xref: /petsc/src/dm/impls/plex/plexfem.c (revision 3113607c97fd174a48c1d34cfdefc0b7eeef3bd7)
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 PetscReal [], PetscScalar []), InsertMode mode, Vec localX)
351 {
352   DM                dmAux;
353   PetscProblem      prob, probAux;
354   Vec               A;
355   PetscSection      section, sectionAux;
356   PetscScalar      *values, *u, *gradU, *a, *gradA, *coefficients, *coefficientsAux;
357   PetscReal        *x, *v0, *J, *invJ, detJ, **basisField, **basisFieldDer, **basisFieldAux, **basisFieldDerAux;
358   PetscInt          Nf, NfAux, cOffset, cOffsetAux, dim, spDim, totDim, numValues, cStart, cEnd, c, f, d, v, comp;
359   PetscErrorCode    ierr;
360 
361   PetscFunctionBegin;
362   ierr = DMGetProblem(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 = PetscProblemGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
368   ierr = PetscProblemGetTabulation(prob, &basisField, &basisFieldDer);CHKERRQ(ierr);
369   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
370   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
371   if (dmAux) {
372     ierr = DMGetProblem(dmAux, &probAux);CHKERRQ(ierr);
373     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
374     ierr = PetscProblemGetTabulation(prob, &basisFieldAux, &basisFieldDerAux);CHKERRQ(ierr);
375     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
376   }
377   ierr = DMPlexInsertBoundaryValuesFEM(dm, localU);CHKERRQ(ierr);
378   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
379   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
380   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
381   ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
382   for (c = cStart; c < cEnd; ++c) {
383     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
384     for (f = 0, v = 0; f < Nf; ++f) {
385       PetscFE        fe;
386       PetscDualSpace sp;
387       PetscInt       Ncf;
388 
389       ierr = PetscProblemGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
390       ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
391       ierr = PetscFEGetNumComponents(fe, &Ncf);CHKERRQ(ierr);
392       ierr = PetscDualSpaceGetDimension(sp, &spDim);CHKERRQ(ierr);
393       for (d = 0; d < spDim; ++d) {
394         PetscQuadrature  quad;
395         const PetscReal *points, *weights;
396         PetscInt         numPoints, q;
397 
398         if (funcs[f]) {
399           ierr = PetscDualSpaceGetFunctional(sp, d, &quad);CHKERRQ(ierr);
400           ierr = PetscQuadratureGetData(quad, NULL, &numPoints, &points, &weights);CHKERRQ(ierr);
401           ierr = PetscFEGetTabulation(fe, numPoints, points, &basisField[f], &basisFieldDer[f], NULL);CHKERRQ(ierr);
402           for (q = 0; q < numPoints; ++q) {
403             CoordinatesRefToReal(dim, dim, v0, J, &points[q*dim], x);
404             ierr = EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, &coefficients[cOffset],       NULL, u, gradU, NULL);CHKERRQ(ierr);
405             ierr = EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, &coefficientsAux[cOffsetAux], NULL, a, gradA, NULL);CHKERRQ(ierr);
406             (*funcs[f])(u, gradU, a, gradA, x, &values[v]);
407           }
408           ierr = PetscFERestoreTabulation(fe, numPoints, points, &basisField[f], &basisFieldDer[f], NULL);CHKERRQ(ierr);
409         } else {
410           for (comp = 0; comp < Ncf; ++comp) values[v+comp] = 0.0;
411         }
412         v += Ncf;
413       }
414     }
415     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
416   }
417   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
418   ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
419   PetscFunctionReturn(0);
420 }
421 
422 #undef __FUNCT__
423 #define __FUNCT__ "DMPlexProjectField"
424 /*@C
425   DMPlexProjectField - This projects the given function of the fields into the function space provided.
426 
427   Input Parameters:
428 + dm      - The DM
429 . fe      - The PetscFE associated with the field
430 . U       - The input field vector
431 . funcs   - The functions to evaluate, one per field
432 - mode    - The insertion mode for values
433 
434   Output Parameter:
435 . X       - The output vector
436 
437   Level: developer
438 
439 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
440 @*/
441 PetscErrorCode DMPlexProjectField(DM dm, PetscFE fe[], PetscFE feAux[], Vec U, void (**funcs)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal [], PetscScalar []), InsertMode mode, Vec X)
442 {
443   Vec            localX, localU;
444   PetscErrorCode ierr;
445 
446   PetscFunctionBegin;
447   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
448   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
449   ierr = DMGetLocalVector(dm, &localU);CHKERRQ(ierr);
450   ierr = DMGlobalToLocalBegin(dm, U, INSERT_VALUES, localU);CHKERRQ(ierr);
451   ierr = DMGlobalToLocalEnd(dm, U, INSERT_VALUES, localU);CHKERRQ(ierr);
452   ierr = DMPlexProjectFieldLocal(dm, localU, funcs, mode, localX);CHKERRQ(ierr);
453   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
454   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
455   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
456   ierr = DMRestoreLocalVector(dm, &localU);CHKERRQ(ierr);
457   PetscFunctionReturn(0);
458 }
459 
460 #undef __FUNCT__
461 #define __FUNCT__ "DMPlexInsertBoundaryValuesFEM"
462 PetscErrorCode DMPlexInsertBoundaryValuesFEM(DM dm, Vec localX)
463 {
464   void        (**funcs)(const PetscReal x[], PetscScalar *u, void *ctx);
465   void         **ctxs;
466   PetscFE       *fe;
467   PetscInt       numFields, f, numBd, b;
468   PetscErrorCode ierr;
469 
470   PetscFunctionBegin;
471   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
472   PetscValidHeaderSpecific(localX, VEC_CLASSID, 2);
473   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
474   ierr = PetscMalloc3(numFields,&fe,numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
475   for (f = 0; f < numFields; ++f) {ierr = DMGetField(dm, f, (PetscObject *) &fe[f]);CHKERRQ(ierr);}
476   /* OPT: Could attempt to do multiple BCs at once */
477   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
478   for (b = 0; b < numBd; ++b) {
479     DMLabel         label;
480     const PetscInt *ids;
481     const char     *labelname;
482     PetscInt        numids, field;
483     PetscBool       isEssential;
484     void          (*func)();
485     void           *ctx;
486 
487     ierr = DMPlexGetBoundary(dm, b, &isEssential, NULL, &labelname, &field, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
488     ierr = DMPlexGetLabel(dm, labelname, &label);CHKERRQ(ierr);
489     for (f = 0; f < numFields; ++f) {
490       funcs[f] = field == f ? (void (*)(const PetscReal[], PetscScalar *, void *)) func : NULL;
491       ctxs[f]  = field == f ? ctx : NULL;
492     }
493     ierr = DMPlexProjectFunctionLabelLocal(dm, label, numids, ids, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
494   }
495   ierr = PetscFree3(fe,funcs,ctxs);CHKERRQ(ierr);
496   PetscFunctionReturn(0);
497 }
498 
499 #undef __FUNCT__
500 #define __FUNCT__ "DMPlexComputeL2Diff"
501 /*@C
502   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
503 
504   Input Parameters:
505 + dm    - The DM
506 . funcs - The functions to evaluate for each field component
507 . ctxs  - Optional array of contexts to pass to each function, or NULL.
