xref: /petsc/src/dm/impls/plex/plexgeometry.c (revision 493de4004d8a6b5b16751267168cdab7e3bbd94a)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #undef __FUNCT__
4 #define __FUNCT__ "DMPlexGetLineIntersection_2D_Internal"
5 static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
6 {
7   const PetscReal p0_x  = segmentA[0*2+0];
8   const PetscReal p0_y  = segmentA[0*2+1];
9   const PetscReal p1_x  = segmentA[1*2+0];
10   const PetscReal p1_y  = segmentA[1*2+1];
11   const PetscReal p2_x  = segmentB[0*2+0];
12   const PetscReal p2_y  = segmentB[0*2+1];
13   const PetscReal p3_x  = segmentB[1*2+0];
14   const PetscReal p3_y  = segmentB[1*2+1];
15   const PetscReal s1_x  = p1_x - p0_x;
16   const PetscReal s1_y  = p1_y - p0_y;
17   const PetscReal s2_x  = p3_x - p2_x;
18   const PetscReal s2_y  = p3_y - p2_y;
19   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);
20 
21   PetscFunctionBegin;
22   *hasIntersection = PETSC_FALSE;
23   /* Non-parallel lines */
24   if (denom != 0.0) {
25     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
26     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;
27 
28     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
29       *hasIntersection = PETSC_TRUE;
30       if (intersection) {
31         intersection[0] = p0_x + (t * s1_x);
32         intersection[1] = p0_y + (t * s1_y);
33       }
34     }
35   }
36   PetscFunctionReturn(0);
37 }
38 
39 #undef __FUNCT__
40 #define __FUNCT__ "DMPlexLocatePoint_Simplex_2D_Internal"
41 static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
42 {
43   const PetscInt  embedDim = 2;
44   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
45   PetscReal       x        = PetscRealPart(point[0]);
46   PetscReal       y        = PetscRealPart(point[1]);
47   PetscReal       v0[2], J[4], invJ[4], detJ;
48   PetscReal       xi, eta;
49   PetscErrorCode  ierr;
50 
51   PetscFunctionBegin;
52   ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
53   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
54   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);
55 
56   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
57   else *cell = -1;
58   PetscFunctionReturn(0);
59 }
60 
61 #undef __FUNCT__
62 #define __FUNCT__ "DMPlexLocatePoint_General_2D_Internal"
63 static PetscErrorCode DMPlexLocatePoint_General_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
64 {
65   PetscSection       coordSection;
66   Vec             coordsLocal;
67   PetscScalar    *coords = NULL;
68   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
69   PetscReal       x         = PetscRealPart(point[0]);
70   PetscReal       y         = PetscRealPart(point[1]);
71   PetscInt        crossings = 0, f;
72   PetscErrorCode  ierr;
73 
74   PetscFunctionBegin;
75   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
76   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
77   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
78   for (f = 0; f < 4; ++f) {
79     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
80     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
81     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
82     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
83     PetscReal slope = (y_j - y_i) / (x_j - x_i);
84     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
85     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
86     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
87     if ((cond1 || cond2)  && above) ++crossings;
88   }
89   if (crossings % 2) *cell = c;
90   else *cell = -1;
91   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "DMPlexLocatePoint_Simplex_3D_Internal"
97 static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
98 {
99   const PetscInt embedDim = 3;
100   PetscReal      v0[3], J[9], invJ[9], detJ;
101   PetscReal      x = PetscRealPart(point[0]);
102   PetscReal      y = PetscRealPart(point[1]);
103   PetscReal      z = PetscRealPart(point[2]);
104   PetscReal      xi, eta, zeta;
105   PetscErrorCode ierr;
106 
107   PetscFunctionBegin;
108   ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
109   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
110   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
111   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);
112 
113   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
114   else *cell = -1;
115   PetscFunctionReturn(0);
116 }
117 
118 #undef __FUNCT__
119 #define __FUNCT__ "DMPlexLocatePoint_General_3D_Internal"
120 static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
121 {
122   PetscSection   coordSection;
123   Vec            coordsLocal;
124   PetscScalar   *coords;
125   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
126                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
127   PetscBool      found = PETSC_TRUE;
128   PetscInt       f;
129   PetscErrorCode ierr;
130 
131   PetscFunctionBegin;
132   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
133   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
134   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
135   for (f = 0; f < 6; ++f) {
136     /* Check the point is under plane */
137     /*   Get face normal */
138     PetscReal v_i[3];
139     PetscReal v_j[3];
140     PetscReal normal[3];
141     PetscReal pp[3];
142     PetscReal dot;
143 
144     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
145     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
146     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
147     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
148     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
149     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
150     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
151     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
152     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
153     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
154     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
155     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
156     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];
157 
158     /* Check that projected point is in face (2D location problem) */
159     if (dot < 0.0) {
160       found = PETSC_FALSE;
161       break;
162     }
163   }
164   if (found) *cell = c;
165   else *cell = -1;
166   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
167   PetscFunctionReturn(0);
168 }
169 
170 #undef __FUNCT__
171 #define __FUNCT__ "PetscGridHashInitialize_Internal"
172 static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
173 {
174   PetscInt d;
175 
176   PetscFunctionBegin;
177   box->dim = dim;
178   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
179   PetscFunctionReturn(0);
180 }
181 
182 #undef __FUNCT__
183 #define __FUNCT__ "PetscGridHashCreate"
184 PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
185 {
186   PetscErrorCode ierr;
187 
188   PetscFunctionBegin;
189   ierr = PetscMalloc1(1, box);CHKERRQ(ierr);
190   ierr = PetscGridHashInitialize_Internal(*box, dim, point);CHKERRQ(ierr);
191   PetscFunctionReturn(0);
192 }
193 
194 #undef __FUNCT__
195 #define __FUNCT__ "PetscGridHashEnlarge"
196 PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
197 {
198   PetscInt d;
199 
200   PetscFunctionBegin;
201   for (d = 0; d < box->dim; ++d) {
202     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
203     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
204   }
205   PetscFunctionReturn(0);
206 }
207 
208 #undef __FUNCT__
209 #define __FUNCT__ "PetscGridHashSetGrid"
210 PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
211 {
212   PetscInt d;
213 
214   PetscFunctionBegin;
215   for (d = 0; d < box->dim; ++d) {
216     box->extent[d] = box->upper[d] - box->lower[d];
217     if (n[d] == PETSC_DETERMINE) {
218       box->h[d] = h[d];
219       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
220     } else {
221       box->n[d] = n[d];
222       box->h[d] = box->extent[d]/n[d];
223     }
224   }
225   PetscFunctionReturn(0);
226 }
227 
228 #undef __FUNCT__
229 #define __FUNCT__ "PetscGridHashGetEnclosingBox"
230 PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
231 {
232   const PetscReal *lower = box->lower;
233   const PetscReal *upper = box->upper;
234   const PetscReal *h     = box->h;
235   const PetscInt  *n     = box->n;
236   const PetscInt   dim   = box->dim;
237   PetscInt         d, p;
238 
239   PetscFunctionBegin;
240   for (p = 0; p < numPoints; ++p) {
241     for (d = 0; d < dim; ++d) {
242       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);
243 
244       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
245       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",
246                                              p, PetscRealPart(points[p*dim+0]), dim > 1 ? PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? PetscRealPart(points[p*dim+2]) : 0.0);
247       dboxes[p*dim+d] = dbox;
248     }
249     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
250   }
251   PetscFunctionReturn(0);
252 }
253 
254 #undef __FUNCT__
255 #define __FUNCT__ "PetscGridHashDestroy"
256 PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
257 {
258   PetscErrorCode ierr;
