xref: /petsc/src/dm/impls/plex/plexfem.c (revision 6f4eac7130eb18a62d917fd72052f9449aec7347)
1 #include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #include <petsc-private/petscfeimpl.h>
4 #include <petscfv.h>
5 
6 #undef __FUNCT__
7 #define __FUNCT__ "DMPlexGetScale"
8 PetscErrorCode DMPlexGetScale(DM dm, PetscUnit unit, PetscReal *scale)
9 {
10   DM_Plex *mesh = (DM_Plex*) dm->data;
11 
12   PetscFunctionBegin;
13   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
14   PetscValidPointer(scale, 3);
15   *scale = mesh->scale[unit];
16   PetscFunctionReturn(0);
17 }
18 
19 #undef __FUNCT__
20 #define __FUNCT__ "DMPlexSetScale"
21 PetscErrorCode DMPlexSetScale(DM dm, PetscUnit unit, PetscReal scale)
22 {
23   DM_Plex *mesh = (DM_Plex*) dm->data;
24 
25   PetscFunctionBegin;
26   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
27   mesh->scale[unit] = scale;
28   PetscFunctionReturn(0);
29 }
30 
31 PETSC_STATIC_INLINE PetscInt epsilon(PetscInt i, PetscInt j, PetscInt k)
32 {
33   switch (i) {
34   case 0:
35     switch (j) {
36     case 0: return 0;
37     case 1:
38       switch (k) {
39       case 0: return 0;
40       case 1: return 0;
41       case 2: return 1;
42       }
43     case 2:
44       switch (k) {
45       case 0: return 0;
46       case 1: return -1;
47       case 2: return 0;
48       }
49     }
50   case 1:
51     switch (j) {
52     case 0:
53       switch (k) {
54       case 0: return 0;
55       case 1: return 0;
56       case 2: return -1;
57       }
58     case 1: return 0;
59     case 2:
60       switch (k) {
61       case 0: return 1;
62       case 1: return 0;
63       case 2: return 0;
64       }
65     }
66   case 2:
67     switch (j) {
68     case 0:
69       switch (k) {
70       case 0: return 0;
71       case 1: return 1;
72       case 2: return 0;
73       }
74     case 1:
75       switch (k) {
76       case 0: return -1;
77       case 1: return 0;
78       case 2: return 0;
79       }
80     case 2: return 0;
81     }
82   }
83   return 0;
84 }
85 
86 #undef __FUNCT__
87 #define __FUNCT__ "DMPlexCreateRigidBody"
88 /*@C
89   DMPlexCreateRigidBody - create rigid body modes from coordinates
90 
91   Collective on DM
92 
93   Input Arguments:
94 + dm - the DM
95 . section - the local section associated with the rigid field, or NULL for the default section
96 - globalSection - the global section associated with the rigid field, or NULL for the default section
97 
98   Output Argument:
99 . sp - the null space
100 
101   Note: This is necessary to take account of Dirichlet conditions on the displacements
102 
103   Level: advanced
104 
105 .seealso: MatNullSpaceCreate()
106 @*/
107 PetscErrorCode DMPlexCreateRigidBody(DM dm, PetscSection section, PetscSection globalSection, MatNullSpace *sp)
108 {
109   MPI_Comm       comm;
110   Vec            coordinates, localMode, mode[6];
111   PetscSection   coordSection;
112   PetscScalar   *coords;
113   PetscInt       dim, vStart, vEnd, v, n, m, d, i, j;
114   PetscErrorCode ierr;
115 
116   PetscFunctionBegin;
117   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
118   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
119   if (dim == 1) {
120     ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
121     PetscFunctionReturn(0);
122   }
123   if (!section)       {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
124   if (!globalSection) {ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);}
125   ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
126   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
127   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
128   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
129   m    = (dim*(dim+1))/2;
130   ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
131   ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
132   ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
133   for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
134   /* Assume P1 */
135   ierr = DMGetLocalVector(dm, &localMode);CHKERRQ(ierr);
136   for (d = 0; d < dim; ++d) {
137     PetscScalar values[3] = {0.0, 0.0, 0.0};
138 
139     values[d] = 1.0;
140     ierr      = VecSet(localMode, 0.0);CHKERRQ(ierr);
141     for (v = vStart; v < vEnd; ++v) {
142       ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
143     }
144     ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
145     ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
146   }
147   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
148   for (d = dim; d < dim*(dim+1)/2; ++d) {
149     PetscInt i, j, k = dim > 2 ? d - dim : d;
150 
151     ierr = VecSet(localMode, 0.0);CHKERRQ(ierr);
152     for (v = vStart; v < vEnd; ++v) {
153       PetscScalar values[3] = {0.0, 0.0, 0.0};
154       PetscInt    off;
155 
156       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
157       for (i = 0; i < dim; ++i) {
158         for (j = 0; j < dim; ++j) {
159           values[j] += epsilon(i, j, k)*PetscRealPart(coords[off+i]);
160         }
161       }
162       ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
163     }
164     ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
165     ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
166   }
167   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
168   ierr = DMRestoreLocalVector(dm, &localMode);CHKERRQ(ierr);
169   for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
170   /* Orthonormalize system */
171   for (i = dim; i < m; ++i) {
172     PetscScalar dots[6];
173 
174     ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
175     for (j = 0; j < i; ++j) dots[j] *= -1.0;
176     ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
177     ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
178   }
179   ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
180   for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
181   PetscFunctionReturn(0);
182 }
183 
184 #undef __FUNCT__
185 #define __FUNCT__ "DMPlexProjectFunctionLabelLocal"
186 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)
187 {
188   PetscDualSpace *sp;
189   PetscSection    section;
190   PetscScalar    *values;
191   PetscReal      *v0, *J, detJ;
192   PetscBool      *fieldActive;
193   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, f, d, v, i, comp;
194   PetscErrorCode  ierr;
195 
196   PetscFunctionBegin;
197   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
198   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
199   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
200   ierr = PetscMalloc3(numFields,&sp,dim,&v0,dim*dim,&J);CHKERRQ(ierr);
201   for (f = 0; f < numFields; ++f) {
202     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
203     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
204     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
205     totDim += spDim*numComp;
206   }
207   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
208   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
209   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
210   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
211   ierr = DMGetWorkArray(dm, numFields, PETSC_BOOL, &fieldActive);CHKERRQ(ierr);
212   for (f = 0; f < numFields; ++f) fieldActive[f] = funcs[f] ? PETSC_TRUE : PETSC_FALSE;
213   for (i = 0; i < numIds; ++i) {
214     IS              pointIS;
215     const PetscInt *points;
216     PetscInt        n, p;
217 
218     ierr = DMLabelGetStratumIS(label, ids[i], &pointIS);CHKERRQ(ierr);
219     ierr = ISGetLocalSize(pointIS, &n);CHKERRQ(ierr);
220     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
221     for (p = 0; p < n; ++p) {
222       const PetscInt    point = points[p];
223       PetscCellGeometry geom;
224 
225       if ((point < cStart) || (point >= cEnd)) continue;
226       ierr = DMPlexComputeCellGeometry(dm, point, v0, J, NULL, &detJ);CHKERRQ(ierr);
227       geom.v0   = v0;
228       geom.J    = J;
229       geom.detJ = &detJ;
230       for (f = 0, v = 0; f < numFields; ++f) {
231         void * const ctx = ctxs ? ctxs[f] : NULL;
232         ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
233         ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
234         for (d = 0; d < spDim; ++d) {
235           if (funcs[f]) {
236             ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
237           } else {
238             for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
239           }
240           v += numComp;
241         }
242       }