508 - X     - The coefficient vector u_h
509 
510   Output Parameter:
511 . diff - The diff ||u - u_h||_2
512 
513   Level: developer
514 
515 .seealso: DMPlexProjectFunction(), DMPlexComputeL2GradientDiff()
516 @*/
517 PetscErrorCode DMPlexComputeL2Diff(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
518 {
519   const PetscInt  debug = 0;
520   PetscSection    section;
521   PetscQuadrature quad;
522   Vec             localX;
523   PetscScalar    *funcVal;
524   PetscReal      *coords, *v0, *J, *invJ, detJ;
525   PetscReal       localDiff = 0.0;
526   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
527   PetscErrorCode  ierr;
528 
529   PetscFunctionBegin;
530   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
531   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
532   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
533   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
534   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
535   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
536   for (field = 0; field < numFields; ++field) {
537     PetscFE  fe;
538     PetscInt Nc;
539 
540     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
541     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
542     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
543     numComponents += Nc;
544   }
545   ierr = DMPlexProjectFunctionLocal(dm, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
546   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
547   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
548   for (c = cStart; c < cEnd; ++c) {
549     PetscScalar *x = NULL;
550     PetscReal    elemDiff = 0.0;
551 
552     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
553     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
554     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
555 
556     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
557       PetscFE          fe;
558       void * const     ctx = ctxs ? ctxs[field] : NULL;
559       const PetscReal *quadPoints, *quadWeights;
560       PetscReal       *basis;
561       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
562 
563       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
564       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
565       ierr = PetscFEGetDimension(fe, &numBasisFuncs);CHKERRQ(ierr);
566       ierr = PetscFEGetNumComponents(fe, &numBasisComps);CHKERRQ(ierr);
567       ierr = PetscFEGetDefaultTabulation(fe, &basis, NULL, NULL);CHKERRQ(ierr);
568       if (debug) {
569         char title[1024];
570         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
571         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
572       }
573       for (q = 0; q < numQuadPoints; ++q) {
574         for (d = 0; d < dim; d++) {
575           coords[d] = v0[d];
576           for (e = 0; e < dim; e++) {
577             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
578           }
579         }
580         (*funcs[field])(coords, funcVal, ctx);
581         for (fc = 0; fc < numBasisComps; ++fc) {
582           PetscScalar interpolant = 0.0;
583 
584           for (f = 0; f < numBasisFuncs; ++f) {
585             const PetscInt fidx = f*numBasisComps+fc;
586             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
587           }
588           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);}
589           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
590         }
591       }
592       comp        += numBasisComps;
593       fieldOffset += numBasisFuncs*numBasisComps;
594     }
595     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
596     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
597     localDiff += elemDiff;
598   }
599   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
600   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
601   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
602   *diff = PetscSqrtReal(*diff);
603   PetscFunctionReturn(0);
604 }
605 
606 #undef __FUNCT__
607 #define __FUNCT__ "DMPlexComputeL2GradientDiff"
608 /*@C
609   DMPlexComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
610 
611   Input Parameters:
612 + dm    - The DM
613 . funcs - The gradient functions to evaluate for each field component
614 . ctxs  - Optional array of contexts to pass to each function, or NULL.