259 
260   PetscFunctionBegin;
261   if (*box) {
262     ierr = PetscSectionDestroy(&(*box)->cellSection);CHKERRQ(ierr);
263     ierr = ISDestroy(&(*box)->cells);CHKERRQ(ierr);
264     ierr = DMLabelDestroy(&(*box)->cellsSparse);CHKERRQ(ierr);
265   }
266   ierr = PetscFree(*box);CHKERRQ(ierr);
267   PetscFunctionReturn(0);
268 }
269 
270 #undef __FUNCT__
271 #define __FUNCT__ "DMPlexLocatePoint_Internal"
272 PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
273 {
274   PetscInt       coneSize;
275   PetscErrorCode ierr;
276 
277   PetscFunctionBegin;
278   switch (dim) {
279   case 2:
280     ierr = DMPlexGetConeSize(dm, cellStart, &coneSize);CHKERRQ(ierr);
281     switch (coneSize) {
282     case 3:
283       ierr = DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
284       break;
285     case 4:
286       ierr = DMPlexLocatePoint_General_2D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
287       break;
288     default:
289       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
290     }
291     break;
292   case 3:
293     ierr = DMPlexGetConeSize(dm, cellStart, &coneSize);CHKERRQ(ierr);
294     switch (coneSize) {
295     case 4:
296       ierr = DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
297       break;
298     case 6:
299       ierr = DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
300       break;
301     default:
302       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
303     }
304     break;
305   default:
306     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %D", dim);
307   }
308   PetscFunctionReturn(0);
309 }
310 
311 #undef __FUNCT__
312 #define __FUNCT__ "DMPlexComputeGridHash_Internal"
313 PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
314 {
315   MPI_Comm           comm;
316   PetscGridHash      lbox;
317   Vec                coordinates;
318   PetscSection       coordSection;
319   Vec                coordsLocal;
320   const PetscScalar *coords;
321   PetscInt          *dboxes, *boxes;
322   PetscInt           n[3] = {10, 10, 10};
323   PetscInt           dim, N, cStart, cEnd, c, i;
324   PetscErrorCode     ierr;
325 
326   PetscFunctionBegin;
327   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
328   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
329   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
330   ierr = VecGetLocalSize(coordinates, &N);CHKERRQ(ierr);
331   ierr = VecGetArrayRead(coordinates, &coords);CHKERRQ(ierr);
332   ierr = PetscGridHashCreate(comm, dim, coords, &lbox);CHKERRQ(ierr);
333   for (i = 0; i < N; i += dim) {ierr = PetscGridHashEnlarge(lbox, &coords[i]);CHKERRQ(ierr);}
334   ierr = VecRestoreArrayRead(coordinates, &coords);CHKERRQ(ierr);
335   ierr = PetscGridHashSetGrid(lbox, n, NULL);CHKERRQ(ierr);
336 #if 0
337   /* Could define a custom reduction to merge these */
338   ierr = MPI_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);CHKERRQ(ierr);
339   ierr = MPI_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);CHKERRQ(ierr);
340 #endif
341   /* Is there a reason to snap the local bounding box to a division of the global box? */
342   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
343   /* Create label */
344   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
345   ierr = DMLabelCreate("cells", &lbox->cellsSparse);CHKERRQ(ierr);
346   ierr = DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);CHKERRQ(ierr);
347   /* Compute boxes which overlap each cell: http://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
348   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
349   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
350   ierr = PetscCalloc2((dim+1) * dim, &dboxes, dim+1, &boxes);CHKERRQ(ierr);
351   for (c = cStart; c < cEnd; ++c) {
352     const PetscReal *h       = lbox->h;
353     PetscScalar     *ccoords = NULL;
354     PetscScalar      point[3];
355     PetscInt         dlim[6], d, e, i, j, k;
356 
357     /* Find boxes enclosing each vertex */
358     ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);CHKERRQ(ierr);
359     ierr = PetscGridHashGetEnclosingBox(lbox, dim+1, ccoords, dboxes, boxes);CHKERRQ(ierr);
360     /* Mark cells containing the vertices */
361     for (e = 0; e < dim+1; ++e) {ierr = DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);CHKERRQ(ierr);}
362     /* Get grid of boxes containing these */
363     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
364     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
365     for (e = 1; e < dim+1; ++e) {
366       for (d = 0; d < dim; ++d) {
367         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
368         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
369       }
370     }
371     /* Check for intersection of box with cell */
372     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
373       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
374         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
375           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
376           PetscScalar    cpoint[3];
377           PetscInt       cell, edge, ii, jj, kk;
378 
379           /* Check whether cell contains any vertex of these subboxes TODO vectorize this */
380           for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
381             for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
382               for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {
383 
384                 ierr = DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);CHKERRQ(ierr);
385                 if (cell >= 0) {DMLabelSetValue(lbox->cellsSparse, c, box);CHKERRQ(ierr); ii = jj = kk = 2;}
386               }
387             }
388           }
389           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
390           for (edge = 0; edge < dim+1; ++edge) {
391             PetscReal segA[6], segB[6];
392 
393             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
394             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
395               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
396                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
397               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
398                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
399                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
400                 for (ii = 0; ii < 2; ++ii) {
401                   PetscBool intersects;
402 
403                   segB[0]     = PetscRealPart(point[0]);
404                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
405                   ierr = DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);CHKERRQ(ierr);
406                   if (intersects) {DMLabelSetValue(lbox->cellsSparse, c, box);CHKERRQ(ierr); edge = ii = jj = kk = dim+1;}
407                 }
408               }
409             }
410           }
411         }
412       }
413     }
414     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);CHKERRQ(ierr);
415   }
416   ierr = PetscFree2(dboxes, boxes);CHKERRQ(ierr);
417   ierr = DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);CHKERRQ(ierr);
418   ierr = DMLabelDestroy(&lbox->cellsSparse);CHKERRQ(ierr);
419   *localBox = lbox;
420   PetscFunctionReturn(0);
421 }
422 
423 #undef __FUNCT__
424 #define __FUNCT__ "DMLocatePoints_Plex"
425 /*
426  Need to implement using the guess
427 */
428 PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, IS *cellIS)
429 {
430   DM_Plex        *mesh = (DM_Plex *) dm->data;
431   PetscInt        bs, numPoints, p;
432   PetscInt        dim, cStart, cEnd, cMax, numCells, c;
433   const PetscInt *boxCells;
434   PetscInt       *cells;
435   PetscScalar    *a;
436   PetscErrorCode  ierr;
437 
438   PetscFunctionBegin;
439   if (!mesh->lbox) {ierr = DMPlexComputeGridHash_Internal(dm, &mesh->lbox);CHKERRQ(ierr);}
440   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
441   ierr = VecGetBlockSize(v, &bs);CHKERRQ(ierr);
442   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);
443   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
444   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
445   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
446   ierr = VecGetLocalSize(v, &numPoints);CHKERRQ(ierr);
447   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
448   numPoints /= bs;
449   ierr       = PetscMalloc1(numPoints, &cells);CHKERRQ(ierr);
450   /* Designate the local box for each point */
451   /* Send points to correct process */
452   /* Search cells that lie in each subbox */
453   /*   Should we bin points before doing search? */
454   ierr = ISGetIndices(mesh->lbox->cells, &boxCells);CHKERRQ(ierr);
455   for (p = 0; p < numPoints; ++p) {
456     const PetscScalar *point = &a[p*bs];
457     PetscInt           dbin[3], bin, cell, cellOffset;
458 
459     ierr = PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);CHKERRQ(ierr);
460     /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
461     ierr = PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);CHKERRQ(ierr);
462     ierr = PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);CHKERRQ(ierr);
463     for (c = cellOffset; c < cellOffset + numCells; ++c) {