243       ierr = DMPlexVecSetFieldClosure_Internal(dm, section, localX, fieldActive, point, values, mode);CHKERRQ(ierr);
244     }
245     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
246     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
247   }
248   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
249   ierr = DMRestoreWorkArray(dm, numFields, PETSC_BOOL, &fieldActive);CHKERRQ(ierr);
250   ierr = PetscFree3(sp,v0,J);CHKERRQ(ierr);
251   PetscFunctionReturn(0);
252 }
253 
254 #undef __FUNCT__
255 #define __FUNCT__ "DMPlexProjectFunctionLocal"
256 PetscErrorCode DMPlexProjectFunctionLocal(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
257 {
258   PetscDualSpace *sp;
259   PetscSection    section;
260   PetscScalar    *values;
261   PetscReal      *v0, *J, detJ;
262   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, c, f, d, v, comp;
263   PetscErrorCode  ierr;
264 
265   PetscFunctionBegin;
266   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
267   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
268   ierr = PetscMalloc1(numFields, &sp);CHKERRQ(ierr);
269   for (f = 0; f < numFields; ++f) {
270     PetscFE fe;
271 
272     ierr = DMGetField(dm, f, (PetscObject *) &fe);CHKERRQ(ierr);
273     ierr = PetscFEGetDualSpace(fe, &sp[f]);CHKERRQ(ierr);
274     ierr = PetscFEGetNumComponents(fe, &numComp);CHKERRQ(ierr);
275     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
276     totDim += spDim*numComp;
277   }
278   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
279   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
280   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
281   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
282   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
283   ierr = PetscMalloc2(dim,&v0,dim*dim,&J);CHKERRQ(ierr);
284   for (c = cStart; c < cEnd; ++c) {
285     PetscCellGeometry geom;
286 
287     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
288     geom.v0   = v0;
289     geom.J    = J;
290     geom.detJ = &detJ;
291     for (f = 0, v = 0; f < numFields; ++f) {
292       PetscFE      fe;
293       void * const ctx = ctxs ? ctxs[f] : NULL;
294 
295       ierr = DMGetField(dm, f, (PetscObject *) &fe);CHKERRQ(ierr);
296       ierr = PetscFEGetNumComponents(fe, &numComp);CHKERRQ(ierr);
297       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
298       for (d = 0; d < spDim; ++d) {
299         if (funcs[f]) {
300           ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
301         } else {
302           for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
303         }
304         v += numComp;
305       }
306     }
307     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
308   }
309   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
310   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
311   ierr = PetscFree(sp);CHKERRQ(ierr);
312   PetscFunctionReturn(0);
313 }
314 
315 #undef __FUNCT__
316 #define __FUNCT__ "DMPlexProjectFunction"
317 /*@C
318   DMPlexProjectFunction - This projects the given function into the function space provided.
319 
320   Input Parameters:
321 + dm      - The DM
322 . funcs   - The coordinate functions to evaluate, one per field
323 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
324 - mode    - The insertion mode for values
325 
326   Output Parameter:
327 . X - vector
328 
329   Level: developer
330 
331 .seealso: DMPlexComputeL2Diff()
332 @*/
333 PetscErrorCode DMPlexProjectFunction(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
334 {
335   Vec            localX;
336   PetscErrorCode ierr;
337 
338   PetscFunctionBegin;
339   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
340   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
341   ierr = DMPlexProjectFunctionLocal(dm, funcs, ctxs, mode, localX);CHKERRQ(ierr);
342   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
343   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
344   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
345   PetscFunctionReturn(0);
346 }
347 
348 #undef __FUNCT__
349 #define __FUNCT__ "DMPlexProjectFieldLocal"
350 PetscErrorCode DMPlexProjectFieldLocal(DM dm, Vec localU, void (**funcs)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal [], PetscScalar []), InsertMode mode, Vec localX)
351 {
352   DM                dmAux;
353   PetscDS           prob, probAux;
354   Vec               A;
355   PetscSection      section, sectionAux;
356   PetscScalar      *values, *u, *u_x, *a, *a_x;
357   PetscReal        *x, *v0, *J, *invJ, detJ, **basisField, **basisFieldDer, **basisFieldAux, **basisFieldDerAux;
358   PetscInt          Nf, dim, spDim, totDim, numValues, cStart, cEnd, c, f, d, v, comp;
359   PetscErrorCode    ierr;
360 
361   PetscFunctionBegin;
362   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
363   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
364   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
365   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
366   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
367   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
368   ierr = PetscDSGetTabulation(prob, &basisField, &basisFieldDer);CHKERRQ(ierr);
369   ierr = PetscDSGetEvaluationArrays(prob, &u, NULL, &u_x);CHKERRQ(ierr);
370   ierr = PetscDSGetRefCoordArrays(prob, &x, NULL);CHKERRQ(ierr);
371   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
372   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
373   if (dmAux) {
374     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
375     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
376     ierr = PetscDSGetTabulation(prob, &basisFieldAux, &basisFieldDerAux);CHKERRQ(ierr);
377     ierr = PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);CHKERRQ(ierr);
378   }
379   ierr = DMPlexInsertBoundaryValuesFEM(dm, localU);CHKERRQ(ierr);
380   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
381   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
382   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
383   ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
384   for (c = cStart; c < cEnd; ++c) {
385     PetscScalar *coefficients = NULL, *coefficientsAux = NULL;
386 
387     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
388     ierr = DMPlexVecGetClosure(dm, section, localU, c, NULL, &coefficients);CHKERRQ(ierr);
389     if (dmAux) {ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &coefficientsAux);CHKERRQ(ierr);}
390     for (f = 0, v = 0; f < Nf; ++f) {
391       PetscFE        fe;
392       PetscDualSpace sp;
393       PetscInt       Ncf;
394 
395       ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
396       ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
397       ierr = PetscFEGetNumComponents(fe, &Ncf);CHKERRQ(ierr);
398       ierr = PetscDualSpaceGetDimension(sp, &spDim);CHKERRQ(ierr);
399       for (d = 0; d < spDim; ++d) {
400         PetscQuadrature  quad;
401         const PetscReal *points, *weights;
402         PetscInt         numPoints, q;
403 
404         if (funcs[f]) {
405           ierr = PetscDualSpaceGetFunctional(sp, d, &quad);CHKERRQ(ierr);
406           ierr = PetscQuadratureGetData(quad, NULL, &numPoints, &points, &weights);CHKERRQ(ierr);
407           ierr = PetscFEGetTabulation(fe, numPoints, points, &basisField[f], &basisFieldDer[f], NULL);CHKERRQ(ierr);
408           for (q = 0; q < numPoints; ++q) {
409             CoordinatesRefToReal(dim, dim, v0, J, &points[q*dim], x);
410             ierr = EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, coefficients,    NULL, u, u_x, NULL);CHKERRQ(ierr);
411             ierr = EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, coefficientsAux, NULL, a, a_x, NULL);CHKERRQ(ierr);
412             (*funcs[f])(u, NULL, u_x, a, NULL, a_x, x, &values[v]);
413           }
414           ierr = PetscFERestoreTabulation(fe, numPoints, points, &basisField[f], &basisFieldDer[f], NULL);CHKERRQ(ierr);
415         } else {
416           for (comp = 0; comp < Ncf; ++comp) values[v+comp] = 0.0;
417         }
418         v += Ncf;
419       }
420     }
421     ierr = DMPlexVecRestoreClosure(dm, section, localU, c, NULL, &coefficients);CHKERRQ(ierr);
422     if (dmAux) {ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &coefficientsAux);CHKERRQ(ierr);}
423     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
424   }
425   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
426   ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
427   PetscFunctionReturn(0);
428 }
429 
430 #undef __FUNCT__
431 #define __FUNCT__ "DMPlexProjectField"
