Actual source code: plexgeometry.c
petsc-3.13.6 2020-09-29
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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(), DMGetCoordinates()
     34: @*/
     35: PetscErrorCode DMPlexFindVertices(DM dm, PetscInt npoints, const PetscReal coord[], PetscReal eps, PetscInt dagPoints[])
     36: {
     37:   PetscInt          c, dim, 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:   DMGetDimension(dm, &dim);
     46:   DMGetCoordinatesLocal(dm, &allCoordsVec);
     47:   VecGetArrayRead(allCoordsVec, &allCoords);
     48:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
     49: #if defined(PETSC_USE_DEBUG)
     50:   /* check coordinate section is consistent with DM dimension */
     51:   {
     52:     PetscSection      cs;
     53:     PetscInt          ndof;

     55:     DMGetCoordinateSection(dm, &cs);
     56:     for (p = vStart; p < vEnd; p++) {
     57:       PetscSectionGetDof(cs, p, &ndof);
     58:       if (PetscUnlikely(ndof != dim)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %D: ndof = %D != %D = dim", p, ndof, dim);
     59:     }
     60:   }
     61: #endif
     62:   if (eps == 0.0) {
     63:     for (i=0,j=0; i < npoints; i++,j+=dim) {
     64:       dagPoints[i] = -1;
     65:       for (p = vStart,o=0; p < vEnd; p++,o+=dim) {
     66:         for (c = 0; c < dim; c++) {
     67:           if (coord[j+c] != PetscRealPart(allCoords[o+c])) break;
     68:         }
     69:         if (c == dim) {
     70:           dagPoints[i] = p;
     71:           break;
     72:         }
     73:       }
     74:     }
     75:     VecRestoreArrayRead(allCoordsVec, &allCoords);
     76:     return(0);
     77:   }
     78:   for (i=0,j=0; i < npoints; i++,j+=dim) {
     79:     dagPoints[i] = -1;
     80:     for (p = vStart,o=0; p < vEnd; p++,o+=dim) {
     81:       norm = 0.0;
     82:       for (c = 0; c < dim; c++) {
     83:         norm += PetscSqr(coord[j+c] - PetscRealPart(allCoords[o+c]));
     84:       }
     85:       norm = PetscSqrtReal(norm);
     86:       if (norm <= eps) {
     87:         dagPoints[i] = p;
     88:         break;
     89:       }
     90:     }
     91:   }
     92:   VecRestoreArrayRead(allCoordsVec, &allCoords);
     93:   return(0);
     94: }

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

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

    119:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
    120:       *hasIntersection = PETSC_TRUE;
    121:       if (intersection) {
    122:         intersection[0] = p0_x + (t * s1_x);
    123:         intersection[1] = p0_y + (t * s1_y);
    124:       }
    125:     }
    126:   }
    127:   return(0);
    128: }

    130: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    131: {
    132:   const PetscInt  embedDim = 2;
    133:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
    134:   PetscReal       x        = PetscRealPart(point[0]);
    135:   PetscReal       y        = PetscRealPart(point[1]);
    136:   PetscReal       v0[2], J[4], invJ[4], detJ;
    137:   PetscReal       xi, eta;
    138:   PetscErrorCode  ierr;

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

    145:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
    146:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    147:   return(0);
    148: }

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

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

    164:   xi  = PetscMax(xi,  0.0);
    165:   eta = PetscMax(eta, 0.0);
    166:   if (xi + eta > 2.0) {
    167:     r    = (xi + eta)/2.0;
    168:     xi  /= r;
    169:     eta /= r;
    170:   }
    171:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
    172:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
    173:   return(0);
    174: }

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

    188:   DMGetCoordinatesLocal(dm, &coordsLocal);
    189:   DMGetCoordinateSection(dm, &coordSection);
    190:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    191:   for (f = 0; f < 4; ++f) {
    192:     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
    193:     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
    194:     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
    195:     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
    196:     PetscReal slope = (y_j - y_i) / (x_j - x_i);
    197:     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
    198:     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
    199:     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
    200:     if ((cond1 || cond2)  && above) ++crossings;
    201:   }
    202:   if (crossings % 2) *cell = c;
    203:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    204:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    205:   return(0);
    206: }

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

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

    224:   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
    225:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    226:   return(0);
    227: }

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

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

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

    267:     /* Check that projected point is in face (2D location problem) */
    268:     if (dot < 0.0) {
    269:       found = PETSC_FALSE;
    270:       break;
    271:     }
    272:   }
    273:   if (found) *cell = c;
    274:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    275:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    276:   return(0);
    277: }

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

    284:   box->dim = dim;
    285:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
    286:   return(0);
    287: }

    289: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    290: {

    294:   PetscMalloc1(1, box);
    295:   PetscGridHashInitialize_Internal(*box, dim, point);
    296:   return(0);
    297: }

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

    304:   for (d = 0; d < box->dim; ++d) {
    305:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    306:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    307:   }
    308:   return(0);
    309: }

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

    314:   Not collective

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

    321:   Level: developer

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

    330:   for (d = 0; d < box->dim; ++d) {
    331:     box->extent[d] = box->upper[d] - box->lower[d];
    332:     if (n[d] == PETSC_DETERMINE) {
    333:       box->h[d] = h[d];
    334:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
    335:     } else {
    336:       box->n[d] = n[d];
    337:       box->h[d] = box->extent[d]/n[d];
    338:     }
    339:   }
    340:   return(0);
    341: }

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

    346:   Not collective

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

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

    357:   Level: developer

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

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

    375:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    376:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
    377:       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",
    378:                                              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);
    379:       dboxes[p*dim+d] = dbox;
    380:     }
    381:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
    382:   }
    383:   return(0);
    384: }

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

    389:  Not collective

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

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

    401:   Level: developer

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

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

    420:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    421:       if (dbox < 0 || dbox >= n[d]) {
    422:         return(0);
    423:       }
    424:       dboxes[p*dim+d] = dbox;
    425:     }
    426:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
    427:   }
    428:   *found = PETSC_TRUE;
    429:   return(0);
    430: }

    432: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    433: {

    437:   if (*box) {
    438:     PetscSectionDestroy(&(*box)->cellSection);
    439:     ISDestroy(&(*box)->cells);
    440:     DMLabelDestroy(&(*box)->cellsSparse);
    441:   }
    442:   PetscFree(*box);
    443:   return(0);
    444: }

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

    452:   DMPlexGetCellType(dm, cellStart, &ct);
    453:   switch (ct) {
    454:     case DM_POLYTOPE_TRIANGLE:
    455:     DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);break;
    456:     case DM_POLYTOPE_QUADRILATERAL:
    457:     DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell);break;
    458:     case DM_POLYTOPE_TETRAHEDRON:
    459:     DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);break;
    460:     case DM_POLYTOPE_HEXAHEDRON:
    461:     DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);break;
    462:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %D with type %s", cellStart, DMPolytopeTypes[ct]);
    463:   }
    464:   return(0);
    465: }

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

    476:   DMPlexGetCellType(dm, cell, &ct);
    477:   switch (ct) {
    478:     case DM_POLYTOPE_TRIANGLE:
    479:     DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);break;
    480: #if 0
    481:     case DM_POLYTOPE_QUADRILATERAL:
    482:     DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);break;
    483:     case DM_POLYTOPE_TETRAHEDRON:
    484:     DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);break;
    485:     case DM_POLYTOPE_HEXAHEDRON:
    486:     DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);break;
    487: #endif
    488:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    489:   }
    490:   return(0);
    491: }

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

    496:   Collective on dm

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

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

    504:   Level: developer

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

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

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

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

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

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

    604:                   segB[0]     = PetscRealPart(point[0]);
    605:                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
    606:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
    607:                   if (intersects) { DMLabelSetValue(lbox->cellsSparse, c, box); edge = ii = jj = kk = dim+1;}
    608:                 }
    609:               }
    610:             }
    611:           }
    612:         }
    613:       }
    614:     }
    615:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
    616:   }
    617:   PetscFree2(dboxes, boxes);
    618:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
    619:   DMLabelDestroy(&lbox->cellsSparse);
    620:   *localBox = lbox;
    621:   return(0);
    622: }

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

    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:   return(0);
    803: }

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

    808:   Not collective

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

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

    817:   Level: developer

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

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

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

    838:   Not collective

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

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

    847:   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

    849:   Level: developer

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

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

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

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

    882: /*@
    883:   DMPlexComputeProjection3Dto2D - Rewrite coordinates to be the 2D projection of the 3D coordinates

    885:   Not collective

    887:   Input Parameter:
    888: . coords - The coordinates of a segment

    890:   Output Parameters:
    891: + coords - The new y- and z-coordinates, and 0 for x
    892: - R - The rotation which accomplishes the projection

    894:   Level: developer

    896: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
    897: @*/
    898: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    899: {
    900:   PetscReal      x1[3],  x2[3], n[3], norm;
    901:   PetscReal      x1p[3], x2p[3], xnp[3];
    902:   PetscReal      sqrtz, alpha;
    903:   const PetscInt dim = 3;
    904:   PetscInt       d, e, p;

    907:   /* 0) Calculate normal vector */
    908:   for (d = 0; d < dim; ++d) {
    909:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
    910:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
    911:   }
    912:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
    913:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
    914:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
    915:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    916:   n[0] /= norm;
    917:   n[1] /= norm;
    918:   n[2] /= norm;
    919:   /* 1) Take the normal vector and rotate until it is \hat z

    921:     Let the normal vector be <nx, ny, nz> and alpha = 1/sqrt(1 - nz^2), then

    923:     R = /  alpha nx nz  alpha ny nz -1/alpha \
    924:         | -alpha ny     alpha nx        0    |
    925:         \     nx            ny         nz    /

