xref: /petsc/src/dm/impls/plex/plexfem.c (revision 95c0884e6f7665b705eebf88174e89dc920c2fc0)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 #include <petscsf.h>
3 
4 #include <petsc/private/hashsetij.h>
5 #include <petsc/private/petscfeimpl.h>
6 #include <petsc/private/petscfvimpl.h>
7 
8 /*@
9   DMPlexGetScale - Get the scale for the specified fundamental unit
10 
11   Not collective
12 
13   Input Arguments:
14 + dm   - the DM
15 - unit - The SI unit
16 
17   Output Argument:
18 . scale - The value used to scale all quantities with this unit
19 
20   Level: advanced
21 
22 .seealso: DMPlexSetScale(), PetscUnit
23 @*/
24 PetscErrorCode DMPlexGetScale(DM dm, PetscUnit unit, PetscReal *scale)
25 {
26   DM_Plex *mesh = (DM_Plex*) dm->data;
27 
28   PetscFunctionBegin;
29   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
30   PetscValidPointer(scale, 3);
31   *scale = mesh->scale[unit];
32   PetscFunctionReturn(0);
33 }
34 
35 /*@
36   DMPlexSetScale - Set the scale for the specified fundamental unit
37 
38   Not collective
39 
40   Input Arguments:
41 + dm   - the DM
42 . unit - The SI unit
43 - scale - The value used to scale all quantities with this unit
44 
45   Level: advanced
46 
47 .seealso: DMPlexGetScale(), PetscUnit
48 @*/
49 PetscErrorCode DMPlexSetScale(DM dm, PetscUnit unit, PetscReal scale)
50 {
51   DM_Plex *mesh = (DM_Plex*) dm->data;
52 
53   PetscFunctionBegin;
54   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
55   mesh->scale[unit] = scale;
56   PetscFunctionReturn(0);
57 }
58 
59 static PetscErrorCode DMPlexProjectRigidBody_Private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *mode, void *ctx)
60 {
61   const PetscInt eps[3][3][3] = {{{0, 0, 0}, {0, 0, 1}, {0, -1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, 0, 0}}, {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}}};
62   PetscInt *ctxInt  = (PetscInt *) ctx;
63   PetscInt  dim2    = ctxInt[0];
64   PetscInt  d       = ctxInt[1];
65   PetscInt  i, j, k = dim > 2 ? d - dim : d;
66 
67   PetscFunctionBegin;
68   if (dim != dim2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input dimension %d does not match context dimension %d", dim, dim2);
69   for (i = 0; i < dim; i++) mode[i] = 0.;
70   if (d < dim) {
71     mode[d] = 1.; /* Translation along axis d */
72   } else {
73     for (i = 0; i < dim; i++) {
74       for (j = 0; j < dim; j++) {
75         mode[j] += eps[i][j][k]*X[i]; /* Rotation about axis d */
76       }
77     }
78   }
79   PetscFunctionReturn(0);
80 }
81 
82 /*@C
83   DMPlexCreateRigidBody - For the default global section, create rigid body modes by function space interpolation
84 
85   Collective on DM
86 
87   Input Arguments:
88 . dm - the DM
89 
90   Output Argument:
91 . sp - the null space
92 
93   Note: This is necessary to provide a suitable coarse space for algebraic multigrid
94 
95   Level: advanced
96 
97 .seealso: MatNullSpaceCreate(), PCGAMG
98 @*/
99 PetscErrorCode DMPlexCreateRigidBody(DM dm, MatNullSpace *sp)
100 {
101   MPI_Comm       comm;
102   Vec            mode[6];
103   PetscSection   section, globalSection;
104   PetscInt       dim, dimEmbed, n, m, d, i, j;
105   PetscErrorCode ierr;
106 
107   PetscFunctionBegin;
108   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
109   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
110   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
111   if (dim == 1) {
112     ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
113     PetscFunctionReturn(0);
114   }
115   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
116   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
117   ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
118   m    = (dim*(dim+1))/2;
119   ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
120   ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
121   ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
122   for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
123   for (d = 0; d < m; d++) {
124     PetscInt         ctx[2];
125     PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *) = DMPlexProjectRigidBody_Private;
126     void            *voidctx = (void *) (&ctx[0]);
127 
128     ctx[0] = dimEmbed;
129     ctx[1] = d;
130     ierr = DMProjectFunction(dm, 0.0, &func, &voidctx, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
131   }
132   for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
133   /* Orthonormalize system */
134   for (i = dim; i < m; ++i) {
135     PetscScalar dots[6];
136 
137     ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
138     for (j = 0; j < i; ++j) dots[j] *= -1.0;
139     ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
140     ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
141   }
142   ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
143   for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
144   PetscFunctionReturn(0);
145 }
146 
147 /*@C
148   DMPlexCreateRigidBodies - For the default global section, create rigid body modes by function space interpolation
149 
150   Collective on DM
151 
152   Input Arguments:
153 + dm    - the DM
154 . nb    - The number of bodies
155 . label - The DMLabel marking each domain
156 . nids  - The number of ids per body
157 - ids   - An array of the label ids in sequence for each domain
158 
159   Output Argument:
160 . sp - the null space
161 
162   Note: This is necessary to provide a suitable coarse space for algebraic multigrid
163 
164   Level: advanced
165 
166 .seealso: MatNullSpaceCreate()
167 @*/
168 PetscErrorCode DMPlexCreateRigidBodies(DM dm, PetscInt nb, DMLabel label, const PetscInt nids[], const PetscInt ids[], MatNullSpace *sp)
169 {
170   MPI_Comm       comm;
171   PetscSection   section, globalSection;
172   Vec           *mode;
173   PetscScalar   *dots;
174   PetscInt       dim, dimEmbed, n, m, b, d, i, j, off;
175   PetscErrorCode ierr;
176 
177   PetscFunctionBegin;
178   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
179   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
180   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
181   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
182   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
183   ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
184   m    = nb * (dim*(dim+1))/2;
185   ierr = PetscMalloc2(m, &mode, m, &dots);CHKERRQ(ierr);
186   ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
187   ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
188   ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
189   for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
190   for (b = 0, off = 0; b < nb; ++b) {
191     for (d = 0; d < m/nb; ++d) {
192       PetscInt         ctx[2];
193       PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *) = DMPlexProjectRigidBody_Private;
194       void            *voidctx = (void *) (&ctx[0]);
195 
196       ctx[0] = dimEmbed;
197       ctx[1] = d;
198       ierr = DMProjectFunctionLabel(dm, 0.0, label, nids[b], &ids[off], 0, NULL, &func, &voidctx, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
199       off   += nids[b];
200     }
201   }
202   for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
203   /* Orthonormalize system */
204   for (i = 0; i < m; ++i) {
205     ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
206     for (j = 0; j < i; ++j) dots[j] *= -1.0;
207     ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
208     ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
209   }
210   ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
211   for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
212   ierr = PetscFree2(mode, dots);CHKERRQ(ierr);
213   PetscFunctionReturn(0);
214 }
215 
216 /*@
217   DMPlexSetMaxProjectionHeight - In DMPlexProjectXXXLocal() functions, the projected values of a basis function's dofs
218   are computed by associating the basis function with one of the mesh points in its transitively-closed support, and
219   evaluating the dual space basis of that point.  A basis function is associated with the point in its
220   transitively-closed support whose mesh height is highest (w.r.t. DAG height), but not greater than the maximum
221   projection height, which is set with this function.  By default, the maximum projection height is zero, which means
222   that only mesh cells are used to project basis functions.  A height of one, for example, evaluates a cell-interior
223   basis functions using its cells dual space basis, but all other basis functions with the dual space basis of a face.
224 
225   Input Parameters:
226 + dm - the DMPlex object
227 - height - the maximum projection height >= 0
228 
229   Level: advanced
230 
231 .seealso: DMPlexGetMaxProjectionHeight(), DMProjectFunctionLocal(), DMProjectFunctionLabelLocal()
232 @*/
233 PetscErrorCode DMPlexSetMaxProjectionHeight(DM dm, PetscInt height)
234 {
235   DM_Plex *plex = (DM_Plex *) dm->data;
236 
237   PetscFunctionBegin;
238   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
239   plex->maxProjectionHeight = height;
240   PetscFunctionReturn(0);
241 }
242 
243 /*@
244   DMPlexGetMaxProjectionHeight - Get the maximum height (w.r.t. DAG) of mesh points used to evaluate dual bases in
245   DMPlexProjectXXXLocal() functions.
246 
247   Input Parameters:
248 . dm - the DMPlex object
249 
250   Output Parameters:
251 . height - the maximum projection height
252 
253   Level: intermediate
254 
255 .seealso: DMPlexSetMaxProjectionHeight(), DMProjectFunctionLocal(), DMProjectFunctionLabelLocal()
256 @*/
257 PetscErrorCode DMPlexGetMaxProjectionHeight(DM dm, PetscInt *height)
258 {
259   DM_Plex *plex = (DM_Plex *) dm->data;
260 
261   PetscFunctionBegin;
262   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
263   *height = plex->maxProjectionHeight;
264   PetscFunctionReturn(0);
265 }
266 
267 /*@C
268   DMPlexInsertBoundaryValuesEssential - Insert boundary values into a local vector
269 
270   Input Parameters:
271 + dm     - The DM, with a PetscDS that matches the problem being constrained
272 . time   - The time
273 . field  - The field to constrain
274 . Nc     - The number of constrained field components, or 0 for all components
275 . comps  - An array of constrained component numbers, or NULL for all components
276 . label  - The DMLabel defining constrained points
277 . numids - The number of DMLabel ids for constrained points
278 . ids    - An array of ids for constrained points
279 . func   - A pointwise function giving boundary values
280 - ctx    - An optional user context for bcFunc
281 
282   Output Parameter:
283 . locX   - A local vector to receives the boundary values
284 
285   Level: developer
286 
287 .seealso: DMPlexInsertBoundaryValuesEssentialField(), DMAddBoundary()
288 @*/
289 PetscErrorCode DMPlexInsertBoundaryValuesEssential(DM dm, PetscReal time, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[], PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void *ctx, Vec locX)
290 {
291   PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
292   void            **ctxs;
293   PetscInt          numFields;
294   PetscErrorCode    ierr;
295 
296   PetscFunctionBegin;
297   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
298   ierr = PetscCalloc2(numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
299   funcs[field] = func;
300   ctxs[field]  = ctx;
301   ierr = DMProjectFunctionLabelLocal(dm, time, label, numids, ids, Nc, comps, funcs, ctxs, INSERT_BC_VALUES, locX);CHKERRQ(ierr);
302   ierr = PetscFree2(funcs,ctxs);CHKERRQ(ierr);
303   PetscFunctionReturn(0);
304 }
305 
306 /*@C
307   DMPlexInsertBoundaryValuesEssentialField - Insert boundary values into a local vector
308 
309   Input Parameters:
310 + dm     - The DM, with a PetscDS that matches the problem being constrained
311 . time   - The time
312 . locU   - A local vector with the input solution values
313 . field  - The field to constrain
314 . Nc     - The number of constrained field components, or 0 for all components
315 . comps  - An array of constrained component numbers, or NULL for all components
316 . label  - The DMLabel defining constrained points
317 . numids - The number of DMLabel ids for constrained points
318 . ids    - An array of ids for constrained points
319 . func   - A pointwise function giving boundary values
320 - ctx    - An optional user context for bcFunc
321 
322   Output Parameter:
323 . locX   - A local vector to receives the boundary values
324 
325   Level: developer
326 
327 .seealso: DMPlexInsertBoundaryValuesEssential(), DMAddBoundary()
328 @*/
329 PetscErrorCode DMPlexInsertBoundaryValuesEssentialField(DM dm, PetscReal time, Vec locU, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[],
330                                                         void (*func)(PetscInt, PetscInt, PetscInt,
