Actual source code: plexgeometry.c
petsc-3.10.5 2019-03-28
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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: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
      7: {
      8:   const PetscReal p0_x  = segmentA[0*2+0];
      9:   const PetscReal p0_y  = segmentA[0*2+1];
     10:   const PetscReal p1_x  = segmentA[1*2+0];
     11:   const PetscReal p1_y  = segmentA[1*2+1];
     12:   const PetscReal p2_x  = segmentB[0*2+0];
     13:   const PetscReal p2_y  = segmentB[0*2+1];
     14:   const PetscReal p3_x  = segmentB[1*2+0];
     15:   const PetscReal p3_y  = segmentB[1*2+1];
     16:   const PetscReal s1_x  = p1_x - p0_x;
     17:   const PetscReal s1_y  = p1_y - p0_y;
     18:   const PetscReal s2_x  = p3_x - p2_x;
     19:   const PetscReal s2_y  = p3_y - p2_y;
     20:   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);

     23:   *hasIntersection = PETSC_FALSE;
     24:   /* Non-parallel lines */
     25:   if (denom != 0.0) {
     26:     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
     27:     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;

     29:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
     30:       *hasIntersection = PETSC_TRUE;
     31:       if (intersection) {
     32:         intersection[0] = p0_x + (t * s1_x);
     33:         intersection[1] = p0_y + (t * s1_y);
     34:       }
     35:     }
     36:   }
     37:   return(0);
     38: }

     40: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
     41: {
     42:   const PetscInt  embedDim = 2;
     43:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
     44:   PetscReal       x        = PetscRealPart(point[0]);
     45:   PetscReal       y        = PetscRealPart(point[1]);
     46:   PetscReal       v0[2], J[4], invJ[4], detJ;
     47:   PetscReal       xi, eta;
     48:   PetscErrorCode  ierr;

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

     55:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
     56:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
     57:   return(0);
     58: }

     60: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
     61: {
     62:   const PetscInt  embedDim = 2;
     63:   PetscReal       x        = PetscRealPart(point[0]);
     64:   PetscReal       y        = PetscRealPart(point[1]);
     65:   PetscReal       v0[2], J[4], invJ[4], detJ;
     66:   PetscReal       xi, eta, r;
     67:   PetscErrorCode  ierr;

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

     74:   xi  = PetscMax(xi,  0.0);
     75:   eta = PetscMax(eta, 0.0);
     76:   if (xi + eta > 2.0) {
     77:     r    = (xi + eta)/2.0;
     78:     xi  /= r;
     79:     eta /= r;
     80:   }
     81:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
     82:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
     83:   return(0);
     84: }

     86: static PetscErrorCode DMPlexLocatePoint_General_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
     87: {
     88:   PetscSection       coordSection;
     89:   Vec             coordsLocal;
     90:   PetscScalar    *coords = NULL;
     91:   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
     92:   PetscReal       x         = PetscRealPart(point[0]);
     93:   PetscReal       y         = PetscRealPart(point[1]);
     94:   PetscInt        crossings = 0, f;
     95:   PetscErrorCode  ierr;

     98:   DMGetCoordinatesLocal(dm, &coordsLocal);
     99:   DMGetCoordinateSection(dm, &coordSection);
    100:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    101:   for (f = 0; f < 4; ++f) {
    102:     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
    103:     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
    104:     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
    105:     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
    106:     PetscReal slope = (y_j - y_i) / (x_j - x_i);
    107:     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
    108:     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
    109:     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
    110:     if ((cond1 || cond2)  && above) ++crossings;
    111:   }
    112:   if (crossings % 2) *cell = c;
    113:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    114:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    115:   return(0);
    116: }

    118: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    119: {
    120:   const PetscInt embedDim = 3;
    121:   PetscReal      v0[3], J[9], invJ[9], detJ;
    122:   PetscReal      x = PetscRealPart(point[0]);
    123:   PetscReal      y = PetscRealPart(point[1]);
    124:   PetscReal      z = PetscRealPart(point[2]);
    125:   PetscReal      xi, eta, zeta;

    129:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
    130:   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
    131:   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
    132:   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);

    134:   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
    135:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    136:   return(0);
    137: }

    139: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
    140: {
    141:   PetscSection   coordSection;
    142:   Vec            coordsLocal;
    143:   PetscScalar   *coords = NULL;
    144:   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
    145:                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
    146:   PetscBool      found = PETSC_TRUE;
    147:   PetscInt       f;

    151:   DMGetCoordinatesLocal(dm, &coordsLocal);
    152:   DMGetCoordinateSection(dm, &coordSection);
    153:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    154:   for (f = 0; f < 6; ++f) {
    155:     /* Check the point is under plane */
    156:     /*   Get face normal */
    157:     PetscReal v_i[3];
    158:     PetscReal v_j[3];
    159:     PetscReal normal[3];
    160:     PetscReal pp[3];
    161:     PetscReal dot;

    163:     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
    164:     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
    165:     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
    166:     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
    167:     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
    168:     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
    169:     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
    170:     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
    171:     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
    172:     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
    173:     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
    174:     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
    175:     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];

    177:     /* Check that projected point is in face (2D location problem) */
    178:     if (dot < 0.0) {
    179:       found = PETSC_FALSE;
    180:       break;
    181:     }
    182:   }
    183:   if (found) *cell = c;
    184:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
    185:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
    186:   return(0);
    187: }

    189: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
    190: {
    191:   PetscInt d;

    194:   box->dim = dim;
    195:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
    196:   return(0);
    197: }

    199: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
    200: {

    204:   PetscMalloc1(1, box);
    205:   PetscGridHashInitialize_Internal(*box, dim, point);
    206:   return(0);
    207: }

    209: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
    210: {
    211:   PetscInt d;

    214:   for (d = 0; d < box->dim; ++d) {
    215:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
    216:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
    217:   }
    218:   return(0);
    219: }

    221: /*
    222:   PetscGridHashSetGrid - Divide the grid into boxes

    224:   Not collective

    226:   Input Parameters:
    227: + box - The grid hash object
    228: . n   - The number of boxes in each dimension, or PETSC_DETERMINE
    229: - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE

    231:   Level: developer

    233: .seealso: PetscGridHashCreate()
    234: */
    235: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
    236: {
    237:   PetscInt d;

    240:   for (d = 0; d < box->dim; ++d) {
    241:     box->extent[d] = box->upper[d] - box->lower[d];
    242:     if (n[d] == PETSC_DETERMINE) {
    243:       box->h[d] = h[d];
    244:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
    245:     } else {
    246:       box->n[d] = n[d];
    247:       box->h[d] = box->extent[d]/n[d];
    248:     }
    249:   }
    250:   return(0);
    251: }

    253: /*
    254:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

    256:   Not collective

    258:   Input Parameters:
    259: + box       - The grid hash object
    260: . numPoints - The number of input points
    261: - points    - The input point coordinates

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

    267:   Level: developer

    269: .seealso: PetscGridHashCreate()
    270: */
    271: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
    272: {
    273:   const PetscReal *lower = box->lower;
    274:   const PetscReal *upper = box->upper;
    275:   const PetscReal *h     = box->h;
    276:   const PetscInt  *n     = box->n;
    277:   const PetscInt   dim   = box->dim;
    278:   PetscInt         d, p;

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

    285:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    286:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
    287:       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",
    288:                                              p, PetscRealPart(points[p*dim+0]), dim > 1 ? PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? PetscRealPart(points[p*dim+2]) : 0.0);
    289:       dboxes[p*dim+d] = dbox;
    290:     }
    291:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
    292:   }
    293:   return(0);
    294: }

    296: /*
    297:  PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point
    298:
    299:  Not collective
    300:
    301:   Input Parameters:
    302: + box       - The grid hash object
    303: . numPoints - The number of input points
    304: - points    - The input point coordinates
    305:
    306:   Output Parameters:
    307: + dboxes    - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
    308: . boxes     - An array of numPoints integers expressing the enclosing box as single number, or NULL
    309: - found     - Flag indicating if point was located within a box
    310:
    311:   Level: developer
    312:
    313: .seealso: PetscGridHashGetEnclosingBox()
    314: */
    315: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[],PetscBool *found)
    316: {
    317:   const PetscReal *lower = box->lower;
    318:   const PetscReal *upper = box->upper;
    319:   const PetscReal *h     = box->h;
    320:   const PetscInt  *n     = box->n;
    321:   const PetscInt   dim   = box->dim;
    322:   PetscInt         d, p;
    323:
    325:   *found = PETSC_FALSE;
    326:   for (p = 0; p < numPoints; ++p) {
    327:     for (d = 0; d < dim; ++d) {
    328:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);
    329:
    330:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
    331:       if (dbox < 0 || dbox >= n[d]) {
    332:         return(0);
    333:       }
    334:       dboxes[p*dim+d] = dbox;
    335:     }
    336:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
    337:   }
    338:   *found = PETSC_TRUE;
    339:   return(0);
    340: }

    342: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
    343: {

    347:   if (*box) {
    348:     PetscSectionDestroy(&(*box)->cellSection);
    349:     ISDestroy(&(*box)->cells);
    350:     DMLabelDestroy(&(*box)->cellsSparse);
    351:   }
    352:   PetscFree(*box);
    353:   return(0);
    354: }

    356: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
    357: {
    358:   PetscInt       coneSize;

    362:   switch (dim) {
    363:   case 2:
    364:     DMPlexGetConeSize(dm, cellStart, &coneSize);
    365:     switch (coneSize) {
    366:     case 3:
    367:       DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);
    368:       break;
    369:     case 4:
    370:       DMPlexLocatePoint_General_2D_Internal(dm, point, cellStart, cell);
    371:       break;
    372:     default:
    373:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
    374:     }
    375:     break;
    376:   case 3:
    377:     DMPlexGetConeSize(dm, cellStart, &coneSize);
    378:     switch (coneSize) {
    379:     case 4:
    380:       DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);
    381:       break;
    382:     case 6:
    383:       DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);
    384:       break;
    385:     default:
    386:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
    387:     }
    388:     break;
    389:   default:
    390:     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %D", dim);
    391:   }
    392:   return(0);
    393: }

    395: /*
    396:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
    397: */
    398: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
    399: {
    400:   PetscInt       coneSize;

    404:   switch (dim) {
    405:   case 2:
    406:     DMPlexGetConeSize(dm, cell, &coneSize);
    407:     switch (coneSize) {
    408:     case 3:
    409:       DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);
    410:       break;
    411: #if 0
    412:     case 4:
    413:       DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);
    414:       break;
    415: #endif
    416:     default:
    417:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell with cone size %D", coneSize);
    418:     }
    419:     break;
    420: #if 0
    421:   case 3:
    422:     DMPlexGetConeSize(dm, cell, &coneSize);
    423:     switch (coneSize) {
    424:     case 4:
    425:       DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);
    426:       break;
    427:     case 6:
    428:       DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);
    429:       break;
    430:     default:
    431:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell with cone size %D", coneSize);
    432:     }
    433:     break;
    434: #endif
    435:   default:
    436:     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for mesh dimension %D", dim);
    437:   }
    438:   return(0);
    439: }

    441: /*
    442:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex

    444:   Collective on DM

    446:   Input Parameter:
    447: . dm - The Plex

    449:   Output Parameter:
    450: . localBox - The grid hash object

    452:   Level: developer

    454: .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
    455: */
    456: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
    457: {
    458:   MPI_Comm           comm;
    459:   PetscGridHash      lbox;
    460:   Vec                coordinates;
    461:   PetscSection       coordSection;
    462:   Vec                coordsLocal;
    463:   const PetscScalar *coords;
    464:   PetscInt          *dboxes, *boxes;
    465:   PetscInt           n[3] = {10, 10, 10};
    466:   PetscInt           dim, N, cStart, cEnd, cMax, c, i;
    467:   PetscErrorCode     ierr;

