xref: /petsc/src/dm/impls/plex/plexfem.c (revision f8527842c040b51bc6a6827ca3e7b202ca73dc6d)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 #include <petscsf.h>
3 
4 #include <petsc/private/petscfeimpl.h>
5 #include <petsc/private/petscfvimpl.h>
6 
7 /*@
8   DMPlexGetScale - Get the scale for the specified fundamental unit
9 
10   Not collective
11 
12   Input Arguments:
13 + dm   - the DM
14 - unit - The SI unit
15 
16   Output Argument:
17 . scale - The value used to scale all quantities with this unit
18 
19   Level: advanced
20 
21 .seealso: DMPlexSetScale(), PetscUnit
22 @*/
23 PetscErrorCode DMPlexGetScale(DM dm, PetscUnit unit, PetscReal *scale)
24 {
25   DM_Plex *mesh = (DM_Plex*) dm->data;
26 
27   PetscFunctionBegin;
28   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
29   PetscValidPointer(scale, 3);
30   *scale = mesh->scale[unit];
31   PetscFunctionReturn(0);
32 }
33 
34 /*@
35   DMPlexSetScale - Set the scale for the specified fundamental unit
36 
37   Not collective
38 
39   Input Arguments:
40 + dm   - the DM
41 . unit - The SI unit
42 - scale - The value used to scale all quantities with this unit
43 
44   Level: advanced
45 
46 .seealso: DMPlexGetScale(), PetscUnit
47 @*/
48 PetscErrorCode DMPlexSetScale(DM dm, PetscUnit unit, PetscReal scale)
49 {
50   DM_Plex *mesh = (DM_Plex*) dm->data;
51 
52   PetscFunctionBegin;
53   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
54   mesh->scale[unit] = scale;
55   PetscFunctionReturn(0);
56 }
57 
58 PETSC_STATIC_INLINE PetscInt epsilon(PetscInt i, PetscInt j, PetscInt k)
59 {
60   switch (i) {
61   case 0:
62     switch (j) {
63     case 0: return 0;
64     case 1:
65       switch (k) {
66       case 0: return 0;
67       case 1: return 0;
68       case 2: return 1;
69       }
70     case 2:
71       switch (k) {
72       case 0: return 0;
73       case 1: return -1;
74       case 2: return 0;
75       }
76     }
77   case 1:
78     switch (j) {
79     case 0:
80       switch (k) {
81       case 0: return 0;
82       case 1: return 0;
83       case 2: return -1;
84       }
85     case 1: return 0;
86     case 2:
87       switch (k) {
88       case 0: return 1;
89       case 1: return 0;
90       case 2: return 0;
91       }
92     }
93   case 2:
94     switch (j) {
95     case 0:
96       switch (k) {
97       case 0: return 0;
98       case 1: return 1;
99       case 2: return 0;
100       }
101     case 1:
102       switch (k) {
103       case 0: return -1;
104       case 1: return 0;
105       case 2: return 0;
106       }
107     case 2: return 0;
108     }
109   }
110   return 0;
111 }
112 
113 static PetscErrorCode DMPlexProjectRigidBody_Private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *mode, void *ctx)
114 {
115   PetscInt *ctxInt  = (PetscInt *) ctx;
116   PetscInt  dim2    = ctxInt[0];
117   PetscInt  d       = ctxInt[1];
118   PetscInt  i, j, k = dim > 2 ? d - dim : d;
119 
120   PetscFunctionBegin;
121   if (dim != dim2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input dimension %d does not match context dimension %d", dim, dim2);
122   for (i = 0; i < dim; i++) mode[i] = 0.;
123   if (d < dim) {
124     mode[d] = 1.;
125   } else {
126     for (i = 0; i < dim; i++) {
127       for (j = 0; j < dim; j++) {
128         mode[j] += epsilon(i, j, k)*X[i];
129       }
130     }
131   }
132   PetscFunctionReturn(0);
133 }
134 
135 /*@C
136   DMPlexCreateRigidBody - for the default global section, create rigid body modes from coordinates
137 
138   Collective on DM
139 
140   Input Arguments:
141 . dm - the DM
142 
143   Output Argument:
144 . sp - the null space
145 
146   Note: This is necessary to take account of Dirichlet conditions on the displacements
147 
148   Level: advanced
149 
150 .seealso: MatNullSpaceCreate()
151 @*/
152 PetscErrorCode DMPlexCreateRigidBody(DM dm, MatNullSpace *sp)
153 {
154   MPI_Comm       comm;
155   Vec            mode[6];
156   PetscSection   section, globalSection;
157   PetscInt       dim, dimEmbed, n, m, d, i, j;
158   PetscErrorCode ierr;
159 
160   PetscFunctionBegin;
161   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
162   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
163   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
164   if (dim == 1) {
165     ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
166     PetscFunctionReturn(0);
167   }
168   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
169   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
170   ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
171   m    = (dim*(dim+1))/2;
172   ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
173   ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
174   ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
175   for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
176   for (d = 0; d < m; d++) {
177     PetscInt         ctx[2];
178     PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *) = DMPlexProjectRigidBody_Private;
179     void            *voidctx = (void *) (&ctx[0]);
180 
181     ctx[0] = dimEmbed;
182     ctx[1] = d;
183     ierr = DMProjectFunction(dm, 0.0, &func, &voidctx, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
184   }
185   for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
186   /* Orthonormalize system */
187   for (i = dim; i < m; ++i) {
188     PetscScalar dots[6];
189 
190     ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
191     for (j = 0; j < i; ++j) dots[j] *= -1.0;
192     ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
193     ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
194   }
195   ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
196   for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
197   PetscFunctionReturn(0);
198 }
199 
200 /*@
201   DMPlexSetMaxProjectionHeight - In DMPlexProjectXXXLocal() functions, the projected values of a basis function's dofs
202   are computed by associating the basis function with one of the mesh points in its transitively-closed support, and
203   evaluating the dual space basis of that point.  A basis function is associated with the point in its
204   transitively-closed support whose mesh height is highest (w.r.t. DAG height), but not greater than the maximum
205   projection height, which is set with this function.  By default, the maximum projection height is zero, which means
206   that only mesh cells are used to project basis functions.  A height of one, for example, evaluates a cell-interior
207   basis functions using its cells dual space basis, but all other basis functions with the dual space basis of a face.
208 
209   Input Parameters:
210 + dm - the DMPlex object
211 - height - the maximum projection height >= 0
212 
213   Level: advanced
214 
215 .seealso: DMPlexGetMaxProjectionHeight(), DMProjectFunctionLocal(), DMProjectFunctionLabelLocal()
216 @*/
217 PetscErrorCode DMPlexSetMaxProjectionHeight(DM dm, PetscInt height)
218 {
219   DM_Plex *plex = (DM_Plex *) dm->data;
220 
221   PetscFunctionBegin;
222   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
223   plex->maxProjectionHeight = height;