    927:     will rotate the normal vector to \hat z
    928:   */
    929:   sqrtz = PetscSqrtReal(1.0 - n[2]*n[2]);
    930:   /* Check for n = z */
    931:   if (sqrtz < 1.0e-10) {
    932:     const PetscInt s = PetscSign(n[2]);
    933:     /* If nz < 0, rotate 180 degrees around x-axis */
    934:     for (p = 3; p < coordSize/3; ++p) {
    935:       coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
    936:       coords[p*2+1] = (PetscRealPart(coords[p*dim+1] - coords[0*dim+1])) * s;
    937:     }
    938:     coords[0] = 0.0;
    939:     coords[1] = 0.0;
    940:     coords[2] = x1[0];
    941:     coords[3] = x1[1] * s;
    942:     coords[4] = x2[0];
    943:     coords[5] = x2[1] * s;
    944:     R[0] = 1.0;     R[1] = 0.0;     R[2] = 0.0;
    945:     R[3] = 0.0;     R[4] = 1.0 * s; R[5] = 0.0;
    946:     R[6] = 0.0;     R[7] = 0.0;     R[8] = 1.0 * s;
    947:     return(0);
    948:   }
    949:   alpha = 1.0/sqrtz;
    950:   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
    951:   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
    952:   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
    953:   for (d = 0; d < dim; ++d) {
    954:     x1p[d] = 0.0;
    955:     x2p[d] = 0.0;
    956:     for (e = 0; e < dim; ++e) {
    957:       x1p[d] += R[d*dim+e]*x1[e];
    958:       x2p[d] += R[d*dim+e]*x2[e];
    959:     }
    960:   }
    961:   if (PetscAbsReal(x1p[2]) > 10. * PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
    962:   if (PetscAbsReal(x2p[2]) > 10. * PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
    963:   /* 2) Project to (x, y) */
    964:   for (p = 3; p < coordSize/3; ++p) {
    965:     for (d = 0; d < dim; ++d) {
    966:       xnp[d] = 0.0;
    967:       for (e = 0; e < dim; ++e) {
    968:         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
    969:       }
    970:       if (d < dim-1) coords[p*2+d] = xnp[d];
    971:     }
    972:   }
    973:   coords[0] = 0.0;
    974:   coords[1] = 0.0;
    975:   coords[2] = x1p[0];
    976:   coords[3] = x1p[1];
    977:   coords[4] = x2p[0];
    978:   coords[5] = x2p[1];
    979:   /* Output R^T which rotates \hat z to the input normal */
    980:   for (d = 0; d < dim; ++d) {
    981:     for (e = d+1; e < dim; ++e) {
    982:       PetscReal tmp;

    984:       tmp        = R[d*dim+e];
    985:       R[d*dim+e] = R[e*dim+d];
    986:       R[e*dim+d] = tmp;
    987:     }
    988:   }
    989:   return(0);
    990: }

    992: PETSC_UNUSED
    993: PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    994: {
    995:   /* Signed volume is 1/2 the determinant

    997:    |  1  1  1 |
    998:    | x0 x1 x2 |
    999:    | y0 y1 y2 |

    1001:      but if x0,y0 is the origin, we have

    1003:    | x1 x2 |
    1004:    | y1 y2 |
    1005:   */
    1006:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    1007:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    1008:   PetscReal       M[4], detM;
    1009:   M[0] = x1; M[1] = x2;
    1010:   M[2] = y1; M[3] = y2;
    1011:   DMPlex_Det2D_Internal(&detM, M);
    1012:   *vol = 0.5*detM;
    1013:   (void)PetscLogFlops(5.0);
    1014: }

    1016: PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1017: {
    1018:   DMPlex_Det2D_Internal(vol, coords);
    1019:   *vol *= 0.5;
    1020: }

    1022: PETSC_UNUSED
    1023: PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    1024: {
    1025:   /* Signed volume is 1/6th of the determinant

    1027:    |  1  1  1  1 |
    1028:    | x0 x1 x2 x3 |
    1029:    | y0 y1 y2 y3 |
    1030:    | z0 z1 z2 z3 |

    1032:      but if x0,y0,z0 is the origin, we have

    1034:    | x1 x2 x3 |
    1035:    | y1 y2 y3 |
    1036:    | z1 z2 z3 |
    1037:   */
    1038:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
    1039:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
    1040:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    1041:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1042:   PetscReal       M[9], detM;
    1043:   M[0] = x1; M[1] = x2; M[2] = x3;
    1044:   M[3] = y1; M[4] = y2; M[5] = y3;
    1045:   M[6] = z1; M[7] = z2; M[8] = z3;
    1046:   DMPlex_Det3D_Internal(&detM, M);
    1047:   *vol = -onesixth*detM;
    1048:   (void)PetscLogFlops(10.0);
    1049: }

    1051: PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1052: {
    1053:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1054:   DMPlex_Det3D_Internal(vol, coords);
    1055:   *vol *= -onesixth;
    1056: }

    1058: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1059: {
    1060:   PetscSection   coordSection;
    1061:   Vec            coordinates;
    1062:   const PetscScalar *coords;
    1063:   PetscInt       dim, d, off;

    1067:   DMGetCoordinatesLocal(dm, &coordinates);
    1068:   DMGetCoordinateSection(dm, &coordSection);
    1069:   PetscSectionGetDof(coordSection,e,&dim);
    1070:   if (!dim) return(0);
    1071:   PetscSectionGetOffset(coordSection,e,&off);
    1072:   VecGetArrayRead(coordinates,&coords);
    1073:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
    1074:   VecRestoreArrayRead(coordinates,&coords);
    1075:   *detJ = 1.;
    1076:   if (J) {
    1077:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1078:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1079:     if (invJ) {
    1080:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1081:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1082:     }
    1083:   }
    1084:   return(0);
    1085: }

    1087: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1088: {
    1089:   PetscSection   coordSection;
    1090:   Vec            coordinates;
    1091:   PetscScalar   *coords = NULL;
    1092:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

    1096:   DMGetCoordinatesLocal(dm, &coordinates);
    1097:   DMGetCoordinateSection(dm, &coordSection);
    1098:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1099:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1100:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1101:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1102:   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1103:   *detJ = 0.0;
    1104:   if (numCoords == 6) {
    1105:     const PetscInt dim = 3;
    1106:     PetscReal      R[9], J0;

    1108:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1109:     DMPlexComputeProjection3Dto1D(coords, R);
    1110:     if (J)    {
    1111:       J0   = 0.5*PetscRealPart(coords[1]);
    1112:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
    1113:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
    1114:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
    1115:       DMPlex_Det3D_Internal(detJ, J);
    1116:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1117:     }
    1118:   } else if (numCoords == 4) {
    1119:     const PetscInt dim = 2;
    1120:     PetscReal      R[4], J0;

    1122:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1123:     DMPlexComputeProjection2Dto1D(coords, R);
    1124:     if (J)    {
    1125:       J0   = 0.5*PetscRealPart(coords[1]);
    1126:       J[0] = R[0]*J0; J[1] = R[1];
    1127:       J[2] = R[2]*J0; J[3] = R[3];
    1128:       DMPlex_Det2D_Internal(detJ, J);
    1129:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1130:     }
    1131:   } else if (numCoords == 2) {
    1132:     const PetscInt dim = 1;

    1134:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1135:     if (J)    {
    1136:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1137:       *detJ = J[0];
    1138:       PetscLogFlops(2.0);
    1139:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
    1140:     }
    1141:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
    1142:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1143:   return(0);
    1144: }

    1146: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1147: {
    1148:   PetscSection   coordSection;
    1149:   Vec            coordinates;
    1150:   PetscScalar   *coords = NULL;
    1151:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1155:   DMGetCoordinatesLocal(dm, &coordinates);
    1156:   DMGetCoordinateSection(dm, &coordSection);
    1157:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1158:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1159:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1160:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1161:   *detJ = 0.0;
    1162:   if (numCoords == 9) {
    1163:     const PetscInt dim = 3;
    1164:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1166:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1167:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1168:     if (J)    {
    1169:       const PetscInt pdim = 2;

    1171:       for (d = 0; d < pdim; d++) {
    1172:         for (f = 0; f < pdim; f++) {
    1173:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1174:         }
    1175:       }
    1176:       PetscLogFlops(8.0);
    1177:       DMPlex_Det3D_Internal(detJ, J0);
    1178:       for (d = 0; d < dim; d++) {
    1179:         for (f = 0; f < dim; f++) {
    1180:           J[d*dim+f] = 0.0;
    1181:           for (g = 0; g < dim; g++) {
    1182:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1183:           }
    1184:         }
    1185:       }
    1186:       PetscLogFlops(18.0);
    1187:     }
    1188:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1189:   } else if (numCoords == 6) {
    1190:     const PetscInt dim = 2;

    1192:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1193:     if (J)    {
    1194:       for (d = 0; d < dim; d++) {
    1195:         for (f = 0; f < dim; f++) {
    1196:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1197:         }
    1198:       }
    1199:       PetscLogFlops(8.0);
    1200:       DMPlex_Det2D_Internal(detJ, J);
    1201:     }
    1202:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1203:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
    1204:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1205:   return(0);
    1206: }

    1208: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1209: {
    1210:   PetscSection   coordSection;
    1211:   Vec            coordinates;
    1212:   PetscScalar   *coords = NULL;
    1213:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1217:   DMGetCoordinatesLocal(dm, &coordinates);
    1218:   DMGetCoordinateSection(dm, &coordSection);
    1219:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1220:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1221:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1222:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1223:   if (!Nq) {
    1224:     PetscInt vorder[4] = {0, 1, 2, 3};

    1226:     if (isTensor) {vorder[2] = 3; vorder[3] = 2;}
    1227:     *detJ = 0.0;
    1228:     if (numCoords == 12) {
    1229:       const PetscInt dim = 3;
    1230:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1232:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1233:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1234:       if (J)    {
    1235:         const PetscInt pdim = 2;

    1237:         for (d = 0; d < pdim; d++) {
    1238:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*pdim+d]) - PetscRealPart(coords[vorder[0]*pdim+d]));
    1239:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[2]*pdim+d]) - PetscRealPart(coords[vorder[1]*pdim+d]));
    1240:         }
    1241:         PetscLogFlops(8.0);
    1242:         DMPlex_Det3D_Internal(detJ, J0);
    1243:         for (d = 0; d < dim; d++) {
    1244:           for (f = 0; f < dim; f++) {
    1245:             J[d*dim+f] = 0.0;
    1246:             for (g = 0; g < dim; g++) {
    1247:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1248:             }
    1249:           }
    1250:         }
    1251:         PetscLogFlops(18.0);
    1252:       }
    1253:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1254:     } else if (numCoords == 8) {
    1255:       const PetscInt dim = 2;

    1257:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1258:       if (J)    {
    1259:         for (d = 0; d < dim; d++) {
    1260:           J[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1261:           J[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[3]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
    1262:         }
    1263:         PetscLogFlops(8.0);
    1264:         DMPlex_Det2D_Internal(detJ, J);
    1265:       }
    1266:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1267:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1268:   } else {
    1269:     const PetscInt Nv = 4;
    1270:     const PetscInt dimR = 2;
    1271:     PetscInt  zToPlex[4] = {0, 1, 3, 2};
    1272:     PetscReal zOrder[12];
    1273:     PetscReal zCoeff[12];
    1274:     PetscInt  i, j, k, l, dim;