    470:   PetscObjectGetComm((PetscObject) dm, &comm);
    471:   DMGetCoordinatesLocal(dm, &coordinates);
    472:   DMGetCoordinateDim(dm, &dim);
    473:   if (dim != 2) SETERRQ(comm, PETSC_ERR_SUP, "I have only coded this for 2D");
    474:   VecGetLocalSize(coordinates, &N);
    475:   VecGetArrayRead(coordinates, &coords);
    476:   PetscGridHashCreate(comm, dim, coords, &lbox);
    477:   for (i = 0; i < N; i += dim) {PetscGridHashEnlarge(lbox, &coords[i]);}
    478:   VecRestoreArrayRead(coordinates, &coords);
    479:   PetscOptionsGetInt(NULL,NULL,"-dm_plex_hash_box_nijk",&n[0],NULL);
    480:   n[1] = n[0];
    481:   n[2] = n[0];
    482:   PetscGridHashSetGrid(lbox, n, NULL);
    483: #if 0
    484:   /* Could define a custom reduction to merge these */
    485:   MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);
    486:   MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);
    487: #endif
    488:   /* Is there a reason to snap the local bounding box to a division of the global box? */
    489:   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
    490:   /* Create label */
    491:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    492:   DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);
    493:   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
    494:   DMLabelCreate("cells", &lbox->cellsSparse);
    495:   DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);
    496:   /* Compute boxes which overlap each cell: http://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
    497:   DMGetCoordinatesLocal(dm, &coordsLocal);
    498:   DMGetCoordinateSection(dm, &coordSection);
    499:   PetscCalloc2(16 * dim, &dboxes, 16, &boxes);
    500:   for (c = cStart; c < cEnd; ++c) {
    501:     const PetscReal *h       = lbox->h;
    502:     PetscScalar     *ccoords = NULL;
    503:     PetscInt         csize   = 0;
    504:     PetscScalar      point[3];
    505:     PetscInt         dlim[6], d, e, i, j, k;

    507:     /* Find boxes enclosing each vertex */
    508:     DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);
    509:     PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);
    510:     /* Mark cells containing the vertices */
    511:     for (e = 0; e < csize/dim; ++e) {DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);}
    512:     /* Get grid of boxes containing these */
    513:     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
    514:     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
    515:     for (e = 1; e < dim+1; ++e) {
    516:       for (d = 0; d < dim; ++d) {
    517:         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
    518:         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
    519:       }
    520:     }
    521:     /* Check for intersection of box with cell */
    522:     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
    523:       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
    524:         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
    525:           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
    526:           PetscScalar    cpoint[3];
    527:           PetscInt       cell, edge, ii, jj, kk;

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

    534:                 DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);
    535:                 if (cell >= 0) {DMLabelSetValue(lbox->cellsSparse, c, box); ii = jj = kk = 2;}
    536:               }
    537:             }
    538:           }
    539:           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
    540:           for (edge = 0; edge < dim+1; ++edge) {
    541:             PetscReal segA[6], segB[6];

    543:             if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected dim %d > 3",dim);
    544:             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
    545:             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
    546:               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
    547:                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
    548:               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
    549:                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
    550:                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
    551:                 for (ii = 0; ii < 2; ++ii) {
    552:                   PetscBool intersects;

    554:                   segB[0]     = PetscRealPart(point[0]);
    555:                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
    556:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
    557:                   if (intersects) {DMLabelSetValue(lbox->cellsSparse, c, box); edge = ii = jj = kk = dim+1;}
    558:                 }
    559:               }
    560:             }
    561:           }
    562:         }
    563:       }
    564:     }
    565:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
    566:   }
    567:   PetscFree2(dboxes, boxes);
    568:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
    569:   DMLabelDestroy(&lbox->cellsSparse);
    570:   *localBox = lbox;
    571:   return(0);
    572: }

    574: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
    575: {
    576:   DM_Plex        *mesh = (DM_Plex *) dm->data;
    577:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
    578:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
    579:   PetscInt        dim, cStart, cEnd, cMax, numCells, c, d;
    580:   const PetscInt *boxCells;
    581:   PetscSFNode    *cells;
    582:   PetscScalar    *a;
    583:   PetscMPIInt     result;
    584:   PetscLogDouble  t0,t1;
    585:   PetscReal       gmin[3],gmax[3];
    586:   PetscInt        terminating_query_type[] = { 0, 0, 0 };
    587:   PetscErrorCode  ierr;

    590:   PetscTime(&t0);
    591:   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.");
    592:   DMGetCoordinateDim(dm, &dim);
    593:   VecGetBlockSize(v, &bs);
    594:   MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);
    595:   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
    596:   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);
    597:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    598:   DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);
    599:   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
    600:   VecGetLocalSize(v, &numPoints);
    601:   VecGetArray(v, &a);
    602:   numPoints /= bs;
    603:   {
    604:     const PetscSFNode *sf_cells;
    605:
    606:     PetscSFGetGraph(cellSF,NULL,NULL,NULL,&sf_cells);
    607:     if (sf_cells) {
    608:       PetscInfo(dm,"[DMLocatePoints_Plex] Re-using existing StarForest node list\n");
    609:       cells = (PetscSFNode*)sf_cells;
    610:       reuse = PETSC_TRUE;
    611:     } else {
    612:       PetscInfo(dm,"[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n");
    613:       PetscMalloc1(numPoints, &cells);
    614:       /* initialize cells if created */
    615:       for (p=0; p<numPoints; p++) {
    616:         cells[p].rank  = 0;
    617:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    618:       }
    619:     }
    620:   }
    621:   /* define domain bounding box */
    622:   {
    623:     Vec coorglobal;
    624:
    625:     DMGetCoordinates(dm,&coorglobal);
    626:     VecStrideMaxAll(coorglobal,NULL,gmax);
    627:     VecStrideMinAll(coorglobal,NULL,gmin);
    628:   }
    629:   if (hash) {
    630:     if (!mesh->lbox) {PetscInfo(dm, "Initializing grid hashing");DMPlexComputeGridHash_Internal(dm, &mesh->lbox);}
    631:     /* Designate the local box for each point */
    632:     /* Send points to correct process */
    633:     /* Search cells that lie in each subbox */
    634:     /*   Should we bin points before doing search? */
    635:     ISGetIndices(mesh->lbox->cells, &boxCells);
    636:   }
    637:   for (p = 0, numFound = 0; p < numPoints; ++p) {
    638:     const PetscScalar *point = &a[p*bs];
    639:     PetscInt           dbin[3] = {-1,-1,-1}, bin, cell = -1, cellOffset;
    640:     PetscBool          point_outside_domain = PETSC_FALSE;

    642:     /* check bounding box of domain */
    643:     for (d=0; d<dim; d++) {
    644:       if (PetscRealPart(point[d]) < gmin[d]) { point_outside_domain = PETSC_TRUE; break; }
    645:       if (PetscRealPart(point[d]) > gmax[d]) { point_outside_domain = PETSC_TRUE; break; }
    646:     }
    647:     if (point_outside_domain) {
    648:       cells[p].rank = 0;
    649:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    650:       terminating_query_type[0]++;
    651:       continue;
    652:     }
    653:
    654:     /* check initial values in cells[].index - abort early if found */
    655:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    656:       c = cells[p].index;
    657:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
    658:       DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    659:       if (cell >= 0) {
    660:         cells[p].rank = 0;
    661:         cells[p].index = cell;
    662:         numFound++;
    663:       }
    664:     }
    665:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
    666:       terminating_query_type[1]++;
    667:       continue;
    668:     }
    669:
    670:     if (hash) {
    671:       PetscBool found_box;
    672:
    673:       /* allow for case that point is outside box - abort early */
    674:       PetscGridHashGetEnclosingBoxQuery(mesh->lbox, 1, point, dbin, &bin,&found_box);
    675:       if (found_box) {
    676:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
    677:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    678:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    679:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    680:           DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);
    681:           if (cell >= 0) {
    682:             cells[p].rank = 0;
    683:             cells[p].index = cell;
    684:             numFound++;
    685:             terminating_query_type[2]++;
    686:             break;
    687:           }
    688:         }
    689:       }
    690:     } else {
    691:       for (c = cStart; c < cEnd; ++c) {
    692:         DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
    693:         if (cell >= 0) {
    694:           cells[p].rank = 0;
    695:           cells[p].index = cell;
    696:           numFound++;
    697:           terminating_query_type[2]++;
    698:           break;
    699:         }
    700:       }
    701:     }
    702:   }
    703:   if (hash) {ISRestoreIndices(mesh->lbox->cells, &boxCells);}
    704:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
    705:     for (p = 0; p < numPoints; p++) {
    706:       const PetscScalar *point = &a[p*bs];
    707:       PetscReal          cpoint[3], diff[3], dist, distMax = PETSC_MAX_REAL;
    708:       PetscInt           dbin[3] = {-1,-1,-1}, bin, cellOffset, d;

    710:       if (cells[p].index < 0) {
    711:         ++numFound;
    712:         PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);
    713:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
    714:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
    715:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
    716:           DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);
    717:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
    718:           dist = DMPlex_NormD_Internal(dim, diff);
    719:           if (dist < distMax) {
    720:             for (d = 0; d < dim; ++d) a[p*bs+d] = cpoint[d];
    721:             cells[p].rank  = 0;
    722:             cells[p].index = boxCells[c];
    723:             distMax = dist;
    724:             break;
    725:           }
    726:         }
    727:       }
    728:     }
    729:   }
    730:   /* This code is only be relevant when interfaced to parallel point location */
    731:   /* Check for highest numbered proc that claims a point (do we care?) */
    732:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
    733:     PetscMalloc1(numFound,&found);
    734:     for (p = 0, numFound = 0; p < numPoints; p++) {
    735:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
    736:         if (numFound < p) {
    737:           cells[numFound] = cells[p];
    738:         }
    739:         found[numFound++] = p;
    740:       }
    741:     }
    742:   }
    743:   VecRestoreArray(v, &a);
    744:   if (!reuse) {
    745:     PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);
    746:   }
    747:   PetscTime(&t1);
    748:   if (hash) {
    749:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside intial cell] : %D [hash]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
    750:   } else {
    751:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside intial cell] : %D [brute-force]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
    752:   }
    753:   PetscInfo3(dm,"[DMLocatePoints_Plex] npoints %D : time(rank0) %1.2e (sec): points/sec %1.4e\n",numPoints,t1-t0,(double)((double)numPoints/(t1-t0)));
    754:   return(0);
    755: }

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

    760:   Not collective

    762:   Input Parameter:
    763: . coords - The coordinates of a segment

    765:   Output Parameters:
    766: + coords - The new y-coordinate, and 0 for x
    767: - R - The rotation which accomplishes the projection

    769:   Level: developer

    771: .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
    772: @*/
    773: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
    774: {
    775:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
    776:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
    777:   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;

    780:   R[0] = c; R[1] = -s;
    781:   R[2] = s; R[3] =  c;
    782:   coords[0] = 0.0;
    783:   coords[1] = r;
    784:   return(0);
    785: }

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

    790:   Not collective

    792:   Input Parameter:
    793: . coords - The coordinates of a segment

    795:   Output Parameters:
    796: + coords - The new y-coordinate, and 0 for x and z
    797: - R - The rotation which accomplishes the projection