331                                                                      const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
332                                                                      const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
333                                                                      PetscReal, const PetscReal[], PetscInt, const PetscScalar[],
334                                                                      PetscScalar[]),
335                                                         void *ctx, Vec locX)
336 {
337   void (**funcs)(PetscInt, PetscInt, PetscInt,
338                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
339                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
340                  PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]);
341   void            **ctxs;
342   PetscInt          numFields;
343   PetscErrorCode    ierr;
344 
345   PetscFunctionBegin;
346   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
347   ierr = PetscCalloc2(numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
348   funcs[field] = func;
349   ctxs[field]  = ctx;
350   ierr = DMProjectFieldLabelLocal(dm, time, label, numids, ids, Nc, comps, locU, funcs, INSERT_BC_VALUES, locX);CHKERRQ(ierr);
351   ierr = PetscFree2(funcs,ctxs);CHKERRQ(ierr);
352   PetscFunctionReturn(0);
353 }
354 
355 /*@C
356   DMPlexInsertBoundaryValuesRiemann - Insert boundary values into a local vector
357 
358   Input Parameters:
359 + dm     - The DM, with a PetscDS that matches the problem being constrained
360 . time   - The time
361 . faceGeometry - A vector with the FVM face geometry information
362 . cellGeometry - A vector with the FVM cell geometry information
363 . Grad         - A vector with the FVM cell gradient information
364 . field  - The field to constrain
365 . Nc     - The number of constrained field components, or 0 for all components
366 . comps  - An array of constrained component numbers, or NULL for all components
367 . label  - The DMLabel defining constrained points
368 . numids - The number of DMLabel ids for constrained points
369 . ids    - An array of ids for constrained points
370 . func   - A pointwise function giving boundary values
371 - ctx    - An optional user context for bcFunc
372 
373   Output Parameter:
374 . locX   - A local vector to receives the boundary values
375 
376   Note: This implementation currently ignores the numcomps/comps argument from DMAddBoundary()
377 
378   Level: developer
379 
380 .seealso: DMPlexInsertBoundaryValuesEssential(), DMPlexInsertBoundaryValuesEssentialField(), DMAddBoundary()
381 @*/
382 PetscErrorCode DMPlexInsertBoundaryValuesRiemann(DM dm, PetscReal time, Vec faceGeometry, Vec cellGeometry, Vec Grad, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[],
383                                                  PetscErrorCode (*func)(PetscReal,const PetscReal*,const PetscReal*,const PetscScalar*,PetscScalar*,void*), void *ctx, Vec locX)
384 {
385   PetscDS            prob;
386   PetscSF            sf;
387   DM                 dmFace, dmCell, dmGrad;
388   const PetscScalar *facegeom, *cellgeom = NULL, *grad;
389   const PetscInt    *leaves;
390   PetscScalar       *x, *fx;
391   PetscInt           dim, nleaves, loc, fStart, fEnd, pdim, i;
392   PetscErrorCode     ierr, ierru = 0;
393 
394   PetscFunctionBegin;
395   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
396   ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
397   nleaves = PetscMax(0, nleaves);
398   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
399   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
400   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
401   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
402   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
403   if (cellGeometry) {
404     ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
405     ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
406   }
407   if (Grad) {
408     PetscFV fv;
409 
410     ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fv);CHKERRQ(ierr);
411     ierr = VecGetDM(Grad, &dmGrad);CHKERRQ(ierr);
412     ierr = VecGetArrayRead(Grad, &grad);CHKERRQ(ierr);
413     ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
414     ierr = DMGetWorkArray(dm, pdim, MPIU_SCALAR, &fx);CHKERRQ(ierr);
415   }
416   ierr = VecGetArray(locX, &x);CHKERRQ(ierr);
417   for (i = 0; i < numids; ++i) {
418     IS              faceIS;
419     const PetscInt *faces;
420     PetscInt        numFaces, f;
421 
422     ierr = DMLabelGetStratumIS(label, ids[i], &faceIS);CHKERRQ(ierr);
423     if (!faceIS) continue; /* No points with that id on this process */
424     ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
425     ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
426     for (f = 0; f < numFaces; ++f) {
427       const PetscInt         face = faces[f], *cells;
428       PetscFVFaceGeom        *fg;
429 
430       if ((face < fStart) || (face >= fEnd)) continue; /* Refinement adds non-faces to labels */
431       ierr = PetscFindInt(face, nleaves, (PetscInt *) leaves, &loc);CHKERRQ(ierr);
432       if (loc >= 0) continue;
433       ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
434       ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
435       if (Grad) {
436         PetscFVCellGeom       *cg;
437         PetscScalar           *cx, *cgrad;
438         PetscScalar           *xG;
439         PetscReal              dx[3];
440         PetscInt               d;
441 
442         ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cg);CHKERRQ(ierr);
443         ierr = DMPlexPointLocalRead(dm, cells[0], x, &cx);CHKERRQ(ierr);
444         ierr = DMPlexPointLocalRead(dmGrad, cells[0], grad, &cgrad);CHKERRQ(ierr);
445         ierr = DMPlexPointLocalFieldRef(dm, cells[1], field, x, &xG);CHKERRQ(ierr);
446         DMPlex_WaxpyD_Internal(dim, -1, cg->centroid, fg->centroid, dx);
447         for (d = 0; d < pdim; ++d) fx[d] = cx[d] + DMPlex_DotD_Internal(dim, &cgrad[d*dim], dx);
448         ierru = (*func)(time, fg->centroid, fg->normal, fx, xG, ctx);
449         if (ierru) {
450           ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
451           ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
452           goto cleanup;
453         }
454       } else {
455         PetscScalar       *xI;
456         PetscScalar       *xG;
457 
458         ierr = DMPlexPointLocalRead(dm, cells[0], x, &xI);CHKERRQ(ierr);
459         ierr = DMPlexPointLocalFieldRef(dm, cells[1], field, x, &xG);CHKERRQ(ierr);
460         ierru = (*func)(time, fg->centroid, fg->normal, xI, xG, ctx);
461         if (ierru) {
462           ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
463           ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
464           goto cleanup;
465         }
466       }
467     }
468     ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
469     ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
470   }
471   cleanup:
472   ierr = VecRestoreArray(locX, &x);CHKERRQ(ierr);
473   if (Grad) {
474     ierr = DMRestoreWorkArray(dm, pdim, MPIU_SCALAR, &fx);CHKERRQ(ierr);
475     ierr = VecRestoreArrayRead(Grad, &grad);CHKERRQ(ierr);
476   }
477   if (cellGeometry) {ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);}
478   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
479   CHKERRQ(ierru);
480   PetscFunctionReturn(0);
481 }
482 
483 PetscErrorCode DMPlexInsertBoundaryValues_Plex(DM dm, PetscBool insertEssential, Vec locX, PetscReal time, Vec faceGeomFVM, Vec cellGeomFVM, Vec gradFVM)
484 {
485   PetscInt       numBd, b;
486   PetscErrorCode ierr;
487 
488   PetscFunctionBegin;
489   ierr = PetscDSGetNumBoundary(dm->prob, &numBd);CHKERRQ(ierr);
490   for (b = 0; b < numBd; ++b) {
491     DMBoundaryConditionType type;
492     const char             *labelname;
493     DMLabel                 label;
494     PetscInt                field, Nc;
495     const PetscInt         *comps;
496     PetscObject             obj;
497     PetscClassId            id;
498     void                    (*func)(void);
499     PetscInt                numids;
500     const PetscInt         *ids;
501     void                   *ctx;
502 
503     ierr = DMGetBoundary(dm, b, &type, NULL, &labelname, &field, &Nc, &comps, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
504     if (insertEssential != (type & DM_BC_ESSENTIAL)) continue;
505     ierr = DMGetLabel(dm, labelname, &label);CHKERRQ(ierr);
506     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
507     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
508     if (id == PETSCFE_CLASSID) {
509       switch (type) {
510         /* for FEM, there is no insertion to be done for non-essential boundary conditions */
511       case DM_BC_ESSENTIAL:
512         ierr = DMPlexLabelAddCells(dm,label);CHKERRQ(ierr);
513         ierr = DMPlexInsertBoundaryValuesEssential(dm, time, field, Nc, comps, label, numids, ids, (PetscErrorCode (*)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *)) func, ctx, locX);CHKERRQ(ierr);
514         ierr = DMPlexLabelClearCells(dm,label);CHKERRQ(ierr);
515         break;
516       case DM_BC_ESSENTIAL_FIELD:
517         ierr = DMPlexLabelAddCells(dm,label);CHKERRQ(ierr);
518         ierr = DMPlexInsertBoundaryValuesEssentialField(dm, time, locX, field, Nc, comps, label, numids, ids,
519                                                         (void (*)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
520                                                                   const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
521                                                                   PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[])) func, ctx, locX);CHKERRQ(ierr);
522         ierr = DMPlexLabelClearCells(dm,label);CHKERRQ(ierr);
523         break;
524       default: break;
525       }
526     } else if (id == PETSCFV_CLASSID) {
527       if (!faceGeomFVM) continue;
528       ierr = DMPlexInsertBoundaryValuesRiemann(dm, time, faceGeomFVM, cellGeomFVM, gradFVM, field, Nc, comps, label, numids, ids,
529                                                (PetscErrorCode (*)(PetscReal,const PetscReal*,const PetscReal*,const PetscScalar*,PetscScalar*,void*)) func, ctx, locX);CHKERRQ(ierr);
530     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
531   }
532   PetscFunctionReturn(0);
533 }
534 
535 /*@
536   DMPlexInsertBoundaryValues - Puts coefficients which represent boundary values into the local solution vector
537 
538   Input Parameters:
539 + dm - The DM
540 . insertEssential - Should I insert essential (e.g. Dirichlet) or inessential (e.g. Neumann) boundary conditions
541 . time - The time
542 . faceGeomFVM - Face geometry data for FV discretizations
543 . cellGeomFVM - Cell geometry data for FV discretizations
544 - gradFVM - Gradient reconstruction data for FV discretizations
545 
546   Output Parameters:
547 . locX - Solution updated with boundary values
548 
549   Level: developer
550 
551 .seealso: DMProjectFunctionLabelLocal()
552 @*/
553 PetscErrorCode DMPlexInsertBoundaryValues(DM dm, PetscBool insertEssential, Vec locX, PetscReal time, Vec faceGeomFVM, Vec cellGeomFVM, Vec gradFVM)
554 {
555   PetscErrorCode ierr;
556 
557   PetscFunctionBegin;
558   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
559   PetscValidHeaderSpecific(locX, VEC_CLASSID, 2);
560   if (faceGeomFVM) {PetscValidHeaderSpecific(faceGeomFVM, VEC_CLASSID, 4);}
561   if (cellGeomFVM) {PetscValidHeaderSpecific(cellGeomFVM, VEC_CLASSID, 5);}
562   if (gradFVM)     {PetscValidHeaderSpecific(gradFVM, VEC_CLASSID, 6);}
563   ierr = PetscTryMethod(dm,"DMPlexInsertBoundaryValues_C",(DM,PetscBool,Vec,PetscReal,Vec,Vec,Vec),(dm,insertEssential,locX,time,faceGeomFVM,cellGeomFVM,gradFVM));CHKERRQ(ierr);
564   PetscFunctionReturn(0);
565 }
566 
567 PetscErrorCode DMComputeL2Diff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
568 {
569   Vec              localX;
570   PetscErrorCode   ierr;
571 
572   PetscFunctionBegin;
573   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
574   ierr = DMPlexInsertBoundaryValues(dm, PETSC_TRUE, localX, time, NULL, NULL, NULL);CHKERRQ(ierr);
575   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
576   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
577   ierr = DMPlexComputeL2DiffLocal(dm, time, funcs, ctxs, localX, diff);CHKERRQ(ierr);
578   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
579   PetscFunctionReturn(0);
580 }
581 
582 /*@C
583   DMComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
584 
585   Input Parameters:
586 + dm     - The DM
587 . time   - The time
588 . funcs  - The functions to evaluate for each field component
589 . ctxs   - Optional array of contexts to pass to each function, or NULL.