    1276:     if (isTensor) {zToPlex[2] = 2; zToPlex[3] = 3;}
    1277:     if (numCoords == 12) {
    1278:       dim = 3;
    1279:     } else if (numCoords == 8) {
    1280:       dim = 2;
    1281:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1282:     for (i = 0; i < Nv; i++) {
    1283:       PetscInt zi = zToPlex[i];

    1285:       for (j = 0; j < dim; j++) {
    1286:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1287:       }
    1288:     }
    1289:     for (j = 0; j < dim; j++) {
    1290:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1291:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1292:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1293:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1294:     }
    1295:     for (i = 0; i < Nq; i++) {
    1296:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    1298:       if (v) {
    1299:         PetscReal extPoint[4];

    1301:         extPoint[0] = 1.;
    1302:         extPoint[1] = xi;
    1303:         extPoint[2] = eta;
    1304:         extPoint[3] = xi * eta;
    1305:         for (j = 0; j < dim; j++) {
    1306:           PetscReal val = 0.;

    1308:           for (k = 0; k < Nv; k++) {
    1309:             val += extPoint[k] * zCoeff[dim * k + j];
    1310:           }
    1311:           v[i * dim + j] = val;
    1312:         }
    1313:       }
    1314:       if (J) {
    1315:         PetscReal extJ[8];

    1317:         extJ[0] = 0.;
    1318:         extJ[1] = 0.;
    1319:         extJ[2] = 1.;
    1320:         extJ[3] = 0.;
    1321:         extJ[4] = 0.;
    1322:         extJ[5] = 1.;
    1323:         extJ[6] = eta;
    1324:         extJ[7] = xi;
    1325:         for (j = 0; j < dim; j++) {
    1326:           for (k = 0; k < dimR; k++) {
    1327:             PetscReal val = 0.;

    1329:             for (l = 0; l < Nv; l++) {
    1330:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1331:             }
    1332:             J[i * dim * dim + dim * j + k] = val;
    1333:           }
    1334:         }
    1335:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    1336:           PetscReal x, y, z;
    1337:           PetscReal *iJ = &J[i * dim * dim];
    1338:           PetscReal norm;

    1340:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    1341:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    1342:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    1343:           norm = PetscSqrtReal(x * x + y * y + z * z);
    1344:           iJ[2] = x / norm;
    1345:           iJ[5] = y / norm;
    1346:           iJ[8] = z / norm;
    1347:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1348:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1349:         } else {
    1350:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    1351:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1352:         }
    1353:       }
    1354:     }
    1355:   }
    1356:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1357:   return(0);
    1358: }

    1360: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1361: {
    1362:   PetscSection   coordSection;
    1363:   Vec            coordinates;
    1364:   PetscScalar   *coords = NULL;
    1365:   const PetscInt dim = 3;
    1366:   PetscInt       d;

    1370:   DMGetCoordinatesLocal(dm, &coordinates);
    1371:   DMGetCoordinateSection(dm, &coordSection);
    1372:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1373:   *detJ = 0.0;
    1374:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1375:   if (J)    {
    1376:     for (d = 0; d < dim; d++) {
    1377:       /* I orient with outward face normals */
    1378:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1379:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1380:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1381:     }
    1382:     PetscLogFlops(18.0);
    1383:     DMPlex_Det3D_Internal(detJ, J);
    1384:   }
    1385:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1386:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1387:   return(0);
    1388: }

    1390: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1391: {
    1392:   PetscSection   coordSection;
    1393:   Vec            coordinates;
    1394:   PetscScalar   *coords = NULL;
    1395:   const PetscInt dim = 3;
    1396:   PetscInt       d;

    1400:   DMGetCoordinatesLocal(dm, &coordinates);
    1401:   DMGetCoordinateSection(dm, &coordSection);
    1402:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1403:   if (!Nq) {
    1404:     *detJ = 0.0;
    1405:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1406:     if (J)    {
    1407:       for (d = 0; d < dim; d++) {
    1408:         J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1409:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1410:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1411:       }
    1412:       PetscLogFlops(18.0);
    1413:       DMPlex_Det3D_Internal(detJ, J);
    1414:     }
    1415:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1416:   } else {
    1417:     const PetscInt Nv = 8;
    1418:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    1419:     const PetscInt dim = 3;
    1420:     const PetscInt dimR = 3;
    1421:     PetscReal zOrder[24];
    1422:     PetscReal zCoeff[24];
    1423:     PetscInt  i, j, k, l;

    1425:     for (i = 0; i < Nv; i++) {
    1426:       PetscInt zi = zToPlex[i];

    1428:       for (j = 0; j < dim; j++) {
    1429:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1430:       }
    1431:     }
    1432:     for (j = 0; j < dim; j++) {
    1433:       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]);
    1434:       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]);
    1435:       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]);
    1436:       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]);
    1437:       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]);
    1438:       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]);
    1439:       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]);
    1440:       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]);
    1441:     }
    1442:     for (i = 0; i < Nq; i++) {
    1443:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    1445:       if (v) {
    1446:         PetscReal extPoint[8];

    1448:         extPoint[0] = 1.;
    1449:         extPoint[1] = xi;
    1450:         extPoint[2] = eta;
    1451:         extPoint[3] = xi * eta;
    1452:         extPoint[4] = theta;
    1453:         extPoint[5] = theta * xi;
    1454:         extPoint[6] = theta * eta;
    1455:         extPoint[7] = theta * eta * xi;
    1456:         for (j = 0; j < dim; j++) {
    1457:           PetscReal val = 0.;

    1459:           for (k = 0; k < Nv; k++) {
    1460:             val += extPoint[k] * zCoeff[dim * k + j];
    1461:           }
    1462:           v[i * dim + j] = val;
    1463:         }
    1464:       }
    1465:       if (J) {
    1466:         PetscReal extJ[24];

    1468:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
    1469:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
    1470:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
    1471:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
    1472:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
    1473:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
    1474:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
    1475:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

    1477:         for (j = 0; j < dim; j++) {
    1478:           for (k = 0; k < dimR; k++) {
    1479:             PetscReal val = 0.;

    1481:             for (l = 0; l < Nv; l++) {
    1482:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1483:             }
    1484:             J[i * dim * dim + dim * j + k] = val;
    1485:           }
    1486:         }
    1487:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1488:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1489:       }
    1490:     }
    1491:   }
    1492:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1493:   return(0);
    1494: }

    1496: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1497: {
    1498:   DMPolytopeType  ct;
    1499:   PetscInt        depth, dim, coordDim, coneSize, i;
    1500:   PetscInt        Nq = 0;
    1501:   const PetscReal *points = NULL;
    1502:   DMLabel         depthLabel;
    1503:   PetscReal       xi0[3] = {-1.,-1.,-1.}, v0[3], J0[9], detJ0;
    1504:   PetscBool       isAffine = PETSC_TRUE;
    1505:   PetscErrorCode  ierr;

    1508:   DMPlexGetDepth(dm, &depth);
    1509:   DMPlexGetConeSize(dm, cell, &coneSize);
    1510:   DMPlexGetDepthLabel(dm, &depthLabel);
    1511:   DMLabelGetValue(depthLabel, cell, &dim);
    1512:   if (depth == 1 && dim == 1) {
    1513:     DMGetDimension(dm, &dim);
    1514:   }
    1515:   DMGetCoordinateDim(dm, &coordDim);
    1516:   if (coordDim > 3) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %D > 3", coordDim);
    1517:   if (quad) {PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);}
    1518:   DMPlexGetCellType(dm, cell, &ct);
    1519:   switch (ct) {
    1520:     case DM_POLYTOPE_POINT:
    1521:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1522:     isAffine = PETSC_FALSE;
    1523:     break;
    1524:     case DM_POLYTOPE_SEGMENT:
    1525:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1526:     if (Nq) {DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1527:     else    {DMPlexComputeLineGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1528:     break;
    1529:     case DM_POLYTOPE_TRIANGLE:
    1530:     if (Nq) {DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1531:     else    {DMPlexComputeTriangleGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1532:     break;
    1533:     case DM_POLYTOPE_QUADRILATERAL:
    1534:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ);
    1535:     isAffine = PETSC_FALSE;
    1536:     break;
    1537:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1538:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ);
    1539:     isAffine = PETSC_FALSE;
    1540:     break;
    1541:     case DM_POLYTOPE_TETRAHEDRON:
    1542:     if (Nq) {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
    1543:     else    {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
    1544:     break;
    1545:     case DM_POLYTOPE_HEXAHEDRON:
    1546:     DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1547:     isAffine = PETSC_FALSE;
    1548:     break;
    1549:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %D with type %s", cell, DMPolytopeTypes[ct]);
    1550:   }
    1551:   if (isAffine && Nq) {
    1552:     if (v) {
    1553:       for (i = 0; i < Nq; i++) {
    1554:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    1555:       }
    1556:     }
    1557:     if (detJ) {
    1558:       for (i = 0; i < Nq; i++) {
    1559:         detJ[i] = detJ0;
    1560:       }
    1561:     }
    1562:     if (J) {
    1563:       PetscInt k;

    1565:       for (i = 0, k = 0; i < Nq; i++) {
    1566:         PetscInt j;

    1568:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1569:           J[k] = J0[j];
    1570:         }
    1571:       }
    1572:     }
    1573:     if (invJ) {
    1574:       PetscInt k;
    1575:       switch (coordDim) {
    1576:       case 0:
    1577:         break;
    1578:       case 1:
    1579:         invJ[0] = 1./J0[0];
    1580:         break;
    1581:       case 2:
    1582:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    1583:         break;
    1584:       case 3:
    1585:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    1586:         break;
    1587:       }
    1588:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    1589:         PetscInt j;

    1591:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1592:           invJ[k] = invJ[j];
    1593:         }
    1594:       }
    1595:     }
    1596:   }
    1597:   return(0);
    1598: }

    1600: /*@C
    1601:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    1603:   Collective on dm

    1605:   Input Arguments:
    1606: + dm   - the DM
    1607: - cell - the cell

    1609:   Output Arguments:
    1610: + v0   - the translation part of this affine transform
    1611: . J    - the Jacobian of the transform from the reference element
    1612: . invJ - the inverse of the Jacobian
    1613: - detJ - the Jacobian determinant

    1615:   Level: advanced

    1617:   Fortran Notes:
    1618:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1619:   include petsc.h90 in your code.

