Date: 2022-03-04T17:38:27+00:00

Actual source code: plexgeometry.c

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

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

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

     11:   Input Parameters:
     12: + dm - The DMPlex object
     13: . npoints - The number of sought points
     14: . coords - The array of coordinates of the sought points
     15: - eps - The tolerance or PETSC_DEFAULT

     17:   Output Parameters:
     18: . dagPoints - The array of found DAG points, or -1 if not found

     20:   Level: intermediate

     22:   Notes:
     23:   The length of the array coords must be npoints * dim where dim is the spatial dimension returned by DMGetDimension().

     25:   The output array dagPoints is NOT newly allocated; the user must pass an array of length npoints.

     27:   Each rank does the search independently; a nonnegative value is returned only if this rank's local DMPlex portion contains the point.

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

     31:   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.

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

     44:   if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
     45:   DMGetCoordinateDim(dm, &cdim);
     46:   DMGetCoordinatesLocal(dm, &allCoordsVec);
     47:   VecGetArrayRead(allCoordsVec, &allCoords);
     48:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
     49:   if (PetscDefined(USE_DEBUG)) {
     50:     /* check coordinate section is consistent with DM dimension */
     51:     PetscSection      cs;
     52:     PetscInt          ndof;

     54:     DMGetCoordinateSection(dm, &cs);
     55:     for (p = vStart; p < vEnd; p++) {
     56:       PetscSectionGetDof(cs, p, &ndof);
     57:       if (PetscUnlikely(ndof != cdim)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %D: ndof = %D != %D = cdim", p, ndof, cdim);
     58:     }
     59:   }
     60:   if (eps == 0.0) {
     61:     for (i=0,j=0; i < npoints; i++,j+=cdim) {
     62:       dagPoints[i] = -1;
     63:       for (p = vStart,o=0; p < vEnd; p++,o+=cdim) {
     64:         for (c = 0; c < cdim; c++) {
     65:           if (coord[j+c] != PetscRealPart(allCoords[o+c])) break;
     66:         }
     67:         if (c == cdim) {
     68:           dagPoints[i] = p;
     69:           break;
     70:         }
     71:       }
     72:     }
     73:     VecRestoreArrayRead(allCoordsVec, &allCoords);
     74:     return(0);
     75:   }
     76:   for (i=0,j=0; i < npoints; i++,j+=cdim) {
     77:     dagPoints[i] = -1;
     78:     for (p = vStart,o=0; p < vEnd; p++,o+=cdim) {
     79:       norm = 0.0;
     80:       for (c = 0; c < cdim; c++) {
     81:         norm += PetscSqr(coord[j+c] - PetscRealPart(allCoords[o+c]));
     82:       }
     83:       norm = PetscSqrtReal(norm);
     84:       if (norm <= eps) {
     85:         dagPoints[i] = p;
     86:         break;
     87:       }
     88:     }
     89:   }
     90:   VecRestoreArrayRead(allCoordsVec, &allCoords);
     91:   return(0);
     92: }

     94: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
     95: {
     96:   const PetscReal p0_x  = segmentA[0*2+0];
     97:   const PetscReal p0_y  = segmentA[0*2+1];
     98:   const PetscReal p1_x  = segmentA[1*2+0];
     99:   const PetscReal p1_y  = segmentA[1*2+1];
    100:   const PetscReal p2_x  = segmentB[0*2+0];
    101:   const PetscReal p2_y  = segmentB[0*2+1];
    102:   const PetscReal p3_x  = segmentB[1*2+0];
    103:   const PetscReal p3_y  = segmentB[1*2+1];
    104:   const PetscReal s1_x  = p1_x - p0_x;
    105:   const PetscReal s1_y  = p1_y - p0_y;
    106:   const PetscReal s2_x  = p3_x - p2_x;
    107:   const PetscReal s2_y  = p3_y - p2_y;
    108:   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);

    111:   *hasIntersection = PETSC_FALSE;
    112:   /* Non-parallel lines */
    113:   if (denom != 0.0) {
    114:     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
    115:     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;

    117:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
    118:       *hasIntersection = PETSC_TRUE;
    119:       if (intersection) {
    120:         intersection[0] = p0_x + (t * s1_x);
    121:         intersection[1] = p0_y + (t * s1_y);
    122:       }
    123:     }
    124:   }
    125:   return(0);
    126: }

    128: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
    129: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
    130: {
    131:   const PetscReal p0_x  = segmentA[0*3+0];
    132:   const PetscReal p0_y  = segmentA[0*3+1];
    133:   const PetscReal p0_z  = segmentA[0*3+2];
    134:   const PetscReal p1_x  = segmentA[1*3+0];
    135:   const PetscReal p1_y  = segmentA[1*3+1];
    136:   const PetscReal p1_z  = segmentA[1*3+2];
    137:   const PetscReal q0_x  = segmentB[0*3+0];
    138:   const PetscReal q0_y  = segmentB[0*3+1];
    139:   const PetscReal q0_z  = segmentB[0*3+2];
    140:   const PetscReal q1_x  = segmentB[1*3+0];
    141:   const PetscReal q1_y  = segmentB[1*3+1];
    142:   const PetscReal q1_z  = segmentB[1*3+2];
    143:   const PetscReal r0_x  = segmentC[0*3+0];
    144:   const PetscReal r0_y  = segmentC[0*3+1];
    145:   const PetscReal r0_z  = segmentC[0*3+2];
    146:   const PetscReal r1_x  = segmentC[1*3+0];
    147:   const PetscReal r1_y  = segmentC[1*3+1];
    148:   const PetscReal r1_z  = segmentC[1*3+2];
    149:   const PetscReal s0_x  = p1_x - p0_x;
    150:   const PetscReal s0_y  = p1_y - p0_y;
    151:   const PetscReal s0_z  = p1_z - p0_z;
    152:   const PetscReal s1_x  = q1_x - q0_x;
    153:   const PetscReal s1_y  = q1_y - q0_y;
    154:   const PetscReal s1_z  = q1_z - q0_z;
    155:   const PetscReal s2_x  = r1_x - r0_x;
    156:   const PetscReal s2_y  = r1_y - r0_y;
    157:   const PetscReal s2_z  = r1_z - r0_z;
    158:   const PetscReal s3_x  = s1_y*s2_z - s1_z*s2_y; /* s1 x s2 */
    159:   const PetscReal s3_y  = s1_z*s2_x - s1_x*s2_z;
    160:   const PetscReal s3_z  = s1_x*s2_y - s1_y*s2_x;
    161:   const PetscReal s4_x  = s0_y*s2_z - s0_z*s2_y; /* s0 x s2 */
    162:   const PetscReal s4_y  = s0_z*s2_x - s0_x*s2_z;
    163:   const PetscReal s4_z  = s0_x*s2_y - s0_y*s2_x;
    164:   const PetscReal s5_x  = s1_y*s0_z - s1_z*s0_y; /* s1 x s0 */
    165:   const PetscReal s5_y  = s1_z*s0_x - s1_x*s0_z;
    166:   const PetscReal s5_z  = s1_x*s0_y - s1_y*s0_x;
    167:   const PetscReal denom = -(s0_x*s3_x + s0_y*s3_y + s0_z*s3_z); /* -s0 . (s1 x s2) */

    170:   *hasIntersection = PETSC_FALSE;
    171:   /* Line not parallel to plane */
    172:   if (denom != 0.0) {
    173:     const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
    174:     const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
    175:     const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;

    177:     if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
    178:       *hasIntersection = PETSC_TRUE;
    179:       if (intersection) {
    180:         intersection[0] = p0_x + (t * s0_x);
    181:         intersection[1] = p0_y + (t * s0_y);
    182:         intersection[2] = p0_z + (t * s0_z);
    183:       }
    184:     }
    185:   }
    186:   return(0);
    187: }

    189: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    190: {
    191:   const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
    192:   const PetscReal x   = PetscRealPart(point[0]);
    193:   PetscReal       v0, J, invJ, detJ;
    194:   PetscReal       xi;
    195:   PetscErrorCode  ierr;

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

    201:   if ((xi >= -eps) && (xi <= 2.+eps)) *cell = c;
    202:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    203:   return(0);
    204: }

    206: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    207: {
    208:   const PetscInt  embedDim = 2;
    209:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    210:   PetscReal       x        = PetscRealPart(point[0]);
    211:   PetscReal       y        = PetscRealPart(point[1]);
    212:   PetscReal       v0[2], J[4], invJ[4], detJ;
    213:   PetscReal       xi, eta;
    214:   PetscErrorCode  ierr;

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

    221:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
    222:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    223:   return(0);
    224: }

    226: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
    227: {
    228:   const PetscInt  embedDim = 2;
    229:   PetscReal       x        = PetscRealPart(point[0]);
    230:   PetscReal       y        = PetscRealPart(point[1]);
    231:   PetscReal       v0[2], J[4], invJ[4], detJ;
    232:   PetscReal       xi, eta, r;
    233:   PetscErrorCode  ierr;

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

    240:   xi  = PetscMax(xi,  0.0);
    241:   eta = PetscMax(eta, 0.0);
    242:   if (xi + eta > 2.0) {
    243:     r    = (xi + eta)/2.0;
    244:     xi  /= r;
    245:     eta /= r;
    246:   }
    247:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
    248:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
    249:   return(0);
    250: }

    252: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    253: {
    254:   PetscSection       coordSection;
    255:   Vec             coordsLocal;
    256:   PetscScalar    *coords = NULL;
    257:   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
    258:   PetscReal       x         = PetscRealPart(point[0]);
    259:   PetscReal       y         = PetscRealPart(point[1]);
    260:   PetscInt        crossings = 0, f;
    261:   PetscErrorCode  ierr;

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

    284: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    285: {
    286:   const PetscInt  embedDim = 3;
    287:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    288:   PetscReal       v0[3], J[9], invJ[9], detJ;
    289:   PetscReal       x = PetscRealPart(point[0]);
    290:   PetscReal       y = PetscRealPart(point[1]);
    291:   PetscReal       z = PetscRealPart(point[2]);
    292:   PetscReal       xi, eta, zeta;
    293:   PetscErrorCode  ierr;

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

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

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

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

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

    344:     /* Check that projected point is in face (2D location problem) */
    345:     if (dot < 0.0) {
    346:       found = PETSC_FALSE;
    347:       break;
    348:     }
    349:   }
    350:   if (found) *cell = c;
    351:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    352:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    353:   return(0);
    354: }

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

    361:   box->dim = dim;
    362:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
    363:   return(0);
    364: }

    366: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    367: {

    371:   PetscMalloc1(1, box);
    372:   PetscGridHashInitialize_Internal(*box, dim, point);
    373:   return(0);
    374: }

    376: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
    377: {
    378:   PetscInt d;

    381:   for (d = 0; d < box->dim; ++d) {
    382:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    383:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    384:   }
    385:   return(0);
    386: }

    388: /*
    389:   PetscGridHashSetGrid - Divide the grid into boxes

    391:   Not collective

    393:   Input Parameters:
    394: + box - The grid hash object
    395: . n   - The number of boxes in each dimension, or PETSC_DETERMINE
    396: - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE

    398:   Level: developer

    400: .seealso: PetscGridHashCreate()
    401: */
    402: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
    403: {
    404:   PetscInt d;

    407:   for (d = 0; d < box->dim; ++d) {
    408:     box->extent[d] = box->upper[d] - box->lower[d];
    409:     if (n[d] == PETSC_DETERMINE) {
    410:       box->h[d] = h[d];
    411:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
    412:     } else {
    413:       box->n[d] = n[d];
    414:       box->h[d] = box->extent[d]/n[d];
    415:     }
    416:   }
    417:   return(0);
    418: }

    420: /*
    421:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

    423:   Not collective

    425:   Input Parameters:
    426: + box       - The grid hash object
    427: . numPoints - The number of input points
    428: - points    - The input point coordinates

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

    434:   Level: developer

    436: .seealso: PetscGridHashCreate()
    437: */
    438: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
    439: {
    440:   const PetscReal *lower = box->lower;
    441:   const PetscReal *upper = box->upper;
    442:   const PetscReal *h     = box->h;
    443:   const PetscInt  *n     = box->n;
    444:   const PetscInt   dim   = box->dim;
    445:   PetscInt         d, p;

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

    452:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    453:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
    454:       if (dbox < 0 || dbox >= n[d]) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %d (%g, %g, %g) is outside of our bounding box",
    455:                                              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);
    456:       dboxes[p*dim+d] = dbox;
    457:     }
    458:     if (boxes) for (d = dim-2, boxes[p] = dboxes[p*dim+dim-1]; d >= 0; --d) boxes[p] = boxes[p]*n[d] + dboxes[p*dim+d];
    459:   }
    460:   return(0);
    461: }

    463: /*
    464:  PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

    466:  Not collective

    468:   Input Parameters:
    469: + box       - The grid hash object
    470: . numPoints - The number of input points
    471: - points    - The input point coordinates

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

    478:   Level: developer

    480: .seealso: PetscGridHashGetEnclosingBox()
    481: */
    482: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[],PetscBool *found)
    483: {
    484:   const PetscReal *lower = box->lower;
    485:   const PetscReal *upper = box->upper;
    486:   const PetscReal *h     = box->h;
    487:   const PetscInt  *n     = box->n;
    488:   const PetscInt   dim   = box->dim;
    489:   PetscInt         d, p;