615 . X     - The coefficient vector u_h
616 - n     - The vector to project along
617 
618   Output Parameter:
619 . diff - The diff ||(grad u - grad u_h) . n||_2
620 
621   Level: developer
622 
623 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
624 @*/
625 PetscErrorCode DMPlexComputeL2GradientDiff(DM dm, void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
626 {
627   const PetscInt  debug = 0;
628   PetscSection    section;
629   PetscQuadrature quad;
630   Vec             localX;
631   PetscScalar    *funcVal, *interpolantVec;
632   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
633   PetscReal       localDiff = 0.0;
634   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
635   PetscErrorCode  ierr;
636 
637   PetscFunctionBegin;
638   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
639   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
640   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
641   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
642   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
643   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
644   for (field = 0; field < numFields; ++field) {
645     PetscFE  fe;
646     PetscInt Nc;
647 
648     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
649     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
650     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
651     numComponents += Nc;
652   }
653   /* ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
654   ierr = PetscMalloc7(numComponents,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
655   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
656   for (c = cStart; c < cEnd; ++c) {
657     PetscScalar *x = NULL;
658     PetscReal    elemDiff = 0.0;
659 
660     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
661     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
662     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
663 
664     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
665       PetscFE          fe;
666       void * const     ctx = ctxs ? ctxs[field] : NULL;
667       const PetscReal *quadPoints, *quadWeights;
668       PetscReal       *basisDer;
669       PetscInt         numQuadPoints, Nb, Ncomp, q, d, e, fc, f, g;
670 
671       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
672       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
673       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
674       ierr = PetscFEGetNumComponents(fe, &Ncomp);CHKERRQ(ierr);
675       ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
676       if (debug) {
677         char title[1024];
678         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
679         ierr = DMPrintCellVector(c, title, Nb*Ncomp, &x[fieldOffset]);CHKERRQ(ierr);
680       }
681       for (q = 0; q < numQuadPoints; ++q) {
682         for (d = 0; d < dim; d++) {
683           coords[d] = v0[d];
684           for (e = 0; e < dim; e++) {
685             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
686           }
687         }
688         (*funcs[field])(coords, n, funcVal, ctx);
689         for (fc = 0; fc < Ncomp; ++fc) {
690           PetscScalar interpolant = 0.0;
691 
692           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
693           for (f = 0; f < Nb; ++f) {
694             const PetscInt fidx = f*Ncomp+fc;
695 
696             for (d = 0; d < dim; ++d) {
697               realSpaceDer[d] = 0.0;
698               for (g = 0; g < dim; ++g) {
699                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+fidx)*dim+g];
700               }
701               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
702             }
703           }
704           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
705           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);}
706           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
707         }
708       }
709       comp        += Ncomp;
710       fieldOffset += Nb*Ncomp;
711     }
712     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
713     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
714     localDiff += elemDiff;
715   }
716   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
717   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
718   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
719   *diff = PetscSqrtReal(*diff);
720   PetscFunctionReturn(0);
721 }
722 
723 #undef __FUNCT__
724 #define __FUNCT__ "DMPlexComputeL2FieldDiff"
725 PetscErrorCode DMPlexComputeL2FieldDiff(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal diff[])
726 {
727   const PetscInt  debug = 0;
728   PetscSection    section;
729   PetscQuadrature quad;
730   Vec             localX;
731   PetscScalar    *funcVal;
732   PetscReal      *coords, *v0, *J, *invJ, detJ;
733   PetscReal      *localDiff;
734   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
735   PetscErrorCode  ierr;
736 
737   PetscFunctionBegin;
738   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
739   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
740   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
741   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
742   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
743   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
744   for (field = 0; field < numFields; ++field) {
745     PetscFE  fe;
746     PetscInt Nc;
747 
748     ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
749     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
750     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
751     numComponents += Nc;
752   }
753   ierr = DMPlexProjectFunctionLocal(dm, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
754   ierr = PetscCalloc6(numFields,&localDiff,numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
755   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
756   for (c = cStart; c < cEnd; ++c) {
757     PetscScalar *x = NULL;
758 
759     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
760     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
761     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
762 
763     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
764       PetscFE          fe;
765       void * const     ctx = ctxs ? ctxs[field] : NULL;
766       const PetscReal *quadPoints, *quadWeights;
767       PetscReal       *basis, elemDiff = 0.0;
768       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
769 
770       ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
771       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
772       ierr = PetscFEGetDimension(fe, &numBasisFuncs);CHKERRQ(ierr);
773       ierr = PetscFEGetNumComponents(fe, &numBasisComps);CHKERRQ(ierr);
774       ierr = PetscFEGetDefaultTabulation(fe, &basis, NULL, NULL);CHKERRQ(ierr);
775       if (debug) {
776         char title[1024];
777         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
778         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
779       }
780       for (q = 0; q < numQuadPoints; ++q) {
781         for (d = 0; d < dim; d++) {
782           coords[d] = v0[d];
783           for (e = 0; e < dim; e++) {
784             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
785           }
786         }
787         (*funcs[field])(coords, funcVal, ctx);
788         for (fc = 0; fc < numBasisComps; ++fc) {
789           PetscScalar interpolant = 0.0;
790 
791           for (f = 0; f < numBasisFuncs; ++f) {
792             const PetscInt fidx = f*numBasisComps+fc;
793             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
794           }
795           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);}
796           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
797         }
798       }
799       comp        += numBasisComps;
800       fieldOffset += numBasisFuncs*numBasisComps;
801       localDiff[field] += elemDiff;
802     }
803     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
804   }
805   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
806   ierr  = MPI_Allreduce(localDiff, diff, numFields, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
807   for (field = 0; field < numFields; ++field) diff[field] = PetscSqrtReal(diff[field]);
808   ierr  = PetscFree6(localDiff,funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
809   PetscFunctionReturn(0);
810 }
811 
812 #undef __FUNCT__
813 #define __FUNCT__ "DMPlexComputeIntegralFEM"
814 /*@
815   DMPlexComputeIntegralFEM - Form the local integral F from the local input X using pointwise functions specified by the user
