xref: /petsc/src/dm/impls/plex/plexgeometry.c (revision 966be33a19c9230d4aa438248a644248d45cc287)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #undef __FUNCT__
4 #define __FUNCT__ "DMPlexGetLineIntersection_2D_Internal"
5 static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
6 {
7   const PetscReal p0_x  = segmentA[0*2+0];
8   const PetscReal p0_y  = segmentA[0*2+1];
9   const PetscReal p1_x  = segmentA[1*2+0];
10   const PetscReal p1_y  = segmentA[1*2+1];
11   const PetscReal p2_x  = segmentB[0*2+0];
12   const PetscReal p2_y  = segmentB[0*2+1];
13   const PetscReal p3_x  = segmentB[1*2+0];
14   const PetscReal p3_y  = segmentB[1*2+1];
15   const PetscReal s1_x  = p1_x - p0_x;
16   const PetscReal s1_y  = p1_y - p0_y;
17   const PetscReal s2_x  = p3_x - p2_x;
18   const PetscReal s2_y  = p3_y - p2_y;
19   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);
20 
21   PetscFunctionBegin;
22   *hasIntersection = PETSC_FALSE;
23   /* Non-parallel lines */
24   if (denom != 0.0) {
25     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
26     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;
27 
28     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
29       *hasIntersection = PETSC_TRUE;
30       if (intersection) {
31         intersection[0] = p0_x + (t * s1_x);
32         intersection[1] = p0_y + (t * s1_y);
33       }
34     }
35   }
36   PetscFunctionReturn(0);
37 }
38 
39 #undef __FUNCT__
40 #define __FUNCT__ "DMPlexLocatePoint_Simplex_2D_Internal"
41 static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
42 {
43   const PetscInt  embedDim = 2;
44   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
45   PetscReal       x        = PetscRealPart(point[0]);
46   PetscReal       y        = PetscRealPart(point[1]);
47   PetscReal       v0[2], J[4], invJ[4], detJ;
48   PetscReal       xi, eta;
49   PetscErrorCode  ierr;
50 
51   PetscFunctionBegin;
52   ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
53   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
54   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);
55 
56   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
57   else *cell = -1;
58   PetscFunctionReturn(0);
59 }
60 
61 #undef __FUNCT__
62 #define __FUNCT__ "DMPlexLocatePoint_General_2D_Internal"
63 static PetscErrorCode DMPlexLocatePoint_General_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
64 {
65   PetscSection       coordSection;
66   Vec             coordsLocal;
67   PetscScalar    *coords = NULL;
68   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
69   PetscReal       x         = PetscRealPart(point[0]);
70   PetscReal       y         = PetscRealPart(point[1]);
71   PetscInt        crossings = 0, f;
72   PetscErrorCode  ierr;
73 
74   PetscFunctionBegin;
75   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
76   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
77   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
78   for (f = 0; f < 4; ++f) {
79     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
80     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
81     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
82     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
83     PetscReal slope = (y_j - y_i) / (x_j - x_i);
84     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
85     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
86     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
87     if ((cond1 || cond2)  && above) ++crossings;
88   }
89   if (crossings % 2) *cell = c;
90   else *cell = -1;
91   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "DMPlexLocatePoint_Simplex_3D_Internal"
97 static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
98 {
99   const PetscInt embedDim = 3;
100   PetscReal      v0[3], J[9], invJ[9], detJ;
101   PetscReal      x = PetscRealPart(point[0]);
102   PetscReal      y = PetscRealPart(point[1]);
103   PetscReal      z = PetscRealPart(point[2]);
104   PetscReal      xi, eta, zeta;
105   PetscErrorCode ierr;
106 
107   PetscFunctionBegin;
108   ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
109   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
110   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
111   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);
112 
113   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
114   else *cell = -1;
115   PetscFunctionReturn(0);
116 }
117 
118 #undef __FUNCT__
119 #define __FUNCT__ "DMPlexLocatePoint_General_3D_Internal"
120 static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
121 {
122   PetscSection   coordSection;
123   Vec            coordsLocal;
124   PetscScalar   *coords;
125   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
126                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
127   PetscBool      found = PETSC_TRUE;
128   PetscInt       f;
129   PetscErrorCode ierr;
130 
131   PetscFunctionBegin;
132   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
133   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
134   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
135   for (f = 0; f < 6; ++f) {
136     /* Check the point is under plane */
137     /*   Get face normal */
138     PetscReal v_i[3];
139     PetscReal v_j[3];
140     PetscReal normal[3];
141     PetscReal pp[3];
142     PetscReal dot;
143 
144     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
145     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
146     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
147     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
148     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
149     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
150     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
151     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
152     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
153     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
154     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
155     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
156     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];
157 
158     /* Check that projected point is in face (2D location problem) */
159     if (dot < 0.0) {
160       found = PETSC_FALSE;
161       break;
162     }
163   }
164   if (found) *cell = c;
165   else *cell = -1;
166   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
167   PetscFunctionReturn(0);
168 }
169 
170 #undef __FUNCT__
171 #define __FUNCT__ "PetscGridHashInitialize_Internal"
172 static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
173 {
174   PetscInt d;
175 
176   PetscFunctionBegin;
177   box->dim = dim;
178   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
179   PetscFunctionReturn(0);
180 }
181 
182 #undef __FUNCT__
183 #define __FUNCT__ "PetscGridHashCreate"
184 PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
185 {
186   PetscErrorCode ierr;
187 
188   PetscFunctionBegin;
189   ierr = PetscMalloc1(1, box);CHKERRQ(ierr);
190   ierr = PetscGridHashInitialize_Internal(*box, dim, point);CHKERRQ(ierr);
191   PetscFunctionReturn(0);
192 }
193 
194 #undef __FUNCT__
195 #define __FUNCT__ "PetscGridHashEnlarge"
196 PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
197 {
198   PetscInt d;
199 
200   PetscFunctionBegin;
201   for (d = 0; d < box->dim; ++d) {
202     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
203     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
204   }
205   PetscFunctionReturn(0);
206 }
207 
208 #undef __FUNCT__
209 #define __FUNCT__ "PetscGridHashSetGrid"
210 PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
211 {
212   PetscInt d;
213 
214   PetscFunctionBegin;
215   for (d = 0; d < box->dim; ++d) {
216     box->extent[d] = box->upper[d] - box->lower[d];
217     if (n[d] == PETSC_DETERMINE) {
218       box->h[d] = h[d];
219       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
220     } else {
221       box->n[d] = n[d];
222       box->h[d] = box->extent[d]/n[d];
223     }
224   }
225   PetscFunctionReturn(0);
226 }
227 
228 #undef __FUNCT__
229 #define __FUNCT__ "PetscGridHashGetEnclosingBox"
230 PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
231 {
232   const PetscReal *lower = box->lower;
233   const PetscReal *upper = box->upper;
234   const PetscReal *h     = box->h;
235   const PetscInt  *n     = box->n;
236   const PetscInt   dim   = box->dim;
237   PetscInt         d, p;
238 
239   PetscFunctionBegin;
240   for (p = 0; p < numPoints; ++p) {
241     for (d = 0; d < dim; ++d) {
242       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);
243 
244       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
245       if (dbox < 0 || dbox >= n[d]) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %d (%g, %g, %g) is outside of our bounding box",
246                                              p, PetscRealPart(points[p*dim+0]), dim > 1 ? PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? PetscRealPart(points[p*dim+2]) : 0.0);
247       dboxes[p*dim+d] = dbox;
248     }
249     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
250   }
251   PetscFunctionReturn(0);
252 }
253 
254 #undef __FUNCT__
255 #define __FUNCT__ "PetscGridHashDestroy"
256 PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
257 {
258   PetscErrorCode ierr;
259 
260   PetscFunctionBegin;
261   if (*box) {
262     ierr = PetscSectionDestroy(&(*box)->cellSection);CHKERRQ(ierr);