    492:   *found = PETSC_FALSE;
    493:   for (p = 0; p < numPoints; ++p) {
    494:     for (d = 0; d < dim; ++d) {
    495:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

    497:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    498:       if (dbox < 0 || dbox >= n[d]) {
    499:         return(0);
    500:       }
    501:       dboxes[p*dim+d] = dbox;
    502:     }
    503:     if (boxes) for (d = dim-2, boxes[p] = dboxes[p*dim+dim-1]; d >= 0; --d) boxes[p] = boxes[p]*n[d] + dboxes[p*dim+d];
    504:   }
    505:   *found = PETSC_TRUE;
    506:   return(0);
    507: }

    509: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    510: {

    514:   if (*box) {
    515:     PetscSectionDestroy(&(*box)->cellSection);
    516:     ISDestroy(&(*box)->cells);
    517:     DMLabelDestroy(&(*box)->cellsSparse);
    518:   }
    519:   PetscFree(*box);
    520:   return(0);
    521: }

    523: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
    524: {
    525:   DMPolytopeType ct;

    529:   DMPlexGetCellType(dm, cellStart, &ct);
    530:   switch (ct) {
    531:     case DM_POLYTOPE_SEGMENT:
    532:     DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell);break;
    533:     case DM_POLYTOPE_TRIANGLE:
    534:     DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);break;
    535:     case DM_POLYTOPE_QUADRILATERAL:
    536:     DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell);break;
    537:     case DM_POLYTOPE_TETRAHEDRON:
    538:     DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);break;
    539:     case DM_POLYTOPE_HEXAHEDRON:
    540:     DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);break;
    541:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %D with type %s", cellStart, DMPolytopeTypes[ct]);
    542:   }
    543:   return(0);
    544: }

    546: /*
    547:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
    548: */
    549: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
    550: {
    551:   DMPolytopeType ct;

    555:   DMPlexGetCellType(dm, cell, &ct);
    556:   switch (ct) {
    557:     case DM_POLYTOPE_TRIANGLE:
    558:     DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);break;
    559: #if 0
    560:     case DM_POLYTOPE_QUADRILATERAL:
    561:     DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);break;
    562:     case DM_POLYTOPE_TETRAHEDRON:
    563:     DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);break;
    564:     case DM_POLYTOPE_HEXAHEDRON:
    565:     DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);break;
    566: #endif
    567:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    568:   }
    569:   return(0);
    570: }

    572: /*
    573:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex

    575:   Collective on dm

    577:   Input Parameter:
    578: . dm - The Plex

    580:   Output Parameter:
    581: . localBox - The grid hash object

    583:   Level: developer

    585: .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
    586: */
    587: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
    588: {
    589:   const PetscInt     debug = 0;
    590:   MPI_Comm           comm;
    591:   PetscGridHash      lbox;
    592:   Vec                coordinates;
    593:   PetscSection       coordSection;
    594:   Vec                coordsLocal;
    595:   const PetscScalar *coords;
    596:   PetscScalar       *edgeCoords;
    597:   PetscInt          *dboxes, *boxes;
    598:   PetscInt           n[3] = {2, 2, 2};
    599:   PetscInt           dim, N, maxConeSize, cStart, cEnd, c, eStart, eEnd, i;
    600:   PetscBool          flg;
    601:   PetscErrorCode     ierr;

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

    643:     /* Get all edges in cell */
    644:     DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure);
    645:     for (cl = 0; cl < Ncl*2; ++cl) {
    646:       if ((closure[cl] >= eStart) && (closure[cl] < eEnd)) {
    647:         PetscScalar *ecoords = &edgeCoords[Ne*dim*2];
    648:         PetscInt     ecsize  = dim*2;

    650:         DMPlexVecGetClosure(dm, coordSection, coordsLocal, closure[cl], &ecsize, &ecoords);
    651:         if (ecsize != dim*2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Got %D coords for edge, instead of %D", ecsize, dim*2);
    652:         ++Ne;
    653:       }
    654:     }
    655:     DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure);
    656:     /* Find boxes enclosing each vertex */
    657:     DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);
    658:     PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);
    659:     /* Mark cells containing the vertices */
    660:     for (e = 0; e < csize/dim; ++e) {
    661:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "Cell %D has vertex in box %D (%D, %D, %D)\n", c, boxes[e], dboxes[e*dim+0], dim > 1 ? dboxes[e*dim+1] : -1, dim > 2 ? dboxes[e*dim+2] : -1);}
    662:       DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);
    663:     }
    664:     /* Get grid of boxes containing these */
    665:     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
    666:     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
    667:     for (e = 1; e < dim+1; ++e) {
    668:       for (d = 0; d < dim; ++d) {
    669:         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
    670:         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
    671:       }
    672:     }
    673:     /* Check for intersection of box with cell */
    674:     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
    675:       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
    676:         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
    677:           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
    678:           PetscScalar    cpoint[3];
    679:           PetscInt       cell, edge, ii, jj, kk;

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

    687:                 DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);
    688:                 if (cell >= 0) {
    689:                   if (debug) {PetscPrintf(PETSC_COMM_SELF, "  Cell %D contains vertex (%.2g, %.2g, %.2g) of box %D\n", c, cpoint[0], cpoint[1], cpoint[2], box);}
    690:                   DMLabelSetValue(lbox->cellsSparse, c, box);
    691:                   jj = kk = 2;
    692:                   break;
    693:                 }
    694:               }
    695:             }
    696:           }
    697:           /* Check whether cell edge intersects any face of these subboxes TODO vectorize this */
    698:           for (edge = 0; edge < Ne; ++edge) {
    699:             PetscReal segA[6] = {0.,0.,0.,0.,0.,0.};
    700:             PetscReal segB[6] = {0.,0.,0.,0.,0.,0.};
    701:             PetscReal segC[6] = {0.,0.,0.,0.,0.,0.};

    703:             if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected dim %d > 3",dim);
    704:             for (d = 0; d < dim*2; ++d) segA[d] = PetscRealPart(edgeCoords[edge*dim*2+d]);
    705:             /* 1D: (x) -- (x+h)               0 -- 1
    706:                2D: (x,   y)   -- (x,   y+h)   (0, 0) -- (0, 1)
    707:                    (x+h, y)   -- (x+h, y+h)   (1, 0) -- (1, 1)
    708:                    (x,   y)   -- (x+h, y)     (0, 0) -- (1, 0)
    709:                    (x,   y+h) -- (x+h, y+h)   (0, 1) -- (1, 1)
    710:                3D: (x,   y,   z)   -- (x,   y+h, z),   (x,   y,   z)   -- (x,   y,   z+h) (0, 0, 0) -- (0, 1, 0), (0, 0, 0) -- (0, 0, 1)
    711:                    (x+h, y,   z)   -- (x+h, y+h, z),   (x+h, y,   z)   -- (x+h, y,   z+h) (1, 0, 0) -- (1, 1, 0), (1, 0, 0) -- (1, 0, 1)
    712:                    (x,   y,   z)   -- (x+h, y,   z),   (x,   y,   z)   -- (x,   y,   z+h) (0, 0, 0) -- (1, 0, 0), (0, 0, 0) -- (0, 0, 1)
    713:                    (x,   y+h, z)   -- (x+h, y+h, z),   (x,   y+h, z)   -- (x,   y+h, z+h) (0, 1, 0) -- (1, 1, 0), (0, 1, 0) -- (0, 1, 1)
    714:                    (x,   y,   z)   -- (x+h, y,   z),   (x,   y,   z)   -- (x,   y+h, z)   (0, 0, 0) -- (1, 0, 0), (0, 0, 0) -- (0, 1, 0)
    715:                    (x,   y,   z+h) -- (x+h, y,   z+h), (x,   y,   z+h) -- (x,   y+h, z+h) (0, 0, 1) -- (1, 0, 1), (0, 0, 1) -- (0, 1, 1)
    716:              */
    717:             /* Loop over faces with normal in direction d */
    718:             for (d = 0; d < dim; ++d) {
    719:               PetscBool intersects = PETSC_FALSE;
    720:               PetscInt  e = (d+1)%dim;
    721:               PetscInt  f = (d+2)%dim;

    723:               /* There are two faces in each dimension */
    724:               for (ii = 0; ii < 2; ++ii) {
    725:                 segB[d]     = PetscRealPart(point[d] + ii*h[d]);
    726:                 segB[dim+d] = PetscRealPart(point[d] + ii*h[d]);
    727:                 segC[d]     = PetscRealPart(point[d] + ii*h[d]);
    728:                 segC[dim+d] = PetscRealPart(point[d] + ii*h[d]);
    729:                 if (dim > 1) {
    730:                   segB[e]     = PetscRealPart(point[e] + 0*h[e]);
    731:                   segB[dim+e] = PetscRealPart(point[e] + 1*h[e]);
    732:                   segC[e]     = PetscRealPart(point[e] + 0*h[e]);
    733:                   segC[dim+e] = PetscRealPart(point[e] + 0*h[e]);
    734:                 }
    735:                 if (dim > 2) {
    736:                   segB[f]     = PetscRealPart(point[f] + 0*h[f]);
    737:                   segB[dim+f] = PetscRealPart(point[f] + 0*h[f]);
    738:                   segC[f]     = PetscRealPart(point[f] + 0*h[f]);
    739:                   segC[dim+f] = PetscRealPart(point[f] + 1*h[f]);
    740:                 }
    741:                 if (dim == 2) {
    742:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
    743:                 } else if (dim == 3) {
    744:                   DMPlexGetLinePlaneIntersection_3D_Internal(segA, segB, segC, NULL, &intersects);
    745:                 }
    746:                 if (intersects) {
    747:                   if (debug) {PetscPrintf(PETSC_COMM_SELF, "  Cell %D edge %D (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g) intersects box %D, face (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g) (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g)\n", c, edge, segA[0], segA[1], segA[2], segA[3], segA[4], segA[5], box, segB[0], segB[1], segB[2], segB[3], segB[4], segB[5], segC[0], segC[1], segC[2], segC[3], segC[4], segC[5]);}
    748:                   DMLabelSetValue(lbox->cellsSparse, c, box); edge = Ne; break;
    749:                 }
    750:               }
    751:             }
    752:           }
    753:         }
    754:       }
    755:     }
    756:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
    757:   }
    758:   PetscFree3(dboxes, boxes, edgeCoords);
    759:   if (debug) {DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF);}
    760:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
    761:   DMLabelDestroy(&lbox->cellsSparse);
    762:   *localBox = lbox;
    763:   return(0);
    764: }

    766: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
    767: {
    768:   const PetscInt  debug = 0;
    769:   DM_Plex        *mesh = (DM_Plex *) dm->data;
    770:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
    771:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
    772:   PetscInt        dim, cStart, cEnd, numCells, c, d;
    773:   const PetscInt *boxCells;
    774:   PetscSFNode    *cells;
    775:   PetscScalar    *a;
    776:   PetscMPIInt     result;
    777:   PetscLogDouble  t0,t1;
    778:   PetscReal       gmin[3],gmax[3];
    779:   PetscInt        terminating_query_type[] = { 0, 0, 0 };
    780:   PetscErrorCode  ierr;

    783:   PetscLogEventBegin(DMPLEX_LocatePoints,0,0,0,0);
    784:   PetscTime(&t0);
    785:   if (ltype == DM_POINTLOCATION_NEAREST && !hash) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing. Use -dm_plex_hash_location to enable it.");
    786:   DMGetCoordinateDim(dm, &dim);
    787:   VecGetBlockSize(v, &bs);
    788:   MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);
    789:   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
    790:   if (bs != dim) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %D must be the mesh coordinate dimension %D", bs, dim);
    791:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    792:   VecGetLocalSize(v, &numPoints);
    793:   VecGetArray(v, &a);
    794:   numPoints /= bs;
    795:   {
    796:     const PetscSFNode *sf_cells;

    798:     PetscSFGetGraph(cellSF,NULL,NULL,NULL,&sf_cells);
    799:     if (sf_cells) {
    800:       PetscInfo(dm,"[DMLocatePoints_Plex] Re-using existing StarForest node list\n");
    801:       cells = (PetscSFNode*)sf_cells;
    802:       reuse = PETSC_TRUE;
    803:     } else {
    804:       PetscInfo(dm,"[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n");
    805:       PetscMalloc1(numPoints, &cells);
    806:       /* initialize cells if created */
    807:       for (p=0; p<numPoints; p++) {
    808:         cells[p].rank  = 0;
    809:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    810:       }
    811:     }
    812:   }
    813:   /* define domain bounding box */
    814:   {
    815:     Vec coorglobal;

    817:     DMGetCoordinates(dm,&coorglobal);
    818:     VecStrideMaxAll(coorglobal,NULL,gmax);
    819:     VecStrideMinAll(coorglobal,NULL,gmin);
    820:   }
    821:   if (hash) {
    822:     if (!mesh->lbox) {PetscInfo(dm, "Initializing grid hashing");DMPlexComputeGridHash_Internal(dm, &mesh->lbox);}
    823:     /* Designate the local box for each point */
    824:     /* Send points to correct process */
    825:     /* Search cells that lie in each subbox */
    826:     /*   Should we bin points before doing search? */
    827:     ISGetIndices(mesh->lbox->cells, &boxCells);
    828:   }
    829:   for (p = 0, numFound = 0; p < numPoints; ++p) {
    830:     const PetscScalar *point = &a[p*bs];
    831:     PetscInt           dbin[3] = {-1,-1,-1}, bin, cell = -1, cellOffset;
    832:     PetscBool          point_outside_domain = PETSC_FALSE;

