xref: /petsc/src/ksp/pc/impls/patch/pcpatch.c (revision 1e5fa6bbe5bad64efe76606acf59583020a15c8f)
1 #include <petsc/private/pcpatchimpl.h>     /*I "petscpc.h" I*/
2 #include <petsc/private/dmpleximpl.h> /* For DMPlexComputeJacobian_Patch_Internal() */
3 #include <petscsf.h>
4 #include <petscbt.h>
5 #include <petscds.h>
6 
7 PetscLogEvent PC_Patch_CreatePatches, PC_Patch_ComputeOp, PC_Patch_Solve, PC_Patch_Scatter, PC_Patch_Apply, PC_Patch_Prealloc;
8 
9 PETSC_STATIC_INLINE PetscErrorCode ObjectView(PetscObject obj, PetscViewer viewer, PetscViewerFormat format)
10 {
11   PetscErrorCode ierr;
12 
13   ierr = PetscViewerPushFormat(viewer, format);CHKERRQ(ierr);
14   ierr = PetscObjectView(obj, viewer);CHKERRQ(ierr);
15   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
16   return(0);
17 }
18 
19 static PetscErrorCode PCPatchConstruct_Star(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
20 {
21   PetscInt       starSize;
22   PetscInt      *star = NULL, si;
23   PetscErrorCode ierr;
24 
25   PetscFunctionBegin;
26   PetscHSetIClear(ht);
27   /* To start with, add the point we care about */
28   ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
29   /* Loop over all the points that this point connects to */
30   ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
31   for (si = 0; si < starSize*2; si += 2) {ierr = PetscHSetIAdd(ht, star[si]);CHKERRQ(ierr);}
32   ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
33   PetscFunctionReturn(0);
34 }
35 
36 static PetscErrorCode PCPatchConstruct_Vanka(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
37 {
38   PC_PATCH      *patch = (PC_PATCH *) vpatch;
39   PetscInt       starSize;
40   PetscInt      *star = NULL;
41   PetscBool      shouldIgnore = PETSC_FALSE;
42   PetscInt       cStart, cEnd, iStart, iEnd, si;
43   PetscErrorCode ierr;
44 
45   PetscFunctionBegin;
46   ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
47   /* To start with, add the point we care about */
48   ierr = PetscHSetIAdd(ht, point);CHKERRQ(ierr);
49   /* Should we ignore any points of a certain dimension? */
50   if (patch->vankadim >= 0) {
51     shouldIgnore = PETSC_TRUE;
52     ierr = DMPlexGetDepthStratum(dm, patch->vankadim, &iStart, &iEnd);CHKERRQ(ierr);
53   }
54   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
55   /* Loop over all the cells that this point connects to */
56   ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
57   for (si = 0; si < starSize*2; si += 2) {
58     const PetscInt cell = star[si];
59     PetscInt       closureSize;
60     PetscInt      *closure = NULL, ci;
61 
62     if (cell < cStart || cell >= cEnd) continue;
63     /* now loop over all entities in the closure of that cell */
64     ierr = DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
65     for (ci = 0; ci < closureSize*2; ci += 2) {
66       const PetscInt newpoint = closure[ci];
67 
68       /* We've been told to ignore entities of this type.*/
69       if (shouldIgnore && newpoint >= iStart && newpoint < iEnd) continue;
70       ierr = PetscHSetIAdd(ht, newpoint);CHKERRQ(ierr);
71     }
72     ierr = DMPlexRestoreTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
73   }
74   ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
75   PetscFunctionReturn(0);
76 }
77 
78 /* The user's already set the patches in patch->userIS. Build the hash tables */
79 static PetscErrorCode PCPatchConstruct_User(void *vpatch, DM dm, PetscInt point, PetscHSetI ht)
80 {
81   PC_PATCH       *patch   = (PC_PATCH *) vpatch;
82   IS              patchis = patch->userIS[point];
83   PetscInt        n;
84   const PetscInt *patchdata;
85   PetscInt        pStart, pEnd, i;
86   PetscErrorCode  ierr;
87 
88   PetscFunctionBegin;
89   ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
90   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
91   ierr = ISGetLocalSize(patchis, &n);CHKERRQ(ierr);
92   ierr = ISGetIndices(patchis, &patchdata);CHKERRQ(ierr);
93   for (i = 0; i < n; ++i) {
94     const PetscInt ownedpoint = patchdata[i];
95 
96     if (ownedpoint < pStart || ownedpoint >= pEnd) {
97       SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D was not in [%D, %D)", ownedpoint, pStart, pEnd);
98     }
99     ierr = PetscHSetIAdd(ht, ownedpoint);CHKERRQ(ierr);
100   }
101   ierr = ISRestoreIndices(patchis, &patchdata);CHKERRQ(ierr);
102   PetscFunctionReturn(0);
103 }
104 
105 static PetscErrorCode PCPatchCreateDefaultSF_Private(PC pc, PetscInt n, const PetscSF *sf, const PetscInt *bs)
106 {
107   PC_PATCH      *patch = (PC_PATCH *) pc->data;
108   PetscInt       i;
109   PetscErrorCode ierr;
110 
111   PetscFunctionBegin;
112   if (n == 1 && bs[0] == 1) {
113     patch->defaultSF = sf[0];
114     ierr = PetscObjectReference((PetscObject) patch->defaultSF);CHKERRQ(ierr);
115   } else {
116     PetscInt     allRoots = 0, allLeaves = 0;
117     PetscInt     leafOffset = 0;
118     PetscInt    *ilocal = NULL;
119     PetscSFNode *iremote = NULL;
120     PetscInt    *remoteOffsets = NULL;
121     PetscInt     index = 0;
122     PetscHMapI   rankToIndex;
123     PetscInt     numRanks = 0;
124     PetscSFNode *remote = NULL;
125     PetscSF      rankSF;
126     PetscInt    *ranks = NULL;
127     PetscInt    *offsets = NULL;
128     MPI_Datatype contig;
129     PetscHSetI   ranksUniq;
130 
131     /* First figure out how many dofs there are in the concatenated numbering.