263     ierr = ISDestroy(&(*box)->cells);CHKERRQ(ierr);
264     ierr = DMLabelDestroy(&(*box)->cellsSparse);CHKERRQ(ierr);
265   }
266   ierr = PetscFree(*box);CHKERRQ(ierr);
267   PetscFunctionReturn(0);
268 }
269 
270 #undef __FUNCT__
271 #define __FUNCT__ "DMPlexLocatePoint_Internal"
272 PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
273 {
274   PetscInt       coneSize;
275   PetscErrorCode ierr;
276 
277   PetscFunctionBegin;
278   switch (dim) {
279   case 2:
280     ierr = DMPlexGetConeSize(dm, cellStart, &coneSize);CHKERRQ(ierr);
281     switch (coneSize) {
282     case 3:
283       ierr = DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
284       break;
285     case 4:
286       ierr = DMPlexLocatePoint_General_2D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
287       break;
288     default:
289       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
290     }
291     break;
292   case 3:
293     ierr = DMPlexGetConeSize(dm, cellStart, &coneSize);CHKERRQ(ierr);
294     switch (coneSize) {
295     case 4:
296       ierr = DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
297       break;
298     case 6:
299       ierr = DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);CHKERRQ(ierr);
300       break;
301     default:
302       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
303     }
304     break;
305   default:
306     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %D", dim);
307   }
308   PetscFunctionReturn(0);
309 }
310 
311 #undef __FUNCT__
312 #define __FUNCT__ "DMPlexComputeGridHash_Internal"
313 PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
314 {
315   MPI_Comm           comm;
316   PetscGridHash      lbox;
317   Vec                coordinates;
318   PetscSection       coordSection;
319   Vec                coordsLocal;
320   const PetscScalar *coords;
321   PetscInt          *dboxes, *boxes;
322   PetscInt           n[3] = {10, 10, 10};
323   PetscInt           dim, N, cStart, cEnd, cMax, c, i;
324   PetscErrorCode     ierr;
325 
326   PetscFunctionBegin;
327   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
328   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
329   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
330   ierr = VecGetLocalSize(coordinates, &N);CHKERRQ(ierr);
331   ierr = VecGetArrayRead(coordinates, &coords);CHKERRQ(ierr);
332   ierr = PetscGridHashCreate(comm, dim, coords, &lbox);CHKERRQ(ierr);
333   for (i = 0; i < N; i += dim) {ierr = PetscGridHashEnlarge(lbox, &coords[i]);CHKERRQ(ierr);}
334   ierr = VecRestoreArrayRead(coordinates, &coords);CHKERRQ(ierr);
335   ierr = PetscGridHashSetGrid(lbox, n, NULL);CHKERRQ(ierr);
336 #if 0
337   /* Could define a custom reduction to merge these */
338   ierr = MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);CHKERRQ(ierr);
339   ierr = MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);CHKERRQ(ierr);
340 #endif
341   /* Is there a reason to snap the local bounding box to a division of the global box? */
342   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
343   /* Create label */
344   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
345   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
346   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
347   ierr = DMLabelCreate("cells", &lbox->cellsSparse);CHKERRQ(ierr);
348   ierr = DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);CHKERRQ(ierr);
349   /* Compute boxes which overlap each cell: http://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
350   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
351   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
352   ierr = PetscCalloc2(16 * dim, &dboxes, 16, &boxes);CHKERRQ(ierr);
353   for (c = cStart; c < cEnd; ++c) {
354     const PetscReal *h       = lbox->h;
355     PetscScalar     *ccoords = NULL;
356     PetscInt         csize   = 0;
357     PetscScalar      point[3];
358     PetscInt         dlim[6], d, e, i, j, k;
359 
360     /* Find boxes enclosing each vertex */
361     ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);CHKERRQ(ierr);
362     ierr = PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);CHKERRQ(ierr);
363     /* Mark cells containing the vertices */
364     for (e = 0; e < csize/dim; ++e) {ierr = DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);CHKERRQ(ierr);}
365     /* Get grid of boxes containing these */
366     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
367     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
368     for (e = 1; e < dim+1; ++e) {
369       for (d = 0; d < dim; ++d) {
370         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
371         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
372       }
373     }
374     /* Check for intersection of box with cell */
375     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
376       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
377         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
378           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
379           PetscScalar    cpoint[3];
380           PetscInt       cell, edge, ii, jj, kk;
381 
382           /* Check whether cell contains any vertex of these subboxes TODO vectorize this */
383           for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
384             for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
385               for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {
386 
387                 ierr = DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);CHKERRQ(ierr);
388                 if (cell >= 0) {DMLabelSetValue(lbox->cellsSparse, c, box);CHKERRQ(ierr); ii = jj = kk = 2;}
389               }
390             }
391           }
392           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
393           for (edge = 0; edge < dim+1; ++edge) {
394             PetscReal segA[6], segB[6];
395 
396             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
397             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
398               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
399                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
400               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
401                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
402                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
403                 for (ii = 0; ii < 2; ++ii) {
404                   PetscBool intersects;
405 
406                   segB[0]     = PetscRealPart(point[0]);
407                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
408                   ierr = DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);CHKERRQ(ierr);
409                   if (intersects) {DMLabelSetValue(lbox->cellsSparse, c, box);CHKERRQ(ierr); edge = ii = jj = kk = dim+1;}
410                 }
411               }
412             }
413           }
414         }
415       }
416     }
417     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);CHKERRQ(ierr);
418   }
419   ierr = PetscFree2(dboxes, boxes);CHKERRQ(ierr);
420   ierr = DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);CHKERRQ(ierr);
421   ierr = DMLabelDestroy(&lbox->cellsSparse);CHKERRQ(ierr);
422   *localBox = lbox;
423   PetscFunctionReturn(0);
424 }
425 
426 #undef __FUNCT__
427 #define __FUNCT__ "DMLocatePoints_Plex"
428 PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, PetscSF cellSF)
429 {
430   DM_Plex        *mesh = (DM_Plex *) dm->data;
431   PetscBool       hash = mesh->useHashLocation;
432   PetscInt        bs, numPoints, p, numFound, *found = NULL;
433   PetscInt        dim, cStart, cEnd, cMax, numCells, c;
434   const PetscInt *boxCells;
435   PetscSFNode    *cells;
436   PetscScalar    *a;
437   PetscMPIInt     result;
438   PetscErrorCode  ierr;
439 
440   PetscFunctionBegin;
441   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
442   ierr = VecGetBlockSize(v, &bs);CHKERRQ(ierr);
443   ierr = MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);CHKERRQ(ierr);
444   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
445   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);
446   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
447   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
448   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
449   ierr = VecGetLocalSize(v, &numPoints);CHKERRQ(ierr);
450   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
451   numPoints /= bs;
452   ierr = PetscMalloc1(numPoints, &cells);CHKERRQ(ierr);
453   if (hash) {
454     if (!mesh->lbox) {ierr = PetscInfo(dm, "Initializing grid hashing");CHKERRQ(ierr);ierr = DMPlexComputeGridHash_Internal(dm, &mesh->lbox);CHKERRQ(ierr);}
455     /* Designate the local box for each point */
456     /* Send points to correct process */
457     /* Search cells that lie in each subbox */
458     /*   Should we bin points before doing search? */
459     ierr = ISGetIndices(mesh->lbox->cells, &boxCells);CHKERRQ(ierr);
460   }
461   for (p = 0, numFound = 0; p < numPoints; ++p) {
462     const PetscScalar *point = &a[p*bs];
463     PetscInt           dbin[3], bin, cell = -1, cellOffset;
464 
465     cells[p].rank  = -1;
466     cells[p].index = -1;
467     if (hash) {
468       ierr = PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);CHKERRQ(ierr);
469       /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
470       ierr = PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);CHKERRQ(ierr);
