Date: 2021-03-03T22:26:50+00:00

Actual source code: plexgeometry.c
petsc-3.14.5 2021-03-03
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      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: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    129: {
    130:   const PetscInt  embedDim = 2;
    131:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    132:   PetscReal       x        = PetscRealPart(point[0]);
    133:   PetscReal       y        = PetscRealPart(point[1]);
    134:   PetscReal       v0[2], J[4], invJ[4], detJ;
    135:   PetscReal       xi, eta;
    136:   PetscErrorCode  ierr;

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

    143:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
    144:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    145:   return(0);
    146: }

    148: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
    149: {
    150:   const PetscInt  embedDim = 2;
    151:   PetscReal       x        = PetscRealPart(point[0]);
    152:   PetscReal       y        = PetscRealPart(point[1]);
    153:   PetscReal       v0[2], J[4], invJ[4], detJ;
    154:   PetscReal       xi, eta, r;
    155:   PetscErrorCode  ierr;

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

    162:   xi  = PetscMax(xi,  0.0);
    163:   eta = PetscMax(eta, 0.0);
    164:   if (xi + eta > 2.0) {
    165:     r    = (xi + eta)/2.0;
    166:     xi  /= r;
    167:     eta /= r;
    168:   }
    169:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
    170:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
    171:   return(0);
    172: }

    174: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    175: {
    176:   PetscSection       coordSection;
    177:   Vec             coordsLocal;
    178:   PetscScalar    *coords = NULL;
    179:   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
    180:   PetscReal       x         = PetscRealPart(point[0]);
    181:   PetscReal       y         = PetscRealPart(point[1]);
    182:   PetscInt        crossings = 0, f;
    183:   PetscErrorCode  ierr;

    186:   DMGetCoordinatesLocal(dm, &coordsLocal);
    187:   DMGetCoordinateSection(dm, &coordSection);
    188:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    189:   for (f = 0; f < 4; ++f) {
    190:     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
    191:     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
    192:     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
    193:     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
    194:     PetscReal slope = (y_j - y_i) / (x_j - x_i);
    195:     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
    196:     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
    197:     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
    198:     if ((cond1 || cond2)  && above) ++crossings;
    199:   }
    200:   if (crossings % 2) *cell = c;
    201:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    202:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    203:   return(0);
    204: }

    206: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    207: {
    208:   const PetscInt  embedDim = 3;
    209:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    210:   PetscReal       v0[3], J[9], invJ[9], detJ;
    211:   PetscReal       x = PetscRealPart(point[0]);
    212:   PetscReal       y = PetscRealPart(point[1]);
    213:   PetscReal       z = PetscRealPart(point[2]);
    214:   PetscReal       xi, eta, zeta;
    215:   PetscErrorCode  ierr;

    218:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    219:   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
    220:   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
    221:   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);

    223:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0+eps)) *cell = c;
    224:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    225:   return(0);
    226: }

    228: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    229: {
    230:   PetscSection   coordSection;
    231:   Vec            coordsLocal;
    232:   PetscScalar   *coords = NULL;
    233:   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
    234:                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
    235:   PetscBool      found = PETSC_TRUE;
    236:   PetscInt       f;

    240:   DMGetCoordinatesLocal(dm, &coordsLocal);
    241:   DMGetCoordinateSection(dm, &coordSection);
    242:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    243:   for (f = 0; f < 6; ++f) {
    244:     /* Check the point is under plane */
    245:     /*   Get face normal */
    246:     PetscReal v_i[3];
    247:     PetscReal v_j[3];
    248:     PetscReal normal[3];
    249:     PetscReal pp[3];
    250:     PetscReal dot;

    252:     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
    253:     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
    254:     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
    255:     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
    256:     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
    257:     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
    258:     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
    259:     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
    260:     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
    261:     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
    262:     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
    263:     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
    264:     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];

    266:     /* Check that projected point is in face (2D location problem) */
    267:     if (dot < 0.0) {
    268:       found = PETSC_FALSE;
    269:       break;
    270:     }
    271:   }
    272:   if (found) *cell = c;
    273:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    274:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    275:   return(0);
    276: }

    278: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
    279: {
    280:   PetscInt d;

    283:   box->dim = dim;
    284:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
    285:   return(0);
    286: }

    288: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    289: {

    293:   PetscMalloc1(1, box);
    294:   PetscGridHashInitialize_Internal(*box, dim, point);
    295:   return(0);
    296: }

    298: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
    299: {
    300:   PetscInt d;

    303:   for (d = 0; d < box->dim; ++d) {
    304:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    305:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    306:   }
    307:   return(0);
    308: }

    310: /*
    311:   PetscGridHashSetGrid - Divide the grid into boxes

    313:   Not collective

    315:   Input Parameters:
    316: + box - The grid hash object
    317: . n   - The number of boxes in each dimension, or PETSC_DETERMINE
    318: - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE

    320:   Level: developer

    322: .seealso: PetscGridHashCreate()
    323: */
    324: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
    325: {
    326:   PetscInt d;

    329:   for (d = 0; d < box->dim; ++d) {
    330:     box->extent[d] = box->upper[d] - box->lower[d];
    331:     if (n[d] == PETSC_DETERMINE) {
    332:       box->h[d] = h[d];
    333:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
    334:     } else {
    335:       box->n[d] = n[d];
    336:       box->h[d] = box->extent[d]/n[d];
    337:     }
    338:   }
    339:   return(0);
    340: }

    342: /*
    343:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

    345:   Not collective

    347:   Input Parameters:
    348: + box       - The grid hash object
    349: . numPoints - The number of input points
    350: - points    - The input point coordinates

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

    356:   Level: developer

    358: .seealso: PetscGridHashCreate()
    359: */
    360: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
    361: {
    362:   const PetscReal *lower = box->lower;
    363:   const PetscReal *upper = box->upper;
    364:   const PetscReal *h     = box->h;
    365:   const PetscInt  *n     = box->n;
    366:   const PetscInt   dim   = box->dim;
    367:   PetscInt         d, p;

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

    374:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    375:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
    376:       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",
    377:                                              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);
    378:       dboxes[p*dim+d] = dbox;
    379:     }
    380:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
    381:   }
    382:   return(0);
    383: }

    385: /*
    386:  PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

    388:  Not collective

    390:   Input Parameters:
    391: + box       - The grid hash object
    392: . numPoints - The number of input points
    393: - points    - The input point coordinates

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

    400:   Level: developer

    402: .seealso: PetscGridHashGetEnclosingBox()
    403: */
    404: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[],PetscBool *found)
    405: {
    406:   const PetscReal *lower = box->lower;
    407:   const PetscReal *upper = box->upper;
    408:   const PetscReal *h     = box->h;
    409:   const PetscInt  *n     = box->n;
    410:   const PetscInt   dim   = box->dim;
    411:   PetscInt         d, p;

    414:   *found = PETSC_FALSE;
    415:   for (p = 0; p < numPoints; ++p) {
    416:     for (d = 0; d < dim; ++d) {
    417:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

    419:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    420:       if (dbox < 0 || dbox >= n[d]) {
    421:         return(0);
    422:       }
    423:       dboxes[p*dim+d] = dbox;
    424:     }
    425:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
    426:   }
    427:   *found = PETSC_TRUE;
    428:   return(0);
    429: }

    431: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    432: {

    436:   if (*box) {
    437:     PetscSectionDestroy(&(*box)->cellSection);
    438:     ISDestroy(&(*box)->cells);
    439:     DMLabelDestroy(&(*box)->cellsSparse);
    440:   }
    441:   PetscFree(*box);
    442:   return(0);
    443: }

    445: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
    446: {
    447:   DMPolytopeType ct;

    451:   DMPlexGetCellType(dm, cellStart, &ct);
    452:   switch (ct) {
    453:     case DM_POLYTOPE_TRIANGLE:
    454:     DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);break;
    455:     case DM_POLYTOPE_QUADRILATERAL:
    456:     DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell);break;
    457:     case DM_POLYTOPE_TETRAHEDRON:
    458:     DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);break;
    459:     case DM_POLYTOPE_HEXAHEDRON:
    460:     DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);break;
    461:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %D with type %s", cellStart, DMPolytopeTypes[ct]);
    462:   }
    463:   return(0);
    464: }

    466: /*
    467:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
    468: */
    469: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
    470: {
    471:   DMPolytopeType ct;

    475:   DMPlexGetCellType(dm, cell, &ct);
    476:   switch (ct) {
    477:     case DM_POLYTOPE_TRIANGLE:
    478:     DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);break;
    479: #if 0
    480:     case DM_POLYTOPE_QUADRILATERAL:
    481:     DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);break;
    482:     case DM_POLYTOPE_TETRAHEDRON:
    483:     DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);break;
    484:     case DM_POLYTOPE_HEXAHEDRON:
    485:     DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);break;
    486: #endif
    487:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    488:   }
    489:   return(0);
    490: }

    492: /*
    493:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex

    495:   Collective on dm

    497:   Input Parameter:
    498: . dm - The Plex

    500:   Output Parameter:
    501: . localBox - The grid hash object

    503:   Level: developer

    505: .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
    506: */
    507: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
    508: {
    509:   MPI_Comm           comm;
    510:   PetscGridHash      lbox;
    511:   Vec                coordinates;
    512:   PetscSection       coordSection;
    513:   Vec                coordsLocal;
    514:   const PetscScalar *coords;
    515:   PetscInt          *dboxes, *boxes;
    516:   PetscInt           n[3] = {10, 10, 10};
    517:   PetscInt           dim, N, cStart, cEnd, c, i;
    518:   PetscErrorCode     ierr;

    521:   PetscObjectGetComm((PetscObject) dm, &comm);
    522:   DMGetCoordinatesLocal(dm, &coordinates);
    523:   DMGetCoordinateDim(dm, &dim);
    524:   if (dim != 2) SETERRQ(comm, PETSC_ERR_SUP, "I have only coded this for 2D");
    525:   VecGetLocalSize(coordinates, &N);
    526:   VecGetArrayRead(coordinates, &coords);
    527:   PetscGridHashCreate(comm, dim, coords, &lbox);
    528:   for (i = 0; i < N; i += dim) {PetscGridHashEnlarge(lbox, &coords[i]);}
    529:   VecRestoreArrayRead(coordinates, &coords);
    530:   PetscOptionsGetInt(NULL,NULL,"-dm_plex_hash_box_nijk",&n[0],NULL);
    531:   n[1] = n[0];
    532:   n[2] = n[0];
    533:   PetscGridHashSetGrid(lbox, n, NULL);
    534: #if 0
    535:   /* Could define a custom reduction to merge these */
    536:   MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);
    537:   MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);
    538: #endif
    539:   /* Is there a reason to snap the local bounding box to a division of the global box? */
    540:   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
    541:   /* Create label */
    542:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    543:   DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse);
    544:   DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);
    545:   /* Compute boxes which overlap each cell: https://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
    546:   DMGetCoordinatesLocal(dm, &coordsLocal);
    547:   DMGetCoordinateSection(dm, &coordSection);
    548:   PetscCalloc2(16 * dim, &dboxes, 16, &boxes);
    549:   for (c = cStart; c < cEnd; ++c) {
    550:     const PetscReal *h       = lbox->h;
    551:     PetscScalar     *ccoords = NULL;
    552:     PetscInt         csize   = 0;
    553:     PetscScalar      point[3];
    554:     PetscInt         dlim[6], d, e, i, j, k;

    556:     /* Find boxes enclosing each vertex */
    557:     DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);
    558:     PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);
    559:     /* Mark cells containing the vertices */
    560:     for (e = 0; e < csize/dim; ++e) {DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);}
    561:     /* Get grid of boxes containing these */
    562:     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
    563:     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
    564:     for (e = 1; e < dim+1; ++e) {
    565:       for (d = 0; d < dim; ++d) {
    566:         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
    567:         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
    568:       }
    569:     }
    570:     /* Check for intersection of box with cell */
    571:     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
    572:       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
    573:         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
    574:           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
    575:           PetscScalar    cpoint[3];
    576:           PetscInt       cell, edge, ii, jj, kk;

