Date: 2026-03-31T05:46:07+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", "sinusoid", "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 PetscReal eps   = PETSC_SQRT_MACHINE_EPSILON;
    440:   PetscReal       xi[2] = {0., 0.};
    441:   PetscReal       x[3], v0[3], J[9], invJ[9], detJ;
    442:   PetscInt        embedDim;

    444:   PetscFunctionBegin;
    445:   PetscCall(DMGetCoordinateDim(dm, &embedDim));
    446:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
    447:   for (PetscInt j = 0; j < embedDim; ++j) x[j] = PetscRealPart(point[j]);
    448:   for (PetscInt i = 0; i < 2; ++i) {
    449:     for (PetscInt j = 0; j < embedDim; ++j) xi[i] += invJ[i * embedDim + j] * (x[j] - v0[j]);
    450:   }
    451:   if ((xi[0] >= -eps) && (xi[1] >= -eps) && (xi[0] + xi[1] <= 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_Linear_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, embedDim;
    490:   PetscBool          isDG;

    492:   PetscFunctionBegin;
    493:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    494:   embedDim = numCoords / 4;
    495:   PetscCheck(!(numCoords % 4), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
    496:   // Treat linear quads as Monge surfaces, so we just locate on the projection to x-y (could instead project to 2D)
    497:   for (PetscInt f = 0; f < 4; ++f) {
    498:     PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 0]);
    499:     PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 1]);
    500:     PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * embedDim + 0]);
    501:     PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * embedDim + 1]);

    503:     if ((x == x_j) && (y == y_j)) {
    504:       // point is a corner
    505:       crossings = 1;
    506:       break;
    507:     }
    508:     if ((y_j > y) != (y_i > y)) {
    509:       PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
    510:       if (slope == 0) {
    511:         // point is a corner
    512:         crossings = 1;
    513:         break;
    514:       }
    515:       if ((slope < 0) != (y_i < y_j)) ++crossings;
    516:     }
    517:   }
    518:   if (crossings % 2) *cell = c;
    519:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    520:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    521:   PetscFunctionReturn(PETSC_SUCCESS);
    522: }

    524: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    525: {
    526:   DM           cdm;
    527:   PetscInt     degree, dimR, dimC;
    528:   PetscFE      fe;
    529:   PetscClassId id;
    530:   PetscSpace   sp;
    531:   PetscReal    pointR[3], ref[3], error;
    532:   Vec          coords;
    533:   PetscBool    found = PETSC_FALSE;

    535:   PetscFunctionBegin;
    536:   PetscCall(DMGetDimension(dm, &dimR));
    537:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    538:   PetscCall(DMGetDimension(cdm, &dimC));
    539:   PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
    540:   PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
    541:   if (id != PETSCFE_CLASSID) degree = 1;
    542:   else {
    543:     PetscCall(PetscFEGetBasisSpace(fe, &sp));
    544:     PetscCall(PetscSpaceGetDegree(sp, &degree, NULL));
    545:   }
    546:   if (degree == 1) {
    547:     /* Use simple location method for linear elements*/
    548:     PetscCall(DMPlexLocatePoint_Quad_2D_Linear_Internal(dm, point, c, cell));
    549:     PetscFunctionReturn(PETSC_SUCCESS);
    550:   }
    551:   /* Otherwise, we have to solve for the real to reference coordinates */
    552:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
    553:   error = PETSC_SQRT_MACHINE_EPSILON;
    554:   for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
    555:   PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
    556:   if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
    557:   if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
    558:   if (PetscDefined(USE_DEBUG) && found) {
    559:     PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);

    561:     normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
    562:     PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
    563:     inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
    564:     if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
    565:     if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
    566:   }
    567:   if (found) *cell = c;
    568:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    569:   PetscFunctionReturn(PETSC_SUCCESS);
    570: }

    572: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    573: {
    574:   const PetscInt  embedDim = 3;
    575:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    576:   PetscReal       v0[3], J[9], invJ[9], detJ;
    577:   PetscReal       x = PetscRealPart(point[0]);
    578:   PetscReal       y = PetscRealPart(point[1]);
    579:   PetscReal       z = PetscRealPart(point[2]);
    580:   PetscReal       xi, eta, zeta;

    582:   PetscFunctionBegin;
    583:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
    584:   xi   = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
    585:   eta  = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
    586:   zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);

    588:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
    589:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    590:   PetscFunctionReturn(PETSC_SUCCESS);
    591: }

    593: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Linear_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    594: {
    595:   const PetscScalar *array;
    596:   PetscScalar       *coords    = NULL;
    597:   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};
    598:   PetscBool          found     = PETSC_TRUE;
    599:   PetscInt           numCoords, f;
    600:   PetscBool          isDG;

    602:   PetscFunctionBegin;
    603:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    604:   PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
    605:   for (f = 0; f < 6; ++f) {
    606:     /* Check the point is under plane */
    607:     /*   Get face normal */
    608:     PetscReal v_i[3];
    609:     PetscReal v_j[3];
    610:     PetscReal normal[3];
    611:     PetscReal pp[3];
    612:     PetscReal dot;

    614:     v_i[0]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
    615:     v_i[1]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
    616:     v_i[2]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
    617:     v_j[0]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
    618:     v_j[1]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
    619:     v_j[2]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
    620:     normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
    621:     normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
    622:     normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
    623:     pp[0]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
    624:     pp[1]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
    625:     pp[2]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
    626:     dot       = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];

    628:     /* Check that projected point is in face (2D location problem) */
    629:     if (dot < 0.0) {
    630:       found = PETSC_FALSE;
    631:       break;
    632:     }
    633:   }
    634:   if (found) *cell = c;
    635:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    636:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    637:   PetscFunctionReturn(PETSC_SUCCESS);
    638: }

    640: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    641: {
    642:   DM           cdm;
    643:   PetscInt     degree, dimR, dimC;
    644:   PetscFE      fe;
    645:   PetscClassId id;
    646:   PetscSpace   sp;
    647:   PetscReal    pointR[3], ref[3], error;
    648:   Vec          coords;
    649:   PetscBool    found = PETSC_FALSE;

    651:   PetscFunctionBegin;
    652:   PetscCall(DMGetDimension(dm, &dimR));
    653:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    654:   PetscCall(DMGetDimension(cdm, &dimC));
    655:   PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
    656:   PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
    657:   if (id != PETSCFE_CLASSID) degree = 1;
    658:   else {
    659:     PetscCall(PetscFEGetBasisSpace(fe, &sp));
    660:     PetscCall(PetscSpaceGetDegree(sp, &degree, NULL));
    661:   }
    662:   if (degree == 1) {
    663:     /* Use simple location method for linear elements*/
    664:     PetscCall(DMPlexLocatePoint_Hex_3D_Linear_Internal(dm, point, c, cell));
    665:     PetscFunctionReturn(PETSC_SUCCESS);
    666:   }
    667:   /* Otherwise, we have to solve for the real to reference coordinates */
    668:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
    669:   error = PETSC_SQRT_MACHINE_EPSILON;
    670:   for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
    671:   PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
    672:   if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
    673:   if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL) || (ref[2] > 1.0 + PETSC_SMALL) || (ref[2] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
    674:   if (PetscDefined(USE_DEBUG) && found) {
    675:     PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);

    677:     normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
    678:     PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
    679:     inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
    680:     if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
    681:     if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
    682:   }
    683:   if (found) *cell = c;
    684:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    685:   PetscFunctionReturn(PETSC_SUCCESS);
    686: }

    688: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
    689: {
    690:   PetscInt d;

    692:   PetscFunctionBegin;
    693:   box->dim = dim;
    694:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
    695:   PetscFunctionReturn(PETSC_SUCCESS);
    696: }

    698: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    699: {
    700:   PetscFunctionBegin;
    701:   PetscCall(PetscCalloc1(1, box));
    702:   PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
    703:   PetscFunctionReturn(PETSC_SUCCESS);
    704: }

    706: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
    707: {
    708:   PetscInt d;

    710:   PetscFunctionBegin;
    711:   for (d = 0; d < box->dim; ++d) {
    712:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    713:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    714:   }
    715:   PetscFunctionReturn(PETSC_SUCCESS);
    716: }

    718: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
    719: {
    720:   Vec                coordinates;
    721:   const PetscScalar *a;
    722:   PetscInt           cdim, cStart, cEnd;

    724:   PetscFunctionBegin;
    725:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    726:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    727:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));

    729:   PetscCall(VecGetArrayRead(coordinates, &a));
    730:   PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
    731:   PetscCall(VecRestoreArrayRead(coordinates, &a));
    732:   for (PetscInt c = cStart; c < cEnd; ++c) {
    733:     const PetscScalar *array;
    734:     PetscScalar       *coords = NULL;
    735:     PetscInt           numCoords;
    736:     PetscBool          isDG;

    738:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    739:     for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
    740:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    741:   }
    742:   PetscFunctionReturn(PETSC_SUCCESS);
    743: }

    745: /*@C
    746:   PetscGridHashSetGrid - Divide the grid into boxes

    748:   Not Collective

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

    755:   Level: developer

    757: .seealso: `DMPLEX`, `PetscGridHashCreate()`
    758: @*/
    759: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
    760: {
    761:   PetscInt d;

    763:   PetscFunctionBegin;
    764:   PetscAssertPointer(n, 2);
    765:   if (h) PetscAssertPointer(h, 3);
    766:   for (d = 0; d < box->dim; ++d) {
    767:     box->extent[d] = box->upper[d] - box->lower[d];
    768:     if (n[d] == PETSC_DETERMINE) {
    769:       PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
    770:       box->h[d] = h[d];
    771:       box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
    772:     } else {
    773:       box->n[d] = n[d];
    774:       box->h[d] = box->extent[d] / n[d];
    775:     }
    776:   }
    777:   PetscFunctionReturn(PETSC_SUCCESS);
    778: }

    780: /*@C
    781:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

    783:   Not Collective

    785:   Input Parameters:
    786: + box       - The grid hash object
    787: . numPoints - The number of input points
    788: - points    - The input point coordinates

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

    794:   Level: developer

    796:   Note:
    797:   This only guarantees that a box contains a point, not that a cell does.

    799: .seealso: `DMPLEX`, `PetscGridHashCreate()`
    800: @*/
    801: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
    802: {
    803:   const PetscReal *lower = box->lower;
    804:   const PetscReal *upper = box->upper;
    805:   const PetscReal *h     = box->h;
    806:   const PetscInt  *n     = box->n;
    807:   const PetscInt   dim   = box->dim;
    808:   PetscInt         d, p;

    810:   PetscFunctionBegin;
    811:   for (p = 0; p < numPoints; ++p) {
    812:     for (d = 0; d < dim; ++d) {
    813:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

    815:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
    816:       if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
    817:       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]);
    818:       dboxes[p * dim + d] = dbox;
    819:     }
    820:     if (boxes)
    821:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
    822:   }
    823:   PetscFunctionReturn(PETSC_SUCCESS);
    824: }

    826: /*
    827:   PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

    829:   Not Collective

    831:   Input Parameters:
    832: + box         - The grid hash object
    833: . cellSection - The PetscSection mapping cells to boxes
    834: . numPoints   - The number of input points
    835: - points      - The input point coordinates

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

    842:   Level: developer

    844:   Note:
    845:   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.

    847: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
    848: */
    849: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
    850: {
    851:   const PetscReal *lower = box->lower;
    852:   const PetscReal *upper = box->upper;
    853:   const PetscReal *h     = box->h;
    854:   const PetscInt  *n     = box->n;
    855:   const PetscInt   dim   = box->dim;
    856:   PetscInt         bStart, bEnd, d, p;

    858:   PetscFunctionBegin;
    860:   *found = PETSC_FALSE;
    861:   PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
    862:   for (p = 0; p < numPoints; ++p) {
    863:     for (d = 0; d < dim; ++d) {
    864:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

    866:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
    867:       if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
    868:       dboxes[p * dim + d] = dbox;
    869:     }
    870:     if (boxes)
    871:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
    872:     // It is possible for a box to overlap no grid cells
    873:     if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
    874:   }
    875:   *found = PETSC_TRUE;
    876:   PetscFunctionReturn(PETSC_SUCCESS);
    877: }

    879: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    880: {
    881:   PetscFunctionBegin;
    882:   if (*box) {
    883:     PetscCall(PetscSectionDestroy(&(*box)->cellSection));
    884:     PetscCall(ISDestroy(&(*box)->cells));
    885:     PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
    886:   }
    887:   PetscCall(PetscFree(*box));
    888:   PetscFunctionReturn(PETSC_SUCCESS);
    889: }

    891: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
    892: {
    893:   DMPolytopeType ct;

    895:   PetscFunctionBegin;
    896:   PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
    897:   switch (ct) {
    898:   case DM_POLYTOPE_SEGMENT:
    899:     PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
    900:     break;
    901:   case DM_POLYTOPE_TRIANGLE:
    902:     PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
    903:     break;
    904:   case DM_POLYTOPE_QUADRILATERAL:
    905:     PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
    906:     break;
    907:   case DM_POLYTOPE_TETRAHEDRON:
    908:     PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
    909:     break;
    910:   case DM_POLYTOPE_HEXAHEDRON:
    911:     PetscCall(DMPlexLocatePoint_Hex_3D_Internal(dm, point, cellStart, cell));
    912:     break;
    913:   default:
    914:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
    915:   }
    916:   PetscFunctionReturn(PETSC_SUCCESS);
    917: }

    919: /*
    920:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
    921: */
    922: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
    923: {
    924:   DMPolytopeType ct;

    926:   PetscFunctionBegin;
    927:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    928:   switch (ct) {
    929:   case DM_POLYTOPE_TRIANGLE:
    930:     PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
    931:     break;
    932: #if 0
    933:     case DM_POLYTOPE_QUADRILATERAL:
    934:     PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
    935:     case DM_POLYTOPE_TETRAHEDRON:
    936:     PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
    937:     case DM_POLYTOPE_HEXAHEDRON:
    938:     PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
    939: #endif
    940:   default:
    941:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
    942:   }
    943:   PetscFunctionReturn(PETSC_SUCCESS);
    944: }

    946: /*
    947:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`

    949:   Collective

    951:   Input Parameter:
    952: . dm - The `DMPLEX`

    954:   Output Parameter:
    955: . localBox - The grid hash object

    957:   Level: developer

    959:   Notes:
    960:   How do we determine all boxes intersecting a given cell?

