = cellCoords;
    3441:       cellCoords = swap;
    3442:     }
    3443:   }
    3444:   PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
    3445:   for (j = 0; j < numPoints; j++) {
    3446:     for (i = 0; i < maxIts; i++) {
    3447:       PetscReal *guess = &refCoords[dimR * j];

    3449:       /* compute -residual and Jacobian */
    3450:       for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
    3451:       for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
    3452:       for (k = 0; k < numV; k++) {
    3453:         PetscReal extCoord = 1.;
    3454:         for (l = 0; l < dimR; l++) {
    3455:           PetscReal coord = guess[l];
    3456:           PetscInt  dep   = (k & (1 << l)) >> l;

    3458:           extCoord *= dep * coord + !dep;
    3459:           extJ[l] = dep;

    3461:           for (m = 0; m < dimR; m++) {
    3462:             PetscReal coord = guess[m];
    3463:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    3464:             PetscReal mult  = dep * coord + !dep;

    3466:             extJ[l] *= mult;
    3467:           }
    3468:         }
    3469:         for (l = 0; l < dimC; l++) {
    3470:           PetscReal coeff = cellCoeffs[dimC * k + l];

    3472:           resNeg[l] -= coeff * extCoord;
    3473:           for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
    3474:         }
    3475:       }
    3476:       if (0 && PetscDefined(USE_DEBUG)) {
    3477:         PetscReal maxAbs = 0.;

    3479:         for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
    3480:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
    3481:       }

    3483:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
    3484:     }
    3485:   }
    3486:   PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
    3487:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
    3488:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3489:   PetscFunctionReturn(PETSC_SUCCESS);
    3490: }

    3492: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    3493: {
    3494:   PetscInt     coordSize, i, j, k, l, numV = (1 << dimR);
    3495:   PetscScalar *coordsScalar = NULL;
    3496:   PetscReal   *cellData, *cellCoords, *cellCoeffs;

    3498:   PetscFunctionBegin;
    3500:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3501:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
    3502:   PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
    3503:   cellCoords = &cellData[0];
    3504:   cellCoeffs = &cellData[coordSize];
    3505:   if (dimR == 2) {
    3506:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    3508:     for (i = 0; i < 4; i++) {
    3509:       PetscInt plexI = zToPlex[i];

    3511:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3512:     }
    3513:   } else if (dimR == 3) {
    3514:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    3516:     for (i = 0; i < 8; i++) {
    3517:       PetscInt plexI = zToPlex[i];

    3519:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3520:     }
    3521:   } else {
    3522:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
    3523:   }
    3524:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    3525:   for (i = 0; i < dimR; i++) {
    3526:     PetscReal *swap;

    3528:     for (j = 0; j < (numV / 2); j++) {
    3529:       for (k = 0; k < dimC; k++) {
    3530:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    3531:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    3532:       }
    3533:     }

    3535:     if (i < dimR - 1) {
    3536:       swap       = cellCoeffs;
    3537:       cellCoeffs = cellCoords;
    3538:       cellCoords = swap;
    3539:     }
    3540:   }
    3541:   PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
    3542:   for (j = 0; j < numPoints; j++) {
    3543:     const PetscReal *guess  = &refCoords[dimR * j];
    3544:     PetscReal       *mapped = &realCoords[dimC * j];

    3546:     for (k = 0; k < numV; k++) {
    3547:       PetscReal extCoord = 1.;
    3548:       for (l = 0; l < dimR; l++) {
    3549:         PetscReal coord = guess[l];
    3550:         PetscInt  dep   = (k & (1 << l)) >> l;

    3552:         extCoord *= dep * coord + !dep;
    3553:       }
    3554:       for (l = 0; l < dimC; l++) {
    3555:         PetscReal coeff = cellCoeffs[dimC * k + l];