    578:           /* Check whether cell contains any vertex of these subboxes TODO vectorize this */
    579:           for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
    580:             for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
    581:               for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {

    583:                 DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);
    584:                 if (cell >= 0) { DMLabelSetValue(lbox->cellsSparse, c, box); ii = jj = kk = 2;}
    585:               }
    586:             }
    587:           }
    588:           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
    589:           for (edge = 0; edge < dim+1; ++edge) {
    590:             PetscReal segA[6], segB[6];

    592:             if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected dim %d > 3",dim);
    593:             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
    594:             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
    595:               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
    596:                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
    597:               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
    598:                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
    599:                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
    600:                 for (ii = 0; ii < 2; ++ii) {
    601:                   PetscBool intersects;

    603:                   segB[0]     = PetscRealPart(point[0]);
    604:                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
    605:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
    606:                   if (intersects) { DMLabelSetValue(lbox->cellsSparse, c, box); edge = ii = jj = kk = dim+1;}
    607:                 }
    608:               }
    609:             }
    610:           }
    611:         }
    612:       }
    613:     }
    614:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
    615:   }
    616:   PetscFree2(dboxes, boxes);
    617:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
    618:   DMLabelDestroy(&lbox->cellsSparse);
    619:   *localBox = lbox;
    620:   return(0);
    621: }

    623: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
    624: {
    625:   DM_Plex        *mesh = (DM_Plex *) dm->data;
    626:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
    627:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
    628:   PetscInt        dim, cStart, cEnd, numCells, c, d;
    629:   const PetscInt *boxCells;
    630:   PetscSFNode    *cells;
    631:   PetscScalar    *a;
    632:   PetscMPIInt     result;
    633:   PetscLogDouble  t0,t1;
    634:   PetscReal       gmin[3],gmax[3];
    635:   PetscInt        terminating_query_type[] = { 0, 0, 0 };
    636:   PetscErrorCode  ierr;

    639:   PetscLogEventBegin(DMPLEX_LocatePoints,0,0,0,0);
    640:   PetscTime(&t0);
    641:   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.");
    642:   DMGetCoordinateDim(dm, &dim);
    643:   VecGetBlockSize(v, &bs);
    644:   MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);
    645:   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
    646:   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);
    647:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    648:   VecGetLocalSize(v, &numPoints);
    649:   VecGetArray(v, &a);
    650:   numPoints /= bs;
    651:   {
    652:     const PetscSFNode *sf_cells;

    654:     PetscSFGetGraph(cellSF,NULL,NULL,NULL,&sf_cells);
    655:     if (sf_cells) {
    656:       PetscInfo(dm,"[DMLocatePoints_Plex] Re-using existing StarForest node list\n");
    657:       cells = (PetscSFNode*)sf_cells;
    658:       reuse = PETSC_TRUE;
    659:     } else {
    660:       PetscInfo(dm,"[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n");
    661:       PetscMalloc1(numPoints, &cells);
    662:       /* initialize cells if created */
    663:       for (p=0; p<numPoints; p++) {
    664:         cells[p].rank  = 0;
    665:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    666:       }
    667:     }
    668:   }
    669:   /* define domain bounding box */
    670:   {
    671:     Vec coorglobal;

    673:     DMGetCoordinates(dm,&coorglobal);
    674:     VecStrideMaxAll(coorglobal,NULL,gmax);
    675:     VecStrideMinAll(coorglobal,NULL,gmin);
    676:   }
    677:   if (hash) {
    678:     if (!mesh->lbox) {PetscInfo(dm, "Initializing grid hashing");DMPlexComputeGridHash_Internal(dm, &mesh->lbox);}
    679:     /* Designate the local box for each point */
    680:     /* Send points to correct process */
    681:     /* Search cells that lie in each subbox */
    682:     /*   Should we bin points before doing search? */
    683:     ISGetIndices(mesh->lbox->cells, &boxCells);
    684:   }
    685:   for (p = 0, numFound = 0; p < numPoints; ++p) {
    686:     const PetscScalar *point = &a[p*bs];
    687:     PetscInt           dbin[3] = {-1,-1,-1}, bin, cell = -1, cellOffset;
    688:     PetscBool          point_outside_domain = PETSC_FALSE;

    690:     /* check bounding box of domain */
    691:     for (d=0; d<dim; d++) {
    692:       if (PetscRealPart(point[d]) < gmin[d]) { point_outside_domain = PETSC_TRUE; break; }
    693:       if (PetscRealPart(point[d]) > gmax[d]) { point_outside_domain = PETSC_TRUE; break; }
    694:     }
    695:     if (point_outside_domain) {
    696:       cells[p].rank = 0;
    697:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    698:       terminating_query_type[0]++;
    699:       continue;
    700:     }

    702:     /* check initial values in cells[].index - abort early if found */
    703:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    704:       c = cells[p].index;
    705:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    706:       DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    707:       if (cell >= 0) {
    708:         cells[p].rank = 0;
    709:         cells[p].index = cell;
    710:         numFound++;
    711:       }
    712:     }
    713:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    714:       terminating_query_type[1]++;
    715:       continue;
    716:     }

    718:     if (hash) {
    719:       PetscBool found_box;

    721:       /* allow for case that point is outside box - abort early */
    722:       PetscGridHashGetEnclosingBoxQuery(mesh->lbox, 1, point, dbin, &bin,&found_box);
    723:       if (found_box) {
    724:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
    725:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    726:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    727:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    728:           DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);
    729:           if (cell >= 0) {
    730:             cells[p].rank = 0;
    731:             cells[p].index = cell;
    732:             numFound++;
    733:             terminating_query_type[2]++;
    734:             break;
    735:           }
    736:         }
    737:       }
    738:     } else {
    739:       for (c = cStart; c < cEnd; ++c) {
    740:         DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    741:         if (cell >= 0) {
    742:           cells[p].rank = 0;
    743:           cells[p].index = cell;
    744:           numFound++;
    745:           terminating_query_type[2]++;
    746:           break;
    747:         }
    748:       }
    749:     }
    750:   }
    751:   if (hash) {ISRestoreIndices(mesh->lbox->cells, &boxCells);}
    752:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
    753:     for (p = 0; p < numPoints; p++) {
    754:       const PetscScalar *point = &a[p*bs];
    755:       PetscReal          cpoint[3], diff[3], dist, distMax = PETSC_MAX_REAL;
    756:       PetscInt           dbin[3] = {-1,-1,-1}, bin, cellOffset, d;

    758:       if (cells[p].index < 0) {
    759:         ++numFound;
    760:         PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);
    761:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    762:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    763:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    764:           DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);
    765:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
    766:           dist = DMPlex_NormD_Internal(dim, diff);
    767:           if (dist < distMax) {
    768:             for (d = 0; d < dim; ++d) a[p*bs+d] = cpoint[d];
    769:             cells[p].rank  = 0;
    770:             cells[p].index = boxCells[c];
    771:             distMax = dist;
    772:             break;
    773:           }
    774:         }
    775:       }
    776:     }
    777:   }
    778:   /* This code is only be relevant when interfaced to parallel point location */
    779:   /* Check for highest numbered proc that claims a point (do we care?) */
    780:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
    781:     PetscMalloc1(numFound,&found);
    782:     for (p = 0, numFound = 0; p < numPoints; p++) {
    783:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
    784:         if (numFound < p) {
    785:           cells[numFound] = cells[p];
    786:         }
    787:         found[numFound++] = p;
    788:       }
    789:     }
    790:   }
    791:   VecRestoreArray(v, &a);
    792:   if (!reuse) {
    793:     PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);
    794:   }
    795:   PetscTime(&t1);
    796:   if (hash) {
    797:     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]);
    798:   } else {
    799:     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]);
    800:   }
    801:   PetscInfo3(dm,"[DMLocatePoints_Plex] npoints %D : time(rank0) %1.2e (sec): points/sec %1.4e\n",numPoints,t1-t0,(double)((double)numPoints/(t1-t0)));
    802:   PetscLogEventEnd(DMPLEX_LocatePoints,0,0,0,0);
    803:   return(0);
    804: }

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

    809:   Not collective

    811:   Input Parameter:
    812: . coords - The coordinates of a segment

    814:   Output Parameters:
    815: + coords - The new y-coordinate, and 0 for x
    816: - R - The rotation which accomplishes the projection

    818:   Level: developer

    820: .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
    821: @*/
    822: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
    823: {
    824:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
    825:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
    826:   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;

    829:   R[0] = c; R[1] = -s;
    830:   R[2] = s; R[3] =  c;
    831:   coords[0] = 0.0;
    832:   coords[1] = r;
    833:   return(0);
    834: }

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

    839:   Not collective

    841:   Input Parameter:
    842: . coords - The coordinates of a segment

    844:   Output Parameters:
    845: + coords - The new y-coordinate, and 0 for x and z
    846: - R - The rotation which accomplishes the projection

    848:   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

    850:   Level: developer

    852: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
    853: @*/
    854: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
    855: {
    856:   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
    857:   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
    858:   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
    859:   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
    860:   PetscReal      rinv = 1. / r;

    863:   x *= rinv; y *= rinv; z *= rinv;
    864:   if (x > 0.) {
    865:     PetscReal inv1pX   = 1./ (1. + x);

    867:     R[0] = x; R[1] = -y;              R[2] = -z;
    868:     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
    869:     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
    870:   }
    871:   else {
    872:     PetscReal inv1mX   = 1./ (1. - x);

    874:     R[0] = x; R[1] = z;               R[2] = y;
    875:     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
    876:     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
    877:   }
    878:   coords[0] = 0.0;
    879:   coords[1] = r;
    880:   return(0);
    881: }

    883: /*@
    884:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
    885:     plane.  The normal is defined by positive orientation of the first 3 points.

    887:   Not collective

    889:   Input Parameter:
    890: + coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)
    891: - coords - The interlaced coordinates of each coplanar 3D point

    893:   Output Parameters:
    894: + coords - The first 2*coordSize/3 entries contain interlaced 2D points, with the rest undefined
    895: - 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.

