xref: /petsc/src/dm/impls/plex/plexgeometry.c (revision 4fc747eaadbeca11629f314a99edccbc2ed7b3d3)
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__ "DMPlexClosestPoint_Simplex_2D_Internal"
63 static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
64 {
65   const PetscInt  embedDim = 2;
66   PetscReal       x        = PetscRealPart(point[0]);
67   PetscReal       y        = PetscRealPart(point[1]);
68   PetscReal       v0[2], J[4], invJ[4], detJ;
69   PetscReal       xi, eta, r;
70   PetscErrorCode  ierr;
71 
72   PetscFunctionBegin;
73   ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
74   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
75   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);
76 
77   xi  = PetscMax(xi,  0.0);
78   eta = PetscMax(eta, 0.0);
79   r   = (xi + eta)/2.0;
80   if (xi + eta > 2.0) {
81     r    = (xi + eta)/2.0;
82     xi  /= r;
83     eta /= r;
84   }
85   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
86   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
87   PetscFunctionReturn(0);
88 }
89 
90 #undef __FUNCT__
91 #define __FUNCT__ "DMPlexLocatePoint_General_2D_Internal"
92 static PetscErrorCode DMPlexLocatePoint_General_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
93 {
94   PetscSection       coordSection;
95   Vec             coordsLocal;
96   PetscScalar    *coords = NULL;
97   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
98   PetscReal       x         = PetscRealPart(point[0]);
99   PetscReal       y         = PetscRealPart(point[1]);
100   PetscInt        crossings = 0, f;
101   PetscErrorCode  ierr;
102 
103   PetscFunctionBegin;
104   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
105   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
106   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
107   for (f = 0; f < 4; ++f) {
108     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
109     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
110     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
111     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
112     PetscReal slope = (y_j - y_i) / (x_j - x_i);
113     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
114     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
115     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
116     if ((cond1 || cond2)  && above) ++crossings;
117   }
118   if (crossings % 2) *cell = c;
119   else *cell = -1;
120   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
121   PetscFunctionReturn(0);
122 }
123 
124 #undef __FUNCT__
125 #define __FUNCT__ "DMPlexLocatePoint_Simplex_3D_Internal"
126 static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
127 {
128   const PetscInt embedDim = 3;
129   PetscReal      v0[3], J[9], invJ[9], detJ;
130   PetscReal      x = PetscRealPart(point[0]);
131   PetscReal      y = PetscRealPart(point[1]);
132   PetscReal      z = PetscRealPart(point[2]);
133   PetscReal      xi, eta, zeta;
134   PetscErrorCode ierr;
135 
136   PetscFunctionBegin;
137   ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
138   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
139   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
140   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);
141 
142   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
143   else *cell = -1;
144   PetscFunctionReturn(0);
145 }
146 
147 #undef __FUNCT__
148 #define __FUNCT__ "DMPlexLocatePoint_General_3D_Internal"
149 static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
150 {
151   PetscSection   coordSection;
152   Vec            coordsLocal;
153   PetscScalar   *coords;
154   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
155                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
156   PetscBool      found = PETSC_TRUE;
157   PetscInt       f;
158   PetscErrorCode ierr;
159 
160   PetscFunctionBegin;
161   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
162   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
163   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
164   for (f = 0; f < 6; ++f) {
165     /* Check the point is under plane */
166     /*   Get face normal */
167     PetscReal v_i[3];
168     PetscReal v_j[3];
169     PetscReal normal[3];
170     PetscReal pp[3];
171     PetscReal dot;
172 
173     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
174     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
175     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
176     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
177     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
178     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
179     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
180     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
181     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
182     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
183     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
184     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
185     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];
186 
187     /* Check that projected point is in face (2D location problem) */
188     if (dot < 0.0) {
189       found = PETSC_FALSE;
190       break;
191     }
192   }
193   if (found) *cell = c;
194   else *cell = -1;
195   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
196   PetscFunctionReturn(0);
197 }
198 
199 #undef __FUNCT__
200 #define __FUNCT__ "PetscGridHashInitialize_Internal"
201 static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
202 {
203   PetscInt d;
204 
205   PetscFunctionBegin;
206   box->dim = dim;
207   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
208   PetscFunctionReturn(0);
209 }
210 
211 #undef __FUNCT__
212 #define __FUNCT__ "PetscGridHashCreate"
213 PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
214 {
215   PetscErrorCode ierr;
216 
217   PetscFunctionBegin;
218   ierr = PetscMalloc1(1, box);CHKERRQ(ierr);
219   ierr = PetscGridHashInitialize_Internal(*box, dim, point);CHKERRQ(ierr);
220   PetscFunctionReturn(0);
221 }
222 
223 #undef __FUNCT__
224 #define __FUNCT__ "PetscGridHashEnlarge"
225 PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
226 {
227   PetscInt d;
228 
229   PetscFunctionBegin;
230   for (d = 0; d < box->dim; ++d) {
231     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
232     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
233   }
234   PetscFunctionReturn(0);
235 }
236 
237 #undef __FUNCT__
238 #define __FUNCT__ "PetscGridHashSetGrid"
239 /*
240   PetscGridHashSetGrid - Divide the grid into boxes
241 
242   Not collective
243 
244   Input Parameters:
245 + box - The grid hash object
246 . n   - The number of boxes in each dimension, or PETSC_DETERMINE
247 - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE
248 
249   Level: developer
250 
251 .seealso: PetscGridHashCreate()
252 */
253 PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
254 {
255   PetscInt d;
256 
257   PetscFunctionBegin;
258   for (d = 0; d < box->dim; ++d) {
259     box->extent[d] = box->upper[d] - box->lower[d];
260     if (n[d] == PETSC_DETERMINE) {
261       box->h[d] = h[d];
262       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
263     } else {
264       box->n[d] = n[d];
265       box->h[d] = box->extent[d]/n[d];
266     }
267   }
268   PetscFunctionReturn(0);
269 }
270 
271 #undef __FUNCT__
272 #define __FUNCT__ "PetscGridHashGetEnclosingBox"
273 /*
274   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point
275 
276   Not collective
277 
278   Input Parameters:
279 + box       - The grid hash object
280 . numPoints - The number of input points
281 - points    - The input point coordinates
282 
283   Output Parameters:
284 + dboxes    - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
285 - boxes     - An array of numPoints integers expressing the enclosing box as single number, or NULL
286 
287   Level: developer
288 
289 .seealso: PetscGridHashCreate()
290 */
291 PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
292 {
293   const PetscReal *lower = box->lower;
294   const PetscReal *upper = box->upper;
295   const PetscReal *h     = box->h;
296   const PetscInt  *n     = box->n;
297   const PetscInt   dim   = box->dim;
298   PetscInt         d, p;
299 
300   PetscFunctionBegin;
301   for (p = 0; p < numPoints; ++p) {
302     for (d = 0; d < dim; ++d) {
303       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);
304 
305       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
306       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",
307                                              p, PetscRealPart(points[p*dim+0]), dim > 1 ? PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? PetscRealPart(points[p*dim+2]) : 0.0);
308       dboxes[p*dim+d] = dbox;
309     }
310     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
311   }
312   PetscFunctionReturn(0);
313 }
314 
315 #undef __FUNCT__
316 #define __FUNCT__ "PetscGridHashDestroy"
317 PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
318 {
319   PetscErrorCode ierr;
320 
321   PetscFunctionBegin;
322   if (*box) {
323     ierr = PetscSectionDestroy(&(*box)->cellSection);CHKERRQ(ierr);
324     ierr = ISDestroy(&(*box)->cells);CHKERRQ(ierr);
325     ierr = DMLabelDestroy(&(*box)->cellsSparse);CHKERRQ(ierr);
326   }
327   ierr = PetscFree(*box);CHKERRQ(ierr);
328   PetscFunctionReturn(0);
329 }
330 
331 #undef __FUNCT__
332 #define __FUNCT__ "DMPlexLocatePoint_Internal"
333 PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
334 {
335   PetscInt       coneSize;
336   PetscErrorCode ierr;
337 
338   PetscFunctionBegin;
339   switch (dim) {
340   case 2:
341     ierr = DMPlexGetConeSize(dm, cellStart, &coneSize);CHKERRQ(ierr);
342     switch (coneSize) {
343     case 3:
344       ierr = DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
345       break;
346     case 4:
347       ierr = DMPlexLocatePoint_General_2D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
348       break;
349     default:
350       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
351     }
352     break;
353   case 3:
354     ierr = DMPlexGetConeSize(dm, cellStart, &coneSize);CHKERRQ(ierr);
355     switch (coneSize) {
356     case 4:
357       ierr = DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
358       break;
359     case 6:
360       ierr = DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
361       break;
362     default:
363       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
364     }
365     break;