816 
817   Input Parameters:
818 + dm - The mesh
819 . X  - Local input vector
820 - user - The user context
821 
822   Output Parameter:
823 . integral - Local integral for each field
824 
825   Level: developer
826 
827 .seealso: DMPlexComputeResidualFEM()
828 @*/
829 PetscErrorCode DMPlexComputeIntegralFEM(DM dm, Vec X, PetscReal *integral, void *user)
830 {
831   DM_Plex          *mesh  = (DM_Plex *) dm->data;
832   DM                dmAux;
833   Vec               localX, A;
834   PetscProblem      prob, probAux = NULL;
835   PetscQuadrature   q;
836   PetscCellGeometry geom;
837   PetscSection      section, sectionAux;
838   PetscReal        *v0, *J, *invJ, *detJ;
839   PetscScalar      *u, *a = NULL;
840   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
841   PetscInt          totDim, totDimAux;
842   PetscErrorCode    ierr;
843 
844   PetscFunctionBegin;
845   /*ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);*/
846   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
847   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
848   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
849   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
850   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
851   ierr = DMGetProblem(dm, &prob);CHKERRQ(ierr);
852   ierr = PetscProblemGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
853   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
854   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
855   numCells = cEnd - cStart;
856   for (f = 0; f < Nf; ++f) {integral[f]    = 0.0;}
857   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
858   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
859   if (dmAux) {
860     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
861     ierr = DMGetProblem(dmAux, &probAux);CHKERRQ(ierr);
862     ierr = PetscProblemGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
863   }
864   ierr = DMPlexInsertBoundaryValuesFEM(dm, localX);CHKERRQ(ierr);
865   ierr = PetscMalloc5(numCells*totDim,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ);CHKERRQ(ierr);
866   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
867   for (c = cStart; c < cEnd; ++c) {
868     PetscScalar *x = NULL;
869     PetscInt     i;
870 
871     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
872     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
873     ierr = DMPlexVecGetClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
874     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
875     ierr = DMPlexVecRestoreClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
876     if (dmAux) {
877       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
878       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
879       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
880     }
881   }
882   for (f = 0; f < Nf; ++f) {
883     PetscFE  fe;
884     PetscInt numQuadPoints, Nb;
885     /* Conforming batches */
886     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
887     /* Remainder */
888     PetscInt Nr, offset;
889 
890     ierr = PetscProblemGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
891     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
892     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
893     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
894     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
895     blockSize = Nb*numQuadPoints;
896     batchSize = numBlocks * blockSize;
897     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
898     numChunks = numCells / (numBatches*batchSize);
899     Ne        = numChunks*numBatches*batchSize;
900     Nr        = numCells % (numBatches*batchSize);
901     offset    = numCells - Nr;
902     geom.v0   = v0;
903     geom.J    = J;
904     geom.invJ = invJ;
905     geom.detJ = detJ;
906     ierr = PetscFEIntegrate(fe, prob, f, Ne, geom, u, probAux, a, integral);CHKERRQ(ierr);
907     geom.v0   = &v0[offset*dim];
908     geom.J    = &J[offset*dim*dim];
909     geom.invJ = &invJ[offset*dim*dim];
910     geom.detJ = &detJ[offset];
911     ierr = PetscFEIntegrate(fe, prob, f, Nr, geom, &u[offset*totDim], probAux, &a[offset*totDimAux], integral);CHKERRQ(ierr);
912   }
913   ierr = PetscFree5(u,v0,J,invJ,detJ);CHKERRQ(ierr);
914   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
915   if (mesh->printFEM) {
916     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Local integral:");CHKERRQ(ierr);
917     for (f = 0; f < Nf; ++f) {ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), " %g", integral[f]);CHKERRQ(ierr);}
918     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "\n");CHKERRQ(ierr);
919   }
920   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
921   /* TODO: Allreduce for integral */
922   /*ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);*/
923   PetscFunctionReturn(0);
924 }
925 
926 #undef __FUNCT__
927 #define __FUNCT__ "DMPlexComputeResidualFEM_Internal"
928 PetscErrorCode DMPlexComputeResidualFEM_Internal(DM dm, Vec X, Vec X_t, Vec F, void *user)
929 {
930   DM_Plex          *mesh  = (DM_Plex *) dm->data;
931   const char       *name  = "Residual";
932   DM                dmAux;
933   DMLabel           depth;
934   Vec               A;
935   PetscProblem      prob, probAux = NULL;
936   PetscQuadrature   q;
937   PetscCellGeometry geom;
938   PetscSection      section, sectionAux;
939   PetscReal        *v0, *J, *invJ, *detJ;
940   PetscScalar      *elemVec, *u, *u_t, *a = NULL;
941   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c, numBd, bd;
942   PetscInt          totDim, totDimBd, totDimAux;
943   PetscErrorCode    ierr;
944 
945   PetscFunctionBegin;
946   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
947   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
948   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
949   ierr = DMGetProblem(dm, &prob);CHKERRQ(ierr);
950   ierr = PetscProblemGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
951   ierr = PetscProblemGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
952   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
953   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
954   numCells = cEnd - cStart;
955   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
956   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
957   if (dmAux) {
958     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
959     ierr = DMGetProblem(dmAux, &probAux);CHKERRQ(ierr);
960     ierr = PetscProblemGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
961   }
962   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
963   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
964   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);
965   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
966   for (c = cStart; c < cEnd; ++c) {
967     PetscScalar *x = NULL, *x_t = NULL;
968     PetscInt     i;
969 
970     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
971     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
972     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
973     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
974     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
975     if (X_t) {
976       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
977       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
978       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
979     }
980     if (dmAux) {
981       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
982       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
983       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
984     }
985   }
986   for (f = 0; f < Nf; ++f) {
987     PetscFE  fe;
988     PetscInt numQuadPoints, Nb;
989     /* Conforming batches */
990     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
991     /* Remainder */
992     PetscInt Nr, offset;
993 
994     ierr = PetscProblemGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
995     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
996     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
997     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
998     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
999     blockSize = Nb*numQuadPoints;
1000     batchSize = numBlocks * blockSize;
1001     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1002     numChunks = numCells / (numBatches*batchSize);
1003     Ne        = numChunks*numBatches*batchSize;
1004     Nr        = numCells % (numBatches*batchSize);
1005     offset    = numCells - Nr;
1006     geom.v0   = v0;