464       ierr = DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);CHKERRQ(ierr);
465       if (cell >= 0) break;
466     }
467     if (cell < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Point %D not found in mesh", p);
468     cells[p] = cell;
469   }
470   ierr = ISRestoreIndices(mesh->lbox->cells, &boxCells);CHKERRQ(ierr);
471   /* Check for highest numbered proc that claims a point (do we care?) */
472   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
473   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, cells, PETSC_OWN_POINTER, cellIS);CHKERRQ(ierr);
474   PetscFunctionReturn(0);
475 }
476 
477 #undef __FUNCT__
478 #define __FUNCT__ "DMPlexComputeProjection2Dto1D_Internal"
479 /*
480   DMPlexComputeProjection2Dto1D_Internal - Rewrite coordinates to be the 1D projection of the 2D
481 */
482 PetscErrorCode DMPlexComputeProjection2Dto1D_Internal(PetscScalar coords[], PetscReal R[])
483 {
484   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
485   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
486   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;
487 
488   PetscFunctionBegin;
489   R[0] = c; R[1] = -s;
490   R[2] = s; R[3] =  c;
491   coords[0] = 0.0;
492   coords[1] = r;
493   PetscFunctionReturn(0);
494 }
495 
496 #undef __FUNCT__
497 #define __FUNCT__ "DMPlexComputeProjection3Dto1D_Internal"
498 /*
499   DMPlexComputeProjection3Dto1D_Internal - Rewrite coordinates to be the 1D projection of the 3D
500 
501   This uses the basis completion described by Frisvad,
502 
503   http://www.imm.dtu.dk/~jerf/papers/abstracts/onb.html
504   DOI:10.1080/2165347X.2012.689606
505 */
506 PetscErrorCode DMPlexComputeProjection3Dto1D_Internal(PetscScalar coords[], PetscReal R[])
507 {
508   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
509   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
510   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
511   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
512   PetscReal      rinv = 1. / r;
513   PetscFunctionBegin;
514 
515   x *= rinv; y *= rinv; z *= rinv;
516   if (x > 0.) {
517     PetscReal inv1pX   = 1./ (1. + x);
518 
519     R[0] = x; R[1] = -y;              R[2] = -z;
520     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
521     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
522   }
523   else {
524     PetscReal inv1mX   = 1./ (1. - x);
525 
526     R[0] = x; R[1] = z;               R[2] = y;
527     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
528     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
529   }
530   coords[0] = 0.0;
531   coords[1] = r;
532   PetscFunctionReturn(0);
533 }
534 
535 #undef __FUNCT__
536 #define __FUNCT__ "DMPlexComputeProjection3Dto2D_Internal"
537 /*
538   DMPlexComputeProjection3Dto2D_Internal - Rewrite coordinates to be the 2D projection of the 3D
539 */
540 PetscErrorCode DMPlexComputeProjection3Dto2D_Internal(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
541 {
542   PetscReal      x1[3],  x2[3], n[3], norm;
543   PetscReal      x1p[3], x2p[3], xnp[3];
544   PetscReal      sqrtz, alpha;
545   const PetscInt dim = 3;
546   PetscInt       d, e, p;
547 
548   PetscFunctionBegin;
549   /* 0) Calculate normal vector */
550   for (d = 0; d < dim; ++d) {
551     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
552     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
553   }
554   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
555   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
556   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
557   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
558   n[0] /= norm;
559   n[1] /= norm;
560   n[2] /= norm;
561   /* 1) Take the normal vector and rotate until it is \hat z
562 
563     Let the normal vector be <nx, ny, nz> and alpha = 1/sqrt(1 - nz^2), then
564 
565     R = /  alpha nx nz  alpha ny nz -1/alpha \
566         | -alpha ny     alpha nx        0    |
567         \     nx            ny         nz    /
568 
569     will rotate the normal vector to \hat z
570   */
571   sqrtz = PetscSqrtReal(1.0 - n[2]*n[2]);
572   /* Check for n = z */
573   if (sqrtz < 1.0e-10) {
574     if (n[2] < 0.0) {
575       if (coordSize > 9) {
576         coords[2] = PetscRealPart(coords[3*dim+0] - coords[0*dim+0]);
577         coords[3] = PetscRealPart(coords[3*dim+1] - coords[0*dim+1]);
578         coords[4] = x2[0];
579         coords[5] = x2[1];
580         coords[6] = x1[0];
581         coords[7] = x1[1];
582       } else {
583         coords[2] = x2[0];
584         coords[3] = x2[1];
585         coords[4] = x1[0];
586         coords[5] = x1[1];
587       }
588       R[0] = 1.0; R[1] = 0.0; R[2] = 0.0;
589       R[3] = 0.0; R[4] = 1.0; R[5] = 0.0;
590       R[6] = 0.0; R[7] = 0.0; R[8] = -1.0;
591     } else {
592       for (p = 3; p < coordSize/3; ++p) {
593         coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
594         coords[p*2+1] = PetscRealPart(coords[p*dim+1] - coords[0*dim+1]);
595       }
596       coords[2] = x1[0];
597       coords[3] = x1[1];
598       coords[4] = x2[0];
599       coords[5] = x2[1];
600       R[0] = 1.0; R[1] = 0.0; R[2] = 0.0;
601       R[3] = 0.0; R[4] = 1.0; R[5] = 0.0;
602       R[6] = 0.0; R[7] = 0.0; R[8] = 1.0;
603     }
604     coords[0] = 0.0;
605     coords[1] = 0.0;
606     PetscFunctionReturn(0);
607   }
608   alpha = 1.0/sqrtz;
609   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
610   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
611   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
612   for (d = 0; d < dim; ++d) {
613     x1p[d] = 0.0;
614     x2p[d] = 0.0;
615     for (e = 0; e < dim; ++e) {
616       x1p[d] += R[d*dim+e]*x1[e];
617       x2p[d] += R[d*dim+e]*x2[e];
618     }
619   }
620   if (PetscAbsReal(x1p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
621   if (PetscAbsReal(x2p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
622   /* 2) Project to (x, y) */
623   for (p = 3; p < coordSize/3; ++p) {
624     for (d = 0; d < dim; ++d) {
625       xnp[d] = 0.0;
626       for (e = 0; e < dim; ++e) {
627         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
628       }
629       if (d < dim-1) coords[p*2+d] = xnp[d];
630     }
631   }
632   coords[0] = 0.0;
633   coords[1] = 0.0;
634   coords[2] = x1p[0];
635   coords[3] = x1p[1];
636   coords[4] = x2p[0];
637   coords[5] = x2p[1];
638   /* Output R^T which rotates \hat z to the input normal */
639   for (d = 0; d < dim; ++d) {
640     for (e = d+1; e < dim; ++e) {
641       PetscReal tmp;
642 
643       tmp        = R[d*dim+e];
644       R[d*dim+e] = R[e*dim+d];
645       R[e*dim+d] = tmp;
646     }
647   }
648   PetscFunctionReturn(0);
649 }
650 
651 #undef __FUNCT__
652 #define __FUNCT__ "Volume_Triangle_Internal"
653 PETSC_UNUSED
654 PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
655 {
656   /* Signed volume is 1/2 the determinant
657 
658    |  1  1  1 |
659    | x0 x1 x2 |
660    | y0 y1 y2 |
661 
662      but if x0,y0 is the origin, we have
663 
664    | x1 x2 |
665    | y1 y2 |
666   */
667   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
668   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
669   PetscReal       M[4], detM;
670   M[0] = x1; M[1] = x2;
671   M[2] = y1; M[3] = y2;
672   DMPlex_Det2D_Internal(&detM, M);
673   *vol = 0.5*detM;
674   (void)PetscLogFlops(5.0);
675 }
676 
677 #undef __FUNCT__
678 #define __FUNCT__ "Volume_Triangle_Origin_Internal"
679 PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
680 {
681   DMPlex_Det2D_Internal(vol, coords);
682   *vol *= 0.5;
683 }
684 
685 #undef __FUNCT__
686 #define __FUNCT__ "Volume_Tetrahedron_Internal"
687 PETSC_UNUSED
688 PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
689 {
690   /* Signed volume is 1/6th of the determinant
691 
692    |  1  1  1  1 |
693    | x0 x1 x2 x3 |
694    | y0 y1 y2 y3 |
695    | z0 z1 z2 z3 |
696 
697      but if x0,y0,z0 is the origin, we have
698 
699    | x1 x2 x3 |
700    | y1 y2 y3 |
701    | z1 z2 z3 |
702   */
703   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
704   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
705   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
706   PetscReal       M[9], detM;
707   M[0] = x1; M[1] = x2; M[2] = x3;
708   M[3] = y1; M[4] = y2; M[5] = y3;
709   M[6] = z1; M[7] = z2; M[8] = z3;
710   DMPlex_Det3D_Internal(&detM, M);
711   *vol = -0.16666666666666666666666*detM;
712   (void)PetscLogFlops(10.0);
713 }
714 
715 #undef __FUNCT__
716 #define __FUNCT__ "Volume_Tetrahedron_Origin_Internal"
717 PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
718 {
719   DMPlex_Det3D_Internal(vol, coords);
720   *vol *= -0.16666666666666666666666;
721 }
722 
723 #undef __FUNCT__
724 #define __FUNCT__ "DMPlexComputeLineGeometry_Internal"
725 static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
726 {
727   PetscSection   coordSection;
728   Vec            coordinates;
729   PetscScalar   *coords = NULL;
730   PetscInt       numCoords, d;
731   PetscErrorCode ierr;
732 
733   PetscFunctionBegin;
734   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
735   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
736   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
737   *detJ = 0.0;
738   if (numCoords == 6) {
