xref: /petsc/src/dm/impls/plex/plexfem.c (revision 772ec989c7718bb40cfbe6762601ac78951cc001)
1 #include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #include <petscfe.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "DMPlexGetScale"
7 PetscErrorCode DMPlexGetScale(DM dm, PetscUnit unit, PetscReal *scale)
8 {
9   DM_Plex *mesh = (DM_Plex*) dm->data;
10 
11   PetscFunctionBegin;
12   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
13   PetscValidPointer(scale, 3);
14   *scale = mesh->scale[unit];
15   PetscFunctionReturn(0);
16 }
17 
18 #undef __FUNCT__
19 #define __FUNCT__ "DMPlexSetScale"
20 PetscErrorCode DMPlexSetScale(DM dm, PetscUnit unit, PetscReal scale)
21 {
22   DM_Plex *mesh = (DM_Plex*) dm->data;
23 
24   PetscFunctionBegin;
25   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
26   mesh->scale[unit] = scale;
27   PetscFunctionReturn(0);
28 }
29 
30 PETSC_STATIC_INLINE PetscInt epsilon(PetscInt i, PetscInt j, PetscInt k)
31 {
32   switch (i) {
33   case 0:
34     switch (j) {
35     case 0: return 0;
36     case 1:
37       switch (k) {
38       case 0: return 0;
39       case 1: return 0;
40       case 2: return 1;
41       }
42     case 2:
43       switch (k) {
44       case 0: return 0;
45       case 1: return -1;
46       case 2: return 0;
47       }
48     }
49   case 1:
50     switch (j) {
51     case 0:
52       switch (k) {
53       case 0: return 0;
54       case 1: return 0;
55       case 2: return -1;
56       }
57     case 1: return 0;
58     case 2:
59       switch (k) {
60       case 0: return 1;
61       case 1: return 0;
62       case 2: return 0;
63       }
64     }
65   case 2:
66     switch (j) {
67     case 0:
68       switch (k) {
69       case 0: return 0;
70       case 1: return 1;
71       case 2: return 0;
72       }
73     case 1:
74       switch (k) {
75       case 0: return -1;
76       case 1: return 0;
77       case 2: return 0;
78       }
79     case 2: return 0;
80     }
81   }
82   return 0;
83 }
84 
85 #undef __FUNCT__
86 #define __FUNCT__ "DMPlexCreateRigidBody"
87 /*@C
88   DMPlexCreateRigidBody - create rigid body modes from coordinates
89 
90   Collective on DM
91 
92   Input Arguments:
93 + dm - the DM
94 . section - the local section associated with the rigid field, or NULL for the default section
95 - globalSection - the global section associated with the rigid field, or NULL for the default section
96 
97   Output Argument:
98 . sp - the null space
99 
100   Note: This is necessary to take account of Dirichlet conditions on the displacements
101 
102   Level: advanced
103 
104 .seealso: MatNullSpaceCreate()
105 @*/
106 PetscErrorCode DMPlexCreateRigidBody(DM dm, PetscSection section, PetscSection globalSection, MatNullSpace *sp)
107 {
108   MPI_Comm       comm;
109   Vec            coordinates, localMode, mode[6];
110   PetscSection   coordSection;
111   PetscScalar   *coords;
112   PetscInt       dim, vStart, vEnd, v, n, m, d, i, j;
113   PetscErrorCode ierr;
114 
115   PetscFunctionBegin;
116   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
117   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
118   if (dim == 1) {
119     ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
120     PetscFunctionReturn(0);
121   }
122   if (!section)       {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
123   if (!globalSection) {ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);}
124   ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
125   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
126   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
127   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
128   m    = (dim*(dim+1))/2;
129   ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
130   ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
131   ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
132   for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
133   /* Assume P1 */
134   ierr = DMGetLocalVector(dm, &localMode);CHKERRQ(ierr);
135   for (d = 0; d < dim; ++d) {
136     PetscScalar values[3] = {0.0, 0.0, 0.0};
137 
138     values[d] = 1.0;
139     ierr      = VecSet(localMode, 0.0);CHKERRQ(ierr);
140     for (v = vStart; v < vEnd; ++v) {
141       ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
142     }
143     ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
144     ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
145   }
146   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
147   for (d = dim; d < dim*(dim+1)/2; ++d) {
148     PetscInt i, j, k = dim > 2 ? d - dim : d;
149 
150     ierr = VecSet(localMode, 0.0);CHKERRQ(ierr);
151     for (v = vStart; v < vEnd; ++v) {
152       PetscScalar values[3] = {0.0, 0.0, 0.0};
153       PetscInt    off;
154 
155       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
156       for (i = 0; i < dim; ++i) {
157         for (j = 0; j < dim; ++j) {
158           values[j] += epsilon(i, j, k)*PetscRealPart(coords[off+i]);
159         }
160       }
161       ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
162     }
163     ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
164     ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
165   }
166   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
167   ierr = DMRestoreLocalVector(dm, &localMode);CHKERRQ(ierr);
168   for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
169   /* Orthonormalize system */
170   for (i = dim; i < m; ++i) {
171     PetscScalar dots[6];
172 
173     ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
174     for (j = 0; j < i; ++j) dots[j] *= -1.0;
175     ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
176     ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
177   }
178   ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
179   for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
180   PetscFunctionReturn(0);
181 }
182 
183 #undef __FUNCT__
184 #define __FUNCT__ "DMPlexProjectFunctionLabelLocal"
185 PetscErrorCode DMPlexProjectFunctionLabelLocal(DM dm, DMLabel label, PetscInt numIds, const PetscInt ids[], PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
186 {
187   PetscDualSpace *sp;
188   PetscSection    section;
189   PetscScalar    *values;
190   PetscReal      *v0, *J, detJ;
191   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, f, d, v, i, comp;
192   PetscErrorCode  ierr;
193 
194   PetscFunctionBegin;
195   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
196   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
197   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
198   ierr = PetscMalloc3(numFields,&sp,dim,&v0,dim*dim,&J);CHKERRQ(ierr);
199   for (f = 0; f < numFields; ++f) {
200     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
201     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
202     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
203     totDim += spDim*numComp;
204   }
205   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
206   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
207   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
208   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
209   for (i = 0; i < numIds; ++i) {
210     IS              pointIS;
211     const PetscInt *points;
212     PetscInt        n, p;
213 
214     ierr = DMLabelGetStratumIS(label, ids[i], &pointIS);CHKERRQ(ierr);
215     ierr = ISGetLocalSize(pointIS, &n);CHKERRQ(ierr);
216     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
217     for (p = 0; p < n; ++p) {
218       const PetscInt    point = points[p];
219       PetscCellGeometry geom;
220 
221       if ((point < cStart) || (point >= cEnd)) continue;
222       ierr = DMPlexComputeCellGeometry(dm, point, v0, J, NULL, &detJ);CHKERRQ(ierr);
223       geom.v0   = v0;
224       geom.J    = J;
225       geom.detJ = &detJ;
226       for (f = 0, v = 0; f < numFields; ++f) {
227         void * const ctx = ctxs ? ctxs[f] : NULL;
228         ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
229         ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
230         for (d = 0; d < spDim; ++d) {
231           if (funcs[f]) {
232             ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
233           } else {
234             for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
235           }
236           v += numComp;
237         }
238       }
239       ierr = DMPlexVecSetClosure(dm, section, localX, point, values, mode);CHKERRQ(ierr);
240     }
241     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
242     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
243   }
244   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
245   ierr = PetscFree3(sp,v0,J);CHKERRQ(ierr);