366   default:
367     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %D", dim);
368   }
369   PetscFunctionReturn(0);
370 }
371 
372 #undef __FUNCT__
373 #define __FUNCT__ "DMPlexClosestPoint_Internal"
374 /*
375   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
376 */
377 PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
378 {
379   PetscInt       coneSize;
380   PetscErrorCode ierr;
381 
382   PetscFunctionBegin;
383   switch (dim) {
384   case 2:
385     ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
386     switch (coneSize) {
387     case 3:
388       ierr = DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);CHKERRQ(ierr);
389       break;
390 #if 0
391     case 4:
392       ierr = DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);CHKERRQ(ierr);
393       break;
394 #endif
395     default:
396       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell with cone size %D", coneSize);
397     }
398     break;
399 #if 0
400   case 3:
401     ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
402     switch (coneSize) {
403     case 4:
404       ierr = DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);CHKERRQ(ierr);
405       break;
406     case 6:
407       ierr = DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);CHKERRQ(ierr);
408       break;
409     default:
410       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell with cone size %D", coneSize);
411     }
412     break;
413 #endif
414   default:
415     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for mesh dimension %D", dim);
416   }
417   PetscFunctionReturn(0);
418 }
419 
420 #undef __FUNCT__
421 #define __FUNCT__ "DMPlexComputeGridHash_Internal"
422 /*
423   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex
424 
425   Collective on DM
426 
427   Input Parameter:
428 . dm - The Plex
429 
430   Output Parameter:
431 . localBox - The grid hash object
432 
433   Level: developer
434 
435 .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
436 */
437 PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
438 {
439   MPI_Comm           comm;
440   PetscGridHash      lbox;
441   Vec                coordinates;
442   PetscSection       coordSection;
443   Vec                coordsLocal;
444   const PetscScalar *coords;
445   PetscInt          *dboxes, *boxes;
446   PetscInt           n[3] = {10, 10, 10};
447   PetscInt           dim, N, cStart, cEnd, cMax, c, i;
448   PetscErrorCode     ierr;
449 
450   PetscFunctionBegin;
451   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
452   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
453   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
454   if (dim != 2) SETERRQ(comm, PETSC_ERR_SUP, "I have only coded this for 2D");
455   ierr = VecGetLocalSize(coordinates, &N);CHKERRQ(ierr);
456   ierr = VecGetArrayRead(coordinates, &coords);CHKERRQ(ierr);
457   ierr = PetscGridHashCreate(comm, dim, coords, &lbox);CHKERRQ(ierr);
458   for (i = 0; i < N; i += dim) {ierr = PetscGridHashEnlarge(lbox, &coords[i]);CHKERRQ(ierr);}
459   ierr = VecRestoreArrayRead(coordinates, &coords);CHKERRQ(ierr);
460   ierr = PetscGridHashSetGrid(lbox, n, NULL);CHKERRQ(ierr);
461 #if 0
462   /* Could define a custom reduction to merge these */
463   ierr = MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);CHKERRQ(ierr);
464   ierr = MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);CHKERRQ(ierr);
465 #endif
466   /* Is there a reason to snap the local bounding box to a division of the global box? */
467   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
468   /* Create label */
469   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
470   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
471   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
472   ierr = DMLabelCreate("cells", &lbox->cellsSparse);CHKERRQ(ierr);
473   ierr = DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);CHKERRQ(ierr);
474   /* Compute boxes which overlap each cell: http://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
475   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
476   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
477   ierr = PetscCalloc2(16 * dim, &dboxes, 16, &boxes);CHKERRQ(ierr);
478   for (c = cStart; c < cEnd; ++c) {
479     const PetscReal *h       = lbox->h;
480     PetscScalar     *ccoords = NULL;
481     PetscInt         csize   = 0;
482     PetscScalar      point[3];
483     PetscInt         dlim[6], d, e, i, j, k;
484 
485     /* Find boxes enclosing each vertex */
486     ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);CHKERRQ(ierr);
487     ierr = PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);CHKERRQ(ierr);
488     /* Mark cells containing the vertices */
489     for (e = 0; e < csize/dim; ++e) {ierr = DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);CHKERRQ(ierr);}
490     /* Get grid of boxes containing these */
491     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
492     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
493     for (e = 1; e < dim+1; ++e) {
494       for (d = 0; d < dim; ++d) {
495         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
496         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
497       }
498     }
499     /* Check for intersection of box with cell */
500     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
501       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
502         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
503           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
504           PetscScalar    cpoint[3];
505           PetscInt       cell, edge, ii, jj, kk;
506 
507           /* Check whether cell contains any vertex of these subboxes TODO vectorize this */
508           for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
509             for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
510               for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {
511 
512                 ierr = DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);CHKERRQ(ierr);
513                 if (cell >= 0) {DMLabelSetValue(lbox->cellsSparse, c, box);CHKERRQ(ierr); ii = jj = kk = 2;}
514               }
515             }
516           }
517           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
518           for (edge = 0; edge < dim+1; ++edge) {
519             PetscReal segA[6], segB[6];
520 
521             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
522             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
523               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
524                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
525               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
526                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
527                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
528                 for (ii = 0; ii < 2; ++ii) {
529                   PetscBool intersects;
530 
531                   segB[0]     = PetscRealPart(point[0]);
532                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
533                   ierr = DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);CHKERRQ(ierr);
534                   if (intersects) {DMLabelSetValue(lbox->cellsSparse, c, box);CHKERRQ(ierr); edge = ii = jj = kk = dim+1;}
535                 }
536               }
537             }
538           }
539         }
540       }
541     }
542     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);CHKERRQ(ierr);
543   }
544   ierr = PetscFree2(dboxes, boxes);CHKERRQ(ierr);
545   ierr = DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);CHKERRQ(ierr);
546   ierr = DMLabelDestroy(&lbox->cellsSparse);CHKERRQ(ierr);
547   *localBox = lbox;
548   PetscFunctionReturn(0);
549 }
550 
551 #undef __FUNCT__
552 #define __FUNCT__ "DMLocatePoints_Plex"
553 PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
554 {
555   DM_Plex        *mesh = (DM_Plex *) dm->data;
556   PetscBool       hash = mesh->useHashLocation;
557   PetscInt        bs, numPoints, p, numFound, *found = NULL;
558   PetscInt        dim, cStart, cEnd, cMax, numCells, c;
559   const PetscInt *boxCells;
560   PetscSFNode    *cells;
561   PetscScalar    *a;
562   PetscMPIInt     result;
563   PetscErrorCode  ierr;
564 
565   PetscFunctionBegin;
566   if (ltype == DM_POINTLOCATION_NEAREST && !hash) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing.");
567   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
568   ierr = VecGetBlockSize(v, &bs);CHKERRQ(ierr);
569   ierr = MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);CHKERRQ(ierr);
570   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
571   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);
572   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
573   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
574   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
575   ierr = VecGetLocalSize(v, &numPoints);CHKERRQ(ierr);
576   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
577   numPoints /= bs;
578   ierr = PetscMalloc1(numPoints, &cells);CHKERRQ(ierr);
579   if (hash) {
580     if (!mesh->lbox) {ierr = PetscInfo(dm, "Initializing grid hashing");CHKERRQ(ierr);ierr = DMPlexComputeGridHash_Internal(dm, &mesh->lbox);CHKERRQ(ierr);}
581     /* Designate the local box for each point */
582     /* Send points to correct process */
583     /* Search cells that lie in each subbox */
584     /*   Should we bin points before doing search? */
585     ierr = ISGetIndices(mesh->lbox->cells, &boxCells);CHKERRQ(ierr);
586   }
587   for (p = 0, numFound = 0; p < numPoints; ++p) {
588     const PetscScalar *point = &a[p*bs];
589     PetscInt           dbin[3], bin, cell = -1, cellOffset;
590 
591     cells[p].rank  = -1;
592     cells[p].index = -1;
593     if (hash) {
594       ierr = PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);CHKERRQ(ierr);
595       /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
596       ierr = PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);CHKERRQ(ierr);
597       ierr = PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);CHKERRQ(ierr);
598       for (c = cellOffset; c < cellOffset + numCells; ++c) {
599         ierr = DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);CHKERRQ(ierr);
600         if (cell >= 0) {
601           cells[p].rank = 0;
602           cells[p].index = cell;
603           numFound++;
604           break;
605         }
606       }
607     } else {
608       for (c = cStart; c < cEnd; ++c) {