590 - localX - The coefficient vector u_h, a local vector
591 
592   Output Parameter:
593 . diff - The diff ||u - u_h||_2
594 
595   Level: developer
596 
597 .seealso: DMProjectFunction(), DMComputeL2FieldDiff(), DMComputeL2GradientDiff()
598 @*/
599 PetscErrorCode DMPlexComputeL2DiffLocal(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec localX, PetscReal *diff)
600 {
601   const PetscInt   debug = 0;
602   PetscSection     section;
603   PetscQuadrature  quad;
604   PetscScalar     *funcVal, *interpolant;
605   PetscReal       *coords, *detJ, *J;
606   PetscReal        localDiff = 0.0;
607   const PetscReal *quadWeights;
608   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cellHeight, cStart, cEnd, cEndInterior, c, field, fieldOffset;
609   PetscErrorCode   ierr;
610 
611   PetscFunctionBegin;
612   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
613   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
614   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
615   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
616   for (field = 0; field < numFields; ++field) {
617     PetscObject  obj;
618     PetscClassId id;
619     PetscInt     Nc;
620 
621     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
622     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
623     if (id == PETSCFE_CLASSID) {
624       PetscFE fe = (PetscFE) obj;
625 
626       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
627       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
628     } else if (id == PETSCFV_CLASSID) {
629       PetscFV fv = (PetscFV) obj;
630 
631       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
632       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
633     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
634     numComponents += Nc;
635   }
636   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, NULL, &quadWeights);CHKERRQ(ierr);
637   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
638   ierr = PetscMalloc5(numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
639   ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
640   ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
641   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
642   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
643   for (c = cStart; c < cEnd; ++c) {
644     PetscScalar *x = NULL;
645     PetscReal    elemDiff = 0.0;
646     PetscInt     qc = 0;
647 
648     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
649     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
650 
651     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
652       PetscObject  obj;
653       PetscClassId id;
654       void * const ctx = ctxs ? ctxs[field] : NULL;
655       PetscInt     Nb, Nc, q, fc;
656 
657       ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
658       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
659       if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
660       else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
661       else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
662       if (debug) {
663         char title[1024];
664         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
665         ierr = DMPrintCellVector(c, title, Nb, &x[fieldOffset]);CHKERRQ(ierr);
666       }
667       for (q = 0; q < Nq; ++q) {
668         if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, point %D", detJ[q], c, q);
669         ierr = (*funcs[field])(coordDim, time, &coords[coordDim * q], Nc, funcVal, ctx);
670         if (ierr) {
671           PetscErrorCode ierr2;
672           ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
673           ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
674           ierr2 = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
675           CHKERRQ(ierr);
676         }
677         if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
678         else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
679         else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
680         for (fc = 0; fc < Nc; ++fc) {
681           const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
682           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q]);CHKERRQ(ierr);}
683           elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
684         }
685       }
686       fieldOffset += Nb;
687       qc += Nc;
688     }
689     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
690     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
691     localDiff += elemDiff;
692   }
693   ierr  = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
694   ierr  = MPIU_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
695   *diff = PetscSqrtReal(*diff);
696   PetscFunctionReturn(0);
697 }
698 
699 PetscErrorCode DMComputeL2GradientDiff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
700 {
701   const PetscInt   debug = 0;
702   PetscSection     section;
703   PetscQuadrature  quad;
704   Vec              localX;
705   PetscScalar     *funcVal, *interpolant;
706   const PetscReal *quadPoints, *quadWeights;
707   PetscReal       *coords, *realSpaceDer, *J, *invJ, *detJ;
708   PetscReal        localDiff = 0.0;
709   PetscInt         dim, coordDim, qNc = 0, Nq = 0, numFields, numComponents = 0, cStart, cEnd, cEndInterior, c, field, fieldOffset;
710   PetscErrorCode   ierr;
711 
712   PetscFunctionBegin;
713   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
714   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
715   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
716   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
717   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
718   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
719   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
720   for (field = 0; field < numFields; ++field) {
721     PetscFE  fe;
722     PetscInt Nc;
723 
724     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
725     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
726     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
727     numComponents += Nc;
728   }
729   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
730   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
731   /* ierr = DMProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
732   ierr = PetscMalloc7(numComponents,&funcVal,coordDim*Nq,&coords,coordDim*Nq,&realSpaceDer,coordDim*coordDim*Nq,&J,coordDim*coordDim*Nq,&invJ,numComponents,&interpolant,Nq,&detJ);CHKERRQ(ierr);
733   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
734   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
735   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
736   for (c = cStart; c < cEnd; ++c) {
737     PetscScalar *x = NULL;
738     PetscReal    elemDiff = 0.0;
739     PetscInt     qc = 0;
740 
741     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, invJ, detJ);CHKERRQ(ierr);
742     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
743 
744     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
745       PetscFE          fe;
746       void * const     ctx = ctxs ? ctxs[field] : NULL;
747       PetscReal       *basisDer;
748       PetscInt         Nb, Nc, q, fc;
749 
750       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
751       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
752       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
753       ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
754       if (debug) {
755         char title[1024];
756         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
757         ierr = DMPrintCellVector(c, title, Nb, &x[fieldOffset]);CHKERRQ(ierr);
758       }
759       for (q = 0; q < Nq; ++q) {
760         if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature points %D", detJ[q], c, q);
761         ierr = (*funcs[field])(coordDim, time, &coords[q*coordDim], n, numFields, funcVal, ctx);
762         if (ierr) {
763           PetscErrorCode ierr2;
764           ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
765           ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
766           ierr2 = PetscFree7(funcVal,coords,realSpaceDer,J,invJ,interpolant,detJ);CHKERRQ(ierr2);
767           CHKERRQ(ierr);
768         }
769         ierr = PetscFEInterpolateGradient_Static(fe, &x[fieldOffset], coordDim, invJ, n, q, interpolant);CHKERRQ(ierr);
770         for (fc = 0; fc < Nc; ++fc) {
771           const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
772           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d fieldDer %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q]);CHKERRQ(ierr);}
773           elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
774         }
775       }
776       fieldOffset += Nb;
777       qc          += Nc;
778     }
779     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
780     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
781     localDiff += elemDiff;
782   }
783   ierr  = PetscFree7(funcVal,coords,realSpaceDer,J,invJ,interpolant,detJ);CHKERRQ(ierr);
784   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
785   ierr  = MPIU_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
786   *diff = PetscSqrtReal(*diff);
787   PetscFunctionReturn(0);
788 }
789 
790 PetscErrorCode DMComputeL2FieldDiff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
791 {
792   const PetscInt   debug = 0;
793   PetscSection     section;
794   PetscQuadrature  quad;
795   Vec              localX;
796   PetscScalar     *funcVal, *interpolant;
797   PetscReal       *coords, *detJ, *J;
798   PetscReal       *localDiff;
799   const PetscReal *quadPoints, *quadWeights;
800   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
801   PetscErrorCode   ierr;
802 
803   PetscFunctionBegin;
804   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
805   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
806   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
807   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
808   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
809   ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
810   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
811   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
812   for (field = 0; field < numFields; ++field) {
813     PetscObject  obj;
814     PetscClassId id;
815     PetscInt     Nc;
816 
817     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
818     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
819     if (id == PETSCFE_CLASSID) {
820       PetscFE fe = (PetscFE) obj;
821 
822       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
823       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
824     } else if (id == PETSCFV_CLASSID) {
825       PetscFV fv = (PetscFV) obj;
826 
827       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
828       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
829     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
830     numComponents += Nc;
831   }
832   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
833   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
834   ierr = PetscCalloc6(numFields,&localDiff,numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
835   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
836   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
837   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
838   for (c = cStart; c < cEnd; ++c) {
839     PetscScalar *x = NULL;
840     PetscInt     qc = 0;
841 
842     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
843     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
844 
845     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
846       PetscObject  obj;
847       PetscClassId id;
848       void * const ctx = ctxs ? ctxs[field] : NULL;
849       PetscInt     Nb, Nc, q, fc;
850 
851       PetscReal       elemDiff = 0.0;
852 
853       ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
854       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
855       if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
856       else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
857       else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
858       if (debug) {
859         char title[1024];
860         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
861         ierr = DMPrintCellVector(c, title, Nb*Nc, &x[fieldOffset]);CHKERRQ(ierr);
862       }
863       for (q = 0; q < Nq; ++q) {
864         if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature point %D", detJ, c, q);
865         ierr = (*funcs[field])(coordDim, time, &coords[coordDim*q], numFields, funcVal, ctx);
866         if (ierr) {
867           PetscErrorCode ierr2;
868           ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
869           ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
870           ierr2 = PetscFree6(localDiff,funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
871           CHKERRQ(ierr);
872         }
873         if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
874         else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
875         else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
876         for (fc = 0; fc < Nc; ++fc) {
877           const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
878           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d point %g %g %g diff %g\n", c, field, coordDim > 0 ? coords[0] : 0., coordDim > 1 ? coords[1] : 0., coordDim > 2 ? coords[2] : 0., PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q]);CHKERRQ(ierr);}
879           elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
880         }
881       }
882       fieldOffset += Nb;
883       qc          += Nc;
884       localDiff[field] += elemDiff;
885     }
886     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
887   }
888   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
889   ierr = MPIU_Allreduce(localDiff, diff, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
890   for (field = 0; field < numFields; ++field) diff[field] = PetscSqrtReal(diff[field]);
891   ierr = PetscFree6(localDiff,funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
892   PetscFunctionReturn(0);
893 }
894 
895 /*@C
896   DMPlexComputeL2DiffVec - This function computes the cellwise L_2 difference between a function u and an FEM interpolant solution u_h, and stores it in a Vec.
897 
898   Input Parameters:
899 + dm    - The DM
900 . time  - The time
901 . funcs - The functions to evaluate for each field component: NULL means that component does not contribute to error calculation
902 . ctxs  - Optional array of contexts to pass to each function, or NULL.
903 - X     - The coefficient vector u_h
904 
905   Output Parameter:
906 . D - A Vec which holds the difference ||u - u_h||_2 for each cell
907 
908   Level: developer
909 
910 .seealso: DMProjectFunction(), DMComputeL2Diff(), DMPlexComputeL2FieldDiff(), DMComputeL2GradientDiff()
911 @*/
912 PetscErrorCode DMPlexComputeL2DiffVec(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, Vec D)
913 {
914   PetscSection     section;
915   PetscQuadrature  quad;
916   Vec              localX;
917   PetscScalar     *funcVal, *interpolant;
918   PetscReal       *coords, *detJ, *J;
919   const PetscReal *quadPoints, *quadWeights;
920   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
921   PetscErrorCode   ierr;
922 
923   PetscFunctionBegin;
924   ierr = VecSet(D, 0.0);CHKERRQ(ierr);
925   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
926   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
927   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
928   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
929   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
930   ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
931   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
932   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
933   for (field = 0; field < numFields; ++field) {
934     PetscObject  obj;
935     PetscClassId id;
936     PetscInt     Nc;
937 
938     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
939     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
940     if (id == PETSCFE_CLASSID) {
941       PetscFE fe = (PetscFE) obj;
942 
943       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
944       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
945     } else if (id == PETSCFV_CLASSID) {
946       PetscFV fv = (PetscFV) obj;
947 
948       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
949       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
950     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
951     numComponents += Nc;
952   }
953   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
954   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
955   ierr = PetscMalloc5(numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
956   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
957   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
958   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
959   for (c = cStart; c < cEnd; ++c) {
960     PetscScalar *x = NULL;
961     PetscScalar  elemDiff = 0.0;
962     PetscInt     qc = 0;
963 
964     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
965     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
966 
967     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
968       PetscObject  obj;
969       PetscClassId id;
970       void * const ctx = ctxs ? ctxs[field] : NULL;
971       PetscInt     Nb, Nc, q, fc;
972 
973       ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
974       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
975       if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
976       else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
977       else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
978       if (funcs[field]) {
979         for (q = 0; q < Nq; ++q) {
980           if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature points %D", (double)detJ[q], c, q);
981           ierr = (*funcs[field])(coordDim, time, &coords[q*coordDim], Nc, funcVal, ctx);
982           if (ierr) {
983             PetscErrorCode ierr2;
984             ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
985             ierr2 = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
986             ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
987             CHKERRQ(ierr);
988           }
989           if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
990           else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
991           else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
992           for (fc = 0; fc < Nc; ++fc) {
993             const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
994             elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
995           }
996         }
997       }
998       fieldOffset += Nb;
999       qc          += Nc;
1000     }
1001     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
1002     ierr = VecSetValue(D, c - cStart, elemDiff, INSERT_VALUES);CHKERRQ(ierr);
1003   }
1004   ierr = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
1005   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
1006   ierr = VecSqrtAbs(D);CHKERRQ(ierr);
1007   PetscFunctionReturn(0);
1008 }
1009 
1010 /*@C
1011   DMPlexComputeGradientClementInterpolant - This function computes the L2 projection of the cellwise gradient of a function u onto P1, and stores it in a Vec.