739     const PetscInt dim = 3;
740     PetscReal      R[9], J0;
741 
742     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
743     ierr = DMPlexComputeProjection3Dto1D_Internal(coords, R);CHKERRQ(ierr);
744     if (J)    {
745       J0   = 0.5*PetscRealPart(coords[1]);
746       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
747       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
748       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
749       DMPlex_Det3D_Internal(detJ, J);
750     }
751     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
752   } else if (numCoords == 4) {
753     const PetscInt dim = 2;
754     PetscReal      R[4], J0;
755 
756     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
757     ierr = DMPlexComputeProjection2Dto1D_Internal(coords, R);CHKERRQ(ierr);
758     if (J)    {
759       J0   = 0.5*PetscRealPart(coords[1]);
760       J[0] = R[0]*J0; J[1] = R[1];
761       J[2] = R[2]*J0; J[3] = R[3];
762       DMPlex_Det2D_Internal(detJ, J);
763     }
764     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
765   } else if (numCoords == 2) {
766     const PetscInt dim = 1;
767 
768     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
769     if (J)    {
770       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
771       *detJ = J[0];
772       ierr = PetscLogFlops(2.0);CHKERRQ(ierr);
773     }
774     if (invJ) {invJ[0] = 1.0/J[0]; ierr = PetscLogFlops(1.0);CHKERRQ(ierr);}
775   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
776   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
777   PetscFunctionReturn(0);
778 }
779 
780 #undef __FUNCT__
781 #define __FUNCT__ "DMPlexComputeTriangleGeometry_Internal"
782 static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
783 {
784   PetscSection   coordSection;
785   Vec            coordinates;
786   PetscScalar   *coords = NULL;
787   PetscInt       numCoords, d, f, g;
788   PetscErrorCode ierr;
789 
790   PetscFunctionBegin;
791   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
792   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
793   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
794   *detJ = 0.0;
795   if (numCoords == 9) {
796     const PetscInt dim = 3;
797     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
798 
799     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
800     ierr = DMPlexComputeProjection3Dto2D_Internal(numCoords, coords, R);CHKERRQ(ierr);
801     if (J)    {
802       const PetscInt pdim = 2;
803 
804       for (d = 0; d < pdim; d++) {
805         for (f = 0; f < pdim; f++) {
806           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
807         }
808       }
809       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
810       DMPlex_Det3D_Internal(detJ, J0);
811       for (d = 0; d < dim; d++) {
812         for (f = 0; f < dim; f++) {
813           J[d*dim+f] = 0.0;
814           for (g = 0; g < dim; g++) {
815             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
816           }
817         }
818       }
819       ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
820     }
821     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
822   } else if (numCoords == 6) {
823     const PetscInt dim = 2;
824 
825     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
826     if (J)    {
827       for (d = 0; d < dim; d++) {
828         for (f = 0; f < dim; f++) {
829           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
830         }
831       }
832       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
833       DMPlex_Det2D_Internal(detJ, J);
834     }
835     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
836   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
837   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
838   PetscFunctionReturn(0);
839 }
840 
841 #undef __FUNCT__
842 #define __FUNCT__ "DMPlexComputeRectangleGeometry_Internal"
843 static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
844 {
845   PetscSection   coordSection;
846   Vec            coordinates;
847   PetscScalar   *coords = NULL;
848   PetscInt       numCoords, d, f, g;
849   PetscErrorCode ierr;
850 
851   PetscFunctionBegin;
852   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
853   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
854   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
855   *detJ = 0.0;
856   if (numCoords == 12) {
857     const PetscInt dim = 3;
858     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
859 
860     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
861     ierr = DMPlexComputeProjection3Dto2D_Internal(numCoords, coords, R);CHKERRQ(ierr);
862     if (J)    {
863       const PetscInt pdim = 2;
864 
865       for (d = 0; d < pdim; d++) {
866         J0[d*dim+0] = 0.5*(PetscRealPart(coords[1*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
867         J0[d*dim+1] = 0.5*(PetscRealPart(coords[3*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
868       }
869       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
870       DMPlex_Det3D_Internal(detJ, J0);
871       for (d = 0; d < dim; d++) {
872         for (f = 0; f < dim; f++) {
873           J[d*dim+f] = 0.0;
874           for (g = 0; g < dim; g++) {
875             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
876           }
877         }
878       }
879       ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
880     }
881     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
882   } else if ((numCoords == 8) || (numCoords == 16)) {
883     const PetscInt dim = 2;
884 
885     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
886     if (J)    {
887       for (d = 0; d < dim; d++) {
888         J[d*dim+0] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
889         J[d*dim+1] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
890       }
891       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
892       DMPlex_Det2D_Internal(detJ, J);
893     }
894     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
895   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
896   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
897   PetscFunctionReturn(0);
898 }
899 
900 #undef __FUNCT__
901 #define __FUNCT__ "DMPlexComputeTetrahedronGeometry_Internal"
902 static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
903 {
904   PetscSection   coordSection;
905   Vec            coordinates;
906   PetscScalar   *coords = NULL;
907   const PetscInt dim = 3;
908   PetscInt       d;
909   PetscErrorCode ierr;
910 
911   PetscFunctionBegin;
912   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
913   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
914   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
915   *detJ = 0.0;
916   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
917   if (J)    {
918     for (d = 0; d < dim; d++) {
919       /* I orient with outward face normals */
920       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
921       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
922       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
923     }
924     ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
925     DMPlex_Det3D_Internal(detJ, J);
926   }
927   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
928   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
929   PetscFunctionReturn(0);
930 }
931 
932 #undef __FUNCT__
933 #define __FUNCT__ "DMPlexComputeHexahedronGeometry_Internal"
934 static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
935 {
936   PetscSection   coordSection;
937   Vec            coordinates;
938   PetscScalar   *coords = NULL;
939   const PetscInt dim = 3;
940   PetscInt       d;
941   PetscErrorCode ierr;
942 
943   PetscFunctionBegin;
944   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
945   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
946   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
947   *detJ = 0.0;
948   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
949   if (J)    {
950     for (d = 0; d < dim; d++) {
951       J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
952       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
953       J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
954     }
955     ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
956     DMPlex_Det3D_Internal(detJ, J);
957   }
958   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
959   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
960   PetscFunctionReturn(0);
961 }
962 
963 #undef __FUNCT__
964 #define __FUNCT__ "DMPlexComputeCellGeometryAffineFEM"
965 /*@C
966   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
967 
968   Collective on DM
969 
970   Input Arguments:
971 + dm   - the DM
972 - cell - the cell
973 
974   Output Arguments:
975 + v0   - the translation part of this affine transform
976 . J    - the Jacobian of the transform from the reference element
977 . invJ - the inverse of the Jacobian
978 - detJ - the Jacobian determinant
979 
980   Level: advanced
981 
982   Fortran Notes:
983   Since it returns arrays, this routine is only available in Fortran 90, and you must
984   include petsc.h90 in your code.