609         ierr = DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);CHKERRQ(ierr);
610         if (cell >= 0) {
611           cells[p].rank = 0;
612           cells[p].index = cell;
613           numFound++;
614           break;
615         }
616       }
617     }
618   }
619   if (hash) {ierr = ISRestoreIndices(mesh->lbox->cells, &boxCells);CHKERRQ(ierr);}
620   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
621     for (p = 0; p < numPoints; p++) {
622       const PetscScalar *point = &a[p*bs];
623       PetscReal          cpoint[3], diff[3], dist, distMax = PETSC_MAX_REAL;
624       PetscInt           dbin[3], bin, cellOffset, d;
625 
626       if (cells[p].rank < 0) {
627         ++numFound;
628         ierr = PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);CHKERRQ(ierr);
629         ierr = PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);CHKERRQ(ierr);
630         ierr = PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);CHKERRQ(ierr);
631         for (c = cellOffset; c < cellOffset + numCells; ++c) {
632           ierr = DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);CHKERRQ(ierr);
633           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
634           dist = DMPlex_NormD_Internal(dim, diff);
635           if (dist < distMax) {
636             for (d = 0; d < dim; ++d) a[p*bs+d] = cpoint[d];
637             cells[p].rank  = 0;
638             cells[p].index = boxCells[c];
639             distMax = dist;
640             break;
641           }
642         }
643       }
644     }
645   }
646   /* This code is only be relevant when interfaced to parallel point location */
647   /* Check for highest numbered proc that claims a point (do we care?) */
648   if (numFound < numPoints) {
649     if (ltype == DM_POINTLOCATION_NEAREST) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Nearest point location does not support parallel point location.");
650     ierr = PetscMalloc1(numFound,&found);CHKERRQ(ierr);
651     for (p = 0, numFound = 0; p < numPoints; p++) {
652       if (cells[p].rank >= 0 && cells[p].index >= 0) {
653         if (numFound < p) {
654           cells[numFound] = cells[p];
655         }
656         found[numFound++] = p;
657       }
658     }
659   }
660   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
661   ierr = PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);CHKERRQ(ierr);
662   PetscFunctionReturn(0);
663 }
664 
665 #undef __FUNCT__
666 #define __FUNCT__ "DMPlexComputeProjection2Dto1D"
667 /*@C
668   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates
669 
670   Not collective
671 
672   Input Parameter:
673 . coords - The coordinates of a segment
674 
675   Output Parameters:
676 + coords - The new y-coordinate, and 0 for x
677 - R - The rotation which accomplishes the projection
678 
679   Level: developer
680 
681 .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
682 @*/
683 PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
684 {
685   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
686   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
687   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;
688 
689   PetscFunctionBegin;
690   R[0] = c; R[1] = -s;
691   R[2] = s; R[3] =  c;
692   coords[0] = 0.0;
693   coords[1] = r;
694   PetscFunctionReturn(0);
695 }
696 
697 #undef __FUNCT__
698 #define __FUNCT__ "DMPlexComputeProjection3Dto1D"
699 /*@C
700   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates
701 
702   Not collective
703 
704   Input Parameter:
705 . coords - The coordinates of a segment
706 
707   Output Parameters:
708 + coords - The new y-coordinate, and 0 for x and z
709 - R - The rotation which accomplishes the projection
710 
711   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
712 
713   Level: developer
714 
715 .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
716 @*/
717 PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
718 {
719   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
720   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
721   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
722   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
723   PetscReal      rinv = 1. / r;
724   PetscFunctionBegin;
725 
726   x *= rinv; y *= rinv; z *= rinv;
727   if (x > 0.) {
728     PetscReal inv1pX   = 1./ (1. + x);
729 
730     R[0] = x; R[1] = -y;              R[2] = -z;
731     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
732     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
733   }
734   else {
735     PetscReal inv1mX   = 1./ (1. - x);
736 
737     R[0] = x; R[1] = z;               R[2] = y;
738     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
739     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
740   }
741   coords[0] = 0.0;
742   coords[1] = r;
743   PetscFunctionReturn(0);
744 }
745 
746 #undef __FUNCT__
747 #define __FUNCT__ "DMPlexComputeProjection3Dto2D"
748 /*@
749   DMPlexComputeProjection3Dto2D - Rewrite coordinates to be the 2D projection of the 3D coordinates
750 
751   Not collective
752 
753   Input Parameter:
754 . coords - The coordinates of a segment
755 
756   Output Parameters:
757 + coords - The new y- and z-coordinates, and 0 for x
758 - R - The rotation which accomplishes the projection
759 
760   Level: developer
761 
762 .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
763 @*/
764 PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
765 {
766   PetscReal      x1[3],  x2[3], n[3], norm;
767   PetscReal      x1p[3], x2p[3], xnp[3];
768   PetscReal      sqrtz, alpha;
769   const PetscInt dim = 3;
770   PetscInt       d, e, p;
771 
772   PetscFunctionBegin;
773   /* 0) Calculate normal vector */
774   for (d = 0; d < dim; ++d) {
775     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
776     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
777   }
778   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
779   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
780   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
781   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
782   n[0] /= norm;
783   n[1] /= norm;
784   n[2] /= norm;
785   /* 1) Take the normal vector and rotate until it is \hat z
786 
787     Let the normal vector be <nx, ny, nz> and alpha = 1/sqrt(1 - nz^2), then
788 
789     R = /  alpha nx nz  alpha ny nz -1/alpha \
790         | -alpha ny     alpha nx        0    |
791         \     nx            ny         nz    /
792 
793     will rotate the normal vector to \hat z
794   */
795   sqrtz = PetscSqrtReal(1.0 - n[2]*n[2]);
796   /* Check for n = z */
797   if (sqrtz < 1.0e-10) {
798     const PetscInt s = PetscSign(n[2]);
799     /* If nz < 0, rotate 180 degrees around x-axis */
800     for (p = 3; p < coordSize/3; ++p) {
801       coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
802       coords[p*2+1] = (PetscRealPart(coords[p*dim+1] - coords[0*dim+1])) * s;
803     }
804     coords[0] = 0.0;
805     coords[1] = 0.0;
806     coords[2] = x1[0];
807     coords[3] = x1[1] * s;
808     coords[4] = x2[0];
809     coords[5] = x2[1] * s;
810     R[0] = 1.0;     R[1] = 0.0;     R[2] = 0.0;
811     R[3] = 0.0;     R[4] = 1.0 * s; R[5] = 0.0;
812     R[6] = 0.0;     R[7] = 0.0;     R[8] = 1.0 * s;
813     PetscFunctionReturn(0);
814   }
815   alpha = 1.0/sqrtz;
816   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
817   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
818   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
819   for (d = 0; d < dim; ++d) {
820     x1p[d] = 0.0;
821     x2p[d] = 0.0;
822     for (e = 0; e < dim; ++e) {
823       x1p[d] += R[d*dim+e]*x1[e];
824       x2p[d] += R[d*dim+e]*x2[e];
825     }
826   }
827   if (PetscAbsReal(x1p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
828   if (PetscAbsReal(x2p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
829   /* 2) Project to (x, y) */
830   for (p = 3; p < coordSize/3; ++p) {
831     for (d = 0; d < dim; ++d) {
832       xnp[d] = 0.0;
833       for (e = 0; e < dim; ++e) {
834         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
835       }
836       if (d < dim-1) coords[p*2+d] = xnp[d];
837     }
838   }
839   coords[0] = 0.0;
840   coords[1] = 0.0;
841   coords[2] = x1p[0];
842   coords[3] = x1p[1];
843   coords[4] = x2p[0];
844   coords[5] = x2p[1];
845   /* Output R^T which rotates \hat z to the input normal */
846   for (d = 0; d < dim; ++d) {
847     for (e = d+1; e < dim; ++e) {
848       PetscReal tmp;
849 
850       tmp        = R[d*dim+e];
851       R[d*dim+e] = R[e*dim+d];
852       R[e*dim+d] = tmp;
853     }
854   }
855   PetscFunctionReturn(0);
856 }
857 
858 #undef __FUNCT__
859 #define __FUNCT__ "Volume_Triangle_Internal"
860 PETSC_UNUSED
861 PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
862 {
863   /* Signed volume is 1/2 the determinant
864 
865    |  1  1  1 |
866    | x0 x1 x2 |
867    | y0 y1 y2 |
868 
869      but if x0,y0 is the origin, we have
870 
871    | x1 x2 |
872    | y1 y2 |
873   */
874   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
875   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
876   PetscReal       M[4], detM;
877   M[0] = x1; M[1] = x2;
878   M[2] = y1; M[3] = y2;
879   DMPlex_Det2D_Internal(&detM, M);
880   *vol = 0.5*detM;
881   (void)PetscLogFlops(5.0);
882 }
883 
884 #undef __FUNCT__
885 #define __FUNCT__ "Volume_Triangle_Origin_Internal"
886 PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
887 {
888   DMPlex_Det2D_Internal(vol, coords);
889   *vol *= 0.5;
890 }
891 
892 #undef __FUNCT__
893 #define __FUNCT__ "Volume_Tetrahedron_Internal"
894 PETSC_UNUSED
895 PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
896 {
897   /* Signed volume is 1/6th of the determinant
898 
899    |  1  1  1  1 |
900    | x0 x1 x2 x3 |
901    | y0 y1 y2 y3 |
902    | z0 z1 z2 z3 |
903 
904      but if x0,y0,z0 is the origin, we have
905 
906    | x1 x2 x3 |
907    | y1 y2 y3 |
908    | z1 z2 z3 |
909   */
910   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
911   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
912   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
913   PetscReal       M[9], detM;
914   M[0] = x1; M[1] = x2; M[2] = x3;
915   M[3] = y1; M[4] = y2; M[5] = y3;
916   M[6] = z1; M[7] = z2; M[8] = z3;
917   DMPlex_Det3D_Internal(&detM, M);
918   *vol = -0.16666666666666666666666*detM;
919   (void)PetscLogFlops(10.0);
920 }
921 
922 #undef __FUNCT__
923 #define __FUNCT__ "Volume_Tetrahedron_Origin_Internal"
924 PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