1012 
1013   Input Parameters:
1014 + dm - The DM
1015 - LocX  - The coefficient vector u_h
1016 
1017   Output Parameter:
1018 . locC - A Vec which holds the Clement interpolant of the gradient
1019 
1020   Notes:
1021     Add citation to (Clement, 1975) and definition of the interpolant
1022   \nabla u_h(v_i) = \sum_{T_i \in support(v_i)} |T_i| \nabla u_h(T_i) / \sum_{T_i \in support(v_i)} |T_i| where |T_i| is the cell volume
1023 
1024   Level: developer
1025 
1026 .seealso: DMProjectFunction(), DMComputeL2Diff(), DMPlexComputeL2FieldDiff(), DMComputeL2GradientDiff()
1027 @*/
1028 PetscErrorCode DMPlexComputeGradientClementInterpolant(DM dm, Vec locX, Vec locC)
1029 {
1030   DM_Plex         *mesh  = (DM_Plex *) dm->data;
1031   PetscInt         debug = mesh->printFEM;
1032   DM               dmC;
1033   PetscSection     section;
1034   PetscQuadrature  quad;
1035   PetscScalar     *interpolant, *gradsum;
1036   PetscReal       *coords, *detJ, *J, *invJ;
1037   const PetscReal *quadPoints, *quadWeights;
1038   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, vStart, vEnd, v, field, fieldOffset;
1039   PetscErrorCode   ierr;
1040 
1041   PetscFunctionBegin;
1042   ierr = VecGetDM(locC, &dmC);CHKERRQ(ierr);
1043   ierr = VecSet(locC, 0.0);CHKERRQ(ierr);
1044   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1045   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
1046   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1047   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1048   for (field = 0; field < numFields; ++field) {
1049     PetscObject  obj;
1050     PetscClassId id;
1051     PetscInt     Nc;
1052 
1053     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1054     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1055     if (id == PETSCFE_CLASSID) {
1056       PetscFE fe = (PetscFE) obj;
1057 
1058       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1059       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1060     } else if (id == PETSCFV_CLASSID) {
1061       PetscFV fv = (PetscFV) obj;
1062 
1063       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
1064       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
1065     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
1066     numComponents += Nc;
1067   }
1068   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
1069   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
1070   ierr = PetscMalloc6(coordDim*numComponents*2,&gradsum,coordDim*numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J,coordDim*coordDim*Nq,&invJ);CHKERRQ(ierr);
1071   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1072   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1073   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1074   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1075   for (v = vStart; v < vEnd; ++v) {
1076     PetscScalar volsum = 0.0;
1077     PetscInt   *star = NULL;
1078     PetscInt    starSize, st, d, fc;
1079 
1080     ierr = PetscMemzero(gradsum, coordDim*numComponents * sizeof(PetscScalar));CHKERRQ(ierr);
1081     ierr = DMPlexGetTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
1082     for (st = 0; st < starSize*2; st += 2) {
1083       const PetscInt cell = star[st];
1084       PetscScalar   *grad = &gradsum[coordDim*numComponents];
1085       PetscScalar   *x    = NULL;
1086       PetscReal      vol  = 0.0;
1087 
1088       if ((cell < cStart) || (cell >= cEnd)) continue;
1089       ierr = DMPlexComputeCellGeometryFEM(dm, cell, quad, coords, J, invJ, detJ);CHKERRQ(ierr);
1090       ierr = DMPlexVecGetClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr);
1091       for (field = 0, fieldOffset = 0; field < numFields; ++field) {
1092         PetscObject  obj;
1093         PetscClassId id;
1094         PetscInt     Nb, Nc, q, qc = 0;
1095 
1096         ierr = PetscMemzero(grad, coordDim*numComponents * sizeof(PetscScalar));CHKERRQ(ierr);
1097         ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1098         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1099         if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
1100         else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
1101         else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
1102         for (q = 0; q < Nq; ++q) {
1103           if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature points %D", (double)detJ[q], cell, q);
1104           if (ierr) {
1105             PetscErrorCode ierr2;
1106             ierr2 = DMPlexVecRestoreClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr2);
1107             ierr2 = DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr2);
1108             ierr2 = PetscFree4(interpolant,coords,detJ,J);CHKERRQ(ierr2);
1109             CHKERRQ(ierr);
1110           }
1111           if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolateGradient_Static((PetscFE) obj, &x[fieldOffset], coordDim, invJ, NULL, q, interpolant);CHKERRQ(ierr);}
1112           else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
1113           for (fc = 0; fc < Nc; ++fc) {
1114             const PetscReal wt = quadWeights[q*qNc+qc+fc];
1115 
1116             for (d = 0; d < coordDim; ++d) grad[fc*coordDim+d] += interpolant[fc*dim+d]*wt*detJ[q];
1117           }
1118           vol += quadWeights[q*qNc]*detJ[q];
1119         }
1120         fieldOffset += Nb;
1121         qc          += Nc;
1122       }
1123       ierr = DMPlexVecRestoreClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr);
1124       for (fc = 0; fc < numComponents; ++fc) {
1125         for (d = 0; d < coordDim; ++d) {
1126           gradsum[fc*coordDim+d] += grad[fc*coordDim+d];
1127         }
1128       }
1129       volsum += vol;
1130       if (debug) {
1131         ierr = PetscPrintf(PETSC_COMM_SELF, "Cell %D gradient: [", cell);CHKERRQ(ierr);
1132         for (fc = 0; fc < numComponents; ++fc) {
1133           for (d = 0; d < coordDim; ++d) {
1134             if (fc || d > 0) {ierr = PetscPrintf(PETSC_COMM_SELF, ", ");CHKERRQ(ierr);}
1135             ierr = PetscPrintf(PETSC_COMM_SELF, "%g", (double)PetscRealPart(grad[fc*coordDim+d]));CHKERRQ(ierr);
1136           }
1137         }
1138         ierr = PetscPrintf(PETSC_COMM_SELF, "]\n");CHKERRQ(ierr);
1139       }
1140     }
1141     for (fc = 0; fc < numComponents; ++fc) {
1142       for (d = 0; d < coordDim; ++d) gradsum[fc*coordDim+d] /= volsum;
1143     }
1144     ierr = DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
1145     ierr = DMPlexVecSetClosure(dmC, NULL, locC, v, gradsum, INSERT_VALUES);CHKERRQ(ierr);
1146   }
1147   ierr = PetscFree6(gradsum,interpolant,coords,detJ,J,invJ);CHKERRQ(ierr);
1148   PetscFunctionReturn(0);
1149 }
1150 
1151 static PetscErrorCode DMPlexComputeIntegral_Internal(DM dm, Vec X, PetscInt cStart, PetscInt cEnd, PetscScalar *cintegral, void *user)
1152 {
1153   DM                 dmAux = NULL;
1154   PetscDS            prob,    probAux = NULL;
1155   PetscSection       section, sectionAux;
1156   Vec                locX,    locA;
1157   PetscInt           dim, numCells = cEnd - cStart, c, f;
1158   PetscBool          useFVM = PETSC_FALSE;
1159   /* DS */
1160   PetscInt           Nf,    totDim,    *uOff, *uOff_x, numConstants;
1161   PetscInt           NfAux, totDimAux, *aOff;
1162   PetscScalar       *u, *a;
1163   const PetscScalar *constants;
1164   /* Geometry */
1165   PetscFEGeom       *cgeomFEM;
1166   DM                 dmGrad;
1167   PetscQuadrature    affineQuad = NULL;
1168   Vec                cellGeometryFVM = NULL, faceGeometryFVM = NULL, locGrad = NULL;
1169   PetscFVCellGeom   *cgeomFVM;
1170   const PetscScalar *lgrad;
1171   PetscBool          isAffine;
1172   DMField            coordField;
1173   IS                 cellIS;
1174   PetscErrorCode     ierr;
1175 
1176   PetscFunctionBegin;
1177   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1178   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1179   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1180   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1181   /* Determine which discretizations we have */
1182   for (f = 0; f < Nf; ++f) {
1183     PetscObject  obj;
1184     PetscClassId id;
1185 
1186     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1187     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1188     if (id == PETSCFV_CLASSID) useFVM = PETSC_TRUE;
1189   }
1190   /* Get local solution with boundary values */
1191   ierr = DMGetLocalVector(dm, &locX);CHKERRQ(ierr);
1192   ierr = DMPlexInsertBoundaryValues(dm, PETSC_TRUE, locX, 0.0, NULL, NULL, NULL);CHKERRQ(ierr);
1193   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, locX);CHKERRQ(ierr);
1194   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, locX);CHKERRQ(ierr);
1195   /* Read DS information */
1196   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1197   ierr = PetscDSGetComponentOffsets(prob, &uOff);CHKERRQ(ierr);
1198   ierr = PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);CHKERRQ(ierr);
1199   ierr = ISCreateStride(PETSC_COMM_SELF,numCells,cStart,1,&cellIS);CHKERRQ(ierr);
1200   ierr = PetscDSGetConstants(prob, &numConstants, &constants);CHKERRQ(ierr);
1201   /* Read Auxiliary DS information */
1202   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1203   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1204   if (dmAux) {
1205     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1206     ierr = PetscDSGetNumFields(probAux, &NfAux);CHKERRQ(ierr);
1207     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1208     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1209     ierr = PetscDSGetComponentOffsets(probAux, &aOff);CHKERRQ(ierr);
1210   }
1211   /* Allocate data  arrays */
1212   ierr = PetscCalloc1(numCells*totDim, &u);CHKERRQ(ierr);
1213   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1214   /* Read out geometry */
1215   ierr = DMGetCoordinateField(dm,&coordField);CHKERRQ(ierr);
1216   ierr = DMFieldGetFEInvariance(coordField,cellIS,NULL,&isAffine,NULL);CHKERRQ(ierr);
1217   if (isAffine) {
1218     ierr = DMFieldCreateDefaultQuadrature(coordField,cellIS,&affineQuad);CHKERRQ(ierr);
1219     if (affineQuad) {
1220       ierr = DMFieldCreateFEGeom(coordField,cellIS,affineQuad,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1221     }
1222   }
1223   if (useFVM) {
1224     PetscFV   fv = NULL;
1225     Vec       grad;
1226     PetscInt  fStart, fEnd;
1227     PetscBool compGrad;
1228 
1229     for (f = 0; f < Nf; ++f) {
1230       PetscObject  obj;
1231       PetscClassId id;
1232 
1233       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1234       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1235       if (id == PETSCFV_CLASSID) {fv = (PetscFV) obj; break;}
1236     }
1237     ierr = PetscFVGetComputeGradients(fv, &compGrad);CHKERRQ(ierr);
1238     ierr = PetscFVSetComputeGradients(fv, PETSC_TRUE);CHKERRQ(ierr);
1239     ierr = DMPlexComputeGeometryFVM(dm, &cellGeometryFVM, &faceGeometryFVM);CHKERRQ(ierr);
1240     ierr = DMPlexComputeGradientFVM(dm, fv, faceGeometryFVM, cellGeometryFVM, &dmGrad);CHKERRQ(ierr);
1241     ierr = PetscFVSetComputeGradients(fv, compGrad);CHKERRQ(ierr);
1242     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1243     /* Reconstruct and limit cell gradients */
1244     ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1245     ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1246     ierr = DMPlexReconstructGradients_Internal(dm, fv, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1247     /* Communicate gradient values */
1248     ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1249     ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1250     ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1251     ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1252     /* Handle non-essential (e.g. outflow) boundary values */
1253     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, 0.0, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1254     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1255   }
1256   /* Read out data from inputs */
1257   for (c = cStart; c < cEnd; ++c) {
1258     PetscScalar *x = NULL;
1259     PetscInt     i;
1260 
1261     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1262     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1263     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1264     if (dmAux) {
1265       ierr = DMPlexVecGetClosure(dmAux, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1266       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1267       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1268     }
1269   }
1270   /* Do integration for each field */
1271   for (f = 0; f < Nf; ++f) {
1272     PetscObject  obj;
1273     PetscClassId id;
1274     PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1275 
1276     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1277     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1278     if (id == PETSCFE_CLASSID) {
1279       PetscFE         fe = (PetscFE) obj;