    1621: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
    1622: @*/
    1623: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1624: {

    1628:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
    1629:   return(0);
    1630: }

    1632: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1633: {
    1634:   PetscQuadrature   feQuad;
    1635:   PetscSection      coordSection;
    1636:   Vec               coordinates;
    1637:   PetscScalar      *coords = NULL;
    1638:   const PetscReal  *quadPoints;
    1639:   PetscTabulation T;
    1640:   PetscInt          dim, cdim, pdim, qdim, Nq, numCoords, q;
    1641:   PetscErrorCode    ierr;

    1644:   DMGetCoordinatesLocal(dm, &coordinates);
    1645:   DMGetCoordinateSection(dm, &coordSection);
    1646:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1647:   DMGetDimension(dm, &dim);
    1648:   DMGetCoordinateDim(dm, &cdim);
    1649:   if (!quad) { /* use the first point of the first functional of the dual space */
    1650:     PetscDualSpace dsp;

    1652:     PetscFEGetDualSpace(fe, &dsp);
    1653:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
    1654:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1655:     Nq = 1;
    1656:   } else {
    1657:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1658:   }
    1659:   PetscFEGetDimension(fe, &pdim);
    1660:   PetscFEGetQuadrature(fe, &feQuad);
    1661:   if (feQuad == quad) {
    1662:     PetscFEGetCellTabulation(fe, &T);
    1663:     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);
    1664:   } else {
    1665:     PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T);
    1666:   }
    1667:   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
    1668:   {
    1669:     const PetscReal *basis    = T->T[0];
    1670:     const PetscReal *basisDer = T->T[1];
    1671:     PetscReal        detJt;

    1673:     if (v) {
    1674:       PetscArrayzero(v, Nq*cdim);
    1675:       for (q = 0; q < Nq; ++q) {
    1676:         PetscInt i, k;

    1678:         for (k = 0; k < pdim; ++k)
    1679:           for (i = 0; i < cdim; ++i)
    1680:             v[q*cdim + i] += basis[q*pdim + k] * PetscRealPart(coords[k*cdim + i]);
    1681:         PetscLogFlops(2.0*pdim*cdim);
    1682:       }
    1683:     }
    1684:     if (J) {
    1685:       PetscArrayzero(J, Nq*cdim*cdim);
    1686:       for (q = 0; q < Nq; ++q) {
    1687:         PetscInt i, j, k, c, r;

    1689:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    1690:         for (k = 0; k < pdim; ++k)
    1691:           for (j = 0; j < dim; ++j)
    1692:             for (i = 0; i < cdim; ++i)
    1693:               J[(q*cdim + i)*cdim + j] += basisDer[(q*pdim + k)*dim + j] * PetscRealPart(coords[k*cdim + i]);
    1694:         PetscLogFlops(2.0*pdim*dim*cdim);
    1695:         if (cdim > dim) {
    1696:           for (c = dim; c < cdim; ++c)
    1697:             for (r = 0; r < cdim; ++r)
    1698:               J[r*cdim+c] = r == c ? 1.0 : 0.0;
    1699:         }
    1700:         if (!detJ && !invJ) continue;
    1701:         detJt = 0.;
    1702:         switch (cdim) {
    1703:         case 3:
    1704:           DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
    1705:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1706:           break;
    1707:         case 2:
    1708:           DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
    1709:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1710:           break;
    1711:         case 1:
    1712:           detJt = J[q*cdim*dim];
    1713:           if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
    1714:         }
    1715:         if (detJ) detJ[q] = detJt;
    1716:       }
    1717:     } else if (detJ || invJ) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
    1718:   }
    1719:   if (feQuad != quad) {PetscTabulationDestroy(&T);}
    1720:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1721:   return(0);
    1722: }

    1724: /*@C
    1725:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    1727:   Collective on dm

    1729:   Input Arguments:
    1730: + dm   - the DM
    1731: . cell - the cell
    1732: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
    1733:          evaluated at the first vertex of the reference element

    1735:   Output Arguments:
    1736: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
    1737: . J    - the Jacobian of the transform from the reference element at each quadrature point
    1738: . invJ - the inverse of the Jacobian at each quadrature point
    1739: - detJ - the Jacobian determinant at each quadrature point

    1741:   Level: advanced

    1743:   Fortran Notes:
    1744:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1745:   include petsc.h90 in your code.

    1747: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1748: @*/
    1749: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1750: {
    1751:   DM             cdm;
    1752:   PetscFE        fe = NULL;

    1757:   DMGetCoordinateDM(dm, &cdm);
    1758:   if (cdm) {
    1759:     PetscClassId id;
    1760:     PetscInt     numFields;
    1761:     PetscDS      prob;
    1762:     PetscObject  disc;

    1764:     DMGetNumFields(cdm, &numFields);
    1765:     if (numFields) {
    1766:       DMGetDS(cdm, &prob);
    1767:       PetscDSGetDiscretization(prob,0,&disc);
    1768:       PetscObjectGetClassId(disc,&id);
    1769:       if (id == PETSCFE_CLASSID) {
    1770:         fe = (PetscFE) disc;
    1771:       }
    1772:     }
    1773:   }
    1774:   if (!fe) {DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);}
    1775:   else     {DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);}
    1776:   return(0);
    1777: }

    1779: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1780: {
    1781:   PetscSection   coordSection;
    1782:   Vec            coordinates;
    1783:   PetscScalar   *coords = NULL;
    1784:   PetscScalar    tmp[2];
    1785:   PetscInt       coordSize, d;

    1789:   DMGetCoordinatesLocal(dm, &coordinates);
    1790:   DMGetCoordinateSection(dm, &coordSection);
    1791:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1792:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
    1793:   if (centroid) {
    1794:     for (d = 0; d < dim; ++d) centroid[d] = 0.5*PetscRealPart(coords[d] + tmp[d]);
    1795:   }
    1796:   if (normal) {
    1797:     PetscReal norm;

    1799:     if (dim != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "We only support 2D edges right now");
    1800:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
    1801:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
    1802:     norm       = DMPlex_NormD_Internal(dim, normal);
    1803:     for (d = 0; d < dim; ++d) normal[d] /= norm;
    1804:   }
    1805:   if (vol) {
    1806:     *vol = 0.0;
    1807:     for (d = 0; d < dim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - tmp[d]));
    1808:     *vol = PetscSqrtReal(*vol);
    1809:   }
    1810:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1811:   return(0);
    1812: }

    1814: /* Centroid_i = (\sum_n A_n Cn_i ) / A */
    1815: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1816: {
    1817:   DMPolytopeType ct;
    1818:   PetscSection   coordSection;
    1819:   Vec            coordinates;
    1820:   PetscScalar   *coords = NULL;
    1821:   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
    1822:   PetscBool      isHybrid = PETSC_FALSE;
    1823:   PetscInt       fv[4] = {0, 1, 2, 3};
    1824:   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;

    1828:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    1829:   DMPlexGetCellType(dm, cell, &ct);
    1830:   switch (ct) {
    1831:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1832:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1833:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1834:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1835:       isHybrid = PETSC_TRUE;
    1836:     default: break;
    1837:   }
    1838:   DMGetCoordinatesLocal(dm, &coordinates);
    1839:   DMPlexGetConeSize(dm, cell, &numCorners);
    1840:   DMGetCoordinateSection(dm, &coordSection);
    1841:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1842:   DMGetCoordinateDim(dm, &dim);
    1843:   /* Side faces for hybrid cells are are stored as tensor products */
    1844:   if (isHybrid && numCorners == 4) {fv[2] = 3; fv[3] = 2;}

    1846:   if (dim > 2 && centroid) {
    1847:     v0[0] = PetscRealPart(coords[0]);
    1848:     v0[1] = PetscRealPart(coords[1]);
    1849:     v0[2] = PetscRealPart(coords[2]);
    1850:   }
    1851:   if (normal) {
    1852:     if (dim > 2) {
    1853:       const PetscReal x0 = PetscRealPart(coords[dim*fv[1]+0] - coords[0]), x1 = PetscRealPart(coords[dim*fv[2]+0] - coords[0]);
    1854:       const PetscReal y0 = PetscRealPart(coords[dim*fv[1]+1] - coords[1]), y1 = PetscRealPart(coords[dim*fv[2]+1] - coords[1]);
    1855:       const PetscReal z0 = PetscRealPart(coords[dim*fv[1]+2] - coords[2]), z1 = PetscRealPart(coords[dim*fv[2]+2] - coords[2]);
    1856:       PetscReal       norm;

    1858:       normal[0] = y0*z1 - z0*y1;
    1859:       normal[1] = z0*x1 - x0*z1;
    1860:       normal[2] = x0*y1 - y0*x1;
    1861:       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
    1862:       normal[0] /= norm;
    1863:       normal[1] /= norm;
    1864:       normal[2] /= norm;
    1865:     } else {
    1866:       for (d = 0; d < dim; ++d) normal[d] = 0.0;
    1867:     }
    1868:   }
    1869:   if (dim == 3) {DMPlexComputeProjection3Dto2D(coordSize, coords, R);}
    1870:   for (p = 0; p < numCorners; ++p) {
    1871:     const PetscInt pi  = p < 4 ? fv[p] : p;
    1872:     const PetscInt pin = p < 3 ? fv[(p+1)%numCorners] : (p+1)%numCorners;
    1873:     /* Need to do this copy to get types right */
    1874:     for (d = 0; d < tdim; ++d) {
    1875:       ctmp[d]      = PetscRealPart(coords[pi*tdim+d]);
    1876:       ctmp[tdim+d] = PetscRealPart(coords[pin*tdim+d]);
    1877:     }
    1878:     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
    1879:     vsum += vtmp;
    1880:     for (d = 0; d < tdim; ++d) {
    1881:       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
    1882:     }
    1883:   }
    1884:   for (d = 0; d < tdim; ++d) {
    1885:     csum[d] /= (tdim+1)*vsum;
    1886:   }
    1887:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1888:   if (vol) *vol = PetscAbsReal(vsum);
    1889:   if (centroid) {
    1890:     if (dim > 2) {
    1891:       for (d = 0; d < dim; ++d) {
    1892:         centroid[d] = v0[d];
    1893:         for (e = 0; e < dim; ++e) {
    1894:           centroid[d] += R[d*dim+e]*csum[e];
    1895:         }
    1896:       }
    1897:     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
    1898:   }
    1899:   return(0);
    1900: }