471       ierr = PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);CHKERRQ(ierr);
472       for (c = cellOffset; c < cellOffset + numCells; ++c) {
473         ierr = DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);CHKERRQ(ierr);
474         if (cell >= 0) {
475           cells[p].rank = 0;
476           cells[p].index = cell;
477           numFound++;
478           break;
479         }
480       }
481     } else {
482       for (c = cStart; c < cEnd; ++c) {
483         ierr = DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);CHKERRQ(ierr);
484         if (cell >= 0) {
485           cells[p].rank = 0;
486           cells[p].index = cell;
487           numFound++;
488           break;
489         }
490       }
491     }
492   }
493   if (hash) {ierr = ISRestoreIndices(mesh->lbox->cells, &boxCells);CHKERRQ(ierr);}
494   /* Check for highest numbered proc that claims a point (do we care?) */
495   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
496   if (numFound < numPoints) {
497     ierr = PetscMalloc1(numFound,&found);CHKERRQ(ierr);
498     for (p = 0, numFound = 0; p < numPoints; p++) {
499       if (cells[p].rank >= 0 && cells[p].index >= 0) {
500         if (numFound < p) {
501           cells[numFound] = cells[p];
502         }
503         found[numFound++] = p;
504       }
505     }
506   }
507   ierr = PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);CHKERRQ(ierr);
508   PetscFunctionReturn(0);
509 }
510 
511 #undef __FUNCT__
512 #define __FUNCT__ "DMPlexComputeProjection2Dto1D_Internal"
513 /*
514   DMPlexComputeProjection2Dto1D_Internal - Rewrite coordinates to be the 1D projection of the 2D
515 */
516 PetscErrorCode DMPlexComputeProjection2Dto1D_Internal(PetscScalar coords[], PetscReal R[])
517 {
518   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
519   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
520   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;
521 
522   PetscFunctionBegin;
523   R[0] = c; R[1] = -s;
524   R[2] = s; R[3] =  c;
525   coords[0] = 0.0;
526   coords[1] = r;
527   PetscFunctionReturn(0);
528 }
529 
530 #undef __FUNCT__
531 #define __FUNCT__ "DMPlexComputeProjection3Dto1D_Internal"
532 /*
533   DMPlexComputeProjection3Dto1D_Internal - Rewrite coordinates to be the 1D projection of the 3D
534 
535   This uses the basis completion described by Frisvad,
536 
537   http://www.imm.dtu.dk/~jerf/papers/abstracts/onb.html
538   DOI:10.1080/2165347X.2012.689606
539 */
540 PetscErrorCode DMPlexComputeProjection3Dto1D_Internal(PetscScalar coords[], PetscReal R[])
541 {
542   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
543   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
544   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
545   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
546   PetscReal      rinv = 1. / r;
547   PetscFunctionBegin;
548 
549   x *= rinv; y *= rinv; z *= rinv;
550   if (x > 0.) {
551     PetscReal inv1pX   = 1./ (1. + x);
552 
553     R[0] = x; R[1] = -y;              R[2] = -z;
554     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
555     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
556   }
557   else {
558     PetscReal inv1mX   = 1./ (1. - x);
559 
560     R[0] = x; R[1] = z;               R[2] = y;
561     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
562     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
563   }
564   coords[0] = 0.0;
565   coords[1] = r;
566   PetscFunctionReturn(0);
567 }
568 
569 #undef __FUNCT__
570 #define __FUNCT__ "DMPlexComputeProjection3Dto2D_Internal"
571 /*
572   DMPlexComputeProjection3Dto2D_Internal - Rewrite coordinates to be the 2D projection of the 3D
573 */
574 PetscErrorCode DMPlexComputeProjection3Dto2D_Internal(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
575 {
576   PetscReal      x1[3],  x2[3], n[3], norm;
577   PetscReal      x1p[3], x2p[3], xnp[3];
578   PetscReal      sqrtz, alpha;
579   const PetscInt dim = 3;
580   PetscInt       d, e, p;
581 
582   PetscFunctionBegin;
583   /* 0) Calculate normal vector */
584   for (d = 0; d < dim; ++d) {
585     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
586     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
587   }
588   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
589   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
590   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
591   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
592   n[0] /= norm;
593   n[1] /= norm;
594   n[2] /= norm;
595   /* 1) Take the normal vector and rotate until it is \hat z
596 
597     Let the normal vector be <nx, ny, nz> and alpha = 1/sqrt(1 - nz^2), then
598 
599     R = /  alpha nx nz  alpha ny nz -1/alpha \
600         | -alpha ny     alpha nx        0    |
601         \     nx            ny         nz    /
602 
603     will rotate the normal vector to \hat z
604   */
605   sqrtz = PetscSqrtReal(1.0 - n[2]*n[2]);
606   /* Check for n = z */
607   if (sqrtz < 1.0e-10) {
608     const PetscInt s = PetscSign(n[2]);
609     /* If nz < 0, rotate 180 degrees around x-axis */
610     for (p = 3; p < coordSize/3; ++p) {
611       coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
612       coords[p*2+1] = (PetscRealPart(coords[p*dim+1] - coords[0*dim+1])) * s;
613     }
614     coords[0] = 0.0;
615     coords[1] = 0.0;
616     coords[2] = x1[0];
617     coords[3] = x1[1] * s;
618     coords[4] = x2[0];
619     coords[5] = x2[1] * s;
620     R[0] = 1.0;     R[1] = 0.0;     R[2] = 0.0;
621     R[3] = 0.0;     R[4] = 1.0 * s; R[5] = 0.0;
622     R[6] = 0.0;     R[7] = 0.0;     R[8] = 1.0 * s;
623     PetscFunctionReturn(0);
624   }
625   alpha = 1.0/sqrtz;
626   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
627   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
628   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
629   for (d = 0; d < dim; ++d) {
630     x1p[d] = 0.0;
631     x2p[d] = 0.0;
632     for (e = 0; e < dim; ++e) {
633       x1p[d] += R[d*dim+e]*x1[e];
634       x2p[d] += R[d*dim+e]*x2[e];
635     }
636   }
637   if (PetscAbsReal(x1p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
638   if (PetscAbsReal(x2p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
639   /* 2) Project to (x, y) */
640   for (p = 3; p < coordSize/3; ++p) {
641     for (d = 0; d < dim; ++d) {
642       xnp[d] = 0.0;
643       for (e = 0; e < dim; ++e) {
644         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
645       }
646       if (d < dim-1) coords[p*2+d] = xnp[d];
647     }
648   }
649   coords[0] = 0.0;
650   coords[1] = 0.0;
651   coords[2] = x1p[0];
652   coords[3] = x1p[1];
653   coords[4] = x2p[0];
654   coords[5] = x2p[1];
655   /* Output R^T which rotates \hat z to the input normal */
656   for (d = 0; d < dim; ++d) {
657     for (e = d+1; e < dim; ++e) {
658       PetscReal tmp;
659 
660       tmp        = R[d*dim+e];
661       R[d*dim+e] = R[e*dim+d];
662       R[e*dim+d] = tmp;
663     }
664   }
665   PetscFunctionReturn(0);
666 }
667 
668 #undef __FUNCT__
669 #define __FUNCT__ "Volume_Triangle_Internal"
670 PETSC_UNUSED
671 PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
672 {
673   /* Signed volume is 1/2 the determinant
674 
675    |  1  1  1 |
676    | x0 x1 x2 |
677    | y0 y1 y2 |
678 
679      but if x0,y0 is the origin, we have
680 
681    | x1 x2 |
682    | y1 y2 |
683   */
684   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
685   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
686   PetscReal       M[4], detM;
687   M[0] = x1; M[1] = x2;
688   M[2] = y1; M[3] = y2;
689   DMPlex_Det2D_Internal(&detM, M);
690   *vol = 0.5*detM;
691   (void)PetscLogFlops(5.0);
692 }
693 
694 #undef __FUNCT__
695 #define __FUNCT__ "Volume_Triangle_Origin_Internal"
696 PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
697 {
698   DMPlex_Det2D_Internal(vol, coords);
699   *vol *= 0.5;
700 }
701 
702 #undef __FUNCT__
703 #define __FUNCT__ "Volume_Tetrahedron_Internal"
704 PETSC_UNUSED
705 PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
706 {
707   /* Signed volume is 1/6th of the determinant
708 
709    |  1  1  1  1 |
710    | x0 x1 x2 x3 |
711    | y0 y1 y2 y3 |
712    | z0 z1 z2 z3 |
713 
714      but if x0,y0,z0 is the origin, we have
715 
716    | x1 x2 x3 |
717    | y1 y2 y3 |
718    | z1 z2 z3 |
719   */
720   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
721   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
722   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
723   PetscReal       M[9], detM;
724   M[0] = x1; M[1] = x2; M[2] = x3;
725   M[3] = y1; M[4] = y2; M[5] = y3;
726   M[6] = z1; M[7] = z2; M[8] = z3;
727   DMPlex_Det3D_Internal(&detM, M);
728   *vol = -0.16666666666666666666666*detM;
729   (void)PetscLogFlops(10.0);
730 }
731 
732 #undef __FUNCT__
733 #define __FUNCT__ "Volume_Tetrahedron_Origin_Internal"
734 PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
735 {
736   DMPlex_Det3D_Internal(vol, coords);
737   *vol *= -0.16666666666666666666666;
738 }
739 
740 #undef __FUNCT__
741 #define __FUNCT__ "DMPlexComputeLineGeometry_Internal"
742 static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
743 {
744   PetscSection   coordSection;
745   Vec            coordinates;
746   PetscScalar   *coords = NULL;
747   PetscInt       numCoords, d;
748   PetscErrorCode ierr;
749 
750   PetscFunctionBegin;
751   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