925 {
926   DMPlex_Det3D_Internal(vol, coords);
927   *vol *= -0.16666666666666666666666;
928 }
929 
930 #undef __FUNCT__
931 #define __FUNCT__ "DMPlexComputeLineGeometry_Internal"
932 static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
933 {
934   PetscSection   coordSection;
935   Vec            coordinates;
936   PetscScalar   *coords = NULL;
937   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;
938   PetscErrorCode ierr;
939 
940   PetscFunctionBegin;
941   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
942   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
943   ierr = PetscSectionGetChart(coordSection,&pStart,&pEnd);CHKERRQ(ierr);
944   if (e >= pStart && e < pEnd) {ierr = PetscSectionGetDof(coordSection,e,&numSelfCoords);CHKERRQ(ierr);}
945   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
946   numCoords = numSelfCoords ? numSelfCoords : numCoords;
947   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
948   *detJ = 0.0;
949   if (numCoords == 6) {
950     const PetscInt dim = 3;
951     PetscReal      R[9], J0;
952 
953     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
954     ierr = DMPlexComputeProjection3Dto1D(coords, R);CHKERRQ(ierr);
955     if (J)    {
956       J0   = 0.5*PetscRealPart(coords[1]);
957       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
958       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
959       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
960       DMPlex_Det3D_Internal(detJ, J);
961       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
962     }
963   } else if (numCoords == 4) {
964     const PetscInt dim = 2;
965     PetscReal      R[4], J0;
966 
967     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
968     ierr = DMPlexComputeProjection2Dto1D(coords, R);CHKERRQ(ierr);
969     if (J)    {
970       J0   = 0.5*PetscRealPart(coords[1]);
971       J[0] = R[0]*J0; J[1] = R[1];
972       J[2] = R[2]*J0; J[3] = R[3];
973       DMPlex_Det2D_Internal(detJ, J);
974       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
975     }
976   } else if (numCoords == 2) {
977     const PetscInt dim = 1;
978 
979     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
980     if (J)    {
981       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
982       *detJ = J[0];
983       ierr = PetscLogFlops(2.0);CHKERRQ(ierr);
984       if (invJ) {invJ[0] = 1.0/J[0]; ierr = PetscLogFlops(1.0);CHKERRQ(ierr);}
985     }
986   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
987   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
988   PetscFunctionReturn(0);
989 }
990 
991 #undef __FUNCT__
992 #define __FUNCT__ "DMPlexComputeTriangleGeometry_Internal"
993 static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
994 {
995   PetscSection   coordSection;
996   Vec            coordinates;
997   PetscScalar   *coords = NULL;
998   PetscInt       numCoords, d, f, g;
999   PetscErrorCode ierr;
1000 
1001   PetscFunctionBegin;
1002   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1003   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1004   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
1005   *detJ = 0.0;
1006   if (numCoords == 9) {
1007     const PetscInt dim = 3;
1008     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
1009 
1010     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1011     ierr = DMPlexComputeProjection3Dto2D(numCoords, coords, R);CHKERRQ(ierr);
1012     if (J)    {
1013       const PetscInt pdim = 2;
1014 
1015       for (d = 0; d < pdim; d++) {
1016         for (f = 0; f < pdim; f++) {
1017           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
1018         }
1019       }
1020       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
1021       DMPlex_Det3D_Internal(detJ, J0);
1022       for (d = 0; d < dim; d++) {
1023         for (f = 0; f < dim; f++) {
1024           J[d*dim+f] = 0.0;
1025           for (g = 0; g < dim; g++) {
1026             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
1027           }
1028         }
1029       }
1030       ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
1031     }
1032     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1033   } else if (numCoords == 6) {
1034     const PetscInt dim = 2;
1035 
1036     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1037     if (J)    {
1038       for (d = 0; d < dim; d++) {
1039         for (f = 0; f < dim; f++) {
1040           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
1041         }
1042       }
1043       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
1044       DMPlex_Det2D_Internal(detJ, J);
1045     }
1046     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1047   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
1048   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
1049   PetscFunctionReturn(0);
1050 }
1051 
1052 #undef __FUNCT__
1053 #define __FUNCT__ "DMPlexComputeRectangleGeometry_Internal"
1054 static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1055 {
1056   PetscSection   coordSection;
1057   Vec            coordinates;
1058   PetscScalar   *coords = NULL;
1059   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;
1060   PetscErrorCode ierr;
1061 
1062   PetscFunctionBegin;
1063   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1064   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1065   ierr = PetscSectionGetChart(coordSection,&pStart,&pEnd);CHKERRQ(ierr);
1066   if (e >= pStart && e < pEnd) {ierr = PetscSectionGetDof(coordSection,e,&numSelfCoords);CHKERRQ(ierr);}
1067   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
1068   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1069   *detJ = 0.0;
1070   if (numCoords == 12) {
1071     const PetscInt dim = 3;
1072     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
1073 
1074     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1075     ierr = DMPlexComputeProjection3Dto2D(numCoords, coords, R);CHKERRQ(ierr);
1076     if (J)    {
1077       const PetscInt pdim = 2;
1078 
1079       for (d = 0; d < pdim; d++) {
1080         J0[d*dim+0] = 0.5*(PetscRealPart(coords[1*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
1081         J0[d*dim+1] = 0.5*(PetscRealPart(coords[3*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
1082       }
1083       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
1084       DMPlex_Det3D_Internal(detJ, J0);
1085       for (d = 0; d < dim; d++) {
1086         for (f = 0; f < dim; f++) {
1087           J[d*dim+f] = 0.0;
1088           for (g = 0; g < dim; g++) {
1089             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
1090           }
1091         }
1092       }
1093       ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
1094     }
1095     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1096   } else if (numCoords == 8) {
1097     const PetscInt dim = 2;
1098 
1099     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1100     if (J)    {
1101       for (d = 0; d < dim; d++) {
1102         J[d*dim+0] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1103         J[d*dim+1] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1104       }
1105       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
1106       DMPlex_Det2D_Internal(detJ, J);
1107     }
1108     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1109   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
1110   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 #undef __FUNCT__
1115 #define __FUNCT__ "DMPlexComputeTetrahedronGeometry_Internal"
1116 static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1117 {
1118   PetscSection   coordSection;
1119   Vec            coordinates;
1120   PetscScalar   *coords = NULL;
1121   const PetscInt dim = 3;
1122   PetscInt       d;
1123   PetscErrorCode ierr;
1124 
1125   PetscFunctionBegin;
1126   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1127   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1128   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
1129   *detJ = 0.0;
1130   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1131   if (J)    {
1132     for (d = 0; d < dim; d++) {
1133       /* I orient with outward face normals */
1134       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
1135       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1136       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1137     }
1138     ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
1139     DMPlex_Det3D_Internal(detJ, J);
1140   }
1141   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1142   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
1143   PetscFunctionReturn(0);
1144 }
1145 
1146 #undef __FUNCT__
1147 #define __FUNCT__ "DMPlexComputeHexahedronGeometry_Internal"
1148 static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1149 {
1150   PetscSection   coordSection;
1151   Vec            coordinates;
1152   PetscScalar   *coords = NULL;
1153   const PetscInt dim = 3;
1154   PetscInt       d;
1155   PetscErrorCode ierr;
1156 
1157   PetscFunctionBegin;
1158   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1159   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1160   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
1161   *detJ = 0.0;
1162   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1163   if (J)    {
1164     for (d = 0; d < dim; d++) {
1165       J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1166       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1167       J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
1168     }
1169     ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
1170     DMPlex_Det3D_Internal(detJ, J);
1171   }
1172   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1173   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
1174   PetscFunctionReturn(0);
1175 }
1176 
1177 #undef __FUNCT__
1178 #define __FUNCT__ "DMPlexComputeCellGeometryAffineFEM"
1179 /*@C
1180   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
1181 
1182   Collective on DM
1183 
1184   Input Arguments:
1185 + dm   - the DM
1186 - cell - the cell
1187 
1188   Output Arguments:
1189 + v0   - the translation part of this affine transform
1190 . J    - the Jacobian of the transform from the reference element
1191 . invJ - the inverse of the Jacobian
1192 - detJ - the Jacobian determinant
1193 
1194   Level: advanced
1195 
1196   Fortran Notes:
1197   Since it returns arrays, this routine is only available in Fortran 90, and you must
1198   include petsc.h90 in your code.