432 /*@C
433   DMPlexProjectField - This projects the given function of the fields into the function space provided.
434 
435   Input Parameters:
436 + dm      - The DM
437 . U       - The input field vector
438 . funcs   - The functions to evaluate, one per field
439 - mode    - The insertion mode for values
440 
441   Output Parameter:
442 . X       - The output vector
443 
444   Level: developer
445 
446 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
447 @*/
448 PetscErrorCode DMPlexProjectField(DM dm, Vec U, void (**funcs)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal [], PetscScalar []), InsertMode mode, Vec X)
449 {
450   Vec            localX, localU;
451   PetscErrorCode ierr;
452 
453   PetscFunctionBegin;
454   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
455   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
456   ierr = DMGetLocalVector(dm, &localU);CHKERRQ(ierr);
457   ierr = DMGlobalToLocalBegin(dm, U, INSERT_VALUES, localU);CHKERRQ(ierr);
458   ierr = DMGlobalToLocalEnd(dm, U, INSERT_VALUES, localU);CHKERRQ(ierr);
459   ierr = DMPlexProjectFieldLocal(dm, localU, funcs, mode, localX);CHKERRQ(ierr);
460   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
461   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
462   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
463   ierr = DMRestoreLocalVector(dm, &localU);CHKERRQ(ierr);
464   PetscFunctionReturn(0);
465 }
466 
467 #undef __FUNCT__
468 #define __FUNCT__ "DMPlexInsertBoundaryValuesFEM"
469 PetscErrorCode DMPlexInsertBoundaryValuesFEM(DM dm, Vec localX)
470 {
471   void        (**funcs)(const PetscReal x[], PetscScalar *u, void *ctx);
472   void         **ctxs;
473   PetscFE       *fe;
474   PetscInt       numFields, f, numBd, b;
475   PetscErrorCode ierr;
476 
477   PetscFunctionBegin;
478   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
479   PetscValidHeaderSpecific(localX, VEC_CLASSID, 2);
480   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
481   ierr = PetscMalloc3(numFields,&fe,numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
482   for (f = 0; f < numFields; ++f) {ierr = DMGetField(dm, f, (PetscObject *) &fe[f]);CHKERRQ(ierr);}
483   /* OPT: Could attempt to do multiple BCs at once */
484   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
485   for (b = 0; b < numBd; ++b) {
486     DMLabel         label;
487     const PetscInt *ids;
488     const char     *labelname;
489     PetscInt        numids, field;
490     PetscBool       isEssential;
491     void          (*func)();
492     void           *ctx;
493 
494     ierr = DMPlexGetBoundary(dm, b, &isEssential, NULL, &labelname, &field, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
495     ierr = DMPlexGetLabel(dm, labelname, &label);CHKERRQ(ierr);
496     for (f = 0; f < numFields; ++f) {
497       funcs[f] = field == f ? (void (*)(const PetscReal[], PetscScalar *, void *)) func : NULL;
498       ctxs[f]  = field == f ? ctx : NULL;
499     }
500     ierr = DMPlexProjectFunctionLabelLocal(dm, label, numids, ids, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
501   }
502   ierr = PetscFree3(fe,funcs,ctxs);CHKERRQ(ierr);
503   PetscFunctionReturn(0);
504 }
505 
506 #undef __FUNCT__
507 #define __FUNCT__ "DMPlexComputeL2Diff"
508 /*@C
509   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
510 
511   Input Parameters:
512 + dm    - The DM
513 . funcs - The functions to evaluate for each field component
514 . ctxs  - Optional array of contexts to pass to each function, or NULL.
515 - X     - The coefficient vector u_h
516 
517   Output Parameter:
518 . diff - The diff ||u - u_h||_2
519 
520   Level: developer
521 
522 .seealso: DMPlexProjectFunction(), DMPlexComputeL2GradientDiff()
523 @*/
524 PetscErrorCode DMPlexComputeL2Diff(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
525 {
526   const PetscInt  debug = 0;
527   PetscSection    section;
528   PetscQuadrature quad;
529   Vec             localX;
530   PetscScalar    *funcVal;
531   PetscReal      *coords, *v0, *J, *invJ, detJ;
532   PetscReal       localDiff = 0.0;
533   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
534   PetscErrorCode  ierr;
535 
536   PetscFunctionBegin;
537   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
538   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
539   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
540   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
541   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
542   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
543   for (field = 0; field < numFields; ++field) {
544     PetscFE  fe;
545     PetscInt Nc;
546 
547     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
548     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
549     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
550     numComponents += Nc;
551   }
552   ierr = DMPlexProjectFunctionLocal(dm, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
553   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
554   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
555   for (c = cStart; c < cEnd; ++c) {
556     PetscScalar *x = NULL;
557     PetscReal    elemDiff = 0.0;
558 
559     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
560     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
561     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
562 
563     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
564       PetscFE          fe;
565       void * const     ctx = ctxs ? ctxs[field] : NULL;
566       const PetscReal *quadPoints, *quadWeights;
567       PetscReal       *basis;
568       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
569 
570       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
571       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
572       ierr = PetscFEGetDimension(fe, &numBasisFuncs);CHKERRQ(ierr);
573       ierr = PetscFEGetNumComponents(fe, &numBasisComps);CHKERRQ(ierr);
574       ierr = PetscFEGetDefaultTabulation(fe, &basis, NULL, NULL);CHKERRQ(ierr);
575       if (debug) {
576         char title[1024];
577         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
578         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
579       }
580       for (q = 0; q < numQuadPoints; ++q) {
581         for (d = 0; d < dim; d++) {
582           coords[d] = v0[d];
583           for (e = 0; e < dim; e++) {
584             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
585           }
586         }
587         (*funcs[field])(coords, funcVal, ctx);
588         for (fc = 0; fc < numBasisComps; ++fc) {
589           PetscScalar interpolant = 0.0;
590 
591           for (f = 0; f < numBasisFuncs; ++f) {
592             const PetscInt fidx = f*numBasisComps+fc;
593             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
594           }
595           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);}
596           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
597         }
598       }
599       comp        += numBasisComps;
600       fieldOffset += numBasisFuncs*numBasisComps;
601     }
602     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
603     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
604     localDiff += elemDiff;
605   }
606   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
607   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
608   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
609   *diff = PetscSqrtReal(*diff);
610   PetscFunctionReturn(0);
611 }
612 
613 #undef __FUNCT__
614 #define __FUNCT__ "DMPlexComputeL2GradientDiff"
615 /*@C
616   DMPlexComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
617 
618   Input Parameters:
619 + dm    - The DM
620 . funcs - The gradient functions to evaluate for each field component
621 . ctxs  - Optional array of contexts to pass to each function, or NULL.
622 . X     - The coefficient vector u_h
623 - n     - The vector to project along
624 
625   Output Parameter:
626 . diff - The diff ||(grad u - grad u_h) . n||_2
627 
628   Level: developer
629 
630 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
631 @*/
632 PetscErrorCode DMPlexComputeL2GradientDiff(DM dm, void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
633 {
634   const PetscInt  debug = 0;
635   PetscSection    section;
636   PetscQuadrature quad;
637   Vec             localX;
638   PetscScalar    *funcVal, *interpolantVec;
639   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
640   PetscReal       localDiff = 0.0;
641   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
642   PetscErrorCode  ierr;
643 
644   PetscFunctionBegin;
645   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
646   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
647   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
648   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
649   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
650   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
651   for (field = 0; field < numFields; ++field) {
652     PetscFE  fe;
653     PetscInt Nc;
654 
655     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
656     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
657     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
658     numComponents += Nc;
659   }
660   /* ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
661   ierr = PetscMalloc7(numComponents,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
662   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
663   for (c = cStart; c < cEnd; ++c) {
664     PetscScalar *x = NULL;
665     PetscReal    elemDiff = 0.0;
666 
667     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
668     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
669     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
670 
671     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
672       PetscFE          fe;
673       void * const     ctx = ctxs ? ctxs[field] : NULL;
674       const PetscReal *quadPoints, *quadWeights;
675       PetscReal       *basisDer;
676       PetscInt         numQuadPoints, Nb, Ncomp, q, d, e, fc, f, g;
677 
678       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
679       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
680       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
681       ierr = PetscFEGetNumComponents(fe, &Ncomp);CHKERRQ(ierr);
682       ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
683       if (debug) {
684         char title[1024];
685         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
686         ierr = DMPrintCellVector(c, title, Nb*Ncomp, &x[fieldOffset]);CHKERRQ(ierr);
687       }
688       for (q = 0; q < numQuadPoints; ++q) {
689         for (d = 0; d < dim; d++) {
690           coords[d] = v0[d];
691           for (e = 0; e < dim; e++) {
692             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
693           }
694         }
695         (*funcs[field])(coords, n, funcVal, ctx);
696         for (fc = 0; fc < Ncomp; ++fc) {
697           PetscScalar interpolant = 0.0;
698 
699           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
700           for (f = 0; f < Nb; ++f) {
701             const PetscInt fidx = f*Ncomp+fc;
702 
703             for (d = 0; d < dim; ++d) {
704               realSpaceDer[d] = 0.0;
705               for (g = 0; g < dim; ++g) {
706                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+fidx)*dim+g];
707               }
708               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
709             }
710           }
711           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
712           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);}
713           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
714         }
715       }
716       comp        += Ncomp;
717       fieldOffset += Nb*Ncomp;
718     }
719     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
720     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
721     localDiff += elemDiff;
722   }
723   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
724   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
725   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
726   *diff = PetscSqrtReal(*diff);
727   PetscFunctionReturn(0);
728 }
729 
730 #undef __FUNCT__
731 #define __FUNCT__ "DMPlexComputeL2FieldDiff"
732 PetscErrorCode DMPlexComputeL2FieldDiff(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal diff[])
733 {
734   const PetscInt  debug = 0;
735   PetscSection    section;
736   PetscQuadrature quad;
737   Vec             localX;
738   PetscScalar    *funcVal;
739   PetscReal      *coords, *v0, *J, *invJ, detJ;
740   PetscReal      *localDiff;
741   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
742   PetscErrorCode  ierr;
743 
744   PetscFunctionBegin;
745   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
746   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
747   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
748   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
749   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
750   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
751   for (field = 0; field < numFields; ++field) {
752     PetscFE  fe;
753     PetscInt Nc;
754 
755     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
756     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
757     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
758     numComponents += Nc;
759   }
760   ierr = DMPlexProjectFunctionLocal(dm, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
761   ierr = PetscCalloc6(numFields,&localDiff,numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
762   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
763   for (c = cStart; c < cEnd; ++c) {
764     PetscScalar *x = NULL;
765 
766     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
767     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
768     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
769 
770     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
771       PetscFE          fe;
772       void * const     ctx = ctxs ? ctxs[field] : NULL;
773       const PetscReal *quadPoints, *quadWeights;
774       PetscReal       *basis, elemDiff = 0.0;
775       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
776 
777       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
778       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
779       ierr = PetscFEGetDimension(fe, &numBasisFuncs);CHKERRQ(ierr);
780       ierr = PetscFEGetNumComponents(fe, &numBasisComps);CHKERRQ(ierr);
781       ierr = PetscFEGetDefaultTabulation(fe, &basis, NULL, NULL);CHKERRQ(ierr);
782       if (debug) {
783         char title[1024];
784         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
785         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
786       }
787       for (q = 0; q < numQuadPoints; ++q) {
788         for (d = 0; d < dim; d++) {
789           coords[d] = v0[d];
790           for (e = 0; e < dim; e++) {
791             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
792           }
793         }
794         (*funcs[field])(coords, funcVal, ctx);
795         for (fc = 0; fc < numBasisComps; ++fc) {
796           PetscScalar interpolant = 0.0;
797 
798           for (f = 0; f < numBasisFuncs; ++f) {
799             const PetscInt fidx = f*numBasisComps+fc;
800             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
801           }
802           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);}
803           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
804         }
805       }
806       comp        += numBasisComps;
807       fieldOffset += numBasisFuncs*numBasisComps;
808       localDiff[field] += elemDiff;
809     }
810     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
811   }
812   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
813   ierr  = MPI_Allreduce(localDiff, diff, numFields, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
814   for (field = 0; field < numFields; ++field) diff[field] = PetscSqrtReal(diff[field]);
815   ierr  = PetscFree6(localDiff,funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
816   PetscFunctionReturn(0);
817 }
818 
819 #undef __FUNCT__
820 #define __FUNCT__ "DMPlexComputeIntegralFEM"
821 /*@
822   DMPlexComputeIntegralFEM - Form the local integral F from the local input X using pointwise functions specified by the user
823 
824   Input Parameters:
825 + dm - The mesh
826 . X  - Local input vector
827 - user - The user context
828 
829   Output Parameter:
830 . integral - Local integral for each field
831 
832   Level: developer
833 
834 .seealso: DMPlexComputeResidualFEM()
835 @*/
836 PetscErrorCode DMPlexComputeIntegralFEM(DM dm, Vec X, PetscReal *integral, void *user)
837 {
838   DM_Plex          *mesh  = (DM_Plex *) dm->data;
839   DM                dmAux;
840   Vec               localX, A;
841   PetscDS           prob, probAux = NULL;
842   PetscQuadrature   q;
843   PetscCellGeometry geom;
844   PetscSection      section, sectionAux;
845   PetscReal        *v0, *J, *invJ, *detJ;
846   PetscScalar      *u, *a = NULL;
847   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
848   PetscInt          totDim, totDimAux;
849   PetscErrorCode    ierr;
850 
851   PetscFunctionBegin;
852   /*ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);*/
853   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
854   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
855   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
856   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
857   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
858   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
859   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
860   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
861   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
862   numCells = cEnd - cStart;
863   for (f = 0; f < Nf; ++f) {integral[f]    = 0.0;}
864   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
865   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
866   if (dmAux) {
867     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
868     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
869     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
870   }
871   ierr = DMPlexInsertBoundaryValuesFEM(dm, localX);CHKERRQ(ierr);
872   ierr = PetscMalloc5(numCells*totDim,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ);CHKERRQ(ierr);
873   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
874   for (c = cStart; c < cEnd; ++c) {
875     PetscScalar *x = NULL;
876     PetscInt     i;
877 
878     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
879     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
880     ierr = DMPlexVecGetClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
881     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
882     ierr = DMPlexVecRestoreClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
883     if (dmAux) {
884       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
885       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
886       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
887     }
888   }
889   for (f = 0; f < Nf; ++f) {
890     PetscFE  fe;
891     PetscInt numQuadPoints, Nb;
892     /* Conforming batches */
893     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
894     /* Remainder */
895     PetscInt Nr, offset;
896 
897     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
898     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
899     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
900     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
901     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
902     blockSize = Nb*numQuadPoints;
903     batchSize = numBlocks * blockSize;
904     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
905     numChunks = numCells / (numBatches*batchSize);
906     Ne        = numChunks*numBatches*batchSize;
907     Nr        = numCells % (numBatches*batchSize);
908     offset    = numCells - Nr;
909     geom.v0   = v0;
910     geom.J    = J;
911     geom.invJ = invJ;
912     geom.detJ = detJ;
913     ierr = PetscFEIntegrate(fe, prob, f, Ne, geom, u, probAux, a, integral);CHKERRQ(ierr);
914     geom.v0   = &v0[offset*dim];
915     geom.J    = &J[offset*dim*dim];
916     geom.invJ = &invJ[offset*dim*dim];
917     geom.detJ = &detJ[offset];
918     ierr = PetscFEIntegrate(fe, prob, f, Nr, geom, &u[offset*totDim], probAux, &a[offset*totDimAux], integral);CHKERRQ(ierr);
919   }
920   ierr = PetscFree5(u,v0,J,invJ,detJ);CHKERRQ(ierr);
921   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
922   if (mesh->printFEM) {
923     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Local integral:");CHKERRQ(ierr);
924     for (f = 0; f < Nf; ++f) {ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), " %g", integral[f]);CHKERRQ(ierr);}
925     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "\n");CHKERRQ(ierr);
926   }
927   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
928   /* TODO: Allreduce for integral */
929   /*ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);*/
930   PetscFunctionReturn(0);
931 }
932 
933 #undef __FUNCT__
934 #define __FUNCT__ "DMPlexComputeResidualFEM_Internal"
935 PetscErrorCode DMPlexComputeResidualFEM_Internal(DM dm, Vec X, Vec X_t, Vec F, void *user)
936 {
937   DM_Plex          *mesh  = (DM_Plex *) dm->data;
938   const char       *name  = "Residual";
939   DM                dmAux;
940   DMLabel           depth;
941   Vec               A;
942   PetscDS           prob, probAux = NULL;
943   PetscQuadrature   q;
944   PetscCellGeometry geom;
945   PetscSection      section, sectionAux;
946   PetscReal        *v0, *J, *invJ, *detJ;
947   PetscScalar      *elemVec, *u, *u_t, *a = NULL;
948   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c, numBd, bd;
949   PetscInt          totDim, totDimBd, totDimAux;
950   PetscErrorCode    ierr;
951 
952   PetscFunctionBegin;
953   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
954   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
955   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
956   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
957   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
958   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
959   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
960   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
961   numCells = cEnd - cStart;
962   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
963   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
964   if (dmAux) {
965     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
966     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
967     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
968   }
969   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
970   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
971   ierr = PetscMalloc7(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*totDim,&elemVec);CHKERRQ(ierr);
972   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
973   for (c = cStart; c < cEnd; ++c) {
974     PetscScalar *x = NULL, *x_t = NULL;
975     PetscInt     i;
976 
977     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
978     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
979     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
980     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
981     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
982     if (X_t) {
983       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
984       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
985       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
986     }
987     if (dmAux) {
988       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
989       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
990       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
991     }
992   }
993   for (f = 0; f < Nf; ++f) {
994     PetscFE  fe;
995     PetscInt numQuadPoints, Nb;
996     /* Conforming batches */
997     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
998     /* Remainder */
999     PetscInt Nr, offset;
1000 
1001     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1002     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1003     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1004     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1005     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1006     blockSize = Nb*numQuadPoints;
1007     batchSize = numBlocks * blockSize;
1008     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1009     numChunks = numCells / (numBatches*batchSize);
1010     Ne        = numChunks*numBatches*batchSize;
1011     Nr        = numCells % (numBatches*batchSize);
1012     offset    = numCells - Nr;
1013     geom.v0   = v0;
1014     geom.J    = J;
1015     geom.invJ = invJ;
1016     geom.detJ = detJ;
1017     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, geom, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
1018     geom.v0   = &v0[offset*dim];
1019     geom.J    = &J[offset*dim*dim];
1020     geom.invJ = &invJ[offset*dim*dim];
1021     geom.detJ = &detJ[offset];
1022     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, geom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);CHKERRQ(ierr);
1023   }
1024   for (c = cStart; c < cEnd; ++c) {
1025     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, totDim, &elemVec[c*totDim]);CHKERRQ(ierr);}
1026     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_VALUES);CHKERRQ(ierr);
1027   }
1028   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1029   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1030   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1031   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1032   for (bd = 0; bd < numBd; ++bd) {
1033     const char     *bdLabel;
1034     DMLabel         label;
1035     IS              pointIS;
1036     const PetscInt *points;
1037     const PetscInt *values;
1038     PetscReal      *n;
1039     PetscInt        field, numValues, numPoints, p, dep, numFaces;
1040     PetscBool       isEssential;
1041 
1042     ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1043     if (isEssential) continue;
1044     if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1045     ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1046     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1047     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1048     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1049     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1050       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1051       if (dep == dim-1) ++numFaces;
1052     }
1053     ierr = PetscMalloc7(numFaces*totDimBd,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1054     if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1055     for (p = 0, f = 0; p < numPoints; ++p) {
1056       const PetscInt point = points[p];
1057       PetscScalar   *x     = NULL;
1058       PetscInt       i;
1059 
1060       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1061       if (dep != dim-1) continue;
1062       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1063       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1064       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1065       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1066       for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1067       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1068       if (X_t) {
1069         ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1070         for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1071         ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1072       }
1073       ++f;
1074     }
1075     for (f = 0; f < Nf; ++f) {
1076       PetscFE  fe;
1077       PetscInt numQuadPoints, Nb;
1078       /* Conforming batches */
1079       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1080       /* Remainder */
1081       PetscInt Nr, offset;
1082 
1083       ierr = PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1084       ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1085       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1086       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1087       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1088       blockSize = Nb*numQuadPoints;
1089       batchSize = numBlocks * blockSize;
1090       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1091       numChunks = numFaces / (numBatches*batchSize);
1092       Ne        = numChunks*numBatches*batchSize;
1093       Nr        = numFaces % (numBatches*batchSize);
1094       offset    = numFaces - Nr;
1095       geom.v0   = v0;
1096       geom.n    = n;
1097       geom.J    = J;
1098       geom.invJ = invJ;
1099       geom.detJ = detJ;
1100       ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, geom, u, u_t, NULL, NULL, elemVec);CHKERRQ(ierr);
1101       geom.v0   = &v0[offset*dim];
1102       geom.n    = &n[offset*dim];
1103       geom.J    = &J[offset*dim*dim];
1104       geom.invJ = &invJ[offset*dim*dim];
1105       geom.detJ = &detJ[offset];
1106       ierr = PetscFEIntegrateBdResidual(fe, prob, f, Nr, geom, &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1107     }
1108     for (p = 0, f = 0; p < numPoints; ++p) {
1109       const PetscInt point = points[p];
1110 
1111       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1112       if (dep != dim-1) continue;
1113       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1114       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*totDimBd], ADD_VALUES);CHKERRQ(ierr);
1115       ++f;
1116     }
1117     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1118     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1119     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1120     if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1121   }
1122   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1123   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1124   PetscFunctionReturn(0);
1125 }
1126 
1127 #undef __FUNCT__
1128 #define __FUNCT__ "DMPlexComputeResidualFEM_Check"
1129 static PetscErrorCode DMPlexComputeResidualFEM_Check(DM dm, Vec X, Vec X_t, Vec F, void *user)
1130 {
1131   DM_Plex          *mesh = (DM_Plex *) dm->data;
1132   DM                dmCh, dmAux;
1133   Vec               A;
1134   PetscDS           prob, probCh, probAux = NULL;
1135   PetscQuadrature   q;
1136   PetscCellGeometry geom;
1137   PetscSection      section, sectionAux;
1138   PetscReal        *v0, *J, *invJ, *detJ;
1139   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1140   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1141   PetscInt          totDim, totDimAux, diffCell = 0;
1142   PetscErrorCode    ierr;
1143 
1144   PetscFunctionBegin;
1145   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1146   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1147   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1148   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1149   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1150   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1151   numCells = cEnd - cStart;
1152   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1153   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1154   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1155   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1156   if (dmAux) {
1157     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1158     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1159     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1160   }
1161   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1162   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1163   ierr = PetscMalloc7(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*totDim,&elemVec);CHKERRQ(ierr);
1164   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1165   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1166   for (c = cStart; c < cEnd; ++c) {
1167     PetscScalar *x = NULL, *x_t = NULL;
1168     PetscInt     i;
1169 
1170     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1171     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1172     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1173     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1174     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1175     if (X_t) {
1176       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1177       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1178       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1179     }
1180     if (dmAux) {
1181       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1182       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1183       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1184     }
1185   }
1186   for (f = 0; f < Nf; ++f) {
1187     PetscFE  fe, feCh;
1188     PetscInt numQuadPoints, Nb;
1189     /* Conforming batches */
1190     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1191     /* Remainder */
1192     PetscInt Nr, offset;
1193 
1194     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1195     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1196     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1197     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1198     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1199     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1200     blockSize = Nb*numQuadPoints;
1201     batchSize = numBlocks * blockSize;
1202     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1203     numChunks = numCells / (numBatches*batchSize);
1204     Ne        = numChunks*numBatches*batchSize;
1205     Nr        = numCells % (numBatches*batchSize);
1206     offset    = numCells - Nr;
1207     geom.v0   = v0;
1208     geom.J    = J;
1209     geom.invJ = invJ;
1210     geom.detJ = detJ;
1211     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, geom, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
1212     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, geom, u, u_t, probAux, a, elemVecCh);CHKERRQ(ierr);
1213     geom.v0   = &v0[offset*dim];
1214     geom.J    = &J[offset*dim*dim];
1215     geom.invJ = &invJ[offset*dim*dim];
1216     geom.detJ = &detJ[offset];
1217     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, geom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);CHKERRQ(ierr);
1218     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, geom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVecCh[offset*totDim]);CHKERRQ(ierr);
1219   }
1220   for (c = cStart; c < cEnd; ++c) {
1221     PetscBool diff = PETSC_FALSE;
1222     PetscInt  d;
1223 
1224     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1225     if (diff) {
1226       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1227       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1228       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1229       ++diffCell;
1230     }
1231     if (diffCell > 9) break;
1232     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_VALUES);CHKERRQ(ierr);
1233   }
1234   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1235   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1236   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1237   PetscFunctionReturn(0);
1238 }
1239 
1240 #undef __FUNCT__
1241 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1242 /*@
1243   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1244 
1245   Input Parameters:
1246 + dm - The mesh
1247 . X  - Local solution
1248 - user - The user context
1249 
1250   Output Parameter:
1251 . F  - Local output vector
1252 
1253   Level: developer
1254 
1255 .seealso: DMPlexComputeJacobianActionFEM()
1256 @*/
1257 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1258 {
1259   PetscObject    check;
1260   PetscErrorCode ierr;
1261 
1262   PetscFunctionBegin;
1263   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", &check);CHKERRQ(ierr);
1264   if (check) {ierr = DMPlexComputeResidualFEM_Check(dm, X, NULL, F, user);CHKERRQ(ierr);}
1265   else       {ierr = DMPlexComputeResidualFEM_Internal(dm, X, NULL, F, user);CHKERRQ(ierr);}
1266   PetscFunctionReturn(0);
1267 }
1268 
1269 #undef __FUNCT__
1270 #define __FUNCT__ "DMPlexTSComputeIFunctionFEM"
1271 /*@
1272   DMPlexTSComputeIFunctionFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1273 
1274   Input Parameters:
1275 + dm - The mesh
1276 . t - The time
1277 . X  - Local solution
1278 . X_t - Local solution time derivative, or NULL
1279 - user - The user context
1280 
1281   Output Parameter:
1282 . F  - Local output vector
1283 
1284   Level: developer
1285 
1286 .seealso: DMPlexComputeJacobianActionFEM()
1287 @*/
1288 PetscErrorCode DMPlexTSComputeIFunctionFEM(DM dm, PetscReal time, Vec X, Vec X_t, Vec F, void *user)
1289 {
1290   PetscErrorCode ierr;
1291 
1292   PetscFunctionBegin;
1293   ierr = DMPlexComputeResidualFEM_Internal(dm, X, X_t, F, user);CHKERRQ(ierr);
1294   PetscFunctionReturn(0);
1295 }
1296 
1297 #undef __FUNCT__
1298 #define __FUNCT__ "DMPlexComputeJacobianFEM_Internal"
1299 PetscErrorCode DMPlexComputeJacobianFEM_Internal(DM dm, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
1300 {
1301   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1302   const char       *name  = "Jacobian";
1303   DM                dmAux;
1304   DMLabel           depth;
1305   Vec               A;
1306   PetscDS           prob, probAux = NULL;
1307   PetscQuadrature   quad;
1308   PetscCellGeometry geom;
1309   PetscSection      section, globalSection, sectionAux;
1310   PetscReal        *v0, *J, *invJ, *detJ;
1311   PetscScalar      *elemMat, *u, *u_t, *a = NULL;
1312   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1313   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
1314   PetscBool         isShell;
1315   PetscErrorCode    ierr;
1316 
1317   PetscFunctionBegin;
1318   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1319   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1320   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1321   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1322   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1323   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1324   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1325   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1326   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1327   numCells = cEnd - cStart;
1328   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1329   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1330   if (dmAux) {
1331     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1332     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1333     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1334   }
1335   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1336   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1337   ierr = PetscMalloc7(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*totDim*totDim,&elemMat);CHKERRQ(ierr);
1338   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1339   for (c = cStart; c < cEnd; ++c) {
1340     PetscScalar *x = NULL,  *x_t = NULL;
1341     PetscInt     i;
1342 
1343     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1344     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1345     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1346     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1347     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1348     if (X_t) {
1349       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1350       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1351       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1352     }
1353     if (dmAux) {
1354       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1355       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1356       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1357     }
1358   }
1359   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1360   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1361     PetscFE  fe;
1362     PetscInt numQuadPoints, Nb;
1363     /* Conforming batches */
1364     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1365     /* Remainder */
1366     PetscInt Nr, offset;
1367 
1368     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1369     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1370     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1371     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1372     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1373     blockSize = Nb*numQuadPoints;
1374     batchSize = numBlocks * blockSize;
1375     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1376     numChunks = numCells / (numBatches*batchSize);
1377     Ne        = numChunks*numBatches*batchSize;
1378     Nr        = numCells % (numBatches*batchSize);
1379     offset    = numCells - Nr;
1380     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1381       geom.v0   = v0;
1382       geom.J    = J;
1383       geom.invJ = invJ;
1384       geom.detJ = detJ;
1385       ierr = PetscFEIntegrateJacobian(fe, prob, fieldI, fieldJ, Ne, geom, u, u_t, probAux, a, elemMat);CHKERRQ(ierr);
1386       geom.v0   = &v0[offset*dim];
1387       geom.J    = &J[offset*dim*dim];
1388       geom.invJ = &invJ[offset*dim*dim];
1389       geom.detJ = &detJ[offset];
1390       ierr = PetscFEIntegrateJacobian(fe, prob, fieldI, fieldJ, Nr, geom, &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
1391     }
1392   }
1393   for (c = cStart; c < cEnd; ++c) {
1394     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[c*totDim*totDim]);CHKERRQ(ierr);}
1395     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
1396   }
1397   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1398   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1399   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1400   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1401   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1402   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1403   for (bd = 0; bd < numBd; ++bd) {
1404     const char     *bdLabel;
1405     DMLabel         label;
1406     IS              pointIS;
1407     const PetscInt *points;
1408     const PetscInt *values;
1409     PetscReal      *n;
1410     PetscInt        field, numValues, numPoints, p, dep, numFaces;
1411     PetscBool       isEssential;
1412 
1413     ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1414     if (isEssential) continue;
1415     if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1416     ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1417     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1418     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1419     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1420     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1421       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1422       if (dep == dim-1) ++numFaces;
1423     }
1424     ierr = PetscMalloc7(numFaces*totDimBd,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
1425     if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1426     for (p = 0, f = 0; p < numPoints; ++p) {
1427       const PetscInt point = points[p];
1428       PetscScalar   *x     = NULL;
1429       PetscInt       i;
1430 
1431       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1432       if (dep != dim-1) continue;
1433       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1434       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1435       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1436       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1437       for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1438       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1439       if (X_t) {
1440         ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1441         for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1442         ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1443       }
1444       ++f;
1445     }
1446     ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
1447     for (fieldI = 0; fieldI < Nf; ++fieldI) {
1448       PetscFE  fe;
1449       PetscInt numQuadPoints, Nb;
1450       /* Conforming batches */
1451       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1452       /* Remainder */
1453       PetscInt Nr, offset;
1454 
1455       ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1456       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1457       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1458       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1459       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1460       blockSize = Nb*numQuadPoints;
1461       batchSize = numBlocks * blockSize;
1462       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1463       numChunks = numFaces / (numBatches*batchSize);
1464       Ne        = numChunks*numBatches*batchSize;
1465       Nr        = numFaces % (numBatches*batchSize);
1466       offset    = numFaces - Nr;
1467       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1468         geom.v0   = v0;
1469         geom.n    = n;
1470         geom.J    = J;
1471         geom.invJ = invJ;
1472         geom.detJ = detJ;
1473         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, geom, u, u_t, NULL, NULL, elemMat);CHKERRQ(ierr);
1474         geom.v0   = &v0[offset*dim];
1475         geom.n    = &n[offset*dim];
1476         geom.J    = &J[offset*dim*dim];
1477         geom.invJ = &invJ[offset*dim*dim];
1478         geom.detJ = &detJ[offset];
1479         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, geom, &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemMat[offset*totDimBd*totDimBd]);CHKERRQ(ierr);
1480       }
1481     }
1482     for (p = 0, f = 0; p < numPoints; ++p) {
1483       const PetscInt point = points[p];
1484 
1485       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1486       if (dep != dim-1) continue;
1487       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
1488       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
1489       ++f;
1490     }
1491     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1492     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1493     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1494     if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1495   }
1496   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1497   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1498   if (mesh->printFEM) {
1499     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1500     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
1501     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1502   }
1503   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1504   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
1505   if (isShell) {
1506     JacActionCtx *jctx;
1507 
1508     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1509     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
1510   }
1511   PetscFunctionReturn(0);
1512 }
1513 
1514 #undef __FUNCT__
1515 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
1516 /*@
1517   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
1518 
1519   Input Parameters:
1520 + dm - The mesh
1521 . X  - Local input vector
1522 - user - The user context
1523 
1524   Output Parameter:
1525 . Jac  - Jacobian matrix
1526 
1527   Note:
1528   The first member of the user context must be an FEMContext.
1529 
1530   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1531   like a GPU, or vectorize on a multicore machine.
1532 
1533   Level: developer
1534 
1535 .seealso: FormFunctionLocal()
1536 @*/
1537 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1538 {
1539   PetscErrorCode ierr;
1540 
1541   PetscFunctionBegin;
1542   ierr = DMPlexComputeJacobianFEM_Internal(dm, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
1543   PetscFunctionReturn(0);
1544 }
1545 
1546 #undef __FUNCT__
1547 #define __FUNCT__ "DMPlexComputeInterpolatorFEM"
1548 /*@
1549   DMPlexComputeInterpolatorFEM - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1550 
1551   Input Parameters:
1552 + dmf  - The fine mesh
1553 . dmc  - The coarse mesh
1554 - user - The user context
1555 
1556   Output Parameter:
1557 . In  - The interpolation matrix
1558 
1559   Note:
1560   The first member of the user context must be an FEMContext.
1561 
1562   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1563   like a GPU, or vectorize on a multicore machine.
1564 
1565   Level: developer
1566 
1567 .seealso: DMPlexComputeJacobianFEM()
1568 @*/
1569 PetscErrorCode DMPlexComputeInterpolatorFEM(DM dmc, DM dmf, Mat In, void *user)
1570 {
1571   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1572   const char       *name  = "Interpolator";
1573   PetscDS           prob;
1574   PetscFE          *feRef;
1575   PetscSection      fsection, fglobalSection;
1576   PetscSection      csection, cglobalSection;
1577   PetscScalar      *elemMat;
1578   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, c;
1579   PetscInt          cTotDim, rTotDim = 0;
1580   PetscErrorCode    ierr;
1581 
1582   PetscFunctionBegin;
1583 #if 0
1584   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1585 #endif
1586   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1587   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1588   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1589   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1590   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1591   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1592   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1593   ierr = DMGetDS(dmf, &prob);CHKERRQ(ierr);
1594   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1595   for (f = 0; f < Nf; ++f) {
1596     PetscFE  fe;
1597     PetscInt rNb, Nc;
1598 
1599     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1600     ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
1601     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1602     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1603     rTotDim += rNb*Nc;
1604   }
1605   ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
1606   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1607   ierr = PetscMalloc1(rTotDim*cTotDim,&elemMat);CHKERRQ(ierr);
1608   ierr = PetscMemzero(elemMat, rTotDim*cTotDim * sizeof(PetscScalar));CHKERRQ(ierr);
1609   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1610     PetscDualSpace   Qref;
1611     PetscQuadrature  f;
1612     const PetscReal *qpoints, *qweights;
1613     PetscReal       *points;
1614     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1615 
1616     /* Compose points from all dual basis functionals */
1617     ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1618     ierr = PetscFEGetNumComponents(feRef[fieldI], &Nc);CHKERRQ(ierr);
1619     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1620     for (i = 0; i < fpdim; ++i) {
1621       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1622       ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1623       npoints += Np;
1624     }
1625     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1626     for (i = 0, k = 0; i < fpdim; ++i) {
1627       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1628       ierr = PetscQuadratureGetData(f, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1629       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1630     }
1631 
1632     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1633       PetscFE    fe;
1634       PetscReal *B;
1635       PetscInt   NcJ, cpdim, j;
1636 
1637       /* Evaluate basis at points */
1638       ierr = PetscDSGetDiscretization(prob, fieldJ, (PetscObject *) &fe);CHKERRQ(ierr);
1639       ierr = PetscFEGetNumComponents(fe, &NcJ);CHKERRQ(ierr);
1640       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);
1641       ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
1642       /* For now, fields only interpolate themselves */
1643       if (fieldI == fieldJ) {
1644         ierr = PetscFEGetTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1645         for (i = 0, k = 0; i < fpdim; ++i) {
1646           ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1647           ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, &qweights);CHKERRQ(ierr);
1648           for (p = 0; p < Np; ++p, ++k) {
1649             for (j = 0; j < cpdim; ++j) {
1650               for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cTotDim + offsetJ + j*NcJ + c] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p];
1651             }
1652           }
1653         }
1654         ierr = PetscFERestoreTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1655       }
1656       offsetJ += cpdim*NcJ;
1657     }
1658     offsetI += fpdim*Nc;
1659     ierr = PetscFree(points);CHKERRQ(ierr);
1660   }
1661   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rTotDim, cTotDim, elemMat);CHKERRQ(ierr);}
1662   for (c = cStart; c < cEnd; ++c) {
1663     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1664   }
1665   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1666   ierr = PetscFree(feRef);CHKERRQ(ierr);
1667   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1668   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1669   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1670   if (mesh->printFEM) {
1671     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1672     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1673     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1674   }
1675 #if 0
1676   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1677 #endif
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "BoundaryDuplicate"
1683 static PetscErrorCode BoundaryDuplicate(DMBoundary bd, DMBoundary *boundary)
1684 {
1685   DMBoundary     b = bd, b2, bold = NULL;
1686   PetscErrorCode ierr;
1687 
1688   PetscFunctionBegin;
1689   *boundary = NULL;
1690   for (; b; b = b->next, bold = b2) {
1691     ierr = PetscNew(&b2);CHKERRQ(ierr);
1692     ierr = PetscStrallocpy(b->name, (char **) &b2->name);CHKERRQ(ierr);
1693     ierr = PetscStrallocpy(b->labelname, (char **) &b2->labelname);CHKERRQ(ierr);
1694     ierr = PetscMalloc1(b->numids, &b2->ids);CHKERRQ(ierr);
1695     ierr = PetscMemcpy(b2->ids, b->ids, b->numids*sizeof(PetscInt));CHKERRQ(ierr);
1696     b2->label     = NULL;
1697     b2->essential = b->essential;
1698     b2->field     = b->field;
1699     b2->func      = b->func;
1700     b2->numids    = b->numids;
1701     b2->ctx       = b->ctx;
1702     b2->next      = NULL;
1703     if (!*boundary) *boundary   = b2;
1704     if (bold)        bold->next = b2;
1705   }
1706   PetscFunctionReturn(0);
1707 }
1708 
1709 #undef __FUNCT__
1710 #define __FUNCT__ "DMPlexCopyBoundary"
1711 PetscErrorCode DMPlexCopyBoundary(DM dm, DM dmNew)
1712 {
1713   DM_Plex       *mesh    = (DM_Plex *) dm->data;
1714   DM_Plex       *meshNew = (DM_Plex *) dmNew->data;
1715   DMBoundary     b;
1716   PetscErrorCode ierr;
1717 
1718   PetscFunctionBegin;
1719   ierr = BoundaryDuplicate(mesh->boundary, &meshNew->boundary);CHKERRQ(ierr);
1720   for (b = meshNew->boundary; b; b = b->next) {
1721     if (b->labelname) {
1722       ierr = DMPlexGetLabel(dmNew, b->labelname, &b->label);CHKERRQ(ierr);
1723       if (!b->label) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Label %s does not exist in this DM", b->labelname);
1724     }
1725   }
1726   PetscFunctionReturn(0);
1727 }
1728 
1729 #undef __FUNCT__
1730 #define __FUNCT__ "DMPlexAddBoundary"
1731 /* The ids can be overridden by the command line option -bc_<boundary name> */
1732 PetscErrorCode DMPlexAddBoundary(DM dm, PetscBool isEssential, const char name[], const char labelname[], PetscInt field, void (*bcFunc)(), PetscInt numids, const PetscInt *ids, void *ctx)
1733 {
1734   DM_Plex       *mesh = (DM_Plex *) dm->data;
1735   DMBoundary     b;
1736   PetscErrorCode ierr;
1737 
1738   PetscFunctionBegin;
1739   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1740   ierr = PetscNew(&b);CHKERRQ(ierr);
1741   ierr = PetscStrallocpy(name, (char **) &b->name);CHKERRQ(ierr);
1742   ierr = PetscStrallocpy(labelname, (char **) &b->labelname);CHKERRQ(ierr);
1743   ierr = PetscMalloc1(numids, &b->ids);CHKERRQ(ierr);
1744   ierr = PetscMemcpy(b->ids, ids, numids*sizeof(PetscInt));CHKERRQ(ierr);
1745   if (b->labelname) {
1746     ierr = DMPlexGetLabel(dm, b->labelname, &b->label);CHKERRQ(ierr);
1747     if (!b->label) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Label %s does not exist in this DM", b->labelname);
1748   }
1749   b->essential   = isEssential;
1750   b->field       = field;
1751   b->func        = bcFunc;
1752   b->numids      = numids;
1753   b->ctx         = ctx;
1754   b->next        = mesh->boundary;
1755   mesh->boundary = b;
1756   PetscFunctionReturn(0);
1757 }
1758 
1759 #undef __FUNCT__
1760 #define __FUNCT__ "DMPlexGetNumBoundary"
1761 PetscErrorCode DMPlexGetNumBoundary(DM dm, PetscInt *numBd)
1762 {
1763   DM_Plex   *mesh = (DM_Plex *) dm->data;
1764   DMBoundary b    = mesh->boundary;
1765 
1766   PetscFunctionBegin;
1767   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1768   PetscValidPointer(numBd, 2);
1769   *numBd = 0;
1770   while (b) {++(*numBd); b = b->next;}
1771   PetscFunctionReturn(0);
1772 }
1773 
1774 #undef __FUNCT__
1775 #define __FUNCT__ "DMPlexGetBoundary"
1776 PetscErrorCode DMPlexGetBoundary(DM dm, PetscInt bd, PetscBool *isEssential, const char **name, const char **labelname, PetscInt *field, void (**func)(), PetscInt *numids, const PetscInt **ids, void **ctx)
1777 {
1778   DM_Plex   *mesh = (DM_Plex *) dm->data;
1779   DMBoundary b    = mesh->boundary;
1780   PetscInt   n    = 0;
1781 
1782   PetscFunctionBegin;
1783   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1784   while (b) {
1785     if (n == bd) break;
1786     b = b->next;
1787     ++n;
1788   }
1789   if (n != bd) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %d is not in [0, %d)", bd, n);
1790   if (isEssential) {
1791     PetscValidPointer(isEssential, 3);
1792     *isEssential = b->essential;
1793   }
1794   if (name) {
1795     PetscValidPointer(name, 4);
1796     *name = b->name;
1797   }
1798   if (labelname) {
1799     PetscValidPointer(labelname, 5);
1800     *labelname = b->labelname;
1801   }
1802   if (field) {
1803     PetscValidPointer(field, 6);
1804     *field = b->field;
1805   }
1806   if (func) {
1807     PetscValidPointer(func, 7);
1808     *func = b->func;
1809   }
1810   if (numids) {
1811     PetscValidPointer(numids, 8);
1812     *numids = b->numids;
1813   }
1814   if (ids) {
1815     PetscValidPointer(ids, 9);
1816     *ids = b->ids;
1817   }
1818   if (ctx) {
1819     PetscValidPointer(ctx, 10);
1820     *ctx = b->ctx;
1821   }
1822   PetscFunctionReturn(0);
1823 }
1824 
1825 #undef __FUNCT__
1826 #define __FUNCT__ "DMPlexIsBoundaryPoint"
1827 PetscErrorCode DMPlexIsBoundaryPoint(DM dm, PetscInt point, PetscBool *isBd)
1828 {
1829   DM_Plex       *mesh = (DM_Plex *) dm->data;
1830   DMBoundary     b    = mesh->boundary;
1831   PetscErrorCode ierr;
1832 
1833   PetscFunctionBegin;
1834   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1835   PetscValidPointer(isBd, 3);
1836   *isBd = PETSC_FALSE;
1837   while (b && !(*isBd)) {
1838     if (b->label) {
1839       PetscInt i;
1840 
1841       for (i = 0; i < b->numids && !(*isBd); ++i) {
1842         ierr = DMLabelStratumHasPoint(b->label, b->ids[i], point, isBd);CHKERRQ(ierr);
1843       }
1844     }
1845     b = b->next;
1846   }
1847   PetscFunctionReturn(0);
1848 }
1849