    799:   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

    801:   Level: developer

    803: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
    804: @*/
    805: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
    806: {
    807:   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
    808:   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
    809:   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
    810:   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
    811:   PetscReal      rinv = 1. / r;

    814:   x *= rinv; y *= rinv; z *= rinv;
    815:   if (x > 0.) {
    816:     PetscReal inv1pX   = 1./ (1. + x);

    818:     R[0] = x; R[1] = -y;              R[2] = -z;
    819:     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
    820:     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
    821:   }
    822:   else {
    823:     PetscReal inv1mX   = 1./ (1. - x);

    825:     R[0] = x; R[1] = z;               R[2] = y;
    826:     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
    827:     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
    828:   }
    829:   coords[0] = 0.0;
    830:   coords[1] = r;
    831:   return(0);
    832: }

    834: /*@
    835:   DMPlexComputeProjection3Dto2D - Rewrite coordinates to be the 2D projection of the 3D coordinates

    837:   Not collective

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

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

    846:   Level: developer

    848: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
    849: @*/
    850: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
    851: {
    852:   PetscReal      x1[3],  x2[3], n[3], norm;
    853:   PetscReal      x1p[3], x2p[3], xnp[3];
    854:   PetscReal      sqrtz, alpha;
    855:   const PetscInt dim = 3;
    856:   PetscInt       d, e, p;

    859:   /* 0) Calculate normal vector */
    860:   for (d = 0; d < dim; ++d) {
    861:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
    862:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
    863:   }
    864:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
    865:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
    866:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
    867:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
    868:   n[0] /= norm;
    869:   n[1] /= norm;
    870:   n[2] /= norm;
    871:   /* 1) Take the normal vector and rotate until it is \hat z

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

    875:     R = /  alpha nx nz  alpha ny nz -1/alpha \
    876:         | -alpha ny     alpha nx        0    |
    877:         \     nx            ny         nz    /

    879:     will rotate the normal vector to \hat z
    880:   */
    881:   sqrtz = PetscSqrtReal(1.0 - n[2]*n[2]);
    882:   /* Check for n = z */
    883:   if (sqrtz < 1.0e-10) {
    884:     const PetscInt s = PetscSign(n[2]);
    885:     /* If nz < 0, rotate 180 degrees around x-axis */
    886:     for (p = 3; p < coordSize/3; ++p) {
    887:       coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
    888:       coords[p*2+1] = (PetscRealPart(coords[p*dim+1] - coords[0*dim+1])) * s;
    889:     }
    890:     coords[0] = 0.0;
    891:     coords[1] = 0.0;
    892:     coords[2] = x1[0];
    893:     coords[3] = x1[1] * s;
    894:     coords[4] = x2[0];
    895:     coords[5] = x2[1] * s;
    896:     R[0] = 1.0;     R[1] = 0.0;     R[2] = 0.0;
    897:     R[3] = 0.0;     R[4] = 1.0 * s; R[5] = 0.0;
    898:     R[6] = 0.0;     R[7] = 0.0;     R[8] = 1.0 * s;
    899:     return(0);
    900:   }
    901:   alpha = 1.0/sqrtz;
    902:   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
    903:   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
    904:   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
    905:   for (d = 0; d < dim; ++d) {
    906:     x1p[d] = 0.0;
    907:     x2p[d] = 0.0;
    908:     for (e = 0; e < dim; ++e) {
    909:       x1p[d] += R[d*dim+e]*x1[e];
    910:       x2p[d] += R[d*dim+e]*x2[e];
    911:     }
    912:   }
    913:   if (PetscAbsReal(x1p[2]) > 10. * PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
    914:   if (PetscAbsReal(x2p[2]) > 10. * PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
    915:   /* 2) Project to (x, y) */
    916:   for (p = 3; p < coordSize/3; ++p) {
    917:     for (d = 0; d < dim; ++d) {
    918:       xnp[d] = 0.0;
    919:       for (e = 0; e < dim; ++e) {
    920:         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
    921:       }
    922:       if (d < dim-1) coords[p*2+d] = xnp[d];
    923:     }
    924:   }
    925:   coords[0] = 0.0;
    926:   coords[1] = 0.0;
    927:   coords[2] = x1p[0];
    928:   coords[3] = x1p[1];
    929:   coords[4] = x2p[0];
    930:   coords[5] = x2p[1];
    931:   /* Output R^T which rotates \hat z to the input normal */
    932:   for (d = 0; d < dim; ++d) {
    933:     for (e = d+1; e < dim; ++e) {
    934:       PetscReal tmp;

    936:       tmp        = R[d*dim+e];
    937:       R[d*dim+e] = R[e*dim+d];
    938:       R[e*dim+d] = tmp;
    939:     }
    940:   }
    941:   return(0);
    942: }

    944: PETSC_UNUSED
    945: PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
    946: {
    947:   /* Signed volume is 1/2 the determinant

    949:    |  1  1  1 |
    950:    | x0 x1 x2 |
    951:    | y0 y1 y2 |

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

    955:    | x1 x2 |
    956:    | y1 y2 |
    957:   */
    958:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
    959:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
    960:   PetscReal       M[4], detM;
    961:   M[0] = x1; M[1] = x2;
    962:   M[2] = y1; M[3] = y2;
    963:   DMPlex_Det2D_Internal(&detM, M);
    964:   *vol = 0.5*detM;
    965:   (void)PetscLogFlops(5.0);
    966: }

    968: PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
    969: {
    970:   DMPlex_Det2D_Internal(vol, coords);
    971:   *vol *= 0.5;
    972: }

    974: PETSC_UNUSED
    975: PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
    976: {
    977:   /* Signed volume is 1/6th of the determinant

    979:    |  1  1  1  1 |
    980:    | x0 x1 x2 x3 |
    981:    | y0 y1 y2 y3 |
    982:    | z0 z1 z2 z3 |

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

    986:    | x1 x2 x3 |
    987:    | y1 y2 y3 |
    988:    | z1 z2 z3 |
    989:   */
    990:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
    991:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
    992:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
    993:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    994:   PetscReal       M[9], detM;
    995:   M[0] = x1; M[1] = x2; M[2] = x3;
    996:   M[3] = y1; M[4] = y2; M[5] = y3;
    997:   M[6] = z1; M[7] = z2; M[8] = z3;
    998:   DMPlex_Det3D_Internal(&detM, M);
    999:   *vol = -onesixth*detM;
    1000:   (void)PetscLogFlops(10.0);
    1001: }

    1003: PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
    1004: {
    1005:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
    1006:   DMPlex_Det3D_Internal(vol, coords);
    1007:   *vol *= -onesixth;
    1008: }

    1010: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1011: {
    1012:   PetscSection   coordSection;
    1013:   Vec            coordinates;
    1014:   const PetscScalar *coords;
    1015:   PetscInt       dim, d, off;

    1019:   DMGetCoordinatesLocal(dm, &coordinates);
    1020:   DMGetCoordinateSection(dm, &coordSection);
    1021:   PetscSectionGetDof(coordSection,e,&dim);
    1022:   if (!dim) return(0);
    1023:   PetscSectionGetOffset(coordSection,e,&off);
    1024:   VecGetArrayRead(coordinates,&coords);
    1025:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
    1026:   VecRestoreArrayRead(coordinates,&coords);
    1027:   *detJ = 1.;
    1028:   if (J) {
    1029:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
    1030:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
    1031:     if (invJ) {
    1032:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
    1033:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
    1034:     }
    1035:   }
    1036:   return(0);
    1037: }

    1039: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1040: {
    1041:   PetscSection   coordSection;
    1042:   Vec            coordinates;
    1043:   PetscScalar   *coords = NULL;
    1044:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

    1048:   DMGetCoordinatesLocal(dm, &coordinates);
    1049:   DMGetCoordinateSection(dm, &coordSection);
    1050:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1051:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1052:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1053:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1054:   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
    1055:   *detJ = 0.0;
    1056:   if (numCoords == 6) {
    1057:     const PetscInt dim = 3;
    1058:     PetscReal      R[9], J0;

    1060:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1061:     DMPlexComputeProjection3Dto1D(coords, R);
    1062:     if (J)    {
    1063:       J0   = 0.5*PetscRealPart(coords[1]);
    1064:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
    1065:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
    1066:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
    1067:       DMPlex_Det3D_Internal(detJ, J);
    1068:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1069:     }
    1070:   } else if (numCoords == 4) {
    1071:     const PetscInt dim = 2;
    1072:     PetscReal      R[4], J0;

    1074:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1075:     DMPlexComputeProjection2Dto1D(coords, R);
    1076:     if (J)    {
    1077:       J0   = 0.5*PetscRealPart(coords[1]);
    1078:       J[0] = R[0]*J0; J[1] = R[1];
    1079:       J[2] = R[2]*J0; J[3] = R[3];
    1080:       DMPlex_Det2D_Internal(detJ, J);
    1081:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1082:     }
    1083:   } else if (numCoords == 2) {
    1084:     const PetscInt dim = 1;

    1086:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1087:     if (J)    {
    1088:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
    1089:       *detJ = J[0];
    1090:       PetscLogFlops(2.0);
    1091:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
    1092:     }
    1093:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
    1094:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1095:   return(0);
    1096: }

    1098: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1099: {
    1100:   PetscSection   coordSection;
    1101:   Vec            coordinates;
    1102:   PetscScalar   *coords = NULL;
    1103:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1107:   DMGetCoordinatesLocal(dm, &coordinates);
    1108:   DMGetCoordinateSection(dm, &coordSection);
    1109:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1110:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1111:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1112:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1113:   *detJ = 0.0;
    1114:   if (numCoords == 9) {
    1115:     const PetscInt dim = 3;
    1116:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1118:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1119:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1120:     if (J)    {
    1121:       const PetscInt pdim = 2;

    1123:       for (d = 0; d < pdim; d++) {
    1124:         for (f = 0; f < pdim; f++) {
    1125:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1126:         }
    1127:       }
    1128:       PetscLogFlops(8.0);
    1129:       DMPlex_Det3D_Internal(detJ, J0);
    1130:       for (d = 0; d < dim; d++) {
    1131:         for (f = 0; f < dim; f++) {
    1132:           J[d*dim+f] = 0.0;
    1133:           for (g = 0; g < dim; g++) {
    1134:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1135:           }
    1136:         }
    1137:       }
    1138:       PetscLogFlops(18.0);
    1139:     }
    1140:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1141:   } else if (numCoords == 6) {
    1142:     const PetscInt dim = 2;

    1144:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1145:     if (J)    {
    1146:       for (d = 0; d < dim; d++) {
    1147:         for (f = 0; f < dim; f++) {
    1148:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1149:         }
    1150:       }
    1151:       PetscLogFlops(8.0);
    1152:       DMPlex_Det2D_Internal(detJ, J);
    1153:     }
    1154:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1155:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
    1156:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1157:   return(0);
    1158: }

    1160: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1161: {
    1162:   PetscSection   coordSection;
    1163:   Vec            coordinates;
    1164:   PetscScalar   *coords = NULL;
    1165:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

    1169:   DMGetCoordinatesLocal(dm, &coordinates);
    1170:   DMGetCoordinateSection(dm, &coordSection);
    1171:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
    1172:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
    1173:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1174:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
    1175:   if (!Nq) {
    1176:     *detJ = 0.0;
    1177:     if (numCoords == 12) {
    1178:       const PetscInt dim = 3;
    1179:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

    1181:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1182:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
    1183:       if (J)    {
    1184:         const PetscInt pdim = 2;