246   PetscFunctionReturn(0);
247 }
248 
249 #undef __FUNCT__
250 #define __FUNCT__ "DMPlexProjectFunctionLocal"
251 PetscErrorCode DMPlexProjectFunctionLocal(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
252 {
253   PetscDualSpace *sp;
254   PetscSection    section;
255   PetscScalar    *values;
256   PetscReal      *v0, *J, detJ;
257   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, c, f, d, v, comp;
258   PetscErrorCode  ierr;
259 
260   PetscFunctionBegin;
261   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
262   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
263   ierr = PetscMalloc1(numFields, &sp);CHKERRQ(ierr);
264   for (f = 0; f < numFields; ++f) {
265     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
266     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
267     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
268     totDim += spDim*numComp;
269   }
270   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
271   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
272   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
273   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
274   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
275   ierr = PetscMalloc2(dim,&v0,dim*dim,&J);CHKERRQ(ierr);
276   for (c = cStart; c < cEnd; ++c) {
277     PetscCellGeometry geom;
278 
279     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
280     geom.v0   = v0;
281     geom.J    = J;
282     geom.detJ = &detJ;
283     for (f = 0, v = 0; f < numFields; ++f) {
284       void * const ctx = ctxs ? ctxs[f] : NULL;
285       ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
286       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
287       for (d = 0; d < spDim; ++d) {
288         if (funcs[f]) {
289           ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
290         } else {
291           for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
292         }
293         v += numComp;
294       }
295     }
296     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
297   }
298   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
299   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
300   ierr = PetscFree(sp);CHKERRQ(ierr);
301   PetscFunctionReturn(0);
302 }
303 
304 #undef __FUNCT__
305 #define __FUNCT__ "DMPlexProjectFunction"
306 /*@C
307   DMPlexProjectFunction - This projects the given function into the function space provided.
308 
309   Input Parameters:
310 + dm      - The DM
311 . fe      - The PetscFE associated with the field
312 . funcs   - The coordinate functions to evaluate, one per field
313 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
314 - mode    - The insertion mode for values
315 
316   Output Parameter:
317 . X - vector
318 
319   Level: developer
320 
321 .seealso: DMPlexComputeL2Diff()
322 @*/
323 PetscErrorCode DMPlexProjectFunction(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
324 {
325   Vec            localX;
326   PetscErrorCode ierr;
327 
328   PetscFunctionBegin;
329   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
330   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
331   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, mode, localX);CHKERRQ(ierr);
332   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
333   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
334   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
335   PetscFunctionReturn(0);
336 }
337 
338 #undef __FUNCT__
339 #define __FUNCT__ "DMPlexInsertBoundaryValuesFEM"
340 PetscErrorCode DMPlexInsertBoundaryValuesFEM(DM dm, Vec localX)
341 {
342   void        (**funcs)(const PetscReal x[], PetscScalar *u, void *ctx);
343   void         **ctxs;
344   PetscFE       *fe;
345   PetscInt       numFields, f, numBd, b;
346   PetscErrorCode ierr;
347 
348   PetscFunctionBegin;
349   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
350   PetscValidHeaderSpecific(localX, VEC_CLASSID, 2);
351   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
352   ierr = PetscMalloc3(numFields,&fe,numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
353   for (f = 0; f < numFields; ++f) {ierr = DMGetField(dm, f, (PetscObject *) &fe[f]);CHKERRQ(ierr);}
354   /* OPT: Could attempt to do multiple BCs at once */
355   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
356   for (b = 0; b < numBd; ++b) {
357     DMLabel         label;
358     const PetscInt *ids;
359     const char     *name;
360     PetscInt        numids, field;
361     PetscBool       isEssential;
362     void          (*func)();
363     void           *ctx;
364 
365     /* TODO: We need to set only the part indicated by the ids */
366     ierr = DMPlexGetBoundary(dm, b, &isEssential, &name, &field, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
367     ierr = DMPlexGetLabel(dm, name, &label);CHKERRQ(ierr);
368     for (f = 0; f < numFields; ++f) {
369       funcs[f] = field == f ? (void (*)(const PetscReal[], PetscScalar *, void *)) func : NULL;
370       ctxs[f]  = field == f ? ctx : NULL;
371     }
372     ierr = DMPlexProjectFunctionLabelLocal(dm, label, numids, ids, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
373   }
374   ierr = PetscFree3(fe,funcs,ctxs);CHKERRQ(ierr);
375   PetscFunctionReturn(0);
376 }
377 
378 /* Assuming dim == 3 */
379 typedef struct {
380   PetscScalar normal[3];   /* Area-scaled normals */
381   PetscScalar centroid[3]; /* Location of centroid (quadrature point) */
382   PetscScalar grad[2][3];  /* Face contribution to gradient in left and right cell */
383 } FaceGeom;
384 
385 #undef __FUNCT__
386 #define __FUNCT__ "DMPlexInsertBoundaryValuesFVM"
387 PetscErrorCode DMPlexInsertBoundaryValuesFVM(DM dm, PetscReal time, Vec locX)
388 {
389   DM                 dmFace;
390   Vec                faceGeometry;
391   DMLabel            label;
392   const PetscScalar *facegeom;
393   PetscScalar       *x;
394   PetscInt           numBd, b, fStart, fEnd;
395   PetscErrorCode     ierr;
396 
397   PetscFunctionBegin;
398   /* TODO Pull this geometry calculation into the library */
399   ierr = PetscObjectQuery((PetscObject) dm, "FaceGeometry", (PetscObject *) &faceGeometry);CHKERRQ(ierr);
400   ierr = DMPlexGetLabel(dm, "Face Sets", &label);CHKERRQ(ierr);
401   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
402   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
403   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
404   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
405   ierr = VecGetArray(locX, &x);CHKERRQ(ierr);
406   for (b = 0; b < numBd; ++b) {
407     PetscErrorCode (*func)(PetscReal,const PetscScalar*,const PetscScalar*,const PetscScalar*,PetscScalar*,void*);
408     const PetscInt  *ids;
409     PetscInt         numids, i;
410     void            *ctx;
411 
412     ierr = DMPlexGetBoundary(dm, b, NULL, NULL, NULL, (void (**)()) &func, &numids, &ids, &ctx);CHKERRQ(ierr);
413     for (i = 0; i < numids; ++i) {
414       IS              faceIS;
415       const PetscInt *faces;
416       PetscInt        numFaces, f;
417 
418       ierr = DMLabelGetStratumIS(label, ids[i], &faceIS);CHKERRQ(ierr);
419       if (!faceIS) continue; /* No points with that id on this process */
420       ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
421       ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
422       for (f = 0; f < numFaces; ++f) {
423         const PetscInt     face = faces[f], *cells;
424         const PetscScalar *xI;
425         PetscScalar       *xG;
426         const FaceGeom    *fg;
427 
428         if ((face < fStart) || (face >= fEnd)) continue; /* Refinement adds non-faces to labels */
429         ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
430         ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
431         ierr = DMPlexPointLocalRead(dm, cells[0], x, &xI);CHKERRQ(ierr);
432         ierr = DMPlexPointLocalRef(dm, cells[1], x, &xG);CHKERRQ(ierr);
433         ierr = (*func)(time, fg->centroid, fg->normal, xI, xG, ctx);CHKERRQ(ierr);
434       }
435       ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
436       ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
437     }
438   }
439   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
440   ierr = VecRestoreArray(locX, &x);CHKERRQ(ierr);
441   PetscFunctionReturn(0);
442 }
443 
444 #undef __FUNCT__
445 #define __FUNCT__ "DMPlexComputeL2Diff"
446 /*@C
447   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
448 
449   Input Parameters:
450 + dm    - The DM
451 . fe    - The PetscFE object for each field
452 . funcs - The functions to evaluate for each field component
453 . ctxs  - Optional array of contexts to pass to each function, or NULL.