224   PetscFunctionReturn(0);
225 }
226 
227 /*@
228   DMPlexGetMaxProjectionHeight - Get the maximum height (w.r.t. DAG) of mesh points used to evaluate dual bases in
229   DMPlexProjectXXXLocal() functions.
230 
231   Input Parameters:
232 . dm - the DMPlex object
233 
234   Output Parameters:
235 . height - the maximum projection height
236 
237   Level: intermediate
238 
239 .seealso: DMPlexSetMaxProjectionHeight(), DMProjectFunctionLocal(), DMProjectFunctionLabelLocal()
240 @*/
241 PetscErrorCode DMPlexGetMaxProjectionHeight(DM dm, PetscInt *height)
242 {
243   DM_Plex *plex = (DM_Plex *) dm->data;
244 
245   PetscFunctionBegin;
246   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
247   *height = plex->maxProjectionHeight;
248   PetscFunctionReturn(0);
249 }
250 
251 /*@C
252   DMPlexInsertBoundaryValuesEssential - Insert boundary values into a local vector
253 
254   Input Parameters:
255 + dm     - The DM, with a PetscDS that matches the problem being constrained
256 . time   - The time
257 . field  - The field to constrain
258 . Nc     - The number of constrained field components, or 0 for all components
259 . comps  - An array of constrained component numbers, or NULL for all components
260 . label  - The DMLabel defining constrained points
261 . numids - The number of DMLabel ids for constrained points
262 . ids    - An array of ids for constrained points
263 . func   - A pointwise function giving boundary values
264 - ctx    - An optional user context for bcFunc
265 
266   Output Parameter:
267 . locX   - A local vector to receives the boundary values
268 
269   Level: developer
270 
271 .seealso: DMPlexInsertBoundaryValuesEssentialField(), DMAddBoundary()
272 @*/
273 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)
274 {
275   PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
276   void            **ctxs;
277   PetscInt          numFields;
278   PetscErrorCode    ierr;
279 
280   PetscFunctionBegin;
281   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
282   ierr = PetscCalloc2(numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
283   funcs[field] = func;
284   ctxs[field]  = ctx;
285   ierr = DMProjectFunctionLabelLocal(dm, time, label, numids, ids, Nc, comps, funcs, ctxs, INSERT_BC_VALUES, locX);CHKERRQ(ierr);
286   ierr = PetscFree2(funcs,ctxs);CHKERRQ(ierr);
287   PetscFunctionReturn(0);
288 }
289 
290 /*@C
291   DMPlexInsertBoundaryValuesEssentialField - Insert boundary values into a local vector
292 
293   Input Parameters:
294 + dm     - The DM, with a PetscDS that matches the problem being constrained
295 . time   - The time
296 . locU   - A local vector with the input solution values
297 . field  - The field to constrain
298 . Nc     - The number of constrained field components, or 0 for all components
299 . comps  - An array of constrained component numbers, or NULL for all components
300 . label  - The DMLabel defining constrained points
301 . numids - The number of DMLabel ids for constrained points
302 . ids    - An array of ids for constrained points
303 . func   - A pointwise function giving boundary values
304 - ctx    - An optional user context for bcFunc
305 
306   Output Parameter:
307 . locX   - A local vector to receives the boundary values
308 
309   Level: developer
310 
311 .seealso: DMPlexInsertBoundaryValuesEssential(), DMAddBoundary()
312 @*/
313 PetscErrorCode DMPlexInsertBoundaryValuesEssentialField(DM dm, PetscReal time, Vec locU, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[],
314                                                         void (*func)(PetscInt, PetscInt, PetscInt,
315                                                                      const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
316                                                                      const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
317                                                                      PetscReal, const PetscReal[], PetscInt, const PetscScalar[],
318                                                                      PetscScalar[]),
319                                                         void *ctx, Vec locX)
320 {
321   void (**funcs)(PetscInt, PetscInt, PetscInt,
322                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
323                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
324                  PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]);
325   void            **ctxs;
326   PetscInt          numFields;
327   PetscErrorCode    ierr;
328 
329   PetscFunctionBegin;
330   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
331   ierr = PetscCalloc2(numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
332   funcs[field] = func;
333   ctxs[field]  = ctx;
334   ierr = DMProjectFieldLabelLocal(dm, time, label, numids, ids, Nc, comps, locU, funcs, INSERT_BC_VALUES, locX);CHKERRQ(ierr);
335   ierr = PetscFree2(funcs,ctxs);CHKERRQ(ierr);
336   PetscFunctionReturn(0);
337 }
338 
339 /*@C
340   DMPlexInsertBoundaryValuesRiemann - Insert boundary values into a local vector
341 
342   Input Parameters:
343 + dm     - The DM, with a PetscDS that matches the problem being constrained
344 . time   - The time
345 . faceGeometry - A vector with the FVM face geometry information
346 . cellGeometry - A vector with the FVM cell geometry information
347 . Grad         - A vector with the FVM cell gradient information
348 . field  - The field to constrain
349 . Nc     - The number of constrained field components, or 0 for all components
350 . comps  - An array of constrained component numbers, or NULL for all components
351 . label  - The DMLabel defining constrained points
352 . numids - The number of DMLabel ids for constrained points
353 . ids    - An array of ids for constrained points
354 . func   - A pointwise function giving boundary values
355 - ctx    - An optional user context for bcFunc
356 
357   Output Parameter:
358 . locX   - A local vector to receives the boundary values
359 
360   Note: This implementation currently ignores the numcomps/comps argument from DMAddBoundary()
361 
362   Level: developer
363 
364 .seealso: DMPlexInsertBoundaryValuesEssential(), DMPlexInsertBoundaryValuesEssentialField(), DMAddBoundary()
365 @*/
366 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[],
367                                                  PetscErrorCode (*func)(PetscReal,const PetscReal*,const PetscReal*,const PetscScalar*,PetscScalar*,void*), void *ctx, Vec locX)
368 {
369   PetscDS            prob;
370   PetscSF            sf;
371   DM                 dmFace, dmCell, dmGrad;
372   const PetscScalar *facegeom, *cellgeom = NULL, *grad;
373   const PetscInt    *leaves;
374   PetscScalar       *x, *fx;
375   PetscInt           dim, nleaves, loc, fStart, fEnd, pdim, i;
376   PetscErrorCode     ierr, ierru = 0;
377 
378   PetscFunctionBegin;
379   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
380   ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
381   nleaves = PetscMax(0, nleaves);
382   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
383   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
384   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
385   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
386   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
387   if (cellGeometry) {
388     ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
389     ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
390   }
391   if (Grad) {
392     PetscFV fv;
393 
394     ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fv);CHKERRQ(ierr);
395     ierr = VecGetDM(Grad, &dmGrad);CHKERRQ(ierr);
396     ierr = VecGetArrayRead(Grad, &grad);CHKERRQ(ierr);
397     ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
398     ierr = DMGetWorkArray(dm, pdim, PETSC_SCALAR, &fx);CHKERRQ(ierr);
399   }
400   ierr = VecGetArray(locX, &x);CHKERRQ(ierr);
401   for (i = 0; i < numids; ++i) {
402     IS              faceIS;
403     const PetscInt *faces;
404     PetscInt        numFaces, f;
405 
406     ierr = DMLabelGetStratumIS(label, ids[i], &faceIS);CHKERRQ(ierr);
407     if (!faceIS) continue; /* No points with that id on this process */
408     ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
409     ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
410     for (f = 0; f < numFaces; ++f) {
411       const PetscInt         face = faces[f], *cells;
412       PetscFVFaceGeom        *fg;
413 
414       if ((face < fStart) || (face >= fEnd)) continue; /* Refinement adds non-faces to labels */
415       ierr = PetscFindInt(face, nleaves, (PetscInt *) leaves, &loc);CHKERRQ(ierr);
416       if (loc >= 0) continue;
417       ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
418       ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
419       if (Grad) {
420         PetscFVCellGeom       *cg;
421         PetscScalar           *cx, *cgrad;
422         PetscScalar           *xG;
423         PetscReal              dx[3];
424         PetscInt               d;
425 
426         ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cg);CHKERRQ(ierr);
427         ierr = DMPlexPointLocalRead(dm, cells[0], x, &cx);CHKERRQ(ierr);
428         ierr = DMPlexPointLocalRead(dmGrad, cells[0], grad, &cgrad);CHKERRQ(ierr);
429         ierr = DMPlexPointLocalFieldRef(dm, cells[1], field, x, &xG);CHKERRQ(ierr);
430         DMPlex_WaxpyD_Internal(dim, -1, cg->centroid, fg->centroid, dx);
431         for (d = 0; d < pdim; ++d) fx[d] = cx[d] + DMPlex_DotD_Internal(dim, &cgrad[d*dim], dx);
432         ierru = (*func)(time, fg->centroid, fg->normal, fx, xG, ctx);
433         if (ierru) {
434           ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
435           ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
436           goto cleanup;
437         }
438       } else {
439         PetscScalar       *xI;
440         PetscScalar       *xG;
441 
442         ierr = DMPlexPointLocalRead(dm, cells[0], x, &xI);CHKERRQ(ierr);
443         ierr = DMPlexPointLocalFieldRef(dm, cells[1], field, x, &xG);CHKERRQ(ierr);
444         ierru = (*func)(time, fg->centroid, fg->normal, xI, xG, ctx);
445         if (ierru) {
446           ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
447           ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
448           goto cleanup;
449         }
450       }
451     }
452     ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
453     ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
454   }
455   cleanup:
456   ierr = VecRestoreArray(locX, &x);CHKERRQ(ierr);
457   if (Grad) {
458     ierr = DMRestoreWorkArray(dm, pdim, PETSC_SCALAR, &fx);CHKERRQ(ierr);
459     ierr = VecRestoreArrayRead(Grad, &grad);CHKERRQ(ierr);
460   }
461   if (cellGeometry) {ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);}
462   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
463   CHKERRQ(ierru);
464   PetscFunctionReturn(0);
465 }
466 
467 PetscErrorCode DMPlexInsertBoundaryValues_Plex(DM dm, PetscBool insertEssential, Vec locX, PetscReal time, Vec faceGeomFVM, Vec cellGeomFVM, Vec gradFVM)
468 {
469   PetscInt       numBd, b;
470   PetscErrorCode ierr;
471 
472   PetscFunctionBegin;
473   ierr = PetscDSGetNumBoundary(dm->prob, &numBd);CHKERRQ(ierr);
474   for (b = 0; b < numBd; ++b) {
475     DMBoundaryConditionType type;
476     const char             *labelname;
477     DMLabel                 label;
478     PetscInt                field, Nc;
479     const PetscInt         *comps;
480     PetscObject             obj;
481     PetscClassId            id;
482     void                    (*func)(void);
483     PetscInt                numids;
484     const PetscInt         *ids;
485     void                   *ctx;
486 
487     ierr = DMGetBoundary(dm, b, &type, NULL, &labelname, &field, &Nc, &comps, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
488     if (insertEssential != (type & DM_BC_ESSENTIAL)) continue;
489     ierr = DMGetLabel(dm, labelname, &label);CHKERRQ(ierr);
490     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
491     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
492     if (id == PETSCFE_CLASSID) {
493       switch (type) {
494         /* for FEM, there is no insertion to be done for non-essential boundary conditions */
495       case DM_BC_ESSENTIAL:
496         ierr = DMPlexLabelAddCells(dm,label);CHKERRQ(ierr);
497         ierr = DMPlexInsertBoundaryValuesEssential(dm, time, field, Nc, comps, label, numids, ids, (PetscErrorCode (*)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *)) func, ctx, locX);CHKERRQ(ierr);
498         ierr = DMPlexLabelClearCells(dm,label);CHKERRQ(ierr);
499         break;
500       case DM_BC_ESSENTIAL_FIELD:
501         ierr = DMPlexLabelAddCells(dm,label);CHKERRQ(ierr);
502         ierr = DMPlexInsertBoundaryValuesEssentialField(dm, time, locX, field, Nc, comps, label, numids, ids,
503                                                         (void (*)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
504                                                                   const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
505                                                                   PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[])) func, ctx, locX);CHKERRQ(ierr);
506         ierr = DMPlexLabelClearCells(dm,label);CHKERRQ(ierr);
507         break;
508       default: break;
509       }
510     } else if (id == PETSCFV_CLASSID) {
511       if (!faceGeomFVM) continue;
512       ierr = DMPlexInsertBoundaryValuesRiemann(dm, time, faceGeomFVM, cellGeomFVM, gradFVM, field, Nc, comps, label, numids, ids,
513                                                (PetscErrorCode (*)(PetscReal,const PetscReal*,const PetscReal*,const PetscScalar*,PetscScalar*,void*)) func, ctx, locX);CHKERRQ(ierr);
514     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
515   }
516   PetscFunctionReturn(0);
517 }
518 
519 /*@
520   DMPlexInsertBoundaryValues - Puts coefficients which represent boundary values into the local solution vector
521 
522   Input Parameters:
523 + dm - The DM
524 . insertEssential - Should I insert essential (e.g. Dirichlet) or inessential (e.g. Neumann) boundary conditions
525 . time - The time
526 . faceGeomFVM - Face geometry data for FV discretizations
527 . cellGeomFVM - Cell geometry data for FV discretizations
528 - gradFVM - Gradient reconstruction data for FV discretizations
529 
530   Output Parameters:
531 . locX - Solution updated with boundary values
532 
533   Level: developer
534 
535 .seealso: DMProjectFunctionLabelLocal()
536 @*/