132      * allRoots: number of owned global dofs;
133      * allLeaves: number of visible dofs (global + ghosted).
134      */
135     for (i = 0; i < n; ++i) {
136       PetscInt nroots, nleaves;
137 
138       ierr = PetscSFGetGraph(sf[i], &nroots, &nleaves, NULL, NULL);CHKERRQ(ierr);
139       allRoots  += nroots * bs[i];
140       allLeaves += nleaves * bs[i];
141     }
142     ierr = PetscMalloc1(allLeaves, &ilocal);CHKERRQ(ierr);
143     ierr = PetscMalloc1(allLeaves, &iremote);CHKERRQ(ierr);
144     /* Now build an SF that just contains process connectivity. */
145     ierr = PetscHSetICreate(&ranksUniq);CHKERRQ(ierr);
146     for (i = 0; i < n; ++i) {
147       const PetscMPIInt *ranks = NULL;
148       PetscInt           nranks, j;
149 
150       ierr = PetscSFSetUp(sf[i]);CHKERRQ(ierr);
151       ierr = PetscSFGetRanks(sf[i], &nranks, &ranks, NULL, NULL, NULL);CHKERRQ(ierr);
152       /* These are all the ranks who communicate with me. */
153       for (j = 0; j < nranks; ++j) {
154         ierr = PetscHSetIAdd(ranksUniq, (PetscInt) ranks[j]);CHKERRQ(ierr);
155       }
156     }
157     ierr = PetscHSetIGetSize(ranksUniq, &numRanks);CHKERRQ(ierr);
158     ierr = PetscMalloc1(numRanks, &remote);CHKERRQ(ierr);
159     ierr = PetscMalloc1(numRanks, &ranks);CHKERRQ(ierr);
160     ierr = PetscHSetIGetElems(ranksUniq, &index, ranks);CHKERRQ(ierr);
161 
162     ierr = PetscHMapICreate(&rankToIndex);CHKERRQ(ierr);
163     for (i = 0; i < numRanks; ++i) {
164       remote[i].rank  = ranks[i];
165       remote[i].index = 0;
166       ierr = PetscHMapISet(rankToIndex, ranks[i], i);CHKERRQ(ierr);
167     }
168     ierr = PetscFree(ranks);CHKERRQ(ierr);
169     ierr = PetscHSetIDestroy(&ranksUniq);CHKERRQ(ierr);
170     ierr = PetscSFCreate(PetscObjectComm((PetscObject) pc), &rankSF);CHKERRQ(ierr);
171     ierr = PetscSFSetGraph(rankSF, 1, numRanks, NULL, PETSC_OWN_POINTER, remote, PETSC_OWN_POINTER);CHKERRQ(ierr);
172     ierr = PetscSFSetUp(rankSF);CHKERRQ(ierr);
173     /* OK, use it to communicate the root offset on the remote
174      * processes for each subspace. */
175     ierr = PetscMalloc1(n, &offsets);CHKERRQ(ierr);
176     ierr = PetscMalloc1(n*numRanks, &remoteOffsets);CHKERRQ(ierr);
177 
178     offsets[0] = 0;
179     for (i = 1; i < n; ++i) {
180       PetscInt nroots;
181 
182       ierr = PetscSFGetGraph(sf[i-1], &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
183       offsets[i] = offsets[i-1] + nroots*bs[i-1];
184     }
185     /* Offsets are the offsets on the current process of the
186      * global dof numbering for the subspaces. */
187     ierr = MPI_Type_contiguous(n, MPIU_INT, &contig);CHKERRQ(ierr);
188     ierr = MPI_Type_commit(&contig);CHKERRQ(ierr);
189 
190     ierr = PetscSFBcastBegin(rankSF, contig, offsets, remoteOffsets);CHKERRQ(ierr);
191     ierr = PetscSFBcastEnd(rankSF, contig, offsets, remoteOffsets);CHKERRQ(ierr);
192     ierr = MPI_Type_free(&contig);CHKERRQ(ierr);
193     ierr = PetscFree(offsets);CHKERRQ(ierr);
194     ierr = PetscSFDestroy(&rankSF);CHKERRQ(ierr);
195     /* Now remoteOffsets contains the offsets on the remote
196      * processes who communicate with me.  So now we can
197      * concatenate the list of SFs into a single one. */
198     index = 0;
199     for (i = 0; i < n; ++i) {
200       const PetscSFNode *remote = NULL;
201       const PetscInt    *local  = NULL;
202       PetscInt           nroots, nleaves, j;
203 
204       ierr = PetscSFGetGraph(sf[i], &nroots, &nleaves, &local, &remote);CHKERRQ(ierr);
205       for (j = 0; j < nleaves; ++j) {
206         PetscInt rank = remote[j].rank;
207         PetscInt idx, rootOffset, k;
208 
209         ierr = PetscHMapIGet(rankToIndex, rank, &idx);CHKERRQ(ierr);
210         if (idx == -1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Didn't find rank, huh?");