    897:   Level: developer

    899: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
    900: @*/
    901: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    902: {
    903:   PetscReal x1[3], x2[3], n[3], c[3], norm;
    904:   const PetscInt dim = 3;
    905:   PetscInt       d, p;

    908:   /* 0) Calculate normal vector */
    909:   for (d = 0; d < dim; ++d) {
    910:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
    911:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
    912:   }
    913:   // n = x1 \otimes x2
    914:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
    915:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
    916:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
    917:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    918:   for (d = 0; d < dim; d++) n[d] /= norm;
    919:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
    920:   for (d = 0; d < dim; d++) x1[d] /= norm;
    921:   // x2 = n \otimes x1
    922:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
    923:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
    924:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
    925:   for (d=0; d<dim; d++) {
    926:     R[d * dim + 0] = x1[d];
    927:     R[d * dim + 1] = x2[d];
    928:     R[d * dim + 2] = n[d];
    929:     c[d] = PetscRealPart(coords[0*dim + d]);
    930:   }
    931:   for (p=0; p<coordSize/dim; p++) {
    932:     PetscReal y[3];
    933:     for (d=0; d<dim; d++) y[d] = PetscRealPart(coords[p*dim + d]) - c[d];
    934:     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];
    935:   }
    936:   return(0);
    937: }

    939: PETSC_UNUSED
    940: PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    941: {
    942:   /* Signed volume is 1/2 the determinant

    944:    |  1  1  1 |
    945:    | x0 x1 x2 |
    946:    | y0 y1 y2 |

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

    950:    | x1 x2 |
    951:    | y1 y2 |
    952:   */
    953:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    954:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    955:   PetscReal       M[4], detM;
    956:   M[0] = x1; M[1] = x2;
    957:   M[2] = y1; M[3] = y2;
    958:   DMPlex_Det2D_Internal(&detM, M);
    959:   *vol = 0.5*detM;
    960:   (void)PetscLogFlops(5.0);
    961: }

    963: PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
    964: {
    965:   DMPlex_Det2D_Internal(vol, coords);
    966:   *vol *= 0.5;
    967: }

    969: PETSC_UNUSED
    970: PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    971: {
    972:   /* Signed volume is 1/6th of the determinant

    974:    |  1  1  1  1 |
    975:    | x0 x1 x2 x3 |
    976:    | y0 y1 y2 y3 |
    977:    | z0 z1 z2 z3 |

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

    981:    | x1 x2 x3 |
    982:    | y1 y2 y3 |
    983:    | z1 z2 z3 |
    984:   */
    985:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
    986:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
    987:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    988:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    989:   PetscReal       M[9], detM;
    990:   M[0] = x1; M[1] = x2; M[2] = x3;
    991:   M[3] = y1; M[4] = y2; M[5] = y3;
    992:   M[6] = z1; M[7] = z2; M[8] = z3;
    993:   DMPlex_Det3D_Internal(&detM, M);
    994:   *vol = -onesixth*detM;
    995:   (void)PetscLogFlops(10.0);
    996: }

    998: PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    999: {
    1000:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1001:   DMPlex_Det3D_Internal(vol, coords);
    1002:   *vol *= -onesixth;
    1003: }

    1005: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1006: {
    1007:   PetscSection   coordSection;
    1008:   Vec            coordinates;
    1009:   const PetscScalar *coords;
    1010:   PetscInt       dim, d, off;

    1014:   DMGetCoordinatesLocal(dm, &coordinates);
    1015:   DMGetCoordinateSection(dm, &coordSection);
    1016:   PetscSectionGetDof(coordSection,e,&dim);
    1017:   if (!dim) return(0);
    1018:   PetscSectionGetOffset(coordSection,e,&off);
    1019:   VecGetArrayRead(coordinates,&coords);
    1020:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
    1021:   VecRestoreArrayRead(coordinates,&coords);
    1022:   *detJ = 1.;
    1023:   if (J) {
    1024:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1025:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1026:     if (invJ) {
    1027:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1028:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1029:     }
    1030:   }
    1031:   return(0);
    1032: }

    1034: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1035: {
    1036:   PetscSection   coordSection;
    1037:   Vec            coordinates;
    1038:   PetscScalar   *coords = NULL;
    1039:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

    1043:   DMGetCoordinatesLocal(dm, &coordinates);
    1044:   DMGetCoordinateSection(dm, &coordSection);
    1045:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1046:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1047:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1048:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1049:   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1050:   *detJ = 0.0;
    1051:   if (numCoords == 6) {
    1052:     const PetscInt dim = 3;
    1053:     PetscReal      R[9], J0;

    1055:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1056:     DMPlexComputeProjection3Dto1D(coords, R);
    1057:     if (J)    {
    1058:       J0   = 0.5*PetscRealPart(coords[1]);
    1059:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
    1060:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
    1061:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
    1062:       DMPlex_Det3D_Internal(detJ, J);
    1063:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1064:     }
    1065:   } else if (numCoords == 4) {
    1066:     const PetscInt dim = 2;
    1067:     PetscReal      R[4], J0;

    1069:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1070:     DMPlexComputeProjection2Dto1D(coords, R);
    1071:     if (J)    {
    1072:       J0   = 0.5*PetscRealPart(coords[1]);
    1073:       J[0] = R[0]*J0; J[1] = R[1];
    1074:       J[2] = R[2]*J0; J[3] = R[3];
    1075:       DMPlex_Det2D_Internal(detJ, J);
    1076:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1077:     }
    1078:   } else if (numCoords == 2) {
    1079:     const PetscInt dim = 1;

    1081:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1082:     if (J)    {
    1083:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1084:       *detJ = J[0];
    1085:       PetscLogFlops(2.0);
    1086:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
    1087:     }
    1088:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
    1089:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1090:   return(0);
    1091: }

    1093: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1094: {
    1095:   PetscSection   coordSection;
    1096:   Vec            coordinates;
    1097:   PetscScalar   *coords = NULL;
    1098:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1102:   DMGetCoordinatesLocal(dm, &coordinates);
    1103:   DMGetCoordinateSection(dm, &coordSection);
    1104:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1105:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1106:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1107:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1108:   *detJ = 0.0;
    1109:   if (numCoords == 9) {
    1110:     const PetscInt dim = 3;
    1111:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1113:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1114:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1115:     if (J)    {
    1116:       const PetscInt pdim = 2;

    1118:       for (d = 0; d < pdim; d++) {
    1119:         for (f = 0; f < pdim; f++) {
    1120:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1121:         }
    1122:       }
    1123:       PetscLogFlops(8.0);
    1124:       DMPlex_Det3D_Internal(detJ, J0);
    1125:       for (d = 0; d < dim; d++) {
    1126:         for (f = 0; f < dim; f++) {
    1127:           J[d*dim+f] = 0.0;
    1128:           for (g = 0; g < dim; g++) {
    1129:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1130:           }
    1131:         }
    1132:       }
    1133:       PetscLogFlops(18.0);
    1134:     }
    1135:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1136:   } else if (numCoords == 6) {
    1137:     const PetscInt dim = 2;

    1139:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1140:     if (J)    {
    1141:       for (d = 0; d < dim; d++) {
    1142:         for (f = 0; f < dim; f++) {
    1143:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1144:         }
    1145:       }
    1146:       PetscLogFlops(8.0);
    1147:       DMPlex_Det2D_Internal(detJ, J);
    1148:     }
    1149:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1150:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
    1151:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1152:   return(0);
    1153: }

    1155: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1156: {
    1157:   PetscSection   coordSection;
    1158:   Vec            coordinates;
    1159:   PetscScalar   *coords = NULL;
    1160:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1164:   DMGetCoordinatesLocal(dm, &coordinates);
    1165:   DMGetCoordinateSection(dm, &coordSection);
    1166:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1167:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1168:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1169:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1170:   if (!Nq) {
    1171:     PetscInt vorder[4] = {0, 1, 2, 3};

    1173:     if (isTensor) {vorder[2] = 3; vorder[3] = 2;}
    1174:     *detJ = 0.0;
    1175:     if (numCoords == 12) {
    1176:       const PetscInt dim = 3;
    1177:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1179:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1180:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1181:       if (J)    {
    1182:         const PetscInt pdim = 2;

    1184:         for (d = 0; d < pdim; d++) {
    1185:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*pdim+d]) - PetscRealPart(coords[vorder[0]*pdim+d]));
    1186:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[2]*pdim+d]) - PetscRealPart(coords[vorder[1]*pdim+d]));
    1187:         }
    1188:         PetscLogFlops(8.0);
    1189:         DMPlex_Det3D_Internal(detJ, J0);
    1190:         for (d = 0; d < dim; d++) {
    1191:           for (f = 0; f < dim; f++) {
    1192:             J[d*dim+f] = 0.0;
    1193:             for (g = 0; g < dim; g++) {
    1194:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1195:             }
    1196:           }
    1197:         }
    1198:         PetscLogFlops(18.0);
    1199:       }
    1200:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1201:     } else if (numCoords == 8) {
    1202:       const PetscInt dim = 2;

    1204:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1205:       if (J)    {
    1206:         for (d = 0; d < dim; d++) {
    1207:           J[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1208:           J[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[3]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1209:         }
    1210:         PetscLogFlops(8.0);
    1211:         DMPlex_Det2D_Internal(detJ, J);
    1212:       }
    1213:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1214:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1215:   } else {
    1216:     const PetscInt Nv = 4;
    1217:     const PetscInt dimR = 2;
    1218:     PetscInt  zToPlex[4] = {0, 1, 3, 2};
    1219:     PetscReal zOrder[12];
    1220:     PetscReal zCoeff[12];
    1221:     PetscInt  i, j, k, l, dim;

    1223:     if (isTensor) {zToPlex[2] = 2; zToPlex[3] = 3;}
    1224:     if (numCoords == 12) {
    1225:       dim = 3;
    1226:     } else if (numCoords == 8) {
    1227:       dim = 2;
    1228:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1229:     for (i = 0; i < Nv; i++) {
    1230:       PetscInt zi = zToPlex[i];

    1232:       for (j = 0; j < dim; j++) {
    1233:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1234:       }
    1235:     }
    1236:     for (j = 0; j < dim; j++) {
    1237:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1238:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1239:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1240:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1241:     }
    1242:     for (i = 0; i < Nq; i++) {
    1243:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    1245:       if (v) {
    1246:         PetscReal extPoint[4];

    1248:         extPoint[0] = 1.;
    1249:         extPoint[1] = xi;
    1250:         extPoint[2] = eta;
    1251:         extPoint[3] = xi * eta;
    1252:         for (j = 0; j < dim; j++) {
    1253:           PetscReal val = 0.;

    1255:           for (k = 0; k < Nv; k++) {
    1256:             val += extPoint[k] * zCoeff[dim * k + j];
    1257:           }
    1258:           v[i * dim + j] = val;
    1259:         }
    1260:       }
    1261:       if (J) {
    1262:         PetscReal extJ[8];

    1264:         extJ[0] = 0.;
    1265:         extJ[1] = 0.;
    1266:         extJ[2] = 1.;
    1267:         extJ[3] = 0.;
    1268:         extJ[4] = 0.;
    1269:         extJ[5] = 1.;
    1270:         extJ[6] = eta;
    1271:         extJ[7] = xi;
    1272:         for (j = 0; j < dim; j++) {
    1273:           for (k = 0; k < dimR; k++) {
    1274:             PetscReal val = 0.;

    1276:             for (l = 0; l < Nv; l++) {
    1277:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1278:             }
    1279:             J[i * dim * dim + dim * j + k] = val;
    1280:           }
    1281:         }
    1282:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    1283:           PetscReal x, y, z;
    1284:           PetscReal *iJ = &J[i * dim * dim];
    1285:           PetscReal norm;

    1287:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    1288:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    1289:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    1290:           norm = PetscSqrtReal(x * x + y * y + z * z);
    1291:           iJ[2] = x / norm;
    1292:           iJ[5] = y / norm;
    1293:           iJ[8] = z / norm;
    1294:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1295:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1296:         } else {
    1297:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    1298:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1299:         }
    1300:       }
    1301:     }
    1302:   }
    1303:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1304:   return(0);
    1305: }

    1307: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1308: {
    1309:   PetscSection   coordSection;
    1310:   Vec            coordinates;
    1311:   PetscScalar   *coords = NULL;
    1312:   const PetscInt dim = 3;
    1313:   PetscInt       d;

    1317:   DMGetCoordinatesLocal(dm, &coordinates);
    1318:   DMGetCoordinateSection(dm, &coordSection);
    1319:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1320:   *detJ = 0.0;
    1321:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1322:   if (J)    {
    1323:     for (d = 0; d < dim; d++) {
    1324:       /* I orient with outward face normals */
    1325:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1326:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1327:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1328:     }
    1329:     PetscLogFlops(18.0);
    1330:     DMPlex_Det3D_Internal(detJ, J);
    1331:   }
    1332:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1333:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1334:   return(0);
    1335: }

    1337: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1338: {
    1339:   PetscSection   coordSection;
    1340:   Vec            coordinates;
    1341:   PetscScalar   *coords = NULL;
    1342:   const PetscInt dim = 3;
    1343:   PetscInt       d;