985 
986 .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinateVec()
987 @*/
988 PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
989 {
990   PetscInt       depth, dim, coneSize;
991   PetscErrorCode ierr;
992 
993   PetscFunctionBegin;
994   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
995   ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
996   if (depth == 1) {
997     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
998   } else {
999     DMLabel depth;
1000 
1001     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1002     ierr = DMLabelGetValue(depth, cell, &dim);CHKERRQ(ierr);
1003   }
1004   switch (dim) {
1005   case 1:
1006     ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1007     break;
1008   case 2:
1009     switch (coneSize) {
1010     case 3:
1011       ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1012       break;
1013     case 4:
1014       ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1015       break;
1016     default:
1017       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1018     }
1019     break;
1020   case 3:
1021     switch (coneSize) {
1022     case 4:
1023       ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1024       break;
1025     case 6: /* Faces */
1026     case 8: /* Vertices */
1027       ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1028       break;
1029     default:
1030         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1031     }
1032       break;
1033   default:
1034     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1035   }
1036   PetscFunctionReturn(0);
1037 }
1038 
1039 #undef __FUNCT__
1040 #define __FUNCT__ "DMPlexComputeIsoparametricGeometry_Internal"
1041 static PetscErrorCode DMPlexComputeIsoparametricGeometry_Internal(DM dm, PetscFE fe, PetscInt point, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1042 {
1043   PetscQuadrature  quad;
1044   PetscSection     coordSection;
1045   Vec              coordinates;
1046   PetscScalar     *coords = NULL;
1047   const PetscReal *quadPoints;
1048   PetscReal       *basisDer;
1049   PetscInt         dim, cdim, pdim, qdim, Nq, numCoords, d, q;
1050   PetscErrorCode   ierr;
1051 
1052   PetscFunctionBegin;
1053   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1054   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1055   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);CHKERRQ(ierr);
1056   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1057   ierr = DMGetCoordinateDim(dm, &cdim);CHKERRQ(ierr);
1058   ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1059   ierr = PetscFEGetDimension(fe, &pdim);CHKERRQ(ierr);
1060   ierr = PetscQuadratureGetData(quad, &qdim, &Nq, &quadPoints, NULL);CHKERRQ(ierr);
1061   ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
1062   *detJ = 0.0;
1063   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
1064   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);
1065   if (v0) {for (d = 0; d < cdim; d++) v0[d] = PetscRealPart(coords[d]);}
1066   if (J) {
1067     for (q = 0; q < Nq; ++q) {
1068       PetscInt i, j, k, c, r;
1069 
1070       /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
1071       for (k = 0; k < pdim; ++k)
1072         for (j = 0; j < dim; ++j)
1073           for (i = 0; i < cdim; ++i)
1074             J[(q*cdim + i)*dim + j] += basisDer[(q*pdim + k)*dim + j] * PetscRealPart(coords[k*cdim + i]);
1075       ierr = PetscLogFlops(2.0*pdim*dim*cdim);CHKERRQ(ierr);
1076       if (cdim > dim) {
1077         for (c = dim; c < cdim; ++c)
1078           for (r = 0; r < cdim; ++r)
1079             J[r*cdim+c] = r == c ? 1.0 : 0.0;
1080       }
1081       switch (cdim) {
1082       case 3:
1083         DMPlex_Det3D_Internal(detJ, J);
1084         if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1085         break;
1086       case 2:
1087         DMPlex_Det2D_Internal(detJ, J);
1088         if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1089         break;
1090       case 1:
1091         *detJ = J[0];
1092         if (invJ) invJ[0] = 1.0/J[0];
1093       }
1094     }
1095   }
1096   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);CHKERRQ(ierr);
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 #undef __FUNCT__
1101 #define __FUNCT__ "DMPlexComputeCellGeometryFEM"
1102 /*@C
1103   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
1104 
1105   Collective on DM
1106 
1107   Input Arguments:
1108 + dm   - the DM
1109 . cell - the cell
1110 - fe   - the finite element containing the quadrature
1111 
1112   Output Arguments:
1113 + v0   - the translation part of this transform
1114 . J    - the Jacobian of the transform from the reference element at each quadrature point
1115 . invJ - the inverse of the Jacobian at each quadrature point
1116 - detJ - the Jacobian determinant at each quadrature point
1117 
1118   Level: advanced
1119 
1120   Fortran Notes:
1121   Since it returns arrays, this routine is only available in Fortran 90, and you must
1122   include petsc.h90 in your code.
1123 
1124 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1125 @*/
1126 PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscFE fe, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1127 {
1128   PetscErrorCode ierr;
1129 
1130   PetscFunctionBegin;
1131   if (!fe) {ierr = DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);}
1132   else     {ierr = DMPlexComputeIsoparametricGeometry_Internal(dm, fe, cell, v0, J, invJ, detJ);CHKERRQ(ierr);}
1133   PetscFunctionReturn(0);
1134 }
1135 
1136 #undef __FUNCT__
1137 #define __FUNCT__ "DMPlexComputeGeometryFVM_1D_Internal"
1138 static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1139 {
1140   PetscSection   coordSection;
1141   Vec            coordinates;
1142   PetscScalar   *coords = NULL;
1143   PetscScalar    tmp[2];
1144   PetscInt       coordSize;
1145   PetscErrorCode ierr;
1146 
1147   PetscFunctionBegin;
1148   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1149   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1150   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1151   if (dim != 2) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "We only support 2D edges right now");
1152   ierr = DMPlexLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);CHKERRQ(ierr);
1153   if (centroid) {
1154     centroid[0] = 0.5*PetscRealPart(coords[0] + tmp[0]);
1155     centroid[1] = 0.5*PetscRealPart(coords[1] + tmp[1]);
1156   }
1157   if (normal) {
1158     PetscReal norm;
1159 
1160     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
1161     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
1162     norm       = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1]);
1163     normal[0] /= norm;
1164     normal[1] /= norm;
1165   }
1166   if (vol) {
1167     *vol = PetscSqrtReal(PetscSqr(PetscRealPart(coords[0] - tmp[0])) + PetscSqr(PetscRealPart(coords[1] - tmp[1])));
1168   }
1169   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1170   PetscFunctionReturn(0);
1171 }
1172 
1173 #undef __FUNCT__
1174 #define __FUNCT__ "DMPlexComputeGeometryFVM_2D_Internal"
1175 /* Centroid_i = (\sum_n A_n Cn_i ) / A */
1176 static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1177 {
1178   PetscSection   coordSection;
1179   Vec            coordinates;
1180   PetscScalar   *coords = NULL;
1181   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
1182   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;
1183   PetscErrorCode ierr;
1184 
1185   PetscFunctionBegin;
1186   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1187   ierr = DMPlexGetConeSize(dm, cell, &numCorners);CHKERRQ(ierr);
1188   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1189   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1190   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
1191   if (normal) {
1192     if (dim > 2) {
1193       const PetscReal x0 = PetscRealPart(coords[dim+0] - coords[0]), x1 = PetscRealPart(coords[dim*2+0] - coords[0]);
1194       const PetscReal y0 = PetscRealPart(coords[dim+1] - coords[1]), y1 = PetscRealPart(coords[dim*2+1] - coords[1]);
1195       const PetscReal z0 = PetscRealPart(coords[dim+2] - coords[2]), z1 = PetscRealPart(coords[dim*2+2] - coords[2]);
1196       PetscReal       norm;
1197 
1198       v0[0]     = PetscRealPart(coords[0]);
1199       v0[1]     = PetscRealPart(coords[1]);
1200       v0[2]     = PetscRealPart(coords[2]);
1201       normal[0] = y0*z1 - z0*y1;
1202       normal[1] = z0*x1 - x0*z1;
1203       normal[2] = x0*y1 - y0*x1;
1204       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
1205       normal[0] /= norm;
1206       normal[1] /= norm;
1207       normal[2] /= norm;
1208     } else {
1209       for (d = 0; d < dim; ++d) normal[d] = 0.0;
1210     }
1211   }
1212   if (dim == 3) {ierr = DMPlexComputeProjection3Dto2D_Internal(coordSize, coords, R);CHKERRQ(ierr);}
1213   for (p = 0; p < numCorners; ++p) {
1214     /* Need to do this copy to get types right */
1215     for (d = 0; d < tdim; ++d) {
1216       ctmp[d]      = PetscRealPart(coords[p*tdim+d]);
1217       ctmp[tdim+d] = PetscRealPart(coords[((p+1)%numCorners)*tdim+d]);