752   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
753   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
754   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
755   *detJ = 0.0;
756   if (numCoords == 6) {
757     const PetscInt dim = 3;
758     PetscReal      R[9], J0;
759 
760     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
761     ierr = DMPlexComputeProjection3Dto1D_Internal(coords, R);CHKERRQ(ierr);
762     if (J)    {
763       J0   = 0.5*PetscRealPart(coords[1]);
764       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
765       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
766       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
767       DMPlex_Det3D_Internal(detJ, J);
768       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
769     }
770   } else if (numCoords == 4) {
771     const PetscInt dim = 2;
772     PetscReal      R[4], J0;
773 
774     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
775     ierr = DMPlexComputeProjection2Dto1D_Internal(coords, R);CHKERRQ(ierr);
776     if (J)    {
777       J0   = 0.5*PetscRealPart(coords[1]);
778       J[0] = R[0]*J0; J[1] = R[1];
779       J[2] = R[2]*J0; J[3] = R[3];
780       DMPlex_Det2D_Internal(detJ, J);
781       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
782     }
783   } else if (numCoords == 2) {
784     const PetscInt dim = 1;
785 
786     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
787     if (J)    {
788       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
789       *detJ = J[0];
790       ierr = PetscLogFlops(2.0);CHKERRQ(ierr);
791       if (invJ) {invJ[0] = 1.0/J[0]; ierr = PetscLogFlops(1.0);CHKERRQ(ierr);}
792     }
793   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
794   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
795   PetscFunctionReturn(0);
796 }
797 
798 #undef __FUNCT__
799 #define __FUNCT__ "DMPlexComputeTriangleGeometry_Internal"
800 static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
801 {
802   PetscSection   coordSection;
803   Vec            coordinates;
804   PetscScalar   *coords = NULL;
805   PetscInt       numCoords, d, f, g;
806   PetscErrorCode ierr;
807 
808   PetscFunctionBegin;
809   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
810   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
811   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
812   *detJ = 0.0;
813   if (numCoords == 9) {
814     const PetscInt dim = 3;
815     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
816 
817     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
818     ierr = DMPlexComputeProjection3Dto2D_Internal(numCoords, coords, R);CHKERRQ(ierr);
819     if (J)    {
820       const PetscInt pdim = 2;
821 
822       for (d = 0; d < pdim; d++) {
823         for (f = 0; f < pdim; f++) {
824           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
825         }
826       }
827       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
828       DMPlex_Det3D_Internal(detJ, J0);
829       for (d = 0; d < dim; d++) {
830         for (f = 0; f < dim; f++) {
831           J[d*dim+f] = 0.0;
832           for (g = 0; g < dim; g++) {
833             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
834           }
835         }
836       }
837       ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
838     }
839     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
840   } else if (numCoords == 6) {
841     const PetscInt dim = 2;
842 
843     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
844     if (J)    {
845       for (d = 0; d < dim; d++) {
846         for (f = 0; f < dim; f++) {
847           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
848         }
849       }
850       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
851       DMPlex_Det2D_Internal(detJ, J);
852     }
853     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
854   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
855   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
856   PetscFunctionReturn(0);
857 }
858 
859 #undef __FUNCT__
860 #define __FUNCT__ "DMPlexComputeRectangleGeometry_Internal"
861 static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
862 {
863   PetscSection   coordSection;
864   Vec            coordinates;
865   PetscScalar   *coords = NULL;
866   PetscInt       numCoords, d, f, g;
867   PetscErrorCode ierr;
868 
869   PetscFunctionBegin;
870   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
871   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
872   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
873   *detJ = 0.0;
874   if (numCoords == 12) {
875     const PetscInt dim = 3;
876     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
877 
878     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
879     ierr = DMPlexComputeProjection3Dto2D_Internal(numCoords, coords, R);CHKERRQ(ierr);
880     if (J)    {
881       const PetscInt pdim = 2;
882 
883       for (d = 0; d < pdim; d++) {
884         J0[d*dim+0] = 0.5*(PetscRealPart(coords[1*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
885         J0[d*dim+1] = 0.5*(PetscRealPart(coords[3*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
886       }
887       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
888       DMPlex_Det3D_Internal(detJ, J0);
889       for (d = 0; d < dim; d++) {
890         for (f = 0; f < dim; f++) {
891           J[d*dim+f] = 0.0;
892           for (g = 0; g < dim; g++) {
893             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
894           }
895         }
896       }
897       ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
898     }
899     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
900   } else if ((numCoords == 8) || (numCoords == 16)) {
901     const PetscInt dim = 2;
902 
903     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
904     if (J)    {
905       for (d = 0; d < dim; d++) {
906         J[d*dim+0] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
907         J[d*dim+1] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
908       }
909       ierr = PetscLogFlops(8.0);CHKERRQ(ierr);
910       DMPlex_Det2D_Internal(detJ, J);
911     }
912     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
913   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
914   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
915   PetscFunctionReturn(0);
916 }
917 
918 #undef __FUNCT__
919 #define __FUNCT__ "DMPlexComputeTetrahedronGeometry_Internal"
920 static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
921 {
922   PetscSection   coordSection;
923   Vec            coordinates;
924   PetscScalar   *coords = NULL;
925   const PetscInt dim = 3;
926   PetscInt       d;
927   PetscErrorCode ierr;
928 
929   PetscFunctionBegin;
930   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
931   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
932   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
933   *detJ = 0.0;
934   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
935   if (J)    {
936     for (d = 0; d < dim; d++) {
937       /* I orient with outward face normals */
938       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
939       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
940       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
941     }
942     ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
943     DMPlex_Det3D_Internal(detJ, J);
944   }
945   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
946   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
947   PetscFunctionReturn(0);
948 }
949 
950 #undef __FUNCT__
951 #define __FUNCT__ "DMPlexComputeHexahedronGeometry_Internal"
952 static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
953 {
954   PetscSection   coordSection;
955   Vec            coordinates;
956   PetscScalar   *coords = NULL;
957   const PetscInt dim = 3;
958   PetscInt       d;
959   PetscErrorCode ierr;
960 
961   PetscFunctionBegin;
962   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
963   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
964   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
965   *detJ = 0.0;
966   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
967   if (J)    {
968     for (d = 0; d < dim; d++) {
969       J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
970       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
971       J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
972     }
973     ierr = PetscLogFlops(18.0);CHKERRQ(ierr);
974     DMPlex_Det3D_Internal(detJ, J);
975   }
976   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
977   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
978   PetscFunctionReturn(0);
979 }
980 
981 #undef __FUNCT__
982 #define __FUNCT__ "DMPlexComputeCellGeometryAffineFEM"
983 /*@C
984   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
985 
986   Collective on DM
987 
988   Input Arguments:
989 + dm   - the DM
990 - cell - the cell
991 
992   Output Arguments:
993 + v0   - the translation part of this affine transform
994 . J    - the Jacobian of the transform from the reference element
995 . invJ - the inverse of the Jacobian
996 - detJ - the Jacobian determinant
997 
998   Level: advanced
999 
1000   Fortran Notes:
1001   Since it returns arrays, this routine is only available in Fortran 90, and you must
1002   include petsc.h90 in your code.