1199 
1200 .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinateVec()
1201 @*/
1202 PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1203 {
1204   PetscInt       depth, dim, coneSize;
1205   PetscErrorCode ierr;
1206 
1207   PetscFunctionBegin;
1208   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1209   ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
1210   if (depth == 1) {
1211     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1212   } else {
1213     DMLabel depth;
1214 
1215     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1216     ierr = DMLabelGetValue(depth, cell, &dim);CHKERRQ(ierr);
1217   }
1218   switch (dim) {
1219   case 1:
1220     ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1221     break;
1222   case 2:
1223     switch (coneSize) {
1224     case 3:
1225       ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1226       break;
1227     case 4:
1228       ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1229       break;
1230     default:
1231       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1232     }
1233     break;
1234   case 3:
1235     switch (coneSize) {
1236     case 4:
1237       ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1238       break;
1239     case 6: /* Faces */
1240     case 8: /* Vertices */
1241       ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1242       break;
1243     default:
1244         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1245     }
1246       break;
1247   default:
1248     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1249   }
1250   PetscFunctionReturn(0);
1251 }
1252 
1253 #undef __FUNCT__
1254 #define __FUNCT__ "DMPlexComputeIsoparametricGeometry_Internal"
1255 static PetscErrorCode DMPlexComputeIsoparametricGeometry_Internal(DM dm, PetscFE fe, PetscInt point, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1256 {
1257   PetscQuadrature  quad;
1258   PetscSection     coordSection;
1259   Vec              coordinates;
1260   PetscScalar     *coords = NULL;
1261   const PetscReal *quadPoints;
1262   PetscReal       *basisDer;
1263   PetscInt         dim, cdim, pdim, qdim, Nq, numCoords, d, q;
1264   PetscErrorCode   ierr;
1265 
1266   PetscFunctionBegin;
1267   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1268   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1269   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);CHKERRQ(ierr);
1270   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1271   ierr = DMGetCoordinateDim(dm, &cdim);CHKERRQ(ierr);
1272   ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1273   ierr = PetscFEGetDimension(fe, &pdim);CHKERRQ(ierr);
1274   ierr = PetscQuadratureGetData(quad, &qdim, &Nq, &quadPoints, NULL);CHKERRQ(ierr);
1275   ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
1276   *detJ = 0.0;
1277   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
1278   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);
1279   if (v0) {for (d = 0; d < cdim; d++) v0[d] = PetscRealPart(coords[d]);}
1280   if (J) {
1281     ierr = PetscMemzero(J, Nq*cdim*dim*sizeof(PetscReal));CHKERRQ(ierr);
1282     for (q = 0; q < Nq; ++q) {
1283       PetscInt i, j, k, c, r;
1284 
1285       /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
1286       for (k = 0; k < pdim; ++k)
1287         for (j = 0; j < dim; ++j)
1288           for (i = 0; i < cdim; ++i)
1289             J[(q*cdim + i)*dim + j] += basisDer[(q*pdim + k)*dim + j] * PetscRealPart(coords[k*cdim + i]);
1290       ierr = PetscLogFlops(2.0*pdim*dim*cdim);CHKERRQ(ierr);
1291       if (cdim > dim) {
1292         for (c = dim; c < cdim; ++c)
1293           for (r = 0; r < cdim; ++r)
1294             J[r*cdim+c] = r == c ? 1.0 : 0.0;
1295       }
1296       switch (cdim) {
1297       case 3:
1298         DMPlex_Det3D_Internal(detJ, J);
1299         if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1300         break;
1301       case 2:
1302         DMPlex_Det2D_Internal(detJ, J);
1303         if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1304         break;
1305       case 1:
1306         *detJ = J[0];
1307         if (invJ) invJ[0] = 1.0/J[0];
1308       }
1309     }
1310   }
1311   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);CHKERRQ(ierr);
1312   PetscFunctionReturn(0);
1313 }
1314 
1315 #undef __FUNCT__
1316 #define __FUNCT__ "DMPlexComputeCellGeometryFEM"
1317 /*@C
1318   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
1319 
1320   Collective on DM
1321 
1322   Input Arguments:
1323 + dm   - the DM
1324 . cell - the cell
1325 - fe   - the finite element containing the quadrature
1326 
1327   Output Arguments:
1328 + v0   - the translation part of this transform
1329 . J    - the Jacobian of the transform from the reference element at each quadrature point
1330 . invJ - the inverse of the Jacobian at each quadrature point
1331 - detJ - the Jacobian determinant at each quadrature point
1332 
1333   Level: advanced
1334 
1335   Fortran Notes:
1336   Since it returns arrays, this routine is only available in Fortran 90, and you must
1337   include petsc.h90 in your code.
1338 
1339 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1340 @*/
1341 PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscFE fe, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1342 {
1343   PetscErrorCode ierr;
1344 
1345   PetscFunctionBegin;
1346   if (!fe) {ierr = DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);}
1347   else     {ierr = DMPlexComputeIsoparametricGeometry_Internal(dm, fe, cell, v0, J, invJ, detJ);CHKERRQ(ierr);}
1348   PetscFunctionReturn(0);
1349 }
1350 
1351 #undef __FUNCT__
1352 #define __FUNCT__ "DMPlexComputeGeometryFVM_1D_Internal"
1353 static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1354 {
1355   PetscSection   coordSection;
1356   Vec            coordinates;
1357   PetscScalar   *coords = NULL;
1358   PetscScalar    tmp[2];
1359   PetscInt       coordSize;
1360   PetscErrorCode ierr;
1361 
1362   PetscFunctionBegin;
1363   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1364   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1365   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1366   if (dim != 2) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "We only support 2D edges right now");
1367   ierr = DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);CHKERRQ(ierr);
1368   if (centroid) {
1369     centroid[0] = 0.5*PetscRealPart(coords[0] + tmp[0]);
1370     centroid[1] = 0.5*PetscRealPart(coords[1] + tmp[1]);
1371   }
1372   if (normal) {
1373     PetscReal norm;
1374 
1375     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
1376     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
1377     norm       = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1]);
1378     normal[0] /= norm;
1379     normal[1] /= norm;
1380   }
1381   if (vol) {
1382     *vol = PetscSqrtReal(PetscSqr(PetscRealPart(coords[0] - tmp[0])) + PetscSqr(PetscRealPart(coords[1] - tmp[1])));
1383   }
1384   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1385   PetscFunctionReturn(0);
1386 }
1387 
1388 #undef __FUNCT__
1389 #define __FUNCT__ "DMPlexComputeGeometryFVM_2D_Internal"
1390 /* Centroid_i = (\sum_n A_n Cn_i ) / A */
1391 static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1392 {
1393   PetscSection   coordSection;
1394   Vec            coordinates;
1395   PetscScalar   *coords = NULL;
1396   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
1397   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;
1398   PetscErrorCode ierr;
1399 
1400   PetscFunctionBegin;
1401   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1402   ierr = DMPlexGetConeSize(dm, cell, &numCorners);CHKERRQ(ierr);
1403   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1404   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1405   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
1406   if (dim > 2 && centroid) {
1407     v0[0] = PetscRealPart(coords[0]);
1408     v0[1] = PetscRealPart(coords[1]);
1409     v0[2] = PetscRealPart(coords[2]);
1410   }
1411   if (normal) {
1412     if (dim > 2) {
1413       const PetscReal x0 = PetscRealPart(coords[dim+0] - coords[0]), x1 = PetscRealPart(coords[dim*2+0] - coords[0]);
1414       const PetscReal y0 = PetscRealPart(coords[dim+1] - coords[1]), y1 = PetscRealPart(coords[dim*2+1] - coords[1]);
1415       const PetscReal z0 = PetscRealPart(coords[dim+2] - coords[2]), z1 = PetscRealPart(coords[dim*2+2] - coords[2]);
1416       PetscReal       norm;
1417 
1418       normal[0] = y0*z1 - z0*y1;
1419       normal[1] = z0*x1 - x0*z1;
1420       normal[2] = x0*y1 - y0*x1;
1421       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
1422       normal[0] /= norm;
1423       normal[1] /= norm;
1424       normal[2] /= norm;
1425     } else {
1426       for (d = 0; d < dim; ++d) normal[d] = 0.0;
1427     }
1428   }
1429   if (dim == 3) {ierr = DMPlexComputeProjection3Dto2D(coordSize, coords, R);CHKERRQ(ierr);}
1430   for (p = 0; p < numCorners; ++p) {
1431     /* Need to do this copy to get types right */
1432     for (d = 0; d < tdim; ++d) {
1433       ctmp[d]      = PetscRealPart(coords[p*tdim+d]);
1434       ctmp[tdim+d] = PetscRealPart(coords[((p+1)%numCorners)*tdim+d]);
1435     }
1436     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
1437     vsum += vtmp;
1438     for (d = 0; d < tdim; ++d) {
1439       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
1440     }
1441   }
1442   for (d = 0; d < tdim; ++d) {
1443     csum[d] /= (tdim+1)*vsum;
1444   }
1445   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1446   if (vol) *vol = PetscAbsReal(vsum);