1007     geom.J    = J;
1008     geom.invJ = invJ;
1009     geom.detJ = detJ;
1010     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, geom, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
1011     geom.v0   = &v0[offset*dim];
1012     geom.J    = &J[offset*dim*dim];
1013     geom.invJ = &invJ[offset*dim*dim];
1014     geom.detJ = &detJ[offset];
1015     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);
1016   }
1017   for (c = cStart; c < cEnd; ++c) {
1018     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, totDim, &elemVec[c*totDim]);CHKERRQ(ierr);}
1019     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_VALUES);CHKERRQ(ierr);
1020   }
1021   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1022   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1023   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1024   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1025   for (bd = 0; bd < numBd; ++bd) {
1026     const char     *bdLabel;
1027     DMLabel         label;
1028     IS              pointIS;
1029     const PetscInt *points;
1030     const PetscInt *values;
1031     PetscReal      *n;
1032     PetscInt        field, numValues, numPoints, p, dep, numFaces;
1033     PetscBool       isEssential;
1034 
1035     ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1036     if (isEssential) continue;
1037     if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1038     ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1039     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1040     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1041     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1042     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1043       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1044       if (dep == dim-1) ++numFaces;
1045     }
1046     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);
1047     if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1048     for (p = 0, f = 0; p < numPoints; ++p) {
1049       const PetscInt point = points[p];
1050       PetscScalar   *x     = NULL;
1051       PetscInt       i;
1052 
1053       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1054       if (dep != dim-1) continue;
1055       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1056       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1057       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1058       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1059       for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1060       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1061       if (X_t) {
1062         ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1063         for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1064         ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1065       }
1066       ++f;
1067     }
1068     for (f = 0; f < Nf; ++f) {
1069       PetscFE  fe;
1070       PetscInt numQuadPoints, Nb;
1071       /* Conforming batches */
1072       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1073       /* Remainder */
1074       PetscInt Nr, offset;
1075 
1076       ierr = PetscProblemGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1077       ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1078       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1079       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1080       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1081       blockSize = Nb*numQuadPoints;
1082       batchSize = numBlocks * blockSize;
1083       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1084       numChunks = numFaces / (numBatches*batchSize);
1085       Ne        = numChunks*numBatches*batchSize;
1086       Nr        = numFaces % (numBatches*batchSize);
1087       offset    = numFaces - Nr;
1088       geom.v0   = v0;
1089       geom.n    = n;
1090       geom.J    = J;
1091       geom.invJ = invJ;
1092       geom.detJ = detJ;
1093       ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, geom, u, u_t, NULL, NULL, elemVec);CHKERRQ(ierr);
1094       geom.v0   = &v0[offset*dim];
1095       geom.n    = &n[offset*dim];
1096       geom.J    = &J[offset*dim*dim];
1097       geom.invJ = &invJ[offset*dim*dim];
1098       geom.detJ = &detJ[offset];
1099       ierr = PetscFEIntegrateBdResidual(fe, prob, f, Nr, geom, &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1100     }
1101     for (p = 0, f = 0; p < numPoints; ++p) {
1102       const PetscInt point = points[p];
1103 
1104       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1105       if (dep != dim-1) continue;
1106       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1107       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*totDimBd], ADD_VALUES);CHKERRQ(ierr);
1108       ++f;
1109     }
1110     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1111     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1112     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1113     if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1114   }
1115   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1116   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1117   PetscFunctionReturn(0);
1118 }
1119 
1120 #undef __FUNCT__
1121 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1122 /*@
1123   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1124 
1125   Input Parameters:
1126 + dm - The mesh
1127 . X  - Local solution
1128 - user - The user context
1129 
1130   Output Parameter:
1131 . F  - Local output vector
1132 
1133   Level: developer
1134 
1135 .seealso: DMPlexComputeJacobianActionFEM()
1136 @*/
1137 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1138 {
1139   PetscErrorCode ierr;
1140 
1141   PetscFunctionBegin;
1142   ierr = DMPlexComputeResidualFEM_Internal(dm, X, NULL, F, user);CHKERRQ(ierr);
1143   PetscFunctionReturn(0);
1144 }
1145 
1146 #undef __FUNCT__
1147 #define __FUNCT__ "DMPlexTSComputeIFunctionFEM"
1148 /*@
1149   DMPlexTSComputeIFunctionFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1150 
1151   Input Parameters:
1152 + dm - The mesh
1153 . t - The time
1154 . X  - Local solution
1155 . X_t - Local solution time derivative, or NULL
1156 - user - The user context
1157 
1158   Output Parameter:
1159 . F  - Local output vector
1160 
1161   Level: developer
1162 
1163 .seealso: DMPlexComputeJacobianActionFEM()
1164 @*/
1165 PetscErrorCode DMPlexTSComputeIFunctionFEM(DM dm, PetscReal time, Vec X, Vec X_t, Vec F, void *user)
1166 {
1167   PetscErrorCode ierr;
1168 
1169   PetscFunctionBegin;
1170   ierr = DMPlexComputeResidualFEM_Internal(dm, X, X_t, F, user);CHKERRQ(ierr);
1171   PetscFunctionReturn(0);
1172 }
1173 
1174 #undef __FUNCT__
1175 #define __FUNCT__ "DMPlexComputeJacobianFEM_Internal"
1176 PetscErrorCode DMPlexComputeJacobianFEM_Internal(DM dm, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
1177 {
1178   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1179   const char       *name  = "Jacobian";
1180   DM                dmAux;
1181   DMLabel           depth;
1182   Vec               A;
1183   PetscProblem      prob, probAux = NULL;
1184   PetscQuadrature   quad;
1185   PetscCellGeometry geom;
1186   PetscSection      section, globalSection, sectionAux;
1187   PetscReal        *v0, *J, *invJ, *detJ;
1188   PetscScalar      *elemMat, *u, *u_t, *a = NULL;
1189   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1190   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
1191   PetscBool         isShell;
1192   PetscErrorCode    ierr;
1193 
1194   PetscFunctionBegin;
1195   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1196   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1197   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1198   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1199   ierr = DMGetProblem(dm, &prob);CHKERRQ(ierr);
1200   ierr = PetscProblemGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1201   ierr = PetscProblemGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1202   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1203   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1204   numCells = cEnd - cStart;
1205   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1206   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1207   if (dmAux) {
1208     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1209     ierr = DMGetProblem(dmAux, &probAux);CHKERRQ(ierr);
1210     ierr = PetscProblemGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1211   }