    1186:         for (d = 0; d < pdim; d++) {
    1187:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[1*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1188:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[3*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
    1189:         }
    1190:         PetscLogFlops(8.0);
    1191:         DMPlex_Det3D_Internal(detJ, J0);
    1192:         for (d = 0; d < dim; d++) {
    1193:           for (f = 0; f < dim; f++) {
    1194:             J[d*dim+f] = 0.0;
    1195:             for (g = 0; g < dim; g++) {
    1196:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
    1197:             }
    1198:           }
    1199:         }
    1200:         PetscLogFlops(18.0);
    1201:       }
    1202:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1203:     } else if (numCoords == 8) {
    1204:       const PetscInt dim = 2;

    1206:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1207:       if (J)    {
    1208:         for (d = 0; d < dim; d++) {
    1209:           J[d*dim+0] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1210:           J[d*dim+1] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1211:         }
    1212:         PetscLogFlops(8.0);
    1213:         DMPlex_Det2D_Internal(detJ, J);
    1214:       }
    1215:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
    1216:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1217:   } else {
    1218:     const PetscInt Nv = 4;
    1219:     const PetscInt dimR = 2;
    1220:     const PetscInt zToPlex[4] = {0, 1, 3, 2};
    1221:     PetscReal zOrder[12];
    1222:     PetscReal zCoeff[12];
    1223:     PetscInt  i, j, k, l, dim;

    1225:     if (numCoords == 12) {
    1226:       dim = 3;
    1227:     } else if (numCoords == 8) {
    1228:       dim = 2;
    1229:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
    1230:     for (i = 0; i < Nv; i++) {
    1231:       PetscInt zi = zToPlex[i];

    1233:       for (j = 0; j < dim; j++) {
    1234:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1235:       }
    1236:     }
    1237:     for (j = 0; j < dim; j++) {
    1238:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1239:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1240:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1241:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
    1242:     }
    1243:     for (i = 0; i < Nq; i++) {
    1244:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

    1246:       if (v) {
    1247:         PetscReal extPoint[4];

    1249:         extPoint[0] = 1.;
    1250:         extPoint[1] = xi;
    1251:         extPoint[2] = eta;
    1252:         extPoint[3] = xi * eta;
    1253:         for (j = 0; j < dim; j++) {
    1254:           PetscReal val = 0.;

    1256:           for (k = 0; k < Nv; k++) {
    1257:             val += extPoint[k] * zCoeff[dim * k + j];
    1258:           }
    1259:           v[i * dim + j] = val;
    1260:         }
    1261:       }
    1262:       if (J) {
    1263:         PetscReal extJ[8];

    1265:         extJ[0] = 0.;
    1266:         extJ[1] = 0.;
    1267:         extJ[2] = 1.;
    1268:         extJ[3] = 0.;
    1269:         extJ[4] = 0.;
    1270:         extJ[5] = 1.;
    1271:         extJ[6] = eta;
    1272:         extJ[7] = xi;
    1273:         for (j = 0; j < dim; j++) {
    1274:           for (k = 0; k < dimR; k++) {
    1275:             PetscReal val = 0.;

    1277:             for (l = 0; l < Nv; l++) {
    1278:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1279:             }
    1280:             J[i * dim * dim + dim * j + k] = val;
    1281:           }
    1282:         }
    1283:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
    1284:           PetscReal x, y, z;
    1285:           PetscReal *iJ = &J[i * dim * dim];
    1286:           PetscReal norm;

    1288:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
    1289:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
    1290:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
    1291:           norm = PetscSqrtReal(x * x + y * y + z * z);
    1292:           iJ[2] = x / norm;
    1293:           iJ[5] = y / norm;
    1294:           iJ[8] = z / norm;
    1295:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1296:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1297:         } else {
    1298:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
    1299:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1300:         }
    1301:       }
    1302:     }
    1303:   }
    1304:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
    1305:   return(0);
    1306: }

    1308: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1309: {
    1310:   PetscSection   coordSection;
    1311:   Vec            coordinates;
    1312:   PetscScalar   *coords = NULL;
    1313:   const PetscInt dim = 3;
    1314:   PetscInt       d;

    1318:   DMGetCoordinatesLocal(dm, &coordinates);
    1319:   DMGetCoordinateSection(dm, &coordSection);
    1320:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1321:   *detJ = 0.0;
    1322:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
    1323:   if (J)    {
    1324:     for (d = 0; d < dim; d++) {
    1325:       /* I orient with outward face normals */
    1326:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1327:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1328:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1329:     }
    1330:     PetscLogFlops(18.0);
    1331:     DMPlex_Det3D_Internal(detJ, J);
    1332:   }
    1333:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1334:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1335:   return(0);
    1336: }

    1338: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1339: {
    1340:   PetscSection   coordSection;
    1341:   Vec            coordinates;
    1342:   PetscScalar   *coords = NULL;
    1343:   const PetscInt dim = 3;
    1344:   PetscInt       d;

    1348:   DMGetCoordinatesLocal(dm, &coordinates);
    1349:   DMGetCoordinateSection(dm, &coordSection);
    1350:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1351:   if (!Nq) {
    1352:     *detJ = 0.0;
    1353:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
    1354:     if (J)    {
    1355:       for (d = 0; d < dim; d++) {
    1356:         J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1357:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1358:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
    1359:       }
    1360:       PetscLogFlops(18.0);
    1361:       DMPlex_Det3D_Internal(detJ, J);
    1362:     }
    1363:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
    1364:   } else {
    1365:     const PetscInt Nv = 8;
    1366:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
    1367:     const PetscInt dim = 3;
    1368:     const PetscInt dimR = 3;
    1369:     PetscReal zOrder[24];
    1370:     PetscReal zCoeff[24];
    1371:     PetscInt  i, j, k, l;

    1373:     for (i = 0; i < Nv; i++) {
    1374:       PetscInt zi = zToPlex[i];

    1376:       for (j = 0; j < dim; j++) {
    1377:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
    1378:       }
    1379:     }
    1380:     for (j = 0; j < dim; j++) {
    1381:       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]);
    1382:       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]);
    1383:       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]);
    1384:       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]);
    1385:       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]);
    1386:       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]);
    1387:       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]);
    1388:       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]);
    1389:     }
    1390:     for (i = 0; i < Nq; i++) {
    1391:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

    1393:       if (v) {
    1394:         PetscReal extPoint[8];

    1396:         extPoint[0] = 1.;
    1397:         extPoint[1] = xi;
    1398:         extPoint[2] = eta;
    1399:         extPoint[3] = xi * eta;
    1400:         extPoint[4] = theta;
    1401:         extPoint[5] = theta * xi;
    1402:         extPoint[6] = theta * eta;
    1403:         extPoint[7] = theta * eta * xi;
    1404:         for (j = 0; j < dim; j++) {
    1405:           PetscReal val = 0.;

    1407:           for (k = 0; k < Nv; k++) {
    1408:             val += extPoint[k] * zCoeff[dim * k + j];
    1409:           }
    1410:           v[i * dim + j] = val;
    1411:         }
    1412:       }
    1413:       if (J) {
    1414:         PetscReal extJ[24];

    1416:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
    1417:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
    1418:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
    1419:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
    1420:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
    1421:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
    1422:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
    1423:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

    1425:         for (j = 0; j < dim; j++) {
    1426:           for (k = 0; k < dimR; k++) {
    1427:             PetscReal val = 0.;

    1429:             for (l = 0; l < Nv; l++) {
    1430:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
    1431:             }
    1432:             J[i * dim * dim + dim * j + k] = val;
    1433:           }
    1434:         }
    1435:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
    1436:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
    1437:       }
    1438:     }
    1439:   }
    1440:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
    1441:   return(0);
    1442: }

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

    1455:   DMPlexGetDepth(dm, &depth);
    1456:   DMPlexGetConeSize(dm, cell, &coneSize);
    1457:   DMPlexGetDepthLabel(dm, &depthLabel);
    1458:   DMLabelGetValue(depthLabel, cell, &dim);
    1459:   if (depth == 1 && dim == 1) {
    1460:     DMGetDimension(dm, &dim);
    1461:   }
    1462:   DMGetCoordinateDim(dm, &coordDim);
    1463:   if (coordDim > 3) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %D > 3", coordDim);
    1464:   if (quad) {PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);}
    1465:   switch (dim) {
    1466:   case 0:
    1467:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1468:     isAffine = PETSC_FALSE;
    1469:     break;
    1470:   case 1:
    1471:     if (Nq) {
    1472:       DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
    1473:     } else {
    1474:       DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1475:     }
    1476:     break;
    1477:   case 2:
    1478:     switch (coneSize) {
    1479:     case 3:
    1480:       if (Nq) {
    1481:         DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
    1482:       } else {
    1483:         DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1484:       }
    1485:       break;
    1486:     case 4:
    1487:       DMPlexComputeRectangleGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1488:       isAffine = PETSC_FALSE;
    1489:       break;
    1490:     default:
    1491:       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
    1492:     }
    1493:     break;
    1494:   case 3:
    1495:     switch (coneSize) {
    1496:     case 4:
    1497:       if (Nq) {
    1498:         DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
    1499:       } else {
    1500:         DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ);
    1501:       }
    1502:       break;
    1503:     case 6: /* Faces */
    1504:     case 8: /* Vertices */
    1505:       DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
    1506:       isAffine = PETSC_FALSE;
    1507:       break;
    1508:     default:
    1509:       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
    1510:     }
    1511:     break;
    1512:   default:
    1513:     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
    1514:   }
    1515:   if (isAffine && Nq) {
    1516:     if (v) {
    1517:       for (i = 0; i < Nq; i++) {
    1518:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
    1519:       }
    1520:     }
    1521:     if (detJ) {
    1522:       for (i = 0; i < Nq; i++) {
    1523:         detJ[i] = detJ0;
    1524:       }
    1525:     }
    1526:     if (J) {
    1527:       PetscInt k;

    1529:       for (i = 0, k = 0; i < Nq; i++) {
    1530:         PetscInt j;

    1532:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1533:           J[k] = J0[j];
    1534:         }
    1535:       }
    1536:     }
    1537:     if (invJ) {
    1538:       PetscInt k;
    1539:       switch (coordDim) {
    1540:       case 0:
    1541:         break;
    1542:       case 1:
    1543:         invJ[0] = 1./J0[0];
    1544:         break;
    1545:       case 2:
    1546:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
    1547:         break;
    1548:       case 3:
    1549:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
    1550:         break;
    1551:       }
    1552:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
    1553:         PetscInt j;

    1555:         for (j = 0; j < coordDim * coordDim; j++, k++) {
    1556:           invJ[k] = invJ[j];
    1557:         }
    1558:       }
    1559:     }
    1560:   }
    1561:   return(0);
    1562: }

    1564: /*@C
    1565:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

    1567:   Collective on DM

    1569:   Input Arguments:
    1570: + dm   - the DM
    1571: - cell - the cell

    1573:   Output Arguments:
    1574: + v0   - the translation part of this affine transform
    1575: . J    - the Jacobian of the transform from the reference element
    1576: . invJ - the inverse of the Jacobian
    1577: - detJ - the Jacobian determinant

    1579:   Level: advanced

    1581:   Fortran Notes:
    1582:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1583:   include petsc.h90 in your code.