1447   if (centroid) {
1448     if (dim > 2) {
1449       for (d = 0; d < dim; ++d) {
1450         centroid[d] = v0[d];
1451         for (e = 0; e < dim; ++e) {
1452           centroid[d] += R[d*dim+e]*csum[e];
1453         }
1454       }
1455     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
1456   }
1457   PetscFunctionReturn(0);
1458 }
1459 
1460 #undef __FUNCT__
1461 #define __FUNCT__ "DMPlexComputeGeometryFVM_3D_Internal"
1462 /* Centroid_i = (\sum_n V_n Cn_i ) / V */
1463 static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1464 {
1465   PetscSection    coordSection;
1466   Vec             coordinates;
1467   PetscScalar    *coords = NULL;
1468   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
1469   const PetscInt *faces, *facesO;
1470   PetscInt        numFaces, f, coordSize, numCorners, p, d;
1471   PetscErrorCode  ierr;
1472 
1473   PetscFunctionBegin;
1474   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
1475   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1476   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1477 
1478   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
1479   ierr = DMPlexGetConeSize(dm, cell, &numFaces);CHKERRQ(ierr);
1480   ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
1481   ierr = DMPlexGetConeOrientation(dm, cell, &facesO);CHKERRQ(ierr);
1482   for (f = 0; f < numFaces; ++f) {
1483     ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
1484     numCorners = coordSize/dim;
1485     switch (numCorners) {
1486     case 3:
1487       for (d = 0; d < dim; ++d) {
1488         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1489         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1490         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
1491       }
1492       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1493       if (facesO[f] < 0) vtmp = -vtmp;
1494       vsum += vtmp;
1495       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
1496         for (d = 0; d < dim; ++d) {
1497           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1498         }
1499       }
1500       break;
1501     case 4:
1502       /* DO FOR PYRAMID */
1503       /* First tet */
1504       for (d = 0; d < dim; ++d) {
1505         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1506         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1507         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
1508       }
1509       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1510       if (facesO[f] < 0) vtmp = -vtmp;
1511       vsum += vtmp;
1512       if (centroid) {
1513         for (d = 0; d < dim; ++d) {
1514           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1515         }
1516       }
1517       /* Second tet */
1518       for (d = 0; d < dim; ++d) {
1519         coordsTmp[0*dim+d] = PetscRealPart(coords[1*dim+d]);
1520         coordsTmp[1*dim+d] = PetscRealPart(coords[2*dim+d]);
1521         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
1522       }
1523       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1524       if (facesO[f] < 0) vtmp = -vtmp;
1525       vsum += vtmp;
1526       if (centroid) {
1527         for (d = 0; d < dim; ++d) {
1528           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1529         }
1530       }
1531       break;
1532     default:
1533       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle faces with %D vertices", numCorners);
1534     }
1535     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
1536   }
1537   if (vol)     *vol = PetscAbsReal(vsum);
1538   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
1539   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
1540   PetscFunctionReturn(0);
1541 }
1542 
1543 #undef __FUNCT__
1544 #define __FUNCT__ "DMPlexComputeCellGeometryFVM"
1545 /*@C
1546   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
1547 
1548   Collective on DM
1549 
1550   Input Arguments:
1551 + dm   - the DM
1552 - cell - the cell
1553 
1554   Output Arguments:
1555 + volume   - the cell volume
1556 . centroid - the cell centroid
1557 - normal - the cell normal, if appropriate
1558 
1559   Level: advanced
1560 
1561   Fortran Notes:
1562   Since it returns arrays, this routine is only available in Fortran 90, and you must
1563   include petsc.h90 in your code.
1564 
1565 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1566 @*/
1567 PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1568 {
1569   PetscInt       depth, dim;
1570   PetscErrorCode ierr;
1571 
1572   PetscFunctionBegin;
1573   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1574   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1575   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
1576   /* We need to keep a pointer to the depth label */
1577   ierr = DMGetLabelValue(dm, "depth", cell, &depth);CHKERRQ(ierr);
1578   /* Cone size is now the number of faces */
1579   switch (depth) {
1580   case 1:
1581     ierr = DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1582     break;
1583   case 2:
1584     ierr = DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1585     break;
1586   case 3:
1587     ierr = DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1588     break;
1589   default:
1590     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1591   }
1592   PetscFunctionReturn(0);
1593 }
1594 
1595 #undef __FUNCT__
1596 #define __FUNCT__ "DMPlexComputeGeometryFEM"
1597 /* This should also take a PetscFE argument I think */
1598 PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
1599 {
1600   DM             dmCell;
1601   Vec            coordinates;
1602   PetscSection   coordSection, sectionCell;
1603   PetscScalar   *cgeom;
1604   PetscInt       cStart, cEnd, cMax, c;
1605   PetscErrorCode ierr;
1606 
1607   PetscFunctionBegin;
1608   ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
1609   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1610   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1611   ierr = DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1612   ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
1613   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);CHKERRQ(ierr);
1614   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1615   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
1616   cEnd = cMax < 0 ? cEnd : cMax;
1617   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1618   /* TODO This needs to be multiplied by Nq for non-affine */
1619   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFECellGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1620   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1621   ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
1622   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1623   ierr = DMCreateLocalVector(dmCell, cellgeom);CHKERRQ(ierr);
1624   ierr = VecGetArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1625   for (c = cStart; c < cEnd; ++c) {
1626     PetscFECellGeom *cg;
1627 
1628     ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1629     ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
1630     ierr = DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v0, cg->J, cg->invJ, &cg->detJ);CHKERRQ(ierr);
1631     if (cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cg->detJ, c);
1632   }
1633   ierr = VecRestoreArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1634   ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1635   PetscFunctionReturn(0);
1636 }
1637 
1638 #undef __FUNCT__
1639 #define __FUNCT__ "DMPlexComputeGeometryFVM"
1640 /*@
1641   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
1642 
1643   Input Parameter:
1644 . dm - The DM
1645 
1646   Output Parameters:
1647 + cellgeom - A Vec of PetscFVCellGeom data
1648 . facegeom - A Vec of PetscFVFaceGeom data
1649 
1650   Level: developer
1651 
1652 .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
1653 @*/
1654 PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
1655 {
1656   DM             dmFace, dmCell;
1657   DMLabel        ghostLabel;
1658   PetscSection   sectionFace, sectionCell;
1659   PetscSection   coordSection;
1660   Vec            coordinates;
1661   PetscScalar   *fgeom, *cgeom;
1662   PetscReal      minradius, gminradius;
1663   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
1664   PetscErrorCode ierr;
1665 
1666   PetscFunctionBegin;
1667   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1668   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1669   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1670   /* Make cell centroids and volumes */
1671   ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
1672   ierr = DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1673   ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
1674   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);CHKERRQ(ierr);
1675   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1676   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1677   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1678   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1679   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1680   ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
1681   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1682   ierr = DMCreateLocalVector(dmCell, cellgeom);CHKERRQ(ierr);
1683   if (cEndInterior < 0) {
1684     cEndInterior = cEnd;
1685   }
1686   ierr = VecGetArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1687   for (c = cStart; c < cEndInterior; ++c) {
1688     PetscFVCellGeom *cg;