1212   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1213   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1214   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);
1215   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1216   for (c = cStart; c < cEnd; ++c) {
1217     PetscScalar *x = NULL,  *x_t = NULL;
1218     PetscInt     i;
1219 
1220     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1221     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1222     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1223     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1224     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1225     if (X_t) {
1226       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1227       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1228       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1229     }
1230     if (dmAux) {
1231       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1232       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1233       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1234     }
1235   }
1236   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1237   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1238     PetscFE  fe;
1239     PetscInt numQuadPoints, Nb;
1240     /* Conforming batches */
1241     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1242     /* Remainder */
1243     PetscInt Nr, offset;
1244 
1245     ierr = PetscProblemGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1246     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1247     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1248     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1249     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1250     blockSize = Nb*numQuadPoints;
1251     batchSize = numBlocks * blockSize;
1252     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1253     numChunks = numCells / (numBatches*batchSize);
1254     Ne        = numChunks*numBatches*batchSize;
1255     Nr        = numCells % (numBatches*batchSize);
1256     offset    = numCells - Nr;
1257     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1258       geom.v0   = v0;
1259       geom.J    = J;
1260       geom.invJ = invJ;
1261       geom.detJ = detJ;
1262       ierr = PetscFEIntegrateJacobian(fe, prob, fieldI, fieldJ, Ne, geom, u, u_t, probAux, a, elemMat);CHKERRQ(ierr);
1263       geom.v0   = &v0[offset*dim];
1264       geom.J    = &J[offset*dim*dim];
1265       geom.invJ = &invJ[offset*dim*dim];
1266       geom.detJ = &detJ[offset];
1267       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);
1268     }
1269   }
1270   for (c = cStart; c < cEnd; ++c) {
1271     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[c*totDim*totDim]);CHKERRQ(ierr);}
1272     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
1273   }
1274   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1275   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1276   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1277   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1278   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1279   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1280   for (bd = 0; bd < numBd; ++bd) {
1281     const char     *bdLabel;
1282     DMLabel         label;
1283     IS              pointIS;
1284     const PetscInt *points;
1285     const PetscInt *values;
1286     PetscReal      *n;
1287     PetscInt        field, numValues, numPoints, p, dep, numFaces;
1288     PetscBool       isEssential;
1289 
1290     ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1291     if (isEssential) continue;
1292     if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1293     ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1294     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1295     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1296     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1297     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1298       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1299       if (dep == dim-1) ++numFaces;
1300     }
1301     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);
1302     if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1303     for (p = 0, f = 0; p < numPoints; ++p) {
1304       const PetscInt point = points[p];
1305       PetscScalar   *x     = NULL;
1306       PetscInt       i;
1307 
1308       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1309       if (dep != dim-1) continue;
1310       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1311       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1312       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1313       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1314       for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1315       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1316       if (X_t) {
1317         ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1318         for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1319         ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1320       }
1321       ++f;
1322     }
1323     ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
1324     for (fieldI = 0; fieldI < Nf; ++fieldI) {
1325       PetscFE  fe;
1326       PetscInt numQuadPoints, Nb;
1327       /* Conforming batches */
1328       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1329       /* Remainder */
1330       PetscInt Nr, offset;
1331 
1332       ierr = PetscProblemGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
1333       ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1334       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1335       ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1336       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1337       blockSize = Nb*numQuadPoints;
1338       batchSize = numBlocks * blockSize;
1339       ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1340       numChunks = numFaces / (numBatches*batchSize);
1341       Ne        = numChunks*numBatches*batchSize;
1342       Nr        = numFaces % (numBatches*batchSize);
1343       offset    = numFaces - Nr;
1344       for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1345         geom.v0   = v0;
1346         geom.n    = n;
1347         geom.J    = J;
1348         geom.invJ = invJ;
1349         geom.detJ = detJ;
1350         ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, geom, u, u_t, NULL, NULL, elemMat);CHKERRQ(ierr);
1351         geom.v0   = &v0[offset*dim];
1352         geom.n    = &n[offset*dim];
1353         geom.J    = &J[offset*dim*dim];
1354         geom.invJ = &invJ[offset*dim*dim];
1355         geom.detJ = &detJ[offset];
1356         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);
1357       }
1358     }
1359     for (p = 0, f = 0; p < numPoints; ++p) {
1360       const PetscInt point = points[p];
1361 
1362       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1363       if (dep != dim-1) continue;
1364       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
1365       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
1366       ++f;
1367     }
1368     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1369     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1370     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1371     if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1372   }
1373   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1374   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1375   if (mesh->printFEM) {
1376     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1377     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
1378     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1379   }
1380   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1381   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
1382   if (isShell) {
1383     JacActionCtx *jctx;
1384 
1385     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1386     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
1387   }
1388   PetscFunctionReturn(0);
1389 }
1390 
1391 #undef __FUNCT__
1392 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
1393 /*@
1394   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
1395 
1396   Input Parameters:
1397 + dm - The mesh
1398 . X  - Local input vector
1399 - user - The user context
1400 
1401   Output Parameter:
1402 . Jac  - Jacobian matrix
1403 
1404   Note:
1405   The first member of the user context must be an FEMContext.
1406 
1407   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1408   like a GPU, or vectorize on a multicore machine.