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

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

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

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

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

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

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

    977: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
    978: */
    979: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
    980: {
    981:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
    982:   PetscGridHash   lbox;
    983:   PetscSF         sf;
    984:   const PetscInt *leaves;
    985:   PetscInt       *dboxes, *boxes;
    986:   PetscInt        cdim, cStart, cEnd, Nl = -1;
    987:   PetscBool       flg;

    989:   PetscFunctionBegin;
    990:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    991:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
    992:   PetscCall(DMPlexCreateGridHash(dm, &lbox));
    993:   {
    994:     PetscInt n[3], d;

    996:     PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
    997:     if (flg) {
    998:       for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
    999:     } else {
    1000:       for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
    1001:     }
    1002:     PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
    1003:     if (debug)
    1004:       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.,
    1005:                             (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.));
    1006:   }

    1008:   PetscCall(DMGetPointSF(dm, &sf));
    1009:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
    1010:   Nl = PetscMax(Nl, 0);
    1011:   PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));

    1013:   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
    1014:   PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
    1015:   for (PetscInt c = cStart; c < cEnd; ++c) {
    1016:     PetscReal          intPoints[6 * 6 * 6 * 3];
    1017:     const PetscScalar *array;
    1018:     PetscScalar       *coords            = NULL;
    1019:     const PetscReal   *h                 = lbox->h;
    1020:     PetscReal          normal[9]         = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
    1021:     PetscReal         *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
    1022:     PetscReal         *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
    1023:     PetscReal          lp[3], up[3], *tmp;
    1024:     PetscInt           numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
    1025:     PetscBool          isDG, lower[3], upper[3];

    1027:     PetscCall(PetscFindInt(c, Nl, leaves, &idx));
    1028:     if (idx >= 0) continue;
    1029:     // Get grid of boxes containing the cell
    1030:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    1031:     PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
    1032:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
    1033:     for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
    1034:     for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
    1035:     for (PetscInt e = 1; e < numCoords / cdim; ++e) {
    1036:       for (PetscInt d = 0; d < cdim; ++d) {
    1037:         dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
    1038:         dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
    1039:       }
    1040:     }
    1041:     if (debug > 4) {
    1042:       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]));
    1043:     }
    1044:     // Initialize with lower planes for first box
    1045:     for (PetscInt d = 0; d < cdim; ++d) {
    1046:       lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
    1047:       up[d] = lp[d] + h[d];
    1048:     }
    1049:     for (PetscInt d = 0; d < cdim; ++d) {
    1050:       PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
    1051:       if (debug > 4) {
    1052:         if (!lowerInt[d])
    1053:           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"));
    1054:         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]));
    1055:       }
    1056:     }
    1057:     // Loop over grid
    1058:     for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
    1059:       if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
    1060:       if (cdim > 2 && debug > 4) {
    1061:         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"));
    1062:         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]));
    1063:       }
    1064:       for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
    1065:         if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
    1066:         if (cdim > 1 && debug > 4) {
    1067:           if (!upperInt[1])
    1068:             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"));
    1069:           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]));
    1070:         }
    1071:         for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
    1072:           const PetscInt box    = (k * lbox->n[1] + j) * lbox->n[0] + i;
    1073:           PetscBool      excNeg = PETSC_TRUE;
    1074:           PetscBool      excPos = PETSC_TRUE;
    1075:           PetscInt       NlInt  = 0;
    1076:           PetscInt       NuInt  = 0;

    1078:           PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
    1079:           if (debug > 4) {
    1080:             if (!upperInt[0])
    1081:               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"));
    1082:             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]));
    1083:           }
    1084:           for (PetscInt d = 0; d < cdim; ++d) {
    1085:             NlInt += lowerInt[d];
    1086:             NuInt += upperInt[d];
    1087:           }
    1088:           // If there is no intersection...
    1089:           if (!NlInt && !NuInt) {
    1090:             // If the cell is on the negative side of the lower planes, it is not in the box
    1091:             for (PetscInt d = 0; d < cdim; ++d)
    1092:               if (lower[d]) {
    1093:                 excNeg = PETSC_FALSE;
    1094:                 break;
    1095:               }
    1096:             // If the cell is on the positive side of the upper planes, it is not in the box
    1097:             for (PetscInt d = 0; d < cdim; ++d)
    1098:               if (!upper[d]) {
    1099:                 excPos = PETSC_FALSE;
    1100:                 break;
    1101:               }
    1102:             if (excNeg || excPos) {
    1103:               if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
    1104:               if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
    1105:               continue;
    1106:             }
    1107:             // Otherwise it is in the box
    1108:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
    1109:             PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1110:             continue;
    1111:           }
    1112:           /*
    1113:             If any intersection point is within the box limits, it is in the box
    1114:             We need to have tolerances here since intersection point calculations can introduce errors
    1115:             Initialize a count to track which planes have intersection outside the box.
    1116:             if two adjacent planes have intersection points upper and lower all outside the box, look
    1117:             first at if another plane has intersection points outside the box, if so, it is inside the cell
    1118:             look next if no intersection points exist on the other planes, and check if the planes are on the
    1119:             outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
    1120:           */
    1121:           PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
    1122:           for (PetscInt plane = 0; plane < cdim; ++plane) {
    1123:             for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
    1124:               PetscInt d;

    1126:               for (d = 0; d < cdim; ++d) {
    1127:                 if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
    1128:                   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
    1129:                   break;
    1130:                 }
    1131:               }
    1132:               if (d == cdim) {
    1133:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
    1134:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1135:                 goto end;
    1136:               }
    1137:             }
    1138:             for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
    1139:               PetscInt d;

    1141:               for (d = 0; d < cdim; ++d) {
    1142:                 if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
    1143:                   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
    1144:                   break;
    1145:                 }
    1146:               }
    1147:               if (d == cdim) {
    1148:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
    1149:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1150:                 goto end;
    1151:               }
    1152:             }
    1153:           }
    1154:           /*
    1155:              Check the planes with intersections
    1156:              in 2D, check if the square falls in the middle of a cell
    1157:              ie all four planes have intersection points outside of the box
    1158:              You do not want to be doing this, because it means your grid hashing is finer than your grid,
    1159:              but we should still support it I guess
    1160:           */
    1161:           if (cdim == 2) {
    1162:             PetscInt nIntersects = 0;
    1163:             for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
    1164:             // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
    1165:             if (nIntersects == 8) {
    1166:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1167:               goto end;
    1168:             }
    1169:           }
    1170:           /*
    1171:              In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
    1172:              we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
    1173:              If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
    1174:           */
    1175:           if (cdim == 3) {
    1176:             PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
    1177:             // Find two adjacent planes with at least 3 intersection points in the upper and lower
    1178:             // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
    1179:             for (PetscInt d = 0; d < cdim; ++d)
    1180:               if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
    1181:                 faces[d]++;
    1182:                 checkInternalFace++;
    1183:               }
    1184:             if (checkInternalFace == 3) {
    1185:               // All planes have 3 intersection points, add it.
    1186:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1187:               goto end;
    1188:             }
    1189:             // Gross, figure out which adjacent faces have at least 3 points
    1190:             PetscInt nonIntersectingFace = -1;
    1191:             if (faces[0] == faces[1]) nonIntersectingFace = 2;
    1192:             if (faces[0] == faces[2]) nonIntersectingFace = 1;
    1193:             if (faces[1] == faces[2]) nonIntersectingFace = 0;
    1194:             if (nonIntersectingFace >= 0) {
    1195:               for (PetscInt plane = 0; plane < cdim; ++plane) {
    1196:                 if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
    1197:                 // 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.
    1198:                 for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
    1199:                   if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
    1200:                 }
    1201:                 for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
    1202:                   if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
    1203:                 }
    1204:                 goto end;
    1205:               }
    1206:               // The points are within the bonds of the non intersecting planes, add it.
    1207:             setpoint:
    1208:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
    1209:               goto end;
    1210:             }
    1211:           }
    1212:         end:
    1213:           lower[0]          = upper[0];
    1214:           lowerInt[0]       = upperInt[0];
    1215:           tmp               = lowerIntPoints[0];
    1216:           lowerIntPoints[0] = upperIntPoints[0];
    1217:           upperIntPoints[0] = tmp;
    1218:         }
    1219:         lp[0]             = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
    1220:         up[0]             = lp[0] + h[0];
    1221:         lower[1]          = upper[1];
    1222:         lowerInt[1]       = upperInt[1];
    1223:         tmp               = lowerIntPoints[1];
    1224:         lowerIntPoints[1] = upperIntPoints[1];
    1225:         upperIntPoints[1] = tmp;
    1226:       }
    1227:       lp[1]             = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
    1228:       up[1]             = lp[1] + h[1];
    1229:       lower[2]          = upper[2];
    1230:       lowerInt[2]       = upperInt[2];
    1231:       tmp               = lowerIntPoints[2];
    1232:       lowerIntPoints[2] = upperIntPoints[2];
    1233:       upperIntPoints[2] = tmp;
    1234:     }
    1235:   }
    1236:   PetscCall(PetscFree2(dboxes, boxes));

    1238:   if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
    1239:   PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
    1240:   PetscCall(DMLabelDestroy(&lbox->cellsSparse));
    1241:   *localBox = lbox;
    1242:   PetscFunctionReturn(PETSC_SUCCESS);
    1243: }

    1245: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
    1246: {
    1247:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
    1248:   DM_Plex        *mesh  = (DM_Plex *)dm->data;
    1249:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
    1250:   PetscInt        bs, numPoints, numFound, *found = NULL;
    1251:   PetscInt        cdim, Nl = 0, cStart, cEnd, numCells;
    1252:   PetscSF         sf;
    1253:   const PetscInt *leaves;
    1254:   const PetscInt *boxCells;
    1255:   PetscSFNode    *cells;
    1256:   PetscScalar    *a;
    1257:   PetscMPIInt     result;
    1258:   PetscLogDouble  t0, t1;
    1259:   PetscReal       gmin[3], gmax[3];
    1260:   PetscInt        terminating_query_type[] = {0, 0, 0};
    1261:   PetscMPIInt     rank;

    1263:   PetscFunctionBegin;
    1264:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
    1265:   PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
    1266:   PetscCall(PetscTime(&t0));
    1267:   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.");
    1268:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    1269:   PetscCall(VecGetBlockSize(v, &bs));
    1270:   PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
    1271:   PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
    1272:   // We ignore extra coordinates
    1273:   PetscCheck(bs >= cdim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, cdim);
    1274:   PetscCall(DMGetCoordinatesLocalSetUp(dm));
    1275:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
    1276:   PetscCall(DMGetPointSF(dm, &sf));
    1277:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
    1278:   Nl = PetscMax(Nl, 0);
    1279:   PetscCall(VecGetLocalSize(v, &numPoints));
    1280:   PetscCall(VecGetArray(v, &a));
    1281:   numPoints /= bs;
    1282:   {
    1283:     const PetscSFNode *sf_cells;

    1285:     PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
    1286:     if (sf_cells) {
    1287:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
    1288:       cells = (PetscSFNode *)sf_cells;
    1289:       reuse = PETSC_TRUE;
    1290:     } else {
    1291:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
    1292:       PetscCall(PetscMalloc1(numPoints, &cells));
    1293:       /* initialize cells if created */
    1294:       for (PetscInt p = 0; p < numPoints; p++) {
    1295:         cells[p].rank  = 0;
    1296:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    1297:       }
    1298:     }
    1299:   }
    1300:   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
    1301:   if (hash) {
    1302:     if (!mesh->lbox) {
    1303:       PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
    1304:       PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
    1305:     }
    1306:     /* Designate the local box for each point */
    1307:     /* Send points to correct process */
    1308:     /* Search cells that lie in each subbox */
    1309:     /*   Should we bin points before doing search? */
    1310:     PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
    1311:   }
    1312:   numFound = 0;
    1313:   for (PetscInt p = 0; p < numPoints; ++p) {
    1314:     const PetscScalar *point   = &a[p * bs];
    1315:     PetscInt           dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
    1316:     PetscBool          point_outside_domain = PETSC_FALSE;

    1318:     /* check bounding box of domain */
    1319:     for (PetscInt d = 0; d < cdim; d++) {
    1320:       if (PetscRealPart(point[d]) < gmin[d]) {
    1321:         point_outside_domain = PETSC_TRUE;
    1322:         break;
    1323:       }
    1324:       if (PetscRealPart(point[d]) > gmax[d]) {
    1325:         point_outside_domain = PETSC_TRUE;
    1326:         break;
    1327:       }
    1328:     }
    1329:     if (point_outside_domain) {
    1330:       cells[p].rank  = 0;
    1331:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    1332:       terminating_query_type[0]++;
    1333:       continue;
    1334:     }

    1336:     /* check initial values in cells[].index - abort early if found */
    1337:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    1338:       PetscInt c = cells[p].index;

    1340:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    1341:       PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
    1342:       if (cell >= 0) {
    1343:         cells[p].rank  = 0;
    1344:         cells[p].index = cell;
    1345:         numFound++;
    1346:       }
    1347:     }
    1348:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    1349:       terminating_query_type[1]++;
    1350:       continue;
    1351:     }

    1353:     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]), cdim > 2 ? (double)PetscRealPart(point[2]) : 0.));
    1354:     if (hash) {
    1355:       PetscBool found_box;

    1357:       /* allow for case that point is outside box - abort early */
    1358:       PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
    1359:       if (found_box) {
    1360:         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], cdim > 2 ? dbin[2] : 0));
    1361:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
    1362:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
    1363:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
    1364:         for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
    1365:           if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]    Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
    1366:           PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, boxCells[c], &cell));
    1367:           if (cell >= 0) {
    1368:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]      FOUND in cell %" PetscInt_FMT "\n", rank, cell));
    1369:             cells[p].rank  = 0;
    1370:             cells[p].index = cell;
    1371:             numFound++;
    1372:             terminating_query_type[2]++;
    1373:             break;
    1374:           }
    1375:         }
    1376:       }
    1377:     } else {
    1378:       PetscBool found = PETSC_FALSE;
    1379:       for (PetscInt c = cStart; c < cEnd; ++c) {
    1380:         PetscInt idx;

    1382:         PetscCall(PetscFindInt(c, Nl, leaves, &idx));
    1383:         if (idx >= 0) continue;
    1384:         PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
    1385:         if (cell >= 0) {
    1386:           cells[p].rank  = 0;
    1387:           cells[p].index = cell;
    1388:           numFound++;
    1389:           terminating_query_type[2]++;
    1390:           found = PETSC_TRUE;
    1391:           break;
    1392:         }
    1393:       }
    1394:       if (!found) terminating_query_type[0]++;
    1395:     }
    1396:   }
    1397:   if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
    1398:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
    1399:     for (PetscInt p = 0; p < numPoints; p++) {
    1400:       const PetscScalar *point     = &a[p * bs];
    1401:       PetscReal          cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
    1402:       PetscInt           dbin[3] = {-1, -1, -1}, bin, cellOffset, bestc = -1;