    1585: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
    1586: @*/
    1587: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1588: {

    1592:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
    1593:   return(0);
    1594: }

    1596: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
    1597: {
    1598:   PetscQuadrature  feQuad;
    1599:   PetscSection     coordSection;
    1600:   Vec              coordinates;
    1601:   PetscScalar     *coords = NULL;
    1602:   const PetscReal *quadPoints;
    1603:   PetscReal       *basisDer, *basis, detJt;
    1604:   PetscInt         dim, cdim, pdim, qdim, Nq, numCoords, q;
    1605:   PetscErrorCode   ierr;

    1608:   DMGetCoordinatesLocal(dm, &coordinates);
    1609:   DMGetCoordinateSection(dm, &coordSection);
    1610:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1611:   DMGetDimension(dm, &dim);
    1612:   DMGetCoordinateDim(dm, &cdim);
    1613:   if (!quad) { /* use the first point of the first functional of the dual space */
    1614:     PetscDualSpace dsp;

    1616:     PetscFEGetDualSpace(fe, &dsp);
    1617:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
    1618:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1619:     Nq = 1;
    1620:   } else {
    1621:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
    1622:   }
    1623:   PetscFEGetDimension(fe, &pdim);
    1624:   PetscFEGetQuadrature(fe, &feQuad);
    1625:   if (feQuad == quad) {
    1626:     PetscFEGetDefaultTabulation(fe, &basis, J ? &basisDer : NULL, NULL);
    1627:     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);
    1628:   } else {
    1629:     PetscFEGetTabulation(fe, Nq, quadPoints, &basis, J ? &basisDer : NULL, NULL);
    1630:   }
    1631:   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
    1632:   if (v) {
    1633:     PetscMemzero(v, Nq*cdim*sizeof(PetscReal));
    1634:     for (q = 0; q < Nq; ++q) {
    1635:       PetscInt i, k;

    1637:       for (k = 0; k < pdim; ++k)
    1638:         for (i = 0; i < cdim; ++i)
    1639:           v[q*cdim + i] += basis[q*pdim + k] * PetscRealPart(coords[k*cdim + i]);
    1640:       PetscLogFlops(2.0*pdim*cdim);
    1641:     }
    1642:   }
    1643:   if (J) {
    1644:     PetscMemzero(J, Nq*cdim*cdim*sizeof(PetscReal));
    1645:     for (q = 0; q < Nq; ++q) {
    1646:       PetscInt i, j, k, c, r;

    1648:       /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
    1649:       for (k = 0; k < pdim; ++k)
    1650:         for (j = 0; j < dim; ++j)
    1651:           for (i = 0; i < cdim; ++i)
    1652:             J[(q*cdim + i)*cdim + j] += basisDer[(q*pdim + k)*dim + j] * PetscRealPart(coords[k*cdim + i]);
    1653:       PetscLogFlops(2.0*pdim*dim*cdim);
    1654:       if (cdim > dim) {
    1655:         for (c = dim; c < cdim; ++c)
    1656:           for (r = 0; r < cdim; ++r)
    1657:             J[r*cdim+c] = r == c ? 1.0 : 0.0;
    1658:       }
    1659:       if (!detJ && !invJ) continue;
    1660:       detJt = 0.;
    1661:       switch (cdim) {
    1662:       case 3:
    1663:         DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
    1664:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1665:         break;
    1666:       case 2:
    1667:         DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
    1668:         if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
    1669:         break;
    1670:       case 1:
    1671:         detJt = J[q*cdim*dim];
    1672:         if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
    1673:       }
    1674:       if (detJ) detJ[q] = detJt;
    1675:     }
    1676:   }
    1677:   else if (detJ || invJ) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
    1678:   if (feQuad != quad) {
    1679:     PetscFERestoreTabulation(fe, Nq, quadPoints, &basis, J ? &basisDer : NULL, NULL);
    1680:   }
    1681:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
    1682:   return(0);
    1683: }

    1685: /*@C
    1686:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

    1688:   Collective on DM

    1690:   Input Arguments:
    1691: + dm   - the DM
    1692: . cell - the cell
    1693: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
    1694:          evaluated at the first vertex of the reference element

    1696:   Output Arguments:
    1697: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
    1698: . J    - the Jacobian of the transform from the reference element at each quadrature point
    1699: . invJ - the inverse of the Jacobian at each quadrature point
    1700: - detJ - the Jacobian determinant at each quadrature point

    1702:   Level: advanced

    1704:   Fortran Notes:
    1705:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1706:   include petsc.h90 in your code.

    1708: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1709: @*/
    1710: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
    1711: {
    1712:   PetscFE        fe = NULL;

    1717:   if (dm->coordinateDM) {
    1718:     PetscClassId id;
    1719:     PetscInt     numFields;
    1720:     PetscDS      prob = dm->coordinateDM->prob;
    1721:     PetscObject  disc;

    1723:     PetscDSGetNumFields(prob, &numFields);
    1724:     if (numFields) {
    1725:       PetscDSGetDiscretization(prob,0,&disc);
    1726:       PetscObjectGetClassId(disc,&id);
    1727:       if (id == PETSCFE_CLASSID) {
    1728:         fe = (PetscFE) disc;
    1729:       }
    1730:     }
    1731:   }
    1732:   if (!fe) {DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);}
    1733:   else     {DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);}
    1734:   return(0);
    1735: }

    1737: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1738: {
    1739:   PetscSection   coordSection;
    1740:   Vec            coordinates;
    1741:   PetscScalar   *coords = NULL;
    1742:   PetscScalar    tmp[2];
    1743:   PetscInt       coordSize;

    1747:   DMGetCoordinatesLocal(dm, &coordinates);
    1748:   DMGetCoordinateSection(dm, &coordSection);
    1749:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1750:   if (dim != 2) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "We only support 2D edges right now");
    1751:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
    1752:   if (centroid) {
    1753:     centroid[0] = 0.5*PetscRealPart(coords[0] + tmp[0]);
    1754:     centroid[1] = 0.5*PetscRealPart(coords[1] + tmp[1]);
    1755:   }
    1756:   if (normal) {
    1757:     PetscReal norm;

    1759:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
    1760:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
    1761:     norm       = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1]);
    1762:     normal[0] /= norm;
    1763:     normal[1] /= norm;
    1764:   }
    1765:   if (vol) {
    1766:     *vol = PetscSqrtReal(PetscSqr(PetscRealPart(coords[0] - tmp[0])) + PetscSqr(PetscRealPart(coords[1] - tmp[1])));
    1767:   }
    1768:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1769:   return(0);
    1770: }

    1772: /* Centroid_i = (\sum_n A_n Cn_i ) / A */
    1773: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1774: {
    1775:   PetscSection   coordSection;
    1776:   Vec            coordinates;
    1777:   PetscScalar   *coords = NULL;
    1778:   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
    1779:   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;

    1783:   DMGetCoordinatesLocal(dm, &coordinates);
    1784:   DMPlexGetConeSize(dm, cell, &numCorners);
    1785:   DMGetCoordinateSection(dm, &coordSection);
    1786:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1787:   DMGetCoordinateDim(dm, &dim);
    1788:   if (dim > 2 && centroid) {
    1789:     v0[0] = PetscRealPart(coords[0]);
    1790:     v0[1] = PetscRealPart(coords[1]);
    1791:     v0[2] = PetscRealPart(coords[2]);
    1792:   }
    1793:   if (normal) {
    1794:     if (dim > 2) {
    1795:       const PetscReal x0 = PetscRealPart(coords[dim+0] - coords[0]), x1 = PetscRealPart(coords[dim*2+0] - coords[0]);
    1796:       const PetscReal y0 = PetscRealPart(coords[dim+1] - coords[1]), y1 = PetscRealPart(coords[dim*2+1] - coords[1]);
    1797:       const PetscReal z0 = PetscRealPart(coords[dim+2] - coords[2]), z1 = PetscRealPart(coords[dim*2+2] - coords[2]);
    1798:       PetscReal       norm;

    1800:       normal[0] = y0*z1 - z0*y1;
    1801:       normal[1] = z0*x1 - x0*z1;
    1802:       normal[2] = x0*y1 - y0*x1;
    1803:       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
    1804:       normal[0] /= norm;
    1805:       normal[1] /= norm;
    1806:       normal[2] /= norm;
    1807:     } else {
    1808:       for (d = 0; d < dim; ++d) normal[d] = 0.0;
    1809:     }
    1810:   }
    1811:   if (dim == 3) {DMPlexComputeProjection3Dto2D(coordSize, coords, R);}
    1812:   for (p = 0; p < numCorners; ++p) {
    1813:     /* Need to do this copy to get types right */
    1814:     for (d = 0; d < tdim; ++d) {
    1815:       ctmp[d]      = PetscRealPart(coords[p*tdim+d]);
    1816:       ctmp[tdim+d] = PetscRealPart(coords[((p+1)%numCorners)*tdim+d]);
    1817:     }
    1818:     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
    1819:     vsum += vtmp;
    1820:     for (d = 0; d < tdim; ++d) {
    1821:       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
    1822:     }
    1823:   }
    1824:   for (d = 0; d < tdim; ++d) {
    1825:     csum[d] /= (tdim+1)*vsum;
    1826:   }
    1827:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
    1828:   if (vol) *vol = PetscAbsReal(vsum);
    1829:   if (centroid) {
    1830:     if (dim > 2) {
    1831:       for (d = 0; d < dim; ++d) {
    1832:         centroid[d] = v0[d];
    1833:         for (e = 0; e < dim; ++e) {
    1834:           centroid[d] += R[d*dim+e]*csum[e];
    1835:         }
    1836:       }
    1837:     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
    1838:   }
    1839:   return(0);
    1840: }

    1842: /* Centroid_i = (\sum_n V_n Cn_i ) / V */
    1843: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1844: {
    1845:   PetscSection    coordSection;
    1846:   Vec             coordinates;
    1847:   PetscScalar    *coords = NULL;
    1848:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
    1849:   const PetscInt *faces, *facesO;
    1850:   PetscInt        numFaces, f, coordSize, numCorners, p, d;
    1851:   PetscErrorCode  ierr;

    1854:   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
    1855:   DMGetCoordinatesLocal(dm, &coordinates);
    1856:   DMGetCoordinateSection(dm, &coordSection);

    1858:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
    1859:   DMPlexGetConeSize(dm, cell, &numFaces);
    1860:   DMPlexGetCone(dm, cell, &faces);
    1861:   DMPlexGetConeOrientation(dm, cell, &facesO);
    1862:   for (f = 0; f < numFaces; ++f) {
    1863:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    1864:     numCorners = coordSize/dim;
    1865:     switch (numCorners) {
    1866:     case 3:
    1867:       for (d = 0; d < dim; ++d) {
    1868:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
    1869:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
    1870:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
    1871:       }
    1872:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1873:       if (facesO[f] < 0) vtmp = -vtmp;
    1874:       vsum += vtmp;
    1875:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
    1876:         for (d = 0; d < dim; ++d) {
    1877:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1878:         }
    1879:       }
    1880:       break;
    1881:     case 4:
    1882:       /* DO FOR PYRAMID */
    1883:       /* First tet */
    1884:       for (d = 0; d < dim; ++d) {
    1885:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
    1886:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
    1887:         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
    1888:       }
    1889:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1890:       if (facesO[f] < 0) vtmp = -vtmp;
    1891:       vsum += vtmp;
    1892:       if (centroid) {
    1893:         for (d = 0; d < dim; ++d) {
    1894:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1895:         }
    1896:       }
    1897:       /* Second tet */
    1898:       for (d = 0; d < dim; ++d) {
    1899:         coordsTmp[0*dim+d] = PetscRealPart(coords[1*dim+d]);
    1900:         coordsTmp[1*dim+d] = PetscRealPart(coords[2*dim+d]);
    1901:         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
    1902:       }
    1903:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
    1904:       if (facesO[f] < 0) vtmp = -vtmp;
    1905:       vsum += vtmp;
    1906:       if (centroid) {
    1907:         for (d = 0; d < dim; ++d) {
    1908:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
    1909:         }
    1910:       }
    1911:       break;
    1912:     default:
    1913:       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle faces with %D vertices", numCorners);
    1914:     }
    1915:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
    1916:   }
    1917:   if (vol)     *vol = PetscAbsReal(vsum);
    1918:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
    1919:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
    1920:   return(0);
    1921: }

    1923: /*@C
    1924:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

    1926:   Collective on DM

    1928:   Input Arguments:
    1929: + dm   - the DM
    1930: - cell - the cell

    1932:   Output Arguments:
    1933: + volume   - the cell volume
    1934: . centroid - the cell centroid
    1935: - normal - the cell normal, if appropriate

    1937:   Level: advanced

    1939:   Fortran Notes:
    1940:   Since it returns arrays, this routine is only available in Fortran 90, and you must
    1941:   include petsc.h90 in your code.