1409 
1410   Level: developer
1411 
1412 .seealso: FormFunctionLocal()
1413 @*/
1414 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1415 {
1416   PetscErrorCode ierr;
1417 
1418   PetscFunctionBegin;
1419   ierr = DMPlexComputeJacobianFEM_Internal(dm, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
1420   PetscFunctionReturn(0);
1421 }
1422 
1423 #undef __FUNCT__
1424 #define __FUNCT__ "DMPlexComputeInterpolatorFEM"
1425 /*@
1426   DMPlexComputeInterpolatorFEM - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1427 
1428   Input Parameters:
1429 + dmf  - The fine mesh
1430 . dmc  - The coarse mesh
1431 - user - The user context
1432 
1433   Output Parameter:
1434 . In  - The interpolation matrix
1435 
1436   Note:
1437   The first member of the user context must be an FEMContext.
1438 
1439   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1440   like a GPU, or vectorize on a multicore machine.
1441 
1442   Level: developer
1443 
1444 .seealso: DMPlexComputeJacobianFEM()
1445 @*/
1446 PetscErrorCode DMPlexComputeInterpolatorFEM(DM dmc, DM dmf, Mat In, void *user)
1447 {
1448   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1449   const char       *name  = "Interpolator";
1450   PetscProblem      prob;
1451   PetscFE          *feRef;
1452   PetscSection      fsection, fglobalSection;
1453   PetscSection      csection, cglobalSection;
1454   PetscScalar      *elemMat;
1455   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, c;
1456   PetscInt          cTotDim, rTotDim = 0;
1457   PetscErrorCode    ierr;
1458 
1459   PetscFunctionBegin;
1460 #if 0
1461   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1462 #endif
1463   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1464   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1465   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1466   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1467   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1468   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1469   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1470   ierr = DMGetProblem(dmf, &prob);CHKERRQ(ierr);
1471   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1472   for (f = 0; f < Nf; ++f) {
1473     PetscFE  fe;
1474     PetscInt rNb, Nc;
1475 
1476     ierr = PetscProblemGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1477     ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
1478     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1479     ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1480     rTotDim += rNb*Nc;
1481   }
1482   ierr = PetscProblemGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
1483   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1484   ierr = PetscMalloc1(rTotDim*cTotDim,&elemMat);CHKERRQ(ierr);
1485   ierr = PetscMemzero(elemMat, rTotDim*cTotDim * sizeof(PetscScalar));CHKERRQ(ierr);
1486   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1487     PetscDualSpace   Qref;
1488     PetscQuadrature  f;
1489     const PetscReal *qpoints, *qweights;
1490     PetscReal       *points;
1491     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1492 
1493     /* Compose points from all dual basis functionals */
1494     ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1495     ierr = PetscFEGetNumComponents(feRef[fieldI], &Nc);CHKERRQ(ierr);
1496     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1497     for (i = 0; i < fpdim; ++i) {
1498       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1499       ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1500       npoints += Np;
1501     }
1502     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1503     for (i = 0, k = 0; i < fpdim; ++i) {
1504       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1505       ierr = PetscQuadratureGetData(f, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1506       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1507     }
1508 
1509     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1510       PetscFE    fe;
1511       PetscReal *B;
1512       PetscInt   NcJ, cpdim, j;
1513 
1514       /* Evaluate basis at points */
1515       ierr = PetscProblemGetDiscretization(prob, fieldJ, (PetscObject *) &fe);CHKERRQ(ierr);
1516       ierr = PetscFEGetNumComponents(fe, &NcJ);CHKERRQ(ierr);
1517       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);
1518       ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
1519       /* For now, fields only interpolate themselves */
1520       if (fieldI == fieldJ) {
1521         ierr = PetscFEGetTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1522         for (i = 0, k = 0; i < fpdim; ++i) {
1523           ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1524           ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, &qweights);CHKERRQ(ierr);
1525           for (p = 0; p < Np; ++p, ++k) {
1526             for (j = 0; j < cpdim; ++j) {
1527               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];
1528             }
1529           }
1530         }
1531         ierr = PetscFERestoreTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1532       }
1533       offsetJ += cpdim*NcJ;
1534     }
1535     offsetI += fpdim*Nc;
1536     ierr = PetscFree(points);CHKERRQ(ierr);
1537   }
1538   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rTotDim, cTotDim, elemMat);CHKERRQ(ierr);}
1539   for (c = cStart; c < cEnd; ++c) {
1540     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1541   }
1542   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1543   ierr = PetscFree(feRef);CHKERRQ(ierr);
1544   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1545   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1546   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1547   if (mesh->printFEM) {
1548     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1549     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1550     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1551   }