1689 
1690     ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1691     ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
1692     ierr = DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);CHKERRQ(ierr);
1693   }
1694   /* Compute face normals and minimum cell radius */
1695   ierr = DMClone(dm, &dmFace);CHKERRQ(ierr);
1696   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);CHKERRQ(ierr);
1697   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1698   ierr = PetscSectionSetChart(sectionFace, fStart, fEnd);CHKERRQ(ierr);
1699   for (f = fStart; f < fEnd; ++f) {ierr = PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1700   ierr = PetscSectionSetUp(sectionFace);CHKERRQ(ierr);
1701   ierr = DMSetDefaultSection(dmFace, sectionFace);CHKERRQ(ierr);
1702   ierr = PetscSectionDestroy(&sectionFace);CHKERRQ(ierr);
1703   ierr = DMCreateLocalVector(dmFace, facegeom);CHKERRQ(ierr);
1704   ierr = VecGetArray(*facegeom, &fgeom);CHKERRQ(ierr);
1705   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1706   minradius = PETSC_MAX_REAL;
1707   for (f = fStart; f < fEnd; ++f) {
1708     PetscFVFaceGeom *fg;
1709     PetscReal        area;
1710     PetscInt         ghost = -1, d, numChildren;
1711 
1712     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1713     ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
1714     if (ghost >= 0 || numChildren) continue;
1715     ierr = DMPlexPointLocalRef(dmFace, f, fgeom, &fg);CHKERRQ(ierr);
1716     ierr = DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);CHKERRQ(ierr);
1717     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
1718     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
1719     {
1720       PetscFVCellGeom *cL, *cR;
1721       PetscInt         ncells;
1722       const PetscInt  *cells;
1723       PetscReal       *lcentroid, *rcentroid;
1724       PetscReal        l[3], r[3], v[3];
1725 
1726       ierr = DMPlexGetSupport(dm, f, &cells);CHKERRQ(ierr);
1727       ierr = DMPlexGetSupportSize(dm, f, &ncells);CHKERRQ(ierr);
1728       ierr = DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);CHKERRQ(ierr);
1729       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
1730       if (ncells > 1) {
1731         ierr = DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);CHKERRQ(ierr);
1732         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
1733       }
1734       else {
1735         rcentroid = fg->centroid;
1736       }
1737       ierr = DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);CHKERRQ(ierr);
1738       ierr = DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);CHKERRQ(ierr);
1739       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
1740       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
1741         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
1742       }
1743       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
1744         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]);
1745         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]);
1746         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
1747       }
1748       if (cells[0] < cEndInterior) {
1749         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
1750         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
1751       }
1752       if (ncells > 1 && cells[1] < cEndInterior) {
1753         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
1754         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
1755       }
1756     }
1757   }
1758   ierr = MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
1759   ierr = DMPlexSetMinRadius(dm, gminradius);CHKERRQ(ierr);
1760   /* Compute centroids of ghost cells */
1761   for (c = cEndInterior; c < cEnd; ++c) {
1762     PetscFVFaceGeom *fg;
1763     const PetscInt  *cone,    *support;
1764     PetscInt         coneSize, supportSize, s;
1765 
1766     ierr = DMPlexGetConeSize(dmCell, c, &coneSize);CHKERRQ(ierr);
1767     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
1768     ierr = DMPlexGetCone(dmCell, c, &cone);CHKERRQ(ierr);
1769     ierr = DMPlexGetSupportSize(dmCell, cone[0], &supportSize);CHKERRQ(ierr);
1770     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
1771     ierr = DMPlexGetSupport(dmCell, cone[0], &support);CHKERRQ(ierr);
1772     ierr = DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);CHKERRQ(ierr);
1773     for (s = 0; s < 2; ++s) {
1774       /* Reflect ghost centroid across plane of face */
1775       if (support[s] == c) {
1776         PetscFVCellGeom       *ci;
1777         PetscFVCellGeom       *cg;
1778         PetscReal              c2f[3], a;
1779 
1780         ierr = DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);CHKERRQ(ierr);
1781         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
1782         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
1783         ierr = DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);CHKERRQ(ierr);
1784         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
1785         cg->volume = ci->volume;
1786       }
1787     }
1788   }
1789   ierr = VecRestoreArray(*facegeom, &fgeom);CHKERRQ(ierr);
1790   ierr = VecRestoreArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1791   ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1792   ierr = DMDestroy(&dmFace);CHKERRQ(ierr);
1793   PetscFunctionReturn(0);
1794 }
1795 
1796 #undef __FUNCT__
1797 #define __FUNCT__ "DMPlexGetMinRadius"
1798 /*@C
1799   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
1800 
1801   Not collective
1802 
1803   Input Argument:
1804 . dm - the DM
1805 
1806   Output Argument:
1807 . minradius - the minium cell radius
1808 
1809   Level: developer
1810 
1811 .seealso: DMGetCoordinates()
1812 @*/
1813 PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
1814 {
1815   PetscFunctionBegin;
1816   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1817   PetscValidPointer(minradius,2);
1818   *minradius = ((DM_Plex*) dm->data)->minradius;
1819   PetscFunctionReturn(0);
1820 }
1821 
1822 #undef __FUNCT__
1823 #define __FUNCT__ "DMPlexSetMinRadius"
1824 /*@C
1825   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
1826 
1827   Logically collective
1828 
1829   Input Arguments:
1830 + dm - the DM
1831 - minradius - the minium cell radius
1832 
1833   Level: developer
1834 
1835 .seealso: DMSetCoordinates()
1836 @*/
1837 PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
1838 {
1839   PetscFunctionBegin;
1840   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1841   ((DM_Plex*) dm->data)->minradius = minradius;
1842   PetscFunctionReturn(0);
1843 }
1844 
1845 #undef __FUNCT__
1846 #define __FUNCT__ "BuildGradientReconstruction_Internal"
1847 static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
1848 {
1849   DMLabel        ghostLabel;
1850   PetscScalar   *dx, *grad, **gref;
1851   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
1852   PetscErrorCode ierr;
1853 
1854   PetscFunctionBegin;
1855   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1856   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1857   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1858   ierr = DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);CHKERRQ(ierr);
1859   ierr = PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);CHKERRQ(ierr);
1860   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1861   ierr = PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);CHKERRQ(ierr);
1862   for (c = cStart; c < cEndInterior; c++) {
1863     const PetscInt        *faces;
1864     PetscInt               numFaces, usedFaces, f, d;
1865     PetscFVCellGeom        *cg;
1866     PetscBool              boundary;
1867     PetscInt               ghost;
1868 
1869     ierr = DMPlexPointLocalRead(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1870     ierr = DMPlexGetConeSize(dm, c, &numFaces);CHKERRQ(ierr);
1871     ierr = DMPlexGetCone(dm, c, &faces);CHKERRQ(ierr);
1872     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
1873     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
1874       PetscFVCellGeom       *cg1;
1875       PetscFVFaceGeom       *fg;
1876       const PetscInt        *fcells;
1877       PetscInt               ncell, side;
1878 
1879       ierr = DMLabelGetValue(ghostLabel, faces[f], &ghost);CHKERRQ(ierr);
1880       ierr = DMIsBoundaryPoint(dm, faces[f], &boundary);CHKERRQ(ierr);
1881       if ((ghost >= 0) || boundary) continue;
1882       ierr  = DMPlexGetSupport(dm, faces[f], &fcells);CHKERRQ(ierr);
1883       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
1884       ncell = fcells[!side];    /* the neighbor */
1885       ierr  = DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);CHKERRQ(ierr);
1886       ierr  = DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);CHKERRQ(ierr);
1887       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
1888       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
1889     }
1890     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
1891     ierr = PetscFVComputeGradient(fvm, usedFaces, dx, grad);CHKERRQ(ierr);
1892     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
1893       ierr = DMLabelGetValue(ghostLabel, faces[f], &ghost);CHKERRQ(ierr);
1894       ierr = DMIsBoundaryPoint(dm, faces[f], &boundary);CHKERRQ(ierr);
1895       if ((ghost >= 0) || boundary) continue;
1896       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
1897       ++usedFaces;
1898     }
1899   }
1900   ierr = PetscFree3(dx, grad, gref);CHKERRQ(ierr);
1901   PetscFunctionReturn(0);
1902 }
1903 
1904 #undef __FUNCT__