211         /* Offset on given rank for ith subspace */
212         rootOffset = remoteOffsets[n*idx + i];
213         for (k = 0; k < bs[i]; ++k) {
214           ilocal[index]        = (local ? local[j] : j)*bs[i] + k + leafOffset;
215           iremote[index].rank  = remote[j].rank;
216           iremote[index].index = remote[j].index*bs[i] + k + rootOffset;
217           ++index;
218         }
219       }
220       leafOffset += nleaves * bs[i];
221     }
222     ierr = PetscHMapIDestroy(&rankToIndex);CHKERRQ(ierr);
223     ierr = PetscFree(remoteOffsets);CHKERRQ(ierr);
224     ierr = PetscSFCreate(PetscObjectComm((PetscObject)pc), &patch->defaultSF);CHKERRQ(ierr);
225     ierr = PetscSFSetGraph(patch->defaultSF, allRoots, allLeaves, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER);CHKERRQ(ierr);
226   }
227   PetscFunctionReturn(0);
228 }
229 
230 /* TODO: Docs */
231 PetscErrorCode PCPatchSetIgnoreDim(PC pc, PetscInt dim)
232 {
233   PC_PATCH *patch = (PC_PATCH *) pc->data;
234   PetscFunctionBegin;
235   patch->ignoredim = dim;
236   PetscFunctionReturn(0);
237 }
238 
239 /* TODO: Docs */
240 PetscErrorCode PCPatchGetIgnoreDim(PC pc, PetscInt *dim)
241 {
242   PC_PATCH *patch = (PC_PATCH *) pc->data;
243   PetscFunctionBegin;
244   *dim = patch->ignoredim;
245   PetscFunctionReturn(0);
246 }
247 
248 /* TODO: Docs */
249 PetscErrorCode PCPatchSetSaveOperators(PC pc, PetscBool flg)
250 {
251   PC_PATCH *patch = (PC_PATCH *) pc->data;
252   PetscFunctionBegin;
253   patch->save_operators = flg;
254   PetscFunctionReturn(0);
255 }
256 
257 /* TODO: Docs */
258 PetscErrorCode PCPatchGetSaveOperators(PC pc, PetscBool *flg)
259 {
260   PC_PATCH *patch = (PC_PATCH *) pc->data;
261   PetscFunctionBegin;
262   *flg = patch->save_operators;
263   PetscFunctionReturn(0);
264 }
265 
266 /* TODO: Docs */
267 PetscErrorCode PCPatchSetPartitionOfUnity(PC pc, PetscBool flg)
268 {
269     PC_PATCH *patch = (PC_PATCH *) pc->data;
270     PetscFunctionBegin;
271     patch->partition_of_unity = flg;
272     PetscFunctionReturn(0);
273 }
274 
275 /* TODO: Docs */
276 PetscErrorCode PCPatchGetPartitionOfUnity(PC pc, PetscBool *flg)
277 {
278     PC_PATCH *patch = (PC_PATCH *) pc->data;
279     PetscFunctionBegin;
280     *flg = patch->partition_of_unity;
281     PetscFunctionReturn(0);
282 }
283 
284 /* TODO: Docs */
285 PetscErrorCode PCPatchSetSubMatType(PC pc, MatType sub_mat_type)
286 {
287   PC_PATCH      *patch = (PC_PATCH *) pc->data;
288   PetscErrorCode ierr;
289 
290   PetscFunctionBegin;
291   if (patch->sub_mat_type) {ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);}
292   ierr = PetscStrallocpy(sub_mat_type, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
293   PetscFunctionReturn(0);
294 }
295 
296 /* TODO: Docs */
297 PetscErrorCode PCPatchGetSubMatType(PC pc, MatType *sub_mat_type)
298 {
299   PC_PATCH *patch = (PC_PATCH *) pc->data;
300   PetscFunctionBegin;
301   *sub_mat_type = patch->sub_mat_type;
302   PetscFunctionReturn(0);
303 }
304 
305 /* TODO: Docs */
306 PetscErrorCode PCPatchSetCellNumbering(PC pc, PetscSection cellNumbering)
307 {
308   PC_PATCH      *patch = (PC_PATCH *) pc->data;
309   PetscErrorCode ierr;
310 
311   PetscFunctionBegin;
312   patch->cellNumbering = cellNumbering;
313   ierr = PetscObjectReference((PetscObject) cellNumbering);CHKERRQ(ierr);
314   PetscFunctionReturn(0);
315 }
316 
317 /* TODO: Docs */
318 PetscErrorCode PCPatchGetCellNumbering(PC pc, PetscSection *cellNumbering)
319 {
320   PC_PATCH *patch = (PC_PATCH *) pc->data;
321   PetscFunctionBegin;
322   *cellNumbering = patch->cellNumbering;
323   PetscFunctionReturn(0);
324 }
325 
326 /* TODO: Docs */
327 PetscErrorCode PCPatchSetConstructType(PC pc, PCPatchConstructType ctype, PetscErrorCode (*func)(PC, PetscInt *, IS **, IS *, void *), void *ctx)