    834:     /* check bounding box of domain */
    835:     for (d=0; d<dim; d++) {
    836:       if (PetscRealPart(point[d]) < gmin[d]) { point_outside_domain = PETSC_TRUE; break; }
    837:       if (PetscRealPart(point[d]) > gmax[d]) { point_outside_domain = PETSC_TRUE; break; }
    838:     }
    839:     if (point_outside_domain) {
    840:       cells[p].rank = 0;
    841:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    842:       terminating_query_type[0]++;
    843:       continue;
    844:     }

    846:     /* check initial values in cells[].index - abort early if found */
    847:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    848:       c = cells[p].index;
    849:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    850:       DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    851:       if (cell >= 0) {
    852:         cells[p].rank = 0;
    853:         cells[p].index = cell;
    854:         numFound++;
    855:       }
    856:     }
    857:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    858:       terminating_query_type[1]++;
    859:       continue;
    860:     }

    862:     if (hash) {
    863:       PetscBool found_box;

    865:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "Checking point %D (%.2g, %.2g, %.2g)\n", p, point[0], point[1], point[2]);}
    866:       /* allow for case that point is outside box - abort early */
    867:       PetscGridHashGetEnclosingBoxQuery(mesh->lbox, 1, point, dbin, &bin,&found_box);
    868:       if (found_box) {
    869:         if (debug) {PetscPrintf(PETSC_COMM_SELF, "  Found point in box %D (%D, %D, %D)\n", bin, dbin[0], dbin[1], dbin[2]);}
    870:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
    871:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    872:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    873:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    874:           if (debug) {PetscPrintf(PETSC_COMM_SELF, "    Checking for point in cell %D\n", boxCells[c]);}
    875:           DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);
    876:           if (cell >= 0) {
    877:             if (debug) {PetscPrintf(PETSC_COMM_SELF, "      FOUND in cell %D\n", cell);}
    878:             cells[p].rank = 0;
    879:             cells[p].index = cell;
    880:             numFound++;
    881:             terminating_query_type[2]++;
    882:             break;
    883:           }
    884:         }
    885:       }
    886:     } else {
    887:       for (c = cStart; c < cEnd; ++c) {
    888:         DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    889:         if (cell >= 0) {
    890:           cells[p].rank = 0;
    891:           cells[p].index = cell;
    892:           numFound++;
    893:           terminating_query_type[2]++;
    894:           break;
    895:         }
    896:       }
    897:     }
    898:   }
    899:   if (hash) {ISRestoreIndices(mesh->lbox->cells, &boxCells);}
    900:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
    901:     for (p = 0; p < numPoints; p++) {
    902:       const PetscScalar *point = &a[p*bs];
    903:       PetscReal          cpoint[3], diff[3], dist, distMax = PETSC_MAX_REAL;
    904:       PetscInt           dbin[3] = {-1,-1,-1}, bin, cellOffset, d;

    906:       if (cells[p].index < 0) {
    907:         ++numFound;
    908:         PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);
    909:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    910:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    911:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    912:           DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);
    913:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
    914:           dist = DMPlex_NormD_Internal(dim, diff);
    915:           if (dist < distMax) {
    916:             for (d = 0; d < dim; ++d) a[p*bs+d] = cpoint[d];
    917:             cells[p].rank  = 0;
    918:             cells[p].index = boxCells[c];
    919:             distMax = dist;
    920:             break;
    921:           }
    922:         }
    923:       }
    924:     }
    925:   }
    926:   /* This code is only be relevant when interfaced to parallel point location */
    927:   /* Check for highest numbered proc that claims a point (do we care?) */
    928:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
    929:     PetscMalloc1(numFound,&found);
    930:     for (p = 0, numFound = 0; p < numPoints; p++) {
    931:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
    932:         if (numFound < p) {
    933:           cells[numFound] = cells[p];
    934:         }
    935:         found[numFound++] = p;
    936:       }
    937:     }
    938:   }
    939:   VecRestoreArray(v, &a);
    940:   if (!reuse) {
    941:     PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);
    942:   }
    943:   PetscTime(&t1);
    944:   if (hash) {
    945:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside initial cell] : %D [hash]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
    946:   } else {
    947:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside initial cell] : %D [brute-force]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
    948:   }
    949:   PetscInfo3(dm,"[DMLocatePoints_Plex] npoints %D : time(rank0) %1.2e (sec): points/sec %1.4e\n",numPoints,t1-t0,(double)((double)numPoints/(t1-t0)));
    950:   PetscLogEventEnd(DMPLEX_LocatePoints,0,0,0,0);
    951:   return(0);
    952: }

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

    957:   Not collective

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

    962:   Output Parameter:
    963: . R - The rotation which accomplishes the projection

    965:   Level: developer

    967: .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
    968: @*/
    969: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
    970: {
    971:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
    972:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
    973:   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;

    976:   R[0] = c; R[1] = -s;
    977:   R[2] = s; R[3] =  c;
    978:   coords[0] = 0.0;
    979:   coords[1] = r;
    980:   return(0);
    981: }

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

    986:   Not collective

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

    991:   Output Parameter:
    992: . R - The rotation which accomplishes the projection

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

    996:   Level: developer

    998: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
    999: @*/
    1000: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
    1001: {
    1002:   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
    1003:   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
    1004:   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
    1005:   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
    1006:   PetscReal      rinv = 1. / r;

    1009:   x *= rinv; y *= rinv; z *= rinv;
    1010:   if (x > 0.) {
    1011:     PetscReal inv1pX   = 1./ (1. + x);

    1013:     R[0] = x; R[1] = -y;              R[2] = -z;
    1014:     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
    1015:     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
    1016:   }
    1017:   else {
    1018:     PetscReal inv1mX   = 1./ (1. - x);

    1020:     R[0] = x; R[1] = z;               R[2] = y;
    1021:     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
    1022:     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
    1023:   }
    1024:   coords[0] = 0.0;
    1025:   coords[1] = r;
    1026:   return(0);
    1027: }

    1029: /*@
    1030:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
    1031:     plane.  The normal is defined by positive orientation of the first 3 points.

    1033:   Not collective

    1035:   Input Parameter:
    1036: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

    1038:   Input/Output Parameter:
    1039: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
    1040:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

    1042:   Output Parameter:
    1043: . 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.

    1045:   Level: developer

    1047: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
    1048: @*/
    1049: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    1050: {
    1051:   PetscReal x1[3], x2[3], n[3], c[3], norm;
    1052:   const PetscInt dim = 3;
    1053:   PetscInt       d, p;

    1056:   /* 0) Calculate normal vector */
    1057:   for (d = 0; d < dim; ++d) {
    1058:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
    1059:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
    1060:   }
    1061:   // n = x1 \otimes x2
    1062:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
    1063:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
    1064:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
    1065:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    1066:   for (d = 0; d < dim; d++) n[d] /= norm;
    1067:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
    1068:   for (d = 0; d < dim; d++) x1[d] /= norm;
    1069:   // x2 = n \otimes x1
    1070:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
    1071:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
    1072:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
    1073:   for (d=0; d<dim; d++) {
    1074:     R[d * dim + 0] = x1[d];
    1075:     R[d * dim + 1] = x2[d];
    1076:     R[d * dim + 2] = n[d];
    1077:     c[d] = PetscRealPart(coords[0*dim + d]);
    1078:   }
    1079:   for (p=0; p<coordSize/dim; p++) {
    1080:     PetscReal y[3];
    1081:     for (d=0; d<dim; d++) y[d] = PetscRealPart(coords[p*dim + d]) - c[d];
    1082:     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];
    1083:   }
    1084:   return(0);
    1085: }

    1087: PETSC_UNUSED
    1088: PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    1089: {
    1090:   /* Signed volume is 1/2 the determinant

    1092:    |  1  1  1 |
    1093:    | x0 x1 x2 |
    1094:    | y0 y1 y2 |

    1096:      but if x0,y0 is the origin, we have

    1098:    | x1 x2 |
    1099:    | y1 y2 |
    1100:   */
    1101:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    1102:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    1103:   PetscReal       M[4], detM;
    1104:   M[0] = x1; M[1] = x2;
    1105:   M[2] = y1; M[3] = y2;
    1106:   DMPlex_Det2D_Internal(&detM, M);
    1107:   *vol = 0.5*detM;
    1108:   (void)PetscLogFlops(5.0);
    1109: }

    1111: PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1112: {
    1113:   DMPlex_Det2D_Internal(vol, coords);
    1114:   *vol *= 0.5;
    1115: }

    1117: PETSC_UNUSED
    1118: PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    1119: {
    1120:   /* Signed volume is 1/6th of the determinant

    1122:    |  1  1  1  1 |
    1123:    | x0 x1 x2 x3 |
    1124:    | y0 y1 y2 y3 |
    1125:    | z0 z1 z2 z3 |

    1127:      but if x0,y0,z0 is the origin, we have

    1129:    | x1 x2 x3 |
    1130:    | y1 y2 y3 |
    1131:    | z1 z2 z3 |
    1132:   */
    1133:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
    1134:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
    1135:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    1136:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1137:   PetscReal       M[9], detM;
    1138:   M[0] = x1; M[1] = x2; M[2] = x3;
    1139:   M[3] = y1; M[4] = y2; M[5] = y3;
    1140:   M[6] = z1; M[7] = z2; M[8] = z3;
    1141:   DMPlex_Det3D_Internal(&detM, M);
    1142:   *vol = -onesixth*detM;
    1143:   (void)PetscLogFlops(10.0);
    1144: }

    1146: PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1147: {
    1148:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1149:   DMPlex_Det3D_Internal(vol, coords);
    1150:   *vol *= -onesixth;
    1151: }

    1153: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1154: {
    1155:   PetscSection   coordSection;
    1156:   Vec            coordinates;
    1157:   const PetscScalar *coords;
    1158:   PetscInt       dim, d, off;

    1162:   DMGetCoordinatesLocal(dm, &coordinates);
    1163:   DMGetCoordinateSection(dm, &coordSection);
    1164:   PetscSectionGetDof(coordSection,e,&dim);
    1165:   if (!dim) return(0);
    1166:   PetscSectionGetOffset(coordSection,e,&off);
    1167:   VecGetArrayRead(coordinates,&coords);
    1168:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
    1169:   VecRestoreArrayRead(coordinates,&coords);
    1170:   *detJ = 1.;
    1171:   if (J) {
    1172:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1173:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1174:     if (invJ) {
    1175:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1176:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1177:     }
    1178:   }
    1179:   return(0);
    1180: }

    1182: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1183: {
    1184:   PetscSection   coordSection;
    1185:   Vec            coordinates;
    1186:   PetscScalar   *coords = NULL;
    1187:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

    1191:   DMGetCoordinatesLocal(dm, &coordinates);
    1192:   DMGetCoordinateSection(dm, &coordSection);
    1193:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1194:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1195:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1196:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1197:   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1198:   *detJ = 0.0;
    1199:   if (numCoords == 6) {
    1200:     const PetscInt dim = 3;
    1201:     PetscReal      R[9], J0;

    1203:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1204:     DMPlexComputeProjection3Dto1D(coords, R);
    1205:     if (J)    {
    1206:       J0   = 0.5*PetscRealPart(coords[1]);
    1207:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
    1208:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
    1209:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
    1210:       DMPlex_Det3D_Internal(detJ, J);
    1211:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1212:     }
    1213:   } else if (numCoords == 4) {
    1214:     const PetscInt dim = 2;
    1215:     PetscReal      R[4], J0;

    1217:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1218:     DMPlexComputeProjection2Dto1D(coords, R);
    1219:     if (J)    {
    1220:       J0   = 0.5*PetscRealPart(coords[1]);
    1221:       J[0] = R[0]*J0; J[1] = R[1];
    1222:       J[2] = R[2]*J0; J[3] = R[3];
    1223:       DMPlex_Det2D_Internal(detJ, J);
    1224:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1225:     }
    1226:   } else if (numCoords == 2) {
    1227:     const PetscInt dim = 1;

    1229:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1230:     if (J)    {
    1231:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1232:       *detJ = J[0];
    1233:       PetscLogFlops(2.0);
    1234:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
    1235:     }
    1236:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
    1237:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1238:   return(0);
    1239: }

    1241: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1242: {
    1243:   PetscSection   coordSection;
    1244:   Vec            coordinates;
    1245:   PetscScalar   *coords = NULL;
    1246:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1250:   DMGetCoordinatesLocal(dm, &coordinates);
    1251:   DMGetCoordinateSection(dm, &coordSection);
    1252:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1253:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1254:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1255:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1256:   *detJ = 0.0;
    1257:   if (numCoords == 9) {
    1258:     const PetscInt dim = 3;
    1259:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1261:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1262:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1263:     if (J)    {
    1264:       const PetscInt pdim = 2;