    3557:         mapped[l] += coeff * extCoord;
    3558:       }
    3559:     }
    3560:   }
    3561:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
    3562:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3563:   PetscFunctionReturn(PETSC_SUCCESS);
    3564: }

    3566: /* TODO: TOBY please fix this for Nc > 1 */
    3567: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    3568: {
    3569:   PetscInt     numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
    3570:   PetscScalar *nodes = NULL;
    3571:   PetscReal   *invV, *modes;
    3572:   PetscReal   *B, *D, *resNeg;
    3573:   PetscScalar *J, *invJ, *work;

    3575:   PetscFunctionBegin;
    3576:   PetscCall(PetscFEGetDimension(fe, &pdim));
    3577:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    3578:   PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
    3579:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
    3580:   /* convert nodes to values in the stable evaluation basis */
    3581:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
    3582:   invV = fe->invV;
    3583:   for (i = 0; i < pdim; ++i) {
    3584:     modes[i] = 0.;
    3585:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3586:   }
    3587:   PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
    3588:   D      = &B[pdim * Nc];
    3589:   resNeg = &D[pdim * Nc * dimR];
    3590:   PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
    3591:   invJ = &J[Nc * dimR];
    3592:   work = &invJ[Nc * dimR];
    3593:   for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
    3594:   for (j = 0; j < numPoints; j++) {
    3595:     for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    3596:       PetscReal *guess = &refCoords[j * dimR];
    3597:       PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
    3598:       for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
    3599:       for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
    3600:       for (k = 0; k < pdim; k++) {
    3601:         for (l = 0; l < Nc; l++) {
    3602:           resNeg[l] -= modes[k] * B[k * Nc + l];
    3603:           for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    3604:         }
    3605:       }
    3606:       if (0 && PetscDefined(USE_DEBUG)) {
    3607:         PetscReal maxAbs = 0.;

    3609:         for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
    3610:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
    3611:       }
    3612:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
    3613:     }
    3614:   }
    3615:   PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
    3616:   PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
    3617:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
    3618:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
    3619:   PetscFunctionReturn(PETSC_SUCCESS);
    3620: }

    3622: /* TODO: TOBY please fix this for Nc > 1 */
    3623: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    3624: {
    3625:   PetscInt     numComp, pdim, i, j, k, l, coordSize;
    3626:   PetscScalar *nodes = NULL;
    3627:   PetscReal   *invV, *modes;
    3628:   PetscReal   *B;

    3630:   PetscFunctionBegin;
    3631:   PetscCall(PetscFEGetDimension(fe, &pdim));
    3632:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    3633:   PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
    3634:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
    3635:   /* convert nodes to values in the stable evaluation basis */
    3636:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
    3637:   invV = fe->invV;
    3638:   for (i = 0; i < pdim; ++i) {
    3639:     modes[i] = 0.;
    3640:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3641:   }
    3642:   PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
    3643:   PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
    3644:   for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
    3645:   for (j = 0; j < numPoints; j++) {
    3646:     PetscReal *mapped = &realCoords[j * Nc];

    3648:     for (k = 0; k < pdim; k++) {
    3649:       for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    3650:     }
    3651:   }
    3652:   PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
    3653:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
    3654:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
    3655:   PetscFunctionReturn(PETSC_SUCCESS);
    3656: }

    3658: /*@
    3659:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
    3660:   using a single element map.

    3662:   Not Collective

    3664:   Input Parameters:
    3665: + dm         - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
    3666:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3667:                as a multilinear map for tensor-product elements
    3668: . cell       - the cell whose map is used.
    3669: . numPoints  - the number of points to locate
    3670: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

    3672:   Output Parameter:
    3673: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)

    3675:   Level: intermediate

    3677:   Notes:
    3678:   This inversion will be accurate inside the reference element, but may be inaccurate for
    3679:   mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)

    3681: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
    3682: @*/
    3683: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    3684: {
    3685:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
    3686:   DM       coordDM = NULL;
    3687:   Vec      coords;
    3688:   PetscFE  fe = NULL;