1280       PetscQuadrature q;
1281       PetscFEGeom     *chunkGeom = NULL;
1282       PetscInt        Nq, Nb;
1283 
1284       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1285       ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1286       ierr = PetscQuadratureGetData(q, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1287       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1288       blockSize = Nb*Nq;
1289       batchSize = numBlocks * blockSize;
1290       ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1291       numChunks = numCells / (numBatches*batchSize);
1292       Ne        = numChunks*numBatches*batchSize;
1293       Nr        = numCells % (numBatches*batchSize);
1294       offset    = numCells - Nr;
1295       if (!affineQuad) {
1296         ierr = DMFieldCreateFEGeom(coordField,cellIS,q,PETSC_FALSE,&cgeomFEM);CHKERRQ(ierr);
1297       }
1298       ierr = PetscFEGeomGetChunk(cgeomFEM,0,offset,&chunkGeom);CHKERRQ(ierr);
1299       ierr = PetscFEIntegrate(fe, prob, f, Ne, chunkGeom, u, probAux, a, cintegral);CHKERRQ(ierr);
1300       ierr = PetscFEGeomGetChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1301       ierr = PetscFEIntegrate(fe, prob, f, Nr, chunkGeom, &u[offset*totDim], probAux, &a[offset*totDimAux], &cintegral[offset*Nf]);CHKERRQ(ierr);
1302       ierr = PetscFEGeomRestoreChunk(cgeomFEM,offset,numCells,&chunkGeom);CHKERRQ(ierr);
1303       if (!affineQuad) {
1304         ierr = PetscFEGeomDestroy(&cgeomFEM);CHKERRQ(ierr);
1305       }
1306     } else if (id == PETSCFV_CLASSID) {
1307       PetscInt       foff;
1308       PetscPointFunc obj_func;
1309       PetscScalar    lint;
1310 
1311       ierr = PetscDSGetObjective(prob, f, &obj_func);CHKERRQ(ierr);
1312       ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1313       if (obj_func) {
1314         for (c = 0; c < numCells; ++c) {
1315           PetscScalar *u_x;
1316 
1317           ierr = DMPlexPointLocalRead(dmGrad, c, lgrad, &u_x);CHKERRQ(ierr);
1318           obj_func(dim, Nf, NfAux, uOff, uOff_x, &u[totDim*c+foff], NULL, u_x, aOff, NULL, &a[totDimAux*c], NULL, NULL, 0.0, cgeomFVM[c].centroid, numConstants, constants, &lint);
1319           cintegral[c*Nf+f] += PetscRealPart(lint)*cgeomFVM[c].volume;
1320         }
1321       }
1322     } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1323   }
1324   /* Cleanup data arrays */
1325   if (useFVM) {
1326     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1327     ierr = VecRestoreArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1328     ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1329     ierr = VecDestroy(&faceGeometryFVM);CHKERRQ(ierr);
1330     ierr = VecDestroy(&cellGeometryFVM);CHKERRQ(ierr);
1331     ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
1332   }
1333   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1334   ierr = PetscFree(u);CHKERRQ(ierr);
1335   /* Cleanup */
1336   if (affineQuad) {
1337     ierr = PetscFEGeomDestroy(&cgeomFEM);CHKERRQ(ierr);
1338   }
1339   ierr = PetscQuadratureDestroy(&affineQuad);CHKERRQ(ierr);
1340   ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
1341   ierr = DMRestoreLocalVector(dm, &locX);CHKERRQ(ierr);
1342   PetscFunctionReturn(0);
1343 }
1344 
1345 /*@
1346   DMPlexComputeIntegralFEM - Form the integral over the domain from the global input X using pointwise functions specified by the user
1347 
1348   Input Parameters:
1349 + dm - The mesh
1350 . X  - Global input vector
1351 - user - The user context
1352 
1353   Output Parameter:
1354 . integral - Integral for each field
1355 
1356   Level: developer
1357 
1358 .seealso: DMPlexComputeResidualFEM()
1359 @*/
1360 PetscErrorCode DMPlexComputeIntegralFEM(DM dm, Vec X, PetscScalar *integral, void *user)
1361 {
1362   DM_Plex       *mesh = (DM_Plex *) dm->data;
1363   PetscScalar   *cintegral, *lintegral;
1364   PetscInt       Nf, f, cellHeight, cStart, cEnd, cEndInterior[4], cell;
1365   PetscErrorCode ierr;
1366 
1367   PetscFunctionBegin;
1368   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1369   PetscValidHeaderSpecific(X, VEC_CLASSID, 2);
1370   PetscValidPointer(integral, 3);
1371   ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
1372   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
1373   ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
1374   ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
1375   ierr = DMPlexGetHybridBounds(dm, &cEndInterior[0], &cEndInterior[1], &cEndInterior[2], &cEndInterior[3]);CHKERRQ(ierr);
1376   cEnd = cEndInterior[cellHeight] < 0 ? cEnd : cEndInterior[cellHeight];
1377   /* TODO Introduce a loop over large chunks (right now this is a single chunk) */
1378   ierr = PetscCalloc2(Nf, &lintegral, (cEnd-cStart)*Nf, &cintegral);CHKERRQ(ierr);
1379   ierr = DMPlexComputeIntegral_Internal(dm, X, cStart, cEnd, cintegral, user);CHKERRQ(ierr);
1380   /* Sum up values */
1381   for (cell = cStart; cell < cEnd; ++cell) {
1382     const PetscInt c = cell - cStart;
1383 
1384     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, "Cell Integral", Nf, &cintegral[c*Nf]);CHKERRQ(ierr);}
1385     for (f = 0; f < Nf; ++f) lintegral[f] += cintegral[c*Nf+f];
1386   }
1387   ierr = MPIU_Allreduce(lintegral, integral, Nf, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
1388   if (mesh->printFEM) {
1389     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Integral:");CHKERRQ(ierr);
1390     for (f = 0; f < Nf; ++f) {ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), " %g", (double) PetscRealPart(integral[f]));CHKERRQ(ierr);}
1391     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "\n");CHKERRQ(ierr);
1392   }
1393   ierr = PetscFree2(lintegral, cintegral);CHKERRQ(ierr);
1394   ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
1395   PetscFunctionReturn(0);
1396 }
1397 
1398 /*@
1399   DMPlexComputeCellwiseIntegralFEM - Form the vector of cellwise integrals F from the global input X using pointwise functions specified by the user
1400 
1401   Input Parameters:
1402 + dm - The mesh
1403 . X  - Global input vector
1404 - user - The user context
1405 
1406   Output Parameter:
1407 . integral - Cellwise integrals for each field
1408 
1409   Level: developer
1410 
1411 .seealso: DMPlexComputeResidualFEM()
1412 @*/
1413 PetscErrorCode DMPlexComputeCellwiseIntegralFEM(DM dm, Vec X, Vec F, void *user)
1414 {
1415   DM_Plex       *mesh = (DM_Plex *) dm->data;
1416   DM             dmF;
1417   PetscSection   sectionF;
1418   PetscScalar   *cintegral, *af;
1419   PetscInt       Nf, f, cellHeight, cStart, cEnd, cEndInterior[4], cell;
1420   PetscErrorCode ierr;
1421 
1422   PetscFunctionBegin;
1423   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1424   PetscValidHeaderSpecific(X, VEC_CLASSID, 2);
1425   PetscValidHeaderSpecific(F, VEC_CLASSID, 3);
1426   ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
1427   ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
1428   ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
1429   ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
1430   ierr = DMPlexGetHybridBounds(dm, &cEndInterior[0], &cEndInterior[1], &cEndInterior[2], &cEndInterior[3]);CHKERRQ(ierr);
1431   cEnd = cEndInterior[cellHeight] < 0 ? cEnd : cEndInterior[cellHeight];
1432   /* TODO Introduce a loop over large chunks (right now this is a single chunk) */
1433   ierr = PetscCalloc1((cEnd-cStart)*Nf, &cintegral);CHKERRQ(ierr);
1434   ierr = DMPlexComputeIntegral_Internal(dm, X, cStart, cEnd, cintegral, user);CHKERRQ(ierr);
1435   /* Put values in F*/
1436   ierr = VecGetDM(F, &dmF);CHKERRQ(ierr);
1437   ierr = DMGetDefaultSection(dmF, &sectionF);CHKERRQ(ierr);
1438   ierr = VecGetArray(F, &af);CHKERRQ(ierr);
1439   for (cell = cStart; cell < cEnd; ++cell) {
1440     const PetscInt c = cell - cStart;
1441     PetscInt       dof, off;
1442 
1443     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, "Cell Integral", Nf, &cintegral[c*Nf]);CHKERRQ(ierr);}
1444     ierr = PetscSectionGetDof(sectionF, cell, &dof);CHKERRQ(ierr);
1445     ierr = PetscSectionGetOffset(sectionF, cell, &off);CHKERRQ(ierr);
1446     if (dof != Nf) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "The number of cell dofs %D != %D", dof, Nf);
1447     for (f = 0; f < Nf; ++f) af[off+f] = cintegral[c*Nf+f];
1448   }
1449   ierr = VecRestoreArray(F, &af);CHKERRQ(ierr);
1450   ierr = PetscFree(cintegral);CHKERRQ(ierr);
1451   ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
1452   PetscFunctionReturn(0);
1453 }
1454 
1455 /*@
1456   DMPlexComputeInterpolatorNested - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1457 
1458   Input Parameters:
1459 + dmf  - The fine mesh
1460 . dmc  - The coarse mesh
1461 - user - The user context
1462 
1463   Output Parameter:
1464 . In  - The interpolation matrix
1465 
1466   Level: developer
1467 
1468 .seealso: DMPlexComputeInterpolatorGeneral(), DMPlexComputeJacobianFEM()
1469 @*/
1470 PetscErrorCode DMPlexComputeInterpolatorNested(DM dmc, DM dmf, Mat In, void *user)
1471 {
1472   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1473   const char       *name  = "Interpolator";
1474   PetscDS           prob;
1475   PetscFE          *feRef;
1476   PetscFV          *fvRef;
1477   PetscSection      fsection, fglobalSection;
1478   PetscSection      csection, cglobalSection;
1479   PetscScalar      *elemMat;
1480   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, cEndInterior, c;
1481   PetscInt          cTotDim, rTotDim = 0;
1482   PetscErrorCode    ierr;
1483 
1484   PetscFunctionBegin;
1485   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1486   ierr = DMGetDimension(dmf, &dim);CHKERRQ(ierr);
1487   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1488   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1489   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1490   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1491   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1492   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1493   ierr = DMPlexGetHybridBounds(dmc, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1494   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1495   ierr = DMGetDS(dmf, &prob);CHKERRQ(ierr);
1496   ierr = PetscCalloc2(Nf,&feRef,Nf,&fvRef);CHKERRQ(ierr);
1497   for (f = 0; f < Nf; ++f) {
1498     PetscObject  obj;
1499     PetscClassId id;
1500     PetscInt     rNb = 0, Nc = 0;
1501 
1502     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1503     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1504     if (id == PETSCFE_CLASSID) {
1505       PetscFE fe = (PetscFE) obj;
1506 
1507       ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
1508       ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1509       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1510     } else if (id == PETSCFV_CLASSID) {
1511       PetscFV        fv = (PetscFV) obj;
1512       PetscDualSpace Q;
1513 
1514       ierr = PetscFVRefine(fv, &fvRef[f]);CHKERRQ(ierr);
1515       ierr = PetscFVGetDualSpace(fvRef[f], &Q);CHKERRQ(ierr);
1516       ierr = PetscDualSpaceGetDimension(Q, &rNb);CHKERRQ(ierr);
1517       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
1518     }
1519     rTotDim += rNb;
1520   }
1521   ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
1522   ierr = PetscMalloc1(rTotDim*cTotDim,&elemMat);CHKERRQ(ierr);
1523   ierr = PetscMemzero(elemMat, rTotDim*cTotDim * sizeof(PetscScalar));CHKERRQ(ierr);
1524   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1525     PetscDualSpace   Qref;
1526     PetscQuadrature  f;
1527     const PetscReal *qpoints, *qweights;
1528     PetscReal       *points;
1529     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1530 
1531     /* Compose points from all dual basis functionals */
1532     if (feRef[fieldI]) {
1533       ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1534       ierr = PetscFEGetNumComponents(feRef[fieldI], &Nc);CHKERRQ(ierr);
1535     } else {
1536       ierr = PetscFVGetDualSpace(fvRef[fieldI], &Qref);CHKERRQ(ierr);
1537       ierr = PetscFVGetNumComponents(fvRef[fieldI], &Nc);CHKERRQ(ierr);
1538     }
1539     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1540     for (i = 0; i < fpdim; ++i) {
1541       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1542       ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1543       npoints += Np;
1544     }
1545     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1546     for (i = 0, k = 0; i < fpdim; ++i) {
1547       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1548       ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1549       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1550     }
1551 
1552     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1553       PetscObject  obj;
1554       PetscClassId id;
1555       PetscReal   *B;
1556       PetscInt     NcJ = 0, cpdim = 0, j, qNc;
1557 
1558       ierr = PetscDSGetDiscretization(prob, fieldJ, &obj);CHKERRQ(ierr);
1559       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1560       if (id == PETSCFE_CLASSID) {