    1347:   DMGetCoordinatesLocal(dm, &coordinates);
    1348:   DMGetCoordinateSection(dm, &coordSection);
    1349:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1350:   if (!Nq) {
    1351:     *detJ = 0.0;
    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[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1356:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1357:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1358:       }
    1359:       PetscLogFlops(18.0);
    1360:       DMPlex_Det3D_Internal(detJ, J);
    1361:     }
    1362:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1363:   } else {
    1364:     const PetscInt Nv = 8;
    1365:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    1366:     const PetscInt dim = 3;
    1367:     const PetscInt dimR = 3;
    1368:     PetscReal zOrder[24];
    1369:     PetscReal zCoeff[24];
    1370:     PetscInt  i, j, k, l;

    1372:     for (i = 0; i < Nv; i++) {
    1373:       PetscInt zi = zToPlex[i];

    1375:       for (j = 0; j < dim; j++) {
    1376:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1377:       }
    1378:     }
    1379:     for (j = 0; j < dim; j++) {
    1380:       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]);
    1381:       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]);
    1382:       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]);
    1383:       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]);
    1384:       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]);
    1385:       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]);
    1386:       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]);
    1387:       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]);
    1388:     }
    1389:     for (i = 0; i < Nq; i++) {
    1390:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    1392:       if (v) {
    1393:         PetscReal extPoint[8];

    1395:         extPoint[0] = 1.;
    1396:         extPoint[1] = xi;
    1397:         extPoint[2] = eta;
    1398:         extPoint[3] = xi * eta;
    1399:         extPoint[4] = theta;
    1400:         extPoint[5] = theta * xi;
    1401:         extPoint[6] = theta * eta;
    1402:         extPoint[7] = theta * eta * xi;
    1403:         for (j = 0; j < dim; j++) {
    1404:           PetscReal val = 0.;

    1406:           for (k = 0; k < Nv; k++) {
    1407:             val += extPoint[k] * zCoeff[dim * k + j];
    1408:           }
    1409:           v[i * dim + j] = val;
    1410:         }
    1411:       }
    1412:       if (J) {
    1413:         PetscReal extJ[24];

    1415:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
    1416:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
    1417:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
    1418:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
    1419:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
    1420:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
    1421:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
    1422:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

    1424:         for (j = 0; j < dim; j++) {
    1425:           for (k = 0; k < dimR; k++) {
    1426:             PetscReal val = 0.;

    1428:             for (l = 0; l < Nv; l++) {
    1429:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1430:             }
    1431:             J[i * dim * dim + dim * j + k] = val;
    1432:           }
    1433:         }
    1434:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1435:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1436:       }
    1437:     }
    1438:   }
    1439:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1440:   return(0);
    1441: }

    1443: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1444: {
    1445:   DMPolytopeType  ct;
    1446:   PetscInt        depth, dim, coordDim, coneSize, i;
    1447:   PetscInt        Nq = 0;
    1448:   const PetscReal *points = NULL;
    1449:   DMLabel         depthLabel;
    1450:   PetscReal       xi0[3] = {-1.,-1.,-1.}, v0[3], J0[9], detJ0;
    1451:   PetscBool       isAffine = PETSC_TRUE;
    1452:   PetscErrorCode  ierr;

    1455:   DMPlexGetDepth(dm, &depth);
    1456:   DMPlexGetConeSize(dm, cell, &coneSize);
    1457:   DMPlexGetDepthLabel(dm, &depthLabel);
    1458:   DMLabelGetValue(depthLabel, cell, &dim);
    1459:   if (depth == 1 && dim == 1) {
    1460:     DMGetDimension(dm, &dim);
    1461:   }
    1462:   DMGetCoordinateDim(dm, &coordDim);
    1463:   if (coordDim > 3) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %D > 3", coordDim);
    1464:   if (quad) {PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);}
    1465:   DMPlexGetCellType(dm, cell, &ct);
    1466:   switch (ct) {
    1467:     case DM_POLYTOPE_POINT:
    1468:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1469:     isAffine = PETSC_FALSE;
    1470:     break;
    1471:     case DM_POLYTOPE_SEGMENT:
    1472:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1473:     if (Nq) {DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1474:     else    {DMPlexComputeLineGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1475:     break;
    1476:     case DM_POLYTOPE_TRIANGLE:
    1477:     if (Nq) {DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1478:     else    {DMPlexComputeTriangleGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1479:     break;
    1480:     case DM_POLYTOPE_QUADRILATERAL:
    1481:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ);
    1482:     isAffine = PETSC_FALSE;
    1483:     break;
    1484:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1485:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ);
    1486:     isAffine = PETSC_FALSE;
    1487:     break;
    1488:     case DM_POLYTOPE_TETRAHEDRON:
    1489:     if (Nq) {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1490:     else    {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1491:     break;
    1492:     case DM_POLYTOPE_HEXAHEDRON:
    1493:     DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1494:     isAffine = PETSC_FALSE;
    1495:     break;
    1496:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    1497:   }
    1498:   if (isAffine && Nq) {
    1499:     if (v) {
    1500:       for (i = 0; i < Nq; i++) {
    1501:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    1502:       }
    1503:     }
    1504:     if (detJ) {
    1505:       for (i = 0; i < Nq; i++) {
    1506:         detJ[i] = detJ0;
    1507:       }
    1508:     }
    1509:     if (J) {
    1510:       PetscInt k;

    1512:       for (i = 0, k = 0; i < Nq; i++) {
    1513:         PetscInt j;

    1515:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1516:           J[k] = J0[j];
    1517:         }
    1518:       }
    1519:     }
    1520:     if (invJ) {
    1521:       PetscInt k;
    1522:       switch (coordDim) {
    1523:       case 0:
    1524:         break;
    1525:       case 1:
    1526:         invJ[0] = 1./J0[0];
    1527:         break;
    1528:       case 2:
    1529:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    1530:         break;
    1531:       case 3:
    1532:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    1533:         break;
    1534:       }
    1535:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    1536:         PetscInt j;

    1538:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1539:           invJ[k] = invJ[j];
    1540:         }
    1541:       }
    1542:     }
    1543:   }
    1544:   return(0);
    1545: }

    1547: /*@C
    1548:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    1550:   Collective on dm

    1552:   Input Arguments:
    1553: + dm   - the DM
    1554: - cell - the cell

    1556:   Output Arguments:
    1557: + v0   - the translation part of this affine transform
    1558: . J    - the Jacobian of the transform from the reference element
    1559: . invJ - the inverse of the Jacobian
    1560: - detJ - the Jacobian determinant

    1562:   Level: advanced

    1564:   Fortran Notes:
    1565:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1566:   include petsc.h90 in your code.

    1568: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
    1569: @*/
    1570: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1571: {

    1575:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
    1576:   return(0);
    1577: }

    1579: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1580: {
    1581:   PetscQuadrature   feQuad;
    1582:   PetscSection      coordSection;
    1583:   Vec               coordinates;
    1584:   PetscScalar      *coords = NULL;
    1585:   const PetscReal  *quadPoints;
    1586:   PetscTabulation T;
    1587:   PetscInt          dim, cdim, pdim, qdim, Nq, numCoords, q;
    1588:   PetscErrorCode    ierr;

    1591:   DMGetCoordinatesLocal(dm, &coordinates);
    1592:   DMGetCoordinateSection(dm, &coordSection);
    1593:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1594:   DMGetDimension(dm, &dim);
    1595:   DMGetCoordinateDim(dm, &cdim);
    1596:   if (!quad) { /* use the first point of the first functional of the dual space */
    1597:     PetscDualSpace dsp;

    1599:     PetscFEGetDualSpace(fe, &dsp);
    1600:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
    1601:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1602:     Nq = 1;
    1603:   } else {
    1604:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1605:   }
    1606:   PetscFEGetDimension(fe, &pdim);
    1607:   PetscFEGetQuadrature(fe, &feQuad);
    1608:   if (feQuad == quad) {
    1609:     PetscFEGetCellTabulation(fe, &T);
    1610:     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);
    1611:   } else {
    1612:     PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T);
    1613:   }
    1614:   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
    1615:   {
    1616:     const PetscReal *basis    = T->T[0];
    1617:     const PetscReal *basisDer = T->T[1];
    1618:     PetscReal        detJt;

    1620:     if (v) {
    1621:       PetscArrayzero(v, Nq*cdim);
    1622:       for (q = 0; q < Nq; ++q) {
    1623:         PetscInt i, k;

    1625:         for (k = 0; k < pdim; ++k) {
    1626:           const PetscInt vertex = k/cdim;
    1627:           for (i = 0; i < cdim; ++i) {
    1628:             v[q*cdim + i] += basis[(q*pdim + k)*cdim + i] * PetscRealPart(coords[vertex*cdim + i]);
    1629:           }
    1630:         }
    1631:         PetscLogFlops(2.0*pdim*cdim);
    1632:       }
    1633:     }
    1634:     if (J) {
    1635:       PetscArrayzero(J, Nq*cdim*cdim);
    1636:       for (q = 0; q < Nq; ++q) {
    1637:         PetscInt i, j, k, c, r;

    1639:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    1640:         for (k = 0; k < pdim; ++k) {
    1641:           const PetscInt vertex = k/cdim;
    1642:           for (j = 0; j < dim; ++j) {
    1643:             for (i = 0; i < cdim; ++i) {
    1644:               J[(q*cdim + i)*cdim + j] += basisDer[((q*pdim + k)*cdim + i)*dim + j] * PetscRealPart(coords[vertex*cdim + i]);
    1645:             }
    1646:           }
    1647:         }
    1648:         PetscLogFlops(2.0*pdim*dim*cdim);
    1649:         if (cdim > dim) {
    1650:           for (c = dim; c < cdim; ++c)
    1651:             for (r = 0; r < cdim; ++r)
    1652:               J[r*cdim+c] = r == c ? 1.0 : 0.0;
    1653:         }
    1654:         if (!detJ && !invJ) continue;
    1655:         detJt = 0.;
    1656:         switch (cdim) {
    1657:         case 3:
    1658:           DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
    1659:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1660:           break;
    1661:         case 2:
    1662:           DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
    1663:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1664:           break;
    1665:         case 1:
    1666:           detJt = J[q*cdim*dim];
    1667:           if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
    1668:         }
    1669:         if (detJ) detJ[q] = detJt;
    1670:       }
    1671:     } else if (detJ || invJ) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
    1672:   }
    1673:   if (feQuad != quad) {PetscTabulationDestroy(&T);}
    1674:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1675:   return(0);
    1676: }

    1678: /*@C
    1679:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    1681:   Collective on dm

    1683:   Input Arguments:
    1684: + dm   - the DM
    1685: . cell - the cell
    1686: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
    1687:          evaluated at the first vertex of the reference element

    1689:   Output Arguments:
    1690: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
    1691: . J    - the Jacobian of the transform from the reference element at each quadrature point
    1692: . invJ - the inverse of the Jacobian at each quadrature point
    1693: - detJ - the Jacobian determinant at each quadrature point

    1695:   Level: advanced

    1697:   Fortran Notes:
    1698:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1699:   include petsc.h90 in your code.