1003 
1004 .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinateVec()
1005 @*/
1006 PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1007 {
1008   PetscInt       depth, dim, coneSize;
1009   PetscErrorCode ierr;
1010 
1011   PetscFunctionBegin;
1012   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1013   ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
1014   if (depth == 1) {
1015     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1016   } else {
1017     DMLabel depth;
1018 
1019     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1020     ierr = DMLabelGetValue(depth, cell, &dim);CHKERRQ(ierr);
1021   }
1022   switch (dim) {
1023   case 1:
1024     ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1025     break;
1026   case 2:
1027     switch (coneSize) {
1028     case 3:
1029       ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1030       break;
1031     case 4:
1032       ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1033       break;
1034     default:
1035       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1036     }
1037     break;
1038   case 3:
1039     switch (coneSize) {
1040     case 4:
1041       ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1042       break;
1043     case 6: /* Faces */
1044     case 8: /* Vertices */
1045       ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
1046       break;
1047     default:
1048         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1049     }
1050       break;
1051   default:
1052     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1053   }
1054   PetscFunctionReturn(0);
1055 }
1056 
1057 #undef __FUNCT__
1058 #define __FUNCT__ "DMPlexComputeIsoparametricGeometry_Internal"
1059 static PetscErrorCode DMPlexComputeIsoparametricGeometry_Internal(DM dm, PetscFE fe, PetscInt point, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1060 {
1061   PetscQuadrature  quad;
1062   PetscSection     coordSection;
1063   Vec              coordinates;
1064   PetscScalar     *coords = NULL;
1065   const PetscReal *quadPoints;
1066   PetscReal       *basisDer;
1067   PetscInt         dim, cdim, pdim, qdim, Nq, numCoords, d, q;
1068   PetscErrorCode   ierr;
1069 
1070   PetscFunctionBegin;
1071   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1072   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1073   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);CHKERRQ(ierr);
1074   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1075   ierr = DMGetCoordinateDim(dm, &cdim);CHKERRQ(ierr);
1076   ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1077   ierr = PetscFEGetDimension(fe, &pdim);CHKERRQ(ierr);
1078   ierr = PetscQuadratureGetData(quad, &qdim, &Nq, &quadPoints, NULL);CHKERRQ(ierr);
1079   ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
1080   *detJ = 0.0;
1081   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
1082   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);
1083   if (v0) {for (d = 0; d < cdim; d++) v0[d] = PetscRealPart(coords[d]);}
1084   if (J) {
1085     for (q = 0; q < Nq; ++q) {
1086       PetscInt i, j, k, c, r;
1087 
1088       /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
1089       for (k = 0; k < pdim; ++k)
1090         for (j = 0; j < dim; ++j)
1091           for (i = 0; i < cdim; ++i)
1092             J[(q*cdim + i)*dim + j] += basisDer[(q*pdim + k)*dim + j] * PetscRealPart(coords[k*cdim + i]);
1093       ierr = PetscLogFlops(2.0*pdim*dim*cdim);CHKERRQ(ierr);
1094       if (cdim > dim) {
1095         for (c = dim; c < cdim; ++c)
1096           for (r = 0; r < cdim; ++r)
1097             J[r*cdim+c] = r == c ? 1.0 : 0.0;
1098       }
1099       switch (cdim) {
1100       case 3:
1101         DMPlex_Det3D_Internal(detJ, J);
1102         if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1103         break;
1104       case 2:
1105         DMPlex_Det2D_Internal(detJ, J);
1106         if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1107         break;
1108       case 1:
1109         *detJ = J[0];
1110         if (invJ) invJ[0] = 1.0/J[0];
1111       }
1112     }
1113   }
1114   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);CHKERRQ(ierr);
1115   PetscFunctionReturn(0);
1116 }
1117 
1118 #undef __FUNCT__
1119 #define __FUNCT__ "DMPlexComputeCellGeometryFEM"
1120 /*@C
1121   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
1122 
1123   Collective on DM
1124 
1125   Input Arguments:
1126 + dm   - the DM
1127 . cell - the cell
1128 - fe   - the finite element containing the quadrature
1129 
1130   Output Arguments:
1131 + v0   - the translation part of this transform
1132 . J    - the Jacobian of the transform from the reference element at each quadrature point
1133 . invJ - the inverse of the Jacobian at each quadrature point
1134 - detJ - the Jacobian determinant at each quadrature point
1135 
1136   Level: advanced
1137 
1138   Fortran Notes:
1139   Since it returns arrays, this routine is only available in Fortran 90, and you must
1140   include petsc.h90 in your code.
1141 
1142 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1143 @*/
1144 PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscFE fe, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1145 {
1146   PetscErrorCode ierr;
1147 
1148   PetscFunctionBegin;
1149   if (!fe) {ierr = DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);}
1150   else     {ierr = DMPlexComputeIsoparametricGeometry_Internal(dm, fe, cell, v0, J, invJ, detJ);CHKERRQ(ierr);}
1151   PetscFunctionReturn(0);
1152 }
1153 
1154 #undef __FUNCT__
1155 #define __FUNCT__ "DMPlexComputeGeometryFVM_1D_Internal"
1156 static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1157 {
1158   PetscSection   coordSection;
1159   Vec            coordinates;
1160   PetscScalar   *coords = NULL;
1161   PetscScalar    tmp[2];
1162   PetscInt       coordSize;
1163   PetscErrorCode ierr;
1164 
1165   PetscFunctionBegin;
1166   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1167   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1168   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1169   if (dim != 2) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "We only support 2D edges right now");
1170   ierr = DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);CHKERRQ(ierr);
1171   if (centroid) {
1172     centroid[0] = 0.5*PetscRealPart(coords[0] + tmp[0]);
1173     centroid[1] = 0.5*PetscRealPart(coords[1] + tmp[1]);
1174   }
1175   if (normal) {
1176     PetscReal norm;
1177 
1178     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
1179     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
1180     norm       = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1]);
1181     normal[0] /= norm;
1182     normal[1] /= norm;
1183   }
1184   if (vol) {
1185     *vol = PetscSqrtReal(PetscSqr(PetscRealPart(coords[0] - tmp[0])) + PetscSqr(PetscRealPart(coords[1] - tmp[1])));
1186   }
1187   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 #undef __FUNCT__
1192 #define __FUNCT__ "DMPlexComputeGeometryFVM_2D_Internal"
1193 /* Centroid_i = (\sum_n A_n Cn_i ) / A */
1194 static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1195 {
1196   PetscSection   coordSection;
1197   Vec            coordinates;
1198   PetscScalar   *coords = NULL;
1199   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
1200   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;
1201   PetscErrorCode ierr;
1202 
1203   PetscFunctionBegin;
1204   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1205   ierr = DMPlexGetConeSize(dm, cell, &numCorners);CHKERRQ(ierr);
1206   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1207   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1208   ierr = DMGetCoordinateDim(dm, &dim);CHKERRQ(ierr);
1209   if (dim > 2 && centroid) {
1210     v0[0] = PetscRealPart(coords[0]);
1211     v0[1] = PetscRealPart(coords[1]);
1212     v0[2] = PetscRealPart(coords[2]);
1213   }
1214   if (normal) {
1215     if (dim > 2) {
1216       const PetscReal x0 = PetscRealPart(coords[dim+0] - coords[0]), x1 = PetscRealPart(coords[dim*2+0] - coords[0]);
1217       const PetscReal y0 = PetscRealPart(coords[dim+1] - coords[1]), y1 = PetscRealPart(coords[dim*2+1] - coords[1]);
1218       const PetscReal z0 = PetscRealPart(coords[dim+2] - coords[2]), z1 = PetscRealPart(coords[dim*2+2] - coords[2]);
1219       PetscReal       norm;
1220 
1221       normal[0] = y0*z1 - z0*y1;
1222       normal[1] = z0*x1 - x0*z1;
1223       normal[2] = x0*y1 - y0*x1;
1224       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
1225       normal[0] /= norm;
1226       normal[1] /= norm;
1227       normal[2] /= norm;
1228     } else {
1229       for (d = 0; d < dim; ++d) normal[d] = 0.0;
1230     }
1231   }
1232   if (dim == 3) {ierr = DMPlexComputeProjection3Dto2D_Internal(coordSize, coords, R);CHKERRQ(ierr);}
1233   for (p = 0; p < numCorners; ++p) {
1234     /* Need to do this copy to get types right */
1235     for (d = 0; d < tdim; ++d) {
1236       ctmp[d]      = PetscRealPart(coords[p*tdim+d]);
1237       ctmp[tdim+d] = PetscRealPart(coords[((p+1)%numCorners)*tdim+d]);
1238     }