    1902: /* Centroid_i = (\sum_n V_n Cn_i ) / V */
    1903: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1904: {
    1905:   DMPolytopeType  ct;
    1906:   PetscSection    coordSection;
    1907:   Vec             coordinates;
    1908:   PetscScalar    *coords = NULL;
    1909:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
    1910:   const PetscInt *faces, *facesO;
    1911:   PetscBool       isHybrid = PETSC_FALSE;
    1912:   PetscInt        numFaces, f, coordSize, p, d;
    1913:   PetscErrorCode  ierr;

    1916:   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
    1917:   /* Must check for hybrid cells because prisms have a different orientation scheme */
    1918:   DMPlexGetCellType(dm, cell, &ct);
    1919:   switch (ct) {
    1920:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1921:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1922:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1923:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1924:       isHybrid = PETSC_TRUE;
    1925:     default: break;
    1926:   }

    1928:   DMGetCoordinatesLocal(dm, &coordinates);
    1929:   DMGetCoordinateSection(dm, &coordSection);

    1931:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    1932:   DMPlexGetConeSize(dm, cell, &numFaces);
    1933:   DMPlexGetCone(dm, cell, &faces);
    1934:   DMPlexGetConeOrientation(dm, cell, &facesO);
    1935:   for (f = 0; f < numFaces; ++f) {
    1936:     PetscBool      flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
    1937:     DMPolytopeType ct;

    1939:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    1940:     DMPlexGetCellType(dm, faces[f], &ct);
    1941:     switch (ct) {
    1942:     case DM_POLYTOPE_TRIANGLE:
    1943:       for (d = 0; d < dim; ++d) {
    1944:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
    1945:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
    1946:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
    1947:       }
    1948:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1949:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    1950:       vsum += vtmp;
    1951:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
    1952:         for (d = 0; d < dim; ++d) {
    1953:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1954:         }
    1955:       }
    1956:       break;
    1957:     case DM_POLYTOPE_QUADRILATERAL:
    1958:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1959:     {
    1960:       PetscInt fv[4] = {0, 1, 2, 3};

    1962:       /* Side faces for hybrid cells are are stored as tensor products */
    1963:       if (isHybrid && f > 1) {fv[2] = 3; fv[3] = 2;}
    1964:       /* DO FOR PYRAMID */
    1965:       /* First tet */
    1966:       for (d = 0; d < dim; ++d) {
    1967:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[0]*dim+d]);
    1968:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
    1969:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
    1970:       }
    1971:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1972:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    1973:       vsum += vtmp;
    1974:       if (centroid) {
    1975:         for (d = 0; d < dim; ++d) {
    1976:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1977:         }
    1978:       }
    1979:       /* Second tet */
    1980:       for (d = 0; d < dim; ++d) {
    1981:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
    1982:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[2]*dim+d]);
    1983:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
    1984:       }
    1985:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1986:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
    1987:       vsum += vtmp;
    1988:       if (centroid) {
    1989:         for (d = 0; d < dim; ++d) {
    1990:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1991:         }
    1992:       }
    1993:       break;
    1994:     }
    1995:     default:
    1996:       SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %D of type %s", faces[f], DMPolytopeTypes[ct]);
    1997:     }
    1998:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    1999:   }
    2000:   if (vol)     *vol = PetscAbsReal(vsum);
    2001:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
    2002:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
    2003:   return(0);
    2004: }

    2006: /*@C
    2007:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    2009:   Collective on dm

    2011:   Input Arguments:
    2012: + dm   - the DM
    2013: - cell - the cell

    2015:   Output Arguments:
    2016: + volume   - the cell volume
    2017: . centroid - the cell centroid
    2018: - normal - the cell normal, if appropriate

    2020:   Level: advanced

    2022:   Fortran Notes:
    2023:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    2024:   include petsc.h90 in your code.

    2026: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    2027: @*/
    2028: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    2029: {
    2030:   PetscInt       depth, dim;

    2034:   DMPlexGetDepth(dm, &depth);
    2035:   DMGetDimension(dm, &dim);
    2036:   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
    2037:   DMPlexGetPointDepth(dm, cell, &depth);
    2038:   switch (depth) {
    2039:   case 1:
    2040:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
    2041:     break;
    2042:   case 2:
    2043:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
    2044:     break;
    2045:   case 3:
    2046:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
    2047:     break;
    2048:   default:
    2049:     SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
    2050:   }
    2051:   return(0);
    2052: }

    2054: /*@
    2055:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

    2057:   Collective on dm

    2059:   Input Parameter:
    2060: . dm - The DMPlex

    2062:   Output Parameter:
    2063: . cellgeom - A vector with the cell geometry data for each cell

    2065:   Level: beginner

    2067: @*/
    2068: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
    2069: {
    2070:   DM             dmCell;
    2071:   Vec            coordinates;
    2072:   PetscSection   coordSection, sectionCell;
    2073:   PetscScalar   *cgeom;
    2074:   PetscInt       cStart, cEnd, c;

    2078:   DMClone(dm, &dmCell);
    2079:   DMGetCoordinateSection(dm, &coordSection);
    2080:   DMGetCoordinatesLocal(dm, &coordinates);
    2081:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2082:   DMSetCoordinatesLocal(dmCell, coordinates);
    2083:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2084:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    2085:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2086:   /* TODO This needs to be multiplied by Nq for non-affine */
    2087:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));}
    2088:   PetscSectionSetUp(sectionCell);
    2089:   DMSetLocalSection(dmCell, sectionCell);
    2090:   PetscSectionDestroy(&sectionCell);
    2091:   DMCreateLocalVector(dmCell, cellgeom);
    2092:   VecGetArray(*cellgeom, &cgeom);
    2093:   for (c = cStart; c < cEnd; ++c) {
    2094:     PetscFEGeom *cg;

    2096:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2097:     PetscArrayzero(cg, 1);
    2098:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
    2099:     if (*cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double) *cg->detJ, c);
    2100:   }
    2101:   return(0);
    2102: }

    2104: /*@
    2105:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2107:   Input Parameter:
    2108: . dm - The DM

    2110:   Output Parameters:
    2111: + cellgeom - A Vec of PetscFVCellGeom data
    2112: - facegeom - A Vec of PetscFVFaceGeom data

    2114:   Level: developer

    2116: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
    2117: @*/
    2118: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2119: {
    2120:   DM             dmFace, dmCell;
    2121:   DMLabel        ghostLabel;
    2122:   PetscSection   sectionFace, sectionCell;
    2123:   PetscSection   coordSection;
    2124:   Vec            coordinates;
    2125:   PetscScalar   *fgeom, *cgeom;
    2126:   PetscReal      minradius, gminradius;
    2127:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2131:   DMGetDimension(dm, &dim);
    2132:   DMGetCoordinateSection(dm, &coordSection);
    2133:   DMGetCoordinatesLocal(dm, &coordinates);
    2134:   /* Make cell centroids and volumes */
    2135:   DMClone(dm, &dmCell);
    2136:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2137:   DMSetCoordinatesLocal(dmCell, coordinates);
    2138:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2139:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2140:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2141:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2142:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));}
    2143:   PetscSectionSetUp(sectionCell);
    2144:   DMSetLocalSection(dmCell, sectionCell);
    2145:   PetscSectionDestroy(&sectionCell);
    2146:   DMCreateLocalVector(dmCell, cellgeom);
    2147:   if (cEndInterior < 0) cEndInterior = cEnd;
    2148:   VecGetArray(*cellgeom, &cgeom);
    2149:   for (c = cStart; c < cEndInterior; ++c) {
    2150:     PetscFVCellGeom *cg;

    2152:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2153:     PetscArrayzero(cg, 1);
    2154:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
    2155:   }
    2156:   /* Compute face normals and minimum cell radius */
    2157:   DMClone(dm, &dmFace);
    2158:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
    2159:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2160:   PetscSectionSetChart(sectionFace, fStart, fEnd);
    2161:   for (f = fStart; f < fEnd; ++f) {PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));}
    2162:   PetscSectionSetUp(sectionFace);
    2163:   DMSetLocalSection(dmFace, sectionFace);
    2164:   PetscSectionDestroy(&sectionFace);
    2165:   DMCreateLocalVector(dmFace, facegeom);
    2166:   VecGetArray(*facegeom, &fgeom);
    2167:   DMGetLabel(dm, "ghost", &ghostLabel);
    2168:   minradius = PETSC_MAX_REAL;
    2169:   for (f = fStart; f < fEnd; ++f) {
    2170:     PetscFVFaceGeom *fg;
    2171:     PetscReal        area;
    2172:     const PetscInt  *cells;
    2173:     PetscInt         ncells, ghost = -1, d, numChildren;

    2175:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2176:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
    2177:     DMPlexGetSupport(dm, f, &cells);
    2178:     DMPlexGetSupportSize(dm, f, &ncells);
    2179:     /* It is possible to get a face with no support when using partition overlap */
    2180:     if (!ncells || ghost >= 0 || numChildren) continue;
    2181:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
    2182:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
    2183:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    2184:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    2185:     {
    2186:       PetscFVCellGeom *cL, *cR;
    2187:       PetscReal       *lcentroid, *rcentroid;
    2188:       PetscReal        l[3], r[3], v[3];

    2190:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
    2191:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    2192:       if (ncells > 1) {
    2193:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
    2194:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    2195:       }
    2196:       else {
    2197:         rcentroid = fg->centroid;
    2198:       }
    2199:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
    2200:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
    2201:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    2202:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    2203:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    2204:       }
    2205:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    2206:         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]);
    2207:         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]);
    2208:         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
    2209:       }
    2210:       if (cells[0] < cEndInterior) {
    2211:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    2212:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2213:       }
    2214:       if (ncells > 1 && cells[1] < cEndInterior) {
    2215:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    2216:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2217:       }
    2218:     }
    2219:   }
    2220:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
    2221:   DMPlexSetMinRadius(dm, gminradius);
    2222:   /* Compute centroids of ghost cells */
    2223:   for (c = cEndInterior; c < cEnd; ++c) {
    2224:     PetscFVFaceGeom *fg;
    2225:     const PetscInt  *cone,    *support;
    2226:     PetscInt         coneSize, supportSize, s;

    2228:     DMPlexGetConeSize(dmCell, c, &coneSize);
    2229:     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
    2230:     DMPlexGetCone(dmCell, c, &cone);
    2231:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
    2232:     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
    2233:     DMPlexGetSupport(dmCell, cone[0], &support);
    2234:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
    2235:     for (s = 0; s < 2; ++s) {
    2236:       /* Reflect ghost centroid across plane of face */
    2237:       if (support[s] == c) {
    2238:         PetscFVCellGeom       *ci;
    2239:         PetscFVCellGeom       *cg;
    2240:         PetscReal              c2f[3], a;