1561         PetscFE fe = (PetscFE) obj;
1562 
1563         /* Evaluate basis at points */
1564         ierr = PetscFEGetNumComponents(fe, &NcJ);CHKERRQ(ierr);
1565         ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
1566         /* For now, fields only interpolate themselves */
1567         if (fieldI == fieldJ) {
1568           if (Nc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %D does not match coarse field %D", Nc, NcJ);
1569           ierr = PetscFEGetTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1570           for (i = 0, k = 0; i < fpdim; ++i) {
1571             ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1572             ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, NULL, &qweights);CHKERRQ(ierr);
1573             if (qNc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in quadrature %D does not match coarse field %D", qNc, NcJ);
1574             for (p = 0; p < Np; ++p, ++k) {
1575               for (j = 0; j < cpdim; ++j) {
1576                 /*
1577                    cTotDim:            Total columns in element interpolation matrix, sum of number of dual basis functionals in each field
1578                    offsetI, offsetJ:   Offsets into the larger element interpolation matrix for different fields
1579                    fpdim, i, cpdim, j: Dofs for fine and coarse grids, correspond to dual space basis functionals
1580                    qNC, Nc, Ncj, c:    Number of components in this field
1581                    Np, p:              Number of quad points in the fine grid functional i
1582                    k:                  i*Np + p, overall point number for the interpolation
1583                 */
1584                 for (c = 0; c < Nc; ++c) elemMat[(offsetI + i)*cTotDim + offsetJ + j] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p*qNc+c];
1585               }
1586             }
1587           }
1588           ierr = PetscFERestoreTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1589         }
1590       } else if (id == PETSCFV_CLASSID) {
1591         PetscFV        fv = (PetscFV) obj;
1592 
1593         /* Evaluate constant function at points */
1594         ierr = PetscFVGetNumComponents(fv, &NcJ);CHKERRQ(ierr);
1595         cpdim = 1;
1596         /* For now, fields only interpolate themselves */
1597         if (fieldI == fieldJ) {
1598           if (Nc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %d does not match coarse field %d", Nc, NcJ);
1599           for (i = 0, k = 0; i < fpdim; ++i) {
1600             ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1601             ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, NULL, &qweights);CHKERRQ(ierr);
1602             if (qNc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in quadrature %D does not match coarse field %D", qNc, NcJ);
1603             for (p = 0; p < Np; ++p, ++k) {
1604               for (j = 0; j < cpdim; ++j) {
1605                 for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cTotDim + offsetJ + j*NcJ + c] += 1.0*qweights[p*qNc+c];
1606               }
1607             }
1608           }
1609         }
1610       }
1611       offsetJ += cpdim;
1612     }
1613     offsetI += fpdim;
1614     ierr = PetscFree(points);CHKERRQ(ierr);
1615   }
1616   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rTotDim, cTotDim, elemMat);CHKERRQ(ierr);}
1617   /* Preallocate matrix */
1618   {
1619     Mat          preallocator;
1620     PetscScalar *vals;
1621     PetscInt    *cellCIndices, *cellFIndices;
1622     PetscInt     locRows, locCols, cell;
1623 
1624     ierr = MatGetLocalSize(In, &locRows, &locCols);CHKERRQ(ierr);
1625     ierr = MatCreate(PetscObjectComm((PetscObject) In), &preallocator);CHKERRQ(ierr);
1626     ierr = MatSetType(preallocator, MATPREALLOCATOR);CHKERRQ(ierr);
1627     ierr = MatSetSizes(preallocator, locRows, locCols, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
1628     ierr = MatSetUp(preallocator);CHKERRQ(ierr);
1629     ierr = PetscCalloc3(rTotDim*cTotDim, &vals,cTotDim,&cellCIndices,rTotDim,&cellFIndices);CHKERRQ(ierr);
1630     for (cell = cStart; cell < cEnd; ++cell) {
1631       ierr = DMPlexMatGetClosureIndicesRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, cell, cellCIndices, cellFIndices);CHKERRQ(ierr);
1632       ierr = MatSetValues(preallocator, rTotDim, cellFIndices, cTotDim, cellCIndices, vals, INSERT_VALUES);CHKERRQ(ierr);
1633     }
1634     ierr = PetscFree3(vals,cellCIndices,cellFIndices);CHKERRQ(ierr);
1635     ierr = MatAssemblyBegin(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1636     ierr = MatAssemblyEnd(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1637     ierr = MatPreallocatorPreallocate(preallocator, PETSC_TRUE, In);CHKERRQ(ierr);
1638     ierr = MatDestroy(&preallocator);CHKERRQ(ierr);
1639   }
1640   /* Fill matrix */
1641   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1642   for (c = cStart; c < cEnd; ++c) {
1643     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1644   }
1645   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1646   ierr = PetscFree2(feRef,fvRef);CHKERRQ(ierr);
1647   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1648   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1649   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1650   if (mesh->printFEM) {
1651     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1652     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1653     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1654   }
1655   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1656   PetscFunctionReturn(0);
1657 }
1658 
1659 PetscErrorCode DMPlexComputeMassMatrixNested(DM dmc, DM dmf, Mat mass, void *user)
1660 {
1661   SETERRQ(PetscObjectComm((PetscObject) dmc), PETSC_ERR_SUP, "Laziness");
1662 }
1663 
1664 /*@
1665   DMPlexComputeInterpolatorGeneral - Form the local portion of the interpolation matrix I from the coarse DM to a non-nested fine DM.
1666 
1667   Input Parameters:
1668 + dmf  - The fine mesh
1669 . dmc  - The coarse mesh
1670 - user - The user context
1671 
1672   Output Parameter:
1673 . In  - The interpolation matrix
1674 
1675   Level: developer
1676 
1677 .seealso: DMPlexComputeInterpolatorNested(), DMPlexComputeJacobianFEM()
1678 @*/
1679 PetscErrorCode DMPlexComputeInterpolatorGeneral(DM dmc, DM dmf, Mat In, void *user)
1680 {
1681   DM_Plex       *mesh = (DM_Plex *) dmf->data;
1682   const char    *name = "Interpolator";
1683   PetscDS        prob;
1684   PetscSection   fsection, csection, globalFSection, globalCSection;
1685   PetscHSetIJ    ht;
1686   PetscLayout    rLayout;
1687   PetscInt      *dnz, *onz;
1688   PetscInt       locRows, rStart, rEnd;
1689   PetscReal     *x, *v0, *J, *invJ, detJ;
1690   PetscReal     *v0c, *Jc, *invJc, detJc;
1691   PetscScalar   *elemMat;
1692   PetscInt       dim, Nf, field, totDim, cStart, cEnd, cell, ccell;
1693   PetscErrorCode ierr;
1694 
1695   PetscFunctionBegin;
1696   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1697   ierr = DMGetCoordinateDim(dmc, &dim);CHKERRQ(ierr);
1698   ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
1699   ierr = PetscDSGetRefCoordArrays(prob, &x, NULL);CHKERRQ(ierr);
1700   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1701   ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
1702   ierr = PetscMalloc3(dim,&v0c,dim*dim,&Jc,dim*dim,&invJc);CHKERRQ(ierr);
1703   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1704   ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);
1705   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1706   ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);
1707   ierr = DMPlexGetHeightStratum(dmf, 0, &cStart, &cEnd);CHKERRQ(ierr);
1708   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1709   ierr = PetscMalloc1(totDim, &elemMat);CHKERRQ(ierr);
1710 
1711   ierr = MatGetLocalSize(In, &locRows, NULL);CHKERRQ(ierr);
1712   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) In), &rLayout);CHKERRQ(ierr);
1713   ierr = PetscLayoutSetLocalSize(rLayout, locRows);CHKERRQ(ierr);
1714   ierr = PetscLayoutSetBlockSize(rLayout, 1);CHKERRQ(ierr);
1715   ierr = PetscLayoutSetUp(rLayout);CHKERRQ(ierr);
1716   ierr = PetscLayoutGetRange(rLayout, &rStart, &rEnd);CHKERRQ(ierr);
1717   ierr = PetscLayoutDestroy(&rLayout);CHKERRQ(ierr);
1718   ierr = PetscCalloc2(locRows,&dnz,locRows,&onz);CHKERRQ(ierr);
1719   ierr = PetscHSetIJCreate(&ht);CHKERRQ(ierr);
1720   for (field = 0; field < Nf; ++field) {
1721     PetscObject      obj;
1722     PetscClassId     id;
1723     PetscDualSpace   Q = NULL;
1724     PetscQuadrature  f;
1725     const PetscReal *qpoints;
1726     PetscInt         Nc, Np, fpdim, i, d;
1727 
1728     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1729     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1730     if (id == PETSCFE_CLASSID) {
1731       PetscFE fe = (PetscFE) obj;
1732 
1733       ierr = PetscFEGetDualSpace(fe, &Q);CHKERRQ(ierr);
1734       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1735     } else if (id == PETSCFV_CLASSID) {
1736       PetscFV fv = (PetscFV) obj;
1737 
1738       ierr = PetscFVGetDualSpace(fv, &Q);CHKERRQ(ierr);
1739       Nc   = 1;
1740     }
1741     ierr = PetscDualSpaceGetDimension(Q, &fpdim);CHKERRQ(ierr);
1742     /* For each fine grid cell */
1743     for (cell = cStart; cell < cEnd; ++cell) {
1744       PetscInt *findices,   *cindices;
1745       PetscInt  numFIndices, numCIndices;
1746 
1747       ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1748       ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
1749       if (numFIndices != fpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of fine indices %d != %d dual basis vecs", numFIndices, fpdim);
1750       for (i = 0; i < fpdim; ++i) {
1751         Vec             pointVec;
1752         PetscScalar    *pV;
1753         PetscSF         coarseCellSF = NULL;
1754         const PetscSFNode *coarseCells;
1755         PetscInt        numCoarseCells, q, c;
1756 
1757         /* Get points from the dual basis functional quadrature */
1758         ierr = PetscDualSpaceGetFunctional(Q, i, &f);CHKERRQ(ierr);
1759         ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1760         ierr = VecCreateSeq(PETSC_COMM_SELF, Np*dim, &pointVec);CHKERRQ(ierr);
1761         ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
1762         ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
1763         for (q = 0; q < Np; ++q) {
1764           const PetscReal xi0[3] = {-1., -1., -1.};
1765 
1766           /* Transform point to real space */
1767           CoordinatesRefToReal(dim, dim, xi0, v0, J, &qpoints[q*dim], x);
1768           for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
1769         }
1770         ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
1771         /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
1772         /* OPT: Pack all quad points from fine cell */
1773         ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
1774         ierr = PetscSFViewFromOptions(coarseCellSF, NULL, "-interp_sf_view");CHKERRQ(ierr);
1775         /* Update preallocation info */
1776         ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
1777         if (numCoarseCells != Np) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
1778         {
1779           PetscHashIJKey key;
1780           PetscBool      missing;
1781 
1782           key.i = findices[i];
1783           if (key.i >= 0) {
1784             /* Get indices for coarse elements */
1785             for (ccell = 0; ccell < numCoarseCells; ++ccell) {
1786               ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1787               for (c = 0; c < numCIndices; ++c) {
1788                 key.j = cindices[c];
1789                 if (key.j < 0) continue;
1790                 ierr = PetscHSetIJQueryAdd(ht, key, &missing);CHKERRQ(ierr);
1791                 if (missing) {
1792                   if ((key.j >= rStart) && (key.j < rEnd)) ++dnz[key.i-rStart];
1793                   else                                     ++onz[key.i-rStart];
1794                 }
1795               }
1796               ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1797             }
1798           }
1799         }
1800         ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
1801         ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
1802       }
1803       ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1804     }
1805   }
1806   ierr = PetscHSetIJDestroy(&ht);CHKERRQ(ierr);
1807   ierr = MatXAIJSetPreallocation(In, 1, dnz, onz, NULL, NULL);CHKERRQ(ierr);
1808   ierr = MatSetOption(In, MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1809   ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
1810   for (field = 0; field < Nf; ++field) {
1811     PetscObject      obj;
1812     PetscClassId     id;
1813     PetscDualSpace   Q = NULL;
1814     PetscQuadrature  f;
1815     const PetscReal *qpoints, *qweights;
1816     PetscInt         Nc, qNc, Np, fpdim, i, d;
1817 