454 - X     - The coefficient vector u_h
455 
456   Output Parameter:
457 . diff - The diff ||u - u_h||_2
458 
459   Level: developer
460 
461 .seealso: DMPlexProjectFunction(), DMPlexComputeL2GradientDiff()
462 @*/
463 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
464 {
465   const PetscInt  debug = 0;
466   PetscSection    section;
467   PetscQuadrature quad;
468   Vec             localX;
469   PetscScalar    *funcVal;
470   PetscReal      *coords, *v0, *J, *invJ, detJ;
471   PetscReal       localDiff = 0.0;
472   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
473   PetscErrorCode  ierr;
474 
475   PetscFunctionBegin;
476   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
477   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
478   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
479   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
480   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
481   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
482   for (field = 0; field < numFields; ++field) {
483     PetscInt Nc;
484 
485     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
486     numComponents += Nc;
487   }
488   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
489   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
490   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
491   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
492   for (c = cStart; c < cEnd; ++c) {
493     PetscScalar *x = NULL;
494     PetscReal    elemDiff = 0.0;
495 
496     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
497     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
498     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
499 
500     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
501       void * const     ctx = ctxs ? ctxs[field] : NULL;
502       const PetscReal *quadPoints, *quadWeights;
503       PetscReal       *basis;
504       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
505 
506       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
507       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
508       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
509       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
510       if (debug) {
511         char title[1024];
512         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
513         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
514       }
515       for (q = 0; q < numQuadPoints; ++q) {
516         for (d = 0; d < dim; d++) {
517           coords[d] = v0[d];
518           for (e = 0; e < dim; e++) {
519             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
520           }
521         }
522         (*funcs[field])(coords, funcVal, ctx);
523         for (fc = 0; fc < numBasisComps; ++fc) {
524           PetscScalar interpolant = 0.0;
525 
526           for (f = 0; f < numBasisFuncs; ++f) {
527             const PetscInt fidx = f*numBasisComps+fc;
528             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
529           }
530           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ);CHKERRQ(ierr);}
531           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
532         }
533       }
534       comp        += numBasisComps;
535       fieldOffset += numBasisFuncs*numBasisComps;
536     }
537     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
538     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
539     localDiff += elemDiff;
540   }
541   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
542   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
543   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
544   *diff = PetscSqrtReal(*diff);
545   PetscFunctionReturn(0);
546 }
547 
548 #undef __FUNCT__
549 #define __FUNCT__ "DMPlexComputeL2GradientDiff"
550 /*@C
551   DMPlexComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
552 
553   Input Parameters:
554 + dm    - The DM
555 . fe    - The PetscFE object for each field
556 . funcs - The gradient functions to evaluate for each field component
557 . ctxs  - Optional array of contexts to pass to each function, or NULL.
558 . X     - The coefficient vector u_h
559 - n     - The vector to project along
560 
561   Output Parameter:
562 . diff - The diff ||(grad u - grad u_h) . n||_2
563 
564   Level: developer
565 
566 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
567 @*/
568 PetscErrorCode DMPlexComputeL2GradientDiff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
569 {
570   const PetscInt  debug = 0;
571   PetscSection    section;
572   PetscQuadrature quad;
573   Vec             localX;
574   PetscScalar    *funcVal, *interpolantVec;
575   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
576   PetscReal       localDiff = 0.0;
577   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
578   PetscErrorCode  ierr;
579 
580   PetscFunctionBegin;
581   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
582   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
583   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
584   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
585   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
586   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
587   for (field = 0; field < numFields; ++field) {
588     PetscInt Nc;
589 
590     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
591     numComponents += Nc;
592   }
593   /* ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
594   ierr = PetscMalloc7(numComponents,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
595   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
596   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
597   for (c = cStart; c < cEnd; ++c) {
598     PetscScalar *x = NULL;
599     PetscReal    elemDiff = 0.0;
600 
601     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
602     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
603     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
604 
605     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
606       void * const     ctx = ctxs ? ctxs[field] : NULL;
607       const PetscReal *quadPoints, *quadWeights;
608       PetscReal       *basisDer;
609       PetscInt         numQuadPoints, Nb, Ncomp, q, d, e, fc, f, g;
610 
611       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
612       ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
613       ierr = PetscFEGetNumComponents(fe[field], &Ncomp);CHKERRQ(ierr);
614       ierr = PetscFEGetDefaultTabulation(fe[field], NULL, &basisDer, NULL);CHKERRQ(ierr);
615       if (debug) {
616         char title[1024];
617         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
618         ierr = DMPrintCellVector(c, title, Nb*Ncomp, &x[fieldOffset]);CHKERRQ(ierr);
619       }
620       for (q = 0; q < numQuadPoints; ++q) {
621         for (d = 0; d < dim; d++) {
622           coords[d] = v0[d];
623           for (e = 0; e < dim; e++) {
624             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
625           }
626         }
627         (*funcs[field])(coords, n, funcVal, ctx);
628         for (fc = 0; fc < Ncomp; ++fc) {
629           PetscScalar interpolant = 0.0;
630 
631           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
632           for (f = 0; f < Nb; ++f) {
633             const PetscInt fidx = f*Ncomp+fc;
634 
635             for (d = 0; d < dim; ++d) {
636               realSpaceDer[d] = 0.0;
637               for (g = 0; g < dim; ++g) {
638                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+fidx)*dim+g];
639               }
640               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
641             }
642           }
643           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
644           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d fieldDer %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ);CHKERRQ(ierr);}
645           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
646         }
647       }
648       comp        += Ncomp;
649       fieldOffset += Nb*Ncomp;
650     }
651     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
652     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
653     localDiff += elemDiff;
654   }
655   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
656   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
657   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
658   *diff = PetscSqrtReal(*diff);
659   PetscFunctionReturn(0);
660 }
661 
662 #undef __FUNCT__
663 #define __FUNCT__ "DMPlexComputeResidualFEM"