    1404:       if (cells[p].index < 0) {
    1405:         PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
    1406:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
    1407:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
    1408:         for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
    1409:           PetscCall(DMPlexClosestPoint_Internal(dm, cdim, point, boxCells[c], cpoint));
    1410:           for (PetscInt d = 0; d < cdim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
    1411:           dist = DMPlex_NormD_Internal(cdim, diff);
    1412:           if (dist < distMax) {
    1413:             for (PetscInt d = 0; d < cdim; ++d) best[d] = cpoint[d];
    1414:             bestc   = boxCells[c];
    1415:             distMax = dist;
    1416:           }
    1417:         }
    1418:         if (distMax < PETSC_MAX_REAL) {
    1419:           ++numFound;
    1420:           cells[p].rank  = 0;
    1421:           cells[p].index = bestc;
    1422:           for (PetscInt d = 0; d < cdim; ++d) a[p * bs + d] = best[d];
    1423:         }
    1424:       }
    1425:     }
    1426:   }
    1427:   /* This code is only be relevant when interfaced to parallel point location */
    1428:   /* Check for highest numbered proc that claims a point (do we care?) */
    1429:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
    1430:     PetscCall(PetscMalloc1(numFound, &found));
    1431:     numFound = 0;
    1432:     for (PetscInt p = 0; p < numPoints; p++) {
    1433:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
    1434:         if (numFound < p) cells[numFound] = cells[p];
    1435:         found[numFound++] = p;
    1436:       }
    1437:     }
    1438:   }
    1439:   PetscCall(VecRestoreArray(v, &a));
    1440:   if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
    1441:   PetscCall(PetscTime(&t1));
    1442:   if (hash) {
    1443:     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]));
    1444:   } else {
    1445:     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]));
    1446:   }
    1447:   PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
    1448:   PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
    1449:   PetscFunctionReturn(PETSC_SUCCESS);
    1450: }

    1452: /*@
    1453:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

    1455:   Not Collective

    1457:   Input/Output Parameter:
    1458: . 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

    1460:   Output Parameter:
    1461: . R - The rotation which accomplishes the projection, array of size 4

    1463:   Level: developer

    1465: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
    1466: @*/
    1467: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
    1468: {
    1469:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
    1470:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
    1471:   const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;

    1473:   PetscFunctionBegin;
    1474:   R[0]      = c;
    1475:   R[1]      = -s;
    1476:   R[2]      = s;
    1477:   R[3]      = c;
    1478:   coords[0] = 0.0;
    1479:   coords[1] = r;
    1480:   PetscFunctionReturn(PETSC_SUCCESS);
    1481: }

    1483: /*@
    1484:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

    1486:   Not Collective

    1488:   Input/Output Parameter:
    1489: . 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

    1491:   Output Parameter:
    1492: . R - The rotation which accomplishes the projection, an array of size 9

    1494:   Level: developer

    1496:   Note:
    1497:   This uses the basis completion described by Frisvad {cite}`frisvad2012building`

    1499: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
    1500: @*/
    1501: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
    1502: {
    1503:   PetscReal x    = PetscRealPart(coords[3] - coords[0]);
    1504:   PetscReal y    = PetscRealPart(coords[4] - coords[1]);
    1505:   PetscReal z    = PetscRealPart(coords[5] - coords[2]);
    1506:   PetscReal r    = PetscSqrtReal(x * x + y * y + z * z);
    1507:   PetscReal rinv = 1. / r;

    1509:   PetscFunctionBegin;
    1510:   x *= rinv;
    1511:   y *= rinv;
    1512:   z *= rinv;
    1513:   if (x > 0.) {
    1514:     PetscReal inv1pX = 1. / (1. + x);

    1516:     R[0] = x;
    1517:     R[1] = -y;
    1518:     R[2] = -z;
    1519:     R[3] = y;
    1520:     R[4] = 1. - y * y * inv1pX;
    1521:     R[5] = -y * z * inv1pX;
    1522:     R[6] = z;
    1523:     R[7] = -y * z * inv1pX;
    1524:     R[8] = 1. - z * z * inv1pX;
    1525:   } else {
    1526:     PetscReal inv1mX = 1. / (1. - x);

    1528:     R[0] = x;
    1529:     R[1] = z;
    1530:     R[2] = y;
    1531:     R[3] = y;
    1532:     R[4] = -y * z * inv1mX;
    1533:     R[5] = 1. - y * y * inv1mX;
    1534:     R[6] = z;
    1535:     R[7] = 1. - z * z * inv1mX;
    1536:     R[8] = -y * z * inv1mX;
    1537:   }
    1538:   coords[0] = 0.0;
    1539:   coords[1] = r;
    1540:   coords[2] = 0.0;
    1541:   PetscFunctionReturn(PETSC_SUCCESS);
    1542: }

    1544: /*@
    1545:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
    1546:   plane.  The normal is defined by positive orientation of the first 3 points.

    1548:   Not Collective

    1550:   Input Parameter:
    1551: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

    1553:   Input/Output Parameter:
    1554: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
    1555:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

    1557:   Output Parameter:
    1558: . 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.

    1560:   Level: developer

    1562: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
    1563: @*/
    1564: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    1565: {
    1566:   PetscReal      x1[3], x2[3], n[3], c[3], norm;
    1567:   const PetscInt dim = 3;
    1568:   PetscInt       d, p;

    1570:   PetscFunctionBegin;
    1571:   /* 0) Calculate normal vector */
    1572:   for (d = 0; d < dim; ++d) {
    1573:     x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
    1574:     x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
    1575:   }
    1576:   // n = x1 \otimes x2
    1577:   n[0] = x1[1] * x2[2] - x1[2] * x2[1];
    1578:   n[1] = x1[2] * x2[0] - x1[0] * x2[2];
    1579:   n[2] = x1[0] * x2[1] - x1[1] * x2[0];
    1580:   norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
    1581:   for (d = 0; d < dim; d++) n[d] /= norm;
    1582:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
    1583:   for (d = 0; d < dim; d++) x1[d] /= norm;
    1584:   // x2 = n \otimes x1
    1585:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
    1586:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
    1587:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
    1588:   for (d = 0; d < dim; d++) {
    1589:     R[d * dim + 0] = x1[d];
    1590:     R[d * dim + 1] = x2[d];
    1591:     R[d * dim + 2] = n[d];
    1592:     c[d]           = PetscRealPart(coords[0 * dim + d]);
    1593:   }
    1594:   for (p = 0; p < coordSize / dim; p++) {
    1595:     PetscReal y[3];
    1596:     for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
    1597:     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];
    1598:   }
    1599:   PetscFunctionReturn(PETSC_SUCCESS);
    1600: }

    1602: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    1603: {
    1604:   /* Signed volume is 1/2 the determinant

    1606:    |  1  1  1 |
    1607:    | x0 x1 x2 |
    1608:    | y0 y1 y2 |

    1610:      but if x0,y0 is the origin, we have

    1612:    | x1 x2 |
    1613:    | y1 y2 |
    1614:   */
    1615:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    1616:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    1617:   PetscReal       M[4], detM;
    1618:   M[0] = x1;
    1619:   M[1] = x2;
    1620:   M[2] = y1;
    1621:   M[3] = y2;
    1622:   DMPlex_Det2D_Internal(&detM, M);
    1623:   *vol = 0.5 * detM;
    1624:   (void)PetscLogFlops(5.0);
    1625: }

    1627: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    1628: {
    1629:   /* Signed volume is 1/6th of the determinant

    1631:    |  1  1  1  1 |
    1632:    | x0 x1 x2 x3 |
    1633:    | y0 y1 y2 y3 |
    1634:    | z0 z1 z2 z3 |

    1636:      but if x0,y0,z0 is the origin, we have

    1638:    | x1 x2 x3 |
    1639:    | y1 y2 y3 |
    1640:    | z1 z2 z3 |
    1641:   */
    1642:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
    1643:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
    1644:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    1645:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
    1646:   PetscReal       M[9], detM;
    1647:   M[0] = x1;
    1648:   M[1] = x2;
    1649:   M[2] = x3;
    1650:   M[3] = y1;
    1651:   M[4] = y2;
    1652:   M[5] = y3;
    1653:   M[6] = z1;
    1654:   M[7] = z2;
    1655:   M[8] = z3;
    1656:   DMPlex_Det3D_Internal(&detM, M);
    1657:   *vol = -onesixth * detM;
    1658:   (void)PetscLogFlops(10.0);
    1659: }

    1661: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1662: {
    1663:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
    1664:   DMPlex_Det3D_Internal(vol, coords);
    1665:   *vol *= -onesixth;
    1666: }

    1668: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1669: {
    1670:   PetscSection       coordSection;
    1671:   Vec                coordinates;
    1672:   const PetscScalar *coords;
    1673:   PetscInt           dim, d, off;

    1675:   PetscFunctionBegin;
    1676:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    1677:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
    1678:   PetscCall(PetscSectionGetDof(coordSection, e, &dim));
    1679:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
    1680:   PetscCall(PetscSectionGetOffset(coordSection, e, &off));
    1681:   PetscCall(VecGetArrayRead(coordinates, &coords));
    1682:   if (v0) {
    1683:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
    1684:   }
    1685:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
    1686:   *detJ = 1.;
    1687:   if (J) {
    1688:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1689:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1690:     if (invJ) {
    1691:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1692:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1693:     }
    1694:   }
    1695:   PetscFunctionReturn(PETSC_SUCCESS);
    1696: }

    1698: /*@C
    1699:   DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity

    1701:   Not Collective

    1703:   Input Parameters:
    1704: + dm   - The `DMPLEX`
    1705: - cell - The cell number

    1707:   Output Parameters:
    1708: + isDG   - Using cellwise coordinates
    1709: . Nc     - The number of coordinates
    1710: . array  - The coordinate array
    1711: - coords - The cell coordinates

    1713:   Level: developer

    1715: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
    1716: @*/
    1717: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
    1718: {
    1719:   DM                 cdm;
    1720:   Vec                coordinates;
    1721:   PetscSection       cs;
    1722:   const PetscScalar *ccoords;
    1723:   PetscInt           pStart, pEnd;

    1725:   PetscFunctionBeginHot;
    1726:   *isDG   = PETSC_FALSE;
    1727:   *Nc     = 0;
    1728:   *array  = NULL;
    1729:   *coords = NULL;
    1730:   /* Check for cellwise coordinates */
    1731:   PetscCall(DMGetCellCoordinateSection(dm, &cs));
    1732:   if (!cs) goto cg;
    1733:   /* Check that the cell exists in the cellwise section */
    1734:   PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
    1735:   if (cell < pStart || cell >= pEnd) goto cg;
    1736:   /* Check for cellwise coordinates for this cell */
    1737:   PetscCall(PetscSectionGetDof(cs, cell, Nc));
    1738:   if (!*Nc) goto cg;
    1739:   /* Check for cellwise coordinates */
    1740:   PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
    1741:   if (!coordinates) goto cg;
    1742:   /* Get cellwise coordinates */
    1743:   PetscCall(DMGetCellCoordinateDM(dm, &cdm));
    1744:   PetscCall(VecGetArrayRead(coordinates, array));
    1745:   PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
    1746:   PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
    1747:   PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
    1748:   PetscCall(VecRestoreArrayRead(coordinates, array));
    1749:   *isDG = PETSC_TRUE;
    1750:   PetscFunctionReturn(PETSC_SUCCESS);
    1751: cg:
    1752:   /* Use continuous coordinates */
    1753:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    1754:   PetscCall(DMGetCoordinateSection(dm, &cs));
    1755:   PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
    1756:   PetscCall(DMPlexVecGetOrientedClosure(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
    1757:   PetscFunctionReturn(PETSC_SUCCESS);
    1758: }

    1760: /*@C
    1761:   DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity

    1763:   Not Collective

    1765:   Input Parameters:
    1766: + dm   - The `DMPLEX`
    1767: - cell - The cell number

    1769:   Output Parameters:
    1770: + isDG   - Using cellwise coordinates
    1771: . Nc     - The number of coordinates
    1772: . array  - The coordinate array
    1773: - coords - The cell coordinates

    1775:   Level: developer

    1777: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
    1778: @*/
    1779: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
    1780: {
    1781:   DM           cdm;
    1782:   PetscSection cs;
    1783:   Vec          coordinates;

    1785:   PetscFunctionBeginHot;
    1786:   if (*isDG) {
    1787:     PetscCall(DMGetCellCoordinateDM(dm, &cdm));
    1788:     PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
    1789:   } else {
    1790:     PetscCall(DMGetCoordinateDM(dm, &cdm));
    1791:     PetscCall(DMGetCoordinateSection(dm, &cs));
    1792:     PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
    1793:     PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
    1794:   }
    1795:   PetscFunctionReturn(PETSC_SUCCESS);
    1796: }

    1798: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1799: {
    1800:   const PetscScalar *array;
    1801:   PetscScalar       *coords = NULL;
    1802:   PetscInt           numCoords, d;
    1803:   PetscBool          isDG;

    1805:   PetscFunctionBegin;
    1806:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1807:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1808:   *detJ = 0.0;
    1809:   if (numCoords == 6) {
    1810:     const PetscInt dim = 3;
    1811:     PetscReal      R[9], J0;

    1813:     if (v0) {
    1814:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1815:     }
    1816:     PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
    1817:     if (J) {
    1818:       J0   = 0.5 * PetscRealPart(coords[1]);
    1819:       J[0] = R[0] * J0;
    1820:       J[1] = R[1];
    1821:       J[2] = R[2];
    1822:       J[3] = R[3] * J0;
    1823:       J[4] = R[4];
    1824:       J[5] = R[5];
    1825:       J[6] = R[6] * J0;
    1826:       J[7] = R[7];
    1827:       J[8] = R[8];
    1828:       DMPlex_Det3D_Internal(detJ, J);
    1829:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1830:     }
    1831:   } else if (numCoords == 4) {
    1832:     const PetscInt dim = 2;
    1833:     PetscReal      R[4], J0;

    1835:     if (v0) {
    1836:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1837:     }
    1838:     PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
    1839:     if (J) {
    1840:       J0   = 0.5 * PetscRealPart(coords[1]);
    1841:       J[0] = R[0] * J0;
    1842:       J[1] = R[1];
    1843:       J[2] = R[2] * J0;
    1844:       J[3] = R[3];
    1845:       DMPlex_Det2D_Internal(detJ, J);
    1846:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
    1847:     }
    1848:   } else if (numCoords == 2) {
    1849:     const PetscInt dim = 1;

    1851:     if (v0) {
    1852:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1853:     }
    1854:     if (J) {
    1855:       J[0]  = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1856:       *detJ = J[0];
    1857:       PetscCall(PetscLogFlops(2.0));
    1858:       if (invJ) {
    1859:         invJ[0] = 1.0 / J[0];
    1860:         PetscCall(PetscLogFlops(1.0));
    1861:       }
    1862:     }
    1863:   } 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);
    1864:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1865:   PetscFunctionReturn(PETSC_SUCCESS);
    1866: }

    1868: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1869: {
    1870:   const PetscScalar *array;
    1871:   PetscScalar       *coords = NULL;
    1872:   PetscInt           numCoords, d;
    1873:   PetscBool          isDG;

    1875:   PetscFunctionBegin;
    1876:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1877:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1878:   *detJ = 0.0;
    1879:   if (numCoords == 9) {
    1880:     const PetscInt dim = 3;
    1881:     PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

    1883:     if (v0) {
    1884:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1885:     }
    1886:     PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
    1887:     if (J) {
    1888:       const PetscInt pdim = 2;