537 PetscErrorCode DMPlexInsertBoundaryValues(DM dm, PetscBool insertEssential, Vec locX, PetscReal time, Vec faceGeomFVM, Vec cellGeomFVM, Vec gradFVM)
538 {
539   PetscErrorCode ierr;
540 
541   PetscFunctionBegin;
542   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
543   PetscValidHeaderSpecific(locX, VEC_CLASSID, 2);
544   if (faceGeomFVM) {PetscValidHeaderSpecific(faceGeomFVM, VEC_CLASSID, 4);}
545   if (cellGeomFVM) {PetscValidHeaderSpecific(cellGeomFVM, VEC_CLASSID, 5);}
546   if (gradFVM)     {PetscValidHeaderSpecific(gradFVM, VEC_CLASSID, 6);}
547   ierr = PetscTryMethod(dm,"DMPlexInsertBoundaryValues_C",(DM,PetscBool,Vec,PetscReal,Vec,Vec,Vec),(dm,insertEssential,locX,time,faceGeomFVM,cellGeomFVM,gradFVM));CHKERRQ(ierr);
548   PetscFunctionReturn(0);
549 }
550 
551 PetscErrorCode DMComputeL2Diff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
552 {
553   const PetscInt   debug = 0;
554   PetscSection     section;
555   PetscQuadrature  quad;
556   Vec              localX;
557   PetscScalar     *funcVal, *interpolant;
558   PetscReal       *coords, *detJ, *J;
559   PetscReal        localDiff = 0.0;
560   const PetscReal *quadWeights;
561   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
562   PetscErrorCode   ierr;
563 
564   PetscFunctionBegin;
565   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
566   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
567   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
568   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
569   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
570   ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
571   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
572   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
573   for (field = 0; field < numFields; ++field) {
574     PetscObject  obj;
575     PetscClassId id;
576     PetscInt     Nc;
577 
578     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
579     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
580     if (id == PETSCFE_CLASSID) {
581       PetscFE fe = (PetscFE) obj;
582 
583       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
584       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
585     } else if (id == PETSCFV_CLASSID) {
586       PetscFV fv = (PetscFV) obj;
587 
588       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
589       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
590     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
591     numComponents += Nc;
592   }
593   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, NULL, &quadWeights);CHKERRQ(ierr);
594   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
595   ierr = PetscMalloc5(numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
596   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
597   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
598   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
599   for (c = cStart; c < cEnd; ++c) {
600     PetscScalar *x = NULL;
601     PetscReal    elemDiff = 0.0;
602     PetscInt     qc = 0;
603 
604     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
605     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
606 
607     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
608       PetscObject  obj;
609       PetscClassId id;
610       void * const ctx = ctxs ? ctxs[field] : NULL;
611       PetscInt     Nb, Nc, q, fc;
612 
613       ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
614       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
615       if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
616       else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
617       else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
618       if (debug) {
619         char title[1024];
620         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
621         ierr = DMPrintCellVector(c, title, Nb*Nc, &x[fieldOffset]);CHKERRQ(ierr);
622       }
623       for (q = 0; q < Nq; ++q) {
624         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);
625         ierr = (*funcs[field])(coordDim, time, &coords[coordDim * q], Nc, funcVal, ctx);
626         if (ierr) {
627           PetscErrorCode ierr2;
628           ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
629           ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
630           ierr2 = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
631           CHKERRQ(ierr);
632         }
633         if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
634         else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
635         else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
636         for (fc = 0; fc < Nc; ++fc) {
637           const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
638           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);}
639           elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
640         }
641       }
642       fieldOffset += Nb;
643       qc += Nc;
644     }
645     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
646     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
647     localDiff += elemDiff;
648   }
649   ierr  = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
650   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
651   ierr  = MPIU_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
652   *diff = PetscSqrtReal(*diff);
653   PetscFunctionReturn(0);
654 }
655 
656 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)
657 {
658   const PetscInt   debug = 0;
659   PetscSection     section;
660   PetscQuadrature  quad;
661   Vec              localX;
662   PetscScalar     *funcVal, *interpolant;
663   const PetscReal *quadPoints, *quadWeights;
664   PetscReal       *coords, *realSpaceDer, *J, *invJ, *detJ;
665   PetscReal        localDiff = 0.0;
666   PetscInt         dim, coordDim, qNc = 0, Nq = 0, numFields, numComponents = 0, cStart, cEnd, cEndInterior, c, field, fieldOffset;
667   PetscErrorCode   ierr;
668 
669   PetscFunctionBegin;
670   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
671   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
672   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
673   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
674   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
675   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
676   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
677   for (field = 0; field < numFields; ++field) {
678     PetscFE  fe;
679     PetscInt Nc;
680 
681     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
682     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
683     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
684     numComponents += Nc;
685   }
686   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
687   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
688   /* ierr = DMProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
689   ierr = PetscMalloc7(numComponents,&funcVal,coordDim*Nq,&coords,coordDim*Nq,&realSpaceDer,coordDim*coordDim*Nq,&J,coordDim*coordDim*Nq,&invJ,numComponents,&interpolant,Nq,&detJ);CHKERRQ(ierr);
690   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
691   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
692   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
693   for (c = cStart; c < cEnd; ++c) {
694     PetscScalar *x = NULL;
695     PetscReal    elemDiff = 0.0;
696     PetscInt     qc = 0;
697 
698     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, invJ, detJ);CHKERRQ(ierr);
699     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
700 
701     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
702       PetscFE          fe;
703       void * const     ctx = ctxs ? ctxs[field] : NULL;
704       PetscReal       *basisDer;
705       PetscInt         Nb, Nc, q, fc;
706 
707       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
708       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
709       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
710       ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
711       if (debug) {
712         char title[1024];
713         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
714         ierr = DMPrintCellVector(c, title, Nb, &x[fieldOffset]);CHKERRQ(ierr);
715       }
716       for (q = 0; q < Nq; ++q) {
717         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);
718         ierr = (*funcs[field])(coordDim, time, &coords[q*coordDim], n, numFields, funcVal, ctx);
719         if (ierr) {
720           PetscErrorCode ierr2;
721           ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
722           ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
723           ierr2 = PetscFree7(funcVal,coords,realSpaceDer,J,invJ,interpolant,detJ);CHKERRQ(ierr2);
724           CHKERRQ(ierr);
725         }
726         ierr = PetscFEInterpolateGradient_Static(fe, &x[fieldOffset], coordDim, invJ, n, q, interpolant);CHKERRQ(ierr);
727         for (fc = 0; fc < Nc; ++fc) {
728           const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
729           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);}
730           elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
731         }
732       }
733       fieldOffset += Nb;
734       qc          += Nc;
735     }
736     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
737     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
738     localDiff += elemDiff;
739   }
740   ierr  = PetscFree7(funcVal,coords,realSpaceDer,J,invJ,interpolant,detJ);CHKERRQ(ierr);
741   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
742   ierr  = MPIU_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
743   *diff = PetscSqrtReal(*diff);
744   PetscFunctionReturn(0);
745 }
746 
747 PetscErrorCode DMComputeL2FieldDiff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
748 {
749   const PetscInt   debug = 0;
750   PetscSection     section;
751   PetscQuadrature  quad;
752   Vec              localX;
753   PetscScalar     *funcVal, *interpolant;
754   PetscReal       *coords, *detJ, *J;
755   PetscReal       *localDiff;
756   const PetscReal *quadPoints, *quadWeights;
757   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
758   PetscErrorCode   ierr;
759 
760   PetscFunctionBegin;
761   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
762   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
763   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
764   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
765   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
766   ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
767   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
768   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
769   for (field = 0; field < numFields; ++field) {
770     PetscObject  obj;
771     PetscClassId id;
772     PetscInt     Nc;
773 
774     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
775     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
776     if (id == PETSCFE_CLASSID) {
777       PetscFE fe = (PetscFE) obj;
778 
779       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
780       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
781     } else if (id == PETSCFV_CLASSID) {
782       PetscFV fv = (PetscFV) obj;
783 
784       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
785       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
786     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
787     numComponents += Nc;
788   }
789   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
790   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
791   ierr = PetscCalloc6(numFields,&localDiff,numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
792   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
793   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
794   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
795   for (c = cStart; c < cEnd; ++c) {
796     PetscScalar *x = NULL;
797     PetscInt     qc = 0;
798 
799     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
800     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
801 
802     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
803       PetscObject  obj;
804       PetscClassId id;
805       void * const ctx = ctxs ? ctxs[field] : NULL;
806       PetscInt     Nb, Nc, q, fc;
807 
808       PetscReal       elemDiff = 0.0;
809 
810       ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
811       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
812       if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
813       else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
814       else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
815       if (debug) {
816         char title[1024];
817         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
818         ierr = DMPrintCellVector(c, title, Nb*Nc, &x[fieldOffset]);CHKERRQ(ierr);
819       }
820       for (q = 0; q < Nq; ++q) {
821         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);
822         ierr = (*funcs[field])(coordDim, time, &coords[coordDim*q], numFields, funcVal, ctx);
823         if (ierr) {
824           PetscErrorCode ierr2;
825           ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
826           ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
827           ierr2 = PetscFree6(localDiff,funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
828           CHKERRQ(ierr);
829         }
830         if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
831         else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
832         else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
833         for (fc = 0; fc < Nc; ++fc) {
834           const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
835           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);}
836           elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
837         }
838       }
839       fieldOffset += Nb;
840       qc          += Nc;
841       localDiff[field] += elemDiff;
842     }
843     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
844   }
845   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
846   ierr = MPIU_Allreduce(localDiff, diff, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
847   for (field = 0; field < numFields; ++field) diff[field] = PetscSqrtReal(diff[field]);
848   ierr = PetscFree6(localDiff,funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
849   PetscFunctionReturn(0);
850 }
851 
852 /*@C
853   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.