664 /*@
665   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
666 
667   Input Parameters:
668 + dm - The mesh
669 . X  - Local input vector
670 - user - The user context
671 
672   Output Parameter:
673 . F  - Local output vector
674 
675   Note:
676   The first member of the user context must be an FEMContext.
677 
678   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
679   like a GPU, or vectorize on a multicore machine.
680 
681   Level: developer
682 
683 .seealso: DMPlexComputeJacobianActionFEM()
684 @*/
685 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
686 {
687   DM_Plex          *mesh  = (DM_Plex *) dm->data;
688   PetscFEM         *fem   = (PetscFEM *) user;
689   PetscFE          *fe    = fem->fe;
690   PetscFE          *feAux = fem->feAux;
691   PetscFE          *feBd  = fem->feBd;
692   const char       *name  = "Residual";
693   DM                dmAux;
694   Vec               A;
695   PetscQuadrature   q;
696   PetscCellGeometry geom;
697   PetscSection      section, sectionAux;
698   PetscReal        *v0, *J, *invJ, *detJ;
699   PetscScalar      *elemVec, *u, *a = NULL;
700   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
701   PetscInt          cellDof = 0, numComponents = 0;
702   PetscInt          cellDofAux = 0, numComponentsAux = 0;
703   PetscErrorCode    ierr;
704 
705   PetscFunctionBegin;
706   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
707   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
708   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
709   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
710   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
711   numCells = cEnd - cStart;
712   for (f = 0; f < Nf; ++f) {
713     PetscInt Nb, Nc;
714 
715     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
716     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
717     cellDof       += Nb*Nc;
718     numComponents += Nc;
719   }
720   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
721   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
722   if (dmAux) {
723     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
724     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
725   }
726   for (f = 0; f < NfAux; ++f) {
727     PetscInt Nb, Nc;
728 
729     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
730     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
731     cellDofAux       += Nb*Nc;
732     numComponentsAux += Nc;
733   }
734   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
735   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
736   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
737   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
738   for (c = cStart; c < cEnd; ++c) {
739     PetscScalar *x = NULL;
740     PetscInt     i;
741 
742     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
743     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
744     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
745     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
746     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
747     if (dmAux) {
748       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
749       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
750       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
751     }
752   }
753   for (f = 0; f < Nf; ++f) {
754     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
755     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
756     PetscInt numQuadPoints, Nb;
757     /* Conforming batches */
758     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
759     /* Remainder */
760     PetscInt Nr, offset;
761 
762     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
763     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
764     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
765     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
766     blockSize = Nb*numQuadPoints;
767     batchSize = numBlocks * blockSize;
768     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
769     numChunks = numCells / (numBatches*batchSize);
770     Ne        = numChunks*numBatches*batchSize;
771     Nr        = numCells % (numBatches*batchSize);
772     offset    = numCells - Nr;
773     geom.v0   = v0;
774     geom.J    = J;
775     geom.invJ = invJ;
776     geom.detJ = detJ;
777     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
778     geom.v0   = &v0[offset*dim];
779     geom.J    = &J[offset*dim*dim];
780     geom.invJ = &invJ[offset*dim*dim];
781     geom.detJ = &detJ[offset];
782     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
783   }
784   for (c = cStart; c < cEnd; ++c) {
785     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
786     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
787   }
788   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
789   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
790   if (feBd) {
791     DMLabel  depth;
792     PetscInt numBd, bd;
793 
794     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
795       PetscInt Nb, Nc;
796 
797       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
798       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
799       cellDof       += Nb*Nc;
800       numComponents += Nc;
801     }
802     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
803     ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
804     for (bd = 0; bd < numBd; ++bd) {
805       const char     *bdLabel;
806       DMLabel         label;
807       IS              pointIS;
808       const PetscInt *points;
809       const PetscInt *values;
810       PetscReal      *n;
811       PetscInt        field, numValues, numPoints, p, dep, numFaces;
812       PetscBool       isEssential;
813 
814       ierr = DMPlexGetBoundary(dm, bd, &isEssential, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
815       if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
816       ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
817       ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
818       ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
819       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
820       for (p = 0, numFaces = 0; p < numPoints; ++p) {
821         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
822         if (dep == dim-1) ++numFaces;
823       }
824       ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof,&elemVec);CHKERRQ(ierr);
825       for (p = 0, f = 0; p < numPoints; ++p) {
826         const PetscInt point = points[p];
827         PetscScalar   *x     = NULL;
828         PetscInt       i;
829 
830         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
831         if (dep != dim-1) continue;
832         ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
833         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
834         if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
835         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
836         for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
837         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
838         ++f;
839       }
840       for (f = 0; f < Nf; ++f) {
841         void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
842         void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
843         PetscInt numQuadPoints, Nb;
844         /* Conforming batches */
845         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
846         /* Remainder */
847         PetscInt Nr, offset;
848 
849         ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
850         ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
851         ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
852         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
853         blockSize = Nb*numQuadPoints;
854         batchSize = numBlocks * blockSize;
855         ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
856         numChunks = numFaces / (numBatches*batchSize);
857         Ne        = numChunks*numBatches*batchSize;
858         Nr        = numFaces % (numBatches*batchSize);
859         offset    = numFaces - Nr;
860         geom.v0   = v0;
861         geom.n    = n;
862         geom.J    = J;
863         geom.invJ = invJ;
864         geom.detJ = detJ;
865         ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
866         geom.v0   = &v0[offset*dim];
867         geom.n    = &n[offset*dim];
868         geom.J    = &J[offset*dim*dim];
869         geom.invJ = &invJ[offset*dim*dim];
870         geom.detJ = &detJ[offset];
871         ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
872       }
873       for (p = 0, f = 0; p < numPoints; ++p) {
874         const PetscInt point = points[p];
875 
876         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
877         if (dep != dim-1) continue;
878         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
879         ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
880         ++f;
881       }
882       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
883       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
884       ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
885     }
886   }
887   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
888   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
889   PetscFunctionReturn(0);
890 }
891 
892 #undef __FUNCT__
893 #define __FUNCT__ "DMPlexComputeIFunctionFEM"
894 /*@
895   DMPlexComputeIFunctionFEM - Form the local implicit function F from the local input X, X_t using pointwise functions specified by the user
896 
897   Input Parameters:
898 + dm - The mesh
899 . time - The current time
900 . X  - Local input vector
901 . X_t  - Time derivative of the local input vector
902 - user - The user context
903 
904   Output Parameter:
905 . F  - Local output vector
906 
907   Note:
908   The first member of the user context must be an FEMContext.
909 
910   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
911   like a GPU, or vectorize on a multicore machine.