328 {
329   PC_PATCH *patch = (PC_PATCH *) pc->data;
330 
331   PetscFunctionBegin;
332   patch->ctype = ctype;
333   switch (ctype) {
334   case PC_PATCH_STAR:
335     patch->user_patches     = PETSC_FALSE;
336     patch->patchconstructop = PCPatchConstruct_Star;
337     break;
338   case PC_PATCH_VANKA:
339     patch->user_patches     = PETSC_FALSE;
340     patch->patchconstructop = PCPatchConstruct_Vanka;
341     break;
342   case PC_PATCH_USER:
343   case PC_PATCH_PYTHON:
344     patch->user_patches     = PETSC_TRUE;
345     patch->patchconstructop = PCPatchConstruct_User;
346     if (func) {
347       patch->userpatchconstructionop = func;
348       patch->userpatchconstructctx   = ctx;
349     }
350     break;
351   default:
352     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_USER, "Unknown patch construction type %D", (PetscInt) patch->ctype);
353   }
354   PetscFunctionReturn(0);
355 }
356 
357 /* TODO: Docs */
358 PetscErrorCode PCPatchGetConstructType(PC pc, PCPatchConstructType *ctype, PetscErrorCode (**func)(PC, PetscInt *, IS **, IS *, void *), void **ctx)
359 {
360   PC_PATCH *patch = (PC_PATCH *) pc->data;
361 
362   PetscFunctionBegin;
363   *ctype = patch->ctype;
364   switch (patch->ctype) {
365   case PC_PATCH_STAR:
366   case PC_PATCH_VANKA:
367     break;
368   case PC_PATCH_USER:
369   case PC_PATCH_PYTHON:
370     *func = patch->userpatchconstructionop;
371     *ctx  = patch->userpatchconstructctx;
372     break;
373   default:
374     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_USER, "Unknown patch construction type %D", (PetscInt) patch->ctype);
375   }
376   PetscFunctionReturn(0);
377 }
378 
379 /* TODO: Docs */
380 PetscErrorCode PCPatchSetDiscretisationInfo(PC pc, PetscInt nsubspaces, DM *dms, PetscInt *bs, PetscInt *nodesPerCell, const PetscInt **cellNodeMap,
381                                             const PetscInt *subspaceOffsets, PetscInt numGhostBcs, const PetscInt *ghostBcNodes, PetscInt numGlobalBcs, const PetscInt *globalBcNodes)
382 {
383   PC_PATCH      *patch = (PC_PATCH *) pc->data;
384   DM             dm;
385   PetscSF       *sfs;
386   PetscInt       cStart, cEnd, i, j;
387   PetscErrorCode ierr;
388 
389   PetscFunctionBegin;
390   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
391   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
392   ierr = PetscMalloc1(nsubspaces, &sfs);CHKERRQ(ierr);
393   ierr = PetscMalloc1(nsubspaces, &patch->dofSection);CHKERRQ(ierr);
394   ierr = PetscMalloc1(nsubspaces, &patch->bs);CHKERRQ(ierr);
395   ierr = PetscMalloc1(nsubspaces, &patch->nodesPerCell);CHKERRQ(ierr);
396   ierr = PetscMalloc1(nsubspaces, &patch->cellNodeMap);CHKERRQ(ierr);
397   ierr = PetscMalloc1(nsubspaces+1, &patch->subspaceOffsets);CHKERRQ(ierr);
398 
399   patch->nsubspaces       = nsubspaces;
400   patch->totalDofsPerCell = 0;
401   for (i = 0; i < nsubspaces; ++i) {
402     ierr = DMGetDefaultSection(dms[i], &patch->dofSection[i]);CHKERRQ(ierr);
403     ierr = PetscObjectReference((PetscObject) patch->dofSection[i]);CHKERRQ(ierr);
404     ierr = DMGetDefaultSF(dms[i], &sfs[i]);CHKERRQ(ierr);
405     patch->bs[i]              = bs[i];
406     patch->nodesPerCell[i]    = nodesPerCell[i];
407     patch->totalDofsPerCell  += nodesPerCell[i]*bs[i];
408     ierr = PetscMalloc1((cEnd-cStart)*nodesPerCell[i]*bs[i], &patch->cellNodeMap[i]);CHKERRQ(ierr);
409     for (j = 0; j < (cEnd-cStart)*nodesPerCell[i]*bs[i]; ++j) patch->cellNodeMap[i][j] = cellNodeMap[i][j];
410     patch->subspaceOffsets[i] = subspaceOffsets[i];
411   }
412   ierr = PCPatchCreateDefaultSF_Private(pc, nsubspaces, sfs, patch->bs);CHKERRQ(ierr);
413   ierr = PetscFree(sfs);CHKERRQ(ierr);
414 