1239     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
1240     vsum += vtmp;
1241     for (d = 0; d < tdim; ++d) {
1242       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
1243     }
1244   }
1245   for (d = 0; d < tdim; ++d) {
1246     csum[d] /= (tdim+1)*vsum;
1247   }
1248   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
1249   if (vol) *vol = PetscAbsReal(vsum);
1250   if (centroid) {
1251     if (dim > 2) {
1252       for (d = 0; d < dim; ++d) {
1253         centroid[d] = v0[d];
1254         for (e = 0; e < dim; ++e) {
1255           centroid[d] += R[d*dim+e]*csum[e];
1256         }
1257       }
1258     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
1259   }
1260   PetscFunctionReturn(0);
1261 }
1262 
1263 #undef __FUNCT__
1264 #define __FUNCT__ "DMPlexComputeGeometryFVM_3D_Internal"
1265 /* Centroid_i = (\sum_n V_n Cn_i ) / V */
1266 static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1267 {
1268   PetscSection    coordSection;
1269   Vec             coordinates;
1270   PetscScalar    *coords = NULL;
1271   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
1272   const PetscInt *faces, *facesO;
1273   PetscInt        numFaces, f, coordSize, numCorners, p, d;
1274   PetscErrorCode  ierr;
1275 
1276   PetscFunctionBegin;
1277   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
1278   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1279   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1280 
1281   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
1282   ierr = DMPlexGetConeSize(dm, cell, &numFaces);CHKERRQ(ierr);
1283   ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
1284   ierr = DMPlexGetConeOrientation(dm, cell, &facesO);CHKERRQ(ierr);
1285   for (f = 0; f < numFaces; ++f) {
1286     ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
1287     numCorners = coordSize/dim;
1288     switch (numCorners) {
1289     case 3:
1290       for (d = 0; d < dim; ++d) {
1291         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1292         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1293         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
1294       }
1295       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1296       if (facesO[f] < 0) vtmp = -vtmp;
1297       vsum += vtmp;
1298       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
1299         for (d = 0; d < dim; ++d) {
1300           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1301         }
1302       }
1303       break;
1304     case 4:
1305       /* DO FOR PYRAMID */
1306       /* First tet */
1307       for (d = 0; d < dim; ++d) {
1308         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1309         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1310         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
1311       }
1312       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1313       if (facesO[f] < 0) vtmp = -vtmp;
1314       vsum += vtmp;
1315       if (centroid) {
1316         for (d = 0; d < dim; ++d) {
1317           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1318         }
1319       }
1320       /* Second tet */
1321       for (d = 0; d < dim; ++d) {
1322         coordsTmp[0*dim+d] = PetscRealPart(coords[1*dim+d]);
1323         coordsTmp[1*dim+d] = PetscRealPart(coords[2*dim+d]);
1324         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
1325       }
1326       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1327       if (facesO[f] < 0) vtmp = -vtmp;
1328       vsum += vtmp;
1329       if (centroid) {
1330         for (d = 0; d < dim; ++d) {
1331           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1332         }
1333       }
1334       break;
1335     default:
1336       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle faces with %D vertices", numCorners);
1337     }
1338     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
1339   }
1340   if (vol)     *vol = PetscAbsReal(vsum);
1341   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
1342   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
1343   PetscFunctionReturn(0);
1344 }
1345 
1346 #undef __FUNCT__
1347 #define __FUNCT__ "DMPlexComputeCellGeometryFVM"
1348 /*@C
1349   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
1350 
1351   Collective on DM
1352 
1353   Input Arguments:
1354 + dm   - the DM
1355 - cell - the cell
1356 
1357   Output Arguments:
1358 + volume   - the cell volume
1359 . centroid - the cell centroid
1360 - normal - the cell normal, if appropriate
1361 
1362   Level: advanced
1363 
1364   Fortran Notes:
1365   Since it returns arrays, this routine is only available in Fortran 90, and you must
1366   include petsc.h90 in your code.
1367 
1368 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1369 @*/
1370 PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1371 {
1372   PetscInt       depth, dim;
1373   PetscErrorCode ierr;
1374 
1375   PetscFunctionBegin;
1376   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1377   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1378   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
1379   /* We need to keep a pointer to the depth label */
1380   ierr = DMGetLabelValue(dm, "depth", cell, &depth);CHKERRQ(ierr);
1381   /* Cone size is now the number of faces */
1382   switch (depth) {
1383   case 1:
1384     ierr = DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1385     break;
1386   case 2:
1387     ierr = DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1388     break;
1389   case 3:
1390     ierr = DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1391     break;
1392   default:
1393     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1394   }
1395   PetscFunctionReturn(0);
1396 }
1397 
1398 #undef __FUNCT__
1399 #define __FUNCT__ "DMPlexComputeGeometryFEM"
1400 /* This should also take a PetscFE argument I think */
1401 PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
1402 {
1403   DM             dmCell;
1404   Vec            coordinates;
1405   PetscSection   coordSection, sectionCell;
1406   PetscScalar   *cgeom;
1407   PetscInt       cStart, cEnd, cMax, c;
1408   PetscErrorCode ierr;
1409 
1410   PetscFunctionBegin;
1411   ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
1412   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1413   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1414   ierr = DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1415   ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
1416   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);CHKERRQ(ierr);
1417   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1418   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
1419   cEnd = cMax < 0 ? cEnd : cMax;
1420   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1421   /* TODO This needs to be multiplied by Nq for non-affine */
1422   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFECellGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1423   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1424   ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
1425   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1426   ierr = DMCreateLocalVector(dmCell, cellgeom);CHKERRQ(ierr);
1427   ierr = VecGetArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1428   for (c = cStart; c < cEnd; ++c) {
1429     PetscFECellGeom *cg;
1430 
1431     ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1432     ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
1433     ierr = DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v0, cg->J, cg->invJ, &cg->detJ);CHKERRQ(ierr);
1434     if (cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cg->detJ, c);
1435   }
1436   ierr = VecRestoreArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1437   ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1438   PetscFunctionReturn(0);
1439 }
1440 
1441 #undef __FUNCT__
1442 #define __FUNCT__ "DMPlexComputeGeometryFVM"
1443 /*@
1444   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
1445 
1446   Input Parameter:
1447 . dm - The DM
1448 
1449   Output Parameters:
1450 + cellgeom - A Vec of PetscFVCellGeom data
1451 . facegeom - A Vec of PetscFVFaceGeom data
1452 
1453   Level: developer
1454 
1455 .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
1456 @*/
1457 PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
1458 {
1459   DM             dmFace, dmCell;
1460   DMLabel        ghostLabel;
1461   PetscSection   sectionFace, sectionCell;
1462   PetscSection   coordSection;
1463   Vec            coordinates;
1464   PetscScalar   *fgeom, *cgeom;
1465   PetscReal      minradius, gminradius;
1466   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
1467   PetscErrorCode ierr;
1468 
1469   PetscFunctionBegin;
1470   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1471   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1472   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1473   /* Make cell centroids and volumes */
1474   ierr = DMClone(dm, &dmCell);CHKERRQ(ierr);
1475   ierr = DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1476   ierr = DMSetCoordinatesLocal(dmCell, coordinates);CHKERRQ(ierr);