854 
855   Input Parameters:
856 + dm    - The DM
857 . time  - The time
858 . funcs - The functions to evaluate for each field component: NULL means that component does not contribute to error calculation
859 . ctxs  - Optional array of contexts to pass to each function, or NULL.
860 - X     - The coefficient vector u_h
861 
862   Output Parameter:
863 . D - A Vec which holds the difference ||u - u_h||_2 for each cell
864 
865   Level: developer
866 
867 .seealso: DMProjectFunction(), DMComputeL2Diff(), DMPlexComputeL2FieldDiff(), DMComputeL2GradientDiff()
868 @*/
869 PetscErrorCode DMPlexComputeL2DiffVec(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, Vec D)
870 {
871   PetscSection     section;
872   PetscQuadrature  quad;
873   Vec              localX;
874   PetscScalar     *funcVal, *interpolant;
875   PetscReal       *coords, *detJ, *J;
876   const PetscReal *quadPoints, *quadWeights;
877   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
878   PetscErrorCode   ierr;
879 
880   PetscFunctionBegin;
881   ierr = VecSet(D, 0.0);CHKERRQ(ierr);
882   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
883   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
884   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
885   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
886   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
887   ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
888   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
889   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
890   for (field = 0; field < numFields; ++field) {
891     PetscObject  obj;
892     PetscClassId id;
893     PetscInt     Nc;
894 
895     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
896     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
897     if (id == PETSCFE_CLASSID) {
898       PetscFE fe = (PetscFE) obj;
899 
900       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
901       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
902     } else if (id == PETSCFV_CLASSID) {
903       PetscFV fv = (PetscFV) obj;
904 
905       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
906       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
907     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
908     numComponents += Nc;
909   }
910   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
911   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
912   ierr = PetscMalloc5(numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
913   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
914   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
915   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
916   for (c = cStart; c < cEnd; ++c) {
917     PetscScalar *x = NULL;
918     PetscScalar  elemDiff = 0.0;
919     PetscInt     qc = 0;
920 
921     ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
922     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
923 
924     for (field = 0, fieldOffset = 0; field < numFields; ++field) {
925       PetscObject  obj;
926       PetscClassId id;
927       void * const ctx = ctxs ? ctxs[field] : NULL;
928       PetscInt     Nb, Nc, q, fc;
929 
930       ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
931       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
932       if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
933       else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
934       else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
935       if (funcs[field]) {
936         for (q = 0; q < Nq; ++q) {
937           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);
938           ierr = (*funcs[field])(dim, time, &coords[q*coordDim], Nc, funcVal, ctx);
939           if (ierr) {
940             PetscErrorCode ierr2;
941             ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
942             ierr2 = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
943             ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
944             CHKERRQ(ierr);
945           }
946           if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
947           else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
948           else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
949           for (fc = 0; fc < Nc; ++fc) {
950             const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
951             elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
952           }
953         }
954       }
955       fieldOffset += Nb;
956       qc          += Nc;
957     }
958     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
959     ierr = VecSetValue(D, c - cStart, elemDiff, INSERT_VALUES);CHKERRQ(ierr);
960   }
961   ierr = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
962   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
963   ierr = VecSqrtAbs(D);CHKERRQ(ierr);
964   PetscFunctionReturn(0);
965 }
966 
967 /*@C
968   DMPlexComputeGradientClementInterpolant - This function computes the L2 projection of the cellwise gradient of a function u onto P1, and stores it in a Vec.
969 
970   Input Parameters:
971 + dm - The DM
972 - LocX  - The coefficient vector u_h
973 
974   Output Parameter:
975 . locC - A Vec which holds the Clement interpolant of the gradient
976 
977   Notes: Add citation to (Clement, 1975) and definition of the interpolant
978   \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
979 
980   Level: developer
981 
982 .seealso: DMProjectFunction(), DMComputeL2Diff(), DMPlexComputeL2FieldDiff(), DMComputeL2GradientDiff()
983 @*/
984 PetscErrorCode DMPlexComputeGradientClementInterpolant(DM dm, Vec locX, Vec locC)
985 {
986   DM_Plex         *mesh  = (DM_Plex *) dm->data;
987   PetscInt         debug = mesh->printFEM;
988   DM               dmC;
989   PetscSection     section;
990   PetscQuadrature  quad;
991   PetscScalar     *interpolant, *gradsum;
992   PetscReal       *coords, *detJ, *J, *invJ;
993   const PetscReal *quadPoints, *quadWeights;
994   PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, vStart, vEnd, v, field, fieldOffset;
995   PetscErrorCode   ierr;
996 
997   PetscFunctionBegin;
998   ierr = VecGetDM(locC, &dmC);CHKERRQ(ierr);
999   ierr = VecSet(locC, 0.0);CHKERRQ(ierr);
1000   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1001   ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
1002   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1003   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1004   for (field = 0; field < numFields; ++field) {
1005     PetscObject  obj;
1006     PetscClassId id;
1007     PetscInt     Nc;
1008 
1009     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1010     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1011     if (id == PETSCFE_CLASSID) {
1012       PetscFE fe = (PetscFE) obj;
1013 
1014       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1015       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1016     } else if (id == PETSCFV_CLASSID) {
1017       PetscFV fv = (PetscFV) obj;
1018 
1019       ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
1020       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
1021     } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
1022     numComponents += Nc;
1023   }
1024   ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
1025   if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
1026   ierr = PetscMalloc6(coordDim*numComponents*2,&gradsum,coordDim*numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J,coordDim*coordDim*Nq,&invJ);CHKERRQ(ierr);
1027   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1028   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1029   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1030   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1031   for (v = vStart; v < vEnd; ++v) {
1032     PetscScalar volsum = 0.0;
1033     PetscInt   *star = NULL;
1034     PetscInt    starSize, st, d, fc;
1035 
1036     ierr = PetscMemzero(gradsum, coordDim*numComponents * sizeof(PetscScalar));CHKERRQ(ierr);
1037     ierr = DMPlexGetTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
1038     for (st = 0; st < starSize*2; st += 2) {
1039       const PetscInt cell = star[st];
1040       PetscScalar   *grad = &gradsum[coordDim*numComponents];
1041       PetscScalar   *x    = NULL;
1042       PetscReal      vol  = 0.0;
1043 
1044       if ((cell < cStart) || (cell >= cEnd)) continue;
1045       ierr = DMPlexComputeCellGeometryFEM(dm, cell, quad, coords, J, invJ, detJ);CHKERRQ(ierr);
1046       ierr = DMPlexVecGetClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr);
1047       for (field = 0, fieldOffset = 0; field < numFields; ++field) {
1048         PetscObject  obj;
1049         PetscClassId id;
1050         PetscInt     Nb, Nc, q, qc = 0;
1051 
1052         ierr = PetscMemzero(grad, coordDim*numComponents * sizeof(PetscScalar));CHKERRQ(ierr);
1053         ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1054         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1055         if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
1056         else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
1057         else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
1058         for (q = 0; q < Nq; ++q) {
1059           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);
1060           if (ierr) {
1061             PetscErrorCode ierr2;
1062             ierr2 = DMPlexVecRestoreClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr2);
1063             ierr2 = DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr2);
1064             ierr2 = PetscFree4(interpolant,coords,detJ,J);CHKERRQ(ierr2);
1065             CHKERRQ(ierr);
1066           }
1067           if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolateGradient_Static((PetscFE) obj, &x[fieldOffset], coordDim, invJ, NULL, q, interpolant);CHKERRQ(ierr);}
1068           else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
1069           for (fc = 0; fc < Nc; ++fc) {
1070             const PetscReal wt = quadWeights[q*qNc+qc+fc];
1071 