    2242:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
    2243:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    2244:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    2245:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
    2246:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
    2247:         cg->volume = ci->volume;
    2248:       }
    2249:     }
    2250:   }
    2251:   VecRestoreArray(*facegeom, &fgeom);
    2252:   VecRestoreArray(*cellgeom, &cgeom);
    2253:   DMDestroy(&dmCell);
    2254:   DMDestroy(&dmFace);
    2255:   return(0);
    2256: }

    2258: /*@C
    2259:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    2261:   Not collective

    2263:   Input Argument:
    2264: . dm - the DM

    2266:   Output Argument:
    2267: . minradius - the minium cell radius

    2269:   Level: developer

    2271: .seealso: DMGetCoordinates()
    2272: @*/
    2273: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    2274: {
    2278:   *minradius = ((DM_Plex*) dm->data)->minradius;
    2279:   return(0);
    2280: }

    2282: /*@C
    2283:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    2285:   Logically collective

    2287:   Input Arguments:
    2288: + dm - the DM
    2289: - minradius - the minium cell radius

    2291:   Level: developer

    2293: .seealso: DMSetCoordinates()
    2294: @*/
    2295: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    2296: {
    2299:   ((DM_Plex*) dm->data)->minradius = minradius;
    2300:   return(0);
    2301: }

    2303: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2304: {
    2305:   DMLabel        ghostLabel;
    2306:   PetscScalar   *dx, *grad, **gref;
    2307:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    2311:   DMGetDimension(dm, &dim);
    2312:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2313:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2314:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
    2315:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2316:   DMGetLabel(dm, "ghost", &ghostLabel);
    2317:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2318:   for (c = cStart; c < cEndInterior; c++) {
    2319:     const PetscInt        *faces;
    2320:     PetscInt               numFaces, usedFaces, f, d;
    2321:     PetscFVCellGeom        *cg;
    2322:     PetscBool              boundary;
    2323:     PetscInt               ghost;

    2325:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2326:     DMPlexGetConeSize(dm, c, &numFaces);
    2327:     DMPlexGetCone(dm, c, &faces);
    2328:     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
    2329:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2330:       PetscFVCellGeom       *cg1;
    2331:       PetscFVFaceGeom       *fg;
    2332:       const PetscInt        *fcells;
    2333:       PetscInt               ncell, side;

    2335:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2336:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2337:       if ((ghost >= 0) || boundary) continue;
    2338:       DMPlexGetSupport(dm, faces[f], &fcells);
    2339:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    2340:       ncell = fcells[!side];    /* the neighbor */
    2341:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
    2342:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2343:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2344:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2345:     }
    2346:     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
    2347:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
    2348:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2349:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2350:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2351:       if ((ghost >= 0) || boundary) continue;
    2352:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
    2353:       ++usedFaces;
    2354:     }
    2355:   }
    2356:   PetscFree3(dx, grad, gref);
    2357:   return(0);
    2358: }

    2360: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2361: {
    2362:   DMLabel        ghostLabel;
    2363:   PetscScalar   *dx, *grad, **gref;
    2364:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    2365:   PetscSection   neighSec;
    2366:   PetscInt     (*neighbors)[2];
    2367:   PetscInt      *counter;

    2371:   DMGetDimension(dm, &dim);
    2372:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2373:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2374:   if (cEndInterior < 0) cEndInterior = cEnd;
    2375:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
    2376:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
    2377:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2378:   DMGetLabel(dm, "ghost", &ghostLabel);
    2379:   for (f = fStart; f < fEnd; f++) {
    2380:     const PetscInt        *fcells;
    2381:     PetscBool              boundary;
    2382:     PetscInt               ghost = -1;
    2383:     PetscInt               numChildren, numCells, c;

    2385:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2386:     DMIsBoundaryPoint(dm, f, &boundary);
    2387:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2388:     if ((ghost >= 0) || boundary || numChildren) continue;
    2389:     DMPlexGetSupportSize(dm, f, &numCells);
    2390:     if (numCells == 2) {
    2391:       DMPlexGetSupport(dm, f, &fcells);
    2392:       for (c = 0; c < 2; c++) {
    2393:         PetscInt cell = fcells[c];

    2395:         if (cell >= cStart && cell < cEndInterior) {
    2396:           PetscSectionAddDof(neighSec,cell,1);
    2397:         }
    2398:       }
    2399:     }
    2400:   }
    2401:   PetscSectionSetUp(neighSec);
    2402:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
    2403:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2404:   nStart = 0;
    2405:   PetscSectionGetStorageSize(neighSec,&nEnd);
    2406:   PetscMalloc1((nEnd-nStart),&neighbors);
    2407:   PetscCalloc1((cEndInterior-cStart),&counter);
    2408:   for (f = fStart; f < fEnd; f++) {
    2409:     const PetscInt        *fcells;
    2410:     PetscBool              boundary;
    2411:     PetscInt               ghost = -1;
    2412:     PetscInt               numChildren, numCells, c;

    2414:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2415:     DMIsBoundaryPoint(dm, f, &boundary);
    2416:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2417:     if ((ghost >= 0) || boundary || numChildren) continue;
    2418:     DMPlexGetSupportSize(dm, f, &numCells);
    2419:     if (numCells == 2) {
    2420:       DMPlexGetSupport(dm, f, &fcells);
    2421:       for (c = 0; c < 2; c++) {
    2422:         PetscInt cell = fcells[c], off;

    2424:         if (cell >= cStart && cell < cEndInterior) {
    2425:           PetscSectionGetOffset(neighSec,cell,&off);
    2426:           off += counter[cell - cStart]++;
    2427:           neighbors[off][0] = f;
    2428:           neighbors[off][1] = fcells[1 - c];
    2429:         }
    2430:       }
    2431:     }
    2432:   }
    2433:   PetscFree(counter);
    2434:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2435:   for (c = cStart; c < cEndInterior; c++) {
    2436:     PetscInt               numFaces, f, d, off, ghost = -1;
    2437:     PetscFVCellGeom        *cg;

    2439:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2440:     PetscSectionGetDof(neighSec, c, &numFaces);
    2441:     PetscSectionGetOffset(neighSec, c, &off);
    2442:     if (ghostLabel) {DMLabelGetValue(ghostLabel, c, &ghost);}
    2443:     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);
    2444:     for (f = 0; f < numFaces; ++f) {
    2445:       PetscFVCellGeom       *cg1;
    2446:       PetscFVFaceGeom       *fg;
    2447:       const PetscInt        *fcells;
    2448:       PetscInt               ncell, side, nface;

    2450:       nface = neighbors[off + f][0];
    2451:       ncell = neighbors[off + f][1];
    2452:       DMPlexGetSupport(dm,nface,&fcells);
    2453:       side  = (c != fcells[0]);
    2454:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
    2455:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2456:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2457:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2458:     }
    2459:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
    2460:     for (f = 0; f < numFaces; ++f) {
    2461:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
    2462:     }
    2463:   }
    2464:   PetscFree3(dx, grad, gref);
    2465:   PetscSectionDestroy(&neighSec);
    2466:   PetscFree(neighbors);
    2467:   return(0);
    2468: }

    2470: /*@
    2471:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    2473:   Collective on dm

    2475:   Input Arguments:
    2476: + dm  - The DM
    2477: . fvm - The PetscFV
    2478: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM()
    2479: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

    2481:   Output Parameters:
    2482: + faceGeometry - The geometric factors for gradient calculation are inserted
    2483: - dmGrad - The DM describing the layout of gradient data

    2485:   Level: developer

    2487: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
    2488: @*/
    2489: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    2490: {
    2491:   DM             dmFace, dmCell;
    2492:   PetscScalar   *fgeom, *cgeom;
    2493:   PetscSection   sectionGrad, parentSection;
    2494:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

    2498:   DMGetDimension(dm, &dim);
    2499:   PetscFVGetNumComponents(fvm, &pdim);
    2500:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2501:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    2502:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    2503:   VecGetDM(faceGeometry, &dmFace);
    2504:   VecGetDM(cellGeometry, &dmCell);
    2505:   VecGetArray(faceGeometry, &fgeom);
    2506:   VecGetArray(cellGeometry, &cgeom);
    2507:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
    2508:   if (!parentSection) {
    2509:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2510:   } else {
    2511:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2512:   }
    2513:   VecRestoreArray(faceGeometry, &fgeom);
    2514:   VecRestoreArray(cellGeometry, &cgeom);
    2515:   /* Create storage for gradients */
    2516:   DMClone(dm, dmGrad);
    2517:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
    2518:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
    2519:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionGrad, c, pdim*dim);}
    2520:   PetscSectionSetUp(sectionGrad);
    2521:   DMSetLocalSection(*dmGrad, sectionGrad);
    2522:   PetscSectionDestroy(&sectionGrad);
    2523:   return(0);
    2524: }

    2526: /*@
    2527:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    2529:   Collective on dm

    2531:   Input Arguments:
    2532: + dm  - The DM
    2533: - fvm - The PetscFV

    2535:   Output Parameters:
    2536: + cellGeometry - The cell geometry
    2537: . faceGeometry - The face geometry
    2538: - dmGrad       - The gradient matrices

    2540:   Level: developer

    2542: .seealso: DMPlexComputeGeometryFVM()
    2543: @*/
    2544: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    2545: {
    2546:   PetscObject    cellgeomobj, facegeomobj;

    2550:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2551:   if (!cellgeomobj) {
    2552:     Vec cellgeomInt, facegeomInt;

    2554:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
    2555:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
    2556:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
    2557:     VecDestroy(&cellgeomInt);
    2558:     VecDestroy(&facegeomInt);
    2559:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2560:   }
    2561:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
    2562:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
    2563:   if (facegeom) *facegeom = (Vec) facegeomobj;
    2564:   if (gradDM) {
    2565:     PetscObject gradobj;
    2566:     PetscBool   computeGradients;

    2568:     PetscFVGetComputeGradients(fv,&computeGradients);
    2569:     if (!computeGradients) {
    2570:       *gradDM = NULL;
    2571:       return(0);
    2572:     }
    2573:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2574:     if (!gradobj) {
    2575:       DM dmGradInt;