912 
913   Level: developer
914 
915 .seealso: DMPlexComputeResidualFEM()
916 @*/
917 PetscErrorCode DMPlexComputeIFunctionFEM(DM dm, PetscReal time, Vec X, Vec X_t, Vec F, void *user)
918 {
919   DM_Plex          *mesh  = (DM_Plex *) dm->data;
920   PetscFEM         *fem   = (PetscFEM *) user;
921   PetscFE          *fe    = fem->fe;
922   PetscFE          *feAux = fem->feAux;
923   PetscFE          *feBd  = fem->feBd;
924   const char       *name  = "Residual";
925   DM                dmAux;
926   Vec               A;
927   PetscQuadrature   q;
928   PetscCellGeometry geom;
929   PetscSection      section, sectionAux;
930   PetscReal        *v0, *J, *invJ, *detJ;
931   PetscScalar      *elemVec, *u, *u_t, *a = NULL;
932   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
933   PetscInt          cellDof = 0, numComponents = 0;
934   PetscInt          cellDofAux = 0, numComponentsAux = 0;
935   PetscErrorCode    ierr;
936 
937   PetscFunctionBegin;
938   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
939   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
940   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
941   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
942   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
943   numCells = cEnd - cStart;
944   for (f = 0; f < Nf; ++f) {
945     PetscInt Nb, Nc;
946 
947     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
948     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
949     cellDof       += Nb*Nc;
950     numComponents += Nc;
951   }
952   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
953   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
954   if (dmAux) {
955     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
956     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
957   }
958   for (f = 0; f < NfAux; ++f) {
959     PetscInt Nb, Nc;
960 
961     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
962     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
963     cellDofAux       += Nb*Nc;
964     numComponentsAux += Nc;
965   }
966   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
967   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
968   ierr = PetscMalloc7(numCells*cellDof,&u,numCells*cellDof,&u_t,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
969   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
970   for (c = cStart; c < cEnd; ++c) {
971     PetscScalar *x = NULL, *x_t = NULL;
972     PetscInt     i;
973 
974     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
975     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
976     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
977     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
978     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
979     ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
980     for (i = 0; i < cellDof; ++i) u_t[c*cellDof+i] = x_t[i];
981     ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
982     if (dmAux) {
983       PetscScalar *x_a = NULL;
984       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
985       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x_a[i];
986       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
987     }
988   }
989   for (f = 0; f < Nf; ++f) {
990     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0IFuncs[f];
991     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1IFuncs[f];
992     PetscInt numQuadPoints, Nb;
993     /* Conforming batches */
994     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
995     /* Remainder */
996     PetscInt Nr, offset;
997 
998     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
999     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1000     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1001     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1002     blockSize = Nb*numQuadPoints;
1003     batchSize = numBlocks * blockSize;
1004     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1005     numChunks = numCells / (numBatches*batchSize);
1006     Ne        = numChunks*numBatches*batchSize;
1007     Nr        = numCells % (numBatches*batchSize);
1008     offset    = numCells - Nr;
1009     geom.v0   = v0;
1010     geom.J    = J;
1011     geom.invJ = invJ;
1012     geom.detJ = detJ;
1013     ierr = PetscFEIntegrateIFunction(fe[f], Ne, Nf, fe, f, geom, u, u_t, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
1014     geom.v0   = &v0[offset*dim];
1015     geom.J    = &J[offset*dim*dim];
1016     geom.invJ = &invJ[offset*dim*dim];
1017     geom.detJ = &detJ[offset];
1018     ierr = PetscFEIntegrateIFunction(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], &u_t[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1019   }
1020   for (c = cStart; c < cEnd; ++c) {
1021     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1022     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1023   }
1024   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1025   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1026   if (feBd) {
1027     DMLabel         label, depth;
1028     IS              pointIS;
1029     const PetscInt *points;
1030     PetscInt        dep, numPoints, p, numFaces;
1031     PetscReal      *n;
1032 
1033     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
1034     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1035     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1036     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1037     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1038     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1039       PetscInt Nb, Nc;
1040 
1041       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1042       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1043       cellDof       += Nb*Nc;
1044       numComponents += Nc;
1045     }
1046     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1047       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1048       if (dep == dim-1) ++numFaces;
1049     }
1050     ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof,&elemVec);CHKERRQ(ierr);
1051     ierr = PetscMalloc1(numFaces*cellDof,&u_t);CHKERRQ(ierr);
1052     for (p = 0, f = 0; p < numPoints; ++p) {
1053       const PetscInt point = points[p];
1054       PetscScalar   *x     = NULL;
1055       PetscInt       i;
1056 
1057       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1058       if (dep != dim-1) continue;
1059       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1060       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1061       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1062       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1063       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1064       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1065       ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1066       for (i = 0; i < cellDof; ++i) u_t[f*cellDof+i] = x[i];
1067       ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1068       ++f;
1069     }
1070     for (f = 0; f < Nf; ++f) {
1071       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdIFuncs[f];
1072       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdIFuncs[f];
1073       PetscInt numQuadPoints, Nb;
1074       /* Conforming batches */
1075       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1076       /* Remainder */
1077       PetscInt Nr, offset;
1078 
1079       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
1080       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1081       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1082       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1083       blockSize = Nb*numQuadPoints;
1084       batchSize = numBlocks * blockSize;
1085       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1086       numChunks = numFaces / (numBatches*batchSize);
1087       Ne        = numChunks*numBatches*batchSize;
1088       Nr        = numFaces % (numBatches*batchSize);
1089       offset    = numFaces - Nr;
1090       geom.v0   = v0;
1091       geom.n    = n;
1092       geom.J    = J;
1093       geom.invJ = invJ;
1094       geom.detJ = detJ;
1095       ierr = PetscFEIntegrateBdIFunction(feBd[f], Ne, Nf, feBd, f, geom, u, u_t, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
1096       geom.v0   = &v0[offset*dim];
1097       geom.n    = &n[offset*dim];
1098       geom.J    = &J[offset*dim*dim];
1099       geom.invJ = &invJ[offset*dim*dim];
1100       geom.detJ = &detJ[offset];
1101       ierr = PetscFEIntegrateBdIFunction(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], &u_t[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1102     }
1103     for (p = 0, f = 0; p < numPoints; ++p) {
1104       const PetscInt point = points[p];
1105 
1106       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1107       if (dep != dim-1) continue;
1108       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
1109       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
1110       ++f;
1111     }
1112     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1113     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1114     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1115     ierr = PetscFree(u_t);CHKERRQ(ierr);
1116   }
1117   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1118   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1119   PetscFunctionReturn(0);