    3690:   PetscFunctionBegin;
    3692:   PetscCall(DMGetDimension(dm, &dimR));
    3693:   PetscCall(DMGetCoordinateDim(dm, &dimC));
    3694:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
    3695:   PetscCall(DMPlexGetDepth(dm, &depth));
    3696:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
    3697:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
    3698:   if (coordDM) {
    3699:     PetscInt coordFields;

    3701:     PetscCall(DMGetNumFields(coordDM, &coordFields));
    3702:     if (coordFields) {
    3703:       PetscClassId id;
    3704:       PetscObject  disc;

    3706:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
    3707:       PetscCall(PetscObjectGetClassId(disc, &id));
    3708:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
    3709:     }
    3710:   }
    3711:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
    3712:   PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
    3713:   if (!fe) { /* implicit discretization: affine or multilinear */
    3714:     PetscInt  coneSize;
    3715:     PetscBool isSimplex, isTensor;

    3717:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
    3718:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3719:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3720:     if (isSimplex) {
    3721:       PetscReal detJ, *v0, *J, *invJ;

    3723:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3724:       J    = &v0[dimC];
    3725:       invJ = &J[dimC * dimC];
    3726:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
    3727:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    3728:         const PetscReal x0[3] = {-1., -1., -1.};

    3730:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    3731:       }
    3732:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3733:     } else if (isTensor) {
    3734:       PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
    3735:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
    3736:   } else {
    3737:     PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
    3738:   }
    3739:   PetscFunctionReturn(PETSC_SUCCESS);
    3740: }

    3742: /*@
    3743:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.

    3745:   Not Collective

    3747:   Input Parameters:
    3748: + dm        - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
    3749:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3750:                as a multilinear map for tensor-product elements
    3751: . cell      - the cell whose map is used.
    3752: . numPoints - the number of points to locate
    3753: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)

    3755:   Output Parameter:
    3756: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

    3758:   Level: intermediate

    3760: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
    3761: @*/
    3762: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    3763: {
    3764:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
    3765:   DM       coordDM = NULL;
    3766:   Vec      coords;
    3767:   PetscFE  fe = NULL;

    3769:   PetscFunctionBegin;
    3771:   PetscCall(DMGetDimension(dm, &dimR));
    3772:   PetscCall(DMGetCoordinateDim(dm, &dimC));
    3773:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
    3774:   PetscCall(DMPlexGetDepth(dm, &depth));
    3775:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
    3776:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
    3777:   if (coordDM) {
    3778:     PetscInt coordFields;

    3780:     PetscCall(DMGetNumFields(coordDM, &coordFields));
    3781:     if (coordFields) {
    3782:       PetscClassId id;
    3783:       PetscObject  disc;

    3785:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
    3786:       PetscCall(PetscObjectGetClassId(disc, &id));
    3787:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
    3788:     }
    3789:   }
    3790:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
    3791:   PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
    3792:   if (!fe) { /* implicit discretization: affine or multilinear */
    3793:     PetscInt  coneSize;
    3794:     PetscBool isSimplex, isTensor;

    3796:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
    3797:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3798:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3799:     if (isSimplex) {
    3800:       PetscReal detJ, *v0, *J;

    3802:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3803:       J = &v0[dimC];
    3804:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
    3805:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3806:         const PetscReal xi0[3] = {-1., -1., -1.};

    3808:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3809:       }
    3810:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3811:     } else if (isTensor) {
    3812:       PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
    3813:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
    3814:   } else {
    3815:     PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
    3816:   }
    3817:   PetscFunctionReturn(PETSC_SUCCESS);
    3818: }

    3820: void coordMap_identity(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    3821: {
    3822:   const PetscInt Nc = uOff[1] - uOff[0];
    3823:   PetscInt       c;