1072             for (d = 0; d < coordDim; ++d) grad[fc*coordDim+d] += interpolant[fc*dim+d]*wt*detJ[q];
1073           }
1074           vol += quadWeights[q*qNc]*detJ[q];
1075         }
1076         fieldOffset += Nb;
1077         qc          += Nc;
1078       }
1079       ierr = DMPlexVecRestoreClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr);
1080       for (fc = 0; fc < numComponents; ++fc) {
1081         for (d = 0; d < coordDim; ++d) {
1082           gradsum[fc*coordDim+d] += grad[fc*coordDim+d];
1083         }
1084       }
1085       volsum += vol;
1086       if (debug) {
1087         ierr = PetscPrintf(PETSC_COMM_SELF, "Cell %d gradient: [", cell);CHKERRQ(ierr);
1088         for (fc = 0; fc < numComponents; ++fc) {
1089           for (d = 0; d < coordDim; ++d) {
1090             if (fc || d > 0) {ierr = PetscPrintf(PETSC_COMM_SELF, ", ");CHKERRQ(ierr);}
1091             ierr = PetscPrintf(PETSC_COMM_SELF, "%g", grad[fc*coordDim+d]);CHKERRQ(ierr);
1092           }
1093         }
1094         ierr = PetscPrintf(PETSC_COMM_SELF, "]\n");CHKERRQ(ierr);
1095       }
1096     }
1097     for (fc = 0; fc < numComponents; ++fc) {
1098       for (d = 0; d < coordDim; ++d) gradsum[fc*coordDim+d] /= volsum;
1099     }
1100     ierr = DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
1101     ierr = DMPlexVecSetClosure(dmC, NULL, locC, v, gradsum, INSERT_VALUES);CHKERRQ(ierr);
1102   }
1103   ierr = PetscFree6(gradsum,interpolant,coords,detJ,J,invJ);CHKERRQ(ierr);
1104   PetscFunctionReturn(0);
1105 }
1106 
1107 /*@
1108   DMPlexComputeIntegralFEM - Form the local integral F from the local input X using pointwise functions specified by the user
1109 
1110   Input Parameters:
1111 + dm - The mesh
1112 . X  - Local input vector
1113 - user - The user context
1114 
1115   Output Parameter:
1116 . integral - Local integral for each field
1117 
1118   Level: developer
1119 
1120 .seealso: DMPlexComputeResidualFEM()
1121 @*/
1122 PetscErrorCode DMPlexComputeIntegralFEM(DM dm, Vec X, PetscReal *integral, void *user)
1123 {
1124   DM_Plex           *mesh  = (DM_Plex *) dm->data;
1125   DM                 dmAux, dmGrad;
1126   Vec                localX, A, cellGeometryFVM = NULL, faceGeometryFVM = NULL, locGrad = NULL;
1127   PetscDS            prob, probAux = NULL;
1128   PetscSection       section, sectionAux;
1129   PetscFV            fvm = NULL;
1130   PetscFECellGeom   *cgeomFEM;
1131   PetscFVFaceGeom   *fgeomFVM;
1132   PetscFVCellGeom   *cgeomFVM;
1133   PetscScalar       *u, *a = NULL;
1134   const PetscScalar *constants, *lgrad;
1135   PetscReal         *lintegral;
1136   PetscInt          *uOff, *uOff_x, *aOff = NULL;
1137   PetscInt           dim, numConstants, Nf, NfAux = 0, f, numCells, cStart, cEnd, cEndInterior, c;
1138   PetscInt           totDim, totDimAux;
1139   PetscBool          useFVM = PETSC_FALSE;
1140   PetscErrorCode     ierr;
1141 
1142   PetscFunctionBegin;
1143   ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
1144   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
1145   ierr = DMPlexInsertBoundaryValues(dm, PETSC_TRUE, localX, 0.0, NULL, NULL, NULL);CHKERRQ(ierr);
1146   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
1147   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
1148   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1149   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1150   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1151   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1152   ierr = PetscDSGetComponentOffsets(prob, &uOff);CHKERRQ(ierr);
1153   ierr = PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);CHKERRQ(ierr);
1154   ierr = PetscDSGetConstants(prob, &numConstants, &constants);CHKERRQ(ierr);
1155   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1156   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1157   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1158   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1159   numCells = cEnd - cStart;
1160   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1161   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1162   if (dmAux) {
1163     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1164     ierr = PetscDSGetNumFields(probAux, &NfAux);CHKERRQ(ierr);
1165     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1166     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1167     ierr = PetscDSGetComponentOffsets(probAux, &aOff);CHKERRQ(ierr);
1168     ierr = PetscDSGetEvaluationArrays(probAux, &a, NULL, NULL);CHKERRQ(ierr);
1169   }
1170   for (f = 0; f < Nf; ++f) {
1171     PetscObject  obj;
1172     PetscClassId id;
1173 
1174     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1175     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1176     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1177   }
1178   if (useFVM) {
1179     Vec       grad;
1180     PetscInt  fStart, fEnd;
1181     PetscBool compGrad;
1182 
1183     ierr = PetscFVGetComputeGradients(fvm, &compGrad);CHKERRQ(ierr);
1184     ierr = PetscFVSetComputeGradients(fvm, PETSC_TRUE);CHKERRQ(ierr);
1185     ierr = DMPlexComputeGeometryFVM(dm, &cellGeometryFVM, &faceGeometryFVM);CHKERRQ(ierr);
1186     ierr = DMPlexComputeGradientFVM(dm, fvm, faceGeometryFVM, cellGeometryFVM, &dmGrad);CHKERRQ(ierr);
1187     ierr = PetscFVSetComputeGradients(fvm, compGrad);CHKERRQ(ierr);
1188     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1189     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1190     /* Reconstruct and limit cell gradients */
1191     ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1192     ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1193     ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, localX, grad);CHKERRQ(ierr);
1194     /* Communicate gradient values */
1195     ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1196     ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1197     ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1198     ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1199     /* Handle non-essential (e.g. outflow) boundary values */
1200     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, localX, 0.0, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1201     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1202   }
1203   ierr = PetscMalloc3(Nf,&lintegral,numCells*totDim,&u,numCells,&cgeomFEM);CHKERRQ(ierr);
1204   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1205   for (f = 0; f < Nf; ++f) {lintegral[f] = 0.0;}
1206   for (c = cStart; c < cEnd; ++c) {
1207     PetscScalar *x = NULL;
1208     PetscInt     i;
1209 
1210     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, cgeomFEM[c].v0, cgeomFEM[c].J, cgeomFEM[c].invJ, &cgeomFEM[c].detJ);CHKERRQ(ierr);
1211     if (cgeomFEM[c].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cgeomFEM[c].detJ, c);
1212     ierr = DMPlexVecGetClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
1213     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1214     ierr = DMPlexVecRestoreClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
1215     if (dmAux) {
1216       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1217       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1218       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1219     }
1220   }
1221   for (f = 0; f < Nf; ++f) {
1222     PetscObject  obj;
1223     PetscClassId id;
1224     PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1225 
1226     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1227     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1228     if (id == PETSCFE_CLASSID) {
1229       PetscFE         fe = (PetscFE) obj;
1230       PetscQuadrature q;
1231       PetscInt        Nq, Nb;
1232 
1233       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1234       ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1235       ierr = PetscQuadratureGetData(q, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1236       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1237       blockSize = Nb*Nq;
1238       batchSize = numBlocks * blockSize;
1239       ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1240       numChunks = numCells / (numBatches*batchSize);
1241       Ne        = numChunks*numBatches*batchSize;
1242       Nr        = numCells % (numBatches*batchSize);
1243       offset    = numCells - Nr;
1244       ierr = PetscFEIntegrate(fe, prob, f, Ne, cgeomFEM, u, probAux, a, lintegral);CHKERRQ(ierr);
1245       ierr = PetscFEIntegrate(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], probAux, &a[offset*totDimAux], lintegral);CHKERRQ(ierr);
1246     } else if (id == PETSCFV_CLASSID) {
1247       /* PetscFV  fv = (PetscFV) obj; */
1248       PetscInt       foff;
1249       PetscPointFunc obj_func;
1250       PetscScalar    lint;
1251 
1252       ierr = PetscDSGetObjective(prob, f, &obj_func);CHKERRQ(ierr);
1253       ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1254       if (obj_func) {
1255         for (c = 0; c < numCells; ++c) {
1256           PetscScalar *u_x;
1257 
1258           ierr = DMPlexPointLocalRead(dmGrad, c, lgrad, &u_x);CHKERRQ(ierr);
1259           obj_func(dim, Nf, NfAux, uOff, uOff_x, &u[totDim*c+foff], NULL, u_x, aOff, NULL, a, NULL, NULL, 0.0, cgeomFVM[c].centroid, numConstants, constants, &lint);
1260           lintegral[f] += PetscRealPart(lint)*cgeomFVM[c].volume;
1261         }
1262       }
1263     } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1264   }
1265   if (useFVM) {
1266     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1267     ierr = VecRestoreArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1268     ierr = VecRestoreArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1269     ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1270     ierr = VecDestroy(&faceGeometryFVM);CHKERRQ(ierr);
1271     ierr = VecDestroy(&cellGeometryFVM);CHKERRQ(ierr);
1272     ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
1273   }
1274   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1275   if (mesh->printFEM) {
1276     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Local integral:");CHKERRQ(ierr);