    1266:       for (d = 0; d < pdim; d++) {
    1267:         for (f = 0; f < pdim; f++) {
    1268:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1269:         }
    1270:       }
    1271:       PetscLogFlops(8.0);
    1272:       DMPlex_Det3D_Internal(detJ, J0);
    1273:       for (d = 0; d < dim; d++) {
    1274:         for (f = 0; f < dim; f++) {
    1275:           J[d*dim+f] = 0.0;
    1276:           for (g = 0; g < dim; g++) {
    1277:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1278:           }
    1279:         }
    1280:       }
    1281:       PetscLogFlops(18.0);
    1282:     }
    1283:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1284:   } else if (numCoords == 6) {
    1285:     const PetscInt dim = 2;

    1287:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1288:     if (J)    {
    1289:       for (d = 0; d < dim; d++) {
    1290:         for (f = 0; f < dim; f++) {
    1291:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1292:         }
    1293:       }
    1294:       PetscLogFlops(8.0);
    1295:       DMPlex_Det2D_Internal(detJ, J);
    1296:     }
    1297:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1298:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
    1299:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1300:   return(0);
    1301: }

    1303: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1304: {
    1305:   PetscSection   coordSection;
    1306:   Vec            coordinates;
    1307:   PetscScalar   *coords = NULL;
    1308:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1312:   DMGetCoordinatesLocal(dm, &coordinates);
    1313:   DMGetCoordinateSection(dm, &coordSection);
    1314:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1315:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1316:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1317:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1318:   if (!Nq) {
    1319:     PetscInt vorder[4] = {0, 1, 2, 3};

    1321:     if (isTensor) {vorder[2] = 3; vorder[3] = 2;}
    1322:     *detJ = 0.0;
    1323:     if (numCoords == 12) {
    1324:       const PetscInt dim = 3;
    1325:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1327:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1328:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1329:       if (J)    {
    1330:         const PetscInt pdim = 2;

    1332:         for (d = 0; d < pdim; d++) {
    1333:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*pdim+d]) - PetscRealPart(coords[vorder[0]*pdim+d]));
    1334:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[2]*pdim+d]) - PetscRealPart(coords[vorder[1]*pdim+d]));
    1335:         }
    1336:         PetscLogFlops(8.0);
    1337:         DMPlex_Det3D_Internal(detJ, J0);
    1338:         for (d = 0; d < dim; d++) {
    1339:           for (f = 0; f < dim; f++) {
    1340:             J[d*dim+f] = 0.0;
    1341:             for (g = 0; g < dim; g++) {
    1342:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1343:             }
    1344:           }
    1345:         }
    1346:         PetscLogFlops(18.0);
    1347:       }
    1348:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1349:     } else if (numCoords == 8) {
    1350:       const PetscInt dim = 2;

    1352:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1353:       if (J)    {
    1354:         for (d = 0; d < dim; d++) {
    1355:           J[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1356:           J[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[3]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1357:         }
    1358:         PetscLogFlops(8.0);
    1359:         DMPlex_Det2D_Internal(detJ, J);
    1360:       }
    1361:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1362:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1363:   } else {
    1364:     const PetscInt Nv = 4;
    1365:     const PetscInt dimR = 2;
    1366:     PetscInt  zToPlex[4] = {0, 1, 3, 2};
    1367:     PetscReal zOrder[12];
    1368:     PetscReal zCoeff[12];
    1369:     PetscInt  i, j, k, l, dim;

    1371:     if (isTensor) {zToPlex[2] = 2; zToPlex[3] = 3;}
    1372:     if (numCoords == 12) {
    1373:       dim = 3;
    1374:     } else if (numCoords == 8) {
    1375:       dim = 2;
    1376:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1377:     for (i = 0; i < Nv; i++) {
    1378:       PetscInt zi = zToPlex[i];

    1380:       for (j = 0; j < dim; j++) {
    1381:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1382:       }
    1383:     }
    1384:     for (j = 0; j < dim; j++) {
    1385:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1386:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1387:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1388:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1389:     }
    1390:     for (i = 0; i < Nq; i++) {
    1391:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    1393:       if (v) {
    1394:         PetscReal extPoint[4];

    1396:         extPoint[0] = 1.;
    1397:         extPoint[1] = xi;
    1398:         extPoint[2] = eta;
    1399:         extPoint[3] = xi * eta;
    1400:         for (j = 0; j < dim; j++) {
    1401:           PetscReal val = 0.;

    1403:           for (k = 0; k < Nv; k++) {
    1404:             val += extPoint[k] * zCoeff[dim * k + j];
    1405:           }
    1406:           v[i * dim + j] = val;
    1407:         }
    1408:       }
    1409:       if (J) {
    1410:         PetscReal extJ[8];

    1412:         extJ[0] = 0.;
    1413:         extJ[1] = 0.;
    1414:         extJ[2] = 1.;
    1415:         extJ[3] = 0.;
    1416:         extJ[4] = 0.;
    1417:         extJ[5] = 1.;
    1418:         extJ[6] = eta;
    1419:         extJ[7] = xi;
    1420:         for (j = 0; j < dim; j++) {
    1421:           for (k = 0; k < dimR; k++) {
    1422:             PetscReal val = 0.;

    1424:             for (l = 0; l < Nv; l++) {
    1425:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1426:             }
    1427:             J[i * dim * dim + dim * j + k] = val;
    1428:           }
    1429:         }
    1430:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    1431:           PetscReal x, y, z;
    1432:           PetscReal *iJ = &J[i * dim * dim];
    1433:           PetscReal norm;

    1435:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    1436:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    1437:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    1438:           norm = PetscSqrtReal(x * x + y * y + z * z);
    1439:           iJ[2] = x / norm;
    1440:           iJ[5] = y / norm;
    1441:           iJ[8] = z / norm;
    1442:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1443:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1444:         } else {
    1445:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    1446:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1447:         }
    1448:       }
    1449:     }
    1450:   }
    1451:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1452:   return(0);
    1453: }

    1455: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1456: {
    1457:   PetscSection   coordSection;
    1458:   Vec            coordinates;
    1459:   PetscScalar   *coords = NULL;
    1460:   const PetscInt dim = 3;
    1461:   PetscInt       d;

    1465:   DMGetCoordinatesLocal(dm, &coordinates);
    1466:   DMGetCoordinateSection(dm, &coordSection);
    1467:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1468:   *detJ = 0.0;
    1469:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1470:   if (J)    {
    1471:     for (d = 0; d < dim; d++) {
    1472:       /* I orient with outward face normals */
    1473:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1474:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1475:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1476:     }
    1477:     PetscLogFlops(18.0);
    1478:     DMPlex_Det3D_Internal(detJ, J);
    1479:   }
    1480:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1481:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1482:   return(0);
    1483: }

    1485: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1486: {
    1487:   PetscSection   coordSection;
    1488:   Vec            coordinates;
    1489:   PetscScalar   *coords = NULL;
    1490:   const PetscInt dim = 3;
    1491:   PetscInt       d;

    1495:   DMGetCoordinatesLocal(dm, &coordinates);
    1496:   DMGetCoordinateSection(dm, &coordSection);
    1497:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1498:   if (!Nq) {
    1499:     *detJ = 0.0;
    1500:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1501:     if (J)    {
    1502:       for (d = 0; d < dim; d++) {
    1503:         J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1504:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1505:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1506:       }
    1507:       PetscLogFlops(18.0);
    1508:       DMPlex_Det3D_Internal(detJ, J);
    1509:     }
    1510:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1511:   } else {
    1512:     const PetscInt Nv = 8;
    1513:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    1514:     const PetscInt dim = 3;
    1515:     const PetscInt dimR = 3;
    1516:     PetscReal zOrder[24];
    1517:     PetscReal zCoeff[24];
    1518:     PetscInt  i, j, k, l;

    1520:     for (i = 0; i < Nv; i++) {
    1521:       PetscInt zi = zToPlex[i];

    1523:       for (j = 0; j < dim; j++) {
    1524:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1525:       }
    1526:     }
    1527:     for (j = 0; j < dim; j++) {
    1528:       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]);
    1529:       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]);
    1530:       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]);
    1531:       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]);
    1532:       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]);
    1533:       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]);
    1534:       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]);
    1535:       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]);
    1536:     }
    1537:     for (i = 0; i < Nq; i++) {
    1538:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    1540:       if (v) {
    1541:         PetscReal extPoint[8];

    1543:         extPoint[0] = 1.;
    1544:         extPoint[1] = xi;
    1545:         extPoint[2] = eta;
    1546:         extPoint[3] = xi * eta;
    1547:         extPoint[4] = theta;
    1548:         extPoint[5] = theta * xi;
    1549:         extPoint[6] = theta * eta;
    1550:         extPoint[7] = theta * eta * xi;
    1551:         for (j = 0; j < dim; j++) {
    1552:           PetscReal val = 0.;

    1554:           for (k = 0; k < Nv; k++) {
    1555:             val += extPoint[k] * zCoeff[dim * k + j];
    1556:           }
    1557:           v[i * dim + j] = val;
    1558:         }
    1559:       }
    1560:       if (J) {
    1561:         PetscReal extJ[24];

    1563:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
    1564:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
    1565:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
    1566:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
    1567:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
    1568:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
    1569:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
    1570:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

    1572:         for (j = 0; j < dim; j++) {
    1573:           for (k = 0; k < dimR; k++) {
    1574:             PetscReal val = 0.;

    1576:             for (l = 0; l < Nv; l++) {
    1577:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1578:             }
    1579:             J[i * dim * dim + dim * j + k] = val;
    1580:           }
    1581:         }
    1582:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1583:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1584:       }
    1585:     }
    1586:   }
    1587:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1588:   return(0);
    1589: }

    1591: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1592: {
    1593:   DMPolytopeType  ct;
    1594:   PetscInt        depth, dim, coordDim, coneSize, i;
    1595:   PetscInt        Nq = 0;
    1596:   const PetscReal *points = NULL;
    1597:   DMLabel         depthLabel;
    1598:   PetscReal       xi0[3] = {-1.,-1.,-1.}, v0[3], J0[9], detJ0;
    1599:   PetscBool       isAffine = PETSC_TRUE;
    1600:   PetscErrorCode  ierr;

    1603:   DMPlexGetDepth(dm, &depth);
    1604:   DMPlexGetConeSize(dm, cell, &coneSize);
    1605:   DMPlexGetDepthLabel(dm, &depthLabel);
    1606:   DMLabelGetValue(depthLabel, cell, &dim);
    1607:   if (depth == 1 && dim == 1) {
    1608:     DMGetDimension(dm, &dim);
    1609:   }
    1610:   DMGetCoordinateDim(dm, &coordDim);
    1611:   if (coordDim > 3) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %D > 3", coordDim);
    1612:   if (quad) {PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);}
    1613:   DMPlexGetCellType(dm, cell, &ct);
    1614:   switch (ct) {
    1615:     case DM_POLYTOPE_POINT:
    1616:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1617:     isAffine = PETSC_FALSE;
    1618:     break;
    1619:     case DM_POLYTOPE_SEGMENT:
    1620:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1621:     if (Nq) {DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1622:     else    {DMPlexComputeLineGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1623:     break;
    1624:     case DM_POLYTOPE_TRIANGLE:
    1625:     if (Nq) {DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1626:     else    {DMPlexComputeTriangleGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1627:     break;
    1628:     case DM_POLYTOPE_QUADRILATERAL:
    1629:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ);
    1630:     isAffine = PETSC_FALSE;
    1631:     break;
    1632:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1633:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ);
    1634:     isAffine = PETSC_FALSE;
    1635:     break;
    1636:     case DM_POLYTOPE_TETRAHEDRON:
    1637:     if (Nq) {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1638:     else    {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1639:     break;
    1640:     case DM_POLYTOPE_HEXAHEDRON:
    1641:     DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1642:     isAffine = PETSC_FALSE;
    1643:     break;
    1644:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    1645:   }
    1646:   if (isAffine && Nq) {
    1647:     if (v) {
    1648:       for (i = 0; i < Nq; i++) {
    1649:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    1650:       }
    1651:     }
    1652:     if (detJ) {
    1653:       for (i = 0; i < Nq; i++) {
    1654:         detJ[i] = detJ0;
    1655:       }
    1656:     }
    1657:     if (J) {
    1658:       PetscInt k;

    1660:       for (i = 0, k = 0; i < Nq; i++) {
    1661:         PetscInt j;

    1663:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1664:           J[k] = J0[j];
    1665:         }
    1666:       }
    1667:     }
    1668:     if (invJ) {
    1669:       PetscInt k;
    1670:       switch (coordDim) {
    1671:       case 0:
    1672:         break;
    1673:       case 1:
    1674:         invJ[0] = 1./J0[0];
    1675:         break;
    1676:       case 2:
    1677:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    1678:         break;
    1679:       case 3:
    1680:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    1681:         break;
    1682:       }
    1683:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    1684:         PetscInt j;

    1686:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1687:           invJ[k] = invJ[j];
    1688:         }
    1689:       }
    1690:     }
    1691:   }
    1692:   return(0);
    1693: }

    1695: /*@C
    1696:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    1698:   Collective on dm

    1700:   Input Parameters:
    1701: + dm   - the DM
    1702: - cell - the cell

    1704:   Output Parameters:
    1705: + v0   - the translation part of this affine transform
    1706: . J    - the Jacobian of the transform from the reference element
    1707: . invJ - the inverse of the Jacobian
    1708: - detJ - the Jacobian determinant

    1710:   Level: advanced

    1712:   Fortran Notes:
    1713:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1714:   include petsc.h90 in your code.