    1701: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1702: @*/
    1703: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1704: {
    1705:   DM             cdm;
    1706:   PetscFE        fe = NULL;

    1711:   DMGetCoordinateDM(dm, &cdm);
    1712:   if (cdm) {
    1713:     PetscClassId id;
    1714:     PetscInt     numFields;
    1715:     PetscDS      prob;
    1716:     PetscObject  disc;

    1718:     DMGetNumFields(cdm, &numFields);
    1719:     if (numFields) {
    1720:       DMGetDS(cdm, &prob);
    1721:       PetscDSGetDiscretization(prob,0,&disc);
    1722:       PetscObjectGetClassId(disc,&id);
    1723:       if (id == PETSCFE_CLASSID) {
    1724:         fe = (PetscFE) disc;
    1725:       }
    1726:     }
    1727:   }
    1728:   if (!fe) {DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);}
    1729:   else     {DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);}
    1730:   return(0);
    1731: }

    1733: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1734: {
    1735:   PetscSection   coordSection;
    1736:   Vec            coordinates;
    1737:   PetscScalar   *coords = NULL;
    1738:   PetscScalar    tmp[2];
    1739:   PetscInt       coordSize, d;

    1743:   DMGetCoordinatesLocal(dm, &coordinates);
    1744:   DMGetCoordinateSection(dm, &coordSection);
    1745:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1746:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
    1747:   if (centroid) {
    1748:     for (d = 0; d < dim; ++d) centroid[d] = 0.5*PetscRealPart(coords[d] + tmp[d]);
    1749:   }
    1750:   if (normal) {
    1751:     PetscReal norm;

    1753:     if (dim != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "We only support 2D edges right now");
    1754:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
    1755:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
    1756:     norm       = DMPlex_NormD_Internal(dim, normal);
    1757:     for (d = 0; d < dim; ++d) normal[d] /= norm;
    1758:   }
    1759:   if (vol) {
    1760:     *vol = 0.0;
    1761:     for (d = 0; d < dim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - tmp[d]));
    1762:     *vol = PetscSqrtReal(*vol);
    1763:   }
    1764:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1765:   return(0);
    1766: }

    1768: /* Centroid_i = (\sum_n A_n Cn_i) / A */
    1769: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1770: {
    1771:   DMPolytopeType ct;
    1772:   PetscSection   coordSection;
    1773:   Vec            coordinates;
    1774:   PetscScalar   *coords = NULL;
    1775:   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
    1776:   PetscBool      isHybrid = PETSC_FALSE;
    1777:   PetscInt       fv[4] = {0, 1, 2, 3};
    1778:   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;

    1782:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    1783:   DMPlexGetCellType(dm, cell, &ct);
    1784:   switch (ct) {
    1785:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1786:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1787:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1788:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1789:       isHybrid = PETSC_TRUE;
    1790:     default: break;
    1791:   }
    1792:   DMGetCoordinatesLocal(dm, &coordinates);
    1793:   DMPlexGetConeSize(dm, cell, &numCorners);
    1794:   DMGetCoordinateSection(dm, &coordSection);
    1795:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1796:   DMGetCoordinateDim(dm, &dim);
    1797:   /* Side faces for hybrid cells are are stored as tensor products */
    1798:   if (isHybrid && numCorners == 4) {fv[2] = 3; fv[3] = 2;}

    1800:   if (dim > 2 && centroid) {
    1801:     v0[0] = PetscRealPart(coords[0]);
    1802:     v0[1] = PetscRealPart(coords[1]);
    1803:     v0[2] = PetscRealPart(coords[2]);
    1804:   }
    1805:   if (normal) {
    1806:     if (dim > 2) {
    1807:       const PetscReal x0 = PetscRealPart(coords[dim*fv[1]+0] - coords[0]), x1 = PetscRealPart(coords[dim*fv[2]+0] - coords[0]);
    1808:       const PetscReal y0 = PetscRealPart(coords[dim*fv[1]+1] - coords[1]), y1 = PetscRealPart(coords[dim*fv[2]+1] - coords[1]);
    1809:       const PetscReal z0 = PetscRealPart(coords[dim*fv[1]+2] - coords[2]), z1 = PetscRealPart(coords[dim*fv[2]+2] - coords[2]);
    1810:       PetscReal       norm;

    1812:       normal[0] = y0*z1 - z0*y1;
    1813:       normal[1] = z0*x1 - x0*z1;
    1814:       normal[2] = x0*y1 - y0*x1;
    1815:       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
    1816:       normal[0] /= norm;
    1817:       normal[1] /= norm;
    1818:       normal[2] /= norm;
    1819:     } else {
    1820:       for (d = 0; d < dim; ++d) normal[d] = 0.0;
    1821:     }
    1822:   }
    1823:   if (dim == 3) {DMPlexComputeProjection3Dto2D(coordSize, coords, R);}
    1824:   for (p = 0; p < numCorners; ++p) {
    1825:     const PetscInt pi  = p < 4 ? fv[p] : p;
    1826:     const PetscInt pin = p < 3 ? fv[(p+1)%numCorners] : (p+1)%numCorners;
    1827:     /* Need to do this copy to get types right */
    1828:     for (d = 0; d < tdim; ++d) {
    1829:       ctmp[d]      = PetscRealPart(coords[pi*tdim+d]);
    1830:       ctmp[tdim+d] = PetscRealPart(coords[pin*tdim+d]);
    1831:     }
    1832:     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
    1833:     vsum += vtmp;
    1834:     for (d = 0; d < tdim; ++d) {
    1835:       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
    1836:     }
    1837:   }
    1838:   for (d = 0; d < tdim; ++d) {
    1839:     csum[d] /= (tdim+1)*vsum;
    1840:   }
    1841:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1842:   if (vol) *vol = PetscAbsReal(vsum);
    1843:   if (centroid) {
    1844:     if (dim > 2) {
    1845:       for (d = 0; d < dim; ++d) {
    1846:         centroid[d] = v0[d];
    1847:         for (e = 0; e < dim; ++e) {
    1848:           centroid[d] += R[d*dim+e]*csum[e];
    1849:         }
    1850:       }
    1851:     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
    1852:   }
    1853:   return(0);
    1854: }

    1856: /* Centroid_i = (\sum_n V_n Cn_i) / V */
    1857: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1858: {
    1859:   DMPolytopeType  ct;
    1860:   PetscSection    coordSection;
    1861:   Vec             coordinates;
    1862:   PetscScalar    *coords = NULL;
    1863:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
    1864:   const PetscInt *faces, *facesO;
    1865:   PetscBool       isHybrid = PETSC_FALSE;
    1866:   PetscInt        numFaces, f, coordSize, p, d;
    1867:   PetscErrorCode  ierr;

    1870:   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
    1871:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    1872:   DMPlexGetCellType(dm, cell, &ct);
    1873:   switch (ct) {
    1874:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1875:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1876:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1877:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1878:       isHybrid = PETSC_TRUE;
    1879:     default: break;
    1880:   }

    1882:   DMGetCoordinatesLocal(dm, &coordinates);
    1883:   DMGetCoordinateSection(dm, &coordSection);

    1885:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    1886:   DMPlexGetConeSize(dm, cell, &numFaces);
    1887:   DMPlexGetCone(dm, cell, &faces);
    1888:   DMPlexGetConeOrientation(dm, cell, &facesO);
    1889:   for (f = 0; f < numFaces; ++f) {
    1890:     PetscBool      flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
    1891:     DMPolytopeType ct;

    1893:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    1894:     DMPlexGetCellType(dm, faces[f], &ct);
    1895:     switch (ct) {
    1896:     case DM_POLYTOPE_TRIANGLE:
    1897:       for (d = 0; d < dim; ++d) {
    1898:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
    1899:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
    1900:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
    1901:       }
    1902:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1903:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    1904:       vsum += vtmp;
    1905:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
    1906:         for (d = 0; d < dim; ++d) {
    1907:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1908:         }
    1909:       }
    1910:       break;
    1911:     case DM_POLYTOPE_QUADRILATERAL:
    1912:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1913:     {
    1914:       PetscInt fv[4] = {0, 1, 2, 3};

    1916:       /* Side faces for hybrid cells are are stored as tensor products */
    1917:       if (isHybrid && f > 1) {fv[2] = 3; fv[3] = 2;}
    1918:       /* DO FOR PYRAMID */
    1919:       /* First tet */
    1920:       for (d = 0; d < dim; ++d) {
    1921:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[0]*dim+d]);
    1922:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
    1923:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
    1924:       }
    1925:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1926:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    1927:       vsum += vtmp;
    1928:       if (centroid) {
    1929:         for (d = 0; d < dim; ++d) {
    1930:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1931:         }
    1932:       }
    1933:       /* Second tet */
    1934:       for (d = 0; d < dim; ++d) {
    1935:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
    1936:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[2]*dim+d]);
    1937:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
    1938:       }
    1939:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1940:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    1941:       vsum += vtmp;
    1942:       if (centroid) {
    1943:         for (d = 0; d < dim; ++d) {
    1944:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1945:         }
    1946:       }
    1947:       break;
    1948:     }
    1949:     default:
    1950:       SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %D of type %s", faces[f], DMPolytopeTypes[ct]);
    1951:     }
    1952:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    1953:   }
    1954:   if (vol)     *vol = PetscAbsReal(vsum);
    1955:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
    1956:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
    1957:   return(0);
    1958: }

    1960: /*@C
    1961:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    1963:   Collective on dm

    1965:   Input Arguments:
    1966: + dm   - the DM
    1967: - cell - the cell

    1969:   Output Arguments:
    1970: + volume   - the cell volume
    1971: . centroid - the cell centroid
    1972: - normal - the cell normal, if appropriate

    1974:   Level: advanced

    1976:   Fortran Notes:
    1977:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1978:   include petsc.h90 in your code.

    1980: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1981: @*/
    1982: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1983: {
    1984:   PetscInt       depth, dim;

    1988:   DMPlexGetDepth(dm, &depth);
    1989:   DMGetDimension(dm, &dim);
    1990:   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
    1991:   DMPlexGetPointDepth(dm, cell, &depth);
    1992:   switch (depth) {
    1993:   case 1:
    1994:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
    1995:     break;
    1996:   case 2:
    1997:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
    1998:     break;
    1999:   case 3:
    2000:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
    2001:     break;
    2002:   default:
    2003:     SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
    2004:   }
    2005:   return(0);
    2006: }

    2008: /*@
    2009:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

    2011:   Collective on dm

    2013:   Input Parameter:
    2014: . dm - The DMPlex

    2016:   Output Parameter:
    2017: . cellgeom - A vector with the cell geometry data for each cell

    2019:   Level: beginner

    2021: @*/
    2022: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
    2023: {
    2024:   DM             dmCell;
    2025:   Vec            coordinates;
    2026:   PetscSection   coordSection, sectionCell;
    2027:   PetscScalar   *cgeom;
    2028:   PetscInt       cStart, cEnd, c;

    2032:   DMClone(dm, &dmCell);
    2033:   DMGetCoordinateSection(dm, &coordSection);
    2034:   DMGetCoordinatesLocal(dm, &coordinates);
    2035:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2036:   DMSetCoordinatesLocal(dmCell, coordinates);
    2037:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2038:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    2039:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2040:   /* TODO This needs to be multiplied by Nq for non-affine */
    2041:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));}
    2042:   PetscSectionSetUp(sectionCell);
    2043:   DMSetLocalSection(dmCell, sectionCell);
    2044:   PetscSectionDestroy(&sectionCell);
    2045:   DMCreateLocalVector(dmCell, cellgeom);
    2046:   VecGetArray(*cellgeom, &cgeom);
    2047:   for (c = cStart; c < cEnd; ++c) {
    2048:     PetscFEGeom *cg;

    2050:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2051:     PetscArrayzero(cg, 1);
    2052:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
    2053:     if (*cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double) *cg->detJ, c);
    2054:   }
    2055:   return(0);
    2056: }

    2058: /*@
    2059:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2061:   Input Parameter:
    2062: . dm - The DM

    2064:   Output Parameters:
    2065: + cellgeom - A Vec of PetscFVCellGeom data
    2066: - facegeom - A Vec of PetscFVFaceGeom data