1277     for (f = 0; f < Nf; ++f) {ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), " %g", lintegral[f]);CHKERRQ(ierr);}
1278     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "\n");CHKERRQ(ierr);
1279   }
1280   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
1281   ierr = MPIU_Allreduce(lintegral, integral, Nf, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
1282   ierr = PetscFree3(lintegral,u,cgeomFEM);CHKERRQ(ierr);
1283   ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
1284   PetscFunctionReturn(0);
1285 }
1286 
1287 /*@
1288   DMPlexComputeInterpolatorNested - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1289 
1290   Input Parameters:
1291 + dmf  - The fine mesh
1292 . dmc  - The coarse mesh
1293 - user - The user context
1294 
1295   Output Parameter:
1296 . In  - The interpolation matrix
1297 
1298   Level: developer
1299 
1300 .seealso: DMPlexComputeInterpolatorGeneral(), DMPlexComputeJacobianFEM()
1301 @*/
1302 PetscErrorCode DMPlexComputeInterpolatorNested(DM dmc, DM dmf, Mat In, void *user)
1303 {
1304   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1305   const char       *name  = "Interpolator";
1306   PetscDS           prob;
1307   PetscFE          *feRef;
1308   PetscFV          *fvRef;
1309   PetscSection      fsection, fglobalSection;
1310   PetscSection      csection, cglobalSection;
1311   PetscScalar      *elemMat;
1312   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, cEndInterior, c;
1313   PetscInt          cTotDim, rTotDim = 0;
1314   PetscErrorCode    ierr;
1315 
1316   PetscFunctionBegin;
1317   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1318   ierr = DMGetDimension(dmf, &dim);CHKERRQ(ierr);
1319   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1320   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1321   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1322   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1323   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1324   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1325   ierr = DMPlexGetHybridBounds(dmc, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1326   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1327   ierr = DMGetDS(dmf, &prob);CHKERRQ(ierr);
1328   ierr = PetscCalloc2(Nf,&feRef,Nf,&fvRef);CHKERRQ(ierr);
1329   for (f = 0; f < Nf; ++f) {
1330     PetscObject  obj;
1331     PetscClassId id;
1332     PetscInt     rNb = 0, Nc = 0;
1333 
1334     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1335     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1336     if (id == PETSCFE_CLASSID) {
1337       PetscFE fe = (PetscFE) obj;
1338 
1339       ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
1340       ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1341       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1342     } else if (id == PETSCFV_CLASSID) {
1343       PetscFV        fv = (PetscFV) obj;
1344       PetscDualSpace Q;
1345 
1346       ierr = PetscFVRefine(fv, &fvRef[f]);CHKERRQ(ierr);
1347       ierr = PetscFVGetDualSpace(fvRef[f], &Q);CHKERRQ(ierr);
1348       ierr = PetscDualSpaceGetDimension(Q, &rNb);CHKERRQ(ierr);
1349       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
1350     }
1351     rTotDim += rNb;
1352   }
1353   ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
1354   ierr = PetscMalloc1(rTotDim*cTotDim,&elemMat);CHKERRQ(ierr);
1355   ierr = PetscMemzero(elemMat, rTotDim*cTotDim * sizeof(PetscScalar));CHKERRQ(ierr);
1356   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1357     PetscDualSpace   Qref;
1358     PetscQuadrature  f;
1359     const PetscReal *qpoints, *qweights;
1360     PetscReal       *points;
1361     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1362 
1363     /* Compose points from all dual basis functionals */
1364     if (feRef[fieldI]) {
1365       ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1366       ierr = PetscFEGetNumComponents(feRef[fieldI], &Nc);CHKERRQ(ierr);
1367     } else {
1368       ierr = PetscFVGetDualSpace(fvRef[fieldI], &Qref);CHKERRQ(ierr);
1369       ierr = PetscFVGetNumComponents(fvRef[fieldI], &Nc);CHKERRQ(ierr);
1370     }
1371     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1372     for (i = 0; i < fpdim; ++i) {
1373       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1374       ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1375       npoints += Np;
1376     }
1377     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1378     for (i = 0, k = 0; i < fpdim; ++i) {
1379       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1380       ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1381       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1382     }
1383 
1384     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1385       PetscObject  obj;
1386       PetscClassId id;
1387       PetscReal   *B;
1388       PetscInt     NcJ = 0, cpdim = 0, j, qNc;
1389 
1390       ierr = PetscDSGetDiscretization(prob, fieldJ, &obj);CHKERRQ(ierr);
1391       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1392       if (id == PETSCFE_CLASSID) {
1393         PetscFE fe = (PetscFE) obj;
1394 
1395         /* Evaluate basis at points */
1396         ierr = PetscFEGetNumComponents(fe, &NcJ);CHKERRQ(ierr);
1397         ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
1398         /* For now, fields only interpolate themselves */
1399         if (fieldI == fieldJ) {
1400           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);
1401           ierr = PetscFEGetTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1402           for (i = 0, k = 0; i < fpdim; ++i) {
1403             ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1404             ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, NULL, &qweights);CHKERRQ(ierr);
1405             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);
1406             for (p = 0; p < Np; ++p, ++k) {
1407               for (j = 0; j < cpdim; ++j) {
1408                 /* NOTE: This is not quite right, unless fpdim == number of fine grid functional quad points */
1409                 for (c = 0; c < Nc; ++c) elemMat[(offsetI + i)*cTotDim + offsetJ + j] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p*qNc+c];
1410               }
1411             }
1412           }
1413           ierr = PetscFERestoreTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1414         }
1415       } else if (id == PETSCFV_CLASSID) {
1416         PetscFV        fv = (PetscFV) obj;
1417 
1418         /* Evaluate constant function at points */
1419         ierr = PetscFVGetNumComponents(fv, &NcJ);CHKERRQ(ierr);
1420         cpdim = 1;
1421         /* For now, fields only interpolate themselves */
1422         if (fieldI == fieldJ) {
1423           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);
1424           for (i = 0, k = 0; i < fpdim; ++i) {
1425             ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1426             ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, NULL, &qweights);CHKERRQ(ierr);
1427             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);
1428             for (p = 0; p < Np; ++p, ++k) {
1429               for (j = 0; j < cpdim; ++j) {
1430                 for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cTotDim + offsetJ + j*NcJ + c] += 1.0*qweights[p*qNc+c];
1431               }
1432             }
1433           }
1434         }
1435       }
1436       offsetJ += cpdim*NcJ;
1437     }
1438     offsetI += fpdim*Nc;
1439     ierr = PetscFree(points);CHKERRQ(ierr);
1440   }
1441   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rTotDim, cTotDim, elemMat);CHKERRQ(ierr);}
1442   /* Preallocate matrix */
1443   {
1444     Mat          preallocator;
1445     PetscScalar *vals;
1446     PetscInt    *cellCIndices, *cellFIndices;
1447     PetscInt     locRows, locCols, cell;
1448 
1449     ierr = MatGetLocalSize(In, &locRows, &locCols);CHKERRQ(ierr);
1450     ierr = MatCreate(PetscObjectComm((PetscObject) In), &preallocator);CHKERRQ(ierr);
1451     ierr = MatSetType(preallocator, MATPREALLOCATOR);CHKERRQ(ierr);
1452     ierr = MatSetSizes(preallocator, locRows, locCols, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
1453     ierr = MatSetUp(preallocator);CHKERRQ(ierr);
1454     ierr = PetscCalloc3(rTotDim*cTotDim, &vals,cTotDim,&cellCIndices,rTotDim,&cellFIndices);CHKERRQ(ierr);
1455     for (cell = cStart; cell < cEnd; ++cell) {
1456       ierr = DMPlexMatGetClosureIndicesRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, cell, cellCIndices, cellFIndices);CHKERRQ(ierr);
1457       ierr = MatSetValues(preallocator, rTotDim, cellFIndices, cTotDim, cellCIndices, vals, INSERT_VALUES);CHKERRQ(ierr);
1458     }
1459     ierr = PetscFree3(vals,cellCIndices,cellFIndices);CHKERRQ(ierr);
1460     ierr = MatAssemblyBegin(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1461     ierr = MatAssemblyEnd(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1462     ierr = MatPreallocatorPreallocate(preallocator, PETSC_TRUE, In);CHKERRQ(ierr);
1463     ierr = MatDestroy(&preallocator);CHKERRQ(ierr);
1464   }
1465   /* Fill matrix */
1466   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1467   for (c = cStart; c < cEnd; ++c) {
1468     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1469   }
1470   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1471   ierr = PetscFree2(feRef,fvRef);CHKERRQ(ierr);
1472   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1473   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1474   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1475   if (mesh->printFEM) {
1476     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1477     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1478     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1479   }
1480   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1481   PetscFunctionReturn(0);
1482 }
1483 
1484 /*@
1485   DMPlexComputeInterpolatorGeneral - Form the local portion of the interpolation matrix I from the coarse DM to a non-nested fine DM.