    2577:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
    2578:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
    2579:       DMDestroy(&dmGradInt);
    2580:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2581:     }
    2582:     *gradDM = (DM) gradobj;
    2583:   }
    2584:   return(0);
    2585: }

    2587: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
    2588: {
    2589:   PetscInt l, m;

    2592:   if (dimC == dimR && dimR <= 3) {
    2593:     /* invert Jacobian, multiply */
    2594:     PetscScalar det, idet;

    2596:     switch (dimR) {
    2597:     case 1:
    2598:       invJ[0] = 1./ J[0];
    2599:       break;
    2600:     case 2:
    2601:       det = J[0] * J[3] - J[1] * J[2];
    2602:       idet = 1./det;
    2603:       invJ[0] =  J[3] * idet;
    2604:       invJ[1] = -J[1] * idet;
    2605:       invJ[2] = -J[2] * idet;
    2606:       invJ[3] =  J[0] * idet;
    2607:       break;
    2608:     case 3:
    2609:       {
    2610:         invJ[0] = J[4] * J[8] - J[5] * J[7];
    2611:         invJ[1] = J[2] * J[7] - J[1] * J[8];
    2612:         invJ[2] = J[1] * J[5] - J[2] * J[4];
    2613:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    2614:         idet = 1./det;
    2615:         invJ[0] *= idet;
    2616:         invJ[1] *= idet;
    2617:         invJ[2] *= idet;
    2618:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
    2619:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
    2620:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
    2621:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
    2622:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
    2623:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
    2624:       }
    2625:       break;
    2626:     }
    2627:     for (l = 0; l < dimR; l++) {
    2628:       for (m = 0; m < dimC; m++) {
    2629:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    2630:       }
    2631:     }
    2632:   } else {
    2633: #if defined(PETSC_USE_COMPLEX)
    2634:     char transpose = 'C';
    2635: #else
    2636:     char transpose = 'T';
    2637: #endif
    2638:     PetscBLASInt m = dimR;
    2639:     PetscBLASInt n = dimC;
    2640:     PetscBLASInt one = 1;
    2641:     PetscBLASInt worksize = dimR * dimC, info;

    2643:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

    2645:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));
    2646:     if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");

    2648:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
    2649:   }
    2650:   return(0);
    2651: }

    2653: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2654: {
    2655:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    2656:   PetscScalar    *coordsScalar = NULL;
    2657:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    2658:   PetscScalar    *J, *invJ, *work;

    2663:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2664:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2665:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2666:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2667:   cellCoords = &cellData[0];
    2668:   cellCoeffs = &cellData[coordSize];
    2669:   extJ       = &cellData[2 * coordSize];
    2670:   resNeg     = &cellData[2 * coordSize + dimR];
    2671:   invJ       = &J[dimR * dimC];
    2672:   work       = &J[2 * dimR * dimC];
    2673:   if (dimR == 2) {
    2674:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2676:     for (i = 0; i < 4; i++) {
    2677:       PetscInt plexI = zToPlex[i];

    2679:       for (j = 0; j < dimC; j++) {
    2680:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2681:       }
    2682:     }
    2683:   } else if (dimR == 3) {
    2684:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2686:     for (i = 0; i < 8; i++) {
    2687:       PetscInt plexI = zToPlex[i];

    2689:       for (j = 0; j < dimC; j++) {
    2690:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2691:       }
    2692:     }
    2693:   } else {
    2694:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2695:   }
    2696:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2697:   for (i = 0; i < dimR; i++) {
    2698:     PetscReal *swap;

    2700:     for (j = 0; j < (numV / 2); j++) {
    2701:       for (k = 0; k < dimC; k++) {
    2702:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2703:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2704:       }
    2705:     }

    2707:     if (i < dimR - 1) {
    2708:       swap = cellCoeffs;
    2709:       cellCoeffs = cellCoords;
    2710:       cellCoords = swap;
    2711:     }
    2712:   }
    2713:   PetscArrayzero(refCoords,numPoints * dimR);
    2714:   for (j = 0; j < numPoints; j++) {
    2715:     for (i = 0; i < maxIts; i++) {
    2716:       PetscReal *guess = &refCoords[dimR * j];

    2718:       /* compute -residual and Jacobian */
    2719:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
    2720:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
    2721:       for (k = 0; k < numV; k++) {
    2722:         PetscReal extCoord = 1.;
    2723:         for (l = 0; l < dimR; l++) {
    2724:           PetscReal coord = guess[l];
    2725:           PetscInt  dep   = (k & (1 << l)) >> l;

    2727:           extCoord *= dep * coord + !dep;
    2728:           extJ[l] = dep;

    2730:           for (m = 0; m < dimR; m++) {
    2731:             PetscReal coord = guess[m];
    2732:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    2733:             PetscReal mult  = dep * coord + !dep;

    2735:             extJ[l] *= mult;
    2736:           }
    2737:         }
    2738:         for (l = 0; l < dimC; l++) {
    2739:           PetscReal coeff = cellCoeffs[dimC * k + l];

    2741:           resNeg[l] -= coeff * extCoord;
    2742:           for (m = 0; m < dimR; m++) {
    2743:             J[dimR * l + m] += coeff * extJ[m];
    2744:           }
    2745:         }
    2746:       }
    2747: #if 0 && defined(PETSC_USE_DEBUG)
    2748:       {
    2749:         PetscReal maxAbs = 0.;

    2751:         for (l = 0; l < dimC; l++) {
    2752:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2753:         }
    2754:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2755:       }
    2756: #endif

    2758:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
    2759:     }
    2760:   }
    2761:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2762:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2763:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2764:   return(0);
    2765: }

    2767: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2768: {
    2769:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
    2770:   PetscScalar    *coordsScalar = NULL;
    2771:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

    2776:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2777:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2778:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2779:   cellCoords = &cellData[0];
    2780:   cellCoeffs = &cellData[coordSize];
    2781:   if (dimR == 2) {
    2782:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2784:     for (i = 0; i < 4; i++) {
    2785:       PetscInt plexI = zToPlex[i];

    2787:       for (j = 0; j < dimC; j++) {
    2788:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2789:       }
    2790:     }
    2791:   } else if (dimR == 3) {
    2792:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2794:     for (i = 0; i < 8; i++) {
    2795:       PetscInt plexI = zToPlex[i];

    2797:       for (j = 0; j < dimC; j++) {
    2798:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2799:       }
    2800:     }
    2801:   } else {
    2802:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2803:   }
    2804:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2805:   for (i = 0; i < dimR; i++) {
    2806:     PetscReal *swap;

    2808:     for (j = 0; j < (numV / 2); j++) {
    2809:       for (k = 0; k < dimC; k++) {
    2810:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2811:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2812:       }
    2813:     }

    2815:     if (i < dimR - 1) {
    2816:       swap = cellCoeffs;
    2817:       cellCoeffs = cellCoords;
    2818:       cellCoords = swap;
    2819:     }
    2820:   }
    2821:   PetscArrayzero(realCoords,numPoints * dimC);
    2822:   for (j = 0; j < numPoints; j++) {
    2823:     const PetscReal *guess  = &refCoords[dimR * j];
    2824:     PetscReal       *mapped = &realCoords[dimC * j];

    2826:     for (k = 0; k < numV; k++) {
    2827:       PetscReal extCoord = 1.;
    2828:       for (l = 0; l < dimR; l++) {
    2829:         PetscReal coord = guess[l];
    2830:         PetscInt  dep   = (k & (1 << l)) >> l;

    2832:         extCoord *= dep * coord + !dep;
    2833:       }
    2834:       for (l = 0; l < dimC; l++) {
    2835:         PetscReal coeff = cellCoeffs[dimC * k + l];

    2837:         mapped[l] += coeff * extCoord;
    2838:       }
    2839:     }
    2840:   }
    2841:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2842:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2843:   return(0);
    2844: }

    2846: /* TODO: TOBY please fix this for Nc > 1 */
    2847: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2848: {
    2849:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
    2850:   PetscScalar    *nodes = NULL;
    2851:   PetscReal      *invV, *modes;
    2852:   PetscReal      *B, *D, *resNeg;
    2853:   PetscScalar    *J, *invJ, *work;

    2857:   PetscFEGetDimension(fe, &pdim);
    2858:   PetscFEGetNumComponents(fe, &numComp);
    2859:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2860:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2861:   /* convert nodes to values in the stable evaluation basis */
    2862:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2863:   invV = fe->invV;
    2864:   for (i = 0; i < pdim; ++i) {
    2865:     modes[i] = 0.;
    2866:     for (j = 0; j < pdim; ++j) {
    2867:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2868:     }
    2869:   }
    2870:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2871:   D      = &B[pdim*Nc];
    2872:   resNeg = &D[pdim*Nc * dimR];
    2873:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2874:   invJ = &J[Nc * dimR];
    2875:   work = &invJ[Nc * dimR];
    2876:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
    2877:   for (j = 0; j < numPoints; j++) {
    2878:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    2879:       PetscReal *guess = &refCoords[j * dimR];
    2880:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
    2881:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
    2882:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
    2883:       for (k = 0; k < pdim; k++) {
    2884:         for (l = 0; l < Nc; l++) {
    2885:           resNeg[l] -= modes[k] * B[k * Nc + l];
    2886:           for (m = 0; m < dimR; m++) {
    2887:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    2888:           }
    2889:         }
    2890:       }
    2891: #if 0 && defined(PETSC_USE_DEBUG)
    2892:       {
    2893:         PetscReal maxAbs = 0.;

    2895:         for (l = 0; l < Nc; l++) {
    2896:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2897:         }
    2898:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
    2899:       }
    2900: #endif
    2901:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
    2902:     }
    2903:   }
    2904:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2905:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2906:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    2907:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2908:   return(0);
    2909: }

    2911: /* TODO: TOBY please fix this for Nc > 1 */
    2912: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2913: {
    2914:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
    2915:   PetscScalar    *nodes = NULL;
    2916:   PetscReal      *invV, *modes;
    2917:   PetscReal      *B;

    2921:   PetscFEGetDimension(fe, &pdim);
    2922:   PetscFEGetNumComponents(fe, &numComp);
    2923:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2924:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2925:   /* convert nodes to values in the stable evaluation basis */
    2926:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2927:   invV = fe->invV;
    2928:   for (i = 0; i < pdim; ++i) {
    2929:     modes[i] = 0.;
    2930:     for (j = 0; j < pdim; ++j) {
    2931:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2932:     }
    2933:   }
    2934:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    2935:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
    2936:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
    2937:   for (j = 0; j < numPoints; j++) {
    2938:     PetscReal *mapped = &realCoords[j * Nc];