    2068:   Level: developer

    2070: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
    2071: @*/
    2072: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2073: {
    2074:   DM             dmFace, dmCell;
    2075:   DMLabel        ghostLabel;
    2076:   PetscSection   sectionFace, sectionCell;
    2077:   PetscSection   coordSection;
    2078:   Vec            coordinates;
    2079:   PetscScalar   *fgeom, *cgeom;
    2080:   PetscReal      minradius, gminradius;
    2081:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2085:   DMGetDimension(dm, &dim);
    2086:   DMGetCoordinateSection(dm, &coordSection);
    2087:   DMGetCoordinatesLocal(dm, &coordinates);
    2088:   /* Make cell centroids and volumes */
    2089:   DMClone(dm, &dmCell);
    2090:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2091:   DMSetCoordinatesLocal(dmCell, coordinates);
    2092:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2093:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2094:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2095:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2096:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));}
    2097:   PetscSectionSetUp(sectionCell);
    2098:   DMSetLocalSection(dmCell, sectionCell);
    2099:   PetscSectionDestroy(&sectionCell);
    2100:   DMCreateLocalVector(dmCell, cellgeom);
    2101:   if (cEndInterior < 0) cEndInterior = cEnd;
    2102:   VecGetArray(*cellgeom, &cgeom);
    2103:   for (c = cStart; c < cEndInterior; ++c) {
    2104:     PetscFVCellGeom *cg;

    2106:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2107:     PetscArrayzero(cg, 1);
    2108:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
    2109:   }
    2110:   /* Compute face normals and minimum cell radius */
    2111:   DMClone(dm, &dmFace);
    2112:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
    2113:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2114:   PetscSectionSetChart(sectionFace, fStart, fEnd);
    2115:   for (f = fStart; f < fEnd; ++f) {PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));}
    2116:   PetscSectionSetUp(sectionFace);
    2117:   DMSetLocalSection(dmFace, sectionFace);
    2118:   PetscSectionDestroy(&sectionFace);
    2119:   DMCreateLocalVector(dmFace, facegeom);
    2120:   VecGetArray(*facegeom, &fgeom);
    2121:   DMGetLabel(dm, "ghost", &ghostLabel);
    2122:   minradius = PETSC_MAX_REAL;
    2123:   for (f = fStart; f < fEnd; ++f) {
    2124:     PetscFVFaceGeom *fg;
    2125:     PetscReal        area;
    2126:     const PetscInt  *cells;
    2127:     PetscInt         ncells, ghost = -1, d, numChildren;

    2129:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2130:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
    2131:     DMPlexGetSupport(dm, f, &cells);
    2132:     DMPlexGetSupportSize(dm, f, &ncells);
    2133:     /* It is possible to get a face with no support when using partition overlap */
    2134:     if (!ncells || ghost >= 0 || numChildren) continue;
    2135:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
    2136:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
    2137:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    2138:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    2139:     {
    2140:       PetscFVCellGeom *cL, *cR;
    2141:       PetscReal       *lcentroid, *rcentroid;
    2142:       PetscReal        l[3], r[3], v[3];

    2144:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
    2145:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    2146:       if (ncells > 1) {
    2147:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
    2148:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    2149:       }
    2150:       else {
    2151:         rcentroid = fg->centroid;
    2152:       }
    2153:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
    2154:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
    2155:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    2156:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    2157:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    2158:       }
    2159:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    2160:         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]);
    2161:         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]);
    2162:         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
    2163:       }
    2164:       if (cells[0] < cEndInterior) {
    2165:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    2166:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2167:       }
    2168:       if (ncells > 1 && cells[1] < cEndInterior) {
    2169:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    2170:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2171:       }
    2172:     }
    2173:   }
    2174:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
    2175:   DMPlexSetMinRadius(dm, gminradius);
    2176:   /* Compute centroids of ghost cells */
    2177:   for (c = cEndInterior; c < cEnd; ++c) {
    2178:     PetscFVFaceGeom *fg;
    2179:     const PetscInt  *cone,    *support;
    2180:     PetscInt         coneSize, supportSize, s;

    2182:     DMPlexGetConeSize(dmCell, c, &coneSize);
    2183:     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
    2184:     DMPlexGetCone(dmCell, c, &cone);
    2185:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
    2186:     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
    2187:     DMPlexGetSupport(dmCell, cone[0], &support);
    2188:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
    2189:     for (s = 0; s < 2; ++s) {
    2190:       /* Reflect ghost centroid across plane of face */
    2191:       if (support[s] == c) {
    2192:         PetscFVCellGeom       *ci;
    2193:         PetscFVCellGeom       *cg;
    2194:         PetscReal              c2f[3], a;

    2196:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
    2197:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    2198:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    2199:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
    2200:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
    2201:         cg->volume = ci->volume;
    2202:       }
    2203:     }
    2204:   }
    2205:   VecRestoreArray(*facegeom, &fgeom);
    2206:   VecRestoreArray(*cellgeom, &cgeom);
    2207:   DMDestroy(&dmCell);
    2208:   DMDestroy(&dmFace);
    2209:   return(0);
    2210: }

    2212: /*@C
    2213:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    2215:   Not collective

    2217:   Input Argument:
    2218: . dm - the DM

    2220:   Output Argument:
    2221: . minradius - the minium cell radius

    2223:   Level: developer

    2225: .seealso: DMGetCoordinates()
    2226: @*/
    2227: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    2228: {
    2232:   *minradius = ((DM_Plex*) dm->data)->minradius;
    2233:   return(0);
    2234: }

    2236: /*@C
    2237:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    2239:   Logically collective

    2241:   Input Arguments:
    2242: + dm - the DM
    2243: - minradius - the minium cell radius

    2245:   Level: developer

    2247: .seealso: DMSetCoordinates()
    2248: @*/
    2249: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    2250: {
    2253:   ((DM_Plex*) dm->data)->minradius = minradius;
    2254:   return(0);
    2255: }

    2257: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2258: {
    2259:   DMLabel        ghostLabel;
    2260:   PetscScalar   *dx, *grad, **gref;
    2261:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    2265:   DMGetDimension(dm, &dim);
    2266:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2267:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2268:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
    2269:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2270:   DMGetLabel(dm, "ghost", &ghostLabel);
    2271:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2272:   for (c = cStart; c < cEndInterior; c++) {
    2273:     const PetscInt        *faces;
    2274:     PetscInt               numFaces, usedFaces, f, d;
    2275:     PetscFVCellGeom        *cg;
    2276:     PetscBool              boundary;
    2277:     PetscInt               ghost;

    2279:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2280:     DMPlexGetConeSize(dm, c, &numFaces);
    2281:     DMPlexGetCone(dm, c, &faces);
    2282:     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
    2283:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2284:       PetscFVCellGeom       *cg1;
    2285:       PetscFVFaceGeom       *fg;
    2286:       const PetscInt        *fcells;
    2287:       PetscInt               ncell, side;

    2289:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2290:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2291:       if ((ghost >= 0) || boundary) continue;
    2292:       DMPlexGetSupport(dm, faces[f], &fcells);
    2293:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    2294:       ncell = fcells[!side];    /* the neighbor */
    2295:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
    2296:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2297:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2298:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2299:     }
    2300:     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
    2301:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
    2302:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2303:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2304:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2305:       if ((ghost >= 0) || boundary) continue;
    2306:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
    2307:       ++usedFaces;
    2308:     }
    2309:   }
    2310:   PetscFree3(dx, grad, gref);
    2311:   return(0);
    2312: }

    2314: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2315: {
    2316:   DMLabel        ghostLabel;
    2317:   PetscScalar   *dx, *grad, **gref;
    2318:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    2319:   PetscSection   neighSec;
    2320:   PetscInt     (*neighbors)[2];
    2321:   PetscInt      *counter;

    2325:   DMGetDimension(dm, &dim);
    2326:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2327:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2328:   if (cEndInterior < 0) cEndInterior = cEnd;
    2329:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
    2330:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
    2331:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2332:   DMGetLabel(dm, "ghost", &ghostLabel);
    2333:   for (f = fStart; f < fEnd; f++) {
    2334:     const PetscInt        *fcells;
    2335:     PetscBool              boundary;
    2336:     PetscInt               ghost = -1;
    2337:     PetscInt               numChildren, numCells, c;

    2339:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2340:     DMIsBoundaryPoint(dm, f, &boundary);
    2341:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2342:     if ((ghost >= 0) || boundary || numChildren) continue;
    2343:     DMPlexGetSupportSize(dm, f, &numCells);
    2344:     if (numCells == 2) {
    2345:       DMPlexGetSupport(dm, f, &fcells);
    2346:       for (c = 0; c < 2; c++) {
    2347:         PetscInt cell = fcells[c];

    2349:         if (cell >= cStart && cell < cEndInterior) {
    2350:           PetscSectionAddDof(neighSec,cell,1);
    2351:         }
    2352:       }
    2353:     }
    2354:   }
    2355:   PetscSectionSetUp(neighSec);
    2356:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
    2357:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2358:   nStart = 0;
    2359:   PetscSectionGetStorageSize(neighSec,&nEnd);
    2360:   PetscMalloc1((nEnd-nStart),&neighbors);
    2361:   PetscCalloc1((cEndInterior-cStart),&counter);
    2362:   for (f = fStart; f < fEnd; f++) {
    2363:     const PetscInt        *fcells;
    2364:     PetscBool              boundary;
    2365:     PetscInt               ghost = -1;
    2366:     PetscInt               numChildren, numCells, c;

    2368:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2369:     DMIsBoundaryPoint(dm, f, &boundary);
    2370:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2371:     if ((ghost >= 0) || boundary || numChildren) continue;
    2372:     DMPlexGetSupportSize(dm, f, &numCells);
    2373:     if (numCells == 2) {
    2374:       DMPlexGetSupport(dm, f, &fcells);
    2375:       for (c = 0; c < 2; c++) {
    2376:         PetscInt cell = fcells[c], off;

    2378:         if (cell >= cStart && cell < cEndInterior) {
    2379:           PetscSectionGetOffset(neighSec,cell,&off);
    2380:           off += counter[cell - cStart]++;
    2381:           neighbors[off][0] = f;
    2382:           neighbors[off][1] = fcells[1 - c];
    2383:         }
    2384:       }
    2385:     }
    2386:   }
    2387:   PetscFree(counter);
    2388:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2389:   for (c = cStart; c < cEndInterior; c++) {
    2390:     PetscInt               numFaces, f, d, off, ghost = -1;
    2391:     PetscFVCellGeom        *cg;

    2393:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2394:     PetscSectionGetDof(neighSec, c, &numFaces);
    2395:     PetscSectionGetOffset(neighSec, c, &off);
    2396:     if (ghostLabel) {DMLabelGetValue(ghostLabel, c, &ghost);}
    2397:     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);
    2398:     for (f = 0; f < numFaces; ++f) {
    2399:       PetscFVCellGeom       *cg1;
    2400:       PetscFVFaceGeom       *fg;
    2401:       const PetscInt        *fcells;
    2402:       PetscInt               ncell, side, nface;

    2404:       nface = neighbors[off + f][0];
    2405:       ncell = neighbors[off + f][1];
    2406:       DMPlexGetSupport(dm,nface,&fcells);
    2407:       side  = (c != fcells[0]);
    2408:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
    2409:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2410:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2411:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2412:     }
    2413:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
    2414:     for (f = 0; f < numFaces; ++f) {
    2415:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
    2416:     }
    2417:   }
    2418:   PetscFree3(dx, grad, gref);
    2419:   PetscSectionDestroy(&neighSec);
    2420:   PetscFree(neighbors);
    2421:   return(0);
    2422: }

    2424: /*@
    2425:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    2427:   Collective on dm

    2429:   Input Arguments:
    2430: + dm  - The DM
    2431: . fvm - The PetscFV
    2432: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM()
    2433: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

    2435:   Output Parameters:
    2436: + faceGeometry - The geometric factors for gradient calculation are inserted
    2437: - dmGrad - The DM describing the layout of gradient data