    1890:       for (d = 0; d < pdim; d++) {
    1891:         for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
    1892:       }
    1893:       PetscCall(PetscLogFlops(8.0));
    1894:       DMPlex_Det3D_Internal(detJ, J0);
    1895:       for (d = 0; d < dim; d++) {
    1896:         for (PetscInt f = 0; f < dim; f++) {
    1897:           J[d * dim + f] = 0.0;
    1898:           for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
    1899:         }
    1900:       }
    1901:       PetscCall(PetscLogFlops(18.0));
    1902:     }
    1903:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1904:   } else if (numCoords == 6) {
    1905:     const PetscInt dim = 2;

    1907:     if (v0) {
    1908:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    1909:     }
    1910:     if (J) {
    1911:       for (d = 0; d < dim; d++) {
    1912:         for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    1913:       }
    1914:       PetscCall(PetscLogFlops(8.0));
    1915:       DMPlex_Det2D_Internal(detJ, J);
    1916:     }
    1917:     if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
    1918:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
    1919:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1920:   PetscFunctionReturn(PETSC_SUCCESS);
    1921: }

    1923: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1924: {
    1925:   const PetscScalar *array;
    1926:   PetscScalar       *coords = NULL;
    1927:   PetscInt           numCoords, d;
    1928:   PetscBool          isDG;

    1930:   PetscFunctionBegin;
    1931:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    1932:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1933:   if (!Nq) {
    1934:     PetscInt vorder[4] = {0, 1, 2, 3};

    1936:     if (isTensor) {
    1937:       vorder[2] = 3;
    1938:       vorder[3] = 2;
    1939:     }
    1940:     *detJ = 0.0;
    1941:     if (numCoords == 12) {
    1942:       const PetscInt dim = 3;
    1943:       PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

    1945:       if (v) {
    1946:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    1947:       }
    1948:       PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
    1949:       if (J) {
    1950:         const PetscInt pdim = 2;

    1952:         for (d = 0; d < pdim; d++) {
    1953:           J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
    1954:           J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
    1955:         }
    1956:         PetscCall(PetscLogFlops(8.0));
    1957:         DMPlex_Det3D_Internal(detJ, J0);
    1958:         for (d = 0; d < dim; d++) {
    1959:           for (PetscInt f = 0; f < dim; f++) {
    1960:             J[d * dim + f] = 0.0;
    1961:             for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
    1962:           }
    1963:         }
    1964:         PetscCall(PetscLogFlops(18.0));
    1965:       }
    1966:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    1967:     } else if (numCoords == 8) {
    1968:       const PetscInt dim = 2;

    1970:       if (v) {
    1971:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    1972:       }
    1973:       if (J) {
    1974:         for (d = 0; d < dim; d++) {
    1975:           J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
    1976:           J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
    1977:         }
    1978:         PetscCall(PetscLogFlops(8.0));
    1979:         DMPlex_Det2D_Internal(detJ, J);
    1980:       }
    1981:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
    1982:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
    1983:   } else {
    1984:     const PetscInt Nv         = 4;
    1985:     const PetscInt dimR       = 2;
    1986:     PetscInt       zToPlex[4] = {0, 1, 3, 2};
    1987:     PetscReal      zOrder[12];
    1988:     PetscReal      zCoeff[12];
    1989:     PetscInt       i, j, k, l, dim;

    1991:     if (isTensor) {
    1992:       zToPlex[2] = 2;
    1993:       zToPlex[3] = 3;
    1994:     }
    1995:     if (numCoords == 12) {
    1996:       dim = 3;
    1997:     } else if (numCoords == 8) {
    1998:       dim = 2;
    1999:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
    2000:     for (i = 0; i < Nv; i++) {
    2001:       PetscInt zi = zToPlex[i];

    2003:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    2004:     }
    2005:     for (j = 0; j < dim; j++) {
    2006:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
    2007:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
    2008:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
    2009:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
    2010:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
    2011:       */
    2012:       zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    2013:       zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    2014:       zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    2015:       zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    2016:     }
    2017:     for (i = 0; i < Nq; i++) {
    2018:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    2020:       if (v) {
    2021:         PetscReal extPoint[4];

    2023:         extPoint[0] = 1.;
    2024:         extPoint[1] = xi;
    2025:         extPoint[2] = eta;
    2026:         extPoint[3] = xi * eta;
    2027:         for (j = 0; j < dim; j++) {
    2028:           PetscReal val = 0.;

    2030:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
    2031:           v[i * dim + j] = val;
    2032:         }
    2033:       }
    2034:       if (J) {
    2035:         PetscReal extJ[8];

    2037:         extJ[0] = 0.;
    2038:         extJ[1] = 0.;
    2039:         extJ[2] = 1.;
    2040:         extJ[3] = 0.;
    2041:         extJ[4] = 0.;
    2042:         extJ[5] = 1.;
    2043:         extJ[6] = eta;
    2044:         extJ[7] = xi;
    2045:         for (j = 0; j < dim; j++) {
    2046:           for (k = 0; k < dimR; k++) {
    2047:             PetscReal val = 0.;

    2049:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    2050:             J[i * dim * dim + dim * j + k] = val;
    2051:           }
    2052:         }
    2053:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    2054:           PetscReal  x, y, z;
    2055:           PetscReal *iJ = &J[i * dim * dim];
    2056:           PetscReal  norm;

    2058:           x     = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    2059:           y     = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    2060:           z     = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    2061:           norm  = PetscSqrtReal(x * x + y * y + z * z);
    2062:           iJ[2] = x / norm;
    2063:           iJ[5] = y / norm;
    2064:           iJ[8] = z / norm;
    2065:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    2066:           if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    2067:         } else {
    2068:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    2069:           if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    2070:         }
    2071:       }
    2072:     }
    2073:   }
    2074:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2075:   PetscFunctionReturn(PETSC_SUCCESS);
    2076: }

    2078: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2079: {
    2080:   const PetscScalar *array;
    2081:   PetscScalar       *coords = NULL;
    2082:   const PetscInt     dim    = 3;
    2083:   PetscInt           numCoords, d;
    2084:   PetscBool          isDG;

    2086:   PetscFunctionBegin;
    2087:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2088:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    2089:   *detJ = 0.0;
    2090:   if (v0) {
    2091:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
    2092:   }
    2093:   if (J) {
    2094:     for (d = 0; d < dim; d++) {
    2095:       /* I orient with outward face normals */
    2096:       J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2097:       J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2098:       J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2099:     }
    2100:     PetscCall(PetscLogFlops(18.0));
    2101:     DMPlex_Det3D_Internal(detJ, J);
    2102:   }
    2103:   if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    2104:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2105:   PetscFunctionReturn(PETSC_SUCCESS);
    2106: }

    2108: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2109: {
    2110:   const PetscScalar *array;
    2111:   PetscScalar       *coords = NULL;
    2112:   const PetscInt     dim    = 3;
    2113:   PetscInt           numCoords, d;
    2114:   PetscBool          isDG;

    2116:   PetscFunctionBegin;
    2117:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2118:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    2119:   if (!Nq) {
    2120:     *detJ = 0.0;
    2121:     if (v) {
    2122:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    2123:     }
    2124:     if (J) {
    2125:       for (d = 0; d < dim; d++) {
    2126:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2127:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2128:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2129:       }
    2130:       PetscCall(PetscLogFlops(18.0));
    2131:       DMPlex_Det3D_Internal(detJ, J);
    2132:     }
    2133:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    2134:   } else {
    2135:     const PetscInt Nv         = 8;
    2136:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    2137:     const PetscInt dim        = 3;
    2138:     const PetscInt dimR       = 3;
    2139:     PetscReal      zOrder[24];
    2140:     PetscReal      zCoeff[24];
    2141:     PetscInt       i, j, k, l;

    2143:     for (i = 0; i < Nv; i++) {
    2144:       PetscInt zi = zToPlex[i];

    2146:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    2147:     }
    2148:     for (j = 0; j < dim; j++) {
    2149:       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]);
    2150:       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]);
    2151:       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]);
    2152:       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]);
    2153:       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]);
    2154:       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]);
    2155:       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]);
    2156:       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]);
    2157:     }
    2158:     for (i = 0; i < Nq; i++) {
    2159:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    2161:       if (v) {
    2162:         PetscReal extPoint[8];

    2164:         extPoint[0] = 1.;
    2165:         extPoint[1] = xi;
    2166:         extPoint[2] = eta;
    2167:         extPoint[3] = xi * eta;
    2168:         extPoint[4] = theta;
    2169:         extPoint[5] = theta * xi;
    2170:         extPoint[6] = theta * eta;
    2171:         extPoint[7] = theta * eta * xi;
    2172:         for (j = 0; j < dim; j++) {
    2173:           PetscReal val = 0.;

    2175:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
    2176:           v[i * dim + j] = val;
    2177:         }
    2178:       }
    2179:       if (J) {
    2180:         PetscReal extJ[24];

    2182:         extJ[0]  = 0.;
    2183:         extJ[1]  = 0.;
    2184:         extJ[2]  = 0.;
    2185:         extJ[3]  = 1.;
    2186:         extJ[4]  = 0.;
    2187:         extJ[5]  = 0.;
    2188:         extJ[6]  = 0.;
    2189:         extJ[7]  = 1.;
    2190:         extJ[8]  = 0.;
    2191:         extJ[9]  = eta;
    2192:         extJ[10] = xi;
    2193:         extJ[11] = 0.;
    2194:         extJ[12] = 0.;
    2195:         extJ[13] = 0.;
    2196:         extJ[14] = 1.;
    2197:         extJ[15] = theta;
    2198:         extJ[16] = 0.;
    2199:         extJ[17] = xi;
    2200:         extJ[18] = 0.;
    2201:         extJ[19] = theta;
    2202:         extJ[20] = eta;
    2203:         extJ[21] = theta * eta;
    2204:         extJ[22] = theta * xi;
    2205:         extJ[23] = eta * xi;

    2207:         for (j = 0; j < dim; j++) {
    2208:           for (k = 0; k < dimR; k++) {
    2209:             PetscReal val = 0.;

    2211:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    2212:             J[i * dim * dim + dim * j + k] = val;
    2213:           }
    2214:         }
    2215:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    2216:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    2217:       }
    2218:     }
    2219:   }
    2220:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2221:   PetscFunctionReturn(PETSC_SUCCESS);
    2222: }

    2224: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2225: {
    2226:   const PetscScalar *array;
    2227:   PetscScalar       *coords = NULL;
    2228:   const PetscInt     dim    = 3;
    2229:   PetscInt           numCoords, d;
    2230:   PetscBool          isDG;

    2232:   PetscFunctionBegin;
    2233:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2234:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    2235:   if (!Nq) {
    2236:     /* Assume that the map to the reference is affine */
    2237:     *detJ = 0.0;
    2238:     if (v) {
    2239:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
    2240:     }
    2241:     if (J) {
    2242:       for (d = 0; d < dim; d++) {
    2243:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2244:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2245:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
    2246:       }
    2247:       PetscCall(PetscLogFlops(18.0));
    2248:       DMPlex_Det3D_Internal(detJ, J);
    2249:     }
    2250:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
    2251:   } else {
    2252:     const PetscInt dim  = 3;
    2253:     const PetscInt dimR = 3;
    2254:     const PetscInt Nv   = 6;
    2255:     PetscReal      verts[18];
    2256:     PetscReal      coeff[18];
    2257:     PetscInt       i, j, k, l;

    2259:     for (i = 0; i < Nv; ++i)
    2260:       for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
    2261:     for (j = 0; j < dim; ++j) {
    2262:       /* Check for triangle,
    2263:            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)
    2264:            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)
    2265:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

    2267:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
    2268:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
    2269:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

    2271:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
    2272:                                  | -1  1 -1 | | phi_1 | =
    2273:                                  \ -1 -1  1 / \ phi_2 /

    2275:           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
    2276:       */
    2277:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
    2278:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
    2279:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
    2280:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
    2281:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
    2282:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
    2283:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
    2284:            1/4 /  0  1  1  0  1  1 \
    2285:                | -1  1  0 -1  0  1 |
    2286:                | -1  0  1 -1  1  0 |
    2287:                |  0 -1 -1  0  1  1 |
    2288:                |  1  0 -1 -1  1  0 |
    2289:                \  1 -1  0 -1  0  1 /
    2290:       */
    2291:       coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
    2292:       coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
    2293:       coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
    2294:       coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
    2295:       coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
    2296:       coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
    2297:       /* For reference prism:
    2298:       {0, 0, 0}
    2299:       {0, 1, 0}
    2300:       {1, 0, 0}
    2301:       {0, 0, 1}
    2302:       {0, 0, 0}
    2303:       {0, 0, 0}
    2304:       */
    2305:     }
    2306:     for (i = 0; i < Nq; ++i) {
    2307:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

    2309:       if (v) {
    2310:         PetscReal extPoint[6];
    2311:         PetscInt  c;

    2313:         extPoint[0] = 1.;
    2314:         extPoint[1] = eta;
    2315:         extPoint[2] = xi;
    2316:         extPoint[3] = zeta;
    2317:         extPoint[4] = xi * zeta;
    2318:         extPoint[5] = eta * zeta;
    2319:         for (c = 0; c < dim; ++c) {
    2320:           PetscReal val = 0.;

    2322:           for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
    2323:           v[i * dim + c] = val;
    2324:         }
    2325:       }
    2326:       if (J) {
    2327:         PetscReal extJ[18];

    2329:         extJ[0]  = 0.;
    2330:         extJ[1]  = 0.;
    2331:         extJ[2]  = 0.;
    2332:         extJ[3]  = 0.;
    2333:         extJ[4]  = 1.;
    2334:         extJ[5]  = 0.;
    2335:         extJ[6]  = 1.;
    2336:         extJ[7]  = 0.;
    2337:         extJ[8]  = 0.;
    2338:         extJ[9]  = 0.;
    2339:         extJ[10] = 0.;
    2340:         extJ[11] = 1.;
    2341:         extJ[12] = zeta;
    2342:         extJ[13] = 0.;
    2343:         extJ[14] = xi;
    2344:         extJ[15] = 0.;
    2345:         extJ[16] = zeta;
    2346:         extJ[17] = eta;

    2348:         for (j = 0; j < dim; j++) {
    2349:           for (k = 0; k < dimR; k++) {
    2350:             PetscReal val = 0.;

    2352:             for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
    2353:             J[i * dim * dim + dim * j + k] = val;
    2354:           }
    2355:         }
    2356:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    2357:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
    2358:       }
    2359:     }
    2360:   }
    2361:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
    2362:   PetscFunctionReturn(PETSC_SUCCESS);
    2363: }

    2365: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    2366: {
    2367:   DMPolytopeType   ct;
    2368:   PetscInt         depth, dim, coordDim, coneSize, i;
    2369:   PetscInt         Nq     = 0;
    2370:   const PetscReal *points = NULL;
    2371:   DMLabel          depthLabel;
    2372:   PetscReal        xi0[3]   = {-1., -1., -1.}, v0[3], J0[9], detJ0;
    2373:   PetscBool        isAffine = PETSC_TRUE;