1486 
1487   Input Parameters:
1488 + dmf  - The fine mesh
1489 . dmc  - The coarse mesh
1490 - user - The user context
1491 
1492   Output Parameter:
1493 . In  - The interpolation matrix
1494 
1495   Level: developer
1496 
1497 .seealso: DMPlexComputeInterpolatorNested(), DMPlexComputeJacobianFEM()
1498 @*/
1499 PetscErrorCode DMPlexComputeInterpolatorGeneral(DM dmc, DM dmf, Mat In, void *user)
1500 {
1501   DM_Plex       *mesh = (DM_Plex *) dmf->data;
1502   const char    *name = "Interpolator";
1503   PetscDS        prob;
1504   PetscSection   fsection, csection, globalFSection, globalCSection;
1505   PetscHashJK    ht;
1506   PetscLayout    rLayout;
1507   PetscInt      *dnz, *onz;
1508   PetscInt       locRows, rStart, rEnd;
1509   PetscReal     *x, *v0, *J, *invJ, detJ;
1510   PetscReal     *v0c, *Jc, *invJc, detJc;
1511   PetscScalar   *elemMat;
1512   PetscInt       dim, Nf, field, totDim, cStart, cEnd, cell, ccell;
1513   PetscErrorCode ierr;
1514 
1515   PetscFunctionBegin;
1516   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1517   ierr = DMGetCoordinateDim(dmc, &dim);CHKERRQ(ierr);
1518   ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
1519   ierr = PetscDSGetRefCoordArrays(prob, &x, NULL);CHKERRQ(ierr);
1520   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1521   ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
1522   ierr = PetscMalloc3(dim,&v0c,dim*dim,&Jc,dim*dim,&invJc);CHKERRQ(ierr);
1523   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1524   ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);
1525   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1526   ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);
1527   ierr = DMPlexGetHeightStratum(dmf, 0, &cStart, &cEnd);CHKERRQ(ierr);
1528   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1529   ierr = PetscMalloc1(totDim, &elemMat);CHKERRQ(ierr);
1530 
1531   ierr = MatGetLocalSize(In, &locRows, NULL);CHKERRQ(ierr);
1532   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) In), &rLayout);CHKERRQ(ierr);
1533   ierr = PetscLayoutSetLocalSize(rLayout, locRows);CHKERRQ(ierr);
1534   ierr = PetscLayoutSetBlockSize(rLayout, 1);CHKERRQ(ierr);
1535   ierr = PetscLayoutSetUp(rLayout);CHKERRQ(ierr);
1536   ierr = PetscLayoutGetRange(rLayout, &rStart, &rEnd);CHKERRQ(ierr);
1537   ierr = PetscLayoutDestroy(&rLayout);CHKERRQ(ierr);
1538   ierr = PetscCalloc2(locRows,&dnz,locRows,&onz);CHKERRQ(ierr);
1539   ierr = PetscHashJKCreate(&ht);CHKERRQ(ierr);
1540   for (field = 0; field < Nf; ++field) {
1541     PetscObject      obj;
1542     PetscClassId     id;
1543     PetscDualSpace   Q = NULL;
1544     PetscQuadrature  f;
1545     const PetscReal *qpoints;
1546     PetscInt         Nc, Np, fpdim, i, d;
1547 
1548     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1549     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1550     if (id == PETSCFE_CLASSID) {
1551       PetscFE fe = (PetscFE) obj;
1552 
1553       ierr = PetscFEGetDualSpace(fe, &Q);CHKERRQ(ierr);
1554       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1555     } else if (id == PETSCFV_CLASSID) {
1556       PetscFV fv = (PetscFV) obj;
1557 
1558       ierr = PetscFVGetDualSpace(fv, &Q);CHKERRQ(ierr);
1559       Nc   = 1;
1560     }
1561     ierr = PetscDualSpaceGetDimension(Q, &fpdim);CHKERRQ(ierr);
1562     /* For each fine grid cell */
1563     for (cell = cStart; cell < cEnd; ++cell) {
1564       PetscInt *findices,   *cindices;
1565       PetscInt  numFIndices, numCIndices;
1566 
1567       ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1568       ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
1569       if (numFIndices != fpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of fine indices %d != %d dual basis vecs", numFIndices, fpdim);
1570       for (i = 0; i < fpdim; ++i) {
1571         Vec             pointVec;
1572         PetscScalar    *pV;
1573         PetscSF         coarseCellSF = NULL;
1574         const PetscSFNode *coarseCells;
1575         PetscInt        numCoarseCells, q, c;
1576 
1577         /* Get points from the dual basis functional quadrature */
1578         ierr = PetscDualSpaceGetFunctional(Q, i, &f);CHKERRQ(ierr);
1579         ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1580         ierr = VecCreateSeq(PETSC_COMM_SELF, Np*dim, &pointVec);CHKERRQ(ierr);
1581         ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
1582         ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
1583         for (q = 0; q < Np; ++q) {
1584           /* Transform point to real space */
1585           CoordinatesRefToReal(dim, dim, v0, J, &qpoints[q*dim], x);
1586           for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
1587         }
1588         ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
1589         /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
1590         /* OPT: Pack all quad points from fine cell */
1591         ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
1592         ierr = PetscSFViewFromOptions(coarseCellSF, NULL, "-interp_sf_view");CHKERRQ(ierr);
1593         /* Update preallocation info */
1594         ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
1595         if (numCoarseCells != Np) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
1596         {
1597           PetscHashJKKey  key;
1598           PetscHashJKIter missing, iter;
1599 
1600           key.j = findices[i];
1601           if (key.j >= 0) {
1602             /* Get indices for coarse elements */
1603             for (ccell = 0; ccell < numCoarseCells; ++ccell) {
1604               ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1605               for (c = 0; c < numCIndices; ++c) {
1606                 key.k = cindices[c];
1607                 if (key.k < 0) continue;
1608                 ierr = PetscHashJKPut(ht, key, &missing, &iter);CHKERRQ(ierr);
1609                 if (missing) {
1610                   ierr = PetscHashJKSet(ht, iter, 1);CHKERRQ(ierr);
1611                   if ((key.k >= rStart) && (key.k < rEnd)) ++dnz[key.j-rStart];
1612                   else                                     ++onz[key.j-rStart];
1613                 }
1614               }
1615               ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1616             }
1617           }
1618         }
1619         ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
1620         ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
1621       }
1622       ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1623     }
1624   }
1625   ierr = PetscHashJKDestroy(&ht);CHKERRQ(ierr);
1626   ierr = MatXAIJSetPreallocation(In, 1, dnz, onz, NULL, NULL);CHKERRQ(ierr);
1627   ierr = MatSetOption(In, MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1628   ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
1629   for (field = 0; field < Nf; ++field) {
1630     PetscObject      obj;
1631     PetscClassId     id;
1632     PetscDualSpace   Q = NULL;
1633     PetscQuadrature  f;
1634     const PetscReal *qpoints, *qweights;
1635     PetscInt         Nc, qNc, Np, fpdim, i, d;
1636 
1637     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1638     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1639     if (id == PETSCFE_CLASSID) {
1640       PetscFE fe = (PetscFE) obj;
1641 
1642       ierr = PetscFEGetDualSpace(fe, &Q);CHKERRQ(ierr);
1643       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1644     } else if (id == PETSCFV_CLASSID) {
1645       PetscFV fv = (PetscFV) obj;
1646 
1647       ierr = PetscFVGetDualSpace(fv, &Q);CHKERRQ(ierr);
1648       Nc   = 1;
1649     }
1650     ierr = PetscDualSpaceGetDimension(Q, &fpdim);CHKERRQ(ierr);
1651     /* For each fine grid cell */
1652     for (cell = cStart; cell < cEnd; ++cell) {
1653       PetscInt *findices,   *cindices;
1654       PetscInt  numFIndices, numCIndices;
1655 
1656       ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1657       ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
1658       if (numFIndices != fpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of fine indices %d != %d dual basis vecs", numFIndices, fpdim);
1659       for (i = 0; i < fpdim; ++i) {
1660         Vec             pointVec;
1661         PetscScalar    *pV;
1662         PetscSF         coarseCellSF = NULL;
1663         const PetscSFNode *coarseCells;
1664         PetscInt        numCoarseCells, cpdim, q, c, j;
1665 
1666         /* Get points from the dual basis functional quadrature */
1667         ierr = PetscDualSpaceGetFunctional(Q, i, &f);CHKERRQ(ierr);
1668         ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, &qpoints, &qweights);CHKERRQ(ierr);
1669         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);
1670         ierr = VecCreateSeq(PETSC_COMM_SELF, Np*dim, &pointVec);CHKERRQ(ierr);
1671         ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
1672         ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
1673         for (q = 0; q < Np; ++q) {
1674           /* Transform point to real space */
1675           CoordinatesRefToReal(dim, dim, v0, J, &qpoints[q*dim], x);
1676           for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
1677         }
1678         ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
1679         /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
1680         /* OPT: Read this out from preallocation information */
1681         ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
1682         /* Update preallocation info */
1683         ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
1684         if (numCoarseCells != Np) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
1685         ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
1686         for (ccell = 0; ccell < numCoarseCells; ++ccell) {
1687           PetscReal pVReal[3];
1688 
1689           ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1690           /* Transform points from real space to coarse reference space */
1691           ierr = DMPlexComputeCellGeometryFEM(dmc, coarseCells[ccell].index, NULL, v0c, Jc, invJc, &detJc);CHKERRQ(ierr);