1818     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1819     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1820     if (id == PETSCFE_CLASSID) {
1821       PetscFE fe = (PetscFE) obj;
1822 
1823       ierr = PetscFEGetDualSpace(fe, &Q);CHKERRQ(ierr);
1824       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1825     } else if (id == PETSCFV_CLASSID) {
1826       PetscFV fv = (PetscFV) obj;
1827 
1828       ierr = PetscFVGetDualSpace(fv, &Q);CHKERRQ(ierr);
1829       Nc   = 1;
1830     } else SETERRQ1(PetscObjectComm((PetscObject)dmc),PETSC_ERR_ARG_WRONG,"Unknown discretization type for field %d",field);
1831     ierr = PetscDualSpaceGetDimension(Q, &fpdim);CHKERRQ(ierr);
1832     /* For each fine grid cell */
1833     for (cell = cStart; cell < cEnd; ++cell) {
1834       PetscInt *findices,   *cindices;
1835       PetscInt  numFIndices, numCIndices;
1836 
1837       ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1838       ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
1839       if (numFIndices != fpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of fine indices %d != %d dual basis vecs", numFIndices, fpdim);
1840       for (i = 0; i < fpdim; ++i) {
1841         Vec             pointVec;
1842         PetscScalar    *pV;
1843         PetscSF         coarseCellSF = NULL;
1844         const PetscSFNode *coarseCells;
1845         PetscInt        numCoarseCells, cpdim, q, c, j;
1846 
1847         /* Get points from the dual basis functional quadrature */
1848         ierr = PetscDualSpaceGetFunctional(Q, i, &f);CHKERRQ(ierr);
1849         ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, &qpoints, &qweights);CHKERRQ(ierr);
1850         if (qNc != Nc) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in quadrature %D does not match coarse field %D", qNc, Nc);
1851         ierr = VecCreateSeq(PETSC_COMM_SELF, Np*dim, &pointVec);CHKERRQ(ierr);
1852         ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
1853         ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
1854         for (q = 0; q < Np; ++q) {
1855           const PetscReal xi0[3] = {-1., -1., -1.};
1856 
1857           /* Transform point to real space */
1858           CoordinatesRefToReal(dim, dim, xi0, v0, J, &qpoints[q*dim], x);
1859           for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
1860         }
1861         ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
1862         /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
1863         /* OPT: Read this out from preallocation information */
1864         ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
1865         /* Update preallocation info */
1866         ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
1867         if (numCoarseCells != Np) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
1868         ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
1869         for (ccell = 0; ccell < numCoarseCells; ++ccell) {
1870           PetscReal pVReal[3];
1871           const PetscReal xi0[3] = {-1., -1., -1.};
1872 
1873           ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1874           /* Transform points from real space to coarse reference space */
1875           ierr = DMPlexComputeCellGeometryFEM(dmc, coarseCells[ccell].index, NULL, v0c, Jc, invJc, &detJc);CHKERRQ(ierr);
1876           for (d = 0; d < dim; ++d) pVReal[d] = PetscRealPart(pV[ccell*dim+d]);
1877           CoordinatesRealToRef(dim, dim, xi0, v0c, invJc, pVReal, x);
1878 
1879           if (id == PETSCFE_CLASSID) {
1880             PetscFE    fe = (PetscFE) obj;
1881             PetscReal *B;
1882 
1883             /* Evaluate coarse basis on contained point */
1884             ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
1885             ierr = PetscFEGetTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);
1886             ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
1887             /* Get elemMat entries by multiplying by weight */
1888             for (j = 0; j < cpdim; ++j) {
1889               for (c = 0; c < Nc; ++c) elemMat[j] += B[j*Nc + c]*qweights[ccell*qNc + c];
1890             }
1891             ierr = PetscFERestoreTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1892           } else {
1893             cpdim = 1;
1894             for (j = 0; j < cpdim; ++j) {
1895               for (c = 0; c < Nc; ++c) elemMat[j] += 1.0*qweights[ccell*qNc + c];
1896             }
1897           }
1898           /* Update interpolator */
1899           if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
1900           if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
1901           ierr = MatSetValues(In, 1, &findices[i], numCIndices, cindices, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1902           ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1903         }
1904         ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
1905         ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
1906         ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
1907       }
1908       ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1909     }
1910   }
1911   ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
1912   ierr = PetscFree3(v0c,Jc,invJc);CHKERRQ(ierr);
1913   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1914   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1915   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1916   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1917   PetscFunctionReturn(0);
1918 }
1919 
1920 /*@
1921   DMPlexComputeMassMatrixGeneral - Form the local portion of the mass matrix M from the coarse DM to a non-nested fine DM.
1922 
1923   Input Parameters:
1924 + dmf  - The fine mesh
1925 . dmc  - The coarse mesh
1926 - user - The user context
1927 
1928   Output Parameter:
1929 . mass  - The mass matrix
1930 
1931   Level: developer
1932 
1933 .seealso: DMPlexComputeMassMatrixNested(), DMPlexComputeInterpolatorNested(), DMPlexComputeInterpolatorGeneral(), DMPlexComputeJacobianFEM()
1934 @*/
1935 PetscErrorCode DMPlexComputeMassMatrixGeneral(DM dmc, DM dmf, Mat mass, void *user)
1936 {
1937   DM_Plex       *mesh = (DM_Plex *) dmf->data;
1938   const char    *name = "Mass Matrix";
1939   PetscDS        prob;
1940   PetscSection   fsection, csection, globalFSection, globalCSection;
1941   PetscHSetIJ    ht;
1942   PetscLayout    rLayout;
1943   PetscInt      *dnz, *onz;
1944   PetscInt       locRows, rStart, rEnd;
1945   PetscReal     *x, *v0, *J, *invJ, detJ;
1946   PetscReal     *v0c, *Jc, *invJc, detJc;
1947   PetscScalar   *elemMat;
1948   PetscInt       dim, Nf, field, totDim, cStart, cEnd, cell, ccell;
1949   PetscErrorCode ierr;
1950 
1951   PetscFunctionBegin;
1952   ierr = DMGetCoordinateDim(dmc, &dim);CHKERRQ(ierr);
1953   ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
1954   ierr = PetscDSGetRefCoordArrays(prob, &x, NULL);CHKERRQ(ierr);
1955   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1956   ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
1957   ierr = PetscMalloc3(dim,&v0c,dim*dim,&Jc,dim*dim,&invJc);CHKERRQ(ierr);
1958   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1959   ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);
1960   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1961   ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);
1962   ierr = DMPlexGetHeightStratum(dmf, 0, &cStart, &cEnd);CHKERRQ(ierr);
1963   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1964   ierr = PetscMalloc1(totDim, &elemMat);CHKERRQ(ierr);
1965 
1966   ierr = MatGetLocalSize(mass, &locRows, NULL);CHKERRQ(ierr);
1967   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) mass), &rLayout);CHKERRQ(ierr);
1968   ierr = PetscLayoutSetLocalSize(rLayout, locRows);CHKERRQ(ierr);
1969   ierr = PetscLayoutSetBlockSize(rLayout, 1);CHKERRQ(ierr);
1970   ierr = PetscLayoutSetUp(rLayout);CHKERRQ(ierr);
1971   ierr = PetscLayoutGetRange(rLayout, &rStart, &rEnd);CHKERRQ(ierr);
1972   ierr = PetscLayoutDestroy(&rLayout);CHKERRQ(ierr);
1973   ierr = PetscCalloc2(locRows,&dnz,locRows,&onz);CHKERRQ(ierr);
1974   ierr = PetscHSetIJCreate(&ht);CHKERRQ(ierr);
1975   for (field = 0; field < Nf; ++field) {
1976     PetscObject      obj;
1977     PetscClassId     id;
1978     PetscQuadrature  quad;
1979     const PetscReal *qpoints;
1980     PetscInt         Nq, Nc, i, d;
1981 
1982     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1983     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1984     if (id == PETSCFE_CLASSID) {ierr = PetscFEGetQuadrature((PetscFE) obj, &quad);CHKERRQ(ierr);}
1985     else                       {ierr = PetscFVGetQuadrature((PetscFV) obj, &quad);CHKERRQ(ierr);}
1986     ierr = PetscQuadratureGetData(quad, NULL, &Nc, &Nq, &qpoints, NULL);CHKERRQ(ierr);
1987     /* For each fine grid cell */
1988     for (cell = cStart; cell < cEnd; ++cell) {
1989       Vec                pointVec;
1990       PetscScalar       *pV;
1991       PetscSF            coarseCellSF = NULL;
1992       const PetscSFNode *coarseCells;
1993       PetscInt           numCoarseCells, q, c;
1994       PetscInt          *findices,   *cindices;
1995       PetscInt           numFIndices, numCIndices;
1996 
1997       ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1998       ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
1999       /* Get points from the quadrature */
2000       ierr = VecCreateSeq(PETSC_COMM_SELF, Nq*dim, &pointVec);CHKERRQ(ierr);
2001       ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
2002       ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
2003       for (q = 0; q < Nq; ++q) {
2004         const PetscReal xi0[3] = {-1., -1., -1.};
2005 
2006         /* Transform point to real space */
2007         CoordinatesRefToReal(dim, dim, xi0, v0, J, &qpoints[q*dim], x);
2008         for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
2009       }
2010       ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
2011       /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
2012       ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
2013       ierr = PetscSFViewFromOptions(coarseCellSF, NULL, "-interp_sf_view");CHKERRQ(ierr);
2014       /* Update preallocation info */
2015       ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
2016       if (numCoarseCells != Nq) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
2017       {
2018         PetscHashIJKey key;
2019         PetscBool      missing;
2020 
2021         for (i = 0; i < numFIndices; ++i) {
2022           key.i = findices[i];
2023           if (key.i >= 0) {
2024             /* Get indices for coarse elements */
2025             for (ccell = 0; ccell < numCoarseCells; ++ccell) {
2026               ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
2027               for (c = 0; c < numCIndices; ++c) {
2028                 key.j = cindices[c];
2029                 if (key.j < 0) continue;
2030                 ierr = PetscHSetIJQueryAdd(ht, key, &missing);CHKERRQ(ierr);
2031                 if (missing) {
2032                   if ((key.j >= rStart) && (key.j < rEnd)) ++dnz[key.i-rStart];
2033                   else                                     ++onz[key.i-rStart];
2034                 }
2035               }
2036               ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
2037             }
2038           }
2039         }
2040       }
2041       ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
2042       ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
2043       ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
2044     }
2045   }
2046   ierr = PetscHSetIJDestroy(&ht);CHKERRQ(ierr);
2047   ierr = MatXAIJSetPreallocation(mass, 1, dnz, onz, NULL, NULL);CHKERRQ(ierr);
2048   ierr = MatSetOption(mass, MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2049   ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
2050   for (field = 0; field < Nf; ++field) {
2051     PetscObject      obj;
2052     PetscClassId     id;
2053     PetscQuadrature  quad;
2054     PetscReal       *Bfine;
2055     const PetscReal *qpoints, *qweights;
2056     PetscInt         Nq, Nc, i, d;
2057 
2058     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
2059     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2060     if (id == PETSCFE_CLASSID) {ierr = PetscFEGetQuadrature((PetscFE) obj, &quad);CHKERRQ(ierr);ierr = PetscFEGetDefaultTabulation((PetscFE) obj, &Bfine, NULL, NULL);CHKERRQ(ierr);}
2061     else                       {ierr = PetscFVGetQuadrature((PetscFV) obj, &quad);CHKERRQ(ierr);}
2062     ierr = PetscQuadratureGetData(quad, NULL, &Nc, &Nq, &qpoints, &qweights);CHKERRQ(ierr);
2063     /* For each fine grid cell */
2064     for (cell = cStart; cell < cEnd; ++cell) {
2065       Vec                pointVec;
2066       PetscScalar       *pV;
2067       PetscSF            coarseCellSF = NULL;
2068       const PetscSFNode *coarseCells;
2069       PetscInt           numCoarseCells, cpdim, q, c, j;
2070       PetscInt          *findices,   *cindices;
2071       PetscInt           numFIndices, numCIndices;