1552 #if 0
1553   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1554 #endif
1555   PetscFunctionReturn(0);
1556 }
1557 
1558 #undef __FUNCT__
1559 #define __FUNCT__ "BoundaryDuplicate"
1560 static PetscErrorCode BoundaryDuplicate(DMBoundary bd, DMBoundary *boundary)
1561 {
1562   DMBoundary     b = bd, b2, bold = NULL;
1563   PetscErrorCode ierr;
1564 
1565   PetscFunctionBegin;
1566   *boundary = NULL;
1567   for (; b; b = b->next, bold = b2) {
1568     ierr = PetscNew(&b2);CHKERRQ(ierr);
1569     ierr = PetscStrallocpy(b->name, (char **) &b2->name);CHKERRQ(ierr);
1570     ierr = PetscStrallocpy(b->labelname, (char **) &b2->labelname);CHKERRQ(ierr);
1571     ierr = PetscMalloc1(b->numids, &b2->ids);CHKERRQ(ierr);
1572     ierr = PetscMemcpy(b2->ids, b->ids, b->numids*sizeof(PetscInt));CHKERRQ(ierr);
1573     b2->label     = NULL;
1574     b2->essential = b->essential;
1575     b2->field     = b->field;
1576     b2->func      = b->func;
1577     b2->numids    = b->numids;
1578     b2->ctx       = b->ctx;
1579     b2->next      = NULL;
1580     if (!*boundary) *boundary   = b2;
1581     if (bold)        bold->next = b2;
1582   }
1583   PetscFunctionReturn(0);
1584 }
1585 
1586 #undef __FUNCT__
1587 #define __FUNCT__ "DMPlexCopyBoundary"
1588 PetscErrorCode DMPlexCopyBoundary(DM dm, DM dmNew)
1589 {
1590   DM_Plex       *mesh    = (DM_Plex *) dm->data;
1591   DM_Plex       *meshNew = (DM_Plex *) dmNew->data;
1592   DMBoundary     b;
1593   PetscErrorCode ierr;
1594 
1595   PetscFunctionBegin;
1596   ierr = BoundaryDuplicate(mesh->boundary, &meshNew->boundary);CHKERRQ(ierr);
1597   for (b = meshNew->boundary; b; b = b->next) {
1598     if (b->labelname) {
1599       ierr = DMPlexGetLabel(dmNew, b->labelname, &b->label);CHKERRQ(ierr);
1600       if (!b->label) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Label %s does not exist in this DM", b->labelname);
1601     }
1602   }
1603   PetscFunctionReturn(0);
1604 }
1605 
1606 #undef __FUNCT__
1607 #define __FUNCT__ "DMPlexAddBoundary"
1608 /* The ids can be overridden by the command line option -bc_<boundary name> */
1609 PetscErrorCode DMPlexAddBoundary(DM dm, PetscBool isEssential, const char name[], const char labelname[], PetscInt field, void (*bcFunc)(), PetscInt numids, const PetscInt *ids, void *ctx)
1610 {
1611   DM_Plex       *mesh = (DM_Plex *) dm->data;
1612   DMBoundary     b;
1613   PetscErrorCode ierr;
1614 
1615   PetscFunctionBegin;
1616   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1617   ierr = PetscNew(&b);CHKERRQ(ierr);
1618   ierr = PetscStrallocpy(name, (char **) &b->name);CHKERRQ(ierr);
1619   ierr = PetscStrallocpy(labelname, (char **) &b->labelname);CHKERRQ(ierr);
1620   ierr = PetscMalloc1(numids, &b->ids);CHKERRQ(ierr);
1621   ierr = PetscMemcpy(b->ids, ids, numids*sizeof(PetscInt));CHKERRQ(ierr);
1622   if (b->labelname) {
1623     ierr = DMPlexGetLabel(dm, b->labelname, &b->label);CHKERRQ(ierr);
1624     if (!b->label) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Label %s does not exist in this DM", b->labelname);
1625   }
1626   b->essential   = isEssential;
1627   b->field       = field;
1628   b->func        = bcFunc;
1629   b->numids      = numids;
1630   b->ctx         = ctx;
1631   b->next        = mesh->boundary;
1632   mesh->boundary = b;
1633   PetscFunctionReturn(0);
1634 }
1635 
1636 #undef __FUNCT__
1637 #define __FUNCT__ "DMPlexGetNumBoundary"
1638 PetscErrorCode DMPlexGetNumBoundary(DM dm, PetscInt *numBd)
1639 {
1640   DM_Plex   *mesh = (DM_Plex *) dm->data;
1641   DMBoundary b    = mesh->boundary;
1642 
1643   PetscFunctionBegin;
1644   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1645   PetscValidPointer(numBd, 2);
1646   *numBd = 0;
1647   while (b) {++(*numBd); b = b->next;}
1648   PetscFunctionReturn(0);
1649 }
1650 
1651 #undef __FUNCT__
1652 #define __FUNCT__ "DMPlexGetBoundary"
1653 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)
1654 {
1655   DM_Plex   *mesh = (DM_Plex *) dm->data;
1656   DMBoundary b    = mesh->boundary;
1657   PetscInt   n    = 0;
1658 
1659   PetscFunctionBegin;
1660   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1661   while (b) {
1662     if (n == bd) break;
1663     b = b->next;
1664     ++n;
1665   }
1666   if (n != bd) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %d is not in [0, %d)", bd, n);
1667   if (isEssential) {
1668     PetscValidPointer(isEssential, 3);
1669     *isEssential = b->essential;
1670   }
1671   if (name) {
1672     PetscValidPointer(name, 4);
1673     *name = b->name;
1674   }
1675   if (labelname) {
1676     PetscValidPointer(labelname, 5);
1677     *labelname = b->labelname;
1678   }
1679   if (field) {
1680     PetscValidPointer(field, 6);
1681     *field = b->field;
1682   }
1683   if (func) {
1684     PetscValidPointer(func, 7);
1685     *func = b->func;
1686   }
1687   if (numids) {
1688     PetscValidPointer(numids, 8);
1689     *numids = b->numids;
1690   }
1691   if (ids) {
1692     PetscValidPointer(ids, 9);
1693     *ids = b->ids;
1694   }
1695   if (ctx) {
1696     PetscValidPointer(ctx, 10);
1697     *ctx = b->ctx;
1698   }
1699   PetscFunctionReturn(0);
1700 }
1701 
1702 #undef __FUNCT__
1703 #define __FUNCT__ "DMPlexIsBoundaryPoint"
1704 PetscErrorCode DMPlexIsBoundaryPoint(DM dm, PetscInt point, PetscBool *isBd)
1705 {
1706   DM_Plex       *mesh = (DM_Plex *) dm->data;
1707   DMBoundary     b    = mesh->boundary;
1708   PetscErrorCode ierr;
1709 
1710   PetscFunctionBegin;
1711   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1712   PetscValidPointer(isBd, 3);
1713   *isBd = PETSC_FALSE;
1714   while (b && !(*isBd)) {
1715     if (b->label) {
1716       PetscInt i;
1717 
1718       for (i = 0; i < b->numids && !(*isBd); ++i) {
1719         ierr = DMLabelStratumHasPoint(b->label, b->ids[i], point, isBd);CHKERRQ(ierr);
1720       }
1721     }
1722     b = b->next;
1723   }
1724   PetscFunctionReturn(0);
1725 }
1726