1477   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);CHKERRQ(ierr);
1478   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1479   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1480   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1481   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1482   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1483   ierr = DMSetDefaultSection(dmCell, sectionCell);CHKERRQ(ierr);
1484   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1485   ierr = DMCreateLocalVector(dmCell, cellgeom);CHKERRQ(ierr);
1486   if (cEndInterior < 0) {
1487     cEndInterior = cEnd;
1488   }
1489   ierr = VecGetArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1490   for (c = cStart; c < cEndInterior; ++c) {
1491     PetscFVCellGeom *cg;
1492 
1493     ierr = DMPlexPointLocalRef(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1494     ierr = PetscMemzero(cg, sizeof(*cg));CHKERRQ(ierr);
1495     ierr = DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);CHKERRQ(ierr);
1496   }
1497   /* Compute face normals and minimum cell radius */
1498   ierr = DMClone(dm, &dmFace);CHKERRQ(ierr);
1499   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);CHKERRQ(ierr);
1500   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1501   ierr = PetscSectionSetChart(sectionFace, fStart, fEnd);CHKERRQ(ierr);
1502   for (f = fStart; f < fEnd; ++f) {ierr = PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));CHKERRQ(ierr);}
1503   ierr = PetscSectionSetUp(sectionFace);CHKERRQ(ierr);
1504   ierr = DMSetDefaultSection(dmFace, sectionFace);CHKERRQ(ierr);
1505   ierr = PetscSectionDestroy(&sectionFace);CHKERRQ(ierr);
1506   ierr = DMCreateLocalVector(dmFace, facegeom);CHKERRQ(ierr);
1507   ierr = VecGetArray(*facegeom, &fgeom);CHKERRQ(ierr);
1508   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1509   minradius = PETSC_MAX_REAL;
1510   for (f = fStart; f < fEnd; ++f) {
1511     PetscFVFaceGeom *fg;
1512     PetscReal        area;
1513     PetscInt         ghost = -1, d, numChildren;
1514 
1515     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1516     ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
1517     if (ghost >= 0 || numChildren) continue;
1518     ierr = DMPlexPointLocalRef(dmFace, f, fgeom, &fg);CHKERRQ(ierr);
1519     ierr = DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);CHKERRQ(ierr);
1520     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
1521     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
1522     {
1523       PetscFVCellGeom *cL, *cR;
1524       PetscInt         ncells;
1525       const PetscInt  *cells;
1526       PetscReal       *lcentroid, *rcentroid;
1527       PetscReal        l[3], r[3], v[3];
1528 
1529       ierr = DMPlexGetSupport(dm, f, &cells);CHKERRQ(ierr);
1530       ierr = DMPlexGetSupportSize(dm, f, &ncells);CHKERRQ(ierr);
1531       ierr = DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);CHKERRQ(ierr);
1532       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
1533       if (ncells > 1) {
1534         ierr = DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);CHKERRQ(ierr);
1535         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
1536       }
1537       else {
1538         rcentroid = fg->centroid;
1539       }
1540       ierr = DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);CHKERRQ(ierr);
1541       ierr = DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);CHKERRQ(ierr);
1542       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
1543       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
1544         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
1545       }
1546       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
1547         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]);
1548         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]);
1549         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
1550       }
1551       if (cells[0] < cEndInterior) {
1552         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
1553         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
1554       }
1555       if (ncells > 1 && cells[1] < cEndInterior) {
1556         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
1557         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
1558       }
1559     }
1560   }
1561   ierr = MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
1562   ierr = DMPlexSetMinRadius(dm, gminradius);CHKERRQ(ierr);
1563   /* Compute centroids of ghost cells */
1564   for (c = cEndInterior; c < cEnd; ++c) {
1565     PetscFVFaceGeom *fg;
1566     const PetscInt  *cone,    *support;
1567     PetscInt         coneSize, supportSize, s;
1568 
1569     ierr = DMPlexGetConeSize(dmCell, c, &coneSize);CHKERRQ(ierr);
1570     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
1571     ierr = DMPlexGetCone(dmCell, c, &cone);CHKERRQ(ierr);
1572     ierr = DMPlexGetSupportSize(dmCell, cone[0], &supportSize);CHKERRQ(ierr);
1573     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
1574     ierr = DMPlexGetSupport(dmCell, cone[0], &support);CHKERRQ(ierr);
1575     ierr = DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);CHKERRQ(ierr);
1576     for (s = 0; s < 2; ++s) {
1577       /* Reflect ghost centroid across plane of face */
1578       if (support[s] == c) {
1579         PetscFVCellGeom       *ci;
1580         PetscFVCellGeom       *cg;
1581         PetscReal              c2f[3], a;
1582 
1583         ierr = DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);CHKERRQ(ierr);
1584         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
1585         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
1586         ierr = DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);CHKERRQ(ierr);
1587         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
1588         cg->volume = ci->volume;
1589       }
1590     }
1591   }
1592   ierr = VecRestoreArray(*facegeom, &fgeom);CHKERRQ(ierr);
1593   ierr = VecRestoreArray(*cellgeom, &cgeom);CHKERRQ(ierr);
1594   ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1595   ierr = DMDestroy(&dmFace);CHKERRQ(ierr);
1596   PetscFunctionReturn(0);
1597 }
1598 
1599 #undef __FUNCT__
1600 #define __FUNCT__ "DMPlexGetMinRadius"
1601 /*@C
1602   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
1603 
1604   Not collective
1605 
1606   Input Argument:
1607 . dm - the DM
1608 
1609   Output Argument:
1610 . minradius - the minium cell radius
1611 
1612   Level: developer
1613 
1614 .seealso: DMGetCoordinates()
1615 @*/
1616 PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
1617 {
1618   PetscFunctionBegin;
1619   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1620   PetscValidPointer(minradius,2);
1621   *minradius = ((DM_Plex*) dm->data)->minradius;
1622   PetscFunctionReturn(0);
1623 }
1624 
1625 #undef __FUNCT__
1626 #define __FUNCT__ "DMPlexSetMinRadius"
1627 /*@C
1628   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
1629 
1630   Logically collective
1631 
1632   Input Arguments:
1633 + dm - the DM
1634 - minradius - the minium cell radius
1635 
1636   Level: developer
1637 
1638 .seealso: DMSetCoordinates()
1639 @*/
1640 PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
1641 {
1642   PetscFunctionBegin;
1643   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
1644   ((DM_Plex*) dm->data)->minradius = minradius;
1645   PetscFunctionReturn(0);
1646 }
1647 
1648 #undef __FUNCT__
1649 #define __FUNCT__ "BuildGradientReconstruction_Internal"
1650 static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
1651 {
1652   DMLabel        ghostLabel;
1653   PetscScalar   *dx, *grad, **gref;
1654   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
1655   PetscErrorCode ierr;
1656 
1657   PetscFunctionBegin;
1658   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1659   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1660   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1661   ierr = DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);CHKERRQ(ierr);
1662   ierr = PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);CHKERRQ(ierr);
1663   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1664   ierr = PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);CHKERRQ(ierr);
1665   for (c = cStart; c < cEndInterior; c++) {
1666     const PetscInt        *faces;
1667     PetscInt               numFaces, usedFaces, f, d;
1668     PetscFVCellGeom        *cg;
1669     PetscBool              boundary;
1670     PetscInt               ghost;
1671 
1672     ierr = DMPlexPointLocalRead(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1673     ierr = DMPlexGetConeSize(dm, c, &numFaces);CHKERRQ(ierr);
1674     ierr = DMPlexGetCone(dm, c, &faces);CHKERRQ(ierr);
1675     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
1676     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
1677       PetscFVCellGeom       *cg1;
1678       PetscFVFaceGeom       *fg;
1679       const PetscInt        *fcells;
1680       PetscInt               ncell, side;