1120 }
1121 
1122 #undef __FUNCT__
1123 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
1124 /*@C
1125   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
1126 
1127   Input Parameters:
1128 + dm - The mesh
1129 . J  - The Jacobian shell matrix
1130 . X  - Local input vector
1131 - user - The user context
1132 
1133   Output Parameter:
1134 . F  - Local output vector
1135 
1136   Note:
1137   The first member of the user context must be an FEMContext.
1138 
1139   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1140   like a GPU, or vectorize on a multicore machine.
1141 
1142   Level: developer
1143 
1144 .seealso: DMPlexComputeResidualFEM()
1145 @*/
1146 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
1147 {
1148   DM_Plex          *mesh = (DM_Plex *) dm->data;
1149   PetscFEM         *fem  = (PetscFEM *) user;
1150   PetscFE          *fe   = fem->fe;
1151   PetscQuadrature   quad;
1152   PetscCellGeometry geom;
1153   PetscSection      section;
1154   JacActionCtx     *jctx;
1155   PetscReal        *v0, *J, *invJ, *detJ;
1156   PetscScalar      *elemVec, *u, *a;
1157   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
1158   PetscInt          cellDof = 0;
1159   PetscErrorCode    ierr;
1160 
1161   PetscFunctionBegin;
1162   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1163   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1164   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1165   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1166   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1167   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1168   numCells = cEnd - cStart;
1169   for (field = 0; field < numFields; ++field) {
1170     PetscInt Nb, Nc;
1171 
1172     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1173     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
1174     cellDof += Nb*Nc;
1175   }
1176   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1177   ierr = PetscMalloc7(numCells*cellDof,&u,numCells*cellDof,&a,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
1178   for (c = cStart; c < cEnd; ++c) {
1179     PetscScalar *x = NULL;
1180     PetscInt     i;
1181 
1182     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1183     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1184     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1185     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1186     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1187     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1188     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
1189     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1190   }
1191   for (field = 0; field < numFields; ++field) {
1192     PetscInt numQuadPoints, Nb;
1193     /* Conforming batches */
1194     PetscInt numBlocks  = 1;
1195     PetscInt numBatches = 1;
1196     PetscInt numChunks, Ne, blockSize, batchSize;
1197     /* Remainder */
1198     PetscInt Nr, offset;
1199 
1200     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
1201     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1202     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1203     blockSize = Nb*numQuadPoints;
1204     batchSize = numBlocks * blockSize;
1205     numChunks = numCells / (numBatches*batchSize);
1206     Ne        = numChunks*numBatches*batchSize;
1207     Nr        = numCells % (numBatches*batchSize);
1208     offset    = numCells - Nr;
1209     geom.v0   = v0;
1210     geom.J    = J;
1211     geom.invJ = invJ;
1212     geom.detJ = detJ;
1213     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
1214     geom.v0   = &v0[offset*dim];
1215     geom.J    = &J[offset*dim*dim];
1216     geom.invJ = &invJ[offset*dim*dim];
1217     geom.detJ = &detJ[offset];
1218     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
1219                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1220   }
1221   for (c = cStart; c < cEnd; ++c) {
1222     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1223     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1224   }
1225   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1226   if (mesh->printFEM) {
1227     PetscMPIInt rank, numProcs;
1228     PetscInt    p;
1229 
1230     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
1231     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
1232     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
1233     for (p = 0; p < numProcs; ++p) {
1234       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
1235       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
1236     }
1237   }
1238   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1239   PetscFunctionReturn(0);
1240 }
1241 
1242 #undef __FUNCT__
1243 #define __FUNCT__ "DMPlexComputeJacobianFEM"
1244 /*@
1245   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
1246 
1247   Input Parameters:
1248 + dm - The mesh
1249 . X  - Local input vector
1250 - user - The user context
1251 
1252   Output Parameter:
1253 . Jac  - Jacobian matrix
1254 
1255   Note:
1256   The first member of the user context must be an FEMContext.
1257 
1258   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1259   like a GPU, or vectorize on a multicore machine.