    2439:   Level: developer

    2441: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
    2442: @*/
    2443: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    2444: {
    2445:   DM             dmFace, dmCell;
    2446:   PetscScalar   *fgeom, *cgeom;
    2447:   PetscSection   sectionGrad, parentSection;
    2448:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

    2452:   DMGetDimension(dm, &dim);
    2453:   PetscFVGetNumComponents(fvm, &pdim);
    2454:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2455:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2456:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    2457:   VecGetDM(faceGeometry, &dmFace);
    2458:   VecGetDM(cellGeometry, &dmCell);
    2459:   VecGetArray(faceGeometry, &fgeom);
    2460:   VecGetArray(cellGeometry, &cgeom);
    2461:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
    2462:   if (!parentSection) {
    2463:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2464:   } else {
    2465:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2466:   }
    2467:   VecRestoreArray(faceGeometry, &fgeom);
    2468:   VecRestoreArray(cellGeometry, &cgeom);
    2469:   /* Create storage for gradients */
    2470:   DMClone(dm, dmGrad);
    2471:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
    2472:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
    2473:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionGrad, c, pdim*dim);}
    2474:   PetscSectionSetUp(sectionGrad);
    2475:   DMSetLocalSection(*dmGrad, sectionGrad);
    2476:   PetscSectionDestroy(&sectionGrad);
    2477:   return(0);
    2478: }

    2480: /*@
    2481:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    2483:   Collective on dm

    2485:   Input Arguments:
    2486: + dm  - The DM
    2487: - fvm - The PetscFV

    2489:   Output Parameters:
    2490: + cellGeometry - The cell geometry
    2491: . faceGeometry - The face geometry
    2492: - dmGrad       - The gradient matrices

    2494:   Level: developer

    2496: .seealso: DMPlexComputeGeometryFVM()
    2497: @*/
    2498: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    2499: {
    2500:   PetscObject    cellgeomobj, facegeomobj;

    2504:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2505:   if (!cellgeomobj) {
    2506:     Vec cellgeomInt, facegeomInt;

    2508:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
    2509:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
    2510:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
    2511:     VecDestroy(&cellgeomInt);
    2512:     VecDestroy(&facegeomInt);
    2513:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2514:   }
    2515:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
    2516:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
    2517:   if (facegeom) *facegeom = (Vec) facegeomobj;
    2518:   if (gradDM) {
    2519:     PetscObject gradobj;
    2520:     PetscBool   computeGradients;

    2522:     PetscFVGetComputeGradients(fv,&computeGradients);
    2523:     if (!computeGradients) {
    2524:       *gradDM = NULL;
    2525:       return(0);
    2526:     }
    2527:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2528:     if (!gradobj) {
    2529:       DM dmGradInt;

    2531:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
    2532:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
    2533:       DMDestroy(&dmGradInt);
    2534:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2535:     }
    2536:     *gradDM = (DM) gradobj;
    2537:   }
    2538:   return(0);
    2539: }

    2541: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
    2542: {
    2543:   PetscInt l, m;

    2546:   if (dimC == dimR && dimR <= 3) {
    2547:     /* invert Jacobian, multiply */
    2548:     PetscScalar det, idet;

    2550:     switch (dimR) {
    2551:     case 1:
    2552:       invJ[0] = 1./ J[0];
    2553:       break;
    2554:     case 2:
    2555:       det = J[0] * J[3] - J[1] * J[2];
    2556:       idet = 1./det;
    2557:       invJ[0] =  J[3] * idet;
    2558:       invJ[1] = -J[1] * idet;
    2559:       invJ[2] = -J[2] * idet;
    2560:       invJ[3] =  J[0] * idet;
    2561:       break;
    2562:     case 3:
    2563:       {
    2564:         invJ[0] = J[4] * J[8] - J[5] * J[7];
    2565:         invJ[1] = J[2] * J[7] - J[1] * J[8];
    2566:         invJ[2] = J[1] * J[5] - J[2] * J[4];
    2567:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    2568:         idet = 1./det;
    2569:         invJ[0] *= idet;
    2570:         invJ[1] *= idet;
    2571:         invJ[2] *= idet;
    2572:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
    2573:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
    2574:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
    2575:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
    2576:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
    2577:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
    2578:       }
    2579:       break;
    2580:     }
    2581:     for (l = 0; l < dimR; l++) {
    2582:       for (m = 0; m < dimC; m++) {
    2583:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    2584:       }
    2585:     }
    2586:   } else {
    2587: #if defined(PETSC_USE_COMPLEX)
    2588:     char transpose = 'C';
    2589: #else
    2590:     char transpose = 'T';
    2591: #endif
    2592:     PetscBLASInt m = dimR;
    2593:     PetscBLASInt n = dimC;
    2594:     PetscBLASInt one = 1;
    2595:     PetscBLASInt worksize = dimR * dimC, info;

    2597:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

    2599:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));
    2600:     if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");

    2602:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
    2603:   }
    2604:   return(0);
    2605: }

    2607: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2608: {
    2609:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    2610:   PetscScalar    *coordsScalar = NULL;
    2611:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    2612:   PetscScalar    *J, *invJ, *work;

    2617:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2618:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2619:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2620:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2621:   cellCoords = &cellData[0];
    2622:   cellCoeffs = &cellData[coordSize];
    2623:   extJ       = &cellData[2 * coordSize];
    2624:   resNeg     = &cellData[2 * coordSize + dimR];
    2625:   invJ       = &J[dimR * dimC];
    2626:   work       = &J[2 * dimR * dimC];
    2627:   if (dimR == 2) {
    2628:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2630:     for (i = 0; i < 4; i++) {
    2631:       PetscInt plexI = zToPlex[i];

    2633:       for (j = 0; j < dimC; j++) {
    2634:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2635:       }
    2636:     }
    2637:   } else if (dimR == 3) {
    2638:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2640:     for (i = 0; i < 8; i++) {
    2641:       PetscInt plexI = zToPlex[i];

    2643:       for (j = 0; j < dimC; j++) {
    2644:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2645:       }
    2646:     }
    2647:   } else {
    2648:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2649:   }
    2650:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2651:   for (i = 0; i < dimR; i++) {
    2652:     PetscReal *swap;

    2654:     for (j = 0; j < (numV / 2); j++) {
    2655:       for (k = 0; k < dimC; k++) {
    2656:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2657:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2658:       }
    2659:     }

    2661:     if (i < dimR - 1) {
    2662:       swap = cellCoeffs;
    2663:       cellCoeffs = cellCoords;
    2664:       cellCoords = swap;
    2665:     }
    2666:   }
    2667:   PetscArrayzero(refCoords,numPoints * dimR);
    2668:   for (j = 0; j < numPoints; j++) {
    2669:     for (i = 0; i < maxIts; i++) {
    2670:       PetscReal *guess = &refCoords[dimR * j];

    2672:       /* compute -residual and Jacobian */
    2673:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
    2674:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
    2675:       for (k = 0; k < numV; k++) {
    2676:         PetscReal extCoord = 1.;
    2677:         for (l = 0; l < dimR; l++) {
    2678:           PetscReal coord = guess[l];
    2679:           PetscInt  dep   = (k & (1 << l)) >> l;

    2681:           extCoord *= dep * coord + !dep;
    2682:           extJ[l] = dep;

    2684:           for (m = 0; m < dimR; m++) {
    2685:             PetscReal coord = guess[m];
    2686:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    2687:             PetscReal mult  = dep * coord + !dep;

    2689:             extJ[l] *= mult;
    2690:           }
    2691:         }
    2692:         for (l = 0; l < dimC; l++) {
    2693:           PetscReal coeff = cellCoeffs[dimC * k + l];

    2695:           resNeg[l] -= coeff * extCoord;
    2696:           for (m = 0; m < dimR; m++) {
    2697:             J[dimR * l + m] += coeff * extJ[m];
    2698:           }
    2699:         }
    2700:       }
    2701:       if (0 && PetscDefined(USE_DEBUG)) {
    2702:         PetscReal maxAbs = 0.;

    2704:         for (l = 0; l < dimC; l++) {
    2705:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2706:         }
    2707:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2708:       }

    2710:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
    2711:     }
    2712:   }
    2713:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2714:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2715:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2716:   return(0);
    2717: }

    2719: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2720: {
    2721:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
    2722:   PetscScalar    *coordsScalar = NULL;
    2723:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

    2728:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2729:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2730:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2731:   cellCoords = &cellData[0];
    2732:   cellCoeffs = &cellData[coordSize];
    2733:   if (dimR == 2) {
    2734:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2736:     for (i = 0; i < 4; i++) {
    2737:       PetscInt plexI = zToPlex[i];

    2739:       for (j = 0; j < dimC; j++) {
    2740:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2741:       }
    2742:     }
    2743:   } else if (dimR == 3) {
    2744:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2746:     for (i = 0; i < 8; i++) {
    2747:       PetscInt plexI = zToPlex[i];

    2749:       for (j = 0; j < dimC; j++) {
    2750:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2751:       }
    2752:     }
    2753:   } else {
    2754:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2755:   }
    2756:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2757:   for (i = 0; i < dimR; i++) {
    2758:     PetscReal *swap;

    2760:     for (j = 0; j < (numV / 2); j++) {
    2761:       for (k = 0; k < dimC; k++) {
    2762:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2763:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2764:       }
    2765:     }

    2767:     if (i < dimR - 1) {
    2768:       swap = cellCoeffs;
    2769:       cellCoeffs = cellCoords;
    2770:       cellCoords = swap;
    2771:     }
    2772:   }
    2773:   PetscArrayzero(realCoords,numPoints * dimC);
    2774:   for (j = 0; j < numPoints; j++) {
    2775:     const PetscReal *guess  = &refCoords[dimR * j];
    2776:     PetscReal       *mapped = &realCoords[dimC * j];

    2778:     for (k = 0; k < numV; k++) {
    2779:       PetscReal extCoord = 1.;
    2780:       for (l = 0; l < dimR; l++) {
    2781:         PetscReal coord = guess[l];
    2782:         PetscInt  dep   = (k & (1 << l)) >> l;

    2784:         extCoord *= dep * coord + !dep;
    2785:       }
    2786:       for (l = 0; l < dimC; l++) {
    2787:         PetscReal coeff = cellCoeffs[dimC * k + l];

    2789:         mapped[l] += coeff * extCoord;
    2790:       }
    2791:     }
    2792:   }
    2793:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2794:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2795:   return(0);
    2796: }

    2798: /* TODO: TOBY please fix this for Nc > 1 */
    2799: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2800: {
    2801:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
    2802:   PetscScalar    *nodes = NULL;
    2803:   PetscReal      *invV, *modes;
    2804:   PetscReal      *B, *D, *resNeg;
    2805:   PetscScalar    *J, *invJ, *work;

    2809:   PetscFEGetDimension(fe, &pdim);
    2810:   PetscFEGetNumComponents(fe, &numComp);
    2811:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2812:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2813:   /* convert nodes to values in the stable evaluation basis */
    2814:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2815:   invV = fe->invV;
    2816:   for (i = 0; i < pdim; ++i) {
    2817:     modes[i] = 0.;
    2818:     for (j = 0; j < pdim; ++j) {
    2819:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2820:     }
    2821:   }
    2822:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2823:   D      = &B[pdim*Nc];
    2824:   resNeg = &D[pdim*Nc * dimR];
    2825:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2826:   invJ = &J[Nc * dimR];
    2827:   work = &invJ[Nc * dimR];
    2828:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
    2829:   for (j = 0; j < numPoints; j++) {
    2830:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    2831:       PetscReal *guess = &refCoords[j * dimR];
    2832:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
    2833:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
    2834:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
    2835:       for (k = 0; k < pdim; k++) {
    2836:         for (l = 0; l < Nc; l++) {
    2837:           resNeg[l] -= modes[k] * B[k * Nc + l];
    2838:           for (m = 0; m < dimR; m++) {
    2839:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    2840:           }
    2841:         }
    2842:       }
    2843:       if (0 && PetscDefined(USE_DEBUG)) {
    2844:         PetscReal maxAbs = 0.;