    1716: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
    1717: @*/
    1718: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1719: {

    1723:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
    1724:   return(0);
    1725: }

    1727: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1728: {
    1729:   PetscQuadrature   feQuad;
    1730:   PetscSection      coordSection;
    1731:   Vec               coordinates;
    1732:   PetscScalar      *coords = NULL;
    1733:   const PetscReal  *quadPoints;
    1734:   PetscTabulation T;
    1735:   PetscInt          dim, cdim, pdim, qdim, Nq, numCoords, q;
    1736:   PetscErrorCode    ierr;

    1739:   DMGetCoordinatesLocal(dm, &coordinates);
    1740:   DMGetCoordinateSection(dm, &coordSection);
    1741:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1742:   DMGetDimension(dm, &dim);
    1743:   DMGetCoordinateDim(dm, &cdim);
    1744:   if (!quad) { /* use the first point of the first functional of the dual space */
    1745:     PetscDualSpace dsp;

    1747:     PetscFEGetDualSpace(fe, &dsp);
    1748:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
    1749:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1750:     Nq = 1;
    1751:   } else {
    1752:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1753:   }
    1754:   PetscFEGetDimension(fe, &pdim);
    1755:   PetscFEGetQuadrature(fe, &feQuad);
    1756:   if (feQuad == quad) {
    1757:     PetscFEGetCellTabulation(fe, J ? 1 : 0, &T);
    1758:     if (numCoords != pdim*cdim) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "There are %d coordinates for point %d != %d*%d", numCoords, point, pdim, cdim);
    1759:   } else {
    1760:     PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T);
    1761:   }
    1762:   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
    1763:   {
    1764:     const PetscReal *basis    = T->T[0];
    1765:     const PetscReal *basisDer = T->T[1];
    1766:     PetscReal        detJt;

    1768: #if defined(PETSC_USE_DEBUG)
    1769:     if (Nq != T->Np)     SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %D != %D", Nq, T->Np);
    1770:     if (pdim != T->Nb)   SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %D != %D", pdim, T->Nb);
    1771:     if (dim != T->Nc)    SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %D != %D", dim, T->Nc);
    1772:     if (cdim != T->cdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %D != %D", cdim, T->cdim);
    1773: #endif
    1774:     if (v) {
    1775:       PetscArrayzero(v, Nq*cdim);
    1776:       for (q = 0; q < Nq; ++q) {
    1777:         PetscInt i, k;

    1779:         for (k = 0; k < pdim; ++k) {
    1780:           const PetscInt vertex = k/cdim;
    1781:           for (i = 0; i < cdim; ++i) {
    1782:             v[q*cdim + i] += basis[(q*pdim + k)*cdim + i] * PetscRealPart(coords[vertex*cdim + i]);
    1783:           }
    1784:         }
    1785:         PetscLogFlops(2.0*pdim*cdim);
    1786:       }
    1787:     }
    1788:     if (J) {
    1789:       PetscArrayzero(J, Nq*cdim*cdim);
    1790:       for (q = 0; q < Nq; ++q) {
    1791:         PetscInt i, j, k, c, r;

    1793:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    1794:         for (k = 0; k < pdim; ++k) {
    1795:           const PetscInt vertex = k/cdim;
    1796:           for (j = 0; j < dim; ++j) {
    1797:             for (i = 0; i < cdim; ++i) {
    1798:               J[(q*cdim + i)*cdim + j] += basisDer[((q*pdim + k)*cdim + i)*dim + j] * PetscRealPart(coords[vertex*cdim + i]);
    1799:             }
    1800:           }
    1801:         }
    1802:         PetscLogFlops(2.0*pdim*dim*cdim);
    1803:         if (cdim > dim) {
    1804:           for (c = dim; c < cdim; ++c)
    1805:             for (r = 0; r < cdim; ++r)
    1806:               J[r*cdim+c] = r == c ? 1.0 : 0.0;
    1807:         }
    1808:         if (!detJ && !invJ) continue;
    1809:         detJt = 0.;
    1810:         switch (cdim) {
    1811:         case 3:
    1812:           DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
    1813:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1814:           break;
    1815:         case 2:
    1816:           DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
    1817:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1818:           break;
    1819:         case 1:
    1820:           detJt = J[q*cdim*dim];
    1821:           if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
    1822:         }
    1823:         if (detJ) detJ[q] = detJt;
    1824:       }
    1825:     } else if (detJ || invJ) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
    1826:   }
    1827:   if (feQuad != quad) {PetscTabulationDestroy(&T);}
    1828:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1829:   return(0);
    1830: }

    1832: /*@C
    1833:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    1835:   Collective on dm

    1837:   Input Parameters:
    1838: + dm   - the DM
    1839: . cell - the cell
    1840: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
    1841:          evaluated at the first vertex of the reference element

    1843:   Output Parameters:
    1844: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
    1845: . J    - the Jacobian of the transform from the reference element at each quadrature point
    1846: . invJ - the inverse of the Jacobian at each quadrature point
    1847: - detJ - the Jacobian determinant at each quadrature point

    1849:   Level: advanced

    1851:   Fortran Notes:
    1852:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1853:   include petsc.h90 in your code.

    1855: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1856: @*/
    1857: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1858: {
    1859:   DM             cdm;
    1860:   PetscFE        fe = NULL;

    1865:   DMGetCoordinateDM(dm, &cdm);
    1866:   if (cdm) {
    1867:     PetscClassId id;
    1868:     PetscInt     numFields;
    1869:     PetscDS      prob;
    1870:     PetscObject  disc;

    1872:     DMGetNumFields(cdm, &numFields);
    1873:     if (numFields) {
    1874:       DMGetDS(cdm, &prob);
    1875:       PetscDSGetDiscretization(prob,0,&disc);
    1876:       PetscObjectGetClassId(disc,&id);
    1877:       if (id == PETSCFE_CLASSID) {
    1878:         fe = (PetscFE) disc;
    1879:       }
    1880:     }
    1881:   }
    1882:   if (!fe) {DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);}
    1883:   else     {DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);}
    1884:   return(0);
    1885: }

    1887: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1888: {
    1889:   PetscSection   coordSection;
    1890:   Vec            coordinates;
    1891:   PetscScalar   *coords = NULL;
    1892:   PetscScalar    tmp[2];
    1893:   PetscInt       coordSize, d;

    1897:   DMGetCoordinatesLocal(dm, &coordinates);
    1898:   DMGetCoordinateSection(dm, &coordSection);
    1899:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1900:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
    1901:   if (centroid) {
    1902:     for (d = 0; d < dim; ++d) centroid[d] = 0.5*PetscRealPart(coords[d] + tmp[d]);
    1903:   }
    1904:   if (normal) {
    1905:     PetscReal norm;

    1907:     if (dim != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "We only support 2D edges right now");
    1908:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
    1909:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
    1910:     norm       = DMPlex_NormD_Internal(dim, normal);
    1911:     for (d = 0; d < dim; ++d) normal[d] /= norm;
    1912:   }
    1913:   if (vol) {
    1914:     *vol = 0.0;
    1915:     for (d = 0; d < dim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - tmp[d]));
    1916:     *vol = PetscSqrtReal(*vol);
    1917:   }
    1918:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1919:   return(0);
    1920: }

    1922: /* Centroid_i = (\sum_n A_n Cn_i) / A */
    1923: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1924: {
    1925:   DMPolytopeType ct;
    1926:   PetscSection   coordSection;
    1927:   Vec            coordinates;
    1928:   PetscScalar   *coords = NULL;
    1929:   PetscInt       fv[4] = {0, 1, 2, 3};
    1930:   PetscInt       cdim, coordSize, numCorners, p, d;

    1934:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    1935:   DMPlexGetCellType(dm, cell, &ct);
    1936:   switch (ct) {
    1937:     case DM_POLYTOPE_SEG_PRISM_TENSOR: fv[2] = 3; fv[3] = 2;break;
    1938:     default: break;
    1939:   }
    1940:   DMGetCoordinatesLocal(dm, &coordinates);
    1941:   DMPlexGetConeSize(dm, cell, &numCorners);
    1942:   DMGetCoordinateSection(dm, &coordSection);
    1943:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1944:   DMGetCoordinateDim(dm, &cdim);

    1946:   if (cdim > 2) {
    1947:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, norm;

    1949:     for (p = 0; p < numCorners-2; ++p) {
    1950:       const PetscReal x0 = PetscRealPart(coords[cdim*fv[p+1]+0] - coords[0]), x1 = PetscRealPart(coords[cdim*fv[p+2]+0] - coords[0]);
    1951:       const PetscReal y0 = PetscRealPart(coords[cdim*fv[p+1]+1] - coords[1]), y1 = PetscRealPart(coords[cdim*fv[p+2]+1] - coords[1]);
    1952:       const PetscReal z0 = PetscRealPart(coords[cdim*fv[p+1]+2] - coords[2]), z1 = PetscRealPart(coords[cdim*fv[p+2]+2] - coords[2]);
    1953:       const PetscReal dx = y0*z1 - z0*y1;
    1954:       const PetscReal dy = z0*x1 - x0*z1;
    1955:       const PetscReal dz = x0*y1 - y0*x1;
    1956:       PetscReal       a  = PetscSqrtReal(dx*dx + dy*dy + dz*dz);

    1958:       n[0] += dx;
    1959:       n[1] += dy;
    1960:       n[2] += dz;
    1961:       c[0] += a * PetscRealPart(coords[0] + coords[cdim*fv[p+1]+0] + coords[cdim*fv[p+2]+0])/3.;
    1962:       c[1] += a * PetscRealPart(coords[1] + coords[cdim*fv[p+1]+1] + coords[cdim*fv[p+2]+1])/3.;
    1963:       c[2] += a * PetscRealPart(coords[2] + coords[cdim*fv[p+1]+2] + coords[cdim*fv[p+2]+2])/3.;
    1964:     }
    1965:     norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    1966:     n[0] /= norm;
    1967:     n[1] /= norm;
    1968:     n[2] /= norm;
    1969:     c[0] /= norm;
    1970:     c[1] /= norm;
    1971:     c[2] /= norm;
    1972:     if (vol) *vol = 0.5*norm;
    1973:     if (centroid) for (d = 0; d < cdim; ++d) centroid[d] = c[d];
    1974:     if (normal) for (d = 0; d < cdim; ++d) normal[d] = n[d];
    1975:   } else {
    1976:     PetscReal vsum = 0.0, csum[2] = {0.0, 0.0}, vtmp, ctmp[4] = {0., 0., 0., 0.};

    1978:     for (p = 0; p < numCorners; ++p) {
    1979:       const PetscInt pi  = p < 4 ? fv[p] : p;
    1980:       const PetscInt pin = p < 3 ? fv[(p+1)%numCorners] : (p+1)%numCorners;
    1981:       /* Need to do this copy to get types right */
    1982:       for (d = 0; d < cdim; ++d) {
    1983:         ctmp[d]      = PetscRealPart(coords[pi*cdim+d]);
    1984:         ctmp[cdim+d] = PetscRealPart(coords[pin*cdim+d]);
    1985:       }
    1986:       Volume_Triangle_Origin_Internal(&vtmp, ctmp);
    1987:       vsum += vtmp;
    1988:       for (d = 0; d < cdim; ++d) csum[d] += (ctmp[d] + ctmp[cdim+d])*vtmp;
    1989:     }
    1990:     if (vol) *vol = PetscAbsReal(vsum);
    1991:     if (centroid) for (d = 0; d < cdim; ++d) centroid[d] = csum[d] / ((cdim+1)*vsum);
    1992:     if (normal) for (d = 0; d < cdim; ++d) normal[d] = 0.0;
    1993:   }
    1994:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1995:   return(0);
    1996: }

    1998: /* Centroid_i = (\sum_n V_n Cn_i) / V */
    1999: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2000: {
    2001:   DMPolytopeType  ct;
    2002:   PetscSection    coordSection;
    2003:   Vec             coordinates;
    2004:   PetscScalar    *coords = NULL;
    2005:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
    2006:   const PetscInt *faces, *facesO;
    2007:   PetscBool       isHybrid = PETSC_FALSE;
    2008:   PetscInt        numFaces, f, coordSize, p, d;
    2009:   PetscErrorCode  ierr;

    2012:   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
    2013:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    2014:   DMPlexGetCellType(dm, cell, &ct);
    2015:   switch (ct) {
    2016:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2017:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2018:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    2019:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    2020:       isHybrid = PETSC_TRUE;
    2021:     default: break;
    2022:   }

    2024:   DMGetCoordinatesLocal(dm, &coordinates);
    2025:   DMGetCoordinateSection(dm, &coordSection);

    2027:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    2028:   DMPlexGetConeSize(dm, cell, &numFaces);
    2029:   DMPlexGetCone(dm, cell, &faces);
    2030:   DMPlexGetConeOrientation(dm, cell, &facesO);
    2031:   for (f = 0; f < numFaces; ++f) {
    2032:     PetscBool      flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
    2033:     DMPolytopeType ct;

    2035:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    2036:     DMPlexGetCellType(dm, faces[f], &ct);
    2037:     switch (ct) {
    2038:     case DM_POLYTOPE_TRIANGLE:
    2039:       for (d = 0; d < dim; ++d) {
    2040:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
    2041:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
    2042:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
    2043:       }
    2044:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2045:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    2046:       vsum += vtmp;
    2047:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
    2048:         for (d = 0; d < dim; ++d) {
    2049:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    2050:         }
    2051:       }
    2052:       break;
    2053:     case DM_POLYTOPE_QUADRILATERAL:
    2054:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2055:     {
    2056:       PetscInt fv[4] = {0, 1, 2, 3};

    2058:       /* Side faces for hybrid cells are are stored as tensor products */
    2059:       if (isHybrid && f > 1) {fv[2] = 3; fv[3] = 2;}
    2060:       /* DO FOR PYRAMID */
    2061:       /* First tet */
    2062:       for (d = 0; d < dim; ++d) {
    2063:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[0]*dim+d]);
    2064:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
    2065:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
    2066:       }
    2067:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2068:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    2069:       vsum += vtmp;
    2070:       if (centroid) {
    2071:         for (d = 0; d < dim; ++d) {
    2072:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    2073:         }
    2074:       }
    2075:       /* Second tet */
    2076:       for (d = 0; d < dim; ++d) {
    2077:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
    2078:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[2]*dim+d]);
    2079:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
    2080:       }
    2081:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    2082:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    2083:       vsum += vtmp;
    2084:       if (centroid) {
    2085:         for (d = 0; d < dim; ++d) {
    2086:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    2087:         }
    2088:       }
    2089:       break;
    2090:     }
    2091:     default:
    2092:       SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %D of type %s", faces[f], DMPolytopeTypes[ct]);
    2093:     }
    2094:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    2095:   }
    2096:   if (vol)     *vol = PetscAbsReal(vsum);
    2097:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
    2098:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
    2099:   return(0);
    2100: }

    2102: /*@C
    2103:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    2105:   Collective on dm

    2107:   Input Parameters:
    2108: + dm   - the DM
    2109: - cell - the cell

    2111:   Output Parameters:
    2112: + volume   - the cell volume
    2113: . centroid - the cell centroid
    2114: - normal - the cell normal, if appropriate

    2116:   Level: advanced

    2118:   Fortran Notes:
    2119:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    2120:   include petsc.h90 in your code.