1260 
1261   Level: developer
1262 
1263 .seealso: FormFunctionLocal()
1264 @*/
1265 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1266 {
1267   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1268   PetscFEM         *fem   = (PetscFEM *) user;
1269   PetscFE          *fe    = fem->fe;
1270   PetscFE          *feAux = fem->feAux;
1271   PetscFE          *feBd  = fem->feBd;
1272   const char       *name  = "Jacobian";
1273   DM                dmAux;
1274   Vec               A;
1275   PetscQuadrature   quad;
1276   PetscCellGeometry geom;
1277   PetscSection      section, globalSection, sectionAux;
1278   PetscReal        *v0, *J, *invJ, *detJ;
1279   PetscScalar      *elemMat, *u, *a;
1280   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1281   PetscInt          cellDof = 0, numComponents = 0;
1282   PetscInt          cellDofAux = 0, numComponentsAux = 0;
1283   PetscBool         isShell;
1284   PetscErrorCode    ierr;
1285 
1286   PetscFunctionBegin;
1287   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1288   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1289   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1290   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1291   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1292   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1293   numCells = cEnd - cStart;
1294   for (f = 0; f < Nf; ++f) {
1295     PetscInt Nb, Nc;
1296 
1297     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1298     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1299     cellDof       += Nb*Nc;
1300     numComponents += Nc;
1301   }
1302   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1303   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1304   if (dmAux) {
1305     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1306     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
1307   }
1308   for (f = 0; f < NfAux; ++f) {
1309     PetscInt Nb, Nc;
1310 
1311     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
1312     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
1313     cellDofAux       += Nb*Nc;
1314     numComponentsAux += Nc;
1315   }
1316   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1317   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1318   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1319   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
1320   for (c = cStart; c < cEnd; ++c) {
1321     PetscScalar *x = NULL;
1322     PetscInt     i;
1323 
1324     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1325     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1326     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1327     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1328     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1329     if (dmAux) {
1330       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1331       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
1332       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1333     }
1334   }
1335   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1336   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1337     PetscInt numQuadPoints, Nb;
1338     /* Conforming batches */
1339     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1340     /* Remainder */
1341     PetscInt Nr, offset;
1342 
1343     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
1344     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
1345     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1346     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1347     blockSize = Nb*numQuadPoints;
1348     batchSize = numBlocks * blockSize;
1349     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1350     numChunks = numCells / (numBatches*batchSize);
1351     Ne        = numChunks*numBatches*batchSize;
1352     Nr        = numCells % (numBatches*batchSize);
1353     offset    = numCells - Nr;
1354     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1355       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
1356       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
1357       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
1358       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
1359 
1360       geom.v0   = v0;
1361       geom.J    = J;
1362       geom.invJ = invJ;
1363       geom.detJ = detJ;
1364       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1365       geom.v0   = &v0[offset*dim];
1366       geom.J    = &J[offset*dim*dim];
1367       geom.invJ = &invJ[offset*dim*dim];
1368       geom.detJ = &detJ[offset];
1369       ierr = PetscFEIntegrateJacobian(fe[fieldI], Nr, Nf, fe, fieldI, fieldJ, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
1370     }
1371   }
1372   for (c = cStart; c < cEnd; ++c) {
1373     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
1374     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1375   }
1376   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1377   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1378   if (feBd) {
1379     DMLabel  depth;
1380     PetscInt numBd, bd;
1381 
1382     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1383       PetscInt Nb, Nc;
1384 
1385       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1386       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1387       cellDof       += Nb*Nc;
1388       numComponents += Nc;
1389     }
1390     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1391     ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1392     for (bd = 0; bd < numBd; ++bd) {
1393       const char     *bdLabel;
1394       DMLabel         label;
1395       IS              pointIS;
1396       const PetscInt *points;
1397       const PetscInt *values;
1398       PetscReal      *n;
1399       PetscInt        field, numValues, numPoints, p, dep, numFaces;
1400       PetscBool       isEssential;
1401 
1402       ierr = DMPlexGetBoundary(dm, bd, &isEssential, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1403       if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1404       ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1405       ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1406       ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1407       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1408       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1409         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1410         if (dep == dim-1) ++numFaces;
1411       }
1412       ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1413       for (p = 0, f = 0; p < numPoints; ++p) {
1414         const PetscInt point = points[p];
1415         PetscScalar   *x     = NULL;
1416         PetscInt       i;
1417 
1418         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1419         if (dep != dim-1) continue;
1420         ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1421         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1422         if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1423         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1424         for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1425         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1426         ++f;
1427       }
1428       ierr = PetscMemzero(elemMat, numFaces*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1429       for (fieldI = 0; fieldI < Nf; ++fieldI) {
1430         PetscInt numQuadPoints, Nb;
1431         /* Conforming batches */
1432         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1433         /* Remainder */
1434         PetscInt Nr, offset;
1435 
1436         ierr = PetscFEGetQuadrature(feBd[fieldI], &quad);CHKERRQ(ierr);
1437         ierr = PetscFEGetDimension(feBd[fieldI], &Nb);CHKERRQ(ierr);
1438         ierr = PetscFEGetTileSizes(feBd[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1439         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1440         blockSize = Nb*numQuadPoints;
1441         batchSize = numBlocks * blockSize;
1442         ierr =  PetscFESetTileSizes(feBd[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1443         numChunks = numFaces / (numBatches*batchSize);
1444         Ne        = numChunks*numBatches*batchSize;
1445         Nr        = numFaces % (numBatches*batchSize);
1446         offset    = numFaces - Nr;
1447         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1448           void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g0BdFuncs[fieldI*Nf+fieldJ];
1449           void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g1BdFuncs[fieldI*Nf+fieldJ];
1450           void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g2BdFuncs[fieldI*Nf+fieldJ];
1451           void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g3BdFuncs[fieldI*Nf+fieldJ];
1452 
1453           geom.v0   = v0;
1454           geom.n    = n;
1455           geom.J    = J;
1456           geom.invJ = invJ;
1457           geom.detJ = detJ;
1458           ierr = PetscFEIntegrateBdJacobian(feBd[fieldI], Ne, Nf, feBd, fieldI, fieldJ, geom, u, 0, NULL, NULL, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1459           geom.v0   = &v0[offset*dim];
1460           geom.n    = &n[offset*dim];
1461           geom.J    = &J[offset*dim*dim];
1462           geom.invJ = &invJ[offset*dim*dim];
1463           geom.detJ = &detJ[offset];
1464           ierr = PetscFEIntegrateBdJacobian(feBd[fieldI], Nr, Nf, feBd, fieldI, fieldJ, geom, &u[offset*cellDof], 0, NULL, NULL, g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
1465         }
1466       }
1467       for (p = 0, f = 0; p < numPoints; ++p) {
1468         const PetscInt point = points[p];
1469 
1470         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1471         if (dep != dim-1) continue;
1472         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", cellDof, cellDof, &elemMat[f*cellDof*cellDof]);CHKERRQ(ierr);}
1473         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1474         ++f;
1475       }
1476       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1477       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1478       ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1479     }
1480   }
1481   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1482   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1483   if (mesh->printFEM) {
1484     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1485     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
1486     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1487   }
1488   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1489   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
1490   if (isShell) {
1491     JacActionCtx *jctx;
1492 
1493     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1494     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
1495   }
1496   PetscFunctionReturn(0);
1497 }
1498 
1499 #undef __FUNCT__
1500 #define __FUNCT__ "DMPlexComputeInterpolatorFEM"
1501 /*@
1502   DMPlexComputeInterpolatorFEM - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1503 
1504   Input Parameters:
1505 + dmf  - The fine mesh
1506 . dmc  - The coarse mesh
1507 - user - The user context
1508 
1509   Output Parameter:
1510 . In  - The interpolation matrix
1511 
1512   Note:
1513   The first member of the user context must be an FEMContext.
1514 
1515   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1516   like a GPU, or vectorize on a multicore machine.
1517 
1518   Level: developer
1519 
1520 .seealso: DMPlexComputeJacobianFEM()
1521 @*/
1522 PetscErrorCode DMPlexComputeInterpolatorFEM(DM dmc, DM dmf, Mat In, void *user)
1523 {
1524   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1525   PetscFEM         *fem   = (PetscFEM *) user;
1526   PetscFE          *fe    = fem->fe;
1527   const char       *name  = "Interpolator";
1528   PetscFE          *feRef;
1529   PetscSection      fsection, fglobalSection;
1530   PetscSection      csection, cglobalSection;
1531   PetscScalar      *elemMat;
1532   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, c;
1533   PetscInt          rCellDof = 0, cCellDof = 0;
1534   PetscErrorCode    ierr;
1535 
1536   PetscFunctionBegin;
1537 #if 0
1538   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1539 #endif
1540   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1541   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1542   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1543   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1544   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1545   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1546   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1547   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1548   for (f = 0; f < Nf; ++f) {
1549     PetscInt rNb, cNb, Nc;
1550 
1551     ierr = PetscFERefine(fe[f], &feRef[f]);CHKERRQ(ierr);
1552     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1553     ierr = PetscFEGetDimension(fe[f], &cNb);CHKERRQ(ierr);
1554     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1555     rCellDof += rNb*Nc;
1556     cCellDof += cNb*Nc;
1557   }
1558   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1559   ierr = PetscMalloc1(rCellDof*cCellDof,&elemMat);CHKERRQ(ierr);
1560   ierr = PetscMemzero(elemMat, rCellDof*cCellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1561   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1562     PetscDualSpace   Qref;
1563     PetscQuadrature  f;
1564     const PetscReal *qpoints, *qweights;
1565     PetscReal       *points;
1566     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1567 
1568     /* Compose points from all dual basis functionals */
1569     ierr = PetscFEGetNumComponents(fe[fieldI], &Nc);CHKERRQ(ierr);
1570     ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1571     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1572     for (i = 0; i < fpdim; ++i) {
1573       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1574       ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1575       npoints += Np;
1576     }
1577     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1578     for (i = 0, k = 0; i < fpdim; ++i) {
1579       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1580       ierr = PetscQuadratureGetData(f, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1581       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1582     }
1583 
1584     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1585       PetscReal *B;
1586       PetscInt   NcJ, cpdim, j;
1587 
1588       /* Evaluate basis at points */
1589       ierr = PetscFEGetNumComponents(fe[fieldJ], &NcJ);CHKERRQ(ierr);
1590       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);
1591       ierr = PetscFEGetDimension(fe[fieldJ], &cpdim);CHKERRQ(ierr);
1592       /* For now, fields only interpolate themselves */
1593       if (fieldI == fieldJ) {
1594         ierr = PetscFEGetTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1595         for (i = 0, k = 0; i < fpdim; ++i) {
1596           ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1597           ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, &qweights);CHKERRQ(ierr);
1598           for (p = 0; p < Np; ++p, ++k) {
1599             for (j = 0; j < cpdim; ++j) {
1600               for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cCellDof + offsetJ + j*NcJ + c] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p];
1601             }
1602           }
1603         }
1604         ierr = PetscFERestoreTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1605       }
1606       offsetJ += cpdim*NcJ;
1607     }
1608     offsetI += fpdim*Nc;
1609     ierr = PetscFree(points);CHKERRQ(ierr);
1610   }
1611   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rCellDof, cCellDof, elemMat);CHKERRQ(ierr);}
1612   for (c = cStart; c < cEnd; ++c) {
1613     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1614   }
1615   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1616   ierr = PetscFree(feRef);CHKERRQ(ierr);
1617   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1618   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1619   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1620   if (mesh->printFEM) {
1621     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1622     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1623     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1624   }
1625 #if 0
1626   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1627 #endif
1628   PetscFunctionReturn(0);
1629 }
1630 
1631 #undef __FUNCT__
1632 #define __FUNCT__ "DMPlexAddBoundary"
1633 /* The ids can be overridden by the command line option -bc_<boundary name> */
1634 PetscErrorCode DMPlexAddBoundary(DM dm, PetscBool isEssential, const char name[], PetscInt field, void (*bcFunc)(), PetscInt numids, const PetscInt *ids, void *ctx)
1635 {
1636   DM_Plex       *mesh = (DM_Plex *) dm->data;
1637   DMBoundary     b;
1638   PetscErrorCode ierr;
1639 
1640   PetscFunctionBegin;
1641   ierr = PetscNew(&b);CHKERRQ(ierr);
1642   ierr = PetscStrallocpy(name, (char **) &b->name);CHKERRQ(ierr);
1643   ierr = PetscMalloc1(numids, &b->ids);CHKERRQ(ierr);
1644   ierr = PetscMemcpy(b->ids, ids, numids*sizeof(PetscInt));CHKERRQ(ierr);
1645   b->essential   = isEssential;
1646   b->field       = field;
1647   b->func        = bcFunc;
1648   b->numids      = numids;
1649   b->ctx         = ctx;
1650   b->next        = mesh->boundary;
1651   mesh->boundary = b;
1652   PetscFunctionReturn(0);
1653 }
1654 
1655 #undef __FUNCT__
1656 #define __FUNCT__ "DMPlexGetNumBoundary"
1657 PetscErrorCode DMPlexGetNumBoundary(DM dm, PetscInt *numBd)
1658 {
1659   DM_Plex   *mesh = (DM_Plex *) dm->data;
1660   DMBoundary b    = mesh->boundary;
1661 
1662   PetscFunctionBegin;
1663   *numBd = 0;
1664   while (b) {++(*numBd); b = b->next;}
1665   PetscFunctionReturn(0);
1666 }
1667 
1668 #undef __FUNCT__
1669 #define __FUNCT__ "DMPlexGetBoundary"
1670 PetscErrorCode DMPlexGetBoundary(DM dm, PetscInt bd, PetscBool *isEssential, const char **name, PetscInt *field, void (**func)(), PetscInt *numids, const PetscInt **ids, void **ctx)
1671 {
1672   DM_Plex   *mesh = (DM_Plex *) dm->data;
1673   DMBoundary b    = mesh->boundary;
1674   PetscInt   n    = 0;
1675 
1676   PetscFunctionBegin;
1677   while (b) {
1678     if (n == bd) break;
1679     b = b->next;
1680     ++n;
1681   }
1682   if (n != bd) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %d is not in [0, %d)", bd, n);
1683   if (isEssential) {
1684     PetscValidPointer(isEssential, 3);
1685     *isEssential = b->essential;
1686   }
1687   if (name) {
1688     PetscValidPointer(name, 4);
1689     *name = b->name;
1690   }
1691   if (field) {
1692     PetscValidPointer(field, 5);
1693     *field = b->field;
1694   }
1695   if (func) {
1696     PetscValidPointer(func, 6);
1697     *func = b->func;
1698   }
1699   if (numids) {
1700     PetscValidPointer(numids, 7);
1701     *numids = b->numids;
1702   }
1703   if (ids) {
1704     PetscValidPointer(ids, 8);
1705     *ids = b->ids;
1706   }
1707   if (ctx) {
1708     PetscValidPointer(ctx, 9);
1709     *ctx = b->ctx;
1710   }
1711   PetscFunctionReturn(0);
1712 }
1713