    1943: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
    1944: @*/
    1945: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
    1946: {
    1947:   PetscInt       depth, dim;

    1951:   DMPlexGetDepth(dm, &depth);
    1952:   DMGetDimension(dm, &dim);
    1953:   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
    1954:   /* We need to keep a pointer to the depth label */
    1955:   DMGetLabelValue(dm, "depth", cell, &depth);
    1956:   /* Cone size is now the number of faces */
    1957:   switch (depth) {
    1958:   case 1:
    1959:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
    1960:     break;
    1961:   case 2:
    1962:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
    1963:     break;
    1964:   case 3:
    1965:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
    1966:     break;
    1967:   default:
    1968:     SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
    1969:   }
    1970:   return(0);
    1971: }

    1973: /*@
    1974:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

    1976:   Collective on dm

    1978:   Input Parameter:
    1979: . dm - The DMPlex

    1981:   Output Parameter:
    1982: . cellgeom - A vector with the cell geometry data for each cell

    1984:   Level: beginner

    1986: .keywords: DMPlexComputeCellGeometryFEM()
    1987: @*/
    1988: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
    1989: {
    1990:   DM             dmCell;
    1991:   Vec            coordinates;
    1992:   PetscSection   coordSection, sectionCell;
    1993:   PetscScalar   *cgeom;
    1994:   PetscInt       cStart, cEnd, cMax, c;

    1998:   DMClone(dm, &dmCell);
    1999:   DMGetCoordinateSection(dm, &coordSection);
    2000:   DMGetCoordinatesLocal(dm, &coordinates);
    2001:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2002:   DMSetCoordinatesLocal(dmCell, coordinates);
    2003:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2004:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2005:   DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);
    2006:   cEnd = cMax < 0 ? cEnd : cMax;
    2007:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2008:   /* TODO This needs to be multiplied by Nq for non-affine */
    2009:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));}
    2010:   PetscSectionSetUp(sectionCell);
    2011:   DMSetSection(dmCell, sectionCell);
    2012:   PetscSectionDestroy(&sectionCell);
    2013:   DMCreateLocalVector(dmCell, cellgeom);
    2014:   VecGetArray(*cellgeom, &cgeom);
    2015:   for (c = cStart; c < cEnd; ++c) {
    2016:     PetscFEGeom *cg;

    2018:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2019:     PetscMemzero(cg, sizeof(*cg));
    2020:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
    2021:     if (*cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cg->detJ, c);
    2022:   }
    2023:   return(0);
    2024: }

    2026: /*@
    2027:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

    2029:   Input Parameter:
    2030: . dm - The DM

    2032:   Output Parameters:
    2033: + cellgeom - A Vec of PetscFVCellGeom data
    2034: . facegeom - A Vec of PetscFVFaceGeom data

    2036:   Level: developer

    2038: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
    2039: @*/
    2040: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
    2041: {
    2042:   DM             dmFace, dmCell;
    2043:   DMLabel        ghostLabel;
    2044:   PetscSection   sectionFace, sectionCell;
    2045:   PetscSection   coordSection;
    2046:   Vec            coordinates;
    2047:   PetscScalar   *fgeom, *cgeom;
    2048:   PetscReal      minradius, gminradius;
    2049:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

    2053:   DMGetDimension(dm, &dim);
    2054:   DMGetCoordinateSection(dm, &coordSection);
    2055:   DMGetCoordinatesLocal(dm, &coordinates);
    2056:   /* Make cell centroids and volumes */
    2057:   DMClone(dm, &dmCell);
    2058:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
    2059:   DMSetCoordinatesLocal(dmCell, coordinates);
    2060:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
    2061:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2062:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
    2063:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    2064:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));}
    2065:   PetscSectionSetUp(sectionCell);
    2066:   DMSetSection(dmCell, sectionCell);
    2067:   PetscSectionDestroy(&sectionCell);
    2068:   DMCreateLocalVector(dmCell, cellgeom);
    2069:   if (cEndInterior < 0) {
    2070:     cEndInterior = cEnd;
    2071:   }
    2072:   VecGetArray(*cellgeom, &cgeom);
    2073:   for (c = cStart; c < cEndInterior; ++c) {
    2074:     PetscFVCellGeom *cg;

    2076:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
    2077:     PetscMemzero(cg, sizeof(*cg));
    2078:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
    2079:   }
    2080:   /* Compute face normals and minimum cell radius */
    2081:   DMClone(dm, &dmFace);
    2082:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
    2083:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2084:   PetscSectionSetChart(sectionFace, fStart, fEnd);
    2085:   for (f = fStart; f < fEnd; ++f) {PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));}
    2086:   PetscSectionSetUp(sectionFace);
    2087:   DMSetSection(dmFace, sectionFace);
    2088:   PetscSectionDestroy(&sectionFace);
    2089:   DMCreateLocalVector(dmFace, facegeom);
    2090:   VecGetArray(*facegeom, &fgeom);
    2091:   DMGetLabel(dm, "ghost", &ghostLabel);
    2092:   minradius = PETSC_MAX_REAL;
    2093:   for (f = fStart; f < fEnd; ++f) {
    2094:     PetscFVFaceGeom *fg;
    2095:     PetscReal        area;
    2096:     PetscInt         ghost = -1, d, numChildren;

    2098:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2099:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
    2100:     if (ghost >= 0 || numChildren) continue;
    2101:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
    2102:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
    2103:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
    2104:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
    2105:     {
    2106:       PetscFVCellGeom *cL, *cR;
    2107:       PetscInt         ncells;
    2108:       const PetscInt  *cells;
    2109:       PetscReal       *lcentroid, *rcentroid;
    2110:       PetscReal        l[3], r[3], v[3];

    2112:       DMPlexGetSupport(dm, f, &cells);
    2113:       DMPlexGetSupportSize(dm, f, &ncells);
    2114:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
    2115:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
    2116:       if (ncells > 1) {
    2117:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
    2118:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
    2119:       }
    2120:       else {
    2121:         rcentroid = fg->centroid;
    2122:       }
    2123:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
    2124:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
    2125:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
    2126:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
    2127:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
    2128:       }
    2129:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
    2130:         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]);
    2131:         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]);
    2132:         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
    2133:       }
    2134:       if (cells[0] < cEndInterior) {
    2135:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
    2136:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2137:       }
    2138:       if (ncells > 1 && cells[1] < cEndInterior) {
    2139:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
    2140:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
    2141:       }
    2142:     }
    2143:   }
    2144:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
    2145:   DMPlexSetMinRadius(dm, gminradius);
    2146:   /* Compute centroids of ghost cells */
    2147:   for (c = cEndInterior; c < cEnd; ++c) {
    2148:     PetscFVFaceGeom *fg;
    2149:     const PetscInt  *cone,    *support;
    2150:     PetscInt         coneSize, supportSize, s;

    2152:     DMPlexGetConeSize(dmCell, c, &coneSize);
    2153:     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
    2154:     DMPlexGetCone(dmCell, c, &cone);
    2155:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
    2156:     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
    2157:     DMPlexGetSupport(dmCell, cone[0], &support);
    2158:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
    2159:     for (s = 0; s < 2; ++s) {
    2160:       /* Reflect ghost centroid across plane of face */
    2161:       if (support[s] == c) {
    2162:         PetscFVCellGeom       *ci;
    2163:         PetscFVCellGeom       *cg;
    2164:         PetscReal              c2f[3], a;

    2166:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
    2167:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
    2168:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
    2169:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
    2170:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
    2171:         cg->volume = ci->volume;
    2172:       }
    2173:     }
    2174:   }
    2175:   VecRestoreArray(*facegeom, &fgeom);
    2176:   VecRestoreArray(*cellgeom, &cgeom);
    2177:   DMDestroy(&dmCell);
    2178:   DMDestroy(&dmFace);
    2179:   return(0);
    2180: }

    2182: /*@C
    2183:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

    2185:   Not collective

    2187:   Input Argument:
    2188: . dm - the DM

    2190:   Output Argument:
    2191: . minradius - the minium cell radius

    2193:   Level: developer

    2195: .seealso: DMGetCoordinates()
    2196: @*/
    2197: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
    2198: {
    2202:   *minradius = ((DM_Plex*) dm->data)->minradius;
    2203:   return(0);
    2204: }

    2206: /*@C
    2207:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

    2209:   Logically collective

    2211:   Input Arguments:
    2212: + dm - the DM
    2213: - minradius - the minium cell radius

    2215:   Level: developer

    2217: .seealso: DMSetCoordinates()
    2218: @*/
    2219: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
    2220: {
    2223:   ((DM_Plex*) dm->data)->minradius = minradius;
    2224:   return(0);
    2225: }

    2227: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2228: {
    2229:   DMLabel        ghostLabel;
    2230:   PetscScalar   *dx, *grad, **gref;
    2231:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

    2235:   DMGetDimension(dm, &dim);
    2236:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2237:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
    2238:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
    2239:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2240:   DMGetLabel(dm, "ghost", &ghostLabel);
    2241:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2242:   for (c = cStart; c < cEndInterior; c++) {
    2243:     const PetscInt        *faces;
    2244:     PetscInt               numFaces, usedFaces, f, d;
    2245:     PetscFVCellGeom        *cg;
    2246:     PetscBool              boundary;
    2247:     PetscInt               ghost;

    2249:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2250:     DMPlexGetConeSize(dm, c, &numFaces);
    2251:     DMPlexGetCone(dm, c, &faces);
    2252:     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
    2253:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2254:       PetscFVCellGeom       *cg1;
    2255:       PetscFVFaceGeom       *fg;
    2256:       const PetscInt        *fcells;
    2257:       PetscInt               ncell, side;

    2259:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2260:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2261:       if ((ghost >= 0) || boundary) continue;
    2262:       DMPlexGetSupport(dm, faces[f], &fcells);
    2263:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
    2264:       ncell = fcells[!side];    /* the neighbor */
    2265:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
    2266:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2267:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2268:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2269:     }
    2270:     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
    2271:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
    2272:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
    2273:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
    2274:       DMIsBoundaryPoint(dm, faces[f], &boundary);
    2275:       if ((ghost >= 0) || boundary) continue;
    2276:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
    2277:       ++usedFaces;
    2278:     }
    2279:   }
    2280:   PetscFree3(dx, grad, gref);
    2281:   return(0);
    2282: }

    2284: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2285: {
    2286:   DMLabel        ghostLabel;
    2287:   PetscScalar   *dx, *grad, **gref;
    2288:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
    2289:   PetscSection   neighSec;
    2290:   PetscInt     (*neighbors)[2];
    2291:   PetscInt      *counter;