    2375:   PetscFunctionBegin;
    2376:   PetscCall(DMPlexGetDepth(dm, &depth));
    2377:   PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
    2378:   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
    2379:   PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
    2380:   if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
    2381:   PetscCall(DMGetCoordinateDim(dm, &coordDim));
    2382:   PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
    2383:   if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
    2384:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    2385:   switch (ct) {
    2386:   case DM_POLYTOPE_POINT:
    2387:     PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2388:     isAffine = PETSC_FALSE;
    2389:     break;
    2390:   case DM_POLYTOPE_SEGMENT:
    2391:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2392:     if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
    2393:     else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2394:     break;
    2395:   case DM_POLYTOPE_TRIANGLE:
    2396:     if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
    2397:     else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2398:     break;
    2399:   case DM_POLYTOPE_QUADRILATERAL:
    2400:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
    2401:     isAffine = PETSC_FALSE;
    2402:     break;
    2403:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2404:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
    2405:     isAffine = PETSC_FALSE;
    2406:     break;
    2407:   case DM_POLYTOPE_TETRAHEDRON:
    2408:     if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
    2409:     else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
    2410:     break;
    2411:   case DM_POLYTOPE_HEXAHEDRON:
    2412:     PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
    2413:     isAffine = PETSC_FALSE;
    2414:     break;
    2415:   case DM_POLYTOPE_TRI_PRISM:
    2416:     PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
    2417:     isAffine = PETSC_FALSE;
    2418:     break;
    2419:   default:
    2420:     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))]);
    2421:   }
    2422:   if (isAffine && Nq) {
    2423:     if (v) {
    2424:       for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    2425:     }
    2426:     if (detJ) {
    2427:       for (i = 0; i < Nq; i++) detJ[i] = detJ0;
    2428:     }
    2429:     if (J) {
    2430:       PetscInt k;

    2432:       for (i = 0, k = 0; i < Nq; i++) {
    2433:         PetscInt j;

    2435:         for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
    2436:       }
    2437:     }
    2438:     if (invJ) {
    2439:       PetscInt k;
    2440:       switch (coordDim) {
    2441:       case 0:
    2442:         break;
    2443:       case 1:
    2444:         invJ[0] = 1. / J0[0];
    2445:         break;
    2446:       case 2:
    2447:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    2448:         break;
    2449:       case 3:
    2450:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    2451:         break;
    2452:       }
    2453:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    2454:         PetscInt j;

    2456:         for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
    2457:       }
    2458:     }
    2459:   }
    2460:   PetscFunctionReturn(PETSC_SUCCESS);
    2461: }

    2463: /*@C
    2464:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    2466:   Collective

    2468:   Input Parameters:
    2469: + dm   - the `DMPLEX`
    2470: - cell - the cell

    2472:   Output Parameters:
    2473: + v0   - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
    2474: . J    - the Jacobian of the transform from the reference element
    2475: . invJ - the inverse of the Jacobian
    2476: - detJ - the Jacobian determinant

    2478:   Level: advanced

    2480: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
    2481: @*/
    2482: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2483: {
    2484:   PetscFunctionBegin;
    2485:   PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
    2486:   PetscFunctionReturn(PETSC_SUCCESS);
    2487: }

    2489: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    2490: {
    2491:   const PetscScalar *array;
    2492:   PetscScalar       *coords = NULL;
    2493:   PetscInt           numCoords;
    2494:   PetscBool          isDG;
    2495:   PetscQuadrature    feQuad;
    2496:   const PetscReal   *quadPoints;
    2497:   PetscTabulation    T;
    2498:   PetscInt           dim, cdim, pdim, qdim, Nq, q;

    2500:   PetscFunctionBegin;
    2501:   PetscCall(DMGetDimension(dm, &dim));
    2502:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2503:   PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
    2504:   if (!quad) { /* use the first point of the first functional of the dual space */
    2505:     PetscDualSpace dsp;

    2507:     PetscCall(PetscFEGetDualSpace(fe, &dsp));
    2508:     PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
    2509:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
    2510:     Nq = 1;
    2511:   } else {
    2512:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
    2513:   }
    2514:   PetscCall(PetscFEGetDimension(fe, &pdim));
    2515:   PetscCall(PetscFEGetQuadrature(fe, &feQuad));
    2516:   if (feQuad == quad) {
    2517:     PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
    2518:     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);
    2519:   } else {
    2520:     PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
    2521:   }
    2522:   PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
    2523:   {
    2524:     const PetscReal *basis    = T->T[0];
    2525:     const PetscReal *basisDer = T->T[1];
    2526:     PetscReal        detJt;

    2528:     PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
    2529:     PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
    2530:     PetscAssert(cdim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->Nc);
    2531:     PetscAssert(dim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->cdim);
    2532:     if (v) {
    2533:       PetscCall(PetscArrayzero(v, Nq * cdim));
    2534:       for (q = 0; q < Nq; ++q) {
    2535:         PetscInt i, k;

    2537:         for (k = 0; k < pdim; ++k) {
    2538:           const PetscInt vertex = k / cdim;
    2539:           for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
    2540:         }
    2541:         PetscCall(PetscLogFlops(2.0 * pdim * cdim));
    2542:       }
    2543:     }
    2544:     if (J) {
    2545:       PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
    2546:       for (q = 0; q < Nq; ++q) {
    2547:         PetscInt i, j, k, c, r;

    2549:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    2550:         for (k = 0; k < pdim; ++k) {
    2551:           const PetscInt vertex = k / cdim;
    2552:           for (j = 0; j < dim; ++j) {
    2553:             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]);
    2554:           }
    2555:         }
    2556:         PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
    2557:         if (cdim > dim) {
    2558:           for (c = dim; c < cdim; ++c)
    2559:             for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
    2560:         }
    2561:         if (!detJ && !invJ) continue;
    2562:         detJt = 0.;
    2563:         switch (cdim) {
    2564:         case 3:
    2565:           DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
    2566:           if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
    2567:           break;
    2568:         case 2:
    2569:           DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
    2570:           if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
    2571:           break;
    2572:         case 1:
    2573:           detJt = J[q * cdim * dim];
    2574:           if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
    2575:         }
    2576:         if (detJ) detJ[q] = detJt;
    2577:       }
    2578:     } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
    2579:   }
    2580:   if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
    2581:   PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
    2582:   PetscFunctionReturn(PETSC_SUCCESS);
    2583: }

    2585: /*@C
    2586:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    2588:   Collective

    2590:   Input Parameters:
    2591: + dm   - the `DMPLEX`
    2592: . cell - the cell
    2593: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If `quad` is `NULL`, geometry will be
    2594:          evaluated at the first vertex of the reference element

    2596:   Output Parameters:
    2597: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element. This is a
    2598:          one-dimensional array of size $cdim * Nq$ where $cdim$ is the dimension of the `DM` coordinate space and $Nq$ is the number of quadrature points
    2599: . J    - the Jacobian of the transform from the reference element at each quadrature point. This is a one-dimensional array of size $Nq * cdim * cdim$ containing
    2600:          each Jacobian in column-major order.
    2601: . invJ - the inverse of the Jacobian at each quadrature point. This is a one-dimensional array of size $Nq * cdim * cdim$ containing
    2602:          each inverse Jacobian in column-major order.
    2603: - detJ - the Jacobian determinant at each quadrature point. This is a one-dimensional array of size $Nq$.

    2605:   Level: advanced

    2607:   Note:
    2608:   Implicit cell geometry must be used when the topological mesh dimension is not equal to the coordinate dimension, for instance for embedded manifolds.

    2610: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
    2611: @*/
    2612: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal detJ[])
    2613: {
    2614:   DM       cdm;
    2615:   PetscFE  fe = NULL;
    2616:   PetscInt dim, cdim;

    2618:   PetscFunctionBegin;
    2619:   PetscAssertPointer(detJ, 7);
    2620:   PetscCall(DMGetDimension(dm, &dim));
    2621:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2622:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    2623:   if (cdm) {
    2624:     PetscClassId id;
    2625:     PetscInt     numFields;
    2626:     PetscDS      prob;
    2627:     PetscObject  disc;

    2629:     PetscCall(DMGetNumFields(cdm, &numFields));
    2630:     if (numFields) {
    2631:       PetscCall(DMGetDS(cdm, &prob));
    2632:       PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
    2633:       PetscCall(PetscObjectGetClassId(disc, &id));
    2634:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
    2635:     }
    2636:   }
    2637:   if (!fe || (dim != cdim)) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
    2638:   else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
    2639:   PetscFunctionReturn(PETSC_SUCCESS);
    2640: }

    2642: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2643: {
    2644:   PetscSection       coordSection;
    2645:   Vec                coordinates;
    2646:   const PetscScalar *coords = NULL;
    2647:   PetscInt           d, dof, off;

    2649:   PetscFunctionBegin;
    2650:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    2651:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
    2652:   PetscCall(VecGetArrayRead(coordinates, &coords));

    2654:   /* for a point the centroid is just the coord */
    2655:   if (centroid) {
    2656:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
    2657:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
    2658:     for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
    2659:   }
    2660:   if (normal) {
    2661:     const PetscInt *support, *cones;
    2662:     PetscInt        supportSize;
    2663:     PetscReal       norm, sign;

    2665:     /* compute the norm based upon the support centroids */
    2666:     PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
    2667:     PetscCall(DMPlexGetSupport(dm, cell, &support));
    2668:     PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));

    2670:     /* Take the normal from the centroid of the support to the vertex*/
    2671:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
    2672:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
    2673:     for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);

    2675:     /* Determine the sign of the normal based upon its location in the support */
    2676:     PetscCall(DMPlexGetCone(dm, support[0], &cones));
    2677:     sign = cones[0] == cell ? 1.0 : -1.0;

    2679:     norm = DMPlex_NormD_Internal(dim, normal);
    2680:     for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
    2681:   }
    2682:   if (vol) *vol = 1.0;
    2683:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
    2684:   PetscFunctionReturn(PETSC_SUCCESS);
    2685: }

    2687: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2688: {
    2689:   const PetscScalar *array;
    2690:   PetscScalar       *coords = NULL;
    2691:   PetscInt           cdim, coordSize, d;
    2692:   PetscBool          isDG;

    2694:   PetscFunctionBegin;
    2695:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2696:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2697:   PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
    2698:   if (centroid) {
    2699:     for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
    2700:   }
    2701:   if (normal) {
    2702:     PetscReal norm;

    2704:     switch (cdim) {
    2705:     case 3:
    2706:       normal[2] = 0.; /* fall through */
    2707:     case 2:
    2708:       normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
    2709:       normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
    2710:       break;
    2711:     case 1:
    2712:       normal[0] = 1.0;
    2713:       break;
    2714:     default:
    2715:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
    2716:     }
    2717:     norm = DMPlex_NormD_Internal(cdim, normal);
    2718:     for (d = 0; d < cdim; ++d) normal[d] /= norm;
    2719:   }
    2720:   if (vol) {
    2721:     *vol = 0.0;
    2722:     for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
    2723:     *vol = PetscSqrtReal(*vol);
    2724:   }
    2725:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2726:   PetscFunctionReturn(PETSC_SUCCESS);
    2727: }

    2729: /* Centroid_i = (\sum_n A_n Cn_i) / A */
    2730: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2731: {
    2732:   DMPolytopeType     ct;
    2733:   const PetscScalar *array;
    2734:   PetscScalar       *coords = NULL;
    2735:   PetscInt           coordSize;
    2736:   PetscBool          isDG;
    2737:   PetscInt           fv[4] = {0, 1, 2, 3};
    2738:   PetscInt           cdim, numCorners, p, d;

    2740:   PetscFunctionBegin;
    2741:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2742:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    2743:   switch (ct) {
    2744:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2745:     fv[2] = 3;
    2746:     fv[3] = 2;
    2747:     break;
    2748:   default:
    2749:     break;
    2750:   }
    2751:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2752:   PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
    2753:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2754:   {
    2755:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

    2757:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
    2758:     for (p = 0; p < numCorners - 2; ++p) {
    2759:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
    2760:       for (d = 0; d < cdim; d++) {
    2761:         e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
    2762:         e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
    2763:       }
    2764:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
    2765:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
    2766:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
    2767:       const PetscReal a  = PetscSqrtReal(dx * dx + dy * dy + dz * dz);

    2769:       n[0] += dx;
    2770:       n[1] += dy;
    2771:       n[2] += dz;
    2772:       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.;
    2773:     }
    2774:     norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
    2775:     // Allow zero volume cells
    2776:     if (norm != 0) {
    2777:       n[0] /= norm;
    2778:       n[1] /= norm;
    2779:       n[2] /= norm;
    2780:       c[0] /= norm;
    2781:       c[1] /= norm;
    2782:       c[2] /= norm;
    2783:     }
    2784:     if (vol) *vol = 0.5 * norm;
    2785:     if (centroid)
    2786:       for (d = 0; d < cdim; ++d) centroid[d] = c[d];
    2787:     if (normal)
    2788:       for (d = 0; d < cdim; ++d) normal[d] = n[d];
    2789:   }
    2790:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2791:   PetscFunctionReturn(PETSC_SUCCESS);
    2792: }

    2794: /* Centroid_i = (\sum_n V_n Cn_i) / V */
    2795: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2796: {
    2797:   DMPolytopeType        ct;
    2798:   const PetscScalar    *array;
    2799:   PetscScalar          *coords = NULL;
    2800:   PetscInt              coordSize;
    2801:   PetscBool             isDG;
    2802:   PetscReal             vsum      = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
    2803:   const PetscInt        order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
    2804:   const PetscInt       *cone, *faceSizes, *faces;
    2805:   const DMPolytopeType *faceTypes;
    2806:   PetscBool             isHybrid = PETSC_FALSE;
    2807:   PetscInt              numFaces, f, fOff = 0, p, d;

    2809:   PetscFunctionBegin;
    2810:   PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
    2811:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2812:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    2813:   switch (ct) {
    2814:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2815:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2816:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
    2817:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    2818:     isHybrid = PETSC_TRUE;
    2819:   default:
    2820:     break;
    2821:   }

    2823:   if (centroid)
    2824:     for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    2825:   PetscCall(DMPlexGetCone(dm, cell, &cone));

    2827:   // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
    2828:   PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
    2829:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2830:   for (f = 0; f < numFaces; ++f) {
    2831:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

    2833:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
    2834:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
    2835:     // so that all tetrahedra have positive volume.
    2836:     if (f == 0)
    2837:       for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
    2838:     switch (faceTypes[f]) {
    2839:     case DM_POLYTOPE_TRIANGLE:
    2840:       for (d = 0; d < dim; ++d) {
    2841:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
    2842:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
    2843:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
    2844:       }
    2845:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2846:       if (flip) vtmp = -vtmp;
    2847:       vsum += vtmp;
    2848:       if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
    2849:         for (d = 0; d < dim; ++d) {
    2850:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
    2851:         }
    2852:       }
    2853:       break;
    2854:     case DM_POLYTOPE_QUADRILATERAL:
    2855:     case DM_POLYTOPE_SEG_PRISM_TENSOR: {
    2856:       PetscInt fv[4] = {0, 1, 2, 3};