415   patch->subspaceOffsets[nsubspaces] = subspaceOffsets[nsubspaces];
416   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGhostBcs, ghostBcNodes, PETSC_COPY_VALUES, &patch->ghostBcNodes);CHKERRQ(ierr);
417   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalBcs, globalBcNodes, PETSC_COPY_VALUES, &patch->globalBcNodes);CHKERRQ(ierr);
418   PetscFunctionReturn(0);
419 }
420 
421 /* TODO: Docs */
422 PetscErrorCode PCPatchSetDiscretisationInfoCombined(PC pc, DM dm, PetscInt *nodesPerCell, const PetscInt **cellNodeMap, PetscInt numGhostBcs, const PetscInt *ghostBcNodes, PetscInt numGlobalBcs, const PetscInt *globalBcNodes)
423 {
424   PC_PATCH      *patch = (PC_PATCH *) pc->data;
425   PetscInt       cStart, cEnd, i, j;
426   PetscErrorCode ierr;
427 
428   PetscFunctionBegin;
429   patch->combined = PETSC_TRUE;
430   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
431   ierr = DMGetNumFields(dm, &patch->nsubspaces);CHKERRQ(ierr);
432   ierr = PetscCalloc1(patch->nsubspaces, &patch->dofSection);CHKERRQ(ierr);
433   ierr = PetscMalloc1(patch->nsubspaces, &patch->bs);CHKERRQ(ierr);
434   ierr = PetscMalloc1(patch->nsubspaces, &patch->nodesPerCell);CHKERRQ(ierr);
435   ierr = PetscMalloc1(patch->nsubspaces, &patch->cellNodeMap);CHKERRQ(ierr);
436   ierr = PetscCalloc1(patch->nsubspaces+1, &patch->subspaceOffsets);CHKERRQ(ierr);
437   ierr = DMGetDefaultSection(dm, &patch->dofSection[0]);CHKERRQ(ierr);
438   ierr = PetscObjectReference((PetscObject) patch->dofSection[0]);CHKERRQ(ierr);
439   ierr = PetscSectionGetStorageSize(patch->dofSection[0], &patch->subspaceOffsets[patch->nsubspaces]);CHKERRQ(ierr);
440   patch->totalDofsPerCell = 0;
441   for (i = 0; i < patch->nsubspaces; ++i) {
442     patch->bs[i]             = 1;
443     patch->nodesPerCell[i]   = nodesPerCell[i];
444     patch->totalDofsPerCell += nodesPerCell[i];
445     ierr = PetscMalloc1((cEnd-cStart)*nodesPerCell[i], &patch->cellNodeMap[i]);CHKERRQ(ierr);
446     for (j = 0; j < (cEnd-cStart)*nodesPerCell[i]; ++j) patch->cellNodeMap[i][j] = cellNodeMap[i][j];
447   }
448   ierr = DMGetDefaultSF(dm, &patch->defaultSF);CHKERRQ(ierr);
449   ierr = PetscObjectReference((PetscObject) patch->defaultSF);CHKERRQ(ierr);
450   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGhostBcs, ghostBcNodes, PETSC_COPY_VALUES, &patch->ghostBcNodes);CHKERRQ(ierr);
451   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalBcs, globalBcNodes, PETSC_COPY_VALUES, &patch->globalBcNodes);CHKERRQ(ierr);
452   PetscFunctionReturn(0);
453 }
454 
455 /*@C
456 
457   PCPatchSetComputeOperator - Set the callback used to compute patch matrices
458 
459   Input Parameters:
460 + pc   - The PC
461 . func - The callback
462 - ctx  - The user context
463 
464   Level: advanced
465 
466   Note:
467   The callback has signature:
468 +  usercomputeop(pc, point, mat, cellIS, n, u, ctx)
469 +  pc     - The PC
470 +  point  - The point
471 +  mat    - The patch matrix
472 +  cellIS - An array of the cell numbers
473 +  n      - The size of g2l
474 +  g2l    - The global to local dof translation table
475 +  ctx    - The user context
476   and can assume that the matrix entries have been set to zero before the call.
477 
478 .seealso: PCPatchGetComputeOperator(), PCPatchSetDiscretisationInfo()
479 @*/
480 PetscErrorCode PCPatchSetComputeOperator(PC pc, PetscErrorCode (*func)(PC, PetscInt, Mat, IS, PetscInt, const PetscInt *, void *), void *ctx)
481 {
482   PC_PATCH *patch = (PC_PATCH *) pc->data;
483 
484   PetscFunctionBegin;
485   patch->usercomputeop  = func;
486   patch->usercomputectx = ctx;
487   PetscFunctionReturn(0);
488 }
489 
490 /* On entry, ht contains the topological entities whose dofs we are responsible for solving for;
491    on exit, cht contains all the topological entities we need to compute their residuals.