    2295:   DMGetDimension(dm, &dim);
    2296:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2297:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
    2298:   if (cEndInterior < 0) {
    2299:     cEndInterior = cEnd;
    2300:   }
    2301:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
    2302:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
    2303:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    2304:   DMGetLabel(dm, "ghost", &ghostLabel);
    2305:   for (f = fStart; f < fEnd; f++) {
    2306:     const PetscInt        *fcells;
    2307:     PetscBool              boundary;
    2308:     PetscInt               ghost = -1;
    2309:     PetscInt               numChildren, numCells, c;

    2311:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2312:     DMIsBoundaryPoint(dm, f, &boundary);
    2313:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2314:     if ((ghost >= 0) || boundary || numChildren) continue;
    2315:     DMPlexGetSupportSize(dm, f, &numCells);
    2316:     if (numCells == 2) {
    2317:       DMPlexGetSupport(dm, f, &fcells);
    2318:       for (c = 0; c < 2; c++) {
    2319:         PetscInt cell = fcells[c];

    2321:         if (cell >= cStart && cell < cEndInterior) {
    2322:           PetscSectionAddDof(neighSec,cell,1);
    2323:         }
    2324:       }
    2325:     }
    2326:   }
    2327:   PetscSectionSetUp(neighSec);
    2328:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
    2329:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
    2330:   nStart = 0;
    2331:   PetscSectionGetStorageSize(neighSec,&nEnd);
    2332:   PetscMalloc1((nEnd-nStart),&neighbors);
    2333:   PetscCalloc1((cEndInterior-cStart),&counter);
    2334:   for (f = fStart; f < fEnd; f++) {
    2335:     const PetscInt        *fcells;
    2336:     PetscBool              boundary;
    2337:     PetscInt               ghost = -1;
    2338:     PetscInt               numChildren, numCells, c;

    2340:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
    2341:     DMIsBoundaryPoint(dm, f, &boundary);
    2342:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
    2343:     if ((ghost >= 0) || boundary || numChildren) continue;
    2344:     DMPlexGetSupportSize(dm, f, &numCells);
    2345:     if (numCells == 2) {
    2346:       DMPlexGetSupport(dm, f, &fcells);
    2347:       for (c = 0; c < 2; c++) {
    2348:         PetscInt cell = fcells[c], off;

    2350:         if (cell >= cStart && cell < cEndInterior) {
    2351:           PetscSectionGetOffset(neighSec,cell,&off);
    2352:           off += counter[cell - cStart]++;
    2353:           neighbors[off][0] = f;
    2354:           neighbors[off][1] = fcells[1 - c];
    2355:         }
    2356:       }
    2357:     }
    2358:   }
    2359:   PetscFree(counter);
    2360:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
    2361:   for (c = cStart; c < cEndInterior; c++) {
    2362:     PetscInt               numFaces, f, d, off, ghost = -1;
    2363:     PetscFVCellGeom        *cg;

    2365:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
    2366:     PetscSectionGetDof(neighSec, c, &numFaces);
    2367:     PetscSectionGetOffset(neighSec, c, &off);
    2368:     if (ghostLabel) {DMLabelGetValue(ghostLabel, c, &ghost);}
    2369:     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);
    2370:     for (f = 0; f < numFaces; ++f) {
    2371:       PetscFVCellGeom       *cg1;
    2372:       PetscFVFaceGeom       *fg;
    2373:       const PetscInt        *fcells;
    2374:       PetscInt               ncell, side, nface;

    2376:       nface = neighbors[off + f][0];
    2377:       ncell = neighbors[off + f][1];
    2378:       DMPlexGetSupport(dm,nface,&fcells);
    2379:       side  = (c != fcells[0]);
    2380:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
    2381:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
    2382:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
    2383:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
    2384:     }
    2385:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
    2386:     for (f = 0; f < numFaces; ++f) {
    2387:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
    2388:     }
    2389:   }
    2390:   PetscFree3(dx, grad, gref);
    2391:   PetscSectionDestroy(&neighSec);
    2392:   PetscFree(neighbors);
    2393:   return(0);
    2394: }

    2396: /*@
    2397:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

    2399:   Collective on DM

    2401:   Input Arguments:
    2402: + dm  - The DM
    2403: . fvm - The PetscFV
    2404: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM()
    2405: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

    2407:   Output Parameters:
    2408: + faceGeometry - The geometric factors for gradient calculation are inserted
    2409: - dmGrad - The DM describing the layout of gradient data

    2411:   Level: developer

    2413: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
    2414: @*/
    2415: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
    2416: {
    2417:   DM             dmFace, dmCell;
    2418:   PetscScalar   *fgeom, *cgeom;
    2419:   PetscSection   sectionGrad, parentSection;
    2420:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

    2424:   DMGetDimension(dm, &dim);
    2425:   PetscFVGetNumComponents(fvm, &pdim);
    2426:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    2427:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
    2428:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
    2429:   VecGetDM(faceGeometry, &dmFace);
    2430:   VecGetDM(cellGeometry, &dmCell);
    2431:   VecGetArray(faceGeometry, &fgeom);
    2432:   VecGetArray(cellGeometry, &cgeom);
    2433:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
    2434:   if (!parentSection) {
    2435:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2436:   } else {
    2437:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
    2438:   }
    2439:   VecRestoreArray(faceGeometry, &fgeom);
    2440:   VecRestoreArray(cellGeometry, &cgeom);
    2441:   /* Create storage for gradients */
    2442:   DMClone(dm, dmGrad);
    2443:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
    2444:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
    2445:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionGrad, c, pdim*dim);}
    2446:   PetscSectionSetUp(sectionGrad);
    2447:   DMSetSection(*dmGrad, sectionGrad);
    2448:   PetscSectionDestroy(&sectionGrad);
    2449:   return(0);
    2450: }

    2452: /*@
    2453:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

    2455:   Collective on DM

    2457:   Input Arguments:
    2458: + dm  - The DM
    2459: - fvm - The PetscFV

    2461:   Output Parameters:
    2462: + cellGeometry - The cell geometry
    2463: . faceGeometry - The face geometry
    2464: - dmGrad       - The gradient matrices

    2466:   Level: developer

    2468: .seealso: DMPlexComputeGeometryFVM()
    2469: @*/
    2470: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
    2471: {
    2472:   PetscObject    cellgeomobj, facegeomobj;

    2476:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2477:   if (!cellgeomobj) {
    2478:     Vec cellgeomInt, facegeomInt;

    2480:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
    2481:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
    2482:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
    2483:     VecDestroy(&cellgeomInt);
    2484:     VecDestroy(&facegeomInt);
    2485:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
    2486:   }
    2487:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
    2488:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
    2489:   if (facegeom) *facegeom = (Vec) facegeomobj;
    2490:   if (gradDM) {
    2491:     PetscObject gradobj;
    2492:     PetscBool   computeGradients;

    2494:     PetscFVGetComputeGradients(fv,&computeGradients);
    2495:     if (!computeGradients) {
    2496:       *gradDM = NULL;
    2497:       return(0);
    2498:     }
    2499:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2500:     if (!gradobj) {
    2501:       DM dmGradInt;

    2503:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
    2504:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
    2505:       DMDestroy(&dmGradInt);
    2506:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
    2507:     }
    2508:     *gradDM = (DM) gradobj;
    2509:   }
    2510:   return(0);
    2511: }

    2513: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
    2514: {
    2515:   PetscInt l, m;

    2518:   if (dimC == dimR && dimR <= 3) {
    2519:     /* invert Jacobian, multiply */
    2520:     PetscScalar det, idet;

    2522:     switch (dimR) {
    2523:     case 1:
    2524:       invJ[0] = 1./ J[0];
    2525:       break;
    2526:     case 2:
    2527:       det = J[0] * J[3] - J[1] * J[2];
    2528:       idet = 1./det;
    2529:       invJ[0] =  J[3] * idet;
    2530:       invJ[1] = -J[1] * idet;
    2531:       invJ[2] = -J[2] * idet;
    2532:       invJ[3] =  J[0] * idet;
    2533:       break;
    2534:     case 3:
    2535:       {
    2536:         invJ[0] = J[4] * J[8] - J[5] * J[7];
    2537:         invJ[1] = J[2] * J[7] - J[1] * J[8];
    2538:         invJ[2] = J[1] * J[5] - J[2] * J[4];
    2539:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
    2540:         idet = 1./det;
    2541:         invJ[0] *= idet;
    2542:         invJ[1] *= idet;
    2543:         invJ[2] *= idet;
    2544:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
    2545:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
    2546:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
    2547:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
    2548:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
    2549:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
    2550:       }
    2551:       break;
    2552:     }
    2553:     for (l = 0; l < dimR; l++) {
    2554:       for (m = 0; m < dimC; m++) {
    2555:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
    2556:       }
    2557:     }
    2558:   } else {
    2559: #if defined(PETSC_USE_COMPLEX)
    2560:     char transpose = 'C';
    2561: #else
    2562:     char transpose = 'T';
    2563: #endif
    2564:     PetscBLASInt m = dimR;
    2565:     PetscBLASInt n = dimC;
    2566:     PetscBLASInt one = 1;
    2567:     PetscBLASInt worksize = dimR * dimC, info;

    2569:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

    2571:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));
    2572:     if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");

    2574:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
    2575:   }
    2576:   return(0);
    2577: }

    2579: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2580: {
    2581:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
    2582:   PetscScalar    *coordsScalar = NULL;
    2583:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
    2584:   PetscScalar    *J, *invJ, *work;

    2589:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2590:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2591:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2592:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2593:   cellCoords = &cellData[0];
    2594:   cellCoeffs = &cellData[coordSize];
    2595:   extJ       = &cellData[2 * coordSize];
    2596:   resNeg     = &cellData[2 * coordSize + dimR];
    2597:   invJ       = &J[dimR * dimC];
    2598:   work       = &J[2 * dimR * dimC];
    2599:   if (dimR == 2) {
    2600:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2602:     for (i = 0; i < 4; i++) {
    2603:       PetscInt plexI = zToPlex[i];

    2605:       for (j = 0; j < dimC; j++) {
    2606:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2607:       }
    2608:     }
    2609:   } else if (dimR == 3) {
    2610:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2612:     for (i = 0; i < 8; i++) {
    2613:       PetscInt plexI = zToPlex[i];

    2615:       for (j = 0; j < dimC; j++) {
    2616:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2617:       }
    2618:     }
    2619:   } else {
    2620:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2621:   }
    2622:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2623:   for (i = 0; i < dimR; i++) {
    2624:     PetscReal *swap;

    2626:     for (j = 0; j < (numV / 2); j++) {
    2627:       for (k = 0; k < dimC; k++) {
    2628:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2629:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2630:       }
    2631:     }

    2633:     if (i < dimR - 1) {
    2634:       swap = cellCoeffs;
    2635:       cellCoeffs = cellCoords;
    2636:       cellCoords = swap;
    2637:     }
    2638:   }
    2639:   PetscMemzero(refCoords,numPoints * dimR * sizeof (PetscReal));
    2640:   for (j = 0; j < numPoints; j++) {
    2641:     for (i = 0; i < maxIts; i++) {
    2642:       PetscReal *guess = &refCoords[dimR * j];

    2644:       /* compute -residual and Jacobian */
    2645:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
    2646:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
    2647:       for (k = 0; k < numV; k++) {
    2648:         PetscReal extCoord = 1.;
    2649:         for (l = 0; l < dimR; l++) {
    2650:           PetscReal coord = guess[l];
    2651:           PetscInt  dep   = (k & (1 << l)) >> l;