2072 
2073       ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
2074       ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
2075       /* Get points from the quadrature */
2076       ierr = VecCreateSeq(PETSC_COMM_SELF, Nq*dim, &pointVec);CHKERRQ(ierr);
2077       ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
2078       ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
2079       for (q = 0; q < Nq; ++q) {
2080         const PetscReal xi0[3] = {-1., -1., -1.};
2081 
2082         /* Transform point to real space */
2083         CoordinatesRefToReal(dim, dim, xi0, v0, J, &qpoints[q*dim], x);
2084         for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
2085       }
2086       ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
2087       /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
2088       ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
2089       /* Update matrix */
2090       ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
2091       if (numCoarseCells != Nq) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
2092       ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
2093       for (ccell = 0; ccell < numCoarseCells; ++ccell) {
2094         PetscReal pVReal[3];
2095         const PetscReal xi0[3] = {-1., -1., -1.};
2096 
2097 
2098         ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
2099         /* Transform points from real space to coarse reference space */
2100         ierr = DMPlexComputeCellGeometryFEM(dmc, coarseCells[ccell].index, NULL, v0c, Jc, invJc, &detJc);CHKERRQ(ierr);
2101         for (d = 0; d < dim; ++d) pVReal[d] = PetscRealPart(pV[ccell*dim+d]);
2102         CoordinatesRealToRef(dim, dim, xi0, v0c, invJc, pVReal, x);
2103 
2104         if (id == PETSCFE_CLASSID) {
2105           PetscFE    fe = (PetscFE) obj;
2106           PetscReal *B;
2107 
2108           /* Evaluate coarse basis on contained point */
2109           ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
2110           ierr = PetscFEGetTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);
2111           /* Get elemMat entries by multiplying by weight */
2112           for (i = 0; i < numFIndices; ++i) {
2113             ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
2114             for (j = 0; j < cpdim; ++j) {
2115               for (c = 0; c < Nc; ++c) elemMat[j] += B[j*Nc + c]*Bfine[(ccell*numFIndices + i)*Nc + c]*qweights[ccell*Nc + c]*detJ;
2116             }
2117             /* Update interpolator */
2118             if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
2119             if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
2120             ierr = MatSetValues(mass, 1, &findices[i], numCIndices, cindices, elemMat, ADD_VALUES);CHKERRQ(ierr);
2121           }
2122           ierr = PetscFERestoreTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
2123         } else {
2124           cpdim = 1;
2125           for (i = 0; i < numFIndices; ++i) {
2126             ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
2127             for (j = 0; j < cpdim; ++j) {
2128               for (c = 0; c < Nc; ++c) elemMat[j] += 1.0*1.0*qweights[ccell*Nc + c]*detJ;
2129             }
2130             /* Update interpolator */
2131             if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
2132             ierr = PetscPrintf(PETSC_COMM_SELF, "Nq: %d %d Nf: %d %d Nc: %d %d\n", ccell, Nq, i, numFIndices, j, numCIndices);CHKERRQ(ierr);
2133             if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
2134             ierr = MatSetValues(mass, 1, &findices[i], numCIndices, cindices, elemMat, ADD_VALUES);CHKERRQ(ierr);
2135           }
2136         }
2137         ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
2138       }
2139       ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
2140       ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
2141       ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
2142       ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
2143     }
2144   }
2145   ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
2146   ierr = PetscFree3(v0c,Jc,invJc);CHKERRQ(ierr);
2147   ierr = PetscFree(elemMat);CHKERRQ(ierr);
2148   ierr = MatAssemblyBegin(mass, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2149   ierr = MatAssemblyEnd(mass, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2150   PetscFunctionReturn(0);
2151 }
2152 
2153 /*@
2154   DMPlexComputeInjectorFEM - Compute a mapping from coarse unknowns to fine unknowns
2155 
2156   Input Parameters:
2157 + dmc  - The coarse mesh
2158 - dmf  - The fine mesh
2159 - user - The user context
2160 
2161   Output Parameter:
2162 . sc   - The mapping
2163 
2164   Level: developer
2165 
2166 .seealso: DMPlexComputeInterpolatorNested(), DMPlexComputeJacobianFEM()
2167 @*/
2168 PetscErrorCode DMPlexComputeInjectorFEM(DM dmc, DM dmf, VecScatter *sc, void *user)
2169 {
2170   PetscDS        prob;
2171   PetscFE       *feRef;
2172   PetscFV       *fvRef;
2173   Vec            fv, cv;
2174   IS             fis, cis;
2175   PetscSection   fsection, fglobalSection, csection, cglobalSection;
2176   PetscInt      *cmap, *cellCIndices, *cellFIndices, *cindices, *findices;
2177   PetscInt       cTotDim, fTotDim = 0, Nf, f, field, cStart, cEnd, cEndInterior, c, dim, d, startC, endC, offsetC, offsetF, m;
2178   PetscErrorCode ierr;
2179 
2180   PetscFunctionBegin;
2181   ierr = PetscLogEventBegin(DMPLEX_InjectorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
2182   ierr = DMGetDimension(dmf, &dim);CHKERRQ(ierr);
2183   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
2184   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
2185   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
2186   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
2187   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
2188   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
2189   ierr = DMPlexGetHybridBounds(dmc, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2190   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2191   ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
2192   ierr = PetscCalloc2(Nf,&feRef,Nf,&fvRef);CHKERRQ(ierr);
2193   for (f = 0; f < Nf; ++f) {
2194     PetscObject  obj;
2195     PetscClassId id;
2196     PetscInt     fNb = 0, Nc = 0;
2197 
2198     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
2199     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2200     if (id == PETSCFE_CLASSID) {
2201       PetscFE fe = (PetscFE) obj;
2202 
2203       ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
2204       ierr = PetscFEGetDimension(feRef[f], &fNb);CHKERRQ(ierr);
2205       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
2206     } else if (id == PETSCFV_CLASSID) {
2207       PetscFV        fv = (PetscFV) obj;
2208       PetscDualSpace Q;
2209 
2210       ierr = PetscFVRefine(fv, &fvRef[f]);CHKERRQ(ierr);
2211       ierr = PetscFVGetDualSpace(fvRef[f], &Q);CHKERRQ(ierr);
2212       ierr = PetscDualSpaceGetDimension(Q, &fNb);CHKERRQ(ierr);
2213       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
2214     }
2215     fTotDim += fNb;
2216   }
2217   ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
2218   ierr = PetscMalloc1(cTotDim,&cmap);CHKERRQ(ierr);
2219   for (field = 0, offsetC = 0, offsetF = 0; field < Nf; ++field) {
2220     PetscFE        feC;
2221     PetscFV        fvC;
2222     PetscDualSpace QF, QC;
2223     PetscInt       order = -1, NcF, NcC, fpdim, cpdim;
2224 
2225     if (feRef[field]) {
2226       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &feC);CHKERRQ(ierr);
2227       ierr = PetscFEGetNumComponents(feC, &NcC);CHKERRQ(ierr);
2228       ierr = PetscFEGetNumComponents(feRef[field], &NcF);CHKERRQ(ierr);
2229       ierr = PetscFEGetDualSpace(feRef[field], &QF);CHKERRQ(ierr);
2230       ierr = PetscDualSpaceGetOrder(QF, &order);CHKERRQ(ierr);
2231       ierr = PetscDualSpaceGetDimension(QF, &fpdim);CHKERRQ(ierr);
2232       ierr = PetscFEGetDualSpace(feC, &QC);CHKERRQ(ierr);
2233       ierr = PetscDualSpaceGetDimension(QC, &cpdim);CHKERRQ(ierr);
2234     } else {
2235       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fvC);CHKERRQ(ierr);
2236       ierr = PetscFVGetNumComponents(fvC, &NcC);CHKERRQ(ierr);
2237       ierr = PetscFVGetNumComponents(fvRef[field], &NcF);CHKERRQ(ierr);
2238       ierr = PetscFVGetDualSpace(fvRef[field], &QF);CHKERRQ(ierr);
2239       ierr = PetscDualSpaceGetDimension(QF, &fpdim);CHKERRQ(ierr);
2240       ierr = PetscFVGetDualSpace(fvC, &QC);CHKERRQ(ierr);
2241       ierr = PetscDualSpaceGetDimension(QC, &cpdim);CHKERRQ(ierr);
2242     }
2243     if (NcF != NcC) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %d does not match coarse field %d", NcF, NcC);
2244     for (c = 0; c < cpdim; ++c) {
2245       PetscQuadrature  cfunc;
2246       const PetscReal *cqpoints, *cqweights;
2247       PetscInt         NqcC, NpC;
2248       PetscBool        found = PETSC_FALSE;
2249 
2250       ierr = PetscDualSpaceGetFunctional(QC, c, &cfunc);CHKERRQ(ierr);
2251       ierr = PetscQuadratureGetData(cfunc, NULL, &NqcC, &NpC, &cqpoints, &cqweights);CHKERRQ(ierr);
2252       if (NqcC != NcC) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of quadrature components %D must match number of field components", NqcC, NcC);
2253       if (NpC != 1 && feRef[field]) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Do not know how to do injection for moments");
2254       for (f = 0; f < fpdim; ++f) {
2255         PetscQuadrature  ffunc;
2256         const PetscReal *fqpoints, *fqweights;
2257         PetscReal        sum = 0.0;
2258         PetscInt         NqcF, NpF;
2259 
2260         ierr = PetscDualSpaceGetFunctional(QF, f, &ffunc);CHKERRQ(ierr);
2261         ierr = PetscQuadratureGetData(ffunc, NULL, &NqcF, &NpF, &fqpoints, &fqweights);CHKERRQ(ierr);
2262         if (NqcF != NcF) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of quadrature components %D must match number of field components", NqcF, NcF);
2263         if (NpC != NpF) continue;
2264         for (d = 0; d < dim; ++d) sum += PetscAbsReal(cqpoints[d] - fqpoints[d]);
2265         if (sum > 1.0e-9) continue;
2266         for (d = 0; d < NcC; ++d) sum += PetscAbsReal(cqweights[d]*fqweights[d]);
2267         if (sum < 1.0e-9) continue;
2268         cmap[offsetC+c] = offsetF+f;
2269         found = PETSC_TRUE;
2270         break;
2271       }
2272       if (!found) {
2273         /* TODO We really want the average here, but some asshole put VecScatter in the interface */
2274         if (fvRef[field] || (feRef[field] && order == 0)) {
2275           cmap[offsetC+c] = offsetF+0;
2276         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate matching functional for injection");
2277       }
2278     }
2279     offsetC += cpdim;
2280     offsetF += fpdim;
2281   }
2282   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);ierr = PetscFVDestroy(&fvRef[f]);CHKERRQ(ierr);}
2283   ierr = PetscFree2(feRef,fvRef);CHKERRQ(ierr);
2284 
2285   ierr = DMGetGlobalVector(dmf, &fv);CHKERRQ(ierr);
2286   ierr = DMGetGlobalVector(dmc, &cv);CHKERRQ(ierr);
2287   ierr = VecGetOwnershipRange(cv, &startC, &endC);CHKERRQ(ierr);
2288   ierr = PetscSectionGetConstrainedStorageSize(cglobalSection, &m);CHKERRQ(ierr);
2289   ierr = PetscMalloc2(cTotDim,&cellCIndices,fTotDim,&cellFIndices);CHKERRQ(ierr);
2290   ierr = PetscMalloc1(m,&cindices);CHKERRQ(ierr);
2291   ierr = PetscMalloc1(m,&findices);CHKERRQ(ierr);
2292   for (d = 0; d < m; ++d) cindices[d] = findices[d] = -1;
2293   for (c = cStart; c < cEnd; ++c) {
2294     ierr = DMPlexMatGetClosureIndicesRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, c, cellCIndices, cellFIndices);CHKERRQ(ierr);
2295     for (d = 0; d < cTotDim; ++d) {
2296       if ((cellCIndices[d] < startC) || (cellCIndices[d] >= endC)) continue;
2297       if ((findices[cellCIndices[d]-startC] >= 0) && (findices[cellCIndices[d]-startC] != cellFIndices[cmap[d]])) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Coarse dof %d maps to both %d and %d", cindices[cellCIndices[d]-startC], findices[cellCIndices[d]-startC], cellFIndices[cmap[d]]);
2298       cindices[cellCIndices[d]-startC] = cellCIndices[d];
2299       findices[cellCIndices[d]-startC] = cellFIndices[cmap[d]];
2300     }
2301   }
2302   ierr = PetscFree(cmap);CHKERRQ(ierr);
2303   ierr = PetscFree2(cellCIndices,cellFIndices);CHKERRQ(ierr);
2304 
2305   ierr = ISCreateGeneral(PETSC_COMM_SELF, m, cindices, PETSC_OWN_POINTER, &cis);CHKERRQ(ierr);
2306   ierr = ISCreateGeneral(PETSC_COMM_SELF, m, findices, PETSC_OWN_POINTER, &fis);CHKERRQ(ierr);
2307   ierr = VecScatterCreate(cv, cis, fv, fis, sc);CHKERRQ(ierr);
2308   ierr = ISDestroy(&cis);CHKERRQ(ierr);
2309   ierr = ISDestroy(&fis);CHKERRQ(ierr);
2310   ierr = DMRestoreGlobalVector(dmf, &fv);CHKERRQ(ierr);
2311   ierr = DMRestoreGlobalVector(dmc, &cv);CHKERRQ(ierr);
2312   ierr = PetscLogEventEnd(DMPLEX_InjectorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
2313   PetscFunctionReturn(0);
2314 }
2315