    2122: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    2123: @*/
    2124: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2125: {
    2126:   PetscInt       depth, dim;

    2130:   DMPlexGetDepth(dm, &depth);
    2131:   DMGetDimension(dm, &dim);
    2132:   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
    2133:   DMPlexGetPointDepth(dm, cell, &depth);
    2134:   switch (depth) {
    2135:   case 1:
    2136:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
    2137:     break;
    2138:   case 2:
    2139:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
    2140:     break;
    2141:   case 3:
    2142:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
    2143:     break;
    2144:   default:
    2145:     SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
    2146:   }
    2147:   return(0);
    2148: }

    2150: /*@
    2151:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

    2153:   Collective on dm

    2155:   Input Parameter:
    2156: . dm - The DMPlex

    2158:   Output Parameter:
    2159: . cellgeom - A vector with the cell geometry data for each cell

    2161:   Level: beginner

    2163: @*/
    2164: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
    2165: {
    2166:   DM             dmCell;
    2167:   Vec            coordinates;
    2168:   PetscSection   coordSection, sectionCell;
    2169:   PetscScalar   *cgeom;
    2170:   PetscInt       cStart, cEnd, c;

    2174:   DMClone(dm, &dmCell);
    2175:   DMGetCoordinateSection(dm, &coordSection);
    2176:   DMGetCoordinatesLocal(dm, &coordinates);
    2177:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2178:   DMSetCoordinatesLocal(dmCell, coordinates);
    2179:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2180:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    2181:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2182:   /* TODO This needs to be multiplied by Nq for non-affine */
    2183:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));}
    2184:   PetscSectionSetUp(sectionCell);
    2185:   DMSetLocalSection(dmCell, sectionCell);
    2186:   PetscSectionDestroy(&sectionCell);
    2187:   DMCreateLocalVector(dmCell, cellgeom);
    2188:   VecGetArray(*cellgeom, &cgeom);
    2189:   for (c = cStart; c < cEnd; ++c) {
    2190:     PetscFEGeom *cg;

    2192:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2193:     PetscArrayzero(cg, 1);
    2194:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
    2195:     if (*cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double) *cg->detJ, c);
    2196:   }
    2197:   return(0);
    2198: }

    2200: /*@
    2201:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2203:   Input Parameter:
    2204: . dm - The DM

    2206:   Output Parameters:
    2207: + cellgeom - A Vec of PetscFVCellGeom data
    2208: - facegeom - A Vec of PetscFVFaceGeom data

    2210:   Level: developer

    2212: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
    2213: @*/
    2214: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2215: {
    2216:   DM             dmFace, dmCell;
    2217:   DMLabel        ghostLabel;
    2218:   PetscSection   sectionFace, sectionCell;
    2219:   PetscSection   coordSection;
    2220:   Vec            coordinates;
    2221:   PetscScalar   *fgeom, *cgeom;
    2222:   PetscReal      minradius, gminradius;
    2223:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2227:   DMGetDimension(dm, &dim);
    2228:   DMGetCoordinateSection(dm, &coordSection);
    2229:   DMGetCoordinatesLocal(dm, &coordinates);
    2230:   /* Make cell centroids and volumes */
    2231:   DMClone(dm, &dmCell);
    2232:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2233:   DMSetCoordinatesLocal(dmCell, coordinates);
    2234:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2235:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2236:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2237:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2238:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));}
    2239:   PetscSectionSetUp(sectionCell);
    2240:   DMSetLocalSection(dmCell, sectionCell);
    2241:   PetscSectionDestroy(&sectionCell);
    2242:   DMCreateLocalVector(dmCell, cellgeom);
    2243:   if (cEndInterior < 0) cEndInterior = cEnd;
    2244:   VecGetArray(*cellgeom, &cgeom);
    2245:   for (c = cStart; c < cEndInterior; ++c) {
    2246:     PetscFVCellGeom *cg;

    2248:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2249:     PetscArrayzero(cg, 1);
    2250:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
    2251:   }
    2252:   /* Compute face normals and minimum cell radius */
    2253:   DMClone(dm, &dmFace);
    2254:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
    2255:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2256:   PetscSectionSetChart(sectionFace, fStart, fEnd);
    2257:   for (f = fStart; f < fEnd; ++f) {PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));}
    2258:   PetscSectionSetUp(sectionFace);
    2259:   DMSetLocalSection(dmFace, sectionFace);
    2260:   PetscSectionDestroy(&sectionFace);
    2261:   DMCreateLocalVector(dmFace, facegeom);
    2262:   VecGetArray(*facegeom, &fgeom);
    2263:   DMGetLabel(dm, "ghost", &ghostLabel);
    2264:   minradius = PETSC_MAX_REAL;
    2265:   for (f = fStart; f < fEnd; ++f) {
    2266:     PetscFVFaceGeom *fg;
    2267:     PetscReal        area;
    2268:     const PetscInt  *cells;
    2269:     PetscInt         ncells, ghost = -1, d, numChildren;

    2271:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2272:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
    2273:     DMPlexGetSupport(dm, f, &cells);
    2274:     DMPlexGetSupportSize(dm, f, &ncells);
    2275:     /* It is possible to get a face with no support when using partition overlap */
    2276:     if (!ncells || ghost >= 0 || numChildren) continue;
    2277:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
    2278:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
    2279:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    2280:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    2281:     {
    2282:       PetscFVCellGeom *cL, *cR;
    2283:       PetscReal       *lcentroid, *rcentroid;
    2284:       PetscReal        l[3], r[3], v[3];

    2286:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
    2287:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    2288:       if (ncells > 1) {
    2289:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
    2290:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    2291:       }
    2292:       else {
    2293:         rcentroid = fg->centroid;
    2294:       }
    2295:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
    2296:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
    2297:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    2298:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    2299:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    2300:       }
    2301:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    2302:         if (dim == 2) SETERRQ5(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d 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]);
    2303:         if (dim == 3) SETERRQ7(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d 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]);
    2304:         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
    2305:       }
    2306:       if (cells[0] < cEndInterior) {
    2307:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    2308:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2309:       }
    2310:       if (ncells > 1 && cells[1] < cEndInterior) {
    2311:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    2312:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2313:       }
    2314:     }
    2315:   }
    2316:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
    2317:   DMPlexSetMinRadius(dm, gminradius);
    2318:   /* Compute centroids of ghost cells */
    2319:   for (c = cEndInterior; c < cEnd; ++c) {
    2320:     PetscFVFaceGeom *fg;
    2321:     const PetscInt  *cone,    *support;
    2322:     PetscInt         coneSize, supportSize, s;

    2324:     DMPlexGetConeSize(dmCell, c, &coneSize);
    2325:     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
    2326:     DMPlexGetCone(dmCell, c, &cone);
    2327:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
    2328:     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
    2329:     DMPlexGetSupport(dmCell, cone[0], &support);
    2330:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
    2331:     for (s = 0; s < 2; ++s) {
    2332:       /* Reflect ghost centroid across plane of face */
    2333:       if (support[s] == c) {
    2334:         PetscFVCellGeom       *ci;
    2335:         PetscFVCellGeom       *cg;
    2336:         PetscReal              c2f[3], a;

    2338:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
    2339:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    2340:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    2341:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
    2342:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
    2343:         cg->volume = ci->volume;
    2344:       }
    2345:     }
    2346:   }
    2347:   VecRestoreArray(*facegeom, &fgeom);
    2348:   VecRestoreArray(*cellgeom, &cgeom);
    2349:   DMDestroy(&dmCell);
    2350:   DMDestroy(&dmFace);
    2351:   return(0);
    2352: }

    2354: /*@C
    2355:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    2357:   Not collective

    2359:   Input Parameter:
    2360: . dm - the DM

    2362:   Output Parameter:
    2363: . minradius - the minimum cell radius

    2365:   Level: developer

    2367: .seealso: DMGetCoordinates()
    2368: @*/
    2369: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    2370: {
    2374:   *minradius = ((DM_Plex*) dm->data)->minradius;
    2375:   return(0);
    2376: }

    2378: /*@C
    2379:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    2381:   Logically collective

    2383:   Input Parameters:
    2384: + dm - the DM
    2385: - minradius - the minimum cell radius

    2387:   Level: developer

    2389: .seealso: DMSetCoordinates()
    2390: @*/
    2391: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    2392: {
    2395:   ((DM_Plex*) dm->data)->minradius = minradius;
    2396:   return(0);
    2397: }

    2399: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2400: {
    2401:   DMLabel        ghostLabel;
    2402:   PetscScalar   *dx, *grad, **gref;
    2403:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    2407:   DMGetDimension(dm, &dim);
    2408:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2409:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2410:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
    2411:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
    2412:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2413:   DMGetLabel(dm, "ghost", &ghostLabel);
    2414:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2415:   for (c = cStart; c < cEndInterior; c++) {
    2416:     const PetscInt        *faces;
    2417:     PetscInt               numFaces, usedFaces, f, d;
    2418:     PetscFVCellGeom        *cg;
    2419:     PetscBool              boundary;
    2420:     PetscInt               ghost;

    2422:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2423:     DMPlexGetConeSize(dm, c, &numFaces);
    2424:     DMPlexGetCone(dm, c, &faces);
    2425:     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
    2426:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2427:       PetscFVCellGeom       *cg1;
    2428:       PetscFVFaceGeom       *fg;
    2429:       const PetscInt        *fcells;
    2430:       PetscInt               ncell, side;

    2432:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2433:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2434:       if ((ghost >= 0) || boundary) continue;
    2435:       DMPlexGetSupport(dm, faces[f], &fcells);
    2436:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    2437:       ncell = fcells[!side];    /* the neighbor */
    2438:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
    2439:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2440:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2441:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2442:     }
    2443:     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
    2444:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
    2445:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2446:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2447:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2448:       if ((ghost >= 0) || boundary) continue;
    2449:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
    2450:       ++usedFaces;
    2451:     }
    2452:   }
    2453:   PetscFree3(dx, grad, gref);
    2454:   return(0);
    2455: }

    2457: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2458: {
    2459:   DMLabel        ghostLabel;
    2460:   PetscScalar   *dx, *grad, **gref;
    2461:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    2462:   PetscSection   neighSec;
    2463:   PetscInt     (*neighbors)[2];
    2464:   PetscInt      *counter;

    2468:   DMGetDimension(dm, &dim);
    2469:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2470:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2471:   if (cEndInterior < 0) cEndInterior = cEnd;
    2472:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
    2473:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
    2474:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2475:   DMGetLabel(dm, "ghost", &ghostLabel);
    2476:   for (f = fStart; f < fEnd; f++) {
    2477:     const PetscInt        *fcells;
    2478:     PetscBool              boundary;
    2479:     PetscInt               ghost = -1;
    2480:     PetscInt               numChildren, numCells, c;

    2482:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2483:     DMIsBoundaryPoint(dm, f, &boundary);
    2484:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2485:     if ((ghost >= 0) || boundary || numChildren) continue;
    2486:     DMPlexGetSupportSize(dm, f, &numCells);
    2487:     if (numCells == 2) {
    2488:       DMPlexGetSupport(dm, f, &fcells);
    2489:       for (c = 0; c < 2; c++) {
    2490:         PetscInt cell = fcells[c];