1692           for (d = 0; d < dim; ++d) pVReal[d] = PetscRealPart(pV[ccell*dim+d]);
1693           CoordinatesRealToRef(dim, dim, v0c, invJc, pVReal, x);
1694 
1695           if (id == PETSCFE_CLASSID) {
1696             PetscFE    fe = (PetscFE) obj;
1697             PetscReal *B;
1698 
1699             /* Evaluate coarse basis on contained point */
1700             ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
1701             ierr = PetscFEGetTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);
1702             ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
1703             /* Get elemMat entries by multiplying by weight */
1704             for (j = 0; j < cpdim; ++j) {
1705               for (c = 0; c < Nc; ++c) elemMat[j] += B[j*Nc + c]*qweights[ccell*qNc + c];
1706             }
1707             ierr = PetscFERestoreTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1708           } else {
1709             cpdim = 1;
1710             for (j = 0; j < cpdim; ++j) {
1711               for (c = 0; c < Nc; ++c) elemMat[j] += 1.0*qweights[ccell*qNc + c];
1712             }
1713           }
1714           /* Update interpolator */
1715           if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
1716           if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
1717           ierr = MatSetValues(In, 1, &findices[i], numCIndices, cindices, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1718           ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
1719         }
1720         ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
1721         ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
1722         ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
1723       }
1724       ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
1725     }
1726   }
1727   ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
1728   ierr = PetscFree3(v0c,Jc,invJc);CHKERRQ(ierr);
1729   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1730   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1731   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1732   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1733   PetscFunctionReturn(0);
1734 }
1735 
1736 /*@
1737   DMPlexComputeInjectorFEM - Compute a mapping from coarse unknowns to fine unknowns
1738 
1739   Input Parameters:
1740 + dmc  - The coarse mesh
1741 - dmf  - The fine mesh
1742 - user - The user context
1743 
1744   Output Parameter:
1745 . sc   - The mapping
1746 
1747   Level: developer
1748 
1749 .seealso: DMPlexComputeInterpolatorNested(), DMPlexComputeJacobianFEM()
1750 @*/
1751 PetscErrorCode DMPlexComputeInjectorFEM(DM dmc, DM dmf, VecScatter *sc, void *user)
1752 {
1753   PetscDS        prob;
1754   PetscFE       *feRef;
1755   PetscFV       *fvRef;
1756   Vec            fv, cv;
1757   IS             fis, cis;
1758   PetscSection   fsection, fglobalSection, csection, cglobalSection;
1759   PetscInt      *cmap, *cellCIndices, *cellFIndices, *cindices, *findices;
1760   PetscInt       cTotDim, fTotDim = 0, Nf, f, field, cStart, cEnd, cEndInterior, c, dim, d, startC, endC, offsetC, offsetF, m;
1761   PetscErrorCode ierr;
1762 
1763   PetscFunctionBegin;
1764   ierr = PetscLogEventBegin(DMPLEX_InjectorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1765   ierr = DMGetDimension(dmf, &dim);CHKERRQ(ierr);
1766   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1767   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1768   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1769   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1770   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1771   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1772   ierr = DMPlexGetHybridBounds(dmc, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1773   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1774   ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
1775   ierr = PetscCalloc2(Nf,&feRef,Nf,&fvRef);CHKERRQ(ierr);
1776   for (f = 0; f < Nf; ++f) {
1777     PetscObject  obj;
1778     PetscClassId id;
1779     PetscInt     fNb = 0, Nc = 0;
1780 
1781     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1782     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1783     if (id == PETSCFE_CLASSID) {
1784       PetscFE fe = (PetscFE) obj;
1785 
1786       ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
1787       ierr = PetscFEGetDimension(feRef[f], &fNb);CHKERRQ(ierr);
1788       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1789     } else if (id == PETSCFV_CLASSID) {
1790       PetscFV        fv = (PetscFV) obj;
1791       PetscDualSpace Q;
1792 
1793       ierr = PetscFVRefine(fv, &fvRef[f]);CHKERRQ(ierr);
1794       ierr = PetscFVGetDualSpace(fvRef[f], &Q);CHKERRQ(ierr);
1795       ierr = PetscDualSpaceGetDimension(Q, &fNb);CHKERRQ(ierr);
1796       ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
1797     }
1798     fTotDim += fNb*Nc;
1799   }
1800   ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
1801   ierr = PetscMalloc1(cTotDim,&cmap);CHKERRQ(ierr);
1802   for (field = 0, offsetC = 0, offsetF = 0; field < Nf; ++field) {
1803     PetscFE        feC;
1804     PetscFV        fvC;
1805     PetscDualSpace QF, QC;
1806     PetscInt       NcF, NcC, fpdim, cpdim;
1807 
1808     if (feRef[field]) {
1809       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &feC);CHKERRQ(ierr);
1810       ierr = PetscFEGetNumComponents(feC, &NcC);CHKERRQ(ierr);
1811       ierr = PetscFEGetNumComponents(feRef[field], &NcF);CHKERRQ(ierr);
1812       ierr = PetscFEGetDualSpace(feRef[field], &QF);CHKERRQ(ierr);
1813       ierr = PetscDualSpaceGetDimension(QF, &fpdim);CHKERRQ(ierr);
1814       ierr = PetscFEGetDualSpace(feC, &QC);CHKERRQ(ierr);
1815       ierr = PetscDualSpaceGetDimension(QC, &cpdim);CHKERRQ(ierr);
1816     } else {
1817       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fvC);CHKERRQ(ierr);
1818       ierr = PetscFVGetNumComponents(fvC, &NcC);CHKERRQ(ierr);
1819       ierr = PetscFVGetNumComponents(fvRef[field], &NcF);CHKERRQ(ierr);
1820       ierr = PetscFVGetDualSpace(fvRef[field], &QF);CHKERRQ(ierr);
1821       ierr = PetscDualSpaceGetDimension(QF, &fpdim);CHKERRQ(ierr);
1822       ierr = PetscFVGetDualSpace(fvC, &QC);CHKERRQ(ierr);
1823       ierr = PetscDualSpaceGetDimension(QC, &cpdim);CHKERRQ(ierr);
1824     }
1825     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);
1826     for (c = 0; c < cpdim; ++c) {
1827       PetscQuadrature  cfunc;
1828       const PetscReal *cqpoints;
1829       PetscInt         NpC;
1830       PetscBool        found = PETSC_FALSE;
1831 
1832       ierr = PetscDualSpaceGetFunctional(QC, c, &cfunc);CHKERRQ(ierr);
1833       ierr = PetscQuadratureGetData(cfunc, NULL, NULL, &NpC, &cqpoints, NULL);CHKERRQ(ierr);
1834       if (NpC != 1 && feRef[field]) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Do not know how to do injection for moments");
1835       for (f = 0; f < fpdim; ++f) {
1836         PetscQuadrature  ffunc;
1837         const PetscReal *fqpoints;
1838         PetscReal        sum = 0.0;
1839         PetscInt         NpF, comp;
1840 
1841         ierr = PetscDualSpaceGetFunctional(QF, f, &ffunc);CHKERRQ(ierr);
1842         ierr = PetscQuadratureGetData(ffunc, NULL, NULL, &NpF, &fqpoints, NULL);CHKERRQ(ierr);
1843         if (NpC != NpF) continue;
1844         for (d = 0; d < dim; ++d) sum += PetscAbsReal(cqpoints[d] - fqpoints[d]);
1845         if (sum > 1.0e-9) continue;
1846         for (comp = 0; comp < NcC; ++comp) {
1847           cmap[(offsetC+c)*NcC+comp] = (offsetF+f)*NcF+comp;
1848         }
1849         found = PETSC_TRUE;
1850         break;
1851       }
1852       if (!found) {
1853         /* TODO We really want the average here, but some asshole put VecScatter in the interface */
1854         if (fvRef[field]) {
1855           PetscInt comp;
1856           for (comp = 0; comp < NcC; ++comp) {
1857             cmap[(offsetC+c)*NcC+comp] = (offsetF+0)*NcF+comp;
1858           }
1859         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate matching functional for injection");
1860       }
1861     }
1862     offsetC += cpdim*NcC;
1863     offsetF += fpdim*NcF;
1864   }
1865   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);ierr = PetscFVDestroy(&fvRef[f]);CHKERRQ(ierr);}
1866   ierr = PetscFree2(feRef,fvRef);CHKERRQ(ierr);
1867 
1868   ierr = DMGetGlobalVector(dmf, &fv);CHKERRQ(ierr);
1869   ierr = DMGetGlobalVector(dmc, &cv);CHKERRQ(ierr);
1870   ierr = VecGetOwnershipRange(cv, &startC, &endC);CHKERRQ(ierr);
1871   ierr = PetscSectionGetConstrainedStorageSize(cglobalSection, &m);CHKERRQ(ierr);
1872   ierr = PetscMalloc2(cTotDim,&cellCIndices,fTotDim,&cellFIndices);CHKERRQ(ierr);
1873   ierr = PetscMalloc1(m,&cindices);CHKERRQ(ierr);
1874   ierr = PetscMalloc1(m,&findices);CHKERRQ(ierr);
1875   for (d = 0; d < m; ++d) cindices[d] = findices[d] = -1;
1876   for (c = cStart; c < cEnd; ++c) {
1877     ierr = DMPlexMatGetClosureIndicesRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, c, cellCIndices, cellFIndices);CHKERRQ(ierr);
1878     for (d = 0; d < cTotDim; ++d) {
1879       if ((cellCIndices[d] < startC) || (cellCIndices[d] >= endC)) continue;
1880       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]]);
1881       cindices[cellCIndices[d]-startC] = cellCIndices[d];
1882       findices[cellCIndices[d]-startC] = cellFIndices[cmap[d]];
1883     }
1884   }
1885   ierr = PetscFree(cmap);CHKERRQ(ierr);
1886   ierr = PetscFree2(cellCIndices,cellFIndices);CHKERRQ(ierr);
1887 
1888   ierr = ISCreateGeneral(PETSC_COMM_SELF, m, cindices, PETSC_OWN_POINTER, &cis);CHKERRQ(ierr);
1889   ierr = ISCreateGeneral(PETSC_COMM_SELF, m, findices, PETSC_OWN_POINTER, &fis);CHKERRQ(ierr);
1890   ierr = VecScatterCreate(cv, cis, fv, fis, sc);CHKERRQ(ierr);
1891   ierr = ISDestroy(&cis);CHKERRQ(ierr);
1892   ierr = ISDestroy(&fis);CHKERRQ(ierr);
1893   ierr = DMRestoreGlobalVector(dmf, &fv);CHKERRQ(ierr);
1894   ierr = DMRestoreGlobalVector(dmc, &cv);CHKERRQ(ierr);
1895   ierr = PetscLogEventEnd(DMPLEX_InjectorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1896   PetscFunctionReturn(0);
1897 }
1898