    3825:   for (c = 0; c < Nc; ++c) f0[c] = u[c];
    3826: }

    3828: /* Shear applies the transformation, assuming we fix z,
    3829:   / 1  0  m_0 \
    3830:   | 0  1  m_1 |
    3831:   \ 0  0   1  /
    3832: */
    3833: void coordMap_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
    3834: {
    3835:   const PetscInt Nc = uOff[1] - uOff[0];
    3836:   const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
    3837:   PetscInt       c;

    3839:   for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
    3840: }

    3842: /* Flare applies the transformation, assuming we fix x_f,

    3844:    x_i = x_i * alpha_i x_f
    3845: */
    3846: void coordMap_flare(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
    3847: {
    3848:   const PetscInt Nc = uOff[1] - uOff[0];
    3849:   const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
    3850:   PetscInt       c;

    3852:   for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
    3853: }

    3855: /*
    3856:   We would like to map the unit square to a quarter of the annulus between circles of radius 1 and 2. We start by mapping the straight sections, which
    3857:   will correspond to the top and bottom of our square. So

    3859:     (0,0)--(1,0)  ==>  (1,0)--(2,0)      Just a shift of (1,0)
    3860:     (0,1)--(1,1)  ==>  (0,1)--(0,2)      Switch x and y

    3862:   So it looks like we want to map each layer in y to a ray, so x is the radius and y is the angle:

    3864:     (x, y)  ==>  (x+1, \pi/2 y)                           in (r', \theta') space
    3865:             ==>  ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
    3866: */
    3867: void coordMap_annulus(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
    3868: {
    3869:   const PetscReal ri = PetscRealPart(constants[0]);
    3870:   const PetscReal ro = PetscRealPart(constants[1]);

    3872:   xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
    3873:   xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
    3874: }

    3876: /*
    3877:   We would like to map the unit cube to a hemisphere of the spherical shell between balls of radius 1 and 2. We want to map the bottom surface onto the
    3878:   lower hemisphere and the upper surface onto the top, letting z be the radius.

    3880:     (x, y)  ==>  ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x)                                                  in (r', \theta', \phi') space
    3881:             ==>  ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
    3882: */
    3883: void coordMap_shell(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
    3884: {
    3885:   const PetscReal pi4    = PETSC_PI / 4.0;
    3886:   const PetscReal ri     = PetscRealPart(constants[0]);
    3887:   const PetscReal ro     = PetscRealPart(constants[1]);
    3888:   const PetscReal rp     = (x[2] + 1) * 0.5 * (ro - ri) + ri;
    3889:   const PetscReal phip   = PetscAtan2Real(x[1], x[0]);
    3890:   const PetscReal thetap = 0.5 * PETSC_PI * (1.0 - ((((phip <= pi4) && (phip >= -pi4)) || ((phip >= 3.0 * pi4) || (phip <= -3.0 * pi4))) ? PetscAbsReal(x[0]) : PetscAbsReal(x[1])));

    3892:   xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
    3893:   xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
    3894:   xp[2] = rp * PetscSinReal(thetap);
    3895: }

    3897: /*@C
    3898:   DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.

    3900:   Not Collective

    3902:   Input Parameters:
    3903: + dm   - The `DM`
    3904: . time - The time
    3905: - func - The function transforming current coordinates to new coordinates

    3907:   Calling sequence of `func`:
    3908: + dim          - The spatial dimension
    3909: . Nf           - The number of input fields (here 1)
    3910: . NfAux        - The number of input auxiliary fields
    3911: . uOff         - The offset of the coordinates in u[] (here 0)
    3912: . uOff_x       - The offset of the coordinates in u_x[] (here 0)
    3913: . u            - The coordinate values at this point in space
    3914: . u_t          - The coordinate time derivative at this point in space (here `NULL`)
    3915: . u_x          - The coordinate derivatives at this point in space
    3916: . aOff         - The offset of each auxiliary field in u[]
    3917: . aOff_x       - The offset of each auxiliary field in u_x[]
    3918: . a            - The auxiliary field values at this point in space
    3919: . a_t          - The auxiliary field time derivative at this point in space (or `NULL`)
    3920: . a_x          - The auxiliary field derivatives at this point in space
    3921: . t            - The current time
    3922: . x            - The coordinates of this point (here not used)
    3923: . numConstants - The number of constants
    3924: . constants    - The value of each constant
    3925: - f            - The new coordinates at this point in space