1218     }
1219     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
1220     vsum += vtmp;
1221     for (d = 0; d < tdim; ++d) {
1222       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
1223     }
1224   }
1225   for (d = 0; d < tdim; ++d) {
1226     csum[d] /= (tdim+1)*vsum;
1227   }
1228   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1229   if (vol) *vol = PetscAbsReal(vsum);
1230   if (centroid) {
1231     if (dim > 2) {
1232       for (d = 0; d < dim; ++d) {
1233         centroid[d] = v0[d];
1234         for (e = 0; e < dim; ++e) {
1235           centroid[d] += R[d*dim+e]*csum[e];
1236         }
1237       }
1238     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
1239   }
1240   PetscFunctionReturn(0);
1241 }
1242 
1243 #undef __FUNCT__
1244 #define __FUNCT__ "DMPlexComputeGeometryFVM_3D_Internal"
1245 /* Centroid_i = (\sum_n V_n Cn_i ) / V */
1246 static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1247 {
1248   PetscSection    coordSection;
1249   Vec             coordinates;
1250   PetscScalar    *coords = NULL;
1251   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
1252   const PetscInt *faces, *facesO;
1253   PetscInt        numFaces, f, coordSize, numCorners, p, d;
1254   PetscErrorCode  ierr;
1255 
1256   PetscFunctionBegin;
1257   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
1258   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1259   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1260 
1261   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
1262   ierr = DMPlexGetConeSize(dm, cell, &numFaces);CHKERRQ(ierr);
1263   ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
1264   ierr = DMPlexGetConeOrientation(dm, cell, &facesO);CHKERRQ(ierr);
1265   for (f = 0; f < numFaces; ++f) {
1266     ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
1267     numCorners = coordSize/dim;
1268     switch (numCorners) {
1269     case 3:
1270       for (d = 0; d < dim; ++d) {
1271         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1272         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1273         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
1274       }
1275       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1276       if (facesO[f] < 0) vtmp = -vtmp;
1277       vsum += vtmp;
1278       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
1279         for (d = 0; d < dim; ++d) {
1280           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1281         }
1282       }
1283       break;
1284     case 4:
1285       /* DO FOR PYRAMID */
1286       /* First tet */
1287       for (d = 0; d < dim; ++d) {
1288         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1289         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1290         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
1291       }
1292       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1293       if (facesO[f] < 0) vtmp = -vtmp;
1294       vsum += vtmp;
1295       if (centroid) {
1296         for (d = 0; d < dim; ++d) {
1297           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1298         }
1299       }
1300       /* Second tet */
1301       for (d = 0; d < dim; ++d) {
1302         coordsTmp[0*dim+d] = PetscRealPart(coords[1*dim+d]);
1303         coordsTmp[1*dim+d] = PetscRealPart(coords[2*dim+d]);
1304         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
1305       }
1306       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1307       if (facesO[f] < 0) vtmp = -vtmp;
1308       vsum += vtmp;
1309       if (centroid) {
1310         for (d = 0; d < dim; ++d) {
1311           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1312         }
1313       }
1314       break;
1315     default:
1316       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle faces with %D vertices", numCorners);
1317     }
1318     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
1319   }
1320   if (vol)     *vol = PetscAbsReal(vsum);
1321   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
1322   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
1323   PetscFunctionReturn(0);
1324 }
1325 
1326 #undef __FUNCT__
1327 #define __FUNCT__ "DMPlexComputeCellGeometryFVM"
1328 /*@C
1329   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
1330 
1331   Collective on DM
1332 
1333   Input Arguments:
1334 + dm   - the DM
1335 - cell - the cell
1336 
1337   Output Arguments:
1338 + volume   - the cell volume
1339 . centroid - the cell centroid
1340 - normal - the cell normal, if appropriate
1341 
1342   Level: advanced
1343 
1344   Fortran Notes:
1345   Since it returns arrays, this routine is only available in Fortran 90, and you must
1346   include petsc.h90 in your code.
1347 
1348 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1349 @*/
1350 PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1351 {
1352   PetscInt       depth, dim;
1353   PetscErrorCode ierr;
1354 
1355   PetscFunctionBegin;
1356   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1357   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1358   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
1359   /* We need to keep a pointer to the depth label */
1360   ierr = DMPlexGetLabelValue(dm, "depth", cell, &depth);CHKERRQ(ierr);
1361   /* Cone size is now the number of faces */
1362   switch (depth) {
1363   case 1:
1364     ierr = DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1365     break;
1366   case 2:
1367     ierr = DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1368     break;
1369   case 3:
1370     ierr = DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1371     break;
1372   default:
1373     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1374   }
1375   PetscFunctionReturn(0);
1376 }
1377 
1378 #undef __FUNCT__
1379 #define __FUNCT__ "DMPlexComputeGeometryFEM"
1380 /* This should also take a PetscFE argument I think */
1381 PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
1382 {
1383   DM             dmCell;
1384   Vec            coordinates;
1385   PetscSection   coordSection, sectionCell;
1386   PetscScalar   *cgeom;
1387   PetscInt       cStart, cEnd, cMax, c;
1388   PetscErrorCode ierr;
1389 
1390   PetscFunctionBegin;
1391   ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
1392   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1393   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1394   ierr = DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1395   ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
1396   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);CHKERRQ(ierr);
1397   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1398   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
1399   cEnd = cMax < 0 ? cEnd : cMax;
1400   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1401   /* TODO This needs to be multiplied by Nq for non-affine */
1402   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFECellGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1403   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1404   ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
1405   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1406   ierr = DMCreateLocalVector(dmCell, cellgeom);CHKERRQ(ierr);
1407   ierr = VecGetArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1408   for (c = cStart; c < cEnd; ++c) {
1409     PetscFECellGeom *cg;
1410 
1411     ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1412     ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
1413     ierr = DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v0, cg->J, cg->invJ, &cg->detJ);CHKERRQ(ierr);
1414     if (cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cg->detJ, c);
1415   }
1416   ierr = VecRestoreArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1417   ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1418   PetscFunctionReturn(0);
1419 }
1420 
1421 #undef __FUNCT__
1422 #define __FUNCT__ "DMPlexComputeGeometryFVM"
1423 /*@
1424   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
1425 
1426   Input Parameter:
1427 . dm - The DM
1428 
1429   Output Parameters:
1430 + cellgeom - A Vec of PetscFVCellGeom data
1431 . facegeom - A Vec of PetscFVFaceGeom data
1432 
1433   Level: developer
1434 
1435 .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
1436 @*/
1437 PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
1438 {
1439   DM             dmFace, dmCell;
1440   DMLabel        ghostLabel;
1441   PetscSection   sectionFace, sectionCell;
1442   PetscSection   coordSection;
1443   Vec            coordinates;
1444   PetscScalar   *fgeom, *cgeom;
1445   PetscReal      minradius, gminradius;
1446   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
1447   PetscErrorCode ierr;
1448 
1449   PetscFunctionBegin;
1450   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1451   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1452   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1453   /* Make cell centroids and volumes */
1454   ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