    2492:         if (cell >= cStart && cell < cEndInterior) {
    2493:           PetscSectionAddDof(neighSec,cell,1);
    2494:         }
    2495:       }
    2496:     }
    2497:   }
    2498:   PetscSectionSetUp(neighSec);
    2499:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
    2500:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2501:   nStart = 0;
    2502:   PetscSectionGetStorageSize(neighSec,&nEnd);
    2503:   PetscMalloc1((nEnd-nStart),&neighbors);
    2504:   PetscCalloc1((cEndInterior-cStart),&counter);
    2505:   for (f = fStart; f < fEnd; f++) {
    2506:     const PetscInt        *fcells;
    2507:     PetscBool              boundary;
    2508:     PetscInt               ghost = -1;
    2509:     PetscInt               numChildren, numCells, c;

    2511:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2512:     DMIsBoundaryPoint(dm, f, &boundary);
    2513:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2514:     if ((ghost >= 0) || boundary || numChildren) continue;
    2515:     DMPlexGetSupportSize(dm, f, &numCells);
    2516:     if (numCells == 2) {
    2517:       DMPlexGetSupport(dm, f, &fcells);
    2518:       for (c = 0; c < 2; c++) {
    2519:         PetscInt cell = fcells[c], off;

    2521:         if (cell >= cStart && cell < cEndInterior) {
    2522:           PetscSectionGetOffset(neighSec,cell,&off);
    2523:           off += counter[cell - cStart]++;
    2524:           neighbors[off][0] = f;
    2525:           neighbors[off][1] = fcells[1 - c];
    2526:         }
    2527:       }
    2528:     }
    2529:   }
    2530:   PetscFree(counter);
    2531:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2532:   for (c = cStart; c < cEndInterior; c++) {
    2533:     PetscInt               numFaces, f, d, off, ghost = -1;
    2534:     PetscFVCellGeom        *cg;

    2536:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2537:     PetscSectionGetDof(neighSec, c, &numFaces);
    2538:     PetscSectionGetOffset(neighSec, c, &off);
    2539:     if (ghostLabel) {DMLabelGetValue(ghostLabel, c, &ghost);}
    2540:     if (ghost < 0 && numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
    2541:     for (f = 0; f < numFaces; ++f) {
    2542:       PetscFVCellGeom       *cg1;
    2543:       PetscFVFaceGeom       *fg;
    2544:       const PetscInt        *fcells;
    2545:       PetscInt               ncell, side, nface;

    2547:       nface = neighbors[off + f][0];
    2548:       ncell = neighbors[off + f][1];
    2549:       DMPlexGetSupport(dm,nface,&fcells);
    2550:       side  = (c != fcells[0]);
    2551:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
    2552:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2553:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2554:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2555:     }
    2556:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
    2557:     for (f = 0; f < numFaces; ++f) {
    2558:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
    2559:     }
    2560:   }
    2561:   PetscFree3(dx, grad, gref);
    2562:   PetscSectionDestroy(&neighSec);
    2563:   PetscFree(neighbors);
    2564:   return(0);
    2565: }

    2567: /*@
    2568:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    2570:   Collective on dm

    2572:   Input Parameters:
    2573: + dm  - The DM
    2574: . fvm - The PetscFV
    2575: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

    2577:   Input/Output Parameter:
    2578: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM(); on output
    2579:                  the geometric factors for gradient calculation are inserted

    2581:   Output Parameter:
    2582: . dmGrad - The DM describing the layout of gradient data

    2584:   Level: developer

    2586: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
    2587: @*/
    2588: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    2589: {
    2590:   DM             dmFace, dmCell;
    2591:   PetscScalar   *fgeom, *cgeom;
    2592:   PetscSection   sectionGrad, parentSection;
    2593:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

    2597:   DMGetDimension(dm, &dim);
    2598:   PetscFVGetNumComponents(fvm, &pdim);
    2599:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2600:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2601:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    2602:   VecGetDM(faceGeometry, &dmFace);
    2603:   VecGetDM(cellGeometry, &dmCell);
    2604:   VecGetArray(faceGeometry, &fgeom);
    2605:   VecGetArray(cellGeometry, &cgeom);
    2606:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
    2607:   if (!parentSection) {
    2608:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2609:   } else {
    2610:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2611:   }
    2612:   VecRestoreArray(faceGeometry, &fgeom);
    2613:   VecRestoreArray(cellGeometry, &cgeom);
    2614:   /* Create storage for gradients */
    2615:   DMClone(dm, dmGrad);
    2616:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
    2617:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
    2618:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionGrad, c, pdim*dim);}
    2619:   PetscSectionSetUp(sectionGrad);
    2620:   DMSetLocalSection(*dmGrad, sectionGrad);
    2621:   PetscSectionDestroy(&sectionGrad);
    2622:   return(0);
    2623: }

    2625: /*@
    2626:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    2628:   Collective on dm

    2630:   Input Parameters:
    2631: + dm  - The DM
    2632: - fv  - The PetscFV

    2634:   Output Parameters:
    2635: + cellGeometry - The cell geometry
    2636: . faceGeometry - The face geometry
    2637: - gradDM       - The gradient matrices

    2639:   Level: developer

    2641: .seealso: DMPlexComputeGeometryFVM()
    2642: @*/
    2643: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    2644: {
    2645:   PetscObject    cellgeomobj, facegeomobj;

    2649:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2650:   if (!cellgeomobj) {
    2651:     Vec cellgeomInt, facegeomInt;

    2653:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
    2654:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
    2655:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
    2656:     VecDestroy(&cellgeomInt);
    2657:     VecDestroy(&facegeomInt);
    2658:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2659:   }
    2660:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
    2661:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
    2662:   if (facegeom) *facegeom = (Vec) facegeomobj;
    2663:   if (gradDM) {
    2664:     PetscObject gradobj;
    2665:     PetscBool   computeGradients;

    2667:     PetscFVGetComputeGradients(fv,&computeGradients);
    2668:     if (!computeGradients) {
    2669:       *gradDM = NULL;
    2670:       return(0);
    2671:     }
    2672:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2673:     if (!gradobj) {
    2674:       DM dmGradInt;

    2676:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
    2677:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
    2678:       DMDestroy(&dmGradInt);
    2679:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2680:     }
    2681:     *gradDM = (DM) gradobj;
    2682:   }
    2683:   return(0);
    2684: }

    2686: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
    2687: {
    2688:   PetscInt l, m;

    2691:   if (dimC == dimR && dimR <= 3) {
    2692:     /* invert Jacobian, multiply */
    2693:     PetscScalar det, idet;

    2695:     switch (dimR) {
    2696:     case 1:
    2697:       invJ[0] = 1./ J[0];
    2698:       break;
    2699:     case 2:
    2700:       det = J[0] * J[3] - J[1] * J[2];
    2701:       idet = 1./det;
    2702:       invJ[0] =  J[3] * idet;
    2703:       invJ[1] = -J[1] * idet;
    2704:       invJ[2] = -J[2] * idet;
    2705:       invJ[3] =  J[0] * idet;
    2706:       break;
    2707:     case 3:
    2708:       {
    2709:         invJ[0] = J[4] * J[8] - J[5] * J[7];
    2710:         invJ[1] = J[2] * J[7] - J[1] * J[8];
    2711:         invJ[2] = J[1] * J[5] - J[2] * J[4];
    2712:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    2713:         idet = 1./det;
    2714:         invJ[0] *= idet;
    2715:         invJ[1] *= idet;
    2716:         invJ[2] *= idet;
    2717:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
    2718:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
    2719:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
    2720:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
    2721:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
    2722:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
    2723:       }
    2724:       break;
    2725:     }
    2726:     for (l = 0; l < dimR; l++) {
    2727:       for (m = 0; m < dimC; m++) {
    2728:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    2729:       }
    2730:     }
    2731:   } else {
    2732: #if defined(PETSC_USE_COMPLEX)
    2733:     char transpose = 'C';
    2734: #else
    2735:     char transpose = 'T';
    2736: #endif
    2737:     PetscBLASInt m = dimR;
    2738:     PetscBLASInt n = dimC;
    2739:     PetscBLASInt one = 1;
    2740:     PetscBLASInt worksize = dimR * dimC, info;

    2742:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

    2744:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));
    2745:     if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");

    2747:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
    2748:   }
    2749:   return(0);
    2750: }

    2752: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2753: {
    2754:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    2755:   PetscScalar    *coordsScalar = NULL;
    2756:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    2757:   PetscScalar    *J, *invJ, *work;

    2762:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2763:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2764:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2765:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2766:   cellCoords = &cellData[0];
    2767:   cellCoeffs = &cellData[coordSize];
    2768:   extJ       = &cellData[2 * coordSize];
    2769:   resNeg     = &cellData[2 * coordSize + dimR];
    2770:   invJ       = &J[dimR * dimC];
    2771:   work       = &J[2 * dimR * dimC];
    2772:   if (dimR == 2) {
    2773:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2775:     for (i = 0; i < 4; i++) {
    2776:       PetscInt plexI = zToPlex[i];

    2778:       for (j = 0; j < dimC; j++) {
    2779:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2780:       }
    2781:     }
    2782:   } else if (dimR == 3) {
    2783:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2785:     for (i = 0; i < 8; i++) {
    2786:       PetscInt plexI = zToPlex[i];

    2788:       for (j = 0; j < dimC; j++) {
    2789:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2790:       }
    2791:     }
    2792:   } else {
    2793:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2794:   }
    2795:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2796:   for (i = 0; i < dimR; i++) {
    2797:     PetscReal *swap;

    2799:     for (j = 0; j < (numV / 2); j++) {
    2800:       for (k = 0; k < dimC; k++) {
    2801:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2802:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2803:       }
    2804:     }

    2806:     if (i < dimR - 1) {
    2807:       swap = cellCoeffs;
    2808:       cellCoeffs = cellCoords;
    2809:       cellCoords = swap;
    2810:     }
    2811:   }
    2812:   PetscArrayzero(refCoords,numPoints * dimR);
    2813:   for (j = 0; j < numPoints; j++) {
    2814:     for (i = 0; i < maxIts; i++) {
    2815:       PetscReal *guess = &refCoords[dimR * j];

    2817:       /* compute -residual and Jacobian */
    2818:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
    2819:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
    2820:       for (k = 0; k < numV; k++) {
    2821:         PetscReal extCoord = 1.;
    2822:         for (l = 0; l < dimR; l++) {
    2823:           PetscReal coord = guess[l];
    2824:           PetscInt  dep   = (k & (1 << l)) >> l;

    2826:           extCoord *= dep * coord + !dep;
    2827:           extJ[l] = dep;

    2829:           for (m = 0; m < dimR; m++) {
    2830:             PetscReal coord = guess[m];
    2831:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    2832:             PetscReal mult  = dep * coord + !dep;

    2834:             extJ[l] *= mult;
    2835:           }
    2836:         }
    2837:         for (l = 0; l < dimC; l++) {
    2838:           PetscReal coeff = cellCoeffs[dimC * k + l];

    2840:           resNeg[l] -= coeff * extCoord;
    2841:           for (m = 0; m < dimR; m++) {
    2842:             J[dimR * l + m] += coeff * extJ[m];
    2843:           }
    2844:         }
    2845:       }
    2846:       if (0 && PetscDefined(USE_DEBUG)) {
    2847:         PetscReal maxAbs = 0.;

    2849:         for (l = 0; l < dimC; l++) {
    2850:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2851:         }
    2852:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2853:       }

    2855:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
    2856:     }
    2857:   }
    2858:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2859:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2860:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2861:   return(0);
    2862: }

    2864: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2865: {
    2866:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
    2867:   PetscScalar    *coordsScalar = NULL;
    2868:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

    2873:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2874:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2875:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2876:   cellCoords = &cellData[0];
    2877:   cellCoeffs = &cellData[coordSize];
    2878:   if (dimR == 2) {
    2879:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2881:     for (i = 0; i < 4; i++) {
    2882:       PetscInt plexI = zToPlex[i];

    2884:       for (j = 0; j < dimC; j++) {
    2885:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2886:       }
    2887:     }
    2888:   } else if (dimR == 3) {
    2889:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2891:     for (i = 0; i < 8; i++) {
    2892:       PetscInt plexI = zToPlex[i];

    2894:       for (j = 0; j < dimC; j++) {
    2895:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2896:       }
    2897:     }
    2898:   } else {
    2899:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2900:   }
    2901:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2902:   for (i = 0; i < dimR; i++) {
    2903:     PetscReal *swap;

    2905:     for (j = 0; j < (numV / 2); j++) {
    2906:       for (k = 0; k < dimC; k++) {
    2907:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2908:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2909:       }
    2910:     }

    2912:     if (i < dimR - 1) {
    2913:       swap = cellCoeffs;
    2914:       cellCoeffs = cellCoords;
    2915:       cellCoords = swap;
    2916:     }
    2917:   }
    2918:   PetscArrayzero(realCoords,numPoints * dimC);
    2919:   for (j = 0; j < numPoints; j++) {
    2920:     const PetscReal *guess  = &refCoords[dimR * j];
    2921:     PetscReal       *mapped = &realCoords[dimC * j];

    2923:     for (k = 0; k < numV; k++) {
    2924:       PetscReal extCoord = 1.;
    2925:       for (l = 0; l < dimR; l++) {
    2926:         PetscReal coord = guess[l];
    2927:         PetscInt  dep   = (k & (1 << l)) >> l;

    2929:         extCoord *= dep * coord + !dep;
    2930:       }
    2931:       for (l = 0; l < dimC; l++) {
    2932:         PetscReal coeff = cellCoeffs[dimC * k + l];