    2858:       /* Side faces for hybrid cells are stored as tensor products */
    2859:       if (isHybrid && f > 1) {
    2860:         fv[2] = 3;
    2861:         fv[3] = 2;
    2862:       }
    2863:       /* DO FOR PYRAMID */
    2864:       /* First tet */
    2865:       for (d = 0; d < dim; ++d) {
    2866:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
    2867:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
    2868:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
    2869:       }
    2870:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2871:       if (flip) vtmp = -vtmp;
    2872:       vsum += vtmp;
    2873:       if (centroid) {
    2874:         for (d = 0; d < dim; ++d) {
    2875:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
    2876:         }
    2877:       }
    2878:       /* Second tet */
    2879:       for (d = 0; d < dim; ++d) {
    2880:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
    2881:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
    2882:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
    2883:       }
    2884:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2885:       if (flip) vtmp = -vtmp;
    2886:       vsum += vtmp;
    2887:       if (centroid) {
    2888:         for (d = 0; d < dim; ++d) {
    2889:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
    2890:         }
    2891:       }
    2892:       break;
    2893:     }
    2894:     default:
    2895:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
    2896:     }
    2897:     fOff += faceSizes[f];
    2898:   }
    2899:   PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
    2900:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
    2901:   if (vol) *vol = PetscAbsReal(vsum);
    2902:   if (normal)
    2903:     for (d = 0; d < dim; ++d) normal[d] = 0.0;
    2904:   if (centroid)
    2905:     for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
    2906:   PetscFunctionReturn(PETSC_SUCCESS);
    2907: }

    2909: /*@C
    2910:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    2912:   Collective

    2914:   Input Parameters:
    2915: + dm   - the `DMPLEX`
    2916: - cell - the cell

    2918:   Output Parameters:
    2919: + vol      - the cell volume
    2920: . centroid - the cell centroid
    2921: - normal   - the cell normal, if appropriate

    2923:   Level: advanced

    2925: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
    2926: @*/
    2927: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2928: {
    2929:   PetscInt depth, dim;

    2931:   PetscFunctionBegin;
    2932:   PetscCall(DMPlexGetDepth(dm, &depth));
    2933:   PetscCall(DMGetDimension(dm, &dim));
    2934:   PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
    2935:   PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
    2936:   switch (depth) {
    2937:   case 0:
    2938:     PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
    2939:     break;
    2940:   case 1:
    2941:     PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
    2942:     break;
    2943:   case 2:
    2944:     PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
    2945:     break;
    2946:   case 3:
    2947:     PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
    2948:     break;
    2949:   default:
    2950:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
    2951:   }
    2952:   PetscFunctionReturn(PETSC_SUCCESS);
    2953: }

    2955: /*@
    2956:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2958:   Input Parameter:
    2959: . dm - The `DMPLEX`

    2961:   Output Parameters:
    2962: + cellgeom - A `Vec` of `PetscFVCellGeom` data
    2963: - facegeom - A `Vec` of `PetscFVFaceGeom` data

    2965:   Level: developer

    2967: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
    2968: @*/
    2969: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2970: {
    2971:   DM           dmFace, dmCell;
    2972:   DMLabel      ghostLabel;
    2973:   PetscSection sectionFace, sectionCell;
    2974:   PetscSection coordSection;
    2975:   Vec          coordinates;
    2976:   PetscScalar *fgeom, *cgeom;
    2977:   PetscReal    minradius, gminradius;
    2978:   PetscInt     dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2980:   PetscFunctionBegin;
    2981:   PetscCall(DMGetDimension(dm, &dim));
    2982:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
    2983:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    2984:   /* Make cell centroids and volumes */
    2985:   PetscCall(DMClone(dm, &dmCell));
    2986:   PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
    2987:   PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
    2988:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell));
    2989:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    2990:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    2991:   PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
    2992:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
    2993:   PetscCall(PetscSectionSetUp(sectionCell));
    2994:   PetscCall(DMSetLocalSection(dmCell, sectionCell));
    2995:   PetscCall(PetscSectionDestroy(&sectionCell));
    2996:   PetscCall(DMCreateLocalVector(dmCell, cellgeom));
    2997:   if (cEndInterior < 0) cEndInterior = cEnd;
    2998:   PetscCall(VecGetArray(*cellgeom, &cgeom));
    2999:   for (c = cStart; c < cEndInterior; ++c) {
    3000:     PetscFVCellGeom *cg;

    3002:     PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
    3003:     PetscCall(PetscArrayzero(cg, 1));
    3004:     PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
    3005:   }
    3006:   /* Compute face normals and minimum cell radius */
    3007:   PetscCall(DMClone(dm, &dmFace));
    3008:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionFace));
    3009:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
    3010:   PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
    3011:   for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
    3012:   PetscCall(PetscSectionSetUp(sectionFace));
    3013:   PetscCall(DMSetLocalSection(dmFace, sectionFace));
    3014:   PetscCall(PetscSectionDestroy(&sectionFace));
    3015:   PetscCall(DMCreateLocalVector(dmFace, facegeom));
    3016:   PetscCall(VecGetArray(*facegeom, &fgeom));
    3017:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
    3018:   minradius = PETSC_MAX_REAL;
    3019:   for (f = fStart; f < fEnd; ++f) {
    3020:     PetscFVFaceGeom *fg;
    3021:     PetscReal        area;
    3022:     const PetscInt  *cells;
    3023:     PetscInt         ncells, ghost = -1, d, numChildren;

    3025:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
    3026:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
    3027:     PetscCall(DMPlexGetSupport(dm, f, &cells));
    3028:     PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
    3029:     /* It is possible to get a face with no support when using partition overlap */
    3030:     if (!ncells || ghost >= 0 || numChildren) continue;
    3031:     PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
    3032:     PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
    3033:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    3034:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    3035:     {
    3036:       PetscFVCellGeom *cL, *cR;
    3037:       PetscReal       *lcentroid, *rcentroid;
    3038:       PetscReal        l[3], r[3], v[3];

    3040:       PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
    3041:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    3042:       if (ncells > 1) {
    3043:         PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
    3044:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    3045:       } else {
    3046:         rcentroid = fg->centroid;
    3047:       }
    3048:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
    3049:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
    3050:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    3051:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    3052:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    3053:       }
    3054:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    3055:         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]);
    3056:         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]);
    3057:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
    3058:       }
    3059:       if (cells[0] < cEndInterior) {
    3060:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    3061:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    3062:       }
    3063:       if (ncells > 1 && cells[1] < cEndInterior) {
    3064:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    3065:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    3066:       }
    3067:     }
    3068:   }
    3069:   PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
    3070:   PetscCall(DMPlexSetMinRadius(dm, gminradius));
    3071:   /* Compute centroids of ghost cells */
    3072:   for (c = cEndInterior; c < cEnd; ++c) {
    3073:     PetscFVFaceGeom *fg;
    3074:     const PetscInt  *cone, *support;
    3075:     PetscInt         coneSize, supportSize, s;

    3077:     PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
    3078:     PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
    3079:     PetscCall(DMPlexGetCone(dmCell, c, &cone));
    3080:     PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
    3081:     PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
    3082:     PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
    3083:     PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
    3084:     for (s = 0; s < 2; ++s) {
    3085:       /* Reflect ghost centroid across plane of face */
    3086:       if (support[s] == c) {
    3087:         PetscFVCellGeom *ci;
    3088:         PetscFVCellGeom *cg;
    3089:         PetscReal        c2f[3], a;

    3091:         PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
    3092:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    3093:         a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    3094:         PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
    3095:         DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
    3096:         cg->volume = ci->volume;
    3097:       }
    3098:     }
    3099:   }
    3100:   PetscCall(VecRestoreArray(*facegeom, &fgeom));
    3101:   PetscCall(VecRestoreArray(*cellgeom, &cgeom));
    3102:   PetscCall(DMDestroy(&dmCell));
    3103:   PetscCall(DMDestroy(&dmFace));
    3104:   PetscFunctionReturn(PETSC_SUCCESS);
    3105: }

    3107: /*@
    3108:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    3110:   Not Collective

    3112:   Input Parameter:
    3113: . dm - the `DMPLEX`

    3115:   Output Parameter:
    3116: . minradius - the minimum cell radius

    3118:   Level: developer

    3120: .seealso: `DMPLEX`, `DMGetCoordinates()`
    3121: @*/
    3122: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    3123: {
    3124:   PetscFunctionBegin;
    3126:   PetscAssertPointer(minradius, 2);
    3127:   *minradius = ((DM_Plex *)dm->data)->minradius;
    3128:   PetscFunctionReturn(PETSC_SUCCESS);
    3129: }

    3131: /*@
    3132:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    3134:   Logically Collective

    3136:   Input Parameters:
    3137: + dm        - the `DMPLEX`
    3138: - minradius - the minimum cell radius

    3140:   Level: developer

    3142: .seealso: `DMPLEX`, `DMSetCoordinates()`
    3143: @*/
    3144: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    3145: {
    3146:   PetscFunctionBegin;
    3148:   ((DM_Plex *)dm->data)->minradius = minradius;
    3149:   PetscFunctionReturn(PETSC_SUCCESS);
    3150: }

    3152: /*@C
    3153:   DMPlexGetCoordinateMap - Returns the function used to map coordinates of newly generated mesh points

    3155:   Not Collective

    3157:   Input Parameter:
    3158: . dm - the `DMPLEX`

    3160:   Output Parameter:
    3161: . coordFunc - the mapping function

    3163:   Level: developer

    3165:   Note:
    3166:   This function maps from the generated coordinate for the new point to the actual coordinate. Thus it is only practical for manifolds with a nice analytical definition that you can get to from any starting point, like a sphere,

    3168: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMPlexSetCoordinateMap()`, `PetscPointFn`
    3169: @*/
    3170: PetscErrorCode DMPlexGetCoordinateMap(DM dm, PetscPointFn **coordFunc)
    3171: {
    3172:   PetscFunctionBegin;
    3174:   PetscAssertPointer(coordFunc, 2);
    3175:   *coordFunc = ((DM_Plex *)dm->data)->coordFunc;
    3176:   PetscFunctionReturn(PETSC_SUCCESS);
    3177: }

    3179: /*@C
    3180:   DMPlexSetCoordinateMap - Sets the function used to map coordinates of newly generated mesh points

    3182:   Logically Collective

    3184:   Input Parameters:
    3185: + dm        - the `DMPLEX`
    3186: - coordFunc - the mapping function

    3188:   Level: developer

    3190:   Note:
    3191:   This function maps from the generated coordinate for the new point to the actual coordinate. Thus it is only practical for manifolds with a nice analytical definition that you can get to from any starting point, like a sphere,

    3193: .seealso: `DMPLEX`, `DMSetCoordinates()`, `DMPlexGetCoordinateMap()`, `PetscPointFn`
    3194: @*/
    3195: PetscErrorCode DMPlexSetCoordinateMap(DM dm, PetscPointFn *coordFunc)
    3196: {
    3197:   PetscFunctionBegin;
    3199:   ((DM_Plex *)dm->data)->coordFunc = coordFunc;
    3200:   PetscFunctionReturn(PETSC_SUCCESS);
    3201: }

    3203: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    3204: {
    3205:   DMLabel      ghostLabel;
    3206:   PetscScalar *dx, *grad, **gref;
    3207:   PetscInt     dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    3209:   PetscFunctionBegin;
    3210:   PetscCall(DMGetDimension(dm, &dim));
    3211:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    3212:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    3213:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
    3214:   PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
    3215:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
    3216:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
    3217:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
    3218:   for (c = cStart; c < cEndInterior; c++) {
    3219:     const PetscInt  *faces;
    3220:     PetscInt         numFaces, usedFaces, f, d;
    3221:     PetscFVCellGeom *cg;
    3222:     PetscBool        boundary;
    3223:     PetscInt         ghost;

    3225:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
    3226:     PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
    3227:     if (ghost >= 0) continue;

    3229:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
    3230:     PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
    3231:     PetscCall(DMPlexGetCone(dm, c, &faces));
    3232:     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);
    3233:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    3234:       PetscFVCellGeom *cg1;
    3235:       PetscFVFaceGeom *fg;
    3236:       const PetscInt  *fcells;
    3237:       PetscInt         ncell, side;

    3239:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
    3240:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
    3241:       if ((ghost >= 0) || boundary) continue;
    3242:       PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
    3243:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    3244:       ncell = fcells[!side];    /* the neighbor */
    3245:       PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
    3246:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
    3247:       for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
    3248:       gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
    3249:     }
    3250:     PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
    3251:     PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
    3252:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    3253:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
    3254:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
    3255:       if ((ghost >= 0) || boundary) continue;
    3256:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
    3257:       ++usedFaces;
    3258:     }
    3259:   }
    3260:   PetscCall(PetscFree3(dx, grad, gref));
    3261:   PetscFunctionReturn(PETSC_SUCCESS);
    3262: }

    3264: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    3265: {
    3266:   DMLabel      ghostLabel;
    3267:   PetscScalar *dx, *grad, **gref;
    3268:   PetscInt     dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    3269:   PetscSection neighSec;
    3270:   PetscInt (*neighbors)[2];
    3271:   PetscInt *counter;

    3273:   PetscFunctionBegin;
    3274:   PetscCall(DMGetDimension(dm, &dim));
    3275:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    3276:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    3277:   if (cEndInterior < 0) cEndInterior = cEnd;
    3278:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
    3279:   PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
    3280:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
    3281:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
    3282:   for (f = fStart; f < fEnd; f++) {
    3283:     const PetscInt *fcells;
    3284:     PetscBool       boundary;
    3285:     PetscInt        ghost = -1;
    3286:     PetscInt        numChildren, numCells, c;

    3288:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
    3289:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
    3290:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
    3291:     if ((ghost >= 0) || boundary || numChildren) continue;
    3292:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
    3293:     if (numCells == 2) {
    3294:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
    3295:       for (c = 0; c < 2; c++) {
    3296:         PetscInt cell = fcells[c];

    3298:         if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
    3299:       }
    3300:     }
    3301:   }
    3302:   PetscCall(PetscSectionSetUp(neighSec));
    3303:   PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
    3304:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
    3305:   nStart = 0;
    3306:   PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
    3307:   PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
    3308:   PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
    3309:   for (f = fStart; f < fEnd; f++) {
    3310:     const PetscInt *fcells;
    3311:     PetscBool       boundary;
    3312:     PetscInt        ghost = -1;
    3313:     PetscInt        numChildren, numCells, c;

    3315:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
    3316:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
    3317:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
    3318:     if ((ghost >= 0) || boundary || numChildren) continue;
    3319:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
    3320:     if (numCells == 2) {
    3321:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
    3322:       for (c = 0; c < 2; c++) {
    3323:         PetscInt cell = fcells[c], off;