    2940:     for (k = 0; k < pdim; k++) {
    2941:       for (l = 0; l < Nc; l++) {
    2942:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    2943:       }
    2944:     }
    2945:   }
    2946:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    2947:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    2948:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2949:   return(0);
    2950: }

    2952: /*@
    2953:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
    2954:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
    2955:   extend uniquely outside the reference cell (e.g, most non-affine maps)

    2957:   Not collective

    2959:   Input Parameters:
    2960: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    2961:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    2962:                as a multilinear map for tensor-product elements
    2963: . cell       - the cell whose map is used.
    2964: . numPoints  - the number of points to locate
    2965: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    2967:   Output Parameters:
    2968: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    2970:   Level: intermediate

    2972: .seealso: DMPlexReferenceToCoordinates()
    2973: @*/
    2974: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    2975: {
    2976:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    2977:   DM             coordDM = NULL;
    2978:   Vec            coords;
    2979:   PetscFE        fe = NULL;

    2984:   DMGetDimension(dm,&dimR);
    2985:   DMGetCoordinateDim(dm,&dimC);
    2986:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    2987:   DMPlexGetDepth(dm,&depth);
    2988:   DMGetCoordinatesLocal(dm,&coords);
    2989:   DMGetCoordinateDM(dm,&coordDM);
    2990:   if (coordDM) {
    2991:     PetscInt coordFields;

    2993:     DMGetNumFields(coordDM,&coordFields);
    2994:     if (coordFields) {
    2995:       PetscClassId id;
    2996:       PetscObject  disc;

    2998:       DMGetField(coordDM,0,NULL,&disc);
    2999:       PetscObjectGetClassId(disc,&id);
    3000:       if (id == PETSCFE_CLASSID) {
    3001:         fe = (PetscFE) disc;
    3002:       }
    3003:     }
    3004:   }
    3005:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3006:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    3007:   if (!fe) { /* implicit discretization: affine or multilinear */
    3008:     PetscInt  coneSize;
    3009:     PetscBool isSimplex, isTensor;

    3011:     DMPlexGetConeSize(dm,cell,&coneSize);
    3012:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3013:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3014:     if (isSimplex) {
    3015:       PetscReal detJ, *v0, *J, *invJ;

    3017:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3018:       J    = &v0[dimC];
    3019:       invJ = &J[dimC * dimC];
    3020:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
    3021:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    3022:         const PetscReal x0[3] = {-1.,-1.,-1.};

    3024:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    3025:       }
    3026:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3027:     } else if (isTensor) {
    3028:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    3029:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3030:   } else {
    3031:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    3032:   }
    3033:   return(0);
    3034: }

    3036: /*@
    3037:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

    3039:   Not collective

    3041:   Input Parameters:
    3042: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    3043:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    3044:                as a multilinear map for tensor-product elements
    3045: . cell       - the cell whose map is used.
    3046: . numPoints  - the number of points to locate
    3047: - refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    3049:   Output Parameters:
    3050: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    3052:    Level: intermediate

    3054: .seealso: DMPlexCoordinatesToReference()
    3055: @*/
    3056: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    3057: {
    3058:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
    3059:   DM             coordDM = NULL;
    3060:   Vec            coords;
    3061:   PetscFE        fe = NULL;

    3066:   DMGetDimension(dm,&dimR);
    3067:   DMGetCoordinateDim(dm,&dimC);
    3068:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    3069:   DMPlexGetDepth(dm,&depth);
    3070:   DMGetCoordinatesLocal(dm,&coords);
    3071:   DMGetCoordinateDM(dm,&coordDM);
    3072:   if (coordDM) {
    3073:     PetscInt coordFields;

    3075:     DMGetNumFields(coordDM,&coordFields);
    3076:     if (coordFields) {
    3077:       PetscClassId id;
    3078:       PetscObject  disc;

    3080:       DMGetField(coordDM,0,NULL,&disc);
    3081:       PetscObjectGetClassId(disc,&id);
    3082:       if (id == PETSCFE_CLASSID) {
    3083:         fe = (PetscFE) disc;
    3084:       }
    3085:     }
    3086:   }
    3087:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
    3088:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    3089:   if (!fe) { /* implicit discretization: affine or multilinear */
    3090:     PetscInt  coneSize;
    3091:     PetscBool isSimplex, isTensor;

    3093:     DMPlexGetConeSize(dm,cell,&coneSize);
    3094:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3095:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3096:     if (isSimplex) {
    3097:       PetscReal detJ, *v0, *J;

    3099:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3100:       J    = &v0[dimC];
    3101:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
    3102:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3103:         const PetscReal xi0[3] = {-1.,-1.,-1.};

    3105:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3106:       }
    3107:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3108:     } else if (isTensor) {
    3109:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3110:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3111:   } else {
    3112:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3113:   }
    3114:   return(0);
    3115: }

    3117: /*@C
    3118:   DMPlexRemapGeometry - This function maps the original DM coordinates to new coordinates.

    3120:   Not collective

    3122:   Input Parameters:
    3123: + dm      - The DM
    3124: . time    - The time
    3125: - func    - The function transforming current coordinates to new coordaintes

    3127:    Calling sequence of func:
    3128: $    func(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3129: $         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3130: $         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3131: $         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]);

    3133: +  dim          - The spatial dimension
    3134: .  Nf           - The number of input fields (here 1)
    3135: .  NfAux        - The number of input auxiliary fields
    3136: .  uOff         - The offset of the coordinates in u[] (here 0)
    3137: .  uOff_x       - The offset of the coordinates in u_x[] (here 0)
    3138: .  u            - The coordinate values at this point in space
    3139: .  u_t          - The coordinate time derivative at this point in space (here NULL)
    3140: .  u_x          - The coordinate derivatives at this point in space
    3141: .  aOff         - The offset of each auxiliary field in u[]
    3142: .  aOff_x       - The offset of each auxiliary field in u_x[]
    3143: .  a            - The auxiliary field values at this point in space
    3144: .  a_t          - The auxiliary field time derivative at this point in space (or NULL)
    3145: .  a_x          - The auxiliary field derivatives at this point in space
    3146: .  t            - The current time
    3147: .  x            - The coordinates of this point (here not used)
    3148: .  numConstants - The number of constants
    3149: .  constants    - The value of each constant
    3150: -  f            - The new coordinates at this point in space

    3152:   Level: intermediate

    3154: .seealso: DMGetCoordinates(), DMGetCoordinatesLocal(), DMGetCoordinateDM(), DMProjectFieldLocal(), DMProjectFieldLabelLocal()
    3155: @*/
    3156: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time,
    3157:                                    void (*func)(PetscInt, PetscInt, PetscInt,
    3158:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3159:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
    3160:                                                 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))
    3161: {
    3162:   DM             cdm;
    3163:   DMField        cf;
    3164:   Vec            lCoords, tmpCoords;

    3168:   DMGetCoordinateDM(dm, &cdm);
    3169:   DMGetCoordinatesLocal(dm, &lCoords);
    3170:   DMGetLocalVector(cdm, &tmpCoords);
    3171:   VecCopy(lCoords, tmpCoords);
    3172:   /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
    3173:   DMGetCoordinateField(dm, &cf);
    3174:   cdm->coordinateField = cf;
    3175:   DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords);
    3176:   cdm->coordinateField = NULL;
    3177:   DMRestoreLocalVector(cdm, &tmpCoords);
    3178:   return(0);
    3179: }

    3181: /* Shear applies the transformation, assuming we fix z,
    3182:   / 1  0  m_0 \
    3183:   | 0  1  m_1 |
    3184:   \ 0  0   1  /
    3185: */
    3186: static void f0_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    3187:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    3188:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    3189:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
    3190: {
    3191:   const PetscInt Nc = uOff[1]-uOff[0];
    3192:   const PetscInt ax = (PetscInt) PetscRealPart(constants[0]);
    3193:   PetscInt       c;

    3195:   for (c = 0; c < Nc; ++c) {
    3196:     coords[c] = u[c] + constants[c+1]*u[ax];
    3197:   }
    3198: }

    3200: /*@C
    3201:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

    3203:   Not collective

    3205:   Input Parameters:
    3206: + dm          - The DM
    3207: . direction   - The shear coordinate direction, e.g. 0 is the x-axis
    3208: - multipliers - The multiplier m for each direction which is not the shear direction

    3210:   Level: intermediate

    3212: .seealso: DMPlexRemapGeometry()
    3213: @*/
    3214: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
    3215: {
    3216:   DM             cdm;
    3217:   PetscDS        cds;
    3218:   PetscObject    obj;
    3219:   PetscClassId   id;
    3220:   PetscScalar   *moduli;
    3221:   const PetscInt dir = (PetscInt) direction;
    3222:   PetscInt       dE, d, e;

    3226:   DMGetCoordinateDM(dm, &cdm);
    3227:   DMGetCoordinateDim(dm, &dE);
    3228:   PetscMalloc1(dE+1, &moduli);
    3229:   moduli[0] = dir;
    3230:   for (d = 0, e = 0; d < dE; ++d) moduli[d] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
    3231:   DMGetDS(cdm, &cds);
    3232:   PetscDSGetDiscretization(cds, 0, &obj);
    3233:   PetscObjectGetClassId(obj, &id);
    3234:   if (id != PETSCFE_CLASSID) {
    3235:     Vec           lCoords;
    3236:     PetscSection  cSection;
    3237:     PetscScalar  *coords;
    3238:     PetscInt      vStart, vEnd, v;

    3240:     DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    3241:     DMGetCoordinateSection(dm, &cSection);
    3242:     DMGetCoordinatesLocal(dm, &lCoords);
    3243:     VecGetArray(lCoords, &coords);
    3244:     for (v = vStart; v < vEnd; ++v) {
    3245:       PetscReal ds;
    3246:       PetscInt  off, c;

    3248:       PetscSectionGetOffset(cSection, v, &off);
    3249:       ds   = PetscRealPart(coords[off+dir]);
    3250:       for (c = 0; c < dE; ++c) coords[off+c] += moduli[c]*ds;
    3251:     }
    3252:     VecRestoreArray(lCoords, &coords);
    3253:   } else {
    3254:     PetscDSSetConstants(cds, dE+1, moduli);
    3255:     DMPlexRemapGeometry(dm, 0.0, f0_shear);
    3256:   }
    3257:   PetscFree(moduli);
    3258:   return(0);
    3259: }