    3927:   Level: intermediate

    3929: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
    3930: @*/
    3931: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time, void (*func)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]))
    3932: {
    3933:   DM           cdm;
    3934:   PetscDS      cds;
    3935:   DMField      cf;
    3936:   PetscObject  obj;
    3937:   PetscClassId id;
    3938:   Vec          lCoords, tmpCoords;

    3940:   PetscFunctionBegin;
    3941:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    3942:   PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
    3943:   PetscCall(DMGetDS(cdm, &cds));
    3944:   PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
    3945:   PetscCall(PetscObjectGetClassId(obj, &id));
    3946:   if (id != PETSCFE_CLASSID) {
    3947:     PetscSection       cSection;
    3948:     const PetscScalar *constants;
    3949:     PetscScalar       *coords, f[16];
    3950:     PetscInt           dim, cdim, Nc, vStart, vEnd;

    3952:     PetscCall(DMGetDimension(dm, &dim));
    3953:     PetscCall(DMGetCoordinateDim(dm, &cdim));
    3954:     PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
    3955:     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    3956:     PetscCall(DMGetCoordinateSection(dm, &cSection));
    3957:     PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
    3958:     PetscCall(VecGetArrayWrite(lCoords, &coords));
    3959:     for (PetscInt v = vStart; v < vEnd; ++v) {
    3960:       PetscInt uOff[2] = {0, cdim};
    3961:       PetscInt off, c;

    3963:       PetscCall(PetscSectionGetOffset(cSection, v, &off));
    3964:       (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
    3965:       for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
    3966:     }
    3967:     PetscCall(VecRestoreArrayWrite(lCoords, &coords));
    3968:   } else {
    3969:     PetscCall(DMGetLocalVector(cdm, &tmpCoords));
    3970:     PetscCall(VecCopy(lCoords, tmpCoords));
    3971:     /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
    3972:     PetscCall(DMGetCoordinateField(dm, &cf));
    3973:     cdm->coordinates[0].field = cf;
    3974:     PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
    3975:     cdm->coordinates[0].field = NULL;
    3976:     PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
    3977:     PetscCall(DMSetCoordinatesLocal(dm, lCoords));
    3978:   }
    3979:   PetscFunctionReturn(PETSC_SUCCESS);
    3980: }

    3982: /*@
    3983:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

    3985:   Not Collective

    3987:   Input Parameters:
    3988: + dm          - The `DMPLEX`
    3989: . direction   - The shear coordinate direction, e.g. `DM_X` is the x-axis
    3990: - multipliers - The multiplier m for each direction which is not the shear direction

    3992:   Level: intermediate

    3994: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
    3995: @*/
    3996: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
    3997: {
    3998:   DM             cdm;
    3999:   PetscDS        cds;
    4000:   PetscScalar   *moduli;
    4001:   const PetscInt dir = (PetscInt)direction;
    4002:   PetscInt       dE, d, e;

    4004:   PetscFunctionBegin;
    4005:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    4006:   PetscCall(DMGetCoordinateDim(dm, &dE));
    4007:   PetscCall(PetscMalloc1(dE + 1, &moduli));
    4008:   moduli[0] = dir;
    4009:   for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
    4010:   PetscCall(DMGetDS(cdm, &cds));
    4011:   PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
    4012:   PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
    4013:   PetscCall(PetscFree(moduli));
    4014:   PetscFunctionReturn(PETSC_SUCCESS);
    4015: }