    3325:         if (cell >= cStart && cell < cEndInterior) {
    3326:           PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
    3327:           off += counter[cell - cStart]++;
    3328:           neighbors[off][0] = f;
    3329:           neighbors[off][1] = fcells[1 - c];
    3330:         }
    3331:       }
    3332:     }
    3333:   }
    3334:   PetscCall(PetscFree(counter));
    3335:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
    3336:   for (c = cStart; c < cEndInterior; c++) {
    3337:     PetscInt         numFaces, f, d, off, ghost = -1;
    3338:     PetscFVCellGeom *cg;

    3340:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
    3341:     PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
    3342:     PetscCall(PetscSectionGetOffset(neighSec, c, &off));

    3344:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
    3345:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
    3346:     if (ghost >= 0) continue;

    3348:     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);
    3349:     for (f = 0; f < numFaces; ++f) {
    3350:       PetscFVCellGeom *cg1;
    3351:       PetscFVFaceGeom *fg;
    3352:       const PetscInt  *fcells;
    3353:       PetscInt         ncell, side, nface;

    3355:       nface = neighbors[off + f][0];
    3356:       ncell = neighbors[off + f][1];
    3357:       PetscCall(DMPlexGetSupport(dm, nface, &fcells));
    3358:       side = (c != fcells[0]);
    3359:       PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
    3360:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
    3361:       for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
    3362:       gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
    3363:     }
    3364:     PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
    3365:     for (f = 0; f < numFaces; ++f) {
    3366:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
    3367:     }
    3368:   }
    3369:   PetscCall(PetscFree3(dx, grad, gref));
    3370:   PetscCall(PetscSectionDestroy(&neighSec));
    3371:   PetscCall(PetscFree(neighbors));
    3372:   PetscFunctionReturn(PETSC_SUCCESS);
    3373: }

    3375: /*@
    3376:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    3378:   Collective

    3380:   Input Parameters:
    3381: + dm           - The `DMPLEX`
    3382: . fvm          - The `PetscFV`
    3383: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`

    3385:   Input/Output Parameter:
    3386: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
    3387:                  the geometric factors for gradient calculation are inserted

    3389:   Output Parameter:
    3390: . dmGrad - The `DM` describing the layout of gradient data

    3392:   Level: developer

    3394: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
    3395: @*/
    3396: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    3397: {
    3398:   DM           dmFace, dmCell;
    3399:   PetscScalar *fgeom, *cgeom;
    3400:   PetscSection sectionGrad, parentSection;
    3401:   PetscInt     dim, pdim, cStart, cEnd, cEndInterior, c;

    3403:   PetscFunctionBegin;
    3404:   PetscCall(DMGetDimension(dm, &dim));
    3405:   PetscCall(PetscFVGetNumComponents(fvm, &pdim));
    3406:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    3407:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
    3408:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    3409:   PetscCall(VecGetDM(faceGeometry, &dmFace));
    3410:   PetscCall(VecGetDM(cellGeometry, &dmCell));
    3411:   PetscCall(VecGetArray(faceGeometry, &fgeom));
    3412:   PetscCall(VecGetArray(cellGeometry, &cgeom));
    3413:   PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
    3414:   if (!parentSection) {
    3415:     PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
    3416:   } else {
    3417:     PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
    3418:   }
    3419:   PetscCall(VecRestoreArray(faceGeometry, &fgeom));
    3420:   PetscCall(VecRestoreArray(cellGeometry, &cgeom));
    3421:   /* Create storage for gradients */
    3422:   PetscCall(DMClone(dm, dmGrad));
    3423:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionGrad));
    3424:   PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
    3425:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
    3426:   PetscCall(PetscSectionSetUp(sectionGrad));
    3427:   PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
    3428:   PetscCall(PetscSectionDestroy(&sectionGrad));
    3429:   PetscFunctionReturn(PETSC_SUCCESS);
    3430: }

    3432: /*@
    3433:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    3435:   Collective

    3437:   Input Parameters:
    3438: + dm - The `DM`
    3439: - fv - The `PetscFV`

    3441:   Output Parameters:
    3442: + cellgeom - The cell geometry
    3443: . facegeom - The face geometry
    3444: - gradDM   - The gradient matrices

    3446:   Level: developer

    3448: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
    3449: @*/
    3450: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    3451: {
    3452:   PetscObject cellgeomobj, facegeomobj;

    3454:   PetscFunctionBegin;
    3455:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
    3456:   if (!cellgeomobj) {
    3457:     Vec cellgeomInt, facegeomInt;

    3459:     PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
    3460:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
    3461:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
    3462:     PetscCall(VecDestroy(&cellgeomInt));
    3463:     PetscCall(VecDestroy(&facegeomInt));
    3464:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
    3465:   }
    3466:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
    3467:   if (cellgeom) *cellgeom = (Vec)cellgeomobj;
    3468:   if (facegeom) *facegeom = (Vec)facegeomobj;
    3469:   if (gradDM) {
    3470:     PetscObject gradobj;
    3471:     PetscBool   computeGradients;

    3473:     PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
    3474:     if (!computeGradients) {
    3475:       *gradDM = NULL;
    3476:       PetscFunctionReturn(PETSC_SUCCESS);
    3477:     }
    3478:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
    3479:     if (!gradobj) {
    3480:       DM dmGradInt;

    3482:       PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
    3483:       PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
    3484:       PetscCall(DMDestroy(&dmGradInt));
    3485:       PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
    3486:     }
    3487:     *gradDM = (DM)gradobj;
    3488:   }
    3489:   PetscFunctionReturn(PETSC_SUCCESS);
    3490: }

    3492: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
    3493: {
    3494:   PetscInt l, m;

    3496:   PetscFunctionBeginHot;
    3497:   if (dimC == dimR && dimR <= 3) {
    3498:     /* invert Jacobian, multiply */
    3499:     PetscScalar det, idet;

    3501:     switch (dimR) {
    3502:     case 1:
    3503:       invJ[0] = 1. / J[0];
    3504:       break;
    3505:     case 2:
    3506:       det     = J[0] * J[3] - J[1] * J[2];
    3507:       idet    = 1. / det;
    3508:       invJ[0] = J[3] * idet;
    3509:       invJ[1] = -J[1] * idet;
    3510:       invJ[2] = -J[2] * idet;
    3511:       invJ[3] = J[0] * idet;
    3512:       break;
    3513:     case 3: {
    3514:       invJ[0] = J[4] * J[8] - J[5] * J[7];
    3515:       invJ[1] = J[2] * J[7] - J[1] * J[8];
    3516:       invJ[2] = J[1] * J[5] - J[2] * J[4];
    3517:       det     = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    3518:       idet    = 1. / det;
    3519:       invJ[0] *= idet;
    3520:       invJ[1] *= idet;
    3521:       invJ[2] *= idet;
    3522:       invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
    3523:       invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
    3524:       invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
    3525:       invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
    3526:       invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
    3527:       invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
    3528:     } break;
    3529:     }
    3530:     for (l = 0; l < dimR; l++) {
    3531:       for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    3532:     }
    3533:   } else {
    3534:     char         transpose = PetscDefined(USE_COMPLEX) ? 'C' : 'T';
    3535:     PetscBLASInt m, n, one = 1, worksize, info;

    3537:     PetscCall(PetscBLASIntCast(dimR, &m));
    3538:     PetscCall(PetscBLASIntCast(dimC, &n));
    3539:     PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
    3540:     for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];

    3542:     PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
    3543:     PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS %" PetscBLASInt_FMT, info);

    3545:     for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
    3546:   }
    3547:   PetscFunctionReturn(PETSC_SUCCESS);
    3548: }

    3550: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    3551: {
    3552:   PetscInt     coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    3553:   PetscScalar *coordsScalar = NULL;
    3554:   PetscReal   *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    3555:   PetscScalar *J, *invJ, *work;

    3557:   PetscFunctionBegin;
    3559:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3560:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
    3561:   PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
    3562:   PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
    3563:   cellCoords = &cellData[0];
    3564:   cellCoeffs = &cellData[coordSize];
    3565:   extJ       = &cellData[2 * coordSize];
    3566:   resNeg     = &cellData[2 * coordSize + dimR];
    3567:   invJ       = &J[dimR * dimC];
    3568:   work       = &J[2 * dimR * dimC];
    3569:   if (dimR == 2) {
    3570:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    3572:     for (i = 0; i < 4; i++) {
    3573:       PetscInt plexI = zToPlex[i];

    3575:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3576:     }
    3577:   } else if (dimR == 3) {
    3578:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    3580:     for (i = 0; i < 8; i++) {
    3581:       PetscInt plexI = zToPlex[i];

    3583:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3584:     }
    3585:   } else {
    3586:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
    3587:   }
    3588:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    3589:   for (i = 0; i < dimR; i++) {
    3590:     PetscReal *swap;

    3592:     for (j = 0; j < (numV / 2); j++) {
    3593:       for (k = 0; k < dimC; k++) {
    3594:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    3595:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    3596:       }
    3597:     }

    3599:     if (i < dimR - 1) {
    3600:       swap       = cellCoeffs;
    3601:       cellCoeffs = cellCoords;
    3602:       cellCoords = swap;
    3603:     }
    3604:   }
    3605:   PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
    3606:   for (j = 0; j < numPoints; j++) {
    3607:     for (i = 0; i < maxIts; i++) {
    3608:       PetscReal *guess = &refCoords[dimR * j];

    3610:       /* compute -residual and Jacobian */
    3611:       for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
    3612:       for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
    3613:       for (k = 0; k < numV; k++) {
    3614:         PetscReal extCoord = 1.;
    3615:         for (l = 0; l < dimR; l++) {
    3616:           PetscReal coord = guess[l];
    3617:           PetscInt  dep   = (k & (1 << l)) >> l;

    3619:           extCoord *= dep * coord + !dep;
    3620:           extJ[l] = dep;

    3622:           for (m = 0; m < dimR; m++) {
    3623:             PetscReal coord = guess[m];
    3624:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    3625:             PetscReal mult  = dep * coord + !dep;

    3627:             extJ[l] *= mult;
    3628:           }
    3629:         }
    3630:         for (l = 0; l < dimC; l++) {
    3631:           PetscReal coeff = cellCoeffs[dimC * k + l];

    3633:           resNeg[l] -= coeff * extCoord;
    3634:           for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
    3635:         }
    3636:       }
    3637:       if (0 && PetscDefined(USE_DEBUG)) {
    3638:         PetscReal maxAbs = 0.;

    3640:         for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
    3641:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
    3642:       }

    3644:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
    3645:     }
    3646:   }
    3647:   PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
    3648:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
    3649:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3650:   PetscFunctionReturn(PETSC_SUCCESS);
    3651: }

    3653: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    3654: {
    3655:   PetscInt     coordSize, i, j, k, l, numV = (1 << dimR);
    3656:   PetscScalar *coordsScalar = NULL;
    3657:   PetscReal   *cellData, *cellCoords, *cellCoeffs;

    3659:   PetscFunctionBegin;
    3661:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3662:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
    3663:   PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
    3664:   cellCoords = &cellData[0];
    3665:   cellCoeffs = &cellData[coordSize];
    3666:   if (dimR == 2) {
    3667:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    3669:     for (i = 0; i < 4; i++) {
    3670:       PetscInt plexI = zToPlex[i];

    3672:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3673:     }
    3674:   } else if (dimR == 3) {
    3675:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    3677:     for (i = 0; i < 8; i++) {
    3678:       PetscInt plexI = zToPlex[i];

    3680:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    3681:     }
    3682:   } else {
    3683:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
    3684:   }
    3685:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    3686:   for (i = 0; i < dimR; i++) {
    3687:     PetscReal *swap;

    3689:     for (j = 0; j < (numV / 2); j++) {
    3690:       for (k = 0; k < dimC; k++) {
    3691:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    3692:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    3693:       }
    3694:     }

    3696:     if (i < dimR - 1) {
    3697:       swap       = cellCoeffs;
    3698:       cellCoeffs = cellCoords;
    3699:       cellCoords = swap;
    3700:     }
    3701:   }
    3702:   PETSC_PRAGMA_DIAGNOSTIC_IGNORED_BEGIN("-Warray-bounds")
    3703:   PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
    3704:   PETSC_PRAGMA_DIAGNOSTIC_IGNORED_END()
    3705:   for (j = 0; j < numPoints; j++) {
    3706:     const PetscReal *guess  = &refCoords[dimR * j];
    3707:     PetscReal       *mapped = &realCoords[dimC * j];

    3709:     for (k = 0; k < numV; k++) {
    3710:       PetscReal extCoord = 1.;
    3711:       for (l = 0; l < dimR; l++) {
    3712:         PetscReal coord = guess[l];
    3713:         PetscInt  dep   = (k & (1 << l)) >> l;

    3715:         extCoord *= dep * coord + !dep;
    3716:       }
    3717:       for (l = 0; l < dimC; l++) {
    3718:         PetscReal coeff = cellCoeffs[dimC * k + l];

    3720:         mapped[l] += coeff * extCoord;
    3721:       }
    3722:     }
    3723:   }
    3724:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
    3725:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
    3726:   PetscFunctionReturn(PETSC_SUCCESS);
    3727: }

    3729: PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR, PetscInt maxIter, PetscReal *tol)
    3730: {
    3731:   PetscInt     numComp, pdim, i, j, k, l, m, coordSize;
    3732:   PetscScalar *nodes = NULL;
    3733:   PetscReal   *invV, *modes;
    3734:   PetscReal   *B, *D, *resNeg;
    3735:   PetscScalar *J, *invJ, *work;
    3736:   PetscReal    tolerance = tol == NULL ? 0.0 : *tol;

    3738:   PetscFunctionBegin;
    3739:   PetscCall(PetscFEGetDimension(fe, &pdim));
    3740:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    3741:   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);
    3742:   /* we shouldn't apply inverse closure permutation, if one exists */
    3743:   PetscCall(DMPlexVecGetOrientedClosure(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
    3744:   /* convert nodes to values in the stable evaluation basis */
    3745:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
    3746:   invV = fe->invV;
    3747:   for (i = 0; i < pdim; ++i) {
    3748:     modes[i] = 0.;
    3749:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3750:   }
    3751:   PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
    3752:   D      = &B[pdim * Nc];
    3753:   resNeg = &D[pdim * Nc * dimR];
    3754:   PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
    3755:   invJ = &J[Nc * dimR];
    3756:   work = &invJ[Nc * dimR];
    3757:   for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
    3758:   for (j = 0; j < numPoints; j++) {
    3759:     PetscReal normPoint = DMPlex_NormD_Internal(Nc, &realCoords[j * Nc]);
    3760:     normPoint           = normPoint > PETSC_SMALL ? normPoint : 1.0;
    3761:     for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    3762:       PetscReal *guess = &refCoords[j * dimR], error = 0;
    3763:       PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
    3764:       for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
    3765:       for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
    3766:       for (k = 0; k < pdim; k++) {
    3767:         for (l = 0; l < Nc; l++) {
    3768:           resNeg[l] -= modes[k] * B[k * Nc + l];
    3769:           for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    3770:         }
    3771:       }
    3772:       if (0 && PetscDefined(USE_DEBUG)) {
    3773:         PetscReal maxAbs = 0.;

    3775:         for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
    3776:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
    3777:       }
    3778:       error = DMPlex_NormD_Internal(Nc, resNeg);
    3779:       if (error < tolerance * normPoint) {
    3780:         if (tol) *tol = error / normPoint;
    3781:         break;
    3782:       }
    3783:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
    3784:     }
    3785:   }
    3786:   PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
    3787:   PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
    3788:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
    3789:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
    3790:   PetscFunctionReturn(PETSC_SUCCESS);
    3791: }

    3793: /* TODO: TOBY please fix this for Nc > 1 */
    3794: PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    3795: {
    3796:   PetscInt     numComp, pdim, i, j, k, l, coordSize;
    3797:   PetscScalar *nodes = NULL;
    3798:   PetscReal   *invV, *modes;
    3799:   PetscReal   *B;

    3801:   PetscFunctionBegin;
    3802:   PetscCall(PetscFEGetDimension(fe, &pdim));
    3803:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    3804:   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);
    3805:   /* we shouldn't apply inverse closure permutation, if one exists */
    3806:   PetscCall(DMPlexVecGetOrientedClosure(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
    3807:   /* convert nodes to values in the stable evaluation basis */
    3808:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
    3809:   invV = fe->invV;
    3810:   for (i = 0; i < pdim; ++i) {
    3811:     modes[i] = 0.;
    3812:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3813:   }
    3814:   PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
    3815:   PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
    3816:   for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
    3817:   for (j = 0; j < numPoints; j++) {
    3818:     PetscReal *mapped = &realCoords[j * Nc];

    3820:     for (k = 0; k < pdim; k++) {
    3821:       for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    3822:     }
    3823:   }
    3824:   PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
    3825:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
    3826:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
    3827:   PetscFunctionReturn(PETSC_SUCCESS);
    3828: }

    3830: /*@
    3831:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
    3832:   using a single element map.