    2846:         for (l = 0; l < Nc; l++) {
    2847:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2848:         }
    2849:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2850:       }
    2851:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
    2852:     }
    2853:   }
    2854:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2855:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2856:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    2857:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2858:   return(0);
    2859: }

    2861: /* TODO: TOBY please fix this for Nc > 1 */
    2862: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2863: {
    2864:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
    2865:   PetscScalar    *nodes = NULL;
    2866:   PetscReal      *invV, *modes;
    2867:   PetscReal      *B;

    2871:   PetscFEGetDimension(fe, &pdim);
    2872:   PetscFEGetNumComponents(fe, &numComp);
    2873:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2874:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2875:   /* convert nodes to values in the stable evaluation basis */
    2876:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2877:   invV = fe->invV;
    2878:   for (i = 0; i < pdim; ++i) {
    2879:     modes[i] = 0.;
    2880:     for (j = 0; j < pdim; ++j) {
    2881:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2882:     }
    2883:   }
    2884:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    2885:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
    2886:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
    2887:   for (j = 0; j < numPoints; j++) {
    2888:     PetscReal *mapped = &realCoords[j * Nc];

    2890:     for (k = 0; k < pdim; k++) {
    2891:       for (l = 0; l < Nc; l++) {
    2892:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    2893:       }
    2894:     }
    2895:   }
    2896:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    2897:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    2898:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2899:   return(0);
    2900: }

    2902: /*@
    2903:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
    2904:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
    2905:   extend uniquely outside the reference cell (e.g, most non-affine maps)

    2907:   Not collective

    2909:   Input Parameters:
    2910: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    2911:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    2912:                as a multilinear map for tensor-product elements
    2913: . cell       - the cell whose map is used.
    2914: . numPoints  - the number of points to locate
    2915: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    2917:   Output Parameters:
    2918: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    2920:   Level: intermediate

    2922: .seealso: DMPlexReferenceToCoordinates()
    2923: @*/
    2924: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    2925: {
    2926:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    2927:   DM             coordDM = NULL;
    2928:   Vec            coords;
    2929:   PetscFE        fe = NULL;

    2934:   DMGetDimension(dm,&dimR);
    2935:   DMGetCoordinateDim(dm,&dimC);
    2936:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    2937:   DMPlexGetDepth(dm,&depth);
    2938:   DMGetCoordinatesLocal(dm,&coords);
    2939:   DMGetCoordinateDM(dm,&coordDM);
    2940:   if (coordDM) {
    2941:     PetscInt coordFields;

    2943:     DMGetNumFields(coordDM,&coordFields);
    2944:     if (coordFields) {
    2945:       PetscClassId id;
    2946:       PetscObject  disc;

    2948:       DMGetField(coordDM,0,NULL,&disc);
    2949:       PetscObjectGetClassId(disc,&id);
    2950:       if (id == PETSCFE_CLASSID) {
    2951:         fe = (PetscFE) disc;
    2952:       }
    2953:     }
    2954:   }
    2955:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    2956:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    2957:   if (!fe) { /* implicit discretization: affine or multilinear */
    2958:     PetscInt  coneSize;
    2959:     PetscBool isSimplex, isTensor;

    2961:     DMPlexGetConeSize(dm,cell,&coneSize);
    2962:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    2963:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    2964:     if (isSimplex) {
    2965:       PetscReal detJ, *v0, *J, *invJ;

    2967:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    2968:       J    = &v0[dimC];
    2969:       invJ = &J[dimC * dimC];
    2970:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
    2971:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    2972:         const PetscReal x0[3] = {-1.,-1.,-1.};

    2974:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    2975:       }
    2976:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    2977:     } else if (isTensor) {
    2978:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    2979:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    2980:   } else {
    2981:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    2982:   }
    2983:   return(0);
    2984: }

    2986: /*@
    2987:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

    2989:   Not collective

    2991:   Input Parameters:
    2992: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    2993:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    2994:                as a multilinear map for tensor-product elements
    2995: . cell       - the cell whose map is used.
    2996: . numPoints  - the number of points to locate
    2997: - refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    2999:   Output Parameters:
    3000: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    3002:    Level: intermediate

    3004: .seealso: DMPlexCoordinatesToReference()
    3005: @*/
    3006: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    3007: {
    3008:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    3009:   DM             coordDM = NULL;
    3010:   Vec            coords;
    3011:   PetscFE        fe = NULL;

    3016:   DMGetDimension(dm,&dimR);
    3017:   DMGetCoordinateDim(dm,&dimC);
    3018:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    3019:   DMPlexGetDepth(dm,&depth);
    3020:   DMGetCoordinatesLocal(dm,&coords);
    3021:   DMGetCoordinateDM(dm,&coordDM);
    3022:   if (coordDM) {
    3023:     PetscInt coordFields;

    3025:     DMGetNumFields(coordDM,&coordFields);
    3026:     if (coordFields) {
    3027:       PetscClassId id;
    3028:       PetscObject  disc;

    3030:       DMGetField(coordDM,0,NULL,&disc);
    3031:       PetscObjectGetClassId(disc,&id);
    3032:       if (id == PETSCFE_CLASSID) {
    3033:         fe = (PetscFE) disc;
    3034:       }
    3035:     }
    3036:   }
    3037:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3038:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    3039:   if (!fe) { /* implicit discretization: affine or multilinear */
    3040:     PetscInt  coneSize;
    3041:     PetscBool isSimplex, isTensor;

    3043:     DMPlexGetConeSize(dm,cell,&coneSize);
    3044:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3045:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3046:     if (isSimplex) {
    3047:       PetscReal detJ, *v0, *J;

    3049:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3050:       J    = &v0[dimC];
    3051:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
    3052:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3053:         const PetscReal xi0[3] = {-1.,-1.,-1.};

    3055:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3056:       }
    3057:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3058:     } else if (isTensor) {
    3059:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3060:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3061:   } else {
    3062:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3063:   }
    3064:   return(0);
    3065: }

    3067: /*@C
    3068:   DMPlexRemapGeometry - This function maps the original DM coordinates to new coordinates.

    3070:   Not collective

    3072:   Input Parameters:
    3073: + dm      - The DM
    3074: . time    - The time
    3075: - func    - The function transforming current coordinates to new coordaintes

    3077:    Calling sequence of func:
    3078: $    func(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3079: $         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3080: $         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3081: $         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]);

    3083: +  dim          - The spatial dimension
    3084: .  Nf           - The number of input fields (here 1)
    3085: .  NfAux        - The number of input auxiliary fields
    3086: .  uOff         - The offset of the coordinates in u[] (here 0)
    3087: .  uOff_x       - The offset of the coordinates in u_x[] (here 0)
    3088: .  u            - The coordinate values at this point in space
    3089: .  u_t          - The coordinate time derivative at this point in space (here NULL)
    3090: .  u_x          - The coordinate derivatives at this point in space
    3091: .  aOff         - The offset of each auxiliary field in u[]
    3092: .  aOff_x       - The offset of each auxiliary field in u_x[]
    3093: .  a            - The auxiliary field values at this point in space
    3094: .  a_t          - The auxiliary field time derivative at this point in space (or NULL)
    3095: .  a_x          - The auxiliary field derivatives at this point in space
    3096: .  t            - The current time
    3097: .  x            - The coordinates of this point (here not used)
    3098: .  numConstants - The number of constants
    3099: .  constants    - The value of each constant
    3100: -  f            - The new coordinates at this point in space

    3102:   Level: intermediate

    3104: .seealso: DMGetCoordinates(), DMGetCoordinatesLocal(), DMGetCoordinateDM(), DMProjectFieldLocal(), DMProjectFieldLabelLocal()
    3105: @*/
    3106: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time,
    3107:                                    void (*func)(PetscInt, PetscInt, PetscInt,
    3108:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3109:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3110:                                                 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))
    3111: {
    3112:   DM             cdm;
    3113:   DMField        cf;
    3114:   Vec            lCoords, tmpCoords;

    3118:   DMGetCoordinateDM(dm, &cdm);
    3119:   DMGetCoordinatesLocal(dm, &lCoords);
    3120:   DMGetLocalVector(cdm, &tmpCoords);
    3121:   VecCopy(lCoords, tmpCoords);
    3122:   /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
    3123:   DMGetCoordinateField(dm, &cf);
    3124:   cdm->coordinateField = cf;
    3125:   DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords);
    3126:   cdm->coordinateField = NULL;
    3127:   DMRestoreLocalVector(cdm, &tmpCoords);
    3128:   DMSetCoordinatesLocal(dm, lCoords);
    3129:   return(0);
    3130: }

    3132: /* Shear applies the transformation, assuming we fix z,
    3133:   / 1  0  m_0 \
    3134:   | 0  1  m_1 |
    3135:   \ 0  0   1  /
    3136: */
    3137: static void f0_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3138:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3139:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3140:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
    3141: {
    3142:   const PetscInt Nc = uOff[1]-uOff[0];
    3143:   const PetscInt ax = (PetscInt) PetscRealPart(constants[0]);
    3144:   PetscInt       c;

    3146:   for (c = 0; c < Nc; ++c) {
    3147:     coords[c] = u[c] + constants[c+1]*u[ax];
    3148:   }
    3149: }

    3151: /*@C
    3152:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

    3154:   Not collective

    3156:   Input Parameters:
    3157: + dm          - The DM
    3158: . direction   - The shear coordinate direction, e.g. 0 is the x-axis
    3159: - multipliers - The multiplier m for each direction which is not the shear direction

    3161:   Level: intermediate

    3163: .seealso: DMPlexRemapGeometry()
    3164: @*/
    3165: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
    3166: {
    3167:   DM             cdm;
    3168:   PetscDS        cds;
    3169:   PetscObject    obj;
    3170:   PetscClassId   id;
    3171:   PetscScalar   *moduli;
    3172:   const PetscInt dir = (PetscInt) direction;
    3173:   PetscInt       dE, d, e;

    3177:   DMGetCoordinateDM(dm, &cdm);
    3178:   DMGetCoordinateDim(dm, &dE);
    3179:   PetscMalloc1(dE+1, &moduli);
    3180:   moduli[0] = dir;
    3181:   for (d = 0, e = 0; d < dE; ++d) moduli[d+1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
    3182:   DMGetDS(cdm, &cds);
    3183:   PetscDSGetDiscretization(cds, 0, &obj);
    3184:   PetscObjectGetClassId(obj, &id);
    3185:   if (id != PETSCFE_CLASSID) {
    3186:     Vec           lCoords;
    3187:     PetscSection  cSection;
    3188:     PetscScalar  *coords;
    3189:     PetscInt      vStart, vEnd, v;

    3191:     DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3192:     DMGetCoordinateSection(dm, &cSection);
    3193:     DMGetCoordinatesLocal(dm, &lCoords);
    3194:     VecGetArray(lCoords, &coords);
    3195:     for (v = vStart; v < vEnd; ++v) {
    3196:       PetscReal ds;
    3197:       PetscInt  off, c;

    3199:       PetscSectionGetOffset(cSection, v, &off);
    3200:       ds   = PetscRealPart(coords[off+dir]);
    3201:       for (c = 0; c < dE; ++c) coords[off+c] += moduli[c]*ds;
    3202:     }
    3203:     VecRestoreArray(lCoords, &coords);
    3204:   } else {
    3205:     PetscDSSetConstants(cds, dE+1, moduli);
    3206:     DMPlexRemapGeometry(dm, 0.0, f0_shear);
    3207:   }
    3208:   PetscFree(moduli);
    3209:   return(0);
    3210: }