1905 #define __FUNCT__ "BuildGradientReconstruction_Internal_Tree"
1906 static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
1907 {
1908   DMLabel        ghostLabel;
1909   PetscScalar   *dx, *grad, **gref;
1910   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
1911   PetscSection   neighSec;
1912   PetscInt     (*neighbors)[2];
1913   PetscInt      *counter;
1914   PetscErrorCode ierr;
1915 
1916   PetscFunctionBegin;
1917   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1918   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1919   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1920   if (cEndInterior < 0) {
1921     cEndInterior = cEnd;
1922   }
1923   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);CHKERRQ(ierr);
1924   ierr = PetscSectionSetChart(neighSec,cStart,cEndInterior);CHKERRQ(ierr);
1925   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1926   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1927   for (f = fStart; f < fEnd; f++) {
1928     const PetscInt        *fcells;
1929     PetscBool              boundary;
1930     PetscInt               ghost = -1;
1931     PetscInt               numChildren, numCells, c;
1932 
1933     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1934     ierr = DMIsBoundaryPoint(dm, f, &boundary);CHKERRQ(ierr);
1935     ierr = DMPlexGetTreeChildren(dm, f, &numChildren, NULL);CHKERRQ(ierr);
1936     if ((ghost >= 0) || boundary || numChildren) continue;
1937     ierr = DMPlexGetSupportSize(dm, f, &numCells);CHKERRQ(ierr);
1938     if (numCells == 2) {
1939       ierr = DMPlexGetSupport(dm, f, &fcells);CHKERRQ(ierr);
1940       for (c = 0; c < 2; c++) {
1941         PetscInt cell = fcells[c];
1942 
1943         if (cell >= cStart && cell < cEndInterior) {
1944           ierr = PetscSectionAddDof(neighSec,cell,1);CHKERRQ(ierr);
1945         }
1946       }
1947     }
1948   }
1949   ierr = PetscSectionSetUp(neighSec);CHKERRQ(ierr);
1950   ierr = PetscSectionGetMaxDof(neighSec,&maxNumFaces);CHKERRQ(ierr);
1951   ierr = PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);CHKERRQ(ierr);
1952   nStart = 0;
1953   ierr = PetscSectionGetStorageSize(neighSec,&nEnd);CHKERRQ(ierr);
1954   ierr = PetscMalloc1((nEnd-nStart),&neighbors);CHKERRQ(ierr);
1955   ierr = PetscCalloc1((cEndInterior-cStart),&counter);CHKERRQ(ierr);
1956   for (f = fStart; f < fEnd; f++) {
1957     const PetscInt        *fcells;
1958     PetscBool              boundary;
1959     PetscInt               ghost = -1;
1960     PetscInt               numChildren, numCells, c;
1961 
1962     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1963     ierr = DMIsBoundaryPoint(dm, f, &boundary);CHKERRQ(ierr);
1964     ierr = DMPlexGetTreeChildren(dm, f, &numChildren, NULL);CHKERRQ(ierr);
1965     if ((ghost >= 0) || boundary || numChildren) continue;
1966     ierr = DMPlexGetSupportSize(dm, f, &numCells);CHKERRQ(ierr);
1967     if (numCells == 2) {
1968       ierr  = DMPlexGetSupport(dm, f, &fcells);CHKERRQ(ierr);
1969       for (c = 0; c < 2; c++) {
1970         PetscInt cell = fcells[c], off;
1971 
1972         if (cell >= cStart && cell < cEndInterior) {
1973           ierr = PetscSectionGetOffset(neighSec,cell,&off);CHKERRQ(ierr);
1974           off += counter[cell - cStart]++;
1975           neighbors[off][0] = f;
1976           neighbors[off][1] = fcells[1 - c];
1977         }
1978       }
1979     }
1980   }
1981   ierr = PetscFree(counter);CHKERRQ(ierr);
1982   ierr = PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);CHKERRQ(ierr);
1983   for (c = cStart; c < cEndInterior; c++) {
1984     PetscInt               numFaces, f, d, off, ghost = -1;
1985     PetscFVCellGeom        *cg;
1986 
1987     ierr = DMPlexPointLocalRead(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1988     ierr = PetscSectionGetDof(neighSec, c, &numFaces);CHKERRQ(ierr);
1989     ierr = PetscSectionGetOffset(neighSec, c, &off);CHKERRQ(ierr);
1990     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, c, &ghost);CHKERRQ(ierr);}
1991     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);
1992     for (f = 0; f < numFaces; ++f) {
1993       PetscFVCellGeom       *cg1;
1994       PetscFVFaceGeom       *fg;
1995       const PetscInt        *fcells;
1996       PetscInt               ncell, side, nface;
1997 
1998       nface = neighbors[off + f][0];
1999       ncell = neighbors[off + f][1];
2000       ierr  = DMPlexGetSupport(dm,nface,&fcells);CHKERRQ(ierr);
2001       side  = (c != fcells[0]);
2002       ierr  = DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);CHKERRQ(ierr);
2003       ierr  = DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);CHKERRQ(ierr);
2004       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
2005       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
2006     }
2007     ierr = PetscFVComputeGradient(fvm, numFaces, dx, grad);CHKERRQ(ierr);
2008     for (f = 0; f < numFaces; ++f) {
2009       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
2010     }
2011   }
2012   ierr = PetscFree3(dx, grad, gref);CHKERRQ(ierr);
2013   ierr = PetscSectionDestroy(&neighSec);CHKERRQ(ierr);
2014   ierr = PetscFree(neighbors);CHKERRQ(ierr);
2015   PetscFunctionReturn(0);
2016 }
2017 
2018 #undef __FUNCT__
2019 #define __FUNCT__ "DMPlexComputeGradientFVM"
2020 /*@
2021   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
2022 
2023   Collective on DM
2024 
2025   Input Arguments:
2026 + dm  - The DM
2027 . fvm - The PetscFV
2028 . faceGeometry - The face geometry from DMPlexGetFaceGeometryFVM()
2029 - cellGeometry - The face geometry from DMPlexGetCellGeometryFVM()
2030 
2031   Output Parameters:
2032 + faceGeometry - The geometric factors for gradient calculation are inserted
2033 - dmGrad - The DM describing the layout of gradient data
2034 
2035   Level: developer
2036 
2037 .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
2038 @*/
2039 PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
2040 {
2041   DM             dmFace, dmCell;
2042   PetscScalar   *fgeom, *cgeom;
2043   PetscSection   sectionGrad, parentSection;
2044   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;
2045   PetscErrorCode ierr;
2046 
2047   PetscFunctionBegin;
2048   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2049   ierr = PetscFVGetNumComponents(fvm, &pdim);CHKERRQ(ierr);
2050   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2051   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2052   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
2053   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
2054   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
2055   ierr = VecGetArray(faceGeometry, &fgeom);CHKERRQ(ierr);
2056   ierr = VecGetArray(cellGeometry, &cgeom);CHKERRQ(ierr);
2057   ierr = DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
2058   if (!parentSection) {
2059     ierr = BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
2060   } else {
2061     ierr = BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
2062   }
2063   ierr = VecRestoreArray(faceGeometry, &fgeom);CHKERRQ(ierr);
2064   ierr = VecRestoreArray(cellGeometry, &cgeom);CHKERRQ(ierr);
2065   /* Create storage for gradients */
2066   ierr = DMClone(dm, dmGrad);CHKERRQ(ierr);
2067   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);CHKERRQ(ierr);
2068   ierr = PetscSectionSetChart(sectionGrad, cStart, cEnd);CHKERRQ(ierr);
2069   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionGrad, c, pdim*dim);CHKERRQ(ierr);}
2070   ierr = PetscSectionSetUp(sectionGrad);CHKERRQ(ierr);
2071   ierr = DMSetDefaultSection(*dmGrad, sectionGrad);CHKERRQ(ierr);
2072   ierr = PetscSectionDestroy(&sectionGrad);CHKERRQ(ierr);
2073   PetscFunctionReturn(0);
2074 }
2075 
2076 #undef __FUNCT__
2077 #define __FUNCT__ "DMPlexGetDataFVM"
2078 PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
2079 {
2080   PetscObject    cellgeomobj, facegeomobj;
2081   PetscErrorCode ierr;
2082 
2083   PetscFunctionBegin;
2084   ierr = PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);CHKERRQ(ierr);
2085   if (!cellgeomobj) {
2086     Vec cellgeomInt, facegeomInt;
2087 
2088     ierr = DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);CHKERRQ(ierr);
2089     ierr = PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);CHKERRQ(ierr);
2090     ierr = PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);CHKERRQ(ierr);
2091     ierr = VecDestroy(&cellgeomInt);CHKERRQ(ierr);
2092     ierr = VecDestroy(&facegeomInt);CHKERRQ(ierr);
2093     ierr = PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);CHKERRQ(ierr);
2094   }
2095   ierr = PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);CHKERRQ(ierr);
2096   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
2097   if (facegeom) *facegeom = (Vec) facegeomobj;
2098   if (gradDM) {
2099     PetscObject gradobj;
2100     PetscBool   computeGradients;
2101 
2102     ierr = PetscFVGetComputeGradients(fv,&computeGradients);CHKERRQ(ierr);
2103     if (!computeGradients) {
2104       *gradDM = NULL;
2105       PetscFunctionReturn(0);
2106     }
2107     ierr = PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);CHKERRQ(ierr);
2108     if (!gradobj) {
2109       DM dmGradInt;
2110 
2111       ierr = DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);CHKERRQ(ierr);
2112       ierr = PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);CHKERRQ(ierr);
2113       ierr = DMDestroy(&dmGradInt);CHKERRQ(ierr);
2114       ierr = PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);CHKERRQ(ierr);
2115     }
2116     *gradDM = (DM) gradobj;
2117   }
2118   PetscFunctionReturn(0);
2119 }
2120