xref: /petsc/src/ksp/pc/impls/patch/pcpatch.c (revision b88cb22de34d34f02467e8cc53d93f0a5be4025e)
1 #include <petsc/private/pcpatchimpl.h>     /*I "petscpc.h" I*/
2 #include <petsc/private/kspimpl.h>         /* For ksp->setfromoptionscalled */
3 #include <petsc/private/dmpleximpl.h> /* For DMPlexComputeJacobian_Patch_Internal() */
4 #include <petscsf.h>
5 #include <petscbt.h>
6 #include <petscds.h>
7 
8 PetscLogEvent PC_Patch_CreatePatches, PC_Patch_ComputeOp, PC_Patch_Solve, PC_Patch_Scatter, PC_Patch_Apply, PC_Patch_Prealloc;
9 
10 PETSC_STATIC_INLINE PetscErrorCode ObjectView(PetscObject obj, PetscViewer viewer, PetscViewerFormat format)
11 {
12   PetscErrorCode ierr;
13 
14   ierr = PetscViewerPushFormat(viewer, format);CHKERRQ(ierr);
15   ierr = PetscObjectView(obj, viewer);CHKERRQ(ierr);
16   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
17   return(0);
18 }
19 
20 static PetscErrorCode PCPatchConstruct_Star(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
21 {
22   PetscInt       starSize;
23   PetscInt      *star = NULL, si;
24   PetscErrorCode ierr;
25 
26   PetscFunctionBegin;
27   PetscHSetIClear(ht);
28   /* To start with, add the point we care about */
29   ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
30   /* Loop over all the points that this point connects to */
31   ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
32   for (si = 0; si < starSize*2; si += 2) {ierr = PetscHSetIAdd(ht, star[si]);CHKERRQ(ierr);}
33   ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
34   PetscFunctionReturn(0);
35 }
36 
37 static PetscErrorCode PCPatchConstruct_Vanka(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
38 {
39   PC_PATCH      *patch = (PC_PATCH *) vpatch;
40   PetscInt       starSize;
41   PetscInt      *star = NULL;
42   PetscBool      shouldIgnore = PETSC_FALSE;
43   PetscInt       cStart, cEnd, iStart, iEnd, si;
44   PetscErrorCode ierr;
45 
46   PetscFunctionBegin;
47   ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
48   /* To start with, add the point we care about */
49   ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
50   /* Should we ignore any points of a certain dimension? */
51   if (patch->vankadim >= 0) {
52     shouldIgnore = PETSC_TRUE;
53     ierr = DMPlexGetDepthStratum(dm, patch->vankadim, &iStart, &iEnd);CHKERRQ(ierr);
54   }
55   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
56   /* Loop over all the cells that this point connects to */
57   ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
58   for (si = 0; si < starSize*2; si += 2) {
59     const PetscInt cell = star[si];
60     PetscInt       closureSize;
61     PetscInt      *closure = NULL, ci;
62 
63     if (cell < cStart || cell >= cEnd) continue;
64     /* now loop over all entities in the closure of that cell */
65     ierr = DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
66     for (ci = 0; ci < closureSize*2; ci += 2) {
67       const PetscInt newpoint = closure[ci];
68 
69       /* We've been told to ignore entities of this type.*/
70       if (shouldIgnore && newpoint >= iStart && newpoint < iEnd) continue;
71       ierr = PetscHSetIAdd(ht, newpoint);CHKERRQ(ierr);
72     }
73     ierr = DMPlexRestoreTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
74   }
75   ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
76   PetscFunctionReturn(0);
77 }
78 
79 static PetscErrorCode PCPatchConstruct_Pardecomp(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
80 {
81   PC_PATCH       *patch = (PC_PATCH *) vpatch;
82   DMLabel         ghost = NULL;
83   const PetscInt *leaves;
84   PetscInt        nleaves, pStart, pEnd, loc;
85   PetscBool       isFiredrake;
86   DM              plex;
87   PetscBool       flg;
88   PetscInt        starSize;
89   PetscInt       *star = NULL;
90   PetscErrorCode  ierr;
91 
92   PetscFunctionBegin;
93   PetscHSetIClear(ht);
94 
95   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
96   ierr = DMPlexGetChart(plex, &pStart, &pEnd);CHKERRQ(ierr);
97 
98   ierr = DMHasLabel(dm, "pyop2_ghost", &isFiredrake);CHKERRQ(ierr);
99   if (isFiredrake) {
100     ierr = DMGetLabel(dm, "pyop2_ghost", &ghost);CHKERRQ(ierr);
101     ierr = DMLabelCreateIndex(ghost, pStart, pEnd);CHKERRQ(ierr);
102   } else {
103     PetscSF sf;
104     ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
105     ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
106     nleaves = PetscMax(nleaves, 0);
107   }
108 
109   for (PetscInt point = pStart; point < pEnd; ++point) {
110     if (ghost) {ierr = DMLabelHasPoint(ghost, point, &flg);CHKERRQ(ierr);}
111     else       {ierr = PetscFindInt(point, nleaves, leaves, &loc);CHKERRQ(ierr); flg = loc >=0 ? PETSC_TRUE : PETSC_FALSE;}
112     /* Not an owned entity, don't make a cell patch. */
113     if (flg) continue;
114     ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
115   }
116 
117   /* Now build the overlap for the patch */
118   for (PetscInt overlapi = 0; overlapi < patch->pardecomp_overlap; ++overlapi) {
119     PetscInt index = 0;
120     PetscInt *htpoints = NULL;
121     PetscInt htsize;
122 
123     ierr = PetscHSetIGetSize(ht, &htsize);CHKERRQ(ierr);
124     ierr = PetscMalloc1(htsize, &htpoints);CHKERRQ(ierr);
125     ierr = PetscHSetIGetElems(ht, &index, htpoints);CHKERRQ(ierr);
126 
127     for (PetscInt i = 0; i < htsize; ++i) {
128       point = htpoints[i];
129 
130       ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
131       for (PetscInt si = 0; si < starSize*2; si += 2) {
132         const PetscInt starp = star[si];
133         PetscInt       closureSize;
134         PetscInt      *closure = NULL, ci;
135 
136         /* now loop over all entities in the closure of starp */
137         ierr = DMPlexGetTransitiveClosure(dm, starp, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
138         for (PetscInt ci = 0; ci < closureSize*2; ci += 2) {
139           const PetscInt closstarp = closure[ci];
140           ierr = PetscHSetIAdd(ht, closstarp);CHKERRQ(ierr);
141         }
142         ierr = DMPlexRestoreTransitiveClosure(dm, starp, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
143       }
144       ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
145     }
146     ierr = PetscFree(htpoints);CHKERRQ(ierr);
147   }
148 
149   PetscFunctionReturn(0);
150 }
151 
152 /* The user's already set the patches in patch->userIS. Build the hash tables */
153 static PetscErrorCode PCPatchConstruct_User(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
154 {
155   PC_PATCH       *patch   = (PC_PATCH *) vpatch;
156   IS              patchis = patch->userIS[point];
157   PetscInt        n;
158   const PetscInt *patchdata;
159   PetscInt        pStart, pEnd, i;
160   PetscErrorCode  ierr;
161 
162   PetscFunctionBegin;
163   ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
164   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
165   ierr = ISGetLocalSize(patchis, &n);CHKERRQ(ierr);
166   ierr = ISGetIndices(patchis, &patchdata);CHKERRQ(ierr);
167   for (i = 0; i < n; ++i) {
168     const PetscInt ownedpoint = patchdata[i];
169 
170     if (ownedpoint < pStart || ownedpoint >= pEnd) {
171       SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D was not in [%D, %D)", ownedpoint, pStart, pEnd);
172     }
173     ierr = PetscHSetIAdd(ht, ownedpoint);CHKERRQ(ierr);
174   }
175   ierr = ISRestoreIndices(patchis, &patchdata);CHKERRQ(ierr);
176   PetscFunctionReturn(0);
177 }
178 
179 static PetscErrorCode PCPatchCreateDefaultSF_Private(PC pc, PetscInt n, const PetscSF *sf, const PetscInt *bs)
180 {
181   PC_PATCH      *patch = (PC_PATCH *) pc->data;
182   PetscInt       i;
183   PetscErrorCode ierr;
184 
185   PetscFunctionBegin;
186   if (n == 1 && bs[0] == 1) {
187     patch->defaultSF = sf[0];
188     ierr = PetscObjectReference((PetscObject) patch->defaultSF);CHKERRQ(ierr);
189   } else {
190     PetscInt     allRoots = 0, allLeaves = 0;
191     PetscInt     leafOffset = 0;
192     PetscInt    *ilocal = NULL;
193     PetscSFNode *iremote = NULL;
194     PetscInt    *remoteOffsets = NULL;
195     PetscInt     index = 0;
196     PetscHMapI   rankToIndex;
197     PetscInt     numRanks = 0;
198     PetscSFNode *remote = NULL;
199     PetscSF      rankSF;
200     PetscInt    *ranks = NULL;
201     PetscInt    *offsets = NULL;
202     MPI_Datatype contig;
203     PetscHSetI   ranksUniq;
204 
205     /* First figure out how many dofs there are in the concatenated numbering.
206      * allRoots: number of owned global dofs;
207      * allLeaves: number of visible dofs (global + ghosted).
208      */
209     for (i = 0; i < n; ++i) {
210       PetscInt nroots, nleaves;
211 
212       ierr = PetscSFGetGraph(sf[i], &nroots, &nleaves, NULL, NULL);CHKERRQ(ierr);
213       allRoots  += nroots * bs[i];
214       allLeaves += nleaves * bs[i];
215     }
216     ierr = PetscMalloc1(allLeaves, &ilocal);CHKERRQ(ierr);
217     ierr = PetscMalloc1(allLeaves, &iremote);CHKERRQ(ierr);
218     /* Now build an SF that just contains process connectivity. */
219     ierr = PetscHSetICreate(&ranksUniq);CHKERRQ(ierr);
220     for (i = 0; i < n; ++i) {
221       const PetscMPIInt *ranks = NULL;
222       PetscInt           nranks, j;
223 
224       ierr = PetscSFSetUp(sf[i]);CHKERRQ(ierr);
225       ierr = PetscSFGetRanks(sf[i], &nranks, &ranks, NULL, NULL, NULL);CHKERRQ(ierr);
226       /* These are all the ranks who communicate with me. */
227       for (j = 0; j < nranks; ++j) {
228         ierr = PetscHSetIAdd(ranksUniq, (PetscInt) ranks[j]);CHKERRQ(ierr);
229       }
230     }
231     ierr = PetscHSetIGetSize(ranksUniq, &numRanks);CHKERRQ(ierr);
232     ierr = PetscMalloc1(numRanks, &remote);CHKERRQ(ierr);
233     ierr = PetscMalloc1(numRanks, &ranks);CHKERRQ(ierr);
234     ierr = PetscHSetIGetElems(ranksUniq, &index, ranks);CHKERRQ(ierr);
235 
236     ierr = PetscHMapICreate(&rankToIndex);CHKERRQ(ierr);
237     for (i = 0; i < numRanks; ++i) {
238       remote[i].rank  = ranks[i];
239       remote[i].index = 0;
240       ierr = PetscHMapISet(rankToIndex, ranks[i], i);CHKERRQ(ierr);
241     }
242     ierr = PetscFree(ranks);CHKERRQ(ierr);
243     ierr = PetscHSetIDestroy(&ranksUniq);CHKERRQ(ierr);
244     ierr = PetscSFCreate(PetscObjectComm((PetscObject) pc), &rankSF);CHKERRQ(ierr);
245     ierr = PetscSFSetGraph(rankSF, 1, numRanks, NULL, PETSC_OWN_POINTER, remote, PETSC_OWN_POINTER);CHKERRQ(ierr);
246     ierr = PetscSFSetUp(rankSF);CHKERRQ(ierr);
247     /* OK, use it to communicate the root offset on the remote
248      * processes for each subspace. */
249     ierr = PetscMalloc1(n, &offsets);CHKERRQ(ierr);
250     ierr = PetscMalloc1(n*numRanks, &remoteOffsets);CHKERRQ(ierr);
251 
252     offsets[0] = 0;
253     for (i = 1; i < n; ++i) {
254       PetscInt nroots;
255 
256       ierr = PetscSFGetGraph(sf[i-1], &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
257       offsets[i] = offsets[i-1] + nroots*bs[i-1];
258     }
259     /* Offsets are the offsets on the current process of the
260      * global dof numbering for the subspaces. */
261     ierr = MPI_Type_contiguous(n, MPIU_INT, &contig);CHKERRQ(ierr);
262     ierr = MPI_Type_commit(&contig);CHKERRQ(ierr);
263 
264     ierr = PetscSFBcastBegin(rankSF, contig, offsets, remoteOffsets);CHKERRQ(ierr);
265     ierr = PetscSFBcastEnd(rankSF, contig, offsets, remoteOffsets);CHKERRQ(ierr);
266     ierr = MPI_Type_free(&contig);CHKERRQ(ierr);
267     ierr = PetscFree(offsets);CHKERRQ(ierr);
268     ierr = PetscSFDestroy(&rankSF);CHKERRQ(ierr);
269     /* Now remoteOffsets contains the offsets on the remote
270      * processes who communicate with me.  So now we can
271      * concatenate the list of SFs into a single one. */
272     index = 0;
273     for (i = 0; i < n; ++i) {
274       const PetscSFNode *remote = NULL;
275       const PetscInt    *local  = NULL;
276       PetscInt           nroots, nleaves, j;
277 
278       ierr = PetscSFGetGraph(sf[i], &nroots, &nleaves, &local, &remote);CHKERRQ(ierr);
279       for (j = 0; j < nleaves; ++j) {
280         PetscInt rank = remote[j].rank;
281         PetscInt idx, rootOffset, k;
282 
283         ierr = PetscHMapIGet(rankToIndex, rank, &idx);CHKERRQ(ierr);
284         if (idx == -1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Didn't find rank, huh?");
285         /* Offset on given rank for ith subspace */
286         rootOffset = remoteOffsets[n*idx + i];
287         for (k = 0; k < bs[i]; ++k) {
288           ilocal[index]        = (local ? local[j] : j)*bs[i] + k + leafOffset;
289           iremote[index].rank  = remote[j].rank;
290           iremote[index].index = remote[j].index*bs[i] + k + rootOffset;
291           ++index;
292         }
293       }
294       leafOffset += nleaves * bs[i];
295     }
296     ierr = PetscHMapIDestroy(&rankToIndex);CHKERRQ(ierr);
297     ierr = PetscFree(remoteOffsets);CHKERRQ(ierr);
298     ierr = PetscSFCreate(PetscObjectComm((PetscObject)pc), &patch->defaultSF);CHKERRQ(ierr);
299     ierr = PetscSFSetGraph(patch->defaultSF, allRoots, allLeaves, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER);CHKERRQ(ierr);
300   }
301   PetscFunctionReturn(0);
302 }
303 
304 /* TODO: Docs */
305 PetscErrorCode PCPatchSetIgnoreDim(PC pc, PetscInt dim)
306 {
307   PC_PATCH *patch = (PC_PATCH *) pc->data;
308   PetscFunctionBegin;
309   patch->ignoredim = dim;
310   PetscFunctionReturn(0);
311 }
312 
313 /* TODO: Docs */
314 PetscErrorCode PCPatchGetIgnoreDim(PC pc, PetscInt *dim)
315 {
316   PC_PATCH *patch = (PC_PATCH *) pc->data;
317   PetscFunctionBegin;
318   *dim = patch->ignoredim;
319   PetscFunctionReturn(0);
320 }
321 
322 /* TODO: Docs */
323 PetscErrorCode PCPatchSetSaveOperators(PC pc, PetscBool flg)
324 {
325   PC_PATCH *patch = (PC_PATCH *) pc->data;
326   PetscFunctionBegin;
327   patch->save_operators = flg;
328   PetscFunctionReturn(0);
329 }
330 
331 /* TODO: Docs */
332 PetscErrorCode PCPatchGetSaveOperators(PC pc, PetscBool *flg)
333 {
334   PC_PATCH *patch = (PC_PATCH *) pc->data;
335   PetscFunctionBegin;
336   *flg = patch->save_operators;
337   PetscFunctionReturn(0);
338 }
339 
340 /* TODO: Docs */
341 PetscErrorCode PCPatchSetPartitionOfUnity(PC pc, PetscBool flg)
342 {
343   PC_PATCH *patch = (PC_PATCH *) pc->data;
344   PetscFunctionBegin;
345   patch->partition_of_unity = flg;
346   PetscFunctionReturn(0);
347 }
348 
349 /* TODO: Docs */
350 PetscErrorCode PCPatchGetPartitionOfUnity(PC pc, PetscBool *flg)
351 {
352   PC_PATCH *patch = (PC_PATCH *) pc->data;
353   PetscFunctionBegin;
354   *flg = patch->partition_of_unity;
355   PetscFunctionReturn(0);
356 }
357 
358 /* TODO: Docs */
359 PetscErrorCode PCPatchSetLocalComposition(PC pc, PCCompositeType type)
360 {
361   PC_PATCH *patch = (PC_PATCH *) pc->data;
362   PetscFunctionBegin;
363   if (type != PC_COMPOSITE_ADDITIVE && type != PC_COMPOSITE_MULTIPLICATIVE) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Only supports additive or multiplicative as the local type");
364   patch->local_composition_type = type;
365   PetscFunctionReturn(0);
366 }
367 
368 /* TODO: Docs */
369 PetscErrorCode PCPatchGetLocalComposition(PC pc, PCCompositeType *type)
370 {
371   PC_PATCH *patch = (PC_PATCH *) pc->data;
372   PetscFunctionBegin;
373   *type = patch->local_composition_type;
374   PetscFunctionReturn(0);
375 }
376 
377 /* TODO: Docs */
378 PetscErrorCode PCPatchSetSubMatType(PC pc, MatType sub_mat_type)
379 {
380   PC_PATCH      *patch = (PC_PATCH *) pc->data;
381   PetscErrorCode ierr;
382 
383   PetscFunctionBegin;
384   if (patch->sub_mat_type) {ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);}
385   ierr = PetscStrallocpy(sub_mat_type, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
386   PetscFunctionReturn(0);
387 }
388 
389 /* TODO: Docs */
390 PetscErrorCode PCPatchGetSubMatType(PC pc, MatType *sub_mat_type)
391 {
392   PC_PATCH *patch = (PC_PATCH *) pc->data;
393   PetscFunctionBegin;
394   *sub_mat_type = patch->sub_mat_type;
395   PetscFunctionReturn(0);
396 }
397 
398 /* TODO: Docs */
399 PetscErrorCode PCPatchSetCellNumbering(PC pc, PetscSection cellNumbering)
400 {
401   PC_PATCH      *patch = (PC_PATCH *) pc->data;
402   PetscErrorCode ierr;
403 
404   PetscFunctionBegin;
405   patch->cellNumbering = cellNumbering;
406   ierr = PetscObjectReference((PetscObject) cellNumbering);CHKERRQ(ierr);
407   PetscFunctionReturn(0);
408 }
409 
410 /* TODO: Docs */
411 PetscErrorCode PCPatchGetCellNumbering(PC pc, PetscSection *cellNumbering)
412 {
413   PC_PATCH *patch = (PC_PATCH *) pc->data;
414   PetscFunctionBegin;
415   *cellNumbering = patch->cellNumbering;
416   PetscFunctionReturn(0);
417 }
418 
419 /* TODO: Docs */
420 PetscErrorCode PCPatchSetConstructType(PC pc, PCPatchConstructType ctype, PetscErrorCode (*func)(PC, PetscInt *, IS **, IS *, void *), void *ctx)
421 {
422   PC_PATCH *patch = (PC_PATCH *) pc->data;
423 
424   PetscFunctionBegin;
425   patch->ctype = ctype;
426   switch (ctype) {
427   case PC_PATCH_STAR:
428     patch->user_patches     = PETSC_FALSE;
429     patch->patchconstructop = PCPatchConstruct_Star;
430     break;
431   case PC_PATCH_VANKA:
432     patch->user_patches     = PETSC_FALSE;
433     patch->patchconstructop = PCPatchConstruct_Vanka;
434     break;
435   case PC_PATCH_PARDECOMP:
436     patch->user_patches     = PETSC_FALSE;
437     patch->patchconstructop = PCPatchConstruct_Pardecomp;
438     break;
439   case PC_PATCH_USER:
440   case PC_PATCH_PYTHON:
441     patch->user_patches     = PETSC_TRUE;
442     patch->patchconstructop = PCPatchConstruct_User;
443     if (func) {
444       patch->userpatchconstructionop = func;
445       patch->userpatchconstructctx   = ctx;
446     }
447     break;
448   default:
449     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_USER, "Unknown patch construction type %D", (PetscInt) patch->ctype);
450   }
451   PetscFunctionReturn(0);
452 }
453 
454 /* TODO: Docs */
455 PetscErrorCode PCPatchGetConstructType(PC pc, PCPatchConstructType *ctype, PetscErrorCode (**func)(PC, PetscInt *, IS **, IS *, void *), void **ctx)
456 {
457   PC_PATCH *patch = (PC_PATCH *) pc->data;
458 
459   PetscFunctionBegin;
460   *ctype = patch->ctype;
461   switch (patch->ctype) {
462   case PC_PATCH_STAR:
463   case PC_PATCH_VANKA:
464   case PC_PATCH_PARDECOMP:
465     break;
466   case PC_PATCH_USER:
467   case PC_PATCH_PYTHON:
468     *func = patch->userpatchconstructionop;
469     *ctx  = patch->userpatchconstructctx;
470     break;
471   default:
472     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_USER, "Unknown patch construction type %D", (PetscInt) patch->ctype);
473   }
474   PetscFunctionReturn(0);
475 }
476 
477 /* TODO: Docs */
478 PetscErrorCode PCPatchSetDiscretisationInfo(PC pc, PetscInt nsubspaces, DM *dms, PetscInt *bs, PetscInt *nodesPerCell, const PetscInt **cellNodeMap,
479                                             const PetscInt *subspaceOffsets, PetscInt numGhostBcs, const PetscInt *ghostBcNodes, PetscInt numGlobalBcs, const PetscInt *globalBcNodes)
480 {
481   PC_PATCH      *patch = (PC_PATCH *) pc->data;
482   DM             dm;
483   PetscSF       *sfs;
484   PetscInt       cStart, cEnd, i, j;
485   PetscErrorCode ierr;
486 
487   PetscFunctionBegin;
488   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
489   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
490   ierr = PetscMalloc1(nsubspaces, &sfs);CHKERRQ(ierr);
491   ierr = PetscMalloc1(nsubspaces, &patch->dofSection);CHKERRQ(ierr);
492   ierr = PetscMalloc1(nsubspaces, &patch->bs);CHKERRQ(ierr);
493   ierr = PetscMalloc1(nsubspaces, &patch->nodesPerCell);CHKERRQ(ierr);
494   ierr = PetscMalloc1(nsubspaces, &patch->cellNodeMap);CHKERRQ(ierr);
495   ierr = PetscMalloc1(nsubspaces+1, &patch->subspaceOffsets);CHKERRQ(ierr);
496 
497   patch->nsubspaces       = nsubspaces;
498   patch->totalDofsPerCell = 0;
499   for (i = 0; i < nsubspaces; ++i) {
500     ierr = DMGetDefaultSection(dms[i], &patch->dofSection[i]);CHKERRQ(ierr);
501     ierr = PetscObjectReference((PetscObject) patch->dofSection[i]);CHKERRQ(ierr);
502     ierr = DMGetDefaultSF(dms[i], &sfs[i]);CHKERRQ(ierr);
503     patch->bs[i]              = bs[i];
504     patch->nodesPerCell[i]    = nodesPerCell[i];
505     patch->totalDofsPerCell  += nodesPerCell[i]*bs[i];
506     ierr = PetscMalloc1((cEnd-cStart)*nodesPerCell[i], &patch->cellNodeMap[i]);CHKERRQ(ierr);
507     for (j = 0; j < (cEnd-cStart)*nodesPerCell[i]; ++j) patch->cellNodeMap[i][j] = cellNodeMap[i][j];
508     patch->subspaceOffsets[i] = subspaceOffsets[i];
509   }
510   ierr = PCPatchCreateDefaultSF_Private(pc, nsubspaces, sfs, patch->bs);CHKERRQ(ierr);
511   ierr = PetscFree(sfs);CHKERRQ(ierr);
512 
513   patch->subspaceOffsets[nsubspaces] = subspaceOffsets[nsubspaces];
514   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGhostBcs, ghostBcNodes, PETSC_COPY_VALUES, &patch->ghostBcNodes);CHKERRQ(ierr);
515   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalBcs, globalBcNodes, PETSC_COPY_VALUES, &patch->globalBcNodes);CHKERRQ(ierr);
516   PetscFunctionReturn(0);
517 }
518 
519 /* TODO: Docs */
520 PetscErrorCode PCPatchSetDiscretisationInfoCombined(PC pc, DM dm, PetscInt *nodesPerCell, const PetscInt **cellNodeMap, PetscInt numGhostBcs, const PetscInt *ghostBcNodes, PetscInt numGlobalBcs, const PetscInt *globalBcNodes)
521 {
522   PC_PATCH      *patch = (PC_PATCH *) pc->data;
523   PetscInt       cStart, cEnd, i, j;
524   PetscErrorCode ierr;
525 
526   PetscFunctionBegin;
527   patch->combined = PETSC_TRUE;
528   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
529   ierr = DMGetNumFields(dm, &patch->nsubspaces);CHKERRQ(ierr);
530   ierr = PetscCalloc1(patch->nsubspaces, &patch->dofSection);CHKERRQ(ierr);
531   ierr = PetscMalloc1(patch->nsubspaces, &patch->bs);CHKERRQ(ierr);
532   ierr = PetscMalloc1(patch->nsubspaces, &patch->nodesPerCell);CHKERRQ(ierr);
533   ierr = PetscMalloc1(patch->nsubspaces, &patch->cellNodeMap);CHKERRQ(ierr);
534   ierr = PetscCalloc1(patch->nsubspaces+1, &patch->subspaceOffsets);CHKERRQ(ierr);
535   ierr = DMGetDefaultSection(dm, &patch->dofSection[0]);CHKERRQ(ierr);
536   ierr = PetscObjectReference((PetscObject) patch->dofSection[0]);CHKERRQ(ierr);
537   ierr = PetscSectionGetStorageSize(patch->dofSection[0], &patch->subspaceOffsets[patch->nsubspaces]);CHKERRQ(ierr);
538   patch->totalDofsPerCell = 0;
539   for (i = 0; i < patch->nsubspaces; ++i) {
540     patch->bs[i]             = 1;
541     patch->nodesPerCell[i]   = nodesPerCell[i];
542     patch->totalDofsPerCell += nodesPerCell[i];
543     ierr = PetscMalloc1((cEnd-cStart)*nodesPerCell[i], &patch->cellNodeMap[i]);CHKERRQ(ierr);
544     for (j = 0; j < (cEnd-cStart)*nodesPerCell[i]; ++j) patch->cellNodeMap[i][j] = cellNodeMap[i][j];
545   }
546   ierr = DMGetDefaultSF(dm, &patch->defaultSF);CHKERRQ(ierr);
547   ierr = PetscObjectReference((PetscObject) patch->defaultSF);CHKERRQ(ierr);
548   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGhostBcs, ghostBcNodes, PETSC_COPY_VALUES, &patch->ghostBcNodes);CHKERRQ(ierr);
549   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalBcs, globalBcNodes, PETSC_COPY_VALUES, &patch->globalBcNodes);CHKERRQ(ierr);
550   PetscFunctionReturn(0);
551 }
552 
553 /*@C
554 
555   PCPatchSetComputeFunction - Set the callback used to compute patch residuals
556 
557   Input Parameters:
558 + pc   - The PC
559 . func - The callback
560 - ctx  - The user context
561 
562   Level: advanced
563 
564   Note:
565   The callback has signature:
566 +  usercomputef(pc, point, x, f, cellIS, n, u, ctx)
567 +  pc     - The PC
568 +  point  - The point
569 +  x      - The input solution (not used in linear problems)
570 +  f      - The patch residual vector
571 +  cellIS - An array of the cell numbers
572 +  n      - The size of g2l
573 +  g2l    - The global to local dof translation table
574 +  ctx    - The user context
575   and can assume that the matrix entries have been set to zero before the call.
576 
577 .seealso: PCPatchSetComputeOperator(), PCPatchGetComputeOperator(), PCPatchSetDiscretisationInfo()
578 @*/
579 PetscErrorCode PCPatchSetComputeFunction(PC pc, PetscErrorCode (*func)(PC, PetscInt, Vec, Vec, IS, PetscInt, const PetscInt *, const PetscInt *, void *), void *ctx)
580 {
581   PC_PATCH *patch = (PC_PATCH *) pc->data;
582 
583   PetscFunctionBegin;
584   patch->usercomputef    = func;
585   patch->usercomputefctx = ctx;
586   PetscFunctionReturn(0);
587 }
588 
589 /*@C
590 
591   PCPatchSetComputeOperator - Set the callback used to compute patch matrices
592 
593   Input Parameters:
594 + pc   - The PC
595 . func - The callback
596 - ctx  - The user context
597 
598   Level: advanced
599 
600   Note:
601   The callback has signature:
602 +  usercomputeop(pc, point, x, mat, cellIS, n, u, ctx)
603 +  pc     - The PC
604 +  point  - The point
605 +  x      - The input solution (not used in linear problems)
606 +  mat    - The patch matrix
607 +  cellIS - An array of the cell numbers
608 +  n      - The size of g2l
609 +  g2l    - The global to local dof translation table
610 +  ctx    - The user context
611   and can assume that the matrix entries have been set to zero before the call.
612 
613 .seealso: PCPatchGetComputeOperator(), PCPatchSetComputeFunction(), PCPatchSetDiscretisationInfo()
614 @*/
615 PetscErrorCode PCPatchSetComputeOperator(PC pc, PetscErrorCode (*func)(PC, PetscInt, Vec, Mat, IS, PetscInt, const PetscInt *, const PetscInt *, void *), void *ctx)
616 {
617   PC_PATCH *patch = (PC_PATCH *) pc->data;
618 
619   PetscFunctionBegin;
620   patch->usercomputeop    = func;
621   patch->usercomputeopctx = ctx;
622   PetscFunctionReturn(0);
623 }
624 
625 /* On entry, ht contains the topological entities whose dofs we are responsible for solving for;
626    on exit, cht contains all the topological entities we need to compute their residuals.
627    In full generality this should incorporate knowledge of the sparsity pattern of the matrix;
628    here we assume a standard FE sparsity pattern.*/
629 /* TODO: Use DMPlexGetAdjacency() */
630 static PetscErrorCode PCPatchCompleteCellPatch(PC pc, PetscHSetI ht, PetscHSetI cht)
631 {
632   DM             dm;
633   PetscHashIter  hi;
634   PetscInt       point;
635   PetscInt      *star = NULL, *closure = NULL;
636   PetscInt       ignoredim, iStart = 0, iEnd = -1, starSize, closureSize, si, ci;
637   PetscErrorCode ierr;
638 
639   PetscFunctionBegin;
640   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
641   ierr = PCPatchGetIgnoreDim(pc, &ignoredim);CHKERRQ(ierr);
642   if (ignoredim >= 0) {ierr = DMPlexGetDepthStratum(dm, ignoredim, &iStart, &iEnd);CHKERRQ(ierr);}
643   ierr = PetscHSetIClear(cht);CHKERRQ(ierr);
644   PetscHashIterBegin(ht, hi);
645   while (!PetscHashIterAtEnd(ht, hi)) {
646 
647     PetscHashIterGetKey(ht, hi, point);
648     PetscHashIterNext(ht, hi);
649 
650     /* Loop over all the cells that this point connects to */
651     ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
652     for (si = 0; si < starSize*2; si += 2) {
653       const PetscInt ownedpoint = star[si];
654       /* TODO Check for point in cht before running through closure again */
655       /* now loop over all entities in the closure of that cell */
656       ierr = DMPlexGetTransitiveClosure(dm, ownedpoint, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
657       for (ci = 0; ci < closureSize*2; ci += 2) {
658         const PetscInt seenpoint = closure[ci];
659         if (ignoredim >= 0 && seenpoint >= iStart && seenpoint < iEnd) continue;
660         ierr = PetscHSetIAdd(cht, seenpoint);CHKERRQ(ierr);
661       }
662       ierr = DMPlexRestoreTransitiveClosure(dm, ownedpoint, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);
663     }
664     ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, NULL, &star);CHKERRQ(ierr);
665   }
666   PetscFunctionReturn(0);
667 }
668 
669 static PetscErrorCode PCPatchGetGlobalDofs(PC pc, PetscSection dofSection[], PetscInt f, PetscBool combined, PetscInt p, PetscInt *dof, PetscInt *off)
670 {
671   PetscErrorCode ierr;
672 
673   PetscFunctionBegin;
674   if (combined) {
675     if (f < 0) {
676       if (dof) {ierr = PetscSectionGetDof(dofSection[0], p, dof);CHKERRQ(ierr);}
677       if (off) {ierr = PetscSectionGetOffset(dofSection[0], p, off);CHKERRQ(ierr);}
678     } else {
679       if (dof) {ierr = PetscSectionGetFieldDof(dofSection[0], p, f, dof);CHKERRQ(ierr);}
680       if (off) {ierr = PetscSectionGetFieldOffset(dofSection[0], p, f, off);CHKERRQ(ierr);}
681     }
682   } else {
683     if (f < 0) {
684       PC_PATCH *patch = (PC_PATCH *) pc->data;
685       PetscInt  fdof, g;
686 
687       if (dof) {
688         *dof = 0;
689         for (g = 0; g < patch->nsubspaces; ++g) {
690           ierr = PetscSectionGetDof(dofSection[g], p, &fdof);CHKERRQ(ierr);
691           *dof += fdof;
692         }
693       }
694       if (off) {
695         *off = 0;
696         for (g = 0; g < patch->nsubspaces; ++g) {
697           ierr = PetscSectionGetOffset(dofSection[g], p, &fdof);CHKERRQ(ierr);
698           *off += fdof;
699         }
700       }
701     } else {
702       if (dof) {ierr = PetscSectionGetDof(dofSection[f], p, dof);CHKERRQ(ierr);}
703       if (off) {ierr = PetscSectionGetOffset(dofSection[f], p, off);CHKERRQ(ierr);}
704     }
705   }
706   PetscFunctionReturn(0);
707 }
708 
709 /* Given a hash table with a set of topological entities (pts), compute the degrees of
710    freedom in global concatenated numbering on those entities.
711    For Vanka smoothing, this needs to do something special: ignore dofs of the
712    constraint subspace on entities that aren't the base entity we're building the patch
713    around. */
714 static PetscErrorCode PCPatchGetPointDofs(PC pc, PetscHSetI pts, PetscHSetI dofs, PetscInt base, PetscHSetI* subspaces_to_exclude)
715 {
716   PC_PATCH      *patch = (PC_PATCH *) pc->data;
717   PetscHashIter  hi;
718   PetscInt       ldof, loff;
719   PetscInt       k, p;
720   PetscErrorCode ierr;
721 
722   PetscFunctionBegin;
723   ierr = PetscHSetIClear(dofs);CHKERRQ(ierr);
724   for (k = 0; k < patch->nsubspaces; ++k) {
725     PetscInt subspaceOffset = patch->subspaceOffsets[k];
726     PetscInt bs             = patch->bs[k];
727     PetscInt j, l;
728 
729     if (subspaces_to_exclude != NULL) {
730       PetscBool should_exclude_k = PETSC_FALSE;
731       PetscHSetIHas(*subspaces_to_exclude, k, &should_exclude_k);
732       if (should_exclude_k) {
733         /* only get this subspace dofs at the base entity, not any others */
734         ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, base, &ldof, &loff);CHKERRQ(ierr);
735         if (0 == ldof) continue;
736         for (j = loff; j < ldof + loff; ++j) {
737           for (l = 0; l < bs; ++l) {
738             PetscInt dof = bs*j + l + subspaceOffset;
739             ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
740           }
741         }
742         continue; /* skip the other dofs of this subspace */
743       }
744     }
745 
746     PetscHashIterBegin(pts, hi);
747     while (!PetscHashIterAtEnd(pts, hi)) {
748       PetscHashIterGetKey(pts, hi, p);
749       PetscHashIterNext(pts, hi);
750       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, p, &ldof, &loff);CHKERRQ(ierr);
751       if (0 == ldof) continue;
752       for (j = loff; j < ldof + loff; ++j) {
753         for (l = 0; l < bs; ++l) {
754           PetscInt dof = bs*j + l + subspaceOffset;
755           ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
756         }
757       }
758     }
759   }
760   PetscFunctionReturn(0);
761 }
762 
763 /* Given two hash tables A and B, compute the keys in B that are not in A, and put them in C */
764 static PetscErrorCode PCPatchComputeSetDifference_Private(PetscHSetI A, PetscHSetI B, PetscHSetI C)
765 {
766   PetscHashIter  hi;
767   PetscInt       key;
768   PetscBool      flg;
769   PetscErrorCode ierr;
770 
771   PetscFunctionBegin;
772   ierr = PetscHSetIClear(C);CHKERRQ(ierr);
773   PetscHashIterBegin(B, hi);
774   while (!PetscHashIterAtEnd(B, hi)) {
775     PetscHashIterGetKey(B, hi, key);
776     PetscHashIterNext(B, hi);
777     ierr = PetscHSetIHas(A, key, &flg);CHKERRQ(ierr);
778     if (!flg) {ierr = PetscHSetIAdd(C, key);CHKERRQ(ierr);}
779   }
780   PetscFunctionReturn(0);
781 }
782 
783 /*
784  * PCPatchCreateCellPatches - create patches.
785  *
786  * Input Parameters:
787  * + dm - The DMPlex object defining the mesh
788  *
789  * Output Parameters:
790  * + cellCounts  - Section with counts of cells around each vertex
791  * . cells       - IS of the cell point indices of cells in each patch
792  * . pointCounts - Section with counts of cells around each vertex
793  * - point       - IS of the cell point indices of cells in each patch
794  */
795 static PetscErrorCode PCPatchCreateCellPatches(PC pc)
796 {
797   PC_PATCH       *patch = (PC_PATCH *) pc->data;
798   DMLabel         ghost = NULL;
799   DM              dm, plex;
800   PetscHSetI      ht, cht;
801   PetscSection    cellCounts,  pointCounts;
802   PetscInt       *cellsArray, *pointsArray;
803   PetscInt        numCells,    numPoints;
804   const PetscInt *leaves;
805   PetscInt        nleaves, pStart, pEnd, cStart, cEnd, vStart, vEnd, v;
806   PetscBool       isFiredrake;
807   PetscErrorCode  ierr;
808 
809   PetscFunctionBegin;
810   /* Used to keep track of the cells in the patch. */
811   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
812   ierr = PetscHSetICreate(&cht);CHKERRQ(ierr);
813 
814   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
815   if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONGSTATE, "DM not yet set on patch PC\n");
816   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
817   ierr = DMPlexGetChart(plex, &pStart, &pEnd);CHKERRQ(ierr);
818   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
819 
820   if (patch->user_patches) {
821     ierr = patch->userpatchconstructionop(pc, &patch->npatch, &patch->userIS, &patch->iterationSet, patch->userpatchconstructctx);CHKERRQ(ierr);
822     vStart = 0; vEnd = patch->npatch;
823   } else if (patch->ctype == PC_PATCH_PARDECOMP) {
824     vStart = 0; vEnd = 1;
825   } else if (patch->codim < 0) {
826     if (patch->dim < 0) {ierr = DMPlexGetDepthStratum(plex,  0,            &vStart, &vEnd);CHKERRQ(ierr);}
827     else                {ierr = DMPlexGetDepthStratum(plex,  patch->dim,   &vStart, &vEnd);CHKERRQ(ierr);}
828   } else                {ierr = DMPlexGetHeightStratum(plex, patch->codim, &vStart, &vEnd);CHKERRQ(ierr);}
829   patch->npatch = vEnd - vStart;
830 
831   /* These labels mark the owned points.  We only create patches around points that this process owns. */
832   ierr = DMHasLabel(dm, "pyop2_ghost", &isFiredrake);CHKERRQ(ierr);
833   if (isFiredrake) {
834     ierr = DMGetLabel(dm, "pyop2_ghost", &ghost);CHKERRQ(ierr);
835     ierr = DMLabelCreateIndex(ghost, pStart, pEnd);CHKERRQ(ierr);
836   } else {
837     PetscSF sf;
838 
839     ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
840     ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
841     nleaves = PetscMax(nleaves, 0);
842   }
843 
844   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->cellCounts);CHKERRQ(ierr);
845   ierr = PetscObjectSetName((PetscObject) patch->cellCounts, "Patch Cell Layout");CHKERRQ(ierr);
846   cellCounts = patch->cellCounts;
847   ierr = PetscSectionSetChart(cellCounts, vStart, vEnd);CHKERRQ(ierr);
848   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->pointCounts);CHKERRQ(ierr);
849   ierr = PetscObjectSetName((PetscObject) patch->pointCounts, "Patch Point Layout");CHKERRQ(ierr);
850   pointCounts = patch->pointCounts;
851   ierr = PetscSectionSetChart(pointCounts, vStart, vEnd);CHKERRQ(ierr);
852   /* Count cells and points in the patch surrounding each entity */
853   for (v = vStart; v < vEnd; ++v) {
854     PetscHashIter hi;
855     PetscInt       chtSize, loc = -1;
856     PetscBool      flg;
857 
858     if (!patch->user_patches && patch->ctype != PC_PATCH_PARDECOMP) {
859       if (ghost) {ierr = DMLabelHasPoint(ghost, v, &flg);CHKERRQ(ierr);}
860       else       {ierr = PetscFindInt(v, nleaves, leaves, &loc);CHKERRQ(ierr); flg = loc >=0 ? PETSC_TRUE : PETSC_FALSE;}
861       /* Not an owned entity, don't make a cell patch. */
862       if (flg) continue;
863     }
864 
865     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
866     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
867     ierr = PetscHSetIGetSize(cht, &chtSize);CHKERRQ(ierr);
868     /* empty patch, continue */
869     if (chtSize == 0) continue;
870 
871     /* safe because size(cht) > 0 from above */
872     PetscHashIterBegin(cht, hi);
873     while (!PetscHashIterAtEnd(cht, hi)) {
874       PetscInt point, pdof;
875 
876       PetscHashIterGetKey(cht, hi, point);
877       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
878       if (pdof)                            {ierr = PetscSectionAddDof(pointCounts, v, 1);CHKERRQ(ierr);}
879       if (point >= cStart && point < cEnd) {ierr = PetscSectionAddDof(cellCounts, v, 1);CHKERRQ(ierr);}
880       PetscHashIterNext(cht, hi);
881     }
882   }
883   if (isFiredrake) {ierr = DMLabelDestroyIndex(ghost);CHKERRQ(ierr);}
884 
885   ierr = PetscSectionSetUp(cellCounts);CHKERRQ(ierr);
886   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
887   ierr = PetscMalloc1(numCells, &cellsArray);CHKERRQ(ierr);
888   ierr = PetscSectionSetUp(pointCounts);CHKERRQ(ierr);
889   ierr = PetscSectionGetStorageSize(pointCounts, &numPoints);CHKERRQ(ierr);
890   ierr = PetscMalloc1(numPoints, &pointsArray);CHKERRQ(ierr);
891 
892   /* Now that we know how much space we need, run through again and actually remember the cells. */
893   for (v = vStart; v < vEnd; v++ ) {
894     PetscHashIter hi;
895     PetscInt       dof, off, cdof, coff, pdof, n = 0, cn = 0;
896 
897     ierr = PetscSectionGetDof(pointCounts, v, &dof);CHKERRQ(ierr);
898     ierr = PetscSectionGetOffset(pointCounts, v, &off);CHKERRQ(ierr);
899     ierr = PetscSectionGetDof(cellCounts, v, &cdof);CHKERRQ(ierr);
900     ierr = PetscSectionGetOffset(cellCounts, v, &coff);CHKERRQ(ierr);
901     if (dof <= 0) continue;
902     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
903     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
904     PetscHashIterBegin(cht, hi);
905     while (!PetscHashIterAtEnd(cht, hi)) {
906       PetscInt point;
907 
908       PetscHashIterGetKey(cht, hi, point);
909       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
910       if (pdof)                            {pointsArray[off + n++] = point;}
911       if (point >= cStart && point < cEnd) {cellsArray[coff + cn++] = point;}
912       PetscHashIterNext(cht, hi);
913     }
914     if (cn != cdof) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of cells in patch %D is %D, but should be %D", v, cn, cdof);
915     if (n  != dof)  SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of points in patch %D is %D, but should be %D", v, n, dof);
916   }
917   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
918   ierr = PetscHSetIDestroy(&cht);CHKERRQ(ierr);
919   ierr = DMDestroy(&plex);CHKERRQ(ierr);
920 
921   ierr = ISCreateGeneral(PETSC_COMM_SELF, numCells,  cellsArray,  PETSC_OWN_POINTER, &patch->cells);CHKERRQ(ierr);
922   ierr = PetscObjectSetName((PetscObject) patch->cells,  "Patch Cells");CHKERRQ(ierr);
923   if (patch->viewCells) {
924     ierr = ObjectView((PetscObject) patch->cellCounts, patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
925     ierr = ObjectView((PetscObject) patch->cells,      patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
926   }
927   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, pointsArray, PETSC_OWN_POINTER, &patch->points);CHKERRQ(ierr);
928   ierr = PetscObjectSetName((PetscObject) patch->points, "Patch Points");CHKERRQ(ierr);
929   if (patch->viewPoints) {
930     ierr = ObjectView((PetscObject) patch->pointCounts, patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
931     ierr = ObjectView((PetscObject) patch->points,      patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
932   }
933   PetscFunctionReturn(0);
934 }
935 
936 /*
937  * PCPatchCreateCellPatchDiscretisationInfo - Build the dof maps for cell patches
938  *
939  * Input Parameters:
940  * + dm - The DMPlex object defining the mesh
941  * . cellCounts - Section with counts of cells around each vertex
942  * . cells - IS of the cell point indices of cells in each patch
943  * . cellNumbering - Section mapping plex cell points to Firedrake cell indices.
944  * . nodesPerCell - number of nodes per cell.
945  * - cellNodeMap - map from cells to node indices (nodesPerCell * numCells)
946  *
947  * Output Parameters:
948  * + dofs - IS of local dof numbers of each cell in the patch, where local is a patch local numbering
949  * . gtolCounts - Section with counts of dofs per cell patch
950  * - gtol - IS mapping from global dofs to local dofs for each patch.
951  */
952 static PetscErrorCode PCPatchCreateCellPatchDiscretisationInfo(PC pc)
953 {
954   PC_PATCH       *patch           = (PC_PATCH *) pc->data;
955   PetscSection    cellCounts      = patch->cellCounts;
956   PetscSection    pointCounts     = patch->pointCounts;
957   PetscSection    gtolCounts, gtolCountsWithArtificial = NULL, gtolCountsWithAll = NULL;
958   IS              cells           = patch->cells;
959   IS              points          = patch->points;
960   PetscSection    cellNumbering   = patch->cellNumbering;
961   PetscInt        Nf              = patch->nsubspaces;
962   PetscInt        numCells, numPoints;
963   PetscInt        numDofs;
964   PetscInt        numGlobalDofs, numGlobalDofsWithArtificial, numGlobalDofsWithAll;
965   PetscInt        totalDofsPerCell = patch->totalDofsPerCell;
966   PetscInt        vStart, vEnd, v;
967   const PetscInt *cellsArray, *pointsArray;
968   PetscInt       *newCellsArray   = NULL;
969   PetscInt       *dofsArray       = NULL;
970   PetscInt       *dofsArrayWithArtificial = NULL;
971   PetscInt       *dofsArrayWithAll = NULL;
972   PetscInt       *offsArray       = NULL;
973   PetscInt       *offsArrayWithArtificial = NULL;
974   PetscInt       *offsArrayWithAll = NULL;
975   PetscInt       *asmArray        = NULL;
976   PetscInt       *asmArrayWithArtificial = NULL;
977   PetscInt       *asmArrayWithAll = NULL;
978   PetscInt       *globalDofsArray = NULL;
979   PetscInt       *globalDofsArrayWithArtificial = NULL;
980   PetscInt       *globalDofsArrayWithAll = NULL;
981   PetscInt        globalIndex     = 0;
982   PetscInt        key             = 0;
983   PetscInt        asmKey          = 0;
984   DM              dm              = NULL;
985   const PetscInt *bcNodes         = NULL;
986   PetscHMapI      ht;
987   PetscHMapI      htWithArtificial;
988   PetscHMapI      htWithAll;
989   PetscHSetI      globalBcs;
990   PetscInt        numBcs;
991   PetscHSetI      ownedpts, seenpts, owneddofs, seendofs, artificialbcs;
992   PetscInt        pStart, pEnd, p, i;
993   char            option[PETSC_MAX_PATH_LEN];
994   PetscBool       isNonlinear;
995   PetscErrorCode  ierr;
996 
997   PetscFunctionBegin;
998 
999   ierr = PCGetDM(pc, &dm); CHKERRQ(ierr);
1000   /* dofcounts section is cellcounts section * dofPerCell */
1001   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
1002   ierr = PetscSectionGetStorageSize(patch->pointCounts, &numPoints);CHKERRQ(ierr);
1003   numDofs = numCells * totalDofsPerCell;
1004   ierr = PetscMalloc1(numDofs, &dofsArray);CHKERRQ(ierr);
1005   ierr = PetscMalloc1(numPoints*Nf, &offsArray);CHKERRQ(ierr);
1006   ierr = PetscMalloc1(numDofs, &asmArray);CHKERRQ(ierr);
1007   ierr = PetscMalloc1(numCells, &newCellsArray);CHKERRQ(ierr);
1008   ierr = PetscSectionGetChart(cellCounts, &vStart, &vEnd);CHKERRQ(ierr);
1009   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->gtolCounts);CHKERRQ(ierr);
1010   gtolCounts = patch->gtolCounts;
1011   ierr = PetscSectionSetChart(gtolCounts, vStart, vEnd);CHKERRQ(ierr);
1012   ierr = PetscObjectSetName((PetscObject) patch->gtolCounts, "Patch Global Index Section");CHKERRQ(ierr);
1013 
1014   if(patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE)
1015   {
1016     ierr = PetscMalloc1(numPoints*Nf, &offsArrayWithArtificial);CHKERRQ(ierr);
1017     ierr = PetscMalloc1(numDofs, &asmArrayWithArtificial);CHKERRQ(ierr);
1018     ierr = PetscMalloc1(numDofs, &dofsArrayWithArtificial);CHKERRQ(ierr);
1019     ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->gtolCountsWithArtificial);CHKERRQ(ierr);
1020     gtolCountsWithArtificial = patch->gtolCountsWithArtificial;
1021     ierr = PetscSectionSetChart(gtolCountsWithArtificial, vStart, vEnd);CHKERRQ(ierr);
1022     ierr = PetscObjectSetName((PetscObject) patch->gtolCountsWithArtificial, "Patch Global Index Section Including Artificial BCs");CHKERRQ(ierr);
1023   }
1024 
1025   isNonlinear = patch->isNonlinear;
1026   if(isNonlinear)
1027   {
1028     ierr = PetscMalloc1(numPoints*Nf, &offsArrayWithAll);CHKERRQ(ierr);
1029     ierr = PetscMalloc1(numDofs, &asmArrayWithAll);CHKERRQ(ierr);
1030     ierr = PetscMalloc1(numDofs, &dofsArrayWithAll);CHKERRQ(ierr);
1031     ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->gtolCountsWithAll);CHKERRQ(ierr);
1032     gtolCountsWithAll = patch->gtolCountsWithAll;
1033     ierr = PetscSectionSetChart(gtolCountsWithAll, vStart, vEnd);CHKERRQ(ierr);
1034     ierr = PetscObjectSetName((PetscObject) patch->gtolCountsWithAll, "Patch Global Index Section Including All BCs");CHKERRQ(ierr);
1035   }
1036 
1037   /* Outside the patch loop, get the dofs that are globally-enforced Dirichlet
1038    conditions */
1039   ierr = PetscHSetICreate(&globalBcs);CHKERRQ(ierr);
1040   ierr = ISGetIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
1041   ierr = ISGetSize(patch->ghostBcNodes, &numBcs); CHKERRQ(ierr);
1042   for (i = 0; i < numBcs; ++i) {
1043     ierr = PetscHSetIAdd(globalBcs, bcNodes[i]);CHKERRQ(ierr); /* these are already in concatenated numbering */
1044   }
1045   ierr = ISRestoreIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
1046   ierr = ISDestroy(&patch->ghostBcNodes); CHKERRQ(ierr); /* memory optimisation */
1047 
1048   /* Hash tables for artificial BC construction */
1049   ierr = PetscHSetICreate(&ownedpts);CHKERRQ(ierr);
1050   ierr = PetscHSetICreate(&seenpts);CHKERRQ(ierr);
1051   ierr = PetscHSetICreate(&owneddofs);CHKERRQ(ierr);
1052   ierr = PetscHSetICreate(&seendofs);CHKERRQ(ierr);
1053   ierr = PetscHSetICreate(&artificialbcs);CHKERRQ(ierr);
1054 
1055   ierr = ISGetIndices(cells, &cellsArray);CHKERRQ(ierr);
1056   ierr = ISGetIndices(points, &pointsArray);CHKERRQ(ierr);
1057   ierr = PetscHMapICreate(&ht);CHKERRQ(ierr);
1058   ierr = PetscHMapICreate(&htWithArtificial);CHKERRQ(ierr);
1059   ierr = PetscHMapICreate(&htWithAll);CHKERRQ(ierr);
1060   for (v = vStart; v < vEnd; ++v) {
1061     PetscInt localIndex = 0;
1062     PetscInt localIndexWithArtificial = 0;
1063     PetscInt localIndexWithAll = 0;
1064     PetscInt dof, off, i, j, k, l;
1065 
1066     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
1067     ierr = PetscHMapIClear(htWithArtificial);CHKERRQ(ierr);
1068     ierr = PetscHMapIClear(htWithAll);CHKERRQ(ierr);
1069     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
1070     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
1071     if (dof <= 0) continue;
1072 
1073     /* Calculate the global numbers of the artificial BC dofs here first */
1074     ierr = patch->patchconstructop((void*)patch, dm, v, ownedpts); CHKERRQ(ierr);
1075     ierr = PCPatchCompleteCellPatch(pc, ownedpts, seenpts); CHKERRQ(ierr);
1076     ierr = PCPatchGetPointDofs(pc, ownedpts, owneddofs, v, &patch->subspaces_to_exclude); CHKERRQ(ierr);
1077     ierr = PCPatchGetPointDofs(pc, seenpts, seendofs, v, NULL); CHKERRQ(ierr);
1078     ierr = PCPatchComputeSetDifference_Private(owneddofs, seendofs, artificialbcs); CHKERRQ(ierr);
1079     if (patch->viewPatches) {
1080       PetscHSetI globalbcdofs;
1081       PetscHashIter hi;
1082       MPI_Comm comm = PetscObjectComm((PetscObject)pc);
1083 
1084       ierr = PetscHSetICreate(&globalbcdofs);CHKERRQ(ierr);
1085       ierr = PetscSynchronizedPrintf(comm, "Patch %d: owned dofs:\n", v); CHKERRQ(ierr);
1086       PetscHashIterBegin(owneddofs, hi);
1087       while (!PetscHashIterAtEnd(owneddofs, hi)) {
1088         PetscInt globalDof;
1089 
1090         PetscHashIterGetKey(owneddofs, hi, globalDof);
1091         PetscHashIterNext(owneddofs, hi);
1092         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
1093       }
1094       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
1095       ierr = PetscSynchronizedPrintf(comm, "Patch %d: seen dofs:\n", v); CHKERRQ(ierr);
1096       PetscHashIterBegin(seendofs, hi);
1097       while (!PetscHashIterAtEnd(seendofs, hi)) {
1098         PetscInt globalDof;
1099         PetscBool flg;
1100 
1101         PetscHashIterGetKey(seendofs, hi, globalDof);
1102         PetscHashIterNext(seendofs, hi);
1103         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
1104 
1105         ierr = PetscHSetIHas(globalBcs, globalDof, &flg);CHKERRQ(ierr);
1106         if (flg) {ierr = PetscHSetIAdd(globalbcdofs, globalDof);CHKERRQ(ierr);}
1107       }
1108       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
1109       ierr = PetscSynchronizedPrintf(comm, "Patch %d: global BCs:\n", v); CHKERRQ(ierr);
1110       ierr = PetscHSetIGetSize(globalbcdofs, &numBcs);CHKERRQ(ierr);
1111       if (numBcs > 0) {
1112         PetscHashIterBegin(globalbcdofs, hi);
1113         while (!PetscHashIterAtEnd(globalbcdofs, hi)) {
1114           PetscInt globalDof;
1115           PetscHashIterGetKey(globalbcdofs, hi, globalDof);
1116           PetscHashIterNext(globalbcdofs, hi);
1117           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof);CHKERRQ(ierr);
1118         }
1119       }
1120       ierr = PetscSynchronizedPrintf(comm, "\n");CHKERRQ(ierr);
1121       ierr = PetscSynchronizedPrintf(comm, "Patch %d: artificial BCs:\n", v);CHKERRQ(ierr);
1122       ierr = PetscHSetIGetSize(artificialbcs, &numBcs);CHKERRQ(ierr);
1123       if (numBcs > 0) {
1124         PetscHashIterBegin(artificialbcs, hi);
1125         while (!PetscHashIterAtEnd(artificialbcs, hi)) {
1126           PetscInt globalDof;
1127           PetscHashIterGetKey(artificialbcs, hi, globalDof);
1128           PetscHashIterNext(artificialbcs, hi);
1129           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
1130         }
1131       }
1132       ierr = PetscSynchronizedPrintf(comm, "\n\n"); CHKERRQ(ierr);
1133       ierr = PetscHSetIDestroy(&globalbcdofs);CHKERRQ(ierr);
1134     }
1135    for (k = 0; k < patch->nsubspaces; ++k) {
1136       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1137       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1138       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1139       PetscInt        bs             = patch->bs[k];
1140 
1141       for (i = off; i < off + dof; ++i) {
1142         /* Walk over the cells in this patch. */
1143         const PetscInt c    = cellsArray[i];
1144         PetscInt       cell = c;
1145 
1146         /* TODO Change this to an IS */
1147         if (cellNumbering) {
1148           ierr = PetscSectionGetDof(cellNumbering, c, &cell);CHKERRQ(ierr);
1149           if (cell <= 0) SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_OUTOFRANGE, "Cell %D doesn't appear in cell numbering map", c);
1150           ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);
1151         }
1152         newCellsArray[i] = cell;
1153         for (j = 0; j < nodesPerCell; ++j) {
1154           /* For each global dof, map it into contiguous local storage. */
1155           const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + subspaceOffset;
1156           /* finally, loop over block size */
1157           for (l = 0; l < bs; ++l) {
1158             PetscInt  localDof;
1159             PetscBool isGlobalBcDof, isArtificialBcDof;
1160 
1161             /* first, check if this is either a globally enforced or locally enforced BC dof */
1162             ierr = PetscHSetIHas(globalBcs, globalDof + l, &isGlobalBcDof);CHKERRQ(ierr);
1163             ierr = PetscHSetIHas(artificialbcs, globalDof + l, &isArtificialBcDof);CHKERRQ(ierr);
1164 
1165             /* if it's either, don't ever give it a local dof number */
1166             if (isGlobalBcDof || isArtificialBcDof) {
1167               dofsArray[globalIndex] = -1; /* don't use this in assembly in this patch */
1168             } else {
1169               ierr = PetscHMapIGet(ht, globalDof + l, &localDof);CHKERRQ(ierr);
1170               if (localDof == -1) {
1171                 localDof = localIndex++;
1172                 ierr = PetscHMapISet(ht, globalDof + l, localDof);CHKERRQ(ierr);
1173               }
1174               if ( globalIndex >= numDofs ) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Found more dofs %D than expected %D", globalIndex+1, numDofs);
1175               /* And store. */
1176               dofsArray[globalIndex] = localDof;
1177             }
1178 
1179             if(patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1180               if (isGlobalBcDof) {
1181                 dofsArrayWithArtificial[globalIndex] = -1; /* don't use this in assembly in this patch */
1182               } else {
1183                 ierr = PetscHMapIGet(htWithArtificial, globalDof + l, &localDof);CHKERRQ(ierr);
1184                 if (localDof == -1) {
1185                   localDof = localIndexWithArtificial++;
1186                   ierr = PetscHMapISet(htWithArtificial, globalDof + l, localDof);CHKERRQ(ierr);
1187                 }
1188                 if ( globalIndex >= numDofs ) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Found more dofs %D than expected %D", globalIndex+1, numDofs);
1189                 /* And store.*/
1190                 dofsArrayWithArtificial[globalIndex] = localDof;
1191               }
1192             }
1193 
1194             if(isNonlinear) {
1195               /* Build the dofmap for the function space with _all_ dofs,
1196                  including those in any kind of boundary condition */
1197               ierr = PetscHMapIGet(htWithAll, globalDof + l, &localDof);CHKERRQ(ierr);
1198               if (localDof == -1) {
1199                 localDof = localIndexWithAll++;
1200                 ierr = PetscHMapISet(htWithAll, globalDof + l, localDof);CHKERRQ(ierr);
1201               }
1202               if ( globalIndex >= numDofs ) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Found more dofs %D than expected %D", globalIndex+1, numDofs);
1203               /* And store.*/
1204               dofsArrayWithAll[globalIndex] = localDof;
1205             }
1206             globalIndex++;
1207           }
1208         }
1209       }
1210     }
1211      /*How many local dofs in this patch? */
1212    if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1213      ierr = PetscHMapIGetSize(htWithArtificial, &dof);CHKERRQ(ierr);
1214      ierr = PetscSectionSetDof(gtolCountsWithArtificial, v, dof);CHKERRQ(ierr);
1215    }
1216    if (isNonlinear) {
1217      ierr = PetscHMapIGetSize(htWithAll, &dof);CHKERRQ(ierr);
1218      ierr = PetscSectionSetDof(gtolCountsWithAll, v, dof);CHKERRQ(ierr);
1219    }
1220     ierr = PetscHMapIGetSize(ht, &dof);CHKERRQ(ierr);
1221     ierr = PetscSectionSetDof(gtolCounts, v, dof);CHKERRQ(ierr);
1222   }
1223   if (globalIndex != numDofs) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Expected number of dofs (%d) doesn't match found number (%d)", numDofs, globalIndex);
1224   ierr = PetscSectionSetUp(gtolCounts);CHKERRQ(ierr);
1225   ierr = PetscSectionGetStorageSize(gtolCounts, &numGlobalDofs);CHKERRQ(ierr);
1226   ierr = PetscMalloc1(numGlobalDofs, &globalDofsArray);CHKERRQ(ierr);
1227 
1228   if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1229     ierr = PetscSectionSetUp(gtolCountsWithArtificial);CHKERRQ(ierr);
1230     ierr = PetscSectionGetStorageSize(gtolCountsWithArtificial, &numGlobalDofsWithArtificial);CHKERRQ(ierr);
1231     ierr = PetscMalloc1(numGlobalDofsWithArtificial, &globalDofsArrayWithArtificial);CHKERRQ(ierr);
1232   }
1233   if (isNonlinear) {
1234     ierr = PetscSectionSetUp(gtolCountsWithAll);CHKERRQ(ierr);
1235     ierr = PetscSectionGetStorageSize(gtolCountsWithAll, &numGlobalDofsWithAll);CHKERRQ(ierr);
1236     ierr = PetscMalloc1(numGlobalDofsWithAll, &globalDofsArrayWithAll);CHKERRQ(ierr);
1237   }
1238   /* Now populate the global to local map.  This could be merged into the above loop if we were willing to deal with reallocs. */
1239   for (v = vStart; v < vEnd; ++v) {
1240     PetscHashIter hi;
1241     PetscInt      dof, off, Np, ooff, i, j, k, l;
1242 
1243     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
1244     ierr = PetscHMapIClear(htWithArtificial);CHKERRQ(ierr);
1245     ierr = PetscHMapIClear(htWithAll);CHKERRQ(ierr);
1246     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
1247     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
1248     ierr = PetscSectionGetDof(pointCounts, v, &Np);CHKERRQ(ierr);
1249     ierr = PetscSectionGetOffset(pointCounts, v, &ooff);CHKERRQ(ierr);
1250     if (dof <= 0) continue;
1251 
1252     for (k = 0; k < patch->nsubspaces; ++k) {
1253       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1254       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1255       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1256       PetscInt        bs             = patch->bs[k];
1257       PetscInt        goff;
1258 
1259       for (i = off; i < off + dof; ++i) {
1260         /* Reconstruct mapping of global-to-local on this patch. */
1261         const PetscInt c    = cellsArray[i];
1262         PetscInt       cell = c;
1263 
1264         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1265         for (j = 0; j < nodesPerCell; ++j) {
1266           for (l = 0; l < bs; ++l) {
1267             const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1268             const PetscInt localDof  = dofsArray[key];
1269             if (localDof >= 0) {ierr = PetscHMapISet(ht, globalDof, localDof);CHKERRQ(ierr);}
1270             if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1271               const PetscInt localDofWithArtificial = dofsArrayWithArtificial[key];
1272               if (localDofWithArtificial >= 0) {
1273                 ierr = PetscHMapISet(htWithArtificial, globalDof, localDofWithArtificial);CHKERRQ(ierr);
1274               }
1275             }
1276             if (isNonlinear) {
1277               const PetscInt localDofWithAll = dofsArrayWithAll[key];
1278               if (localDofWithAll >= 0) {
1279                 ierr = PetscHMapISet(htWithAll, globalDof, localDofWithAll);CHKERRQ(ierr);
1280               }
1281             }
1282             key++;
1283           }
1284         }
1285       }
1286 
1287       /* Shove it in the output data structure. */
1288       ierr = PetscSectionGetOffset(gtolCounts, v, &goff);CHKERRQ(ierr);
1289       PetscHashIterBegin(ht, hi);
1290       while (!PetscHashIterAtEnd(ht, hi)) {
1291         PetscInt globalDof, localDof;
1292 
1293         PetscHashIterGetKey(ht, hi, globalDof);
1294         PetscHashIterGetVal(ht, hi, localDof);
1295         if (globalDof >= 0) globalDofsArray[goff + localDof] = globalDof;
1296         PetscHashIterNext(ht, hi);
1297       }
1298 
1299       if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1300         ierr = PetscSectionGetOffset(gtolCountsWithArtificial, v, &goff);CHKERRQ(ierr);
1301         PetscHashIterBegin(htWithArtificial, hi);
1302         while (!PetscHashIterAtEnd(htWithArtificial, hi)) {
1303           PetscInt globalDof, localDof;
1304           PetscHashIterGetKey(htWithArtificial, hi, globalDof);
1305           PetscHashIterGetVal(htWithArtificial, hi, localDof);
1306           if (globalDof >= 0) globalDofsArrayWithArtificial[goff + localDof] = globalDof;
1307           PetscHashIterNext(htWithArtificial, hi);
1308         }
1309       }
1310       if (isNonlinear) {
1311         ierr = PetscSectionGetOffset(gtolCountsWithAll, v, &goff);CHKERRQ(ierr);
1312         PetscHashIterBegin(htWithAll, hi);
1313         while (!PetscHashIterAtEnd(htWithAll, hi)) {
1314           PetscInt globalDof, localDof;
1315           PetscHashIterGetKey(htWithAll, hi, globalDof);
1316           PetscHashIterGetVal(htWithAll, hi, localDof);
1317           if (globalDof >= 0) globalDofsArrayWithAll[goff + localDof] = globalDof;
1318           PetscHashIterNext(htWithAll, hi);
1319         }
1320       }
1321 
1322       for (p = 0; p < Np; ++p) {
1323         const PetscInt point = pointsArray[ooff + p];
1324         PetscInt       globalDof, localDof;
1325 
1326         ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, point, NULL, &globalDof);CHKERRQ(ierr);
1327         ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1328         offsArray[(ooff + p)*Nf + k] = localDof;
1329         if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1330           ierr = PetscHMapIGet(htWithArtificial, globalDof, &localDof);CHKERRQ(ierr);
1331           offsArrayWithArtificial[(ooff + p)*Nf + k] = localDof;
1332         }
1333         if (isNonlinear) {
1334           ierr = PetscHMapIGet(htWithAll, globalDof, &localDof);CHKERRQ(ierr);
1335           offsArrayWithAll[(ooff + p)*Nf + k] = localDof;
1336         }
1337       }
1338     }
1339 
1340     ierr = PetscHSetIDestroy(&globalBcs);CHKERRQ(ierr);
1341     ierr = PetscHSetIDestroy(&ownedpts);CHKERRQ(ierr);
1342     ierr = PetscHSetIDestroy(&seenpts);CHKERRQ(ierr);
1343     ierr = PetscHSetIDestroy(&owneddofs);CHKERRQ(ierr);
1344     ierr = PetscHSetIDestroy(&seendofs);CHKERRQ(ierr);
1345     ierr = PetscHSetIDestroy(&artificialbcs);CHKERRQ(ierr);
1346 
1347       /* At this point, we have a hash table ht built that maps globalDof -> localDof.
1348      We need to create the dof table laid out cellwise first, then by subspace,
1349      as the assembler assembles cell-wise and we need to stuff the different
1350      contributions of the different function spaces to the right places. So we loop
1351      over cells, then over subspaces. */
1352     if (patch->nsubspaces > 1) { /* for nsubspaces = 1, data we need is already in dofsArray */
1353       for (i = off; i < off + dof; ++i) {
1354         const PetscInt c    = cellsArray[i];
1355         PetscInt       cell = c;
1356 
1357         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1358         for (k = 0; k < patch->nsubspaces; ++k) {
1359           const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1360           PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1361           PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1362           PetscInt        bs             = patch->bs[k];
1363 
1364           for (j = 0; j < nodesPerCell; ++j) {
1365             for (l = 0; l < bs; ++l) {
1366               const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1367               PetscInt       localDof;
1368 
1369               ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1370               /* If it's not in the hash table, i.e. is a BC dof,
1371                then the PetscHSetIMap above gives -1, which matches
1372                exactly the convention for PETSc's matrix assembly to
1373                ignore the dof. So we don't need to do anything here */
1374               asmArray[asmKey] = localDof;
1375               if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1376                 ierr = PetscHMapIGet(htWithArtificial, globalDof, &localDof);CHKERRQ(ierr);
1377                 asmArrayWithArtificial[asmKey] = localDof;
1378               }
1379               if (isNonlinear) {
1380                 ierr = PetscHMapIGet(htWithAll, globalDof, &localDof);CHKERRQ(ierr);
1381                 asmArrayWithAll[asmKey] = localDof;
1382               }
1383               asmKey++;
1384             }
1385           }
1386         }
1387       }
1388     }
1389   }
1390   if (1 == patch->nsubspaces) {
1391     ierr = PetscMemcpy(asmArray, dofsArray, numDofs * sizeof(PetscInt));CHKERRQ(ierr);
1392     if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1393       ierr = PetscMemcpy(asmArrayWithArtificial, dofsArrayWithArtificial, numDofs * sizeof(PetscInt));CHKERRQ(ierr);
1394     }
1395     if (isNonlinear) {
1396       ierr = PetscMemcpy(asmArrayWithAll, dofsArrayWithAll, numDofs * sizeof(PetscInt));CHKERRQ(ierr);
1397     }
1398   }
1399 
1400   ierr = PetscHMapIDestroy(&ht);CHKERRQ(ierr);
1401   ierr = PetscHMapIDestroy(&htWithArtificial);CHKERRQ(ierr);
1402   ierr = PetscHMapIDestroy(&htWithAll);CHKERRQ(ierr);
1403   ierr = ISRestoreIndices(cells, &cellsArray);CHKERRQ(ierr);
1404   ierr = ISRestoreIndices(points, &pointsArray);CHKERRQ(ierr);
1405   ierr = PetscFree(dofsArray);CHKERRQ(ierr);
1406   if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1407     ierr = PetscFree(dofsArrayWithArtificial);CHKERRQ(ierr);
1408   }
1409   if (isNonlinear) {
1410     ierr = PetscFree(dofsArrayWithAll);CHKERRQ(ierr);
1411   }
1412   /* Create placeholder section for map from points to patch dofs */
1413   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->patchSection);CHKERRQ(ierr);
1414   ierr = PetscSectionSetNumFields(patch->patchSection, patch->nsubspaces);CHKERRQ(ierr);
1415   if (patch->combined) {
1416     PetscInt numFields;
1417     ierr = PetscSectionGetNumFields(patch->dofSection[0], &numFields);CHKERRQ(ierr);
1418     if (numFields != patch->nsubspaces) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Mismatch between number of section fields %D and number of subspaces %D", numFields, patch->nsubspaces);
1419     ierr = PetscSectionGetChart(patch->dofSection[0], &pStart, &pEnd);CHKERRQ(ierr);
1420     ierr = PetscSectionSetChart(patch->patchSection, pStart, pEnd);CHKERRQ(ierr);
1421     for (p = pStart; p < pEnd; ++p) {
1422       PetscInt dof, fdof, f;
1423 
1424       ierr = PetscSectionGetDof(patch->dofSection[0], p, &dof);CHKERRQ(ierr);
1425       ierr = PetscSectionSetDof(patch->patchSection, p, dof);CHKERRQ(ierr);
1426       for (f = 0; f < patch->nsubspaces; ++f) {
1427         ierr = PetscSectionGetFieldDof(patch->dofSection[0], p, f, &fdof);CHKERRQ(ierr);
1428         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, fdof);CHKERRQ(ierr);
1429       }
1430     }
1431   } else {
1432     PetscInt pStartf, pEndf, f;
1433     pStart = PETSC_MAX_INT;
1434     pEnd = PETSC_MIN_INT;
1435     for (f = 0; f < patch->nsubspaces; ++f) {
1436       ierr = PetscSectionGetChart(patch->dofSection[f], &pStartf, &pEndf);CHKERRQ(ierr);
1437       pStart = PetscMin(pStart, pStartf);
1438       pEnd = PetscMax(pEnd, pEndf);
1439     }
1440     ierr = PetscSectionSetChart(patch->patchSection, pStart, pEnd);CHKERRQ(ierr);
1441     for (f = 0; f < patch->nsubspaces; ++f) {
1442       ierr = PetscSectionGetChart(patch->dofSection[f], &pStartf, &pEndf);CHKERRQ(ierr);
1443       for (p = pStartf; p < pEndf; ++p) {
1444         PetscInt fdof;
1445         ierr = PetscSectionGetDof(patch->dofSection[f], p, &fdof);CHKERRQ(ierr);
1446         ierr = PetscSectionAddDof(patch->patchSection, p, fdof);CHKERRQ(ierr);
1447         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, fdof);CHKERRQ(ierr);
1448       }
1449     }
1450   }
1451   ierr = PetscSectionSetUp(patch->patchSection);CHKERRQ(ierr);
1452   ierr = PetscSectionSetUseFieldOffsets(patch->patchSection, PETSC_TRUE);CHKERRQ(ierr);
1453   /* Replace cell indices with firedrake-numbered ones. */
1454   ierr = ISGeneralSetIndices(cells, numCells, (const PetscInt *) newCellsArray, PETSC_OWN_POINTER);CHKERRQ(ierr);
1455   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalDofs, globalDofsArray, PETSC_OWN_POINTER, &patch->gtol);CHKERRQ(ierr);
1456   ierr = PetscObjectSetName((PetscObject) patch->gtol, "Global Indices");CHKERRQ(ierr);
1457   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_g2l_view", patch->classname);CHKERRQ(ierr);
1458   ierr = PetscSectionViewFromOptions(patch->gtolCounts, (PetscObject) pc, option);CHKERRQ(ierr);
1459   ierr = ISViewFromOptions(patch->gtol, (PetscObject) pc, option);CHKERRQ(ierr);
1460   ierr = ISCreateGeneral(PETSC_COMM_SELF, numDofs, asmArray, PETSC_OWN_POINTER, &patch->dofs);CHKERRQ(ierr);
1461   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints*Nf, offsArray, PETSC_OWN_POINTER, &patch->offs);CHKERRQ(ierr);
1462   if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1463     ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalDofsWithArtificial, globalDofsArrayWithArtificial, PETSC_OWN_POINTER, &patch->gtolWithArtificial);CHKERRQ(ierr);
1464     ierr = ISCreateGeneral(PETSC_COMM_SELF, numDofs, asmArrayWithArtificial, PETSC_OWN_POINTER, &patch->dofsWithArtificial);CHKERRQ(ierr);
1465     ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints*Nf, offsArrayWithArtificial, PETSC_OWN_POINTER, &patch->offsWithArtificial);CHKERRQ(ierr);
1466   }
1467   if (isNonlinear) {
1468     ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalDofsWithAll, globalDofsArrayWithAll, PETSC_OWN_POINTER, &patch->gtolWithAll);CHKERRQ(ierr);
1469     ierr = ISCreateGeneral(PETSC_COMM_SELF, numDofs, asmArrayWithAll, PETSC_OWN_POINTER, &patch->dofsWithAll);CHKERRQ(ierr);
1470     ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints*Nf, offsArrayWithAll, PETSC_OWN_POINTER, &patch->offsWithAll);CHKERRQ(ierr);
1471   }
1472   PetscFunctionReturn(0);
1473 }
1474 
1475 static PetscErrorCode PCPatchZeroFillMatrix_Private(Mat mat, const PetscInt ncell, const PetscInt ndof, const PetscInt *dof)
1476 {
1477   PetscScalar    *values = NULL;
1478   PetscInt        rows, c, i;
1479   PetscErrorCode  ierr;
1480 
1481   PetscFunctionBegin;
1482   ierr = PetscCalloc1(ndof*ndof, &values);CHKERRQ(ierr);
1483   for (c = 0; c < ncell; ++c) {
1484     const PetscInt *idx = &dof[ndof*c];
1485     ierr = MatSetValues(mat, ndof, idx, ndof, idx, values, INSERT_VALUES);CHKERRQ(ierr);
1486   }
1487   ierr = MatGetLocalSize(mat, &rows, NULL);CHKERRQ(ierr);
1488   for (i = 0; i < rows; ++i) {
1489     ierr = MatSetValues(mat, 1, &i, 1, &i, values, INSERT_VALUES);CHKERRQ(ierr);
1490   }
1491   ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1492   ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1493   ierr = PetscFree(values);CHKERRQ(ierr);
1494   PetscFunctionReturn(0);
1495 }
1496 
1497 static PetscErrorCode PCPatchCreateMatrix_Private(PC pc, PetscInt point, Mat *mat, PetscBool withArtificial)
1498 {
1499   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1500   Vec            x, y;
1501   PetscBool      flg;
1502   PetscInt       csize, rsize;
1503   const char    *prefix = NULL;
1504   PetscErrorCode ierr;
1505 
1506   PetscFunctionBegin;
1507   if(withArtificial) {
1508     /* would be nice if we could create a rectangular matrix of size numDofsWithArtificial x numDofs here */
1509     x = patch->patchRHSWithArtificial[point];
1510     y = patch->patchRHSWithArtificial[point];
1511   } else {
1512     x = patch->patchRHS[point];
1513     y = patch->patchUpdate[point];
1514   }
1515 
1516   ierr = VecGetSize(x, &csize);CHKERRQ(ierr);
1517   ierr = VecGetSize(y, &rsize);CHKERRQ(ierr);
1518   ierr = MatCreate(PETSC_COMM_SELF, mat);CHKERRQ(ierr);
1519   ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1520   ierr = MatSetOptionsPrefix(*mat, prefix);CHKERRQ(ierr);
1521   ierr = MatAppendOptionsPrefix(*mat, "pc_patch_sub_");CHKERRQ(ierr);
1522   if (patch->sub_mat_type)       {ierr = MatSetType(*mat, patch->sub_mat_type);CHKERRQ(ierr);}
1523   else if (!patch->sub_mat_type) {ierr = MatSetType(*mat, MATDENSE);CHKERRQ(ierr);}
1524   ierr = MatSetSizes(*mat, rsize, csize, rsize, csize);CHKERRQ(ierr);
1525   ierr = PetscObjectTypeCompare((PetscObject) *mat, MATDENSE, &flg);CHKERRQ(ierr);
1526   if (!flg) {ierr = PetscObjectTypeCompare((PetscObject)*mat, MATSEQDENSE, &flg);CHKERRQ(ierr);}
1527   /* Sparse patch matrices */
1528   if (!flg) {
1529     PetscBT         bt;
1530     PetscInt       *dnnz      = NULL;
1531     const PetscInt *dofsArray = NULL;
1532     PetscInt        pStart, pEnd, ncell, offset, c, i, j;
1533 
1534     if(withArtificial) {
1535       ierr = ISGetIndices(patch->dofsWithArtificial, &dofsArray);CHKERRQ(ierr);
1536     } else {
1537       ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1538     }
1539     ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1540     point += pStart;
1541     if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1542     ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1543     ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1544     ierr = PetscLogEventBegin(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1545     /* A PetscBT uses N^2 bits to store the sparsity pattern on a
1546      * patch. This is probably OK if the patches are not too big,
1547      * but uses too much memory. We therefore switch based on rsize. */
1548     if (rsize < 3000) { /* FIXME: I picked this switch value out of my hat */
1549       ierr = PetscCalloc1(rsize, &dnnz);CHKERRQ(ierr);
1550       ierr = PetscBTCreate(rsize*rsize, &bt);CHKERRQ(ierr);
1551       for (c = 0; c < ncell; ++c) {
1552         const PetscInt *idx = dofsArray + (offset + c)*patch->totalDofsPerCell;
1553         for (i = 0; i < patch->totalDofsPerCell; ++i) {
1554           const PetscInt row = idx[i];
1555           if (row < 0) continue;
1556           for (j = 0; j < patch->totalDofsPerCell; ++j) {
1557             const PetscInt col = idx[j];
1558             const PetscInt key = row*rsize + col;
1559             if (col < 0) continue;
1560             if (!PetscBTLookupSet(bt, key)) ++dnnz[row];
1561           }
1562         }
1563       }
1564       ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
1565       ierr = MatXAIJSetPreallocation(*mat, 1, dnnz, NULL, NULL, NULL);CHKERRQ(ierr);
1566       ierr = PetscFree(dnnz);CHKERRQ(ierr);
1567       ierr = PCPatchZeroFillMatrix_Private(*mat, ncell, patch->totalDofsPerCell, &dofsArray[offset*patch->totalDofsPerCell]);CHKERRQ(ierr);
1568     } else { /* rsize too big, use MATPREALLOCATOR */
1569       Mat preallocator;
1570       PetscScalar* vals;
1571 
1572       ierr = PetscCalloc1(patch->totalDofsPerCell*patch->totalDofsPerCell, &vals);CHKERRQ(ierr);
1573       ierr = MatCreate(PETSC_COMM_SELF, &preallocator);CHKERRQ(ierr);
1574       ierr = MatSetType(preallocator, MATPREALLOCATOR);CHKERRQ(ierr);
1575       ierr = MatSetSizes(preallocator, rsize, rsize, rsize, rsize);CHKERRQ(ierr);
1576       ierr = MatSetUp(preallocator);CHKERRQ(ierr);
1577       for (c = 0; c < ncell; ++c) {
1578         const PetscInt *idx = dofsArray + (offset + c)*patch->totalDofsPerCell;
1579         ierr = MatSetValues(preallocator, patch->totalDofsPerCell, idx, patch->totalDofsPerCell, idx, vals, INSERT_VALUES);CHKERRQ(ierr);
1580       }
1581       ierr = PetscFree(vals);CHKERRQ(ierr);
1582       ierr = MatAssemblyBegin(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1583       ierr = MatAssemblyEnd(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1584       ierr = MatPreallocatorPreallocate(preallocator, PETSC_TRUE, *mat);CHKERRQ(ierr);
1585       ierr = MatDestroy(&preallocator);CHKERRQ(ierr);
1586     }
1587     ierr = PetscLogEventEnd(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1588     if(withArtificial) {
1589       ierr = ISRestoreIndices(patch->dofsWithArtificial, &dofsArray);CHKERRQ(ierr);
1590     } else {
1591       ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1592     }
1593   }
1594   ierr = MatSetUp(*mat);CHKERRQ(ierr);
1595   PetscFunctionReturn(0);
1596 }
1597 
1598 static PetscErrorCode PCPatchComputeFunction_DMPlex_Private(PC pc, PetscInt patchNum, Vec x, Vec F, IS cellIS, PetscInt n, const PetscInt *l2p, const PetscInt *l2pWithAll, void *ctx)
1599 {
1600   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1601   DM              dm;
1602   PetscSection    s;
1603   const PetscInt *parray, *oarray;
1604   PetscInt        Nf = patch->nsubspaces, Np, poff, p, f;
1605   PetscErrorCode  ierr;
1606 
1607   PetscFunctionBegin;
1608   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1609   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1610   /* Set offset into patch */
1611   ierr = PetscSectionGetDof(patch->pointCounts, patchNum, &Np);CHKERRQ(ierr);
1612   ierr = PetscSectionGetOffset(patch->pointCounts, patchNum, &poff);CHKERRQ(ierr);
1613   ierr = ISGetIndices(patch->points, &parray);CHKERRQ(ierr);
1614   ierr = ISGetIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1615   for (f = 0; f < Nf; ++f) {
1616     for (p = 0; p < Np; ++p) {
1617       const PetscInt point = parray[poff+p];
1618       PetscInt       dof;
1619 
1620       ierr = PetscSectionGetFieldDof(patch->patchSection, point, f, &dof);CHKERRQ(ierr);
1621       ierr = PetscSectionSetFieldOffset(patch->patchSection, point, f, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);
1622       if (patch->nsubspaces == 1) {ierr = PetscSectionSetOffset(patch->patchSection, point, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);}
1623       else                        {ierr = PetscSectionSetOffset(patch->patchSection, point, -1);CHKERRQ(ierr);}
1624     }
1625   }
1626   ierr = ISRestoreIndices(patch->points, &parray);CHKERRQ(ierr);
1627   ierr = ISRestoreIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1628   if (patch->viewSection) {ierr = ObjectView((PetscObject) patch->patchSection, patch->viewerSection, patch->formatSection);CHKERRQ(ierr);}
1629   ierr = DMPlexComputeResidual_Patch_Internal(pc->dm, patch->patchSection, cellIS, 0.0, x, NULL, F, ctx);CHKERRQ(ierr);
1630   PetscFunctionReturn(0);
1631 }
1632 
1633 PetscErrorCode PCPatchComputeFunction_Internal(PC pc, Vec x, Vec F, PetscInt point)
1634 {
1635   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1636   const PetscInt *dofsArray;
1637   const PetscInt *dofsArrayWithAll;
1638   const PetscInt *cellsArray;
1639   PetscInt        ncell, offset, pStart, pEnd;
1640   PetscErrorCode  ierr;
1641 
1642   PetscFunctionBegin;
1643   ierr = PetscLogEventBegin(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1644   if (!patch->usercomputeop) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call PCPatchSetComputeOperator() to set user callback\n");
1645   ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1646   ierr = ISGetIndices(patch->dofsWithAll, &dofsArrayWithAll);CHKERRQ(ierr);
1647   ierr = ISGetIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1648   ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1649 
1650   point += pStart;
1651   if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1652 
1653   ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1654   ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1655   if (ncell <= 0) {
1656     ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1657     PetscFunctionReturn(0);
1658   }
1659   PetscStackPush("PCPatch user callback");
1660   /* Cannot reuse the same IS because the geometry info is being cached in it */
1661   ierr = ISCreateGeneral(PETSC_COMM_SELF, ncell, cellsArray + offset, PETSC_USE_POINTER, &patch->cellIS);CHKERRQ(ierr);
1662   ierr = patch->usercomputef(pc, point, x, F, patch->cellIS, ncell*patch->totalDofsPerCell, dofsArray + offset*patch->totalDofsPerCell,
1663                                                                                             dofsArrayWithAll + offset*patch->totalDofsPerCell,
1664                                                                                             patch->usercomputefctx);CHKERRQ(ierr);
1665   PetscStackPop;
1666   ierr = ISDestroy(&patch->cellIS);CHKERRQ(ierr);
1667   ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1668   ierr = ISRestoreIndices(patch->dofsWithAll, &dofsArrayWithAll);CHKERRQ(ierr);
1669   ierr = ISRestoreIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1670   if (patch->viewMatrix) {
1671     char name[PETSC_MAX_PATH_LEN];
1672 
1673     ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN-1, "Patch vector for Point %D", point);CHKERRQ(ierr);
1674     ierr = PetscObjectSetName((PetscObject) F, name);CHKERRQ(ierr);
1675     ierr = ObjectView((PetscObject) F, patch->viewerMatrix, patch->formatMatrix);CHKERRQ(ierr);
1676   }
1677   ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 static PetscErrorCode PCPatchComputeOperator_DMPlex_Private(PC pc, PetscInt patchNum, Vec x, Mat J, IS cellIS, PetscInt n, const PetscInt *l2p, const PetscInt *l2pWithAll, void *ctx)
1682 {
1683   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1684   DM              dm;
1685   PetscSection    s;
1686   const PetscInt *parray, *oarray;
1687   PetscInt        Nf = patch->nsubspaces, Np, poff, p, f;
1688   PetscErrorCode  ierr;
1689 
1690   PetscFunctionBegin;
1691   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1692   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1693   /* Set offset into patch */
1694   ierr = PetscSectionGetDof(patch->pointCounts, patchNum, &Np);CHKERRQ(ierr);
1695   ierr = PetscSectionGetOffset(patch->pointCounts, patchNum, &poff);CHKERRQ(ierr);
1696   ierr = ISGetIndices(patch->points, &parray);CHKERRQ(ierr);
1697   ierr = ISGetIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1698   for (f = 0; f < Nf; ++f) {
1699     for (p = 0; p < Np; ++p) {
1700       const PetscInt point = parray[poff+p];
1701       PetscInt       dof;
1702 
1703       ierr = PetscSectionGetFieldDof(patch->patchSection, point, f, &dof);CHKERRQ(ierr);
1704       ierr = PetscSectionSetFieldOffset(patch->patchSection, point, f, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);
1705       if (patch->nsubspaces == 1) {ierr = PetscSectionSetOffset(patch->patchSection, point, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);}
1706       else                        {ierr = PetscSectionSetOffset(patch->patchSection, point, -1);CHKERRQ(ierr);}
1707     }
1708   }
1709   ierr = ISRestoreIndices(patch->points, &parray);CHKERRQ(ierr);
1710   ierr = ISRestoreIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1711   if (patch->viewSection) {ierr = ObjectView((PetscObject) patch->patchSection, patch->viewerSection, patch->formatSection);CHKERRQ(ierr);}
1712   /* TODO Shut off MatViewFromOptions() in MatAssemblyEnd() here */
1713   ierr = DMPlexComputeJacobian_Patch_Internal(pc->dm, patch->patchSection, patch->patchSection, cellIS, 0.0, 0.0, x, NULL, J, J, ctx);CHKERRQ(ierr);
1714   PetscFunctionReturn(0);
1715 }
1716 
1717 PetscErrorCode PCPatchComputeOperator_Internal(PC pc, Vec x, Mat mat, PetscInt point, PetscBool withArtificial)
1718 {
1719   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1720   const PetscInt *dofsArray;
1721   const PetscInt *dofsArrayWithArtificial = NULL;
1722   const PetscInt *dofsArrayWithAll = NULL;
1723   const PetscInt *cellsArray;
1724   PetscInt        ncell, offset, pStart, pEnd;
1725   PetscBool       isNonlinear;
1726   PetscErrorCode  ierr;
1727 
1728   PetscFunctionBegin;
1729   ierr = PetscLogEventBegin(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1730   isNonlinear = patch->isNonlinear;
1731   if (!patch->usercomputeop) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call PCPatchSetComputeOperator() to set user callback\n");
1732   if(withArtificial) {
1733     ierr = ISGetIndices(patch->dofsWithArtificial, &dofsArray);CHKERRQ(ierr);
1734   } else {
1735     ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1736   }
1737   if (isNonlinear) {
1738     ierr = ISGetIndices(patch->dofsWithAll, &dofsArrayWithAll);CHKERRQ(ierr);
1739   }
1740   ierr = ISGetIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1741   ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1742 
1743   point += pStart;
1744   if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1745 
1746   ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1747   ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1748   if (ncell <= 0) {
1749     ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1750     PetscFunctionReturn(0);
1751   }
1752   PetscStackPush("PCPatch user callback");
1753   /* Cannot reuse the same IS because the geometry info is being cached in it */
1754   ierr = ISCreateGeneral(PETSC_COMM_SELF, ncell, cellsArray + offset, PETSC_USE_POINTER, &patch->cellIS);CHKERRQ(ierr);
1755   ierr = patch->usercomputeop(pc, point, x, mat, patch->cellIS, ncell*patch->totalDofsPerCell, dofsArray + offset*patch->totalDofsPerCell, dofsArrayWithAll ? dofsArrayWithAll + offset*patch->totalDofsPerCell : NULL, patch->usercomputeopctx);CHKERRQ(ierr);
1756   PetscStackPop;
1757   ierr = ISDestroy(&patch->cellIS);CHKERRQ(ierr);
1758   if(withArtificial) {
1759     ierr = ISRestoreIndices(patch->dofsWithArtificial, &dofsArray);CHKERRQ(ierr);
1760   } else {
1761     ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1762   }
1763   if (isNonlinear) {
1764     ierr = ISRestoreIndices(patch->dofsWithAll, &dofsArrayWithAll);CHKERRQ(ierr);
1765   }
1766   ierr = ISRestoreIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1767   if (patch->viewMatrix) {
1768     char name[PETSC_MAX_PATH_LEN];
1769 
1770     ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN-1, "Patch matrix for Point %D", point);CHKERRQ(ierr);
1771     ierr = PetscObjectSetName((PetscObject) mat, name);CHKERRQ(ierr);
1772     ierr = ObjectView((PetscObject) mat, patch->viewerMatrix, patch->formatMatrix);CHKERRQ(ierr);
1773   }
1774   ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1775   PetscFunctionReturn(0);
1776 }
1777 
1778 PetscErrorCode PCPatch_ScatterLocal_Private(PC pc, PetscInt p, Vec x, Vec y, InsertMode mode, ScatterMode scat, PatchScatterType scattertype)
1779 {
1780   PC_PATCH          *patch     = (PC_PATCH *) pc->data;
1781   const PetscScalar *xArray    = NULL;
1782   PetscScalar       *yArray    = NULL;
1783   const PetscInt    *gtolArray = NULL;
1784   PetscInt           dof, offset, lidx;
1785   PetscErrorCode     ierr;
1786 
1787   PetscFunctionBeginHot;
1788   ierr = PetscLogEventBegin(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1789   ierr = VecGetArrayRead(x, &xArray);CHKERRQ(ierr);
1790   ierr = VecGetArray(y, &yArray);CHKERRQ(ierr);
1791   if (scattertype == SCATTER_WITHARTIFICIAL) {
1792     ierr = PetscSectionGetDof(patch->gtolCountsWithArtificial, p, &dof);CHKERRQ(ierr);
1793     ierr = PetscSectionGetOffset(patch->gtolCountsWithArtificial, p, &offset);CHKERRQ(ierr);
1794     ierr = ISGetIndices(patch->gtolWithArtificial, &gtolArray);CHKERRQ(ierr);
1795   } else if (scattertype == SCATTER_WITHALL) {
1796     ierr = PetscSectionGetDof(patch->gtolCountsWithAll, p, &dof);CHKERRQ(ierr);
1797     ierr = PetscSectionGetOffset(patch->gtolCountsWithAll, p, &offset);CHKERRQ(ierr);
1798     ierr = ISGetIndices(patch->gtolWithAll, &gtolArray);CHKERRQ(ierr);
1799   } else {
1800     ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1801     ierr = PetscSectionGetOffset(patch->gtolCounts, p, &offset);CHKERRQ(ierr);
1802     ierr = ISGetIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1803   }
1804   if (mode == INSERT_VALUES && scat != SCATTER_FORWARD) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't insert if not scattering forward\n");
1805   if (mode == ADD_VALUES    && scat != SCATTER_REVERSE) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't add if not scattering reverse\n");
1806   for (lidx = 0; lidx < dof; ++lidx) {
1807     const PetscInt gidx = gtolArray[offset+lidx];
1808 
1809     if (mode == INSERT_VALUES) yArray[lidx]  = xArray[gidx]; /* Forward */
1810     else                       yArray[gidx] += xArray[lidx]; /* Reverse */
1811   }
1812   if (scattertype == SCATTER_WITHARTIFICIAL) {
1813     ierr = ISRestoreIndices(patch->gtolWithArtificial, &gtolArray);CHKERRQ(ierr);
1814   } else if (scattertype == SCATTER_WITHALL) {
1815     ierr = ISRestoreIndices(patch->gtolWithAll, &gtolArray);CHKERRQ(ierr);
1816   } else {
1817     ierr = ISRestoreIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1818   }
1819   ierr = VecRestoreArrayRead(x, &xArray);CHKERRQ(ierr);
1820   ierr = VecRestoreArray(y, &yArray);CHKERRQ(ierr);
1821   ierr = PetscLogEventEnd(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1822   PetscFunctionReturn(0);
1823 }
1824 
1825 static PetscErrorCode PCSetUp_PATCH_Linear(PC pc)
1826 {
1827   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1828   const char    *prefix;
1829   PetscInt       i;
1830   PetscErrorCode ierr;
1831 
1832   PetscFunctionBegin;
1833   if (!pc->setupcalled) {
1834     ierr = PetscMalloc1(patch->npatch, &patch->solver);CHKERRQ(ierr);
1835     ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1836     for (i = 0; i < patch->npatch; ++i) {
1837       KSP ksp;
1838       PC  subpc;
1839 
1840       ierr = KSPCreate(PETSC_COMM_SELF, &ksp);CHKERRQ(ierr);
1841       ierr = KSPSetOptionsPrefix(ksp, prefix);CHKERRQ(ierr);
1842       ierr = KSPAppendOptionsPrefix(ksp, "sub_");CHKERRQ(ierr);
1843       ierr = PetscObjectIncrementTabLevel((PetscObject) ksp, (PetscObject) pc, 1);CHKERRQ(ierr);
1844       ierr = KSPGetPC(ksp, &subpc);CHKERRQ(ierr);
1845       ierr = PetscObjectIncrementTabLevel((PetscObject) subpc, (PetscObject) pc, 1);CHKERRQ(ierr);
1846       ierr = PetscLogObjectParent((PetscObject) pc, (PetscObject) ksp);CHKERRQ(ierr);
1847       patch->solver[i] = (PetscObject) ksp;
1848     }
1849   }
1850   if (patch->save_operators) {
1851     for (i = 0; i < patch->npatch; ++i) {
1852       ierr = MatZeroEntries(patch->mat[i]);CHKERRQ(ierr);
1853       ierr = PCPatchComputeOperator_Internal(pc, NULL, patch->mat[i], i, PETSC_FALSE);CHKERRQ(ierr);
1854       ierr = KSPSetOperators((KSP) patch->solver[i], patch->mat[i], patch->mat[i]);CHKERRQ(ierr);
1855     }
1856   }
1857   if(patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1858     for (i = 0; i < patch->npatch; ++i) {
1859       /* Instead of padding patch->patchUpdate with zeros to get */
1860       /* patch->patchUpdateWithArtificial and then multiplying with the matrix, */
1861       /* just get rid of the columns that correspond to the dofs with */
1862       /* artificial bcs. That's of course fairly inefficient, hopefully we */
1863       /* can just assemble the rectangular matrix in the first place. */
1864       Mat matSquare;
1865       IS rowis;
1866       PetscInt dof;
1867 
1868       ierr = MatGetSize(patch->mat[i], &dof, NULL);CHKERRQ(ierr);
1869       if (dof == 0) {
1870         patch->matWithArtificial[i] = NULL;
1871         continue;
1872       }
1873 
1874       ierr = PCPatchCreateMatrix_Private(pc, i, &matSquare, PETSC_TRUE);CHKERRQ(ierr);
1875       ierr = MatZeroEntries(matSquare);CHKERRQ(ierr);
1876       ierr = PCPatchComputeOperator_Internal(pc, NULL, matSquare, i, PETSC_TRUE);CHKERRQ(ierr);
1877 
1878       ierr = MatGetSize(matSquare, &dof, NULL);CHKERRQ(ierr);
1879       ierr = ISCreateStride(PETSC_COMM_SELF, dof, 0, 1, &rowis); CHKERRQ(ierr);
1880       if(pc->setupcalled) {
1881         ierr = MatCreateSubMatrix(matSquare, rowis, patch->dofMappingWithoutToWithArtificial[i], MAT_REUSE_MATRIX, &patch->matWithArtificial[i]); CHKERRQ(ierr);
1882       } else {
1883         ierr = MatCreateSubMatrix(matSquare, rowis, patch->dofMappingWithoutToWithArtificial[i], MAT_INITIAL_MATRIX, &patch->matWithArtificial[i]); CHKERRQ(ierr);
1884       }
1885       ierr = ISDestroy(&rowis); CHKERRQ(ierr);
1886       ierr = MatDestroy(&matSquare);CHKERRQ(ierr);
1887     }
1888   }
1889   PetscFunctionReturn(0);
1890 }
1891 
1892 static PetscErrorCode PCSetUp_PATCH(PC pc)
1893 {
1894   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1895   PetscInt       i;
1896   PetscBool       isNonlinear;
1897   PetscErrorCode ierr;
1898 
1899   PetscFunctionBegin;
1900   if (!pc->setupcalled) {
1901     PetscInt pStart, pEnd, p;
1902     PetscInt localSize;
1903 
1904     ierr = PetscLogEventBegin(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1905 
1906     isNonlinear = patch->isNonlinear;
1907     if (!patch->nsubspaces) {
1908       DM           dm;
1909       PetscDS      prob;
1910       PetscSection s;
1911       PetscInt     cStart, cEnd, c, Nf, f, numGlobalBcs = 0, *globalBcs, *Nb, totNb = 0, **cellDofs;
1912 
1913       ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1914       if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONG, "Must set DM for PCPATCH or call PCPatchSetDiscretisationInfo()");
1915       ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1916       ierr = PetscSectionGetNumFields(s, &Nf);CHKERRQ(ierr);
1917       ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
1918       for (p = pStart; p < pEnd; ++p) {
1919         PetscInt cdof;
1920         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1921         numGlobalBcs += cdof;
1922       }
1923       ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1924       ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1925       ierr = PetscMalloc3(Nf, &Nb, Nf, &cellDofs, numGlobalBcs, &globalBcs);CHKERRQ(ierr);
1926       for (f = 0; f < Nf; ++f) {
1927         PetscFE        fe;
1928         PetscDualSpace sp;
1929         PetscInt       cdoff = 0;
1930 
1931         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1932         /* ierr = PetscFEGetNumComponents(fe, &Nc[f]);CHKERRQ(ierr); */
1933         ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
1934         ierr = PetscDualSpaceGetDimension(sp, &Nb[f]);CHKERRQ(ierr);
1935         totNb += Nb[f];
1936 
1937         ierr = PetscMalloc1((cEnd-cStart)*Nb[f], &cellDofs[f]);CHKERRQ(ierr);
1938         for (c = cStart; c < cEnd; ++c) {
1939           PetscInt *closure = NULL;
1940           PetscInt  clSize  = 0, cl;
1941 
1942           ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1943           for (cl = 0; cl < clSize*2; cl += 2) {
1944             const PetscInt p = closure[cl];
1945             PetscInt       fdof, d, foff;
1946 
1947             ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
1948             ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
1949             for (d = 0; d < fdof; ++d, ++cdoff) cellDofs[f][cdoff] = foff + d;
1950           }
1951           ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1952         }
1953         if (cdoff != (cEnd-cStart)*Nb[f]) SETERRQ4(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_SIZ, "Total number of cellDofs %D for field %D should be Nc (%D) * cellDof (%D)", cdoff, f, cEnd-cStart, Nb[f]);
1954       }
1955       numGlobalBcs = 0;
1956       for (p = pStart; p < pEnd; ++p) {
1957         const PetscInt *ind;
1958         PetscInt        off, cdof, d;
1959 
1960         ierr = PetscSectionGetOffset(s, p, &off);CHKERRQ(ierr);
1961         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1962         ierr = PetscSectionGetConstraintIndices(s, p, &ind);CHKERRQ(ierr);
1963         for (d = 0; d < cdof; ++d) globalBcs[numGlobalBcs++] = off + ind[d];
1964       }
1965 
1966       ierr = PCPatchSetDiscretisationInfoCombined(pc, dm, Nb, (const PetscInt **) cellDofs, numGlobalBcs, globalBcs, numGlobalBcs, globalBcs);CHKERRQ(ierr);
1967       for (f = 0; f < Nf; ++f) {
1968         ierr = PetscFree(cellDofs[f]);CHKERRQ(ierr);
1969       }
1970       ierr = PetscFree3(Nb, cellDofs, globalBcs);CHKERRQ(ierr);
1971       ierr = PCPatchSetComputeFunction(pc, PCPatchComputeFunction_DMPlex_Private, NULL);CHKERRQ(ierr);
1972       ierr = PCPatchSetComputeOperator(pc, PCPatchComputeOperator_DMPlex_Private, NULL);CHKERRQ(ierr);
1973     }
1974 
1975     localSize = patch->subspaceOffsets[patch->nsubspaces];
1976     ierr = VecCreateSeq(PETSC_COMM_SELF, localSize, &patch->localRHS);CHKERRQ(ierr);
1977     ierr = VecSetUp(patch->localRHS);CHKERRQ(ierr);
1978     ierr = VecDuplicate(patch->localRHS, &patch->localUpdate);CHKERRQ(ierr);
1979     ierr = PCPatchCreateCellPatches(pc);CHKERRQ(ierr);
1980     ierr = PCPatchCreateCellPatchDiscretisationInfo(pc);CHKERRQ(ierr);
1981 
1982     /* OK, now build the work vectors */
1983     ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, &pEnd);CHKERRQ(ierr);
1984     ierr = PetscMalloc1(patch->npatch, &patch->patchRHS);CHKERRQ(ierr);
1985     ierr = PetscMalloc1(patch->npatch, &patch->patchUpdate);CHKERRQ(ierr);
1986 
1987     if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
1988       ierr = PetscMalloc1(patch->npatch, &patch->patchRHSWithArtificial);CHKERRQ(ierr);
1989       ierr = PetscMalloc1(patch->npatch, &patch->dofMappingWithoutToWithArtificial);CHKERRQ(ierr);
1990     }
1991     if (isNonlinear) {
1992       ierr = PetscMalloc1(patch->npatch, &patch->dofMappingWithoutToWithAll);CHKERRQ(ierr);
1993     }
1994     for (p = pStart; p < pEnd; ++p) {
1995       PetscInt dof;
1996 
1997       ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1998       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchRHS[p-pStart]);CHKERRQ(ierr);
1999       ierr = VecSetUp(patch->patchRHS[p-pStart]);CHKERRQ(ierr);
2000       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchUpdate[p-pStart]);CHKERRQ(ierr);
2001       ierr = VecSetUp(patch->patchUpdate[p-pStart]);CHKERRQ(ierr);
2002       if (patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
2003         const PetscInt    *gtolArray, *gtolArrayWithArtificial = NULL;
2004         PetscInt           numPatchDofs, offset;
2005         PetscInt           numPatchDofsWithArtificial, offsetWithArtificial;
2006         PetscInt           dofWithoutArtificialCounter = 0;
2007         PetscInt          *patchWithoutArtificialToWithArtificialArray;
2008 
2009         ierr = PetscSectionGetDof(patch->gtolCountsWithArtificial, p, &dof);CHKERRQ(ierr);
2010         ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchRHSWithArtificial[p-pStart]);CHKERRQ(ierr);
2011         ierr = VecSetUp(patch->patchRHSWithArtificial[p-pStart]);CHKERRQ(ierr);
2012 
2013         /* Now build the mapping that for a dof in a patch WITHOUT dofs that have artificial bcs gives the */
2014         /* the index in the patch with all dofs */
2015         ierr = ISGetIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
2016 
2017         ierr = PetscSectionGetDof(patch->gtolCounts, p, &numPatchDofs);CHKERRQ(ierr);
2018         if (numPatchDofs == 0) {
2019           patch->dofMappingWithoutToWithArtificial[p-pStart] = NULL;
2020           continue;
2021         }
2022 
2023         ierr = PetscSectionGetOffset(patch->gtolCounts, p, &offset);CHKERRQ(ierr);
2024         ierr = ISGetIndices(patch->gtolWithArtificial, &gtolArrayWithArtificial);CHKERRQ(ierr);
2025         ierr = PetscSectionGetDof(patch->gtolCountsWithArtificial, p, &numPatchDofsWithArtificial);CHKERRQ(ierr);
2026         ierr = PetscSectionGetOffset(patch->gtolCountsWithArtificial, p, &offsetWithArtificial);CHKERRQ(ierr);
2027 
2028         ierr = PetscMalloc1(numPatchDofs, &patchWithoutArtificialToWithArtificialArray);CHKERRQ(ierr);
2029         for (i=0; i<numPatchDofsWithArtificial; i++) {
2030           if (gtolArrayWithArtificial[i+offsetWithArtificial] == gtolArray[offset+dofWithoutArtificialCounter]) {
2031             patchWithoutArtificialToWithArtificialArray[dofWithoutArtificialCounter] = i;
2032             dofWithoutArtificialCounter++;
2033             if (dofWithoutArtificialCounter == numPatchDofs)
2034               break;
2035           }
2036         }
2037         ierr = ISCreateGeneral(PETSC_COMM_SELF, numPatchDofs, patchWithoutArtificialToWithArtificialArray, PETSC_OWN_POINTER, &patch->dofMappingWithoutToWithArtificial[p-pStart]);CHKERRQ(ierr);
2038         ierr = ISRestoreIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
2039         ierr = ISRestoreIndices(patch->gtolWithArtificial, &gtolArrayWithArtificial);CHKERRQ(ierr);
2040       }
2041       if (isNonlinear) {
2042         const PetscInt    *gtolArray, *gtolArrayWithAll = NULL;
2043         PetscInt           numPatchDofs, offset;
2044         PetscInt           numPatchDofsWithAll, offsetWithAll;
2045         PetscInt           dofWithoutAllCounter = 0;
2046         PetscInt          *patchWithoutAllToWithAllArray;
2047 
2048         /* Now build the mapping that for a dof in a patch WITHOUT dofs that have artificial bcs gives the */
2049         /* the index in the patch with all dofs */
2050         ierr = ISGetIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
2051 
2052         ierr = PetscSectionGetDof(patch->gtolCounts, p, &numPatchDofs);CHKERRQ(ierr);
2053         if (numPatchDofs == 0) {
2054           patch->dofMappingWithoutToWithAll[p-pStart] = NULL;
2055           continue;
2056         }
2057 
2058         ierr = PetscSectionGetOffset(patch->gtolCounts, p, &offset);CHKERRQ(ierr);
2059         ierr = ISGetIndices(patch->gtolWithAll, &gtolArrayWithAll);CHKERRQ(ierr);
2060         ierr = PetscSectionGetDof(patch->gtolCountsWithAll, p, &numPatchDofsWithAll);CHKERRQ(ierr);
2061         ierr = PetscSectionGetOffset(patch->gtolCountsWithAll, p, &offsetWithAll);CHKERRQ(ierr);
2062 
2063         ierr = PetscMalloc1(numPatchDofs, &patchWithoutAllToWithAllArray);CHKERRQ(ierr);
2064 
2065         for (i=0; i<numPatchDofsWithAll; i++) {
2066           if (gtolArrayWithAll[i+offsetWithAll] == gtolArray[offset+dofWithoutAllCounter]) {
2067             patchWithoutAllToWithAllArray[dofWithoutAllCounter] = i;
2068             dofWithoutAllCounter++;
2069             if (dofWithoutAllCounter == numPatchDofs)
2070               break;
2071           }
2072         }
2073         ierr = ISCreateGeneral(PETSC_COMM_SELF, numPatchDofs, patchWithoutAllToWithAllArray, PETSC_OWN_POINTER, &patch->dofMappingWithoutToWithAll[p-pStart]);CHKERRQ(ierr);
2074         ierr = ISRestoreIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
2075         ierr = ISRestoreIndices(patch->gtolWithAll, &gtolArrayWithAll);CHKERRQ(ierr);
2076       }
2077     }
2078     if (patch->save_operators) {
2079       ierr = PetscMalloc1(patch->npatch, &patch->mat);CHKERRQ(ierr);
2080       for (i = 0; i < patch->npatch; ++i) {
2081         ierr = PCPatchCreateMatrix_Private(pc, i, &patch->mat[i], PETSC_FALSE);CHKERRQ(ierr);
2082       }
2083     }
2084     ierr = PetscLogEventEnd(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
2085 
2086     /* If desired, calculate weights for dof multiplicity */
2087     if (patch->partition_of_unity) {
2088       PetscScalar *input = NULL;
2089       PetscScalar *output = NULL;
2090       Vec global;
2091 
2092       ierr = VecDuplicate(patch->localRHS, &patch->dof_weights);CHKERRQ(ierr);
2093       if(patch->local_composition_type == PC_COMPOSITE_ADDITIVE) {
2094         for (i = 0; i < patch->npatch; ++i) {
2095           PetscInt dof;
2096 
2097           ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &dof);CHKERRQ(ierr);
2098           if (dof <= 0) continue;
2099           ierr = VecSet(patch->patchRHS[i], 1.0);CHKERRQ(ierr);
2100           ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchRHS[i], patch->dof_weights, ADD_VALUES, SCATTER_REVERSE, SCATTER_INTERIOR);CHKERRQ(ierr);
2101         }
2102       } else {
2103         /* multiplicative is actually only locally multiplicative and globally additive. need the pou where the mesh decomposition overlaps */
2104         ierr = VecSet(patch->dof_weights, 1.0);CHKERRQ(ierr);
2105       }
2106 
2107       VecDuplicate(patch->dof_weights, &global);
2108       VecSet(global, 0.);
2109 
2110       ierr = VecGetArray(patch->dof_weights, &input);CHKERRQ(ierr);
2111       ierr = VecGetArray(global, &output);CHKERRQ(ierr);
2112       ierr = PetscSFReduceBegin(patch->defaultSF, MPIU_SCALAR, input, output, MPI_SUM);CHKERRQ(ierr);
2113       ierr = PetscSFReduceEnd(patch->defaultSF, MPIU_SCALAR, input, output, MPI_SUM);CHKERRQ(ierr);
2114       ierr = VecRestoreArray(patch->dof_weights, &input);CHKERRQ(ierr);
2115       ierr = VecRestoreArray(global, &output);CHKERRQ(ierr);
2116 
2117       ierr = VecReciprocal(global);CHKERRQ(ierr);
2118 
2119       ierr = VecGetArray(patch->dof_weights, &output);CHKERRQ(ierr);
2120       ierr = VecGetArray(global, &input);CHKERRQ(ierr);
2121       ierr = PetscSFBcastBegin(patch->defaultSF, MPIU_SCALAR, input, output);CHKERRQ(ierr);
2122       ierr = PetscSFBcastEnd(patch->defaultSF, MPIU_SCALAR, input, output);CHKERRQ(ierr);
2123       ierr = VecRestoreArray(patch->dof_weights, &output);CHKERRQ(ierr);
2124       ierr = VecRestoreArray(global, &input);CHKERRQ(ierr);
2125       ierr = VecDestroy(&global);CHKERRQ(ierr);
2126     }
2127     if(patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE && patch->save_operators) {
2128       ierr = PetscMalloc1(patch->npatch, &patch->matWithArtificial);CHKERRQ(ierr);
2129     }
2130   }
2131   ierr = (*patch->setupsolver)(pc);CHKERRQ(ierr);
2132   PetscFunctionReturn(0);
2133 }
2134 
2135 static PetscErrorCode PCApply_PATCH_Linear(PC pc, PetscInt i, Vec x, Vec y)
2136 {
2137   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2138   KSP            ksp   = (KSP) patch->solver[i];
2139   PetscErrorCode ierr;
2140 
2141   PetscFunctionBegin;
2142   if (!patch->save_operators) {
2143     Mat mat;
2144 
2145     ierr = PCPatchCreateMatrix_Private(pc, i, &mat, PETSC_FALSE);CHKERRQ(ierr);
2146     /* Populate operator here. */
2147     ierr = PCPatchComputeOperator_Internal(pc, NULL, mat, i, PETSC_FALSE);CHKERRQ(ierr);
2148     ierr = KSPSetOperators(ksp, mat, mat);CHKERRQ(ierr);
2149     /* Drop reference so the KSPSetOperators below will blow it away. */
2150     ierr = MatDestroy(&mat);CHKERRQ(ierr);
2151   }
2152   ierr = PetscLogEventBegin(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
2153   if (!ksp->setfromoptionscalled) {
2154     ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
2155   }
2156   ierr = KSPSolve(ksp, x, y);CHKERRQ(ierr);
2157   ierr = PetscLogEventEnd(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
2158   if (!patch->save_operators) {
2159     PC pc;
2160     ierr = KSPSetOperators(ksp, NULL, NULL);CHKERRQ(ierr);
2161     ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
2162     /* Destroy PC context too, otherwise the factored matrix hangs around. */
2163     ierr = PCReset(pc);CHKERRQ(ierr);
2164   }
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 static PetscErrorCode PCUpdateMultiplicative_PATCH_Linear(PC pc, PetscInt i, PetscInt pStart)
2169 {
2170   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2171   Mat multMat;
2172   PetscErrorCode ierr;
2173 
2174   PetscFunctionBegin;
2175 
2176   if (patch->save_operators) {
2177     multMat = patch->matWithArtificial[i];
2178   } else {
2179     /*Very inefficient, hopefully we can just assemble the rectangular matrix in the first place.*/
2180     Mat matSquare;
2181     PetscInt dof;
2182     IS rowis;
2183     ierr = PCPatchCreateMatrix_Private(pc, i, &matSquare, PETSC_TRUE);CHKERRQ(ierr);
2184     ierr = MatZeroEntries(matSquare);CHKERRQ(ierr);
2185     ierr = PCPatchComputeOperator_Internal(pc, NULL, matSquare, i, PETSC_TRUE);CHKERRQ(ierr);
2186     ierr = MatGetSize(matSquare, &dof, NULL);CHKERRQ(ierr);
2187     ierr = ISCreateStride(PETSC_COMM_SELF, dof, 0, 1, &rowis); CHKERRQ(ierr);
2188     ierr = MatCreateSubMatrix(matSquare, rowis, patch->dofMappingWithoutToWithArtificial[i], MAT_INITIAL_MATRIX, &multMat); CHKERRQ(ierr);
2189     ierr = MatDestroy(&matSquare);CHKERRQ(ierr);
2190     ierr = ISDestroy(&rowis); CHKERRQ(ierr);
2191   }
2192   ierr = MatMult(multMat, patch->patchUpdate[i], patch->patchRHSWithArtificial[i]); CHKERRQ(ierr);
2193   ierr = VecScale(patch->patchRHSWithArtificial[i], -1.0); CHKERRQ(ierr);
2194   ierr = PCPatch_ScatterLocal_Private(pc, i + pStart, patch->patchRHSWithArtificial[i], patch->localRHS, ADD_VALUES, SCATTER_REVERSE, SCATTER_WITHARTIFICIAL); CHKERRQ(ierr);
2195   if (!patch->save_operators) {
2196     ierr = MatDestroy(&multMat); CHKERRQ(ierr);
2197   }
2198   PetscFunctionReturn(0);
2199 }
2200 
2201 static PetscErrorCode PCApply_PATCH(PC pc, Vec x, Vec y)
2202 {
2203   PC_PATCH          *patch    = (PC_PATCH *) pc->data;
2204   const PetscScalar *globalRHS  = NULL;
2205   PetscScalar       *localRHS   = NULL;
2206   PetscScalar       *globalUpdate  = NULL;
2207   const PetscInt    *bcNodes  = NULL;
2208   PetscInt           nsweep   = patch->symmetrise_sweep ? 2 : 1;
2209   PetscInt           start[2] = {0, 0};
2210   PetscInt           end[2]   = {-1, -1};
2211   const PetscInt     inc[2]   = {1, -1};
2212   const PetscScalar *localUpdate;
2213   const PetscInt    *iterationSet;
2214   PetscInt           pStart, numBcs, n, sweep, bc, j;
2215   PetscErrorCode     ierr;
2216 
2217   PetscFunctionBegin;
2218   ierr = PetscLogEventBegin(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
2219   ierr = PetscOptionsPushGetViewerOff(PETSC_TRUE);CHKERRQ(ierr);
2220   /* start, end, inc have 2 entries to manage a second backward sweep if we symmetrize */
2221   end[0]   = patch->npatch;
2222   start[1] = patch->npatch-1;
2223   if (patch->user_patches) {
2224     ierr = ISGetLocalSize(patch->iterationSet, &end[0]);CHKERRQ(ierr);
2225     start[1] = end[0] - 1;
2226     ierr = ISGetIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);
2227   }
2228   /* Scatter from global space into overlapped local spaces */
2229   ierr = VecGetArrayRead(x, &globalRHS);CHKERRQ(ierr);
2230   ierr = VecGetArray(patch->localRHS, &localRHS);CHKERRQ(ierr);
2231   ierr = PetscSFBcastBegin(patch->defaultSF, MPIU_SCALAR, globalRHS, localRHS);CHKERRQ(ierr);
2232   ierr = PetscSFBcastEnd(patch->defaultSF, MPIU_SCALAR, globalRHS, localRHS);CHKERRQ(ierr);
2233   ierr = VecRestoreArrayRead(x, &globalRHS);CHKERRQ(ierr);
2234   ierr = VecRestoreArray(patch->localRHS, &localRHS);CHKERRQ(ierr);
2235 
2236   ierr = VecSet(patch->localUpdate, 0.0);CHKERRQ(ierr);
2237   ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, NULL);CHKERRQ(ierr);
2238   for (sweep = 0; sweep < nsweep; sweep++) {
2239     for (j = start[sweep]; j*inc[sweep] < end[sweep]*inc[sweep]; j += inc[sweep]) {
2240       PetscInt i       = patch->user_patches ? iterationSet[j] : j;
2241       PetscInt start, len;
2242 
2243       ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &len);CHKERRQ(ierr);
2244       ierr = PetscSectionGetOffset(patch->gtolCounts, i+pStart, &start);CHKERRQ(ierr);
2245       /* TODO: Squash out these guys in the setup as well. */
2246       if (len <= 0) continue;
2247       /* TODO: Do we need different scatters for X and Y? */
2248       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->localRHS, patch->patchRHS[i], INSERT_VALUES, SCATTER_FORWARD, SCATTER_INTERIOR);CHKERRQ(ierr);
2249       ierr = (*patch->applysolver)(pc, i, patch->patchRHS[i], patch->patchUpdate[i]);CHKERRQ(ierr);
2250       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchUpdate[i], patch->localUpdate, ADD_VALUES, SCATTER_REVERSE, SCATTER_INTERIOR);CHKERRQ(ierr);
2251       if(patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
2252         ierr = (*patch->updatemultiplicative)(pc, i, pStart);CHKERRQ(ierr);
2253       }
2254     }
2255   }
2256   if (patch->user_patches) {ierr = ISRestoreIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);}
2257   /* XXX: should we do this on the global vector? */
2258   if (patch->partition_of_unity) {
2259     ierr = VecPointwiseMult(patch->localUpdate, patch->localUpdate, patch->dof_weights);CHKERRQ(ierr);
2260   }
2261   /* Now patch->localUpdate contains the solution of the patch solves, so we need to combine them all. */
2262   ierr = VecSet(y, 0.0);CHKERRQ(ierr);
2263   ierr = VecGetArray(y, &globalUpdate);CHKERRQ(ierr);
2264   ierr = VecGetArrayRead(patch->localUpdate, &localUpdate);CHKERRQ(ierr);
2265   ierr = PetscSFReduceBegin(patch->defaultSF, MPIU_SCALAR, localUpdate, globalUpdate, MPI_SUM);CHKERRQ(ierr);
2266   ierr = PetscSFReduceEnd(patch->defaultSF, MPIU_SCALAR, localUpdate, globalUpdate, MPI_SUM);CHKERRQ(ierr);
2267   ierr = VecRestoreArrayRead(patch->localUpdate, &localUpdate);CHKERRQ(ierr);
2268 
2269   /* Now we need to send the global BC values through */
2270   ierr = VecGetArrayRead(x, &globalRHS);CHKERRQ(ierr);
2271   ierr = ISGetSize(patch->globalBcNodes, &numBcs);CHKERRQ(ierr);
2272   ierr = ISGetIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
2273   ierr = VecGetLocalSize(x, &n);CHKERRQ(ierr);
2274   for (bc = 0; bc < numBcs; ++bc) {
2275     const PetscInt idx = bcNodes[bc];
2276     if (idx < n) globalUpdate[idx] = globalRHS[idx];
2277   }
2278 
2279   ierr = ISRestoreIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
2280   ierr = VecRestoreArrayRead(x, &globalRHS);CHKERRQ(ierr);
2281   ierr = VecRestoreArray(y, &globalUpdate);CHKERRQ(ierr);
2282 
2283   ierr = PetscOptionsPopGetViewerOff();CHKERRQ(ierr);
2284   ierr = PetscLogEventEnd(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
2285   PetscFunctionReturn(0);
2286 }
2287 
2288 static PetscErrorCode PCReset_PATCH_Linear(PC pc)
2289 {
2290   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2291   PetscInt       i;
2292   PetscErrorCode ierr;
2293 
2294   PetscFunctionBegin;
2295   if (patch->solver) {
2296     for (i = 0; i < patch->npatch; ++i) {ierr = KSPReset((KSP) patch->solver[i]);CHKERRQ(ierr);}
2297   }
2298   PetscFunctionReturn(0);
2299 }
2300 
2301 static PetscErrorCode PCReset_PATCH(PC pc)
2302 {
2303   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2304   PetscInt       i;
2305   PetscErrorCode ierr;
2306 
2307   PetscFunctionBegin;
2308   /* TODO: Get rid of all these ifs */
2309   ierr = PetscSFDestroy(&patch->defaultSF);CHKERRQ(ierr);
2310   ierr = PetscSectionDestroy(&patch->cellCounts);CHKERRQ(ierr);
2311   ierr = PetscSectionDestroy(&patch->pointCounts);CHKERRQ(ierr);
2312   ierr = PetscSectionDestroy(&patch->cellNumbering);CHKERRQ(ierr);
2313   ierr = PetscSectionDestroy(&patch->gtolCounts);CHKERRQ(ierr);
2314   ierr = ISDestroy(&patch->gtol);CHKERRQ(ierr);
2315   ierr = ISDestroy(&patch->cells);CHKERRQ(ierr);
2316   ierr = ISDestroy(&patch->points);CHKERRQ(ierr);
2317   ierr = ISDestroy(&patch->dofs);CHKERRQ(ierr);
2318   ierr = ISDestroy(&patch->offs);CHKERRQ(ierr);
2319   ierr = PetscSectionDestroy(&patch->patchSection);CHKERRQ(ierr);
2320   ierr = ISDestroy(&patch->ghostBcNodes);CHKERRQ(ierr);
2321   ierr = ISDestroy(&patch->globalBcNodes);CHKERRQ(ierr);
2322   ierr = PetscSectionDestroy(&patch->gtolCountsWithArtificial);CHKERRQ(ierr);
2323   ierr = ISDestroy(&patch->gtolWithArtificial);CHKERRQ(ierr);
2324   ierr = ISDestroy(&patch->dofsWithArtificial);CHKERRQ(ierr);
2325   ierr = ISDestroy(&patch->offsWithArtificial);CHKERRQ(ierr);
2326   ierr = PetscSectionDestroy(&patch->gtolCountsWithAll);CHKERRQ(ierr);
2327   ierr = ISDestroy(&patch->gtolWithAll);CHKERRQ(ierr);
2328   ierr = ISDestroy(&patch->dofsWithAll);CHKERRQ(ierr);
2329   ierr = ISDestroy(&patch->offsWithAll);CHKERRQ(ierr);
2330 
2331 
2332   if (patch->dofSection) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscSectionDestroy(&patch->dofSection[i]);CHKERRQ(ierr);}
2333   ierr = PetscFree(patch->dofSection);CHKERRQ(ierr);
2334   ierr = PetscFree(patch->bs);CHKERRQ(ierr);
2335   ierr = PetscFree(patch->nodesPerCell);CHKERRQ(ierr);
2336   if (patch->cellNodeMap) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscFree(patch->cellNodeMap[i]);CHKERRQ(ierr);}
2337   ierr = PetscFree(patch->cellNodeMap);CHKERRQ(ierr);
2338   ierr = PetscFree(patch->subspaceOffsets);CHKERRQ(ierr);
2339 
2340   ierr = (*patch->resetsolver)(pc);CHKERRQ(ierr);
2341 
2342   if (patch->subspaces_to_exclude) {
2343     PetscHSetIDestroy(&patch->subspaces_to_exclude);
2344   }
2345 
2346   ierr = VecDestroy(&patch->localRHS);CHKERRQ(ierr);
2347   ierr = VecDestroy(&patch->localUpdate);CHKERRQ(ierr);
2348   if (patch->patchRHS) {
2349     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchRHS[i]);CHKERRQ(ierr);}
2350     ierr = PetscFree(patch->patchRHS);CHKERRQ(ierr);
2351   }
2352   if (patch->patchUpdate) {
2353     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchUpdate[i]);CHKERRQ(ierr);}
2354     ierr = PetscFree(patch->patchUpdate);CHKERRQ(ierr);
2355   }
2356   ierr = VecDestroy(&patch->dof_weights);CHKERRQ(ierr);
2357   if (patch->patch_dof_weights) {
2358     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patch_dof_weights[i]);CHKERRQ(ierr);}
2359     ierr = PetscFree(patch->patch_dof_weights);CHKERRQ(ierr);
2360   }
2361   if (patch->mat) {
2362     for (i = 0; i < patch->npatch; ++i) {ierr = MatDestroy(&patch->mat[i]);CHKERRQ(ierr);}
2363     ierr = PetscFree(patch->mat);CHKERRQ(ierr);
2364   }
2365   if (patch->matWithArtificial) {
2366     for (i = 0; i < patch->npatch; ++i) {ierr = MatDestroy(&patch->matWithArtificial[i]);CHKERRQ(ierr);}
2367     ierr = PetscFree(patch->matWithArtificial);CHKERRQ(ierr);
2368   }
2369   if (patch->patchRHSWithArtificial) {
2370     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchRHSWithArtificial[i]);CHKERRQ(ierr);}
2371     ierr = PetscFree(patch->patchRHSWithArtificial);CHKERRQ(ierr);
2372   }
2373   if(patch->dofMappingWithoutToWithArtificial) {
2374     for (i = 0; i < patch->npatch; ++i) {ierr = ISDestroy(&patch->dofMappingWithoutToWithArtificial[i]);CHKERRQ(ierr);}
2375     ierr = PetscFree(patch->dofMappingWithoutToWithArtificial);CHKERRQ(ierr);
2376 
2377   }
2378   if(patch->dofMappingWithoutToWithAll) {
2379     for (i = 0; i < patch->npatch; ++i) {ierr = ISDestroy(&patch->dofMappingWithoutToWithAll[i]);CHKERRQ(ierr);}
2380     ierr = PetscFree(patch->dofMappingWithoutToWithAll);CHKERRQ(ierr);
2381 
2382   }
2383   ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);
2384   if (patch->userIS) {
2385     for (i = 0; i < patch->npatch; ++i) {ierr = ISDestroy(&patch->userIS[i]);CHKERRQ(ierr);}
2386     ierr = PetscFree(patch->userIS);CHKERRQ(ierr);
2387   }
2388   patch->bs          = 0;
2389   patch->cellNodeMap = NULL;
2390   patch->nsubspaces  = 0;
2391   ierr = ISDestroy(&patch->iterationSet);CHKERRQ(ierr);
2392 
2393   ierr = PetscViewerDestroy(&patch->viewerSection);CHKERRQ(ierr);
2394   PetscFunctionReturn(0);
2395 }
2396 
2397 static PetscErrorCode PCDestroy_PATCH_Linear(PC pc)
2398 {
2399   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2400   PetscInt       i;
2401   PetscErrorCode ierr;
2402 
2403   PetscFunctionBegin;
2404   if (patch->solver) {
2405     for (i = 0; i < patch->npatch; ++i) {ierr = KSPDestroy((KSP *) &patch->solver[i]);CHKERRQ(ierr);}
2406     ierr = PetscFree(patch->solver);CHKERRQ(ierr);
2407   }
2408   PetscFunctionReturn(0);
2409 }
2410 
2411 static PetscErrorCode PCDestroy_PATCH(PC pc)
2412 {
2413   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2414   PetscErrorCode ierr;
2415 
2416   PetscFunctionBegin;
2417   ierr = PCReset_PATCH(pc);CHKERRQ(ierr);
2418   ierr = (*patch->destroysolver)(pc);CHKERRQ(ierr);
2419   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2420   PetscFunctionReturn(0);
2421 }
2422 
2423 static PetscErrorCode PCSetFromOptions_PATCH(PetscOptionItems *PetscOptionsObject, PC pc)
2424 {
2425   PC_PATCH            *patch = (PC_PATCH *) pc->data;
2426   PCPatchConstructType patchConstructionType = PC_PATCH_STAR;
2427   char                 sub_mat_type[PETSC_MAX_PATH_LEN];
2428   char                 option[PETSC_MAX_PATH_LEN];
2429   const char          *prefix;
2430   PetscBool            flg, dimflg, codimflg;
2431   MPI_Comm             comm;
2432   PetscInt            *ifields, nfields, k;
2433   PetscErrorCode       ierr;
2434   PCCompositeType loctype = PC_COMPOSITE_ADDITIVE;
2435 
2436   PetscFunctionBegin;
2437   ierr = PetscObjectGetComm((PetscObject) pc, &comm);CHKERRQ(ierr);
2438   ierr = PetscObjectGetOptionsPrefix((PetscObject) pc, &prefix);CHKERRQ(ierr);
2439   ierr = PetscOptionsHead(PetscOptionsObject, "Patch solver options");CHKERRQ(ierr);
2440 
2441   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_save_operators", patch->classname);
2442   ierr = PetscOptionsBool(option,  "Store all patch operators for lifetime of object?", "PCPatchSetSaveOperators", patch->save_operators, &patch->save_operators, &flg);CHKERRQ(ierr);
2443 
2444   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_partition_of_unity", patch->classname);
2445   ierr = PetscOptionsBool(option, "Weight contributions by dof multiplicity?", "PCPatchSetPartitionOfUnity", patch->partition_of_unity, &patch->partition_of_unity, &flg);CHKERRQ(ierr);
2446 
2447   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_local_type", patch->classname);
2448   ierr = PetscOptionsEnum(option,"Type of local solver composition (additive or multiplicative)","PCPatchSetLocalComposition",PCCompositeTypes,(PetscEnum)loctype,(PetscEnum*)&loctype,&flg);CHKERRQ(ierr);
2449   if(flg) { ierr = PCPatchSetLocalComposition(pc, loctype);CHKERRQ(ierr);}
2450 
2451   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_construct_dim", patch->classname);
2452   ierr = PetscOptionsInt(option, "What dimension of mesh point to construct patches by? (0 = vertices)", "PCPATCH", patch->dim, &patch->dim, &dimflg);CHKERRQ(ierr);
2453   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_construct_codim", patch->classname);
2454   ierr = PetscOptionsInt(option, "What co-dimension of mesh point to construct patches by? (0 = cells)", "PCPATCH", patch->codim, &patch->codim, &codimflg);CHKERRQ(ierr);
2455   if (dimflg && codimflg) {SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Can only set one of dimension or co-dimension");CHKERRQ(ierr);}
2456 
2457   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_construct_type", patch->classname);
2458   ierr = PetscOptionsEnum(option, "How should the patches be constructed?", "PCPatchSetConstructType", PCPatchConstructTypes, (PetscEnum) patchConstructionType, (PetscEnum *) &patchConstructionType, &flg);CHKERRQ(ierr);
2459   if (flg) {ierr = PCPatchSetConstructType(pc, patchConstructionType, NULL, NULL);CHKERRQ(ierr);}
2460 
2461   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_vanka_dim", patch->classname);
2462   ierr = PetscOptionsInt(option, "Topological dimension of entities for Vanka to ignore", "PCPATCH", patch->vankadim, &patch->vankadim, &flg);CHKERRQ(ierr);
2463 
2464   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_ignore_dim", patch->classname);
2465   ierr = PetscOptionsInt(option, "Topological dimension of entities for completion to ignore", "PCPATCH", patch->ignoredim, &patch->ignoredim, &flg);CHKERRQ(ierr);
2466 
2467   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_pardecomp_overlap", patch->classname);
2468   ierr = PetscOptionsInt(option, "What overlap should we use in construct type pardecomp?", "PCPATCH", patch->pardecomp_overlap, &patch->pardecomp_overlap, &flg);CHKERRQ(ierr);
2469 
2470   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_sub_mat_type", patch->classname);
2471   ierr = PetscOptionsFList(option, "Matrix type for patch solves", "PCPatchSetSubMatType", MatList, NULL, sub_mat_type, PETSC_MAX_PATH_LEN, &flg);CHKERRQ(ierr);
2472   if (flg) {ierr = PCPatchSetSubMatType(pc, sub_mat_type);CHKERRQ(ierr);}
2473 
2474   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_symmetrise_sweep", patch->classname);
2475   ierr = PetscOptionsBool(option, "Go start->end, end->start?", "PCPATCH", patch->symmetrise_sweep, &patch->symmetrise_sweep, &flg);CHKERRQ(ierr);
2476 
2477   /* If the user has set the number of subspaces, use that for the buffer size,
2478      otherwise use a large number */
2479   if (patch->nsubspaces <= 0) {
2480     nfields = 128;
2481   } else {
2482     nfields = patch->nsubspaces;
2483   }
2484   ierr = PetscMalloc1(nfields, &ifields);CHKERRQ(ierr);
2485   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_exclude_subspaces", patch->classname);
2486   ierr = PetscOptionsGetIntArray(((PetscObject)pc)->options,((PetscObject)pc)->prefix,option,ifields,&nfields,&flg);CHKERRQ(ierr);
2487   if (flg && (patchConstructionType == PC_PATCH_USER)) SETERRQ(comm, PETSC_ERR_ARG_INCOMP, "We cannot support excluding a subspace with user patches because we do not index patches with a mesh point");
2488   if (flg) {
2489     PetscHSetIClear(patch->subspaces_to_exclude);
2490     for (k = 0; k < nfields; k++) {
2491       PetscHSetIAdd(patch->subspaces_to_exclude, ifields[k]);
2492     }
2493   }
2494   ierr = PetscFree(ifields);CHKERRQ(ierr);
2495 
2496   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_patches_view", patch->classname);
2497   ierr = PetscOptionsBool(option, "Print out information during patch construction", "PCPATCH", patch->viewPatches, &patch->viewPatches, &flg);CHKERRQ(ierr);
2498 
2499   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_cells_view", patch->classname);
2500   ierr = PetscOptionsGetViewer(comm,((PetscObject) pc)->options,prefix, option,   &patch->viewerCells,   &patch->formatCells,   &patch->viewCells);CHKERRQ(ierr);
2501   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_points_view", patch->classname);
2502   ierr = PetscOptionsGetViewer(comm,((PetscObject) pc)->options,prefix, option,  &patch->viewerPoints,  &patch->formatPoints,  &patch->viewPoints);CHKERRQ(ierr);
2503   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_section_view", patch->classname);
2504   ierr = PetscOptionsGetViewer(comm,((PetscObject) pc)->options,prefix, option, &patch->viewerSection, &patch->formatSection, &patch->viewSection);CHKERRQ(ierr);
2505   ierr = PetscSNPrintf(option, PETSC_MAX_PATH_LEN, "-%s_patch_mat_view", patch->classname);
2506   ierr = PetscOptionsGetViewer(comm,((PetscObject) pc)->options,prefix, option,     &patch->viewerMatrix,  &patch->formatMatrix,  &patch->viewMatrix);CHKERRQ(ierr);
2507   ierr = PetscOptionsTail();CHKERRQ(ierr);
2508   patch->optionsSet = PETSC_TRUE;
2509   PetscFunctionReturn(0);
2510 }
2511 
2512 static PetscErrorCode PCSetUpOnBlocks_PATCH(PC pc)
2513 {
2514   PC_PATCH          *patch = (PC_PATCH*) pc->data;
2515   KSPConvergedReason reason;
2516   PetscInt           i;
2517   PetscErrorCode     ierr;
2518 
2519   PetscFunctionBegin;
2520   if (!patch->save_operators) {
2521     /* Can't do this here because the sub KSPs don't have an operator attached yet. */
2522     PetscFunctionReturn(0);
2523   }
2524   for (i = 0; i < patch->npatch; ++i) {
2525     if (!((KSP) patch->solver[i])->setfromoptionscalled) {
2526       ierr = KSPSetFromOptions((KSP) patch->solver[i]);CHKERRQ(ierr);
2527     }
2528     ierr = KSPSetUp((KSP) patch->solver[i]);CHKERRQ(ierr);
2529     ierr = KSPGetConvergedReason((KSP) patch->solver[i], &reason);CHKERRQ(ierr);
2530     if (reason == KSP_DIVERGED_PCSETUP_FAILED) pc->failedreason = PC_SUBPC_ERROR;
2531   }
2532   PetscFunctionReturn(0);
2533 }
2534 
2535 static PetscErrorCode PCView_PATCH(PC pc, PetscViewer viewer)
2536 {
2537   PC_PATCH      *patch = (PC_PATCH *) pc->data;
2538   PetscViewer    sviewer;
2539   PetscBool      isascii;
2540   PetscMPIInt    rank;
2541   PetscErrorCode ierr;
2542 
2543   PetscFunctionBegin;
2544   /* TODO Redo tabbing with set tbas in new style */
2545   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
2546   if (!isascii) PetscFunctionReturn(0);
2547   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) pc), &rank);CHKERRQ(ierr);
2548   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2549   ierr = PetscViewerASCIIPrintf(viewer, "Subspace Correction preconditioner with %d patches\n", patch->npatch);CHKERRQ(ierr);
2550   if(patch->local_composition_type == PC_COMPOSITE_MULTIPLICATIVE) {
2551     ierr = PetscViewerASCIIPrintf(viewer, "Schwarz type: multiplicative\n");CHKERRQ(ierr);
2552   } else {
2553     ierr = PetscViewerASCIIPrintf(viewer, "Schwarz type: additive\n");CHKERRQ(ierr);
2554   }
2555   if (patch->partition_of_unity) {ierr = PetscViewerASCIIPrintf(viewer, "Weighting by partition of unity\n");CHKERRQ(ierr);}
2556   else                           {ierr = PetscViewerASCIIPrintf(viewer, "Not weighting by partition of unity\n");CHKERRQ(ierr);}
2557   if (patch->symmetrise_sweep) {ierr = PetscViewerASCIIPrintf(viewer, "Symmetrising sweep (start->end, then end->start)\n");CHKERRQ(ierr);}
2558   else                         {ierr = PetscViewerASCIIPrintf(viewer, "Not symmetrising sweep\n");CHKERRQ(ierr);}
2559   if (!patch->save_operators) {ierr = PetscViewerASCIIPrintf(viewer, "Not saving patch operators (rebuilt every PCApply)\n");CHKERRQ(ierr);}
2560   else                        {ierr = PetscViewerASCIIPrintf(viewer, "Saving patch operators (rebuilt every PCSetUp)\n");CHKERRQ(ierr);}
2561   if (patch->patchconstructop == PCPatchConstruct_Star)       {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: star\n");CHKERRQ(ierr);}
2562   else if (patch->patchconstructop == PCPatchConstruct_Vanka) {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: Vanka\n");CHKERRQ(ierr);}
2563   else if (patch->patchconstructop == PCPatchConstruct_User)  {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: user-specified\n");CHKERRQ(ierr);}
2564   else                                                        {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: unknown\n");CHKERRQ(ierr);}
2565   ierr = PetscViewerASCIIPrintf(viewer, "Solver on patches (all same):\n");CHKERRQ(ierr);
2566   if (patch->solver) {
2567     ierr = PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
2568     if (!rank) {
2569       ierr = PetscViewerASCIIPushTab(sviewer);CHKERRQ(ierr);
2570       ierr = PetscObjectView(patch->solver[0], sviewer);CHKERRQ(ierr);
2571       ierr = PetscViewerASCIIPopTab(sviewer);CHKERRQ(ierr);
2572     }
2573     ierr = PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
2574   } else {
2575     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2576     ierr = PetscViewerASCIIPrintf(viewer, "Solver not yet set.\n");CHKERRQ(ierr);
2577     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2578   }
2579   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2580   PetscFunctionReturn(0);
2581 }
2582 
2583 /*MC
2584   PCPATCH - A PC object that encapsulates flexible definition of blocks for overlapping and non-overlapping
2585             small block additive preconditioners. Block definition is based on topology from
2586             a DM and equation numbering from a PetscSection.
2587 
2588   Options Database Keys:
2589 + -pc_patch_cells_view   - Views the process local cell numbers for each patch
2590 . -pc_patch_points_view  - Views the process local mesh point numbers for each patch
2591 . -pc_patch_g2l_view     - Views the map between global dofs and patch local dofs for each patch
2592 . -pc_patch_patches_view - Views the global dofs associated with each patch and its boundary
2593 - -pc_patch_sub_mat_view - Views the matrix associated with each patch
2594 
2595   Level: intermediate
2596 
2597 .seealso: PCType, PCCreate(), PCSetType()
2598 M*/
2599 PETSC_EXTERN PetscErrorCode PCCreate_Patch(PC pc)
2600 {
2601   PC_PATCH      *patch;
2602   PetscErrorCode ierr;
2603 
2604   PetscFunctionBegin;
2605   ierr = PetscNewLog(pc, &patch);CHKERRQ(ierr);
2606 
2607   if (patch->subspaces_to_exclude) {
2608     PetscHSetIDestroy(&patch->subspaces_to_exclude);
2609   }
2610   PetscHSetICreate(&patch->subspaces_to_exclude);
2611 
2612   patch->classname = "pc";
2613   patch->isNonlinear = PETSC_FALSE;
2614 
2615   /* Set some defaults */
2616   patch->combined           = PETSC_FALSE;
2617   patch->save_operators     = PETSC_TRUE;
2618   patch->local_composition_type = PC_COMPOSITE_ADDITIVE;
2619   patch->partition_of_unity = PETSC_FALSE;
2620   patch->codim              = -1;
2621   patch->dim                = -1;
2622   patch->vankadim           = -1;
2623   patch->ignoredim          = -1;
2624   patch->pardecomp_overlap  = 0;
2625   patch->patchconstructop   = PCPatchConstruct_Star;
2626   patch->symmetrise_sweep   = PETSC_FALSE;
2627   patch->npatch             = 0;
2628   patch->userIS             = NULL;
2629   patch->optionsSet         = PETSC_FALSE;
2630   patch->iterationSet       = NULL;
2631   patch->user_patches       = PETSC_FALSE;
2632   ierr = PetscStrallocpy(MATDENSE, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
2633   patch->viewPatches        = PETSC_FALSE;
2634   patch->viewCells          = PETSC_FALSE;
2635   patch->viewPoints         = PETSC_FALSE;
2636   patch->viewSection        = PETSC_FALSE;
2637   patch->viewMatrix         = PETSC_FALSE;
2638   patch->setupsolver        = PCSetUp_PATCH_Linear;
2639   patch->applysolver        = PCApply_PATCH_Linear;
2640   patch->resetsolver        = PCReset_PATCH_Linear;
2641   patch->destroysolver      = PCDestroy_PATCH_Linear;
2642   patch->updatemultiplicative = PCUpdateMultiplicative_PATCH_Linear;
2643   patch->dofMappingWithoutToWithArtificial = NULL;
2644   patch->dofMappingWithoutToWithAll = NULL;
2645 
2646   pc->data                 = (void *) patch;
2647   pc->ops->apply           = PCApply_PATCH;
2648   pc->ops->applytranspose  = 0; /* PCApplyTranspose_PATCH; */
2649   pc->ops->setup           = PCSetUp_PATCH;
2650   pc->ops->reset           = PCReset_PATCH;
2651   pc->ops->destroy         = PCDestroy_PATCH;
2652   pc->ops->setfromoptions  = PCSetFromOptions_PATCH;
2653   pc->ops->setuponblocks   = PCSetUpOnBlocks_PATCH;
2654   pc->ops->view            = PCView_PATCH;
2655   pc->ops->applyrichardson = 0;
2656 
2657   PetscFunctionReturn(0);
2658 }
2659