xref: /petsc/src/dm/impls/plex/plexfem.c (revision 0225b034c86b0edb3f72a5595b25f4568e6aee07)
1 #include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #include <petscfe.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   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, f, d, v, i, comp;
193   PetscErrorCode  ierr;
194 
195   PetscFunctionBegin;
196   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
197   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
198   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
199   ierr = PetscMalloc3(numFields,&sp,dim,&v0,dim*dim,&J);CHKERRQ(ierr);
200   for (f = 0; f < numFields; ++f) {
201     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
202     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
203     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
204     totDim += spDim*numComp;
205   }
206   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
207   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
208   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
209   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
210   for (i = 0; i < numIds; ++i) {
211     IS              pointIS;
212     const PetscInt *points;
213     PetscInt        n, p;
214 
215     ierr = DMLabelGetStratumIS(label, ids[i], &pointIS);CHKERRQ(ierr);
216     ierr = ISGetLocalSize(pointIS, &n);CHKERRQ(ierr);
217     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
218     for (p = 0; p < n; ++p) {
219       const PetscInt    point = points[p];
220       PetscCellGeometry geom;
221 
222       if ((point < cStart) || (point >= cEnd)) continue;
223       ierr = DMPlexComputeCellGeometry(dm, point, v0, J, NULL, &detJ);CHKERRQ(ierr);
224       geom.v0   = v0;
225       geom.J    = J;
226       geom.detJ = &detJ;
227       for (f = 0, v = 0; f < numFields; ++f) {
228         void * const ctx = ctxs ? ctxs[f] : NULL;
229         ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
230         ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
231         for (d = 0; d < spDim; ++d) {
232           if (funcs[f]) {
233             ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
234           } else {
235             for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
236           }
237           v += numComp;
238         }
239       }
240       ierr = DMPlexVecSetClosure(dm, section, localX, point, values, mode);CHKERRQ(ierr);
241     }
242     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
243     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
244   }
245   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
246   ierr = PetscFree3(sp,v0,J);CHKERRQ(ierr);
247   PetscFunctionReturn(0);
248 }
249 
250 #undef __FUNCT__
251 #define __FUNCT__ "DMPlexProjectFunctionLocal"
252 PetscErrorCode DMPlexProjectFunctionLocal(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
253 {
254   PetscDualSpace *sp;
255   PetscSection    section;
256   PetscScalar    *values;
257   PetscReal      *v0, *J, detJ;
258   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, c, f, d, v, comp;
259   PetscErrorCode  ierr;
260 
261   PetscFunctionBegin;
262   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
263   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
264   ierr = PetscMalloc1(numFields, &sp);CHKERRQ(ierr);
265   for (f = 0; f < numFields; ++f) {
266     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
267     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
268     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
269     totDim += spDim*numComp;
270   }
271   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
272   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
273   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
274   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
275   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
276   ierr = PetscMalloc2(dim,&v0,dim*dim,&J);CHKERRQ(ierr);
277   for (c = cStart; c < cEnd; ++c) {
278     PetscCellGeometry geom;
279 
280     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
281     geom.v0   = v0;
282     geom.J    = J;
283     geom.detJ = &detJ;
284     for (f = 0, v = 0; f < numFields; ++f) {
285       void * const ctx = ctxs ? ctxs[f] : NULL;
286       ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
287       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
288       for (d = 0; d < spDim; ++d) {
289         if (funcs[f]) {
290           ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
291         } else {
292           for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
293         }
294         v += numComp;
295       }
296     }
297     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
298   }
299   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
300   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
301   ierr = PetscFree(sp);CHKERRQ(ierr);
302   PetscFunctionReturn(0);
303 }
304 
305 #undef __FUNCT__
306 #define __FUNCT__ "DMPlexProjectFunction"
307 /*@C
308   DMPlexProjectFunction - This projects the given function into the function space provided.
309 
310   Input Parameters:
311 + dm      - The DM
312 . fe      - The PetscFE associated with the field
313 . funcs   - The coordinate functions to evaluate, one per field
314 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
315 - mode    - The insertion mode for values
316 
317   Output Parameter:
318 . X - vector
319 
320   Level: developer
321 
322 .seealso: DMPlexComputeL2Diff()
323 @*/
324 PetscErrorCode DMPlexProjectFunction(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
325 {
326   Vec            localX;
327   PetscErrorCode ierr;
328 
329   PetscFunctionBegin;
330   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
331   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
332   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, mode, localX);CHKERRQ(ierr);
333   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
334   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
335   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
336   PetscFunctionReturn(0);
337 }
338 
339 #undef __FUNCT__
340 #define __FUNCT__ "DMPlexInsertBoundaryValuesFEM"
341 PetscErrorCode DMPlexInsertBoundaryValuesFEM(DM dm, Vec localX)
342 {
343   void        (**funcs)(const PetscReal x[], PetscScalar *u, void *ctx);
344   void         **ctxs;
345   PetscFE       *fe;
346   PetscInt       numFields, f, numBd, b;
347   PetscErrorCode ierr;
348 
349   PetscFunctionBegin;
350   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
351   PetscValidHeaderSpecific(localX, VEC_CLASSID, 2);
352   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
353   ierr = PetscMalloc3(numFields,&fe,numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
354   for (f = 0; f < numFields; ++f) {ierr = DMGetField(dm, f, (PetscObject *) &fe[f]);CHKERRQ(ierr);}
355   /* OPT: Could attempt to do multiple BCs at once */
356   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
357   for (b = 0; b < numBd; ++b) {
358     DMLabel         label;
359     const PetscInt *ids;
360     const char     *labelname;
361     PetscInt        numids, field;
362     PetscBool       isEssential;
363     void          (*func)();
364     void           *ctx;
365 
366     /* TODO: We need to set only the part indicated by the ids */
367     ierr = DMPlexGetBoundary(dm, b, &isEssential, NULL, &labelname, &field, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
368     ierr = DMPlexGetLabel(dm, labelname, &label);CHKERRQ(ierr);
369     for (f = 0; f < numFields; ++f) {
370       funcs[f] = field == f ? (void (*)(const PetscReal[], PetscScalar *, void *)) func : NULL;
371       ctxs[f]  = field == f ? ctx : NULL;
372     }
373     ierr = DMPlexProjectFunctionLabelLocal(dm, label, numids, ids, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
374   }
375   ierr = PetscFree3(fe,funcs,ctxs);CHKERRQ(ierr);
376   PetscFunctionReturn(0);
377 }
378 
379 #undef __FUNCT__
380 #define __FUNCT__ "DMPlexComputeL2Diff"
381 /*@C
382   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
383 
384   Input Parameters:
385 + dm    - The DM
386 . fe    - The PetscFE object for each field
387 . funcs - The functions to evaluate for each field component
388 . ctxs  - Optional array of contexts to pass to each function, or NULL.
389 - X     - The coefficient vector u_h
390 
391   Output Parameter:
392 . diff - The diff ||u - u_h||_2
393 
394   Level: developer
395 
396 .seealso: DMPlexProjectFunction(), DMPlexComputeL2GradientDiff()
397 @*/
398 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
399 {
400   const PetscInt  debug = 0;
401   PetscSection    section;
402   PetscQuadrature quad;
403   Vec             localX;
404   PetscScalar    *funcVal;
405   PetscReal      *coords, *v0, *J, *invJ, detJ;
406   PetscReal       localDiff = 0.0;
407   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
408   PetscErrorCode  ierr;
409 
410   PetscFunctionBegin;
411   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
412   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
413   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
414   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
415   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
416   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
417   for (field = 0; field < numFields; ++field) {
418     PetscInt Nc;
419 
420     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
421     numComponents += Nc;
422   }
423   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
424   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
425   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
426   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
427   for (c = cStart; c < cEnd; ++c) {
428     PetscScalar *x = NULL;
429     PetscReal    elemDiff = 0.0;
430 
431     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
432     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
433     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
434 
435     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
436       void * const     ctx = ctxs ? ctxs[field] : NULL;
437       const PetscReal *quadPoints, *quadWeights;
438       PetscReal       *basis;
439       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
440 
441       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
442       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
443       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
444       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
445       if (debug) {
446         char title[1024];
447         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
448         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
449       }
450       for (q = 0; q < numQuadPoints; ++q) {
451         for (d = 0; d < dim; d++) {
452           coords[d] = v0[d];
453           for (e = 0; e < dim; e++) {
454             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
455           }
456         }
457         (*funcs[field])(coords, funcVal, ctx);
458         for (fc = 0; fc < numBasisComps; ++fc) {
459           PetscScalar interpolant = 0.0;
460 
461           for (f = 0; f < numBasisFuncs; ++f) {
462             const PetscInt fidx = f*numBasisComps+fc;
463             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
464           }
465           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);}
466           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
467         }
468       }
469       comp        += numBasisComps;
470       fieldOffset += numBasisFuncs*numBasisComps;
471     }
472     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
473     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
474     localDiff += elemDiff;
475   }
476   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
477   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
478   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
479   *diff = PetscSqrtReal(*diff);
480   PetscFunctionReturn(0);
481 }
482 
483 #undef __FUNCT__
484 #define __FUNCT__ "DMPlexComputeL2GradientDiff"
485 /*@C
486   DMPlexComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
487 
488   Input Parameters:
489 + dm    - The DM
490 . fe    - The PetscFE object for each field
491 . funcs - The gradient functions to evaluate for each field component
492 . ctxs  - Optional array of contexts to pass to each function, or NULL.
493 . X     - The coefficient vector u_h
494 - n     - The vector to project along
495 
496   Output Parameter:
497 . diff - The diff ||(grad u - grad u_h) . n||_2
498 
499   Level: developer
500 
501 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
502 @*/
503 PetscErrorCode DMPlexComputeL2GradientDiff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
504 {
505   const PetscInt  debug = 0;
506   PetscSection    section;
507   PetscQuadrature quad;
508   Vec             localX;
509   PetscScalar    *funcVal, *interpolantVec;
510   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
511   PetscReal       localDiff = 0.0;
512   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
513   PetscErrorCode  ierr;
514 
515   PetscFunctionBegin;
516   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
517   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
518   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
519   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
520   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
521   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
522   for (field = 0; field < numFields; ++field) {
523     PetscInt Nc;
524 
525     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
526     numComponents += Nc;
527   }
528   /* ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
529   ierr = PetscMalloc7(numComponents,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
530   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
531   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
532   for (c = cStart; c < cEnd; ++c) {
533     PetscScalar *x = NULL;
534     PetscReal    elemDiff = 0.0;
535 
536     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
537     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
538     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
539 
540     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
541       void * const     ctx = ctxs ? ctxs[field] : NULL;
542       const PetscReal *quadPoints, *quadWeights;
543       PetscReal       *basisDer;
544       PetscInt         numQuadPoints, Nb, Ncomp, q, d, e, fc, f, g;
545 
546       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
547       ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
548       ierr = PetscFEGetNumComponents(fe[field], &Ncomp);CHKERRQ(ierr);
549       ierr = PetscFEGetDefaultTabulation(fe[field], NULL, &basisDer, NULL);CHKERRQ(ierr);
550       if (debug) {
551         char title[1024];
552         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
553         ierr = DMPrintCellVector(c, title, Nb*Ncomp, &x[fieldOffset]);CHKERRQ(ierr);
554       }
555       for (q = 0; q < numQuadPoints; ++q) {
556         for (d = 0; d < dim; d++) {
557           coords[d] = v0[d];
558           for (e = 0; e < dim; e++) {
559             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
560           }
561         }
562         (*funcs[field])(coords, n, funcVal, ctx);
563         for (fc = 0; fc < Ncomp; ++fc) {
564           PetscScalar interpolant = 0.0;
565 
566           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
567           for (f = 0; f < Nb; ++f) {
568             const PetscInt fidx = f*Ncomp+fc;
569 
570             for (d = 0; d < dim; ++d) {
571               realSpaceDer[d] = 0.0;
572               for (g = 0; g < dim; ++g) {
573                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+fidx)*dim+g];
574               }
575               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
576             }
577           }
578           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
579           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);}
580           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
581         }
582       }
583       comp        += Ncomp;
584       fieldOffset += Nb*Ncomp;
585     }
586     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
587     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
588     localDiff += elemDiff;
589   }
590   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
591   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
592   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
593   *diff = PetscSqrtReal(*diff);
594   PetscFunctionReturn(0);
595 }
596 
597 #undef __FUNCT__
598 #define __FUNCT__ "DMPlexComputeResidualFEM"
599 /*@
600   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
601 
602   Input Parameters:
603 + dm - The mesh
604 . X  - Local input vector
605 - user - The user context
606 
607   Output Parameter:
608 . F  - Local output vector
609 
610   Note:
611   The first member of the user context must be an FEMContext.
612 
613   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
614   like a GPU, or vectorize on a multicore machine.
615 
616   Level: developer
617 
618 .seealso: DMPlexComputeJacobianActionFEM()
619 @*/
620 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
621 {
622   DM_Plex          *mesh  = (DM_Plex *) dm->data;
623   PetscFEM         *fem   = (PetscFEM *) user;
624   PetscFE          *fe    = fem->fe;
625   PetscFE          *feAux = fem->feAux;
626   PetscFE          *feBd  = fem->feBd;
627   const char       *name  = "Residual";
628   DM                dmAux;
629   Vec               A;
630   PetscQuadrature   q;
631   PetscCellGeometry geom;
632   PetscSection      section, sectionAux;
633   PetscReal        *v0, *J, *invJ, *detJ;
634   PetscScalar      *elemVec, *u, *a = NULL;
635   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
636   PetscInt          cellDof = 0, numComponents = 0;
637   PetscInt          cellDofAux = 0, numComponentsAux = 0;
638   PetscErrorCode    ierr;
639 
640   PetscFunctionBegin;
641   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
642   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
643   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
644   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
645   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
646   numCells = cEnd - cStart;
647   for (f = 0; f < Nf; ++f) {
648     PetscInt Nb, Nc;
649 
650     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
651     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
652     cellDof       += Nb*Nc;
653     numComponents += Nc;
654   }
655   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
656   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
657   if (dmAux) {
658     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
659     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
660   }
661   for (f = 0; f < NfAux; ++f) {
662     PetscInt Nb, Nc;
663 
664     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
665     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
666     cellDofAux       += Nb*Nc;
667     numComponentsAux += Nc;
668   }
669   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
670   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
671   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
672   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
673   for (c = cStart; c < cEnd; ++c) {
674     PetscScalar *x = NULL;
675     PetscInt     i;
676 
677     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
678     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
679     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
680     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
681     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
682     if (dmAux) {
683       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
684       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
685       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
686     }
687   }
688   for (f = 0; f < Nf; ++f) {
689     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
690     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
691     PetscInt numQuadPoints, Nb;
692     /* Conforming batches */
693     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
694     /* Remainder */
695     PetscInt Nr, offset;
696 
697     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
698     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
699     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
700     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
701     blockSize = Nb*numQuadPoints;
702     batchSize = numBlocks * blockSize;
703     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
704     numChunks = numCells / (numBatches*batchSize);
705     Ne        = numChunks*numBatches*batchSize;
706     Nr        = numCells % (numBatches*batchSize);
707     offset    = numCells - Nr;
708     geom.v0   = v0;
709     geom.J    = J;
710     geom.invJ = invJ;
711     geom.detJ = detJ;
712     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
713     geom.v0   = &v0[offset*dim];
714     geom.J    = &J[offset*dim*dim];
715     geom.invJ = &invJ[offset*dim*dim];
716     geom.detJ = &detJ[offset];
717     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
718   }
719   for (c = cStart; c < cEnd; ++c) {
720     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
721     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
722   }
723   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
724   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
725   if (feBd) {
726     DMLabel  depth;
727     PetscInt numBd, bd;
728 
729     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
730       PetscInt Nb, Nc;
731 
732       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
733       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
734       cellDof       += Nb*Nc;
735       numComponents += Nc;
736     }
737     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
738     ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
739     for (bd = 0; bd < numBd; ++bd) {
740       const char     *bdLabel;
741       DMLabel         label;
742       IS              pointIS;
743       const PetscInt *points;
744       const PetscInt *values;
745       PetscReal      *n;
746       PetscInt        field, numValues, numPoints, p, dep, numFaces;
747       PetscBool       isEssential;
748 
749       ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
750       if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
751       ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
752       ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
753       ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
754       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
755       for (p = 0, numFaces = 0; p < numPoints; ++p) {
756         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
757         if (dep == dim-1) ++numFaces;
758       }
759       ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof,&elemVec);CHKERRQ(ierr);
760       for (p = 0, f = 0; p < numPoints; ++p) {
761         const PetscInt point = points[p];
762         PetscScalar   *x     = NULL;
763         PetscInt       i;
764 
765         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
766         if (dep != dim-1) continue;
767         ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
768         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
769         if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
770         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
771         for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
772         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
773         ++f;
774       }
775       for (f = 0; f < Nf; ++f) {
776         void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
777         void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
778         PetscInt numQuadPoints, Nb;
779         /* Conforming batches */
780         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
781         /* Remainder */
782         PetscInt Nr, offset;
783 
784         ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
785         ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
786         ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
787         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
788         blockSize = Nb*numQuadPoints;
789         batchSize = numBlocks * blockSize;
790         ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
791         numChunks = numFaces / (numBatches*batchSize);
792         Ne        = numChunks*numBatches*batchSize;
793         Nr        = numFaces % (numBatches*batchSize);
794         offset    = numFaces - Nr;
795         geom.v0   = v0;
796         geom.n    = n;
797         geom.J    = J;
798         geom.invJ = invJ;
799         geom.detJ = detJ;
800         ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
801         geom.v0   = &v0[offset*dim];
802         geom.n    = &n[offset*dim];
803         geom.J    = &J[offset*dim*dim];
804         geom.invJ = &invJ[offset*dim*dim];
805         geom.detJ = &detJ[offset];
806         ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
807       }
808       for (p = 0, f = 0; p < numPoints; ++p) {
809         const PetscInt point = points[p];
810 
811         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
812         if (dep != dim-1) continue;
813         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
814         ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
815         ++f;
816       }
817       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
818       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
819       ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
820     }
821   }
822   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
823   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
824   PetscFunctionReturn(0);
825 }
826 
827 #undef __FUNCT__
828 #define __FUNCT__ "DMPlexComputeIFunctionFEM"
829 /*@
830   DMPlexComputeIFunctionFEM - Form the local implicit function F from the local input X, X_t using pointwise functions specified by the user
831 
832   Input Parameters:
833 + dm - The mesh
834 . time - The current time
835 . X  - Local input vector
836 . X_t  - Time derivative of the local input vector
837 - user - The user context
838 
839   Output Parameter:
840 . F  - Local output vector
841 
842   Note:
843   The first member of the user context must be an FEMContext.
844 
845   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
846   like a GPU, or vectorize on a multicore machine.
847 
848   Level: developer
849 
850 .seealso: DMPlexComputeResidualFEM()
851 @*/
852 PetscErrorCode DMPlexComputeIFunctionFEM(DM dm, PetscReal time, Vec X, Vec X_t, Vec F, void *user)
853 {
854   DM_Plex          *mesh  = (DM_Plex *) dm->data;
855   PetscFEM         *fem   = (PetscFEM *) user;
856   PetscFE          *fe    = fem->fe;
857   PetscFE          *feAux = fem->feAux;
858   PetscFE          *feBd  = fem->feBd;
859   const char       *name  = "Residual";
860   DM                dmAux;
861   Vec               A;
862   PetscQuadrature   q;
863   PetscCellGeometry geom;
864   PetscSection      section, sectionAux;
865   PetscReal        *v0, *J, *invJ, *detJ;
866   PetscScalar      *elemVec, *u, *u_t, *a = NULL;
867   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
868   PetscInt          cellDof = 0, numComponents = 0;
869   PetscInt          cellDofAux = 0, numComponentsAux = 0;
870   PetscErrorCode    ierr;
871 
872   PetscFunctionBegin;
873   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
874   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
875   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
876   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
877   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
878   numCells = cEnd - cStart;
879   for (f = 0; f < Nf; ++f) {
880     PetscInt Nb, Nc;
881 
882     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
883     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
884     cellDof       += Nb*Nc;
885     numComponents += Nc;
886   }
887   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
888   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
889   if (dmAux) {
890     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
891     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
892   }
893   for (f = 0; f < NfAux; ++f) {
894     PetscInt Nb, Nc;
895 
896     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
897     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
898     cellDofAux       += Nb*Nc;
899     numComponentsAux += Nc;
900   }
901   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
902   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
903   ierr = PetscMalloc7(numCells*cellDof,&u,numCells*cellDof,&u_t,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
904   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
905   for (c = cStart; c < cEnd; ++c) {
906     PetscScalar *x = NULL, *x_t = NULL;
907     PetscInt     i;
908 
909     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
910     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
911     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
912     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
913     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
914     ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
915     for (i = 0; i < cellDof; ++i) u_t[c*cellDof+i] = x_t[i];
916     ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
917     if (dmAux) {
918       PetscScalar *x_a = NULL;
919       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
920       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x_a[i];
921       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
922     }
923   }
924   for (f = 0; f < Nf; ++f) {
925     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0IFuncs[f];
926     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1IFuncs[f];
927     PetscInt numQuadPoints, Nb;
928     /* Conforming batches */
929     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
930     /* Remainder */
931     PetscInt Nr, offset;
932 
933     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
934     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
935     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
936     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
937     blockSize = Nb*numQuadPoints;
938     batchSize = numBlocks * blockSize;
939     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
940     numChunks = numCells / (numBatches*batchSize);
941     Ne        = numChunks*numBatches*batchSize;
942     Nr        = numCells % (numBatches*batchSize);
943     offset    = numCells - Nr;
944     geom.v0   = v0;
945     geom.J    = J;
946     geom.invJ = invJ;
947     geom.detJ = detJ;
948     ierr = PetscFEIntegrateIFunction(fe[f], Ne, Nf, fe, f, geom, u, u_t, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
949     geom.v0   = &v0[offset*dim];
950     geom.J    = &J[offset*dim*dim];
951     geom.invJ = &invJ[offset*dim*dim];
952     geom.detJ = &detJ[offset];
953     ierr = PetscFEIntegrateIFunction(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], &u_t[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
954   }
955   for (c = cStart; c < cEnd; ++c) {
956     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
957     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
958   }
959   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
960   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
961   if (feBd) {
962     DMLabel         label, depth;
963     IS              pointIS;
964     const PetscInt *points;
965     PetscInt        dep, numPoints, p, numFaces;
966     PetscReal      *n;
967 
968     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
969     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
970     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
971     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
972     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
973     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
974       PetscInt Nb, Nc;
975 
976       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
977       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
978       cellDof       += Nb*Nc;
979       numComponents += Nc;
980     }
981     for (p = 0, numFaces = 0; p < numPoints; ++p) {
982       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
983       if (dep == dim-1) ++numFaces;
984     }
985     ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof,&elemVec);CHKERRQ(ierr);
986     ierr = PetscMalloc1(numFaces*cellDof,&u_t);CHKERRQ(ierr);
987     for (p = 0, f = 0; p < numPoints; ++p) {
988       const PetscInt point = points[p];
989       PetscScalar   *x     = NULL;
990       PetscInt       i;
991 
992       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
993       if (dep != dim-1) continue;
994       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
995       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
996       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
997       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
998       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
999       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1000       ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1001       for (i = 0; i < cellDof; ++i) u_t[f*cellDof+i] = x[i];
1002       ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1003       ++f;
1004     }
1005     for (f = 0; f < Nf; ++f) {
1006       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdIFuncs[f];
1007       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdIFuncs[f];
1008       PetscInt numQuadPoints, Nb;
1009       /* Conforming batches */
1010       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1011       /* Remainder */
1012       PetscInt Nr, offset;
1013 
1014       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
1015       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1016       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1017       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1018       blockSize = Nb*numQuadPoints;
1019       batchSize = numBlocks * blockSize;
1020       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1021       numChunks = numFaces / (numBatches*batchSize);
1022       Ne        = numChunks*numBatches*batchSize;
1023       Nr        = numFaces % (numBatches*batchSize);
1024       offset    = numFaces - Nr;
1025       geom.v0   = v0;
1026       geom.n    = n;
1027       geom.J    = J;
1028       geom.invJ = invJ;
1029       geom.detJ = detJ;
1030       ierr = PetscFEIntegrateBdIFunction(feBd[f], Ne, Nf, feBd, f, geom, u, u_t, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
1031       geom.v0   = &v0[offset*dim];
1032       geom.n    = &n[offset*dim];
1033       geom.J    = &J[offset*dim*dim];
1034       geom.invJ = &invJ[offset*dim*dim];
1035       geom.detJ = &detJ[offset];
1036       ierr = PetscFEIntegrateBdIFunction(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], &u_t[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1037     }
1038     for (p = 0, f = 0; p < numPoints; ++p) {
1039       const PetscInt point = points[p];
1040 
1041       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1042       if (dep != dim-1) continue;
1043       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
1044       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
1045       ++f;
1046     }
1047     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1048     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1049     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1050     ierr = PetscFree(u_t);CHKERRQ(ierr);
1051   }
1052   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1053   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1054   PetscFunctionReturn(0);
1055 }
1056 
1057 #undef __FUNCT__
1058 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
1059 /*@C
1060   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
1061 
1062   Input Parameters:
1063 + dm - The mesh
1064 . J  - The Jacobian shell matrix
1065 . X  - Local input vector
1066 - user - The user context
1067 
1068   Output Parameter:
1069 . F  - Local output vector
1070 
1071   Note:
1072   The first member of the user context must be an FEMContext.
1073 
1074   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1075   like a GPU, or vectorize on a multicore machine.
1076 
1077   Level: developer
1078 
1079 .seealso: DMPlexComputeResidualFEM()
1080 @*/
1081 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
1082 {
1083   DM_Plex          *mesh = (DM_Plex *) dm->data;
1084   PetscFEM         *fem  = (PetscFEM *) user;
1085   PetscFE          *fe   = fem->fe;
1086   PetscQuadrature   quad;
1087   PetscCellGeometry geom;
1088   PetscSection      section;
1089   JacActionCtx     *jctx;
1090   PetscReal        *v0, *J, *invJ, *detJ;
1091   PetscScalar      *elemVec, *u, *a;
1092   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
1093   PetscInt          cellDof = 0;
1094   PetscErrorCode    ierr;
1095 
1096   PetscFunctionBegin;
1097   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1098   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1099   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1100   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1101   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1102   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1103   numCells = cEnd - cStart;
1104   for (field = 0; field < numFields; ++field) {
1105     PetscInt Nb, Nc;
1106 
1107     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1108     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
1109     cellDof += Nb*Nc;
1110   }
1111   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1112   ierr = PetscMalloc7(numCells*cellDof,&u,numCells*cellDof,&a,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
1113   for (c = cStart; c < cEnd; ++c) {
1114     PetscScalar *x = NULL;
1115     PetscInt     i;
1116 
1117     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1118     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1119     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1120     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1121     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1122     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1123     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
1124     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1125   }
1126   for (field = 0; field < numFields; ++field) {
1127     PetscInt numQuadPoints, Nb;
1128     /* Conforming batches */
1129     PetscInt numBlocks  = 1;
1130     PetscInt numBatches = 1;
1131     PetscInt numChunks, Ne, blockSize, batchSize;
1132     /* Remainder */
1133     PetscInt Nr, offset;
1134 
1135     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
1136     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1137     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1138     blockSize = Nb*numQuadPoints;
1139     batchSize = numBlocks * blockSize;
1140     numChunks = numCells / (numBatches*batchSize);
1141     Ne        = numChunks*numBatches*batchSize;
1142     Nr        = numCells % (numBatches*batchSize);
1143     offset    = numCells - Nr;
1144     geom.v0   = v0;
1145     geom.J    = J;
1146     geom.invJ = invJ;
1147     geom.detJ = detJ;
1148     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
1149     geom.v0   = &v0[offset*dim];
1150     geom.J    = &J[offset*dim*dim];
1151     geom.invJ = &invJ[offset*dim*dim];
1152     geom.detJ = &detJ[offset];
1153     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
1154                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1155   }
1156   for (c = cStart; c < cEnd; ++c) {
1157     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1158     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1159   }
1160   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1161   if (mesh->printFEM) {
1162     PetscMPIInt rank, numProcs;
1163     PetscInt    p;
1164 
1165     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
1166     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
1167     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
1168     for (p = 0; p < numProcs; ++p) {
1169       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
1170       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
1171     }
1172   }
1173   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1174   PetscFunctionReturn(0);
1175 }
1176 
1177 #undef __FUNCT__
1178 #define __FUNCT__ "DMPlexComputeJacobianFEM"
1179 /*@
1180   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
1181 
1182   Input Parameters:
1183 + dm - The mesh
1184 . X  - Local input vector
1185 - user - The user context
1186 
1187   Output Parameter:
1188 . Jac  - Jacobian matrix
1189 
1190   Note:
1191   The first member of the user context must be an FEMContext.
1192 
1193   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1194   like a GPU, or vectorize on a multicore machine.
1195 
1196   Level: developer
1197 
1198 .seealso: FormFunctionLocal()
1199 @*/
1200 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1201 {
1202   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1203   PetscFEM         *fem   = (PetscFEM *) user;
1204   PetscFE          *fe    = fem->fe;
1205   PetscFE          *feAux = fem->feAux;
1206   PetscFE          *feBd  = fem->feBd;
1207   const char       *name  = "Jacobian";
1208   DM                dmAux;
1209   Vec               A;
1210   PetscQuadrature   quad;
1211   PetscCellGeometry geom;
1212   PetscSection      section, globalSection, sectionAux;
1213   PetscReal        *v0, *J, *invJ, *detJ;
1214   PetscScalar      *elemMat, *u, *a;
1215   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1216   PetscInt          cellDof = 0, numComponents = 0;
1217   PetscInt          cellDofAux = 0, numComponentsAux = 0;
1218   PetscBool         isShell;
1219   PetscErrorCode    ierr;
1220 
1221   PetscFunctionBegin;
1222   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1223   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1224   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1225   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1226   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1227   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1228   numCells = cEnd - cStart;
1229   for (f = 0; f < Nf; ++f) {
1230     PetscInt Nb, Nc;
1231 
1232     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1233     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1234     cellDof       += Nb*Nc;
1235     numComponents += Nc;
1236   }
1237   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1238   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1239   if (dmAux) {
1240     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1241     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
1242   }
1243   for (f = 0; f < NfAux; ++f) {
1244     PetscInt Nb, Nc;
1245 
1246     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
1247     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
1248     cellDofAux       += Nb*Nc;
1249     numComponentsAux += Nc;
1250   }
1251   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1252   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1253   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1254   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
1255   for (c = cStart; c < cEnd; ++c) {
1256     PetscScalar *x = NULL;
1257     PetscInt     i;
1258 
1259     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1260     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1261     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1262     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1263     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1264     if (dmAux) {
1265       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1266       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
1267       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1268     }
1269   }
1270   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1271   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1272     PetscInt numQuadPoints, Nb;
1273     /* Conforming batches */
1274     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1275     /* Remainder */
1276     PetscInt Nr, offset;
1277 
1278     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
1279     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
1280     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1281     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1282     blockSize = Nb*numQuadPoints;
1283     batchSize = numBlocks * blockSize;
1284     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1285     numChunks = numCells / (numBatches*batchSize);
1286     Ne        = numChunks*numBatches*batchSize;
1287     Nr        = numCells % (numBatches*batchSize);
1288     offset    = numCells - Nr;
1289     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1290       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
1291       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
1292       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
1293       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
1294 
1295       geom.v0   = v0;
1296       geom.J    = J;
1297       geom.invJ = invJ;
1298       geom.detJ = detJ;
1299       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1300       geom.v0   = &v0[offset*dim];
1301       geom.J    = &J[offset*dim*dim];
1302       geom.invJ = &invJ[offset*dim*dim];
1303       geom.detJ = &detJ[offset];
1304       ierr = PetscFEIntegrateJacobian(fe[fieldI], Nr, Nf, fe, fieldI, fieldJ, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
1305     }
1306   }
1307   for (c = cStart; c < cEnd; ++c) {
1308     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
1309     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1310   }
1311   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1312   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1313   if (feBd) {
1314     DMLabel  depth;
1315     PetscInt numBd, bd;
1316 
1317     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1318       PetscInt Nb, Nc;
1319 
1320       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1321       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1322       cellDof       += Nb*Nc;
1323       numComponents += Nc;
1324     }
1325     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1326     ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1327     for (bd = 0; bd < numBd; ++bd) {
1328       const char     *bdLabel;
1329       DMLabel         label;
1330       IS              pointIS;
1331       const PetscInt *points;
1332       const PetscInt *values;
1333       PetscReal      *n;
1334       PetscInt        field, numValues, numPoints, p, dep, numFaces;
1335       PetscBool       isEssential;
1336 
1337       ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1338       if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1339       ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1340       ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1341       ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1342       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1343       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1344         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1345         if (dep == dim-1) ++numFaces;
1346       }
1347       ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1348       for (p = 0, f = 0; p < numPoints; ++p) {
1349         const PetscInt point = points[p];
1350         PetscScalar   *x     = NULL;
1351         PetscInt       i;
1352 
1353         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1354         if (dep != dim-1) continue;
1355         ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1356         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1357         if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1358         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1359         for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1360         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1361         ++f;
1362       }
1363       ierr = PetscMemzero(elemMat, numFaces*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1364       for (fieldI = 0; fieldI < Nf; ++fieldI) {
1365         PetscInt numQuadPoints, Nb;
1366         /* Conforming batches */
1367         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1368         /* Remainder */
1369         PetscInt Nr, offset;
1370 
1371         ierr = PetscFEGetQuadrature(feBd[fieldI], &quad);CHKERRQ(ierr);
1372         ierr = PetscFEGetDimension(feBd[fieldI], &Nb);CHKERRQ(ierr);
1373         ierr = PetscFEGetTileSizes(feBd[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1374         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1375         blockSize = Nb*numQuadPoints;
1376         batchSize = numBlocks * blockSize;
1377         ierr =  PetscFESetTileSizes(feBd[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1378         numChunks = numFaces / (numBatches*batchSize);
1379         Ne        = numChunks*numBatches*batchSize;
1380         Nr        = numFaces % (numBatches*batchSize);
1381         offset    = numFaces - Nr;
1382         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1383           void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g0BdFuncs[fieldI*Nf+fieldJ];
1384           void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g1BdFuncs[fieldI*Nf+fieldJ];
1385           void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g2BdFuncs[fieldI*Nf+fieldJ];
1386           void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g3BdFuncs[fieldI*Nf+fieldJ];
1387 
1388           geom.v0   = v0;
1389           geom.n    = n;
1390           geom.J    = J;
1391           geom.invJ = invJ;
1392           geom.detJ = detJ;
1393           ierr = PetscFEIntegrateBdJacobian(feBd[fieldI], Ne, Nf, feBd, fieldI, fieldJ, geom, u, 0, NULL, NULL, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1394           geom.v0   = &v0[offset*dim];
1395           geom.n    = &n[offset*dim];
1396           geom.J    = &J[offset*dim*dim];
1397           geom.invJ = &invJ[offset*dim*dim];
1398           geom.detJ = &detJ[offset];
1399           ierr = PetscFEIntegrateBdJacobian(feBd[fieldI], Nr, Nf, feBd, fieldI, fieldJ, geom, &u[offset*cellDof], 0, NULL, NULL, g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
1400         }
1401       }
1402       for (p = 0, f = 0; p < numPoints; ++p) {
1403         const PetscInt point = points[p];
1404 
1405         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1406         if (dep != dim-1) continue;
1407         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", cellDof, cellDof, &elemMat[f*cellDof*cellDof]);CHKERRQ(ierr);}
1408         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1409         ++f;
1410       }
1411       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1412       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1413       ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1414     }
1415   }
1416   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1417   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1418   if (mesh->printFEM) {
1419     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1420     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
1421     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1422   }
1423   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1424   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
1425   if (isShell) {
1426     JacActionCtx *jctx;
1427 
1428     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1429     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
1430   }
1431   PetscFunctionReturn(0);
1432 }
1433 
1434 #undef __FUNCT__
1435 #define __FUNCT__ "DMPlexComputeInterpolatorFEM"
1436 /*@
1437   DMPlexComputeInterpolatorFEM - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1438 
1439   Input Parameters:
1440 + dmf  - The fine mesh
1441 . dmc  - The coarse mesh
1442 - user - The user context
1443 
1444   Output Parameter:
1445 . In  - The interpolation matrix
1446 
1447   Note:
1448   The first member of the user context must be an FEMContext.
1449 
1450   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1451   like a GPU, or vectorize on a multicore machine.
1452 
1453   Level: developer
1454 
1455 .seealso: DMPlexComputeJacobianFEM()
1456 @*/
1457 PetscErrorCode DMPlexComputeInterpolatorFEM(DM dmc, DM dmf, Mat In, void *user)
1458 {
1459   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1460   PetscFEM         *fem   = (PetscFEM *) user;
1461   PetscFE          *fe    = fem->fe;
1462   const char       *name  = "Interpolator";
1463   PetscFE          *feRef;
1464   PetscSection      fsection, fglobalSection;
1465   PetscSection      csection, cglobalSection;
1466   PetscScalar      *elemMat;
1467   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, c;
1468   PetscInt          rCellDof = 0, cCellDof = 0;
1469   PetscErrorCode    ierr;
1470 
1471   PetscFunctionBegin;
1472 #if 0
1473   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1474 #endif
1475   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1476   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1477   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1478   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1479   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1480   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1481   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1482   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1483   for (f = 0; f < Nf; ++f) {
1484     PetscInt rNb, cNb, Nc;
1485 
1486     ierr = PetscFERefine(fe[f], &feRef[f]);CHKERRQ(ierr);
1487     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1488     ierr = PetscFEGetDimension(fe[f], &cNb);CHKERRQ(ierr);
1489     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1490     rCellDof += rNb*Nc;
1491     cCellDof += cNb*Nc;
1492   }
1493   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1494   ierr = PetscMalloc1(rCellDof*cCellDof,&elemMat);CHKERRQ(ierr);
1495   ierr = PetscMemzero(elemMat, rCellDof*cCellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1496   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1497     PetscDualSpace   Qref;
1498     PetscQuadrature  f;
1499     const PetscReal *qpoints, *qweights;
1500     PetscReal       *points;
1501     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1502 
1503     /* Compose points from all dual basis functionals */
1504     ierr = PetscFEGetNumComponents(fe[fieldI], &Nc);CHKERRQ(ierr);
1505     ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1506     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1507     for (i = 0; i < fpdim; ++i) {
1508       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1509       ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1510       npoints += Np;
1511     }
1512     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1513     for (i = 0, k = 0; i < fpdim; ++i) {
1514       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1515       ierr = PetscQuadratureGetData(f, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1516       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1517     }
1518 
1519     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1520       PetscReal *B;
1521       PetscInt   NcJ, cpdim, j;
1522 
1523       /* Evaluate basis at points */
1524       ierr = PetscFEGetNumComponents(fe[fieldJ], &NcJ);CHKERRQ(ierr);
1525       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);
1526       ierr = PetscFEGetDimension(fe[fieldJ], &cpdim);CHKERRQ(ierr);
1527       /* For now, fields only interpolate themselves */
1528       if (fieldI == fieldJ) {
1529         ierr = PetscFEGetTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1530         for (i = 0, k = 0; i < fpdim; ++i) {
1531           ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1532           ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, &qweights);CHKERRQ(ierr);
1533           for (p = 0; p < Np; ++p, ++k) {
1534             for (j = 0; j < cpdim; ++j) {
1535               for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cCellDof + offsetJ + j*NcJ + c] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p];
1536             }
1537           }
1538         }
1539         ierr = PetscFERestoreTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1540       }
1541       offsetJ += cpdim*NcJ;
1542     }
1543     offsetI += fpdim*Nc;
1544     ierr = PetscFree(points);CHKERRQ(ierr);
1545   }
1546   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rCellDof, cCellDof, elemMat);CHKERRQ(ierr);}
1547   for (c = cStart; c < cEnd; ++c) {
1548     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1549   }
1550   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1551   ierr = PetscFree(feRef);CHKERRQ(ierr);
1552   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1553   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1554   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1555   if (mesh->printFEM) {
1556     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1557     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1558     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1559   }
1560 #if 0
1561   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1562 #endif
1563   PetscFunctionReturn(0);
1564 }
1565 
1566 #undef __FUNCT__
1567 #define __FUNCT__ "DMPlexAddBoundary"
1568 /* The ids can be overridden by the command line option -bc_<boundary name> */
1569 PetscErrorCode DMPlexAddBoundary(DM dm, PetscBool isEssential, const char name[], const char labelname[], PetscInt field, void (*bcFunc)(), PetscInt numids, const PetscInt *ids, void *ctx)
1570 {
1571   DM_Plex       *mesh = (DM_Plex *) dm->data;
1572   DMBoundary     b;
1573   PetscErrorCode ierr;
1574 
1575   PetscFunctionBegin;
1576   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1577   ierr = PetscNew(&b);CHKERRQ(ierr);
1578   ierr = PetscStrallocpy(name, (char **) &b->name);CHKERRQ(ierr);
1579   ierr = PetscStrallocpy(labelname, (char **) &b->labelname);CHKERRQ(ierr);
1580   ierr = PetscMalloc1(numids, &b->ids);CHKERRQ(ierr);
1581   ierr = PetscMemcpy(b->ids, ids, numids*sizeof(PetscInt));CHKERRQ(ierr);
1582   if (b->labelname) {
1583     ierr = DMPlexGetLabel(dm, b->labelname, &b->label);CHKERRQ(ierr);
1584     if (!b->label) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Label %s does not exist in this DM", b->labelname);
1585   }
1586   b->essential   = isEssential;
1587   b->field       = field;
1588   b->func        = bcFunc;
1589   b->numids      = numids;
1590   b->ctx         = ctx;
1591   b->next        = mesh->boundary;
1592   mesh->boundary = b;
1593   PetscFunctionReturn(0);
1594 }
1595 
1596 #undef __FUNCT__
1597 #define __FUNCT__ "DMPlexGetNumBoundary"
1598 PetscErrorCode DMPlexGetNumBoundary(DM dm, PetscInt *numBd)
1599 {
1600   DM_Plex   *mesh = (DM_Plex *) dm->data;
1601   DMBoundary b    = mesh->boundary;
1602 
1603   PetscFunctionBegin;
1604   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1605   PetscValidPointer(numBd, 2);
1606   *numBd = 0;
1607   while (b) {++(*numBd); b = b->next;}
1608   PetscFunctionReturn(0);
1609 }
1610 
1611 #undef __FUNCT__
1612 #define __FUNCT__ "DMPlexGetBoundary"
1613 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)
1614 {
1615   DM_Plex   *mesh = (DM_Plex *) dm->data;
1616   DMBoundary b    = mesh->boundary;
1617   PetscInt   n    = 0;
1618 
1619   PetscFunctionBegin;
1620   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1621   while (b) {
1622     if (n == bd) break;
1623     b = b->next;
1624     ++n;
1625   }
1626   if (n != bd) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %d is not in [0, %d)", bd, n);
1627   if (isEssential) {
1628     PetscValidPointer(isEssential, 3);
1629     *isEssential = b->essential;
1630   }
1631   if (name) {
1632     PetscValidPointer(name, 4);
1633     *name = b->name;
1634   }
1635   if (labelname) {
1636     PetscValidPointer(labelname, 5);
1637     *labelname = b->labelname;
1638   }
1639   if (field) {
1640     PetscValidPointer(field, 6);
1641     *field = b->field;
1642   }
1643   if (func) {
1644     PetscValidPointer(func, 7);
1645     *func = b->func;
1646   }
1647   if (numids) {
1648     PetscValidPointer(numids, 8);
1649     *numids = b->numids;
1650   }
1651   if (ids) {
1652     PetscValidPointer(ids, 9);
1653     *ids = b->ids;
1654   }
1655   if (ctx) {
1656     PetscValidPointer(ctx, 10);
1657     *ctx = b->ctx;
1658   }
1659   PetscFunctionReturn(0);
1660 }
1661 
1662 #undef __FUNCT__
1663 #define __FUNCT__ "DMPlexIsBoundaryPoint"
1664 PetscErrorCode DMPlexIsBoundaryPoint(DM dm, PetscInt point, PetscBool *isBd)
1665 {
1666   DM_Plex       *mesh = (DM_Plex *) dm->data;
1667   DMBoundary     b    = mesh->boundary;
1668   PetscErrorCode ierr;
1669 
1670   PetscFunctionBegin;
1671   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1672   PetscValidPointer(isBd, 3);
1673   *isBd = PETSC_FALSE;
1674   while (b && !(*isBd)) {
1675     if (b->label) {
1676       PetscInt i;
1677 
1678       for (i = 0; i < b->numids && !(*isBd); ++i) {
1679         ierr = DMLabelStratumHasPoint(b->label, b->ids[i], point, isBd);CHKERRQ(ierr);
1680       }
1681     }
1682     b = b->next;
1683   }
1684   PetscFunctionReturn(0);
1685 }
1686