    3834:   Not Collective

    3836:   Input Parameters:
    3837: + dm         - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
    3838:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3839:                as a multilinear map for tensor-product elements
    3840: . cell       - the cell whose map is used.
    3841: . numPoints  - the number of points to locate
    3842: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

    3844:   Output Parameter:
    3845: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)

    3847:   Level: intermediate

    3849:   Notes:
    3850:   This inversion will be accurate inside the reference element, but may be inaccurate for
    3851:   mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)

    3853: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
    3854: @*/
    3855: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    3856: {
    3857:   PetscInt       dimC, dimR, depth, i, cellHeight, height;
    3858:   DMPolytopeType ct;
    3859:   DM             coordDM = NULL;
    3860:   Vec            coords;
    3861:   PetscFE        fe = NULL;

    3863:   PetscFunctionBegin;
    3865:   PetscCall(DMGetDimension(dm, &dimR));
    3866:   PetscCall(DMGetCoordinateDim(dm, &dimC));
    3867:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
    3868:   PetscCall(DMPlexGetDepth(dm, &depth));
    3869:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
    3870:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
    3871:   PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
    3872:   if (coordDM) {
    3873:     PetscInt coordFields;

    3875:     PetscCall(DMGetNumFields(coordDM, &coordFields));
    3876:     if (coordFields) {
    3877:       PetscClassId id;
    3878:       PetscObject  disc;

    3880:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
    3881:       PetscCall(PetscObjectGetClassId(disc, &id));
    3882:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
    3883:     }
    3884:   }
    3885:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    3886:   PetscCall(DMPlexGetPointHeight(dm, cell, &height));
    3887:   PetscCheck(height == cellHeight, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in a cell, height = %" PetscInt_FMT, cell, height);
    3888:   PetscCheck(!DMPolytopeTypeIsHybrid(ct) && ct != DM_POLYTOPE_FV_GHOST, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " is unsupported cell type %s", cell, DMPolytopeTypes[ct]);
    3889:   if (!fe) { /* implicit discretization: affine or multilinear */
    3890:     PetscInt  coneSize;
    3891:     PetscBool isSimplex, isTensor;

    3893:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
    3894:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3895:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3896:     if (isSimplex) {
    3897:       PetscReal detJ, *v0, *J, *invJ;

    3899:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3900:       J    = &v0[dimC];
    3901:       invJ = &J[dimC * dimC];
    3902:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
    3903:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    3904:         const PetscReal x0[3] = {-1., -1., -1.};

    3906:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    3907:       }
    3908:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3909:     } else if (isTensor) {
    3910:       PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
    3911:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
    3912:   } else {
    3913:     PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR, 7, NULL));
    3914:   }
    3915:   PetscFunctionReturn(PETSC_SUCCESS);
    3916: }

    3918: /*@
    3919:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.

    3921:   Not Collective

    3923:   Input Parameters:
    3924: + dm        - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
    3925:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3926:                as a multilinear map for tensor-product elements
    3927: . cell      - the cell whose map is used.
    3928: . numPoints - the number of points to locate
    3929: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)

    3931:   Output Parameter:
    3932: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

    3934:   Level: intermediate

    3936: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
    3937: @*/
    3938: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    3939: {
    3940:   PetscInt       dimC, dimR, depth, i, cellHeight, height;
    3941:   DMPolytopeType ct;
    3942:   DM             coordDM = NULL;
    3943:   Vec            coords;
    3944:   PetscFE        fe = NULL;

    3946:   PetscFunctionBegin;
    3948:   PetscCall(DMGetDimension(dm, &dimR));
    3949:   PetscCall(DMGetCoordinateDim(dm, &dimC));
    3950:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
    3951:   PetscCall(DMPlexGetDepth(dm, &depth));
    3952:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
    3953:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
    3954:   PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
    3955:   if (coordDM) {
    3956:     PetscInt coordFields;

    3958:     PetscCall(DMGetNumFields(coordDM, &coordFields));
    3959:     if (coordFields) {
    3960:       PetscClassId id;
    3961:       PetscObject  disc;

    3963:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
    3964:       PetscCall(PetscObjectGetClassId(disc, &id));
    3965:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
    3966:     }
    3967:   }
    3968:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
    3969:   PetscCall(DMPlexGetPointHeight(dm, cell, &height));
    3970:   PetscCheck(height == cellHeight, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in a cell, height = %" PetscInt_FMT, cell, height);
    3971:   PetscCheck(!DMPolytopeTypeIsHybrid(ct) && ct != DM_POLYTOPE_FV_GHOST, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " is unsupported cell type %s", cell, DMPolytopeTypes[ct]);
    3972:   if (!fe) { /* implicit discretization: affine or multilinear */
    3973:     PetscInt  coneSize;
    3974:     PetscBool isSimplex, isTensor;

    3976:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
    3977:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3978:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3979:     if (isSimplex) {
    3980:       PetscReal detJ, *v0, *J;

    3982:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3983:       J = &v0[dimC];
    3984:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
    3985:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3986:         const PetscReal xi0[3] = {-1., -1., -1.};

    3988:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3989:       }
    3990:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
    3991:     } else if (isTensor) {
    3992:       PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
    3993:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
    3994:   } else {
    3995:     PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
    3996:   }
    3997:   PetscFunctionReturn(PETSC_SUCCESS);
    3998: }

    4000: 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[])
    4001: {
    4002:   const PetscInt Nc = uOff[1] - uOff[0];
    4003:   PetscInt       c;

    4005:   for (c = 0; c < Nc; ++c) f0[c] = u[c];
    4006: }

    4008: /* Shear applies the transformation, assuming we fix z,
    4009:   / 1  0  m_0 \
    4010:   | 0  1  m_1 |
    4011:   \ 0  0   1  /
    4012: */
    4013: 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[])
    4014: {
    4015:   const PetscInt Nc = uOff[1] - uOff[0];
    4016:   const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
    4017:   PetscInt       c;

    4019:   for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
    4020: }

    4022: /* Flare applies the transformation, assuming we fix x_f,

    4024:    x_i = x_i * alpha_i x_f
    4025: */
    4026: 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[])
    4027: {
    4028:   const PetscInt Nc = uOff[1] - uOff[0];
    4029:   const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
    4030:   PetscInt       c;

    4032:   for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
    4033: }

    4035: /*
    4036:   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
    4037:   will correspond to the top and bottom of our square. So

    4039:     (0,0)--(1,0)  ==>  (1,0)--(2,0)      Just a shift of (1,0)
    4040:     (0,1)--(1,1)  ==>  (0,1)--(0,2)      Switch x and y

    4042:   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:

    4044:     (x, y)  ==>  (x+1, \pi/2 y)                           in (r', \theta') space
    4045:             ==>  ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
    4046: */
    4047: 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[])
    4048: {
    4049:   const PetscReal ri = PetscRealPart(constants[0]);
    4050:   const PetscReal ro = PetscRealPart(constants[1]);

    4052:   xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
    4053:   xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
    4054: }

    4056: /*
    4057:   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
    4058:   lower hemisphere and the upper surface onto the top, letting z be the radius.

    4060:     (x, y)  ==>  ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x)                                                  in (r', \theta', \phi') space
    4061:             ==>  ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
    4062: */
    4063: 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[])
    4064: {
    4065:   const PetscReal pi4    = PETSC_PI / 4.0;
    4066:   const PetscReal ri     = PetscRealPart(constants[0]);
    4067:   const PetscReal ro     = PetscRealPart(constants[1]);
    4068:   const PetscReal rp     = (x[2] + 1) * 0.5 * (ro - ri) + ri;
    4069:   const PetscReal phip   = PetscAtan2Real(x[1], x[0]);
    4070:   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])));

    4072:   xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
    4073:   xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
    4074:   xp[2] = rp * PetscSinReal(thetap);
    4075: }

    4077: void coordMap_sinusoid(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[])
    4078: {
    4079:   const PetscReal c = PetscRealPart(constants[0]);
    4080:   const PetscReal m = PetscRealPart(constants[1]);
    4081:   const PetscReal n = PetscRealPart(constants[2]);

    4083:   xp[0] = x[0];
    4084:   xp[1] = x[1];
    4085:   if (dim > 2) xp[2] = c * PetscCosReal(2. * m * PETSC_PI * x[0]) * PetscCosReal(2. * n * PETSC_PI * x[1]);
    4086: }

    4088: /*@C
    4089:   DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.

    4091:   Not Collective

    4093:   Input Parameters:
    4094: + dm   - The `DM`
    4095: . time - The time
    4096: - func - The function transforming current coordinates to new coordinates

    4098:   Calling sequence of `func`:
    4099: + dim          - The spatial dimension
    4100: . Nf           - The number of input fields (here 1)
    4101: . NfAux        - The number of input auxiliary fields
    4102: . uOff         - The offset of the coordinates in u[] (here 0)
    4103: . uOff_x       - The offset of the coordinates in u_x[] (here 0)
    4104: . u            - The coordinate values at this point in space
    4105: . u_t          - The coordinate time derivative at this point in space (here `NULL`)
    4106: . u_x          - The coordinate derivatives at this point in space
    4107: . aOff         - The offset of each auxiliary field in u[]
    4108: . aOff_x       - The offset of each auxiliary field in u_x[]
    4109: . a            - The auxiliary field values at this point in space
    4110: . a_t          - The auxiliary field time derivative at this point in space (or `NULL`)
    4111: . a_x          - The auxiliary field derivatives at this point in space
    4112: . t            - The current time
    4113: . x            - The coordinates of this point (here not used)
    4114: . numConstants - The number of constants
    4115: . constants    - The value of each constant
    4116: - f            - The new coordinates at this point in space

    4118:   Level: intermediate

    4120: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
    4121: @*/
    4122: 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[]))
    4123: {
    4124:   DM           cdm;
    4125:   PetscDS      cds;
    4126:   DMField      cf;
    4127:   PetscObject  obj;
    4128:   PetscClassId id;
    4129:   Vec          lCoords, tmpCoords;

    4131:   PetscFunctionBegin;
    4132:   if (!func) PetscCall(DMPlexGetCoordinateMap(dm, &func));
    4133:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    4134:   PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
    4135:   PetscCall(DMGetDS(cdm, &cds));
    4136:   PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
    4137:   PetscCall(PetscObjectGetClassId(obj, &id));
    4138:   if (id != PETSCFE_CLASSID) {
    4139:     PetscSection       cSection;
    4140:     const PetscScalar *constants;
    4141:     PetscScalar       *coords, f[16];
    4142:     PetscInt           dim, cdim, Nc, vStart, vEnd;

    4144:     PetscCall(DMGetDimension(dm, &dim));
    4145:     PetscCall(DMGetCoordinateDim(dm, &cdim));
    4146:     PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
    4147:     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    4148:     PetscCall(DMGetCoordinateSection(dm, &cSection));
    4149:     PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
    4150:     PetscCall(VecGetArrayWrite(lCoords, &coords));
    4151:     for (PetscInt v = vStart; v < vEnd; ++v) {
    4152:       PetscInt uOff[2] = {0, cdim};
    4153:       PetscInt off, c;

    4155:       PetscCall(PetscSectionGetOffset(cSection, v, &off));
    4156:       (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
    4157:       for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
    4158:     }
    4159:     PetscCall(VecRestoreArrayWrite(lCoords, &coords));
    4160:   } else {
    4161:     PetscCall(DMGetLocalVector(cdm, &tmpCoords));
    4162:     PetscCall(VecCopy(lCoords, tmpCoords));
    4163:     /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
    4164:     PetscCall(DMGetCoordinateField(dm, &cf));
    4165:     cdm->coordinates[0].field = cf;
    4166:     PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
    4167:     cdm->coordinates[0].field = NULL;
    4168:     PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
    4169:     PetscCall(DMSetCoordinatesLocal(dm, lCoords));
    4170:   }
    4171:   PetscFunctionReturn(PETSC_SUCCESS);
    4172: }

    4174: /*@
    4175:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

    4177:   Not Collective

    4179:   Input Parameters:
    4180: + dm          - The `DMPLEX`
    4181: . direction   - The shear coordinate direction, e.g. `DM_X` is the x-axis
    4182: - multipliers - The multiplier m for each direction which is not the shear direction

    4184:   Level: intermediate

    4186: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
    4187: @*/
    4188: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
    4189: {
    4190:   DM             cdm;
    4191:   PetscDS        cds;
    4192:   PetscScalar   *moduli;
    4193:   const PetscInt dir = (PetscInt)direction;
    4194:   PetscInt       dE, d, e;

    4196:   PetscFunctionBegin;
    4197:   PetscCall(DMGetCoordinateDM(dm, &cdm));
    4198:   PetscCall(DMGetCoordinateDim(dm, &dE));
    4199:   PetscCall(PetscMalloc1(dE + 1, &moduli));
    4200:   moduli[0] = dir;
    4201:   for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
    4202:   PetscCall(DMGetDS(cdm, &cds));
    4203:   PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
    4204:   PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
    4205:   PetscCall(PetscFree(moduli));
    4206:   PetscFunctionReturn(PETSC_SUCCESS);
    4207: }