    2934:         mapped[l] += coeff * extCoord;
    2935:       }
    2936:     }
    2937:   }
    2938:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2939:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2940:   return(0);
    2941: }

    2943: /* TODO: TOBY please fix this for Nc > 1 */
    2944: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2945: {
    2946:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
    2947:   PetscScalar    *nodes = NULL;
    2948:   PetscReal      *invV, *modes;
    2949:   PetscReal      *B, *D, *resNeg;
    2950:   PetscScalar    *J, *invJ, *work;

    2954:   PetscFEGetDimension(fe, &pdim);
    2955:   PetscFEGetNumComponents(fe, &numComp);
    2956:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2957:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2958:   /* convert nodes to values in the stable evaluation basis */
    2959:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2960:   invV = fe->invV;
    2961:   for (i = 0; i < pdim; ++i) {
    2962:     modes[i] = 0.;
    2963:     for (j = 0; j < pdim; ++j) {
    2964:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2965:     }
    2966:   }
    2967:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2968:   D      = &B[pdim*Nc];
    2969:   resNeg = &D[pdim*Nc * dimR];
    2970:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2971:   invJ = &J[Nc * dimR];
    2972:   work = &invJ[Nc * dimR];
    2973:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
    2974:   for (j = 0; j < numPoints; j++) {
    2975:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    2976:       PetscReal *guess = &refCoords[j * dimR];
    2977:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
    2978:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
    2979:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
    2980:       for (k = 0; k < pdim; k++) {
    2981:         for (l = 0; l < Nc; l++) {
    2982:           resNeg[l] -= modes[k] * B[k * Nc + l];
    2983:           for (m = 0; m < dimR; m++) {
    2984:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    2985:           }
    2986:         }
    2987:       }
    2988:       if (0 && PetscDefined(USE_DEBUG)) {
    2989:         PetscReal maxAbs = 0.;

    2991:         for (l = 0; l < Nc; l++) {
    2992:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2993:         }
    2994:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2995:       }
    2996:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
    2997:     }
    2998:   }
    2999:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    3000:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    3001:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    3002:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3003:   return(0);
    3004: }

    3006: /* TODO: TOBY please fix this for Nc > 1 */
    3007: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    3008: {
    3009:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
    3010:   PetscScalar    *nodes = NULL;
    3011:   PetscReal      *invV, *modes;
    3012:   PetscReal      *B;

    3016:   PetscFEGetDimension(fe, &pdim);
    3017:   PetscFEGetNumComponents(fe, &numComp);
    3018:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    3019:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3020:   /* convert nodes to values in the stable evaluation basis */
    3021:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    3022:   invV = fe->invV;
    3023:   for (i = 0; i < pdim; ++i) {
    3024:     modes[i] = 0.;
    3025:     for (j = 0; j < pdim; ++j) {
    3026:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    3027:     }
    3028:   }
    3029:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    3030:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
    3031:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
    3032:   for (j = 0; j < numPoints; j++) {
    3033:     PetscReal *mapped = &realCoords[j * Nc];

    3035:     for (k = 0; k < pdim; k++) {
    3036:       for (l = 0; l < Nc; l++) {
    3037:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    3038:       }
    3039:     }
    3040:   }
    3041:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    3042:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    3043:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    3044:   return(0);
    3045: }

    3047: /*@
    3048:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
    3049:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
    3050:   extend uniquely outside the reference cell (e.g, most non-affine maps)

    3052:   Not collective

    3054:   Input Parameters:
    3055: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    3056:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3057:                as a multilinear map for tensor-product elements
    3058: . cell       - the cell whose map is used.
    3059: . numPoints  - the number of points to locate
    3060: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    3062:   Output Parameters:
    3063: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    3065:   Level: intermediate

    3067: .seealso: DMPlexReferenceToCoordinates()
    3068: @*/
    3069: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    3070: {
    3071:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    3072:   DM             coordDM = NULL;
    3073:   Vec            coords;
    3074:   PetscFE        fe = NULL;

    3079:   DMGetDimension(dm,&dimR);
    3080:   DMGetCoordinateDim(dm,&dimC);
    3081:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    3082:   DMPlexGetDepth(dm,&depth);
    3083:   DMGetCoordinatesLocal(dm,&coords);
    3084:   DMGetCoordinateDM(dm,&coordDM);
    3085:   if (coordDM) {
    3086:     PetscInt coordFields;

    3088:     DMGetNumFields(coordDM,&coordFields);
    3089:     if (coordFields) {
    3090:       PetscClassId id;
    3091:       PetscObject  disc;

    3093:       DMGetField(coordDM,0,NULL,&disc);
    3094:       PetscObjectGetClassId(disc,&id);
    3095:       if (id == PETSCFE_CLASSID) {
    3096:         fe = (PetscFE) disc;
    3097:       }
    3098:     }
    3099:   }
    3100:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3101:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    3102:   if (!fe) { /* implicit discretization: affine or multilinear */
    3103:     PetscInt  coneSize;
    3104:     PetscBool isSimplex, isTensor;

    3106:     DMPlexGetConeSize(dm,cell,&coneSize);
    3107:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3108:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3109:     if (isSimplex) {
    3110:       PetscReal detJ, *v0, *J, *invJ;

    3112:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3113:       J    = &v0[dimC];
    3114:       invJ = &J[dimC * dimC];
    3115:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
    3116:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    3117:         const PetscReal x0[3] = {-1.,-1.,-1.};

    3119:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    3120:       }
    3121:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3122:     } else if (isTensor) {
    3123:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    3124:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3125:   } else {
    3126:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    3127:   }
    3128:   return(0);
    3129: }

    3131: /*@
    3132:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

    3134:   Not collective

    3136:   Input Parameters:
    3137: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    3138:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3139:                as a multilinear map for tensor-product elements
    3140: . cell       - the cell whose map is used.
    3141: . numPoints  - the number of points to locate
    3142: - refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    3144:   Output Parameters:
    3145: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    3147:    Level: intermediate

    3149: .seealso: DMPlexCoordinatesToReference()
    3150: @*/
    3151: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    3152: {
    3153:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    3154:   DM             coordDM = NULL;
    3155:   Vec            coords;
    3156:   PetscFE        fe = NULL;

    3161:   DMGetDimension(dm,&dimR);
    3162:   DMGetCoordinateDim(dm,&dimC);
    3163:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    3164:   DMPlexGetDepth(dm,&depth);
    3165:   DMGetCoordinatesLocal(dm,&coords);
    3166:   DMGetCoordinateDM(dm,&coordDM);
    3167:   if (coordDM) {
    3168:     PetscInt coordFields;

    3170:     DMGetNumFields(coordDM,&coordFields);
    3171:     if (coordFields) {
    3172:       PetscClassId id;
    3173:       PetscObject  disc;

    3175:       DMGetField(coordDM,0,NULL,&disc);
    3176:       PetscObjectGetClassId(disc,&id);
    3177:       if (id == PETSCFE_CLASSID) {
    3178:         fe = (PetscFE) disc;
    3179:       }
    3180:     }
    3181:   }
    3182:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3183:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    3184:   if (!fe) { /* implicit discretization: affine or multilinear */
    3185:     PetscInt  coneSize;
    3186:     PetscBool isSimplex, isTensor;

    3188:     DMPlexGetConeSize(dm,cell,&coneSize);
    3189:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3190:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3191:     if (isSimplex) {
    3192:       PetscReal detJ, *v0, *J;

    3194:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3195:       J    = &v0[dimC];
    3196:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
    3197:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3198:         const PetscReal xi0[3] = {-1.,-1.,-1.};

    3200:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3201:       }
    3202:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3203:     } else if (isTensor) {
    3204:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3205:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3206:   } else {
    3207:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3208:   }
    3209:   return(0);
    3210: }

    3212: /*@C
    3213:   DMPlexRemapGeometry - This function maps the original DM coordinates to new coordinates.

    3215:   Not collective

    3217:   Input Parameters:
    3218: + dm      - The DM
    3219: . time    - The time
    3220: - func    - The function transforming current coordinates to new coordaintes

    3222:    Calling sequence of func:
    3223: $    func(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3224: $         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3225: $         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3226: $         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]);

    3228: +  dim          - The spatial dimension
    3229: .  Nf           - The number of input fields (here 1)
    3230: .  NfAux        - The number of input auxiliary fields
    3231: .  uOff         - The offset of the coordinates in u[] (here 0)
    3232: .  uOff_x       - The offset of the coordinates in u_x[] (here 0)
    3233: .  u            - The coordinate values at this point in space
    3234: .  u_t          - The coordinate time derivative at this point in space (here NULL)
    3235: .  u_x          - The coordinate derivatives at this point in space
    3236: .  aOff         - The offset of each auxiliary field in u[]
    3237: .  aOff_x       - The offset of each auxiliary field in u_x[]
    3238: .  a            - The auxiliary field values at this point in space
    3239: .  a_t          - The auxiliary field time derivative at this point in space (or NULL)
    3240: .  a_x          - The auxiliary field derivatives at this point in space
    3241: .  t            - The current time
    3242: .  x            - The coordinates of this point (here not used)
    3243: .  numConstants - The number of constants
    3244: .  constants    - The value of each constant
    3245: -  f            - The new coordinates at this point in space

    3247:   Level: intermediate

    3249: .seealso: DMGetCoordinates(), DMGetCoordinatesLocal(), DMGetCoordinateDM(), DMProjectFieldLocal(), DMProjectFieldLabelLocal()
    3250: @*/
    3251: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time,
    3252:                                    void (*func)(PetscInt, PetscInt, PetscInt,
    3253:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3254:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3255:                                                 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))
    3256: {
    3257:   DM             cdm;
    3258:   DMField        cf;
    3259:   Vec            lCoords, tmpCoords;

    3263:   DMGetCoordinateDM(dm, &cdm);
    3264:   DMGetCoordinatesLocal(dm, &lCoords);
    3265:   DMGetLocalVector(cdm, &tmpCoords);
    3266:   VecCopy(lCoords, tmpCoords);
    3267:   /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
    3268:   DMGetCoordinateField(dm, &cf);
    3269:   cdm->coordinateField = cf;
    3270:   DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords);
    3271:   cdm->coordinateField = NULL;
    3272:   DMRestoreLocalVector(cdm, &tmpCoords);
    3273:   DMSetCoordinatesLocal(dm, lCoords);
    3274:   return(0);
    3275: }

    3277: /* Shear applies the transformation, assuming we fix z,
    3278:   / 1  0  m_0 \
    3279:   | 0  1  m_1 |
    3280:   \ 0  0   1  /
    3281: */
    3282: static void f0_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3283:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3284:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3285:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
    3286: {
    3287:   const PetscInt Nc = uOff[1]-uOff[0];
    3288:   const PetscInt ax = (PetscInt) PetscRealPart(constants[0]);
    3289:   PetscInt       c;

    3291:   for (c = 0; c < Nc; ++c) {
    3292:     coords[c] = u[c] + constants[c+1]*u[ax];
    3293:   }
    3294: }

    3296: /*@C
    3297:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

    3299:   Not collective

    3301:   Input Parameters:
    3302: + dm          - The DM
    3303: . direction   - The shear coordinate direction, e.g. 0 is the x-axis
    3304: - multipliers - The multiplier m for each direction which is not the shear direction

    3306:   Level: intermediate

    3308: .seealso: DMPlexRemapGeometry()
    3309: @*/
    3310: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
    3311: {
    3312:   DM             cdm;
    3313:   PetscDS        cds;
    3314:   PetscObject    obj;
    3315:   PetscClassId   id;
    3316:   PetscScalar   *moduli;
    3317:   const PetscInt dir = (PetscInt) direction;
    3318:   PetscInt       dE, d, e;

    3322:   DMGetCoordinateDM(dm, &cdm);
    3323:   DMGetCoordinateDim(dm, &dE);
    3324:   PetscMalloc1(dE+1, &moduli);
    3325:   moduli[0] = dir;
    3326:   for (d = 0, e = 0; d < dE; ++d) moduli[d+1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
    3327:   DMGetDS(cdm, &cds);
    3328:   PetscDSGetDiscretization(cds, 0, &obj);
    3329:   PetscObjectGetClassId(obj, &id);
    3330:   if (id != PETSCFE_CLASSID) {
    3331:     Vec           lCoords;
    3332:     PetscSection  cSection;
    3333:     PetscScalar  *coords;
    3334:     PetscInt      vStart, vEnd, v;

    3336:     DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3337:     DMGetCoordinateSection(dm, &cSection);
    3338:     DMGetCoordinatesLocal(dm, &lCoords);
    3339:     VecGetArray(lCoords, &coords);
    3340:     for (v = vStart; v < vEnd; ++v) {
    3341:       PetscReal ds;
    3342:       PetscInt  off, c;

    3344:       PetscSectionGetOffset(cSection, v, &off);
    3345:       ds   = PetscRealPart(coords[off+dir]);
    3346:       for (c = 0; c < dE; ++c) coords[off+c] += moduli[c]*ds;
    3347:     }
    3348:     VecRestoreArray(lCoords, &coords);
    3349:   } else {
    3350:     PetscDSSetConstants(cds, dE+1, moduli);
    3351:     DMPlexRemapGeometry(dm, 0.0, f0_shear);
    3352:   }
    3353:   PetscFree(moduli);
    3354:   return(0);
    3355: }