    2653:           extCoord *= dep * coord + !dep;
    2654:           extJ[l] = dep;

    2656:           for (m = 0; m < dimR; m++) {
    2657:             PetscReal coord = guess[m];
    2658:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
    2659:             PetscReal mult  = dep * coord + !dep;

    2661:             extJ[l] *= mult;
    2662:           }
    2663:         }
    2664:         for (l = 0; l < dimC; l++) {
    2665:           PetscReal coeff = cellCoeffs[dimC * k + l];

    2667:           resNeg[l] -= coeff * extCoord;
    2668:           for (m = 0; m < dimR; m++) {
    2669:             J[dimR * l + m] += coeff * extJ[m];
    2670:           }
    2671:         }
    2672:       }
    2673: #if 0 && defined(PETSC_USE_DEBUG)
    2674:       {
    2675:         PetscReal maxAbs = 0.;

    2677:         for (l = 0; l < dimC; l++) {
    2678:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2679:         }
    2680:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,maxAbs);
    2681:       }
    2682: #endif

    2684:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
    2685:     }
    2686:   }
    2687:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
    2688:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
    2689:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2690:   return(0);
    2691: }

    2693: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
    2694: {
    2695:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
    2696:   PetscScalar    *coordsScalar = NULL;
    2697:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

    2702:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2703:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
    2704:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2705:   cellCoords = &cellData[0];
    2706:   cellCoeffs = &cellData[coordSize];
    2707:   if (dimR == 2) {
    2708:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

    2710:     for (i = 0; i < 4; i++) {
    2711:       PetscInt plexI = zToPlex[i];

    2713:       for (j = 0; j < dimC; j++) {
    2714:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2715:       }
    2716:     }
    2717:   } else if (dimR == 3) {
    2718:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

    2720:     for (i = 0; i < 8; i++) {
    2721:       PetscInt plexI = zToPlex[i];

    2723:       for (j = 0; j < dimC; j++) {
    2724:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
    2725:       }
    2726:     }
    2727:   } else {
    2728:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
    2729:   }
    2730:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
    2731:   for (i = 0; i < dimR; i++) {
    2732:     PetscReal *swap;

    2734:     for (j = 0; j < (numV / 2); j++) {
    2735:       for (k = 0; k < dimC; k++) {
    2736:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
    2737:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
    2738:       }
    2739:     }

    2741:     if (i < dimR - 1) {
    2742:       swap = cellCoeffs;
    2743:       cellCoeffs = cellCoords;
    2744:       cellCoords = swap;
    2745:     }
    2746:   }
    2747:   PetscMemzero(realCoords,numPoints * dimC * sizeof (PetscReal));
    2748:   for (j = 0; j < numPoints; j++) {
    2749:     const PetscReal *guess  = &refCoords[dimR * j];
    2750:     PetscReal       *mapped = &realCoords[dimC * j];

    2752:     for (k = 0; k < numV; k++) {
    2753:       PetscReal extCoord = 1.;
    2754:       for (l = 0; l < dimR; l++) {
    2755:         PetscReal coord = guess[l];
    2756:         PetscInt  dep   = (k & (1 << l)) >> l;

    2758:         extCoord *= dep * coord + !dep;
    2759:       }
    2760:       for (l = 0; l < dimC; l++) {
    2761:         PetscReal coeff = cellCoeffs[dimC * k + l];

    2763:         mapped[l] += coeff * extCoord;
    2764:       }
    2765:     }
    2766:   }
    2767:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
    2768:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
    2769:   return(0);
    2770: }

    2772: /* TODO: TOBY please fix this for Nc > 1 */
    2773: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2774: {
    2775:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
    2776:   PetscScalar    *nodes = NULL;
    2777:   PetscReal      *invV, *modes;
    2778:   PetscReal      *B, *D, *resNeg;
    2779:   PetscScalar    *J, *invJ, *work;

    2783:   PetscFEGetDimension(fe, &pdim);
    2784:   PetscFEGetNumComponents(fe, &numComp);
    2785:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2786:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2787:   /* convert nodes to values in the stable evaluation basis */
    2788:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2789:   invV = fe->invV;
    2790:   for (i = 0; i < pdim; ++i) {
    2791:     modes[i] = 0.;
    2792:     for (j = 0; j < pdim; ++j) {
    2793:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2794:     }
    2795:   }
    2796:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2797:   D      = &B[pdim*Nc];
    2798:   resNeg = &D[pdim*Nc * dimR];
    2799:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2800:   invJ = &J[Nc * dimR];
    2801:   work = &invJ[Nc * dimR];
    2802:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
    2803:   for (j = 0; j < numPoints; j++) {
    2804:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
    2805:       PetscReal *guess = &refCoords[j * dimR];
    2806:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
    2807:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
    2808:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
    2809:       for (k = 0; k < pdim; k++) {
    2810:         for (l = 0; l < Nc; l++) {
    2811:           resNeg[l] -= modes[k] * B[k * Nc + l];
    2812:           for (m = 0; m < dimR; m++) {
    2813:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
    2814:           }
    2815:         }
    2816:       }
    2817: #if 0 && defined(PETSC_USE_DEBUG)
    2818:       {
    2819:         PetscReal maxAbs = 0.;

    2821:         for (l = 0; l < Nc; l++) {
    2822:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
    2823:         }
    2824:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,maxAbs);
    2825:       }
    2826: #endif
    2827:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
    2828:     }
    2829:   }
    2830:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
    2831:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
    2832:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    2833:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2834:   return(0);
    2835: }

    2837: /* TODO: TOBY please fix this for Nc > 1 */
    2838: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
    2839: {
    2840:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
    2841:   PetscScalar    *nodes = NULL;
    2842:   PetscReal      *invV, *modes;
    2843:   PetscReal      *B;

    2847:   PetscFEGetDimension(fe, &pdim);
    2848:   PetscFEGetNumComponents(fe, &numComp);
    2849:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
    2850:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2851:   /* convert nodes to values in the stable evaluation basis */
    2852:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
    2853:   invV = fe->invV;
    2854:   for (i = 0; i < pdim; ++i) {
    2855:     modes[i] = 0.;
    2856:     for (j = 0; j < pdim; ++j) {
    2857:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
    2858:     }
    2859:   }
    2860:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    2861:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
    2862:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
    2863:   for (j = 0; j < numPoints; j++) {
    2864:     PetscReal *mapped = &realCoords[j * Nc];

    2866:     for (k = 0; k < pdim; k++) {
    2867:       for (l = 0; l < Nc; l++) {
    2868:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
    2869:       }
    2870:     }
    2871:   }
    2872:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
    2873:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
    2874:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
    2875:   return(0);
    2876: }

    2878: /*@
    2879:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
    2880:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
    2881:   extend uniquely outside the reference cell (e.g, most non-affine maps)

    2883:   Not collective

    2885:   Input Parameters:
    2886: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    2887:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    2888:                as a multilinear map for tensor-product elements
    2889: . cell       - the cell whose map is used.
    2890: . numPoints  - the number of points to locate
    2891: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    2893:   Output Parameters:
    2894: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    2896:   Level: intermediate
    2897: @*/
    2898: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
    2899: {
    2900:   PetscInt       dimC, dimR, depth, cStart, cEnd, cEndInterior, i;
    2901:   DM             coordDM = NULL;
    2902:   Vec            coords;
    2903:   PetscFE        fe = NULL;

    2908:   DMGetDimension(dm,&dimR);
    2909:   DMGetCoordinateDim(dm,&dimC);
    2910:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    2911:   DMPlexGetDepth(dm,&depth);
    2912:   DMGetCoordinatesLocal(dm,&coords);
    2913:   DMGetCoordinateDM(dm,&coordDM);
    2914:   if (coordDM) {
    2915:     PetscInt coordFields;

    2917:     DMGetNumFields(coordDM,&coordFields);
    2918:     if (coordFields) {
    2919:       PetscClassId id;
    2920:       PetscObject  disc;

    2922:       DMGetField(coordDM,0,&disc);
    2923:       PetscObjectGetClassId(disc,&id);
    2924:       if (id == PETSCFE_CLASSID) {
    2925:         fe = (PetscFE) disc;
    2926:       }
    2927:     }
    2928:   }
    2929:   DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
    2930:   DMPlexGetHybridBounds(dm,&cEndInterior,NULL,NULL,NULL);
    2931:   cEnd = cEndInterior > 0 ? cEndInterior : cEnd;
    2932:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    2933:   if (!fe) { /* implicit discretization: affine or multilinear */
    2934:     PetscInt  coneSize;
    2935:     PetscBool isSimplex, isTensor;

    2937:     DMPlexGetConeSize(dm,cell,&coneSize);
    2938:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    2939:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    2940:     if (isSimplex) {
    2941:       PetscReal detJ, *v0, *J, *invJ;

    2943:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    2944:       J    = &v0[dimC];
    2945:       invJ = &J[dimC * dimC];
    2946:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
    2947:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
    2948:         const PetscReal x0[3] = {-1.,-1.,-1.};

    2950:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
    2951:       }
    2952:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    2953:     } else if (isTensor) {
    2954:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    2955:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    2956:   } else {
    2957:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
    2958:   }
    2959:   return(0);
    2960: }

    2962: /*@
    2963:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

    2965:   Not collective

    2967:   Input Parameters:
    2968: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
    2969:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
    2970:                as a multilinear map for tensor-product elements
    2971: . cell       - the cell whose map is used.
    2972: . numPoints  - the number of points to locate
    2973: + refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

    2975:   Output Parameters:
    2976: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

    2978:    Level: intermediate
    2979: @*/
    2980: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
    2981: {
    2982:   PetscInt       dimC, dimR, depth, cStart, cEnd, cEndInterior, i;
    2983:   DM             coordDM = NULL;
    2984:   Vec            coords;
    2985:   PetscFE        fe = NULL;

    2990:   DMGetDimension(dm,&dimR);
    2991:   DMGetCoordinateDim(dm,&dimC);
    2992:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
    2993:   DMPlexGetDepth(dm,&depth);
    2994:   DMGetCoordinatesLocal(dm,&coords);
    2995:   DMGetCoordinateDM(dm,&coordDM);
    2996:   if (coordDM) {
    2997:     PetscInt coordFields;

    2999:     DMGetNumFields(coordDM,&coordFields);
    3000:     if (coordFields) {
    3001:       PetscClassId id;
    3002:       PetscObject  disc;

    3004:       DMGetField(coordDM,0,&disc);
    3005:       PetscObjectGetClassId(disc,&id);
    3006:       if (id == PETSCFE_CLASSID) {
    3007:         fe = (PetscFE) disc;
    3008:       }
    3009:     }
    3010:   }
    3011:   DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
    3012:   DMPlexGetHybridBounds(dm,&cEndInterior,NULL,NULL,NULL);
    3013:   cEnd = cEndInterior > 0 ? cEndInterior : cEnd;
    3014:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
    3015:   if (!fe) { /* implicit discretization: affine or multilinear */
    3016:     PetscInt  coneSize;
    3017:     PetscBool isSimplex, isTensor;

    3019:     DMPlexGetConeSize(dm,cell,&coneSize);
    3020:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
    3021:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
    3022:     if (isSimplex) {
    3023:       PetscReal detJ, *v0, *J;

    3025:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3026:       J    = &v0[dimC];
    3027:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
    3028:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
    3029:         const PetscReal xi0[3] = {-1.,-1.,-1.};

    3031:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
    3032:       }
    3033:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
    3034:     } else if (isTensor) {
    3035:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3036:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
    3037:   } else {
    3038:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
    3039:   }
    3040:   return(0);
    3041: }