1681 
1682       ierr = DMLabelGetValue(ghostLabel, faces[f], &ghost);CHKERRQ(ierr);
1683       ierr = DMIsBoundaryPoint(dm, faces[f], &boundary);CHKERRQ(ierr);
1684       if ((ghost >= 0) || boundary) continue;
1685       ierr  = DMPlexGetSupport(dm, faces[f], &fcells);CHKERRQ(ierr);
1686       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
1687       ncell = fcells[!side];    /* the neighbor */
1688       ierr  = DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);CHKERRQ(ierr);
1689       ierr  = DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);CHKERRQ(ierr);
1690       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
1691       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
1692     }
1693     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
1694     ierr = PetscFVComputeGradient(fvm, usedFaces, dx, grad);CHKERRQ(ierr);
1695     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
1696       ierr = DMLabelGetValue(ghostLabel, faces[f], &ghost);CHKERRQ(ierr);
1697       ierr = DMIsBoundaryPoint(dm, faces[f], &boundary);CHKERRQ(ierr);
1698       if ((ghost >= 0) || boundary) continue;
1699       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
1700       ++usedFaces;
1701     }
1702   }
1703   ierr = PetscFree3(dx, grad, gref);CHKERRQ(ierr);
1704   PetscFunctionReturn(0);
1705 }
1706 
1707 #undef __FUNCT__
1708 #define __FUNCT__ "BuildGradientReconstruction_Internal_Tree"
1709 static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
1710 {
1711   DMLabel        ghostLabel;
1712   PetscScalar   *dx, *grad, **gref;
1713   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
1714   PetscSection   neighSec;
1715   PetscInt     (*neighbors)[2];
1716   PetscInt      *counter;
1717   PetscErrorCode ierr;
1718 
1719   PetscFunctionBegin;
1720   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1721   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1722   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1723   if (cEndInterior < 0) {
1724     cEndInterior = cEnd;
1725   }
1726   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);CHKERRQ(ierr);
1727   ierr = PetscSectionSetChart(neighSec,cStart,cEndInterior);CHKERRQ(ierr);
1728   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1729   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1730   for (f = fStart; f < fEnd; f++) {
1731     const PetscInt        *fcells;
1732     PetscBool              boundary;
1733     PetscInt               ghost = -1;
1734     PetscInt               numChildren, numCells, c;
1735 
1736     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1737     ierr = DMIsBoundaryPoint(dm, f, &boundary);CHKERRQ(ierr);
1738     ierr = DMPlexGetTreeChildren(dm, f, &numChildren, NULL);CHKERRQ(ierr);
1739     if ((ghost >= 0) || boundary || numChildren) continue;
1740     ierr = DMPlexGetSupportSize(dm, f, &numCells);CHKERRQ(ierr);
1741     if (numCells == 2) {
1742       ierr = DMPlexGetSupport(dm, f, &fcells);CHKERRQ(ierr);
1743       for (c = 0; c < 2; c++) {
1744         PetscInt cell = fcells[c];
1745 
1746         if (cell >= cStart && cell < cEndInterior) {
1747           ierr = PetscSectionAddDof(neighSec,cell,1);CHKERRQ(ierr);
1748         }
1749       }
1750     }
1751   }
1752   ierr = PetscSectionSetUp(neighSec);CHKERRQ(ierr);
1753   ierr = PetscSectionGetMaxDof(neighSec,&maxNumFaces);CHKERRQ(ierr);
1754   ierr = PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);CHKERRQ(ierr);
1755   nStart = 0;
1756   ierr = PetscSectionGetStorageSize(neighSec,&nEnd);CHKERRQ(ierr);
1757   ierr = PetscMalloc1((nEnd-nStart),&neighbors);CHKERRQ(ierr);
1758   ierr = PetscCalloc1((cEndInterior-cStart),&counter);CHKERRQ(ierr);
1759   for (f = fStart; f < fEnd; f++) {
1760     const PetscInt        *fcells;
1761     PetscBool              boundary;
1762     PetscInt               ghost = -1;
1763     PetscInt               numChildren, numCells, c;
1764 
1765     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, f, &ghost);CHKERRQ(ierr);}
1766     ierr = DMIsBoundaryPoint(dm, f, &boundary);CHKERRQ(ierr);
1767     ierr = DMPlexGetTreeChildren(dm, f, &numChildren, NULL);CHKERRQ(ierr);
1768     if ((ghost >= 0) || boundary || numChildren) continue;
1769     ierr = DMPlexGetSupportSize(dm, f, &numCells);CHKERRQ(ierr);
1770     if (numCells == 2) {
1771       ierr  = DMPlexGetSupport(dm, f, &fcells);CHKERRQ(ierr);
1772       for (c = 0; c < 2; c++) {
1773         PetscInt cell = fcells[c], off;
1774 
1775         if (cell >= cStart && cell < cEndInterior) {
1776           ierr = PetscSectionGetOffset(neighSec,cell,&off);CHKERRQ(ierr);
1777           off += counter[cell - cStart]++;
1778           neighbors[off][0] = f;
1779           neighbors[off][1] = fcells[1 - c];
1780         }
1781       }
1782     }
1783   }
1784   ierr = PetscFree(counter);CHKERRQ(ierr);
1785   ierr = PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);CHKERRQ(ierr);
1786   for (c = cStart; c < cEndInterior; c++) {
1787     PetscInt               numFaces, f, d, off, ghost = -1;
1788     PetscFVCellGeom        *cg;
1789 
1790     ierr = DMPlexPointLocalRead(dmCell, c, cgeom, &cg);CHKERRQ(ierr);
1791     ierr = PetscSectionGetDof(neighSec, c, &numFaces);CHKERRQ(ierr);
1792     ierr = PetscSectionGetOffset(neighSec, c, &off);CHKERRQ(ierr);
1793     if (ghostLabel) {ierr = DMLabelGetValue(ghostLabel, c, &ghost);CHKERRQ(ierr);}
1794     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);
1795     for (f = 0; f < numFaces; ++f) {
1796       PetscFVCellGeom       *cg1;
1797       PetscFVFaceGeom       *fg;
1798       const PetscInt        *fcells;
1799       PetscInt               ncell, side, nface;
1800 
1801       nface = neighbors[off + f][0];
1802       ncell = neighbors[off + f][1];
1803       ierr  = DMPlexGetSupport(dm,nface,&fcells);CHKERRQ(ierr);
1804       side  = (c != fcells[0]);
1805       ierr  = DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);CHKERRQ(ierr);
1806       ierr  = DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);CHKERRQ(ierr);
1807       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
1808       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
1809     }
1810     ierr = PetscFVComputeGradient(fvm, numFaces, dx, grad);CHKERRQ(ierr);
1811     for (f = 0; f < numFaces; ++f) {
1812       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
1813     }
1814   }
1815   ierr = PetscFree3(dx, grad, gref);CHKERRQ(ierr);
1816   ierr = PetscSectionDestroy(&neighSec);CHKERRQ(ierr);
1817   ierr = PetscFree(neighbors);CHKERRQ(ierr);
1818   PetscFunctionReturn(0);
1819 }
1820 
1821 #undef __FUNCT__
1822 #define __FUNCT__ "DMPlexComputeGradientFVM"
1823 /*@
1824   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
1825 
1826   Collective on DM
1827 
1828   Input Arguments:
1829 + dm  - The DM
1830 . fvm - The PetscFV
1831 . faceGeometry - The face geometry from DMPlexGetFaceGeometryFVM()
1832 - cellGeometry - The face geometry from DMPlexGetCellGeometryFVM()
1833 
1834   Output Parameters:
1835 + faceGeometry - The geometric factors for gradient calculation are inserted
1836 - dmGrad - The DM describing the layout of gradient data
1837 
1838   Level: developer
1839 
1840 .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
1841 @*/
1842 PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
1843 {
1844   DM             dmFace, dmCell;
1845   PetscScalar   *fgeom, *cgeom;
1846   PetscSection   sectionGrad, parentSection;
1847   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;
1848   PetscErrorCode ierr;
1849 
1850   PetscFunctionBegin;
1851   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1852   ierr = PetscFVGetNumComponents(fvm, &pdim);CHKERRQ(ierr);
1853   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1854   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1855   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
1856   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1857   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1858   ierr = VecGetArray(faceGeometry, &fgeom);CHKERRQ(ierr);
1859   ierr = VecGetArray(cellGeometry, &cgeom);CHKERRQ(ierr);
1860   ierr = DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1861   if (!parentSection) {
1862     ierr = BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
1863   }
1864   else {
1865     ierr = BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);CHKERRQ(ierr);
1866   }
1867   ierr = VecRestoreArray(faceGeometry, &fgeom);CHKERRQ(ierr);
1868   ierr = VecRestoreArray(cellGeometry, &cgeom);CHKERRQ(ierr);
1869   /* Create storage for gradients */
1870   ierr = DMClone(dm, dmGrad);CHKERRQ(ierr);
1871   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);CHKERRQ(ierr);
1872   ierr = PetscSectionSetChart(sectionGrad, cStart, cEnd);CHKERRQ(ierr);
1873   for (c = cStart; c < cEnd; ++c) {ierr = PetscSectionSetDof(sectionGrad, c, pdim*dim);CHKERRQ(ierr);}
1874   ierr = PetscSectionSetUp(sectionGrad);CHKERRQ(ierr);
1875   ierr = DMSetDefaultSection(*dmGrad, sectionGrad);CHKERRQ(ierr);
1876   ierr = PetscSectionDestroy(&sectionGrad);CHKERRQ(ierr);
1877   PetscFunctionReturn(0);
1878 }
1879