1455   ierr = DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1456   ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
1457   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);CHKERRQ(ierr);
1458   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1459   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1460   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1461   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1462   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1463   ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
1464   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1465   ierr = DMCreateLocalVector(dmCell, cellgeom);CHKERRQ(ierr);
1466   if (cEndInterior < 0) {
1467     cEndInterior = cEnd;
1468   }
1469   ierr = VecGetArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1470   for (c = cStart; c < cEndInterior; ++c) {
1471     PetscFVCellGeom *cg;
1472 
1473     ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1474     ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
1475     ierr = DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);CHKERRQ(ierr);
1476   }
1477   /* Compute face normals and minimum cell radius */
1478   ierr = DMClone(dm, &dmFace);CHKERRQ(ierr);
1479   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);CHKERRQ(ierr);
1480   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1481   ierr = PetscSectionSetChart(sectionFace, fStart, fEnd);CHKERRQ(ierr);
1482   for (f = fStart; f < fEnd; ++f) {ierr = PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1483   ierr = PetscSectionSetUp(sectionFace);CHKERRQ(ierr);
1484   ierr = DMSetDefaultSection(dmFace, sectionFace);CHKERRQ(ierr);
1485   ierr = PetscSectionDestroy(&sectionFace);CHKERRQ(ierr);
1486   ierr = DMCreateLocalVector(dmFace, facegeom);CHKERRQ(ierr);
1487   ierr = VecGetArray(*facegeom, &fgeom);CHKERRQ(ierr);
1488   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1489   minradius = PETSC_MAX_REAL;
1490   for (f = fStart; f < fEnd; ++f) {
1491     PetscFVFaceGeom *fg;
1492     PetscReal        area;
1493     PetscInt         ghost = -1, d, numChildren;
1494 
1495     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1496     ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
1497     if (ghost >= 0 || numChildren) continue;
1498     ierr = DMPlexPointLocalRef(dmFace, f, fgeom, &fg);CHKERRQ(ierr);
1499     ierr = DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);CHKERRQ(ierr);
1500     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
1501     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
1502     {
1503       PetscFVCellGeom *cL, *cR;
1504       PetscInt         ncells;
1505       const PetscInt  *cells;
1506       PetscReal       *lcentroid, *rcentroid;
1507       PetscReal        l[3], r[3], v[3];
1508 
1509       ierr = DMPlexGetSupport(dm, f, &cells);CHKERRQ(ierr);
1510       ierr = DMPlexGetSupportSize(dm, f, &ncells);CHKERRQ(ierr);
1511       ierr = DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);CHKERRQ(ierr);
1512       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
1513       if (ncells > 1) {
1514         ierr = DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);CHKERRQ(ierr);
1515         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
1516       }
1517       else {
1518         rcentroid = fg->centroid;
1519       }
1520       ierr = DMPlexLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);CHKERRQ(ierr);
1521       ierr = DMPlexLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);CHKERRQ(ierr);
1522       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
1523       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
1524         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
1525       }
1526       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
1527         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]);
1528         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]);
1529         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
1530       }
1531       if (cells[0] < cEndInterior) {
1532         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
1533         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
1534       }
1535       if (ncells > 1 && cells[1] < cEndInterior) {
1536         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
1537         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
1538       }
1539     }
1540   }
1541   ierr = MPI_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
1542   ierr = DMPlexSetMinRadius(dm, gminradius);CHKERRQ(ierr);
1543   /* Compute centroids of ghost cells */
1544   for (c = cEndInterior; c < cEnd; ++c) {
1545     PetscFVFaceGeom *fg;
1546     const PetscInt  *cone,    *support;
1547     PetscInt         coneSize, supportSize, s;
1548 
1549     ierr = DMPlexGetConeSize(dmCell, c, &coneSize);CHKERRQ(ierr);
1550     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
1551     ierr = DMPlexGetCone(dmCell, c, &cone);CHKERRQ(ierr);
1552     ierr = DMPlexGetSupportSize(dmCell, cone[0], &supportSize);CHKERRQ(ierr);
1553     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
1554     ierr = DMPlexGetSupport(dmCell, cone[0], &support);CHKERRQ(ierr);
1555     ierr = DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);CHKERRQ(ierr);
1556     for (s = 0; s < 2; ++s) {
1557       /* Reflect ghost centroid across plane of face */
1558       if (support[s] == c) {
1559         const PetscFVCellGeom *ci;
1560         PetscFVCellGeom       *cg;
1561         PetscReal              c2f[3], a;
1562 
1563         ierr = DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);CHKERRQ(ierr);
1564         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
1565         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
1566         ierr = DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);CHKERRQ(ierr);
1567         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
1568         cg->volume = ci->volume;
1569       }
1570     }
1571   }
1572   ierr = VecRestoreArray(*facegeom, &fgeom);CHKERRQ(ierr);
1573   ierr = VecRestoreArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1574   ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1575   ierr = DMDestroy(&dmFace);CHKERRQ(ierr);
1576   PetscFunctionReturn(0);
1577 }
1578 
1579 #undef __FUNCT__
1580 #define __FUNCT__ "DMPlexGetMinRadius"
1581 /*@C
1582   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
1583 
1584   Not collective
1585 
1586   Input Argument:
1587 . dm - the DM
1588 
1589   Output Argument:
1590 . minradius - the minium cell radius
1591 
1592   Level: developer
1593 
1594 .seealso: DMGetCoordinates()
1595 @*/
1596 PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
1597 {
1598   PetscFunctionBegin;
1599   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1600   PetscValidPointer(minradius,2);
1601   *minradius = ((DM_Plex*) dm->data)->minradius;
1602   PetscFunctionReturn(0);
1603 }
1604 
1605 #undef __FUNCT__
1606 #define __FUNCT__ "DMPlexSetMinRadius"
1607 /*@C
1608   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
1609 
1610   Logically collective
1611 
1612   Input Arguments:
1613 + dm - the DM
1614 - minradius - the minium cell radius
1615 
1616   Level: developer
1617 
1618 .seealso: DMSetCoordinates()
1619 @*/
1620 PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
1621 {
1622   PetscFunctionBegin;
1623   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1624   ((DM_Plex*) dm->data)->minradius = minradius;
1625   PetscFunctionReturn(0);
1626 }
1627 
1628 #undef __FUNCT__
1629 #define __FUNCT__ "BuildGradientReconstruction_Internal"
1630 static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
1631 {
1632   DMLabel        ghostLabel;
1633   PetscScalar   *dx, *grad, **gref;
1634   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
1635   PetscErrorCode ierr;
1636 
1637   PetscFunctionBegin;
1638   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1639   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1640   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1641   ierr = DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);CHKERRQ(ierr);
1642   ierr = PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);CHKERRQ(ierr);
1643   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1644   ierr = PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);CHKERRQ(ierr);
1645   for (c = cStart; c < cEndInterior; c++) {
1646     const PetscInt        *faces;
1647     PetscInt               numFaces, usedFaces, f, d;
1648     const PetscFVCellGeom *cg;
1649     PetscBool              boundary;
1650     PetscInt               ghost;
1651 
1652     ierr = DMPlexPointLocalRead(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1653     ierr = DMPlexGetConeSize(dm, c, &numFaces);CHKERRQ(ierr);
1654     ierr = DMPlexGetCone(dm, c, &faces);CHKERRQ(ierr);
1655     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
1656     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
1657       const PetscFVCellGeom *cg1;
1658       PetscFVFaceGeom       *fg;
1659       const PetscInt        *fcells;
1660       PetscInt               ncell, side;
1661 
1662       ierr = DMLabelGetValue(ghostLabel, faces[f], &ghost);CHKERRQ(ierr);
1663       ierr = DMPlexIsBoundaryPoint(dm, faces[f], &boundary);CHKERRQ(ierr);
1664       if ((ghost >= 0) || boundary) continue;
1665       ierr  = DMPlexGetSupport(dm, faces[f], &fcells);CHKERRQ(ierr);
1666       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
1667       ncell = fcells[!side];    /* the neighbor */
1668       ierr  = DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);CHKERRQ(ierr);
1669       ierr  = DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);CHKERRQ(ierr);
1670       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
1671       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
1672     }
1673     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
1674     ierr = PetscFVComputeGradient(fvm, usedFaces, dx, grad);CHKERRQ(ierr);
1675     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
1676       ierr = DMLabelGetValue(ghostLabel, faces[f], &ghost);CHKERRQ(ierr);
1677       ierr = DMPlexIsBoundaryPoint(dm, faces[f], &boundary);CHKERRQ(ierr);
1678       if ((ghost >= 0) || boundary) continue;
1679       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
1680       ++usedFaces;
1681     }
1682   }
1683   ierr = PetscFree3(dx, grad, gref);CHKERRQ(ierr);
1684   PetscFunctionReturn(0);
1685 }
1686 
1687 #undef __FUNCT__
1688 #define __FUNCT__ "BuildGradientReconstruction_Internal_Tree"
1689 static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
1690 {
1691   DMLabel        ghostLabel;
1692   PetscScalar   *dx, *grad, **gref;
1693   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
1694   PetscSection   neighSec;
1695   PetscInt     (*neighbors)[2];
1696   PetscInt      *counter;
1697   PetscErrorCode ierr;
1698 
1699   PetscFunctionBegin;
1700   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1701   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1702   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1703   if (cEndInterior < 0) {
1704     cEndInterior = cEnd;
1705   }
1706   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);CHKERRQ(ierr);
1707   ierr = PetscSectionSetChart(neighSec,cStart,cEndInterior);CHKERRQ(ierr);
1708   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1709   ierr = DMPlexGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1710   for (f = fStart; f < fEnd; f++) {
1711     const PetscInt        *fcells;
1712     PetscBool              boundary;
1713     PetscInt               ghost = -1;
1714     PetscInt               numChildren, numCells, c;
1715 
1716     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1717     ierr = DMPlexIsBoundaryPoint(dm, f, &boundary);CHKERRQ(ierr);
1718     ierr = DMPlexGetTreeChildren(dm, f, &numChildren, NULL);CHKERRQ(ierr);
1719     if ((ghost >= 0) || boundary || numChildren) continue;
1720     ierr = DMPlexGetSupportSize(dm, f, &numCells);CHKERRQ(ierr);
1721     if (numCells == 2) {
1722       ierr = DMPlexGetSupport(dm, f, &fcells);CHKERRQ(ierr);
1723       for (c = 0; c < 2; c++) {
1724         PetscInt cell = fcells[c];
1725 
1726         if (cell >= cStart && cell < cEndInterior) {
1727           ierr = PetscSectionAddDof(neighSec,cell,1);CHKERRQ(ierr);
1728         }
1729       }
1730     }
1731   }
1732   ierr = PetscSectionSetUp(neighSec);CHKERRQ(ierr);
1733   ierr = PetscSectionGetMaxDof(neighSec,&maxNumFaces);CHKERRQ(ierr);
1734   ierr = PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);CHKERRQ(ierr);
1735   nStart = 0;
1736   ierr = PetscSectionGetStorageSize(neighSec,&nEnd);CHKERRQ(ierr);
1737   ierr = PetscMalloc1((nEnd-nStart),&neighbors);CHKERRQ(ierr);
1738   ierr = PetscCalloc1((cEndInterior-cStart),&counter);CHKERRQ(ierr);
1739   for (f = fStart; f < fEnd; f++) {
1740     const PetscInt        *fcells;
1741     PetscBool              boundary;
1742     PetscInt               ghost = -1;
1743     PetscInt               numChildren, numCells, c;
1744 
1745     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1746     ierr = DMPlexIsBoundaryPoint(dm, f, &boundary);CHKERRQ(ierr);
1747     ierr = DMPlexGetTreeChildren(dm, f, &numChildren, NULL);CHKERRQ(ierr);
1748     if ((ghost >= 0) || boundary || numChildren) continue;
1749     ierr = DMPlexGetSupportSize(dm, f, &numCells);CHKERRQ(ierr);
1750     if (numCells == 2) {
1751       ierr  = DMPlexGetSupport(dm, f, &fcells);CHKERRQ(ierr);
1752       for (c = 0; c < 2; c++) {
1753         PetscInt cell = fcells[c], off;
1754 
1755         if (cell >= cStart && cell < cEndInterior) {
1756           ierr = PetscSectionGetOffset(neighSec,cell,&off);CHKERRQ(ierr);
1757           off += counter[cell - cStart]++;
1758           neighbors[off][0] = f;
1759           neighbors[off][1] = fcells[1 - c];
1760         }
1761       }
1762     }
1763   }
1764   ierr = PetscFree(counter);CHKERRQ(ierr);
1765   ierr = PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);CHKERRQ(ierr);
1766   for (c = cStart; c < cEndInterior; c++) {
1767     PetscInt               numFaces, f, d, off, ghost = -1;
1768     const PetscFVCellGeom *cg;
1769 
1770     ierr = DMPlexPointLocalRead(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1771     ierr = PetscSectionGetDof(neighSec, c, &numFaces);CHKERRQ(ierr);
1772     ierr = PetscSectionGetOffset(neighSec, c, &off);CHKERRQ(ierr);
1773     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, c, &ghost);CHKERRQ(ierr);}
1774     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);
1775     for (f = 0; f < numFaces; ++f) {
1776       const PetscFVCellGeom *cg1;
1777       PetscFVFaceGeom       *fg;
1778       const PetscInt        *fcells;
1779       PetscInt               ncell, side, nface;
1780 
1781       nface = neighbors[off + f][0];
1782       ncell = neighbors[off + f][1];
1783       ierr  = DMPlexGetSupport(dm,nface,&fcells);CHKERRQ(ierr);
1784       side  = (c != fcells[0]);
1785       ierr  = DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);CHKERRQ(ierr);
1786       ierr  = DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);CHKERRQ(ierr);
1787       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
1788       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
1789     }
1790     ierr = PetscFVComputeGradient(fvm, numFaces, dx, grad);CHKERRQ(ierr);
1791     for (f = 0; f < numFaces; ++f) {
1792       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
1793     }
1794   }
1795   ierr = PetscFree3(dx, grad, gref);CHKERRQ(ierr);
1796   ierr = PetscSectionDestroy(&neighSec);CHKERRQ(ierr);
1797   ierr = PetscFree(neighbors);CHKERRQ(ierr);
1798   PetscFunctionReturn(0);
1799 }
1800 
1801 #undef __FUNCT__
1802 #define __FUNCT__ "DMPlexComputeGradientFVM"
1803 /*@
1804   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
1805 
1806   Collective on DM
1807 
1808   Input Arguments:
1809 + dm  - The DM
1810 . fvm - The PetscFV
1811 . faceGeometry - The face geometry from DMPlexGetFaceGeometryFVM()
1812 - cellGeometry - The face geometry from DMPlexGetCellGeometryFVM()
1813 
1814   Output Parameters:
1815 + faceGeometry - The geometric factors for gradient calculation are inserted
1816 - dmGrad - The DM describing the layout of gradient data
1817 
1818   Level: developer
1819 
1820 .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
1821 @*/
1822 PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
1823 {
1824   DM             dmFace, dmCell;
1825   PetscScalar   *fgeom, *cgeom;
1826   PetscSection   sectionGrad, parentSection;
1827   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;
1828   PetscErrorCode ierr;
1829 
1830   PetscFunctionBegin;
1831   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1832   ierr = PetscFVGetNumComponents(fvm, &pdim);CHKERRQ(ierr);
1833   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1834   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1835   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
1836   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1837   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1838   ierr = VecGetArray(faceGeometry, &fgeom);CHKERRQ(ierr);
1839   ierr = VecGetArray(cellGeometry, &cgeom);CHKERRQ(ierr);
1840   ierr = DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1841   if (!parentSection) {
1842     ierr = BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
1843   }
1844   else {
1845     ierr = BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
1846   }
1847   ierr = VecRestoreArray(faceGeometry, &fgeom);CHKERRQ(ierr);
1848   ierr = VecRestoreArray(cellGeometry, &cgeom);CHKERRQ(ierr);
1849   /* Create storage for gradients */
1850   ierr = DMClone(dm, dmGrad);CHKERRQ(ierr);
1851   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);CHKERRQ(ierr);
1852   ierr = PetscSectionSetChart(sectionGrad, cStart, cEnd);CHKERRQ(ierr);
1853   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionGrad, c, pdim*dim);CHKERRQ(ierr);}
1854   ierr = PetscSectionSetUp(sectionGrad);CHKERRQ(ierr);
1855   ierr = DMSetDefaultSection(*dmGrad, sectionGrad);CHKERRQ(ierr);
1856   ierr = PetscSectionDestroy(&sectionGrad);CHKERRQ(ierr);
1857   PetscFunctionReturn(0);
1858 }
1859