492    In full generality this should incorporate knowledge of the sparsity pattern of the matrix;
493    here we assume a standard FE sparsity pattern.*/
494 /* TODO: Use DMPlexGetAdjacency() */
495 static PetscErrorCode PCPatchCompleteCellPatch(PC pc, PetscHSetI ht, PetscHSetI cht)
496 {
497   DM             dm;
498   PetscHashIter  hi;
499   PetscInt       point;
500   PetscInt      *star = NULL, *closure = NULL;
501   PetscInt       ignoredim, iStart = 0, iEnd = -1, starSize, closureSize, si, ci;
502   PetscErrorCode ierr;
503 
504   PetscFunctionBegin;
505   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
506   ierr = PCPatchGetIgnoreDim(pc, &ignoredim);CHKERRQ(ierr);
507   if (ignoredim >= 0) {ierr = DMPlexGetDepthStratum(dm, ignoredim, &iStart, &iEnd);CHKERRQ(ierr);}
508   ierr = PetscHSetIClear(cht);CHKERRQ(ierr);
509   PetscHashIterBegin(ht, hi);
510   while (!PetscHashIterAtEnd(ht, hi)) {
511 
512     PetscHashIterGetKey(ht, hi, point);
513     PetscHashIterNext(ht, hi);
514 
515     /* Loop over all the cells that this point connects to */
516     ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
517     for (si = 0; si < starSize*2; si += 2) {
518       const PetscInt ownedpoint = star[si];
519       /* TODO Check for point in cht before running through closure again */
520       /* now loop over all entities in the closure of that cell */
521       ierr = DMPlexGetTransitiveClosure(dm, ownedpoint, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
522       for (ci = 0; ci < closureSize*2; ci += 2) {
523         const PetscInt seenpoint = closure[ci];
524         if (ignoredim >= 0 && seenpoint >= iStart && seenpoint < iEnd) continue;
525         ierr = PetscHSetIAdd(cht, seenpoint);CHKERRQ(ierr);
526       }
527     }
528   }
529   ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);
530   ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_FALSE, NULL, &star);CHKERRQ(ierr);
531   PetscFunctionReturn(0);
532 }
533 
534 static PetscErrorCode PCPatchGetGlobalDofs(PC pc, PetscSection dofSection[], PetscInt f, PetscBool combined, PetscInt p, PetscInt *dof, PetscInt *off)
535 {
536   PetscErrorCode ierr;
537 
538   PetscFunctionBegin;
539   if (combined) {
540     if (f < 0) {
541       if (dof) {ierr = PetscSectionGetDof(dofSection[0], p, dof);CHKERRQ(ierr);}
542       if (off) {ierr = PetscSectionGetOffset(dofSection[0], p, off);CHKERRQ(ierr);}
543     } else {
544       if (dof) {ierr = PetscSectionGetFieldDof(dofSection[0], p, f, dof);CHKERRQ(ierr);}
545       if (off) {ierr = PetscSectionGetFieldOffset(dofSection[0], p, f, off);CHKERRQ(ierr);}
546     }
547   } else {
548     if (f < 0) {
549       PC_PATCH *patch = (PC_PATCH *) pc->data;
550       PetscInt  fdof, g;
551 
552       if (dof) {
553         *dof = 0;
554         for (g = 0; g < patch->nsubspaces; ++g) {
555           ierr = PetscSectionGetDof(dofSection[g], p, &fdof);CHKERRQ(ierr);
556           *dof += fdof;
557         }
558       }
559       if (off) {ierr = PetscSectionGetOffset(dofSection[0], p, off);CHKERRQ(ierr);}
560     } else {
561       if (dof) {ierr = PetscSectionGetDof(dofSection[f], p, dof);CHKERRQ(ierr);}
562       if (off) {ierr = PetscSectionGetOffset(dofSection[f], p, off);CHKERRQ(ierr);}
563     }
564   }
565   PetscFunctionReturn(0);
566 }
567 
568 /* Given a hash table with a set of topological entities (pts), compute the degrees of
569    freedom in global concatenated numbering on those entities.
570    For Vanka smoothing, this needs to do something special: ignore dofs of the
571    constraint subspace on entities that aren't the base entity we're building the patch
572    around. */
573 static PetscErrorCode PCPatchGetPointDofs(PC pc, PetscHSetI pts, PetscHSetI dofs, PetscInt base, PetscHSetI* subspaces_to_exclude)
574 {
575   PC_PATCH      *patch = (PC_PATCH *) pc->data;
576   PetscHashIter  hi;
577   PetscInt       ldof, loff;
578   PetscInt       k, p;
579   PetscErrorCode ierr;
580 
581   PetscFunctionBegin;
582   ierr = PetscHSetIClear(dofs);CHKERRQ(ierr);
583   for (k = 0; k < patch->nsubspaces; ++k) {
584     PetscInt subspaceOffset = patch->subspaceOffsets[k];
585     PetscInt bs             = patch->bs[k];
586     PetscInt j, l;
587 
588     if (subspaces_to_exclude != NULL) {
589       PetscBool should_exclude_k = PETSC_FALSE;
590       PetscHSetIHas(*subspaces_to_exclude, k, &should_exclude_k);
591       if (should_exclude_k) {
592         /* only get this subspace dofs at the base entity, not any others */
593         ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, base, &ldof, &loff);CHKERRQ(ierr);
594         if (0 == ldof) continue;
595         for (j = loff; j < ldof + loff; ++j) {
596           for (l = 0; l < bs; ++l) {
597             PetscInt dof = bs*j + l + subspaceOffset;
598             ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
599           }
600         }
601         continue; /* skip the other dofs of this subspace */
602       }
603     }
604 
605     PetscHashIterBegin(pts, hi);
606     while (!PetscHashIterAtEnd(pts, hi)) {
607       PetscHashIterGetKey(pts, hi, p);
608       PetscHashIterNext(pts, hi);
609       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, p, &ldof, &loff);CHKERRQ(ierr);
610       if (0 == ldof) continue;
611       for (j = loff; j < ldof + loff; ++j) {
612         for (l = 0; l < bs; ++l) {
613           PetscInt dof = bs*j + l + subspaceOffset;
614           ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
615         }
616       }
617     }
618   }
619   PetscFunctionReturn(0);
620 }
621 
622 /* Given two hash tables A and B, compute the keys in B that are not in A, and put them in C */
623 static PetscErrorCode PCPatchComputeSetDifference_Private(PetscHSetI A, PetscHSetI B, PetscHSetI C)
624 {
625   PetscHashIter  hi;
626   PetscInt       key;
627   PetscBool      flg;
628   PetscErrorCode ierr;
629 
630   PetscFunctionBegin;
631   ierr = PetscHSetIClear(C);CHKERRQ(ierr);
632   PetscHashIterBegin(B, hi);
633   while (!PetscHashIterAtEnd(B, hi)) {
634     PetscHashIterGetKey(B, hi, key);
635     PetscHashIterNext(B, hi);
636     ierr = PetscHSetIHas(A, key, &flg);CHKERRQ(ierr);
637     if (!flg) {ierr = PetscHSetIAdd(C, key);CHKERRQ(ierr);}
638   }
639   PetscFunctionReturn(0);
640 }
641 
642 /*
643  * PCPatchCreateCellPatches - create patches.
644  *
645  * Input Parameters:
646  * + dm - The DMPlex object defining the mesh
647  *
648  * Output Parameters:
649  * + cellCounts  - Section with counts of cells around each vertex
650  * . cells       - IS of the cell point indices of cells in each patch
651  * . pointCounts - Section with counts of cells around each vertex
652  * - point       - IS of the cell point indices of cells in each patch
653  */
654 static PetscErrorCode PCPatchCreateCellPatches(PC pc)
655 {
656   PC_PATCH       *patch = (PC_PATCH *) pc->data;
657   DMLabel         ghost = NULL;
658   DM              dm, plex;
659   PetscHSetI      ht, cht;
660   PetscSection    cellCounts,  pointCounts;
661   PetscInt       *cellsArray, *pointsArray;
662   PetscInt        numCells,    numPoints;
663   const PetscInt *leaves;
664   PetscInt        nleaves, pStart, pEnd, cStart, cEnd, vStart, vEnd, v;
665   PetscBool       isFiredrake;
666   PetscErrorCode  ierr;
667 
668   PetscFunctionBegin;
669   /* Used to keep track of the cells in the patch. */
670   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
671   ierr = PetscHSetICreate(&cht);CHKERRQ(ierr);
672 
673   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
674   if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONGSTATE, "DM not yet set on patch PC\n");
675   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
676   ierr = DMPlexGetChart(plex, &pStart, &pEnd);CHKERRQ(ierr);
677   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
678 
679   if (patch->user_patches) {
680     ierr = patch->userpatchconstructionop(pc, &patch->npatch, &patch->userIS, &patch->iterationSet, patch->userpatchconstructctx);CHKERRQ(ierr);
681     vStart = 0; vEnd = patch->npatch;
682   } else if (patch->codim < 0) {
683     if (patch->dim < 0) {ierr = DMPlexGetDepthStratum(plex,  0,            &vStart, &vEnd);CHKERRQ(ierr);}
684     else                {ierr = DMPlexGetDepthStratum(plex,  patch->dim,   &vStart, &vEnd);CHKERRQ(ierr);}
685   } else                {ierr = DMPlexGetHeightStratum(plex, patch->codim, &vStart, &vEnd);CHKERRQ(ierr);}
686   patch->npatch = vEnd - vStart;
687 
688   /* These labels mark the owned points.  We only create patches around points that this process owns. */
689   ierr = DMHasLabel(dm, "pyop2_ghost", &isFiredrake);CHKERRQ(ierr);
690   if (isFiredrake) {
691     ierr = DMGetLabel(dm, "pyop2_ghost", &ghost);CHKERRQ(ierr);
692     ierr = DMLabelCreateIndex(ghost, pStart, pEnd);CHKERRQ(ierr);
693   } else {
694     PetscSF sf;
695 
696     ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
697     ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
698     nleaves = PetscMax(nleaves, 0);
699   }
700 
701   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->cellCounts);CHKERRQ(ierr);
702   ierr = PetscObjectSetName((PetscObject) patch->cellCounts, "Patch Cell Layout");CHKERRQ(ierr);
703   cellCounts = patch->cellCounts;
704   ierr = PetscSectionSetChart(cellCounts, vStart, vEnd);CHKERRQ(ierr);
705   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->pointCounts);CHKERRQ(ierr);
706   ierr = PetscObjectSetName((PetscObject) patch->pointCounts, "Patch Point Layout");CHKERRQ(ierr);
707   pointCounts = patch->pointCounts;
708   ierr = PetscSectionSetChart(pointCounts, vStart, vEnd);CHKERRQ(ierr);
709   /* Count cells and points in the patch surrounding each entity */
710   for (v = vStart; v < vEnd; ++v) {
711     PetscHashIter hi;
712     PetscInt       chtSize, loc = -1;
713     PetscBool      flg;
714 
715     if (!patch->user_patches) {
716       if (ghost) {ierr = DMLabelHasPoint(ghost, v, &flg);CHKERRQ(ierr);}
717       else       {ierr = PetscFindInt(v, nleaves, leaves, &loc);CHKERRQ(ierr); flg = loc >=0 ? PETSC_TRUE : PETSC_FALSE;}
718       /* Not an owned entity, don't make a cell patch. */
719       if (flg) continue;
720     }
721 
722     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
723     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
724     ierr = PetscHSetIGetSize(cht, &chtSize);CHKERRQ(ierr);
725     /* empty patch, continue */
726     if (chtSize == 0) continue;
727 
728     /* safe because size(cht) > 0 from above */
729     PetscHashIterBegin(cht, hi);
730     while (!PetscHashIterAtEnd(cht, hi)) {
731       PetscInt point, pdof;
732 
733       PetscHashIterGetKey(cht, hi, point);
734       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
735       if (pdof)                            {ierr = PetscSectionAddDof(pointCounts, v, 1);CHKERRQ(ierr);}
736       if (point >= cStart && point < cEnd) {ierr = PetscSectionAddDof(cellCounts, v, 1);CHKERRQ(ierr);}
737       PetscHashIterNext(cht, hi);
738     }
739   }
740   if (isFiredrake) {ierr = DMLabelDestroyIndex(ghost);CHKERRQ(ierr);}
741 
742   ierr = PetscSectionSetUp(cellCounts);CHKERRQ(ierr);
743   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
744   ierr = PetscMalloc1(numCells, &cellsArray);CHKERRQ(ierr);
745   ierr = PetscSectionSetUp(pointCounts);CHKERRQ(ierr);
746   ierr = PetscSectionGetStorageSize(pointCounts, &numPoints);CHKERRQ(ierr);
747   ierr = PetscMalloc1(numPoints, &pointsArray);CHKERRQ(ierr);
748 
749   /* Now that we know how much space we need, run through again and actually remember the cells. */
750   for (v = vStart; v < vEnd; v++ ) {
751     PetscHashIter hi;
752     PetscInt       dof, off, cdof, coff, pdof, n = 0, cn = 0;
753 
754     ierr = PetscSectionGetDof(pointCounts, v, &dof);CHKERRQ(ierr);
755     ierr = PetscSectionGetOffset(pointCounts, v, &off);CHKERRQ(ierr);
756     ierr = PetscSectionGetDof(cellCounts, v, &cdof);CHKERRQ(ierr);
757     ierr = PetscSectionGetOffset(cellCounts, v, &coff);CHKERRQ(ierr);
758     if (dof <= 0) continue;
759     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
760     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
761     PetscHashIterBegin(cht, hi);
762     while (!PetscHashIterAtEnd(cht, hi)) {
763       PetscInt point;
764 
765       PetscHashIterGetKey(cht, hi, point);
766       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
767       if (pdof)                            {pointsArray[off + n++] = point;}
768       if (point >= cStart && point < cEnd) {cellsArray[coff + cn++] = point;}
769       PetscHashIterNext(cht, hi);
770     }
771     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);
772     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);
773   }
774   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
775   ierr = PetscHSetIDestroy(&cht);CHKERRQ(ierr);
776   ierr = DMDestroy(&plex);CHKERRQ(ierr);
777 
778   ierr = ISCreateGeneral(PETSC_COMM_SELF, numCells,  cellsArray,  PETSC_OWN_POINTER, &patch->cells);CHKERRQ(ierr);
779   ierr = PetscObjectSetName((PetscObject) patch->cells,  "Patch Cells");CHKERRQ(ierr);
780   if (patch->viewCells) {
781     ierr = ObjectView((PetscObject) patch->cellCounts, patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
782     ierr = ObjectView((PetscObject) patch->cells,      patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
783   }
784   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, pointsArray, PETSC_OWN_POINTER, &patch->points);CHKERRQ(ierr);
785   ierr = PetscObjectSetName((PetscObject) patch->points, "Patch Points");CHKERRQ(ierr);
786   if (patch->viewPoints) {
787     ierr = ObjectView((PetscObject) patch->pointCounts, patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
788     ierr = ObjectView((PetscObject) patch->points,      patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
789   }
790   PetscFunctionReturn(0);
791 }
792 
793 /*
794  * PCPatchCreateCellPatchDiscretisationInfo - Build the dof maps for cell patches
795  *
796  * Input Parameters:
797  * + dm - The DMPlex object defining the mesh
798  * . cellCounts - Section with counts of cells around each vertex
799  * . cells - IS of the cell point indices of cells in each patch
800  * . cellNumbering - Section mapping plex cell points to Firedrake cell indices.
801  * . nodesPerCell - number of nodes per cell.
802  * - cellNodeMap - map from cells to node indices (nodesPerCell * numCells)
803  *
804  * Output Parameters:
805  * + dofs - IS of local dof numbers of each cell in the patch, where local is a patch local numbering
806  * . gtolCounts - Section with counts of dofs per cell patch
807  * - gtol - IS mapping from global dofs to local dofs for each patch.
808  */
809 static PetscErrorCode PCPatchCreateCellPatchDiscretisationInfo(PC pc)
810 {
811   PC_PATCH       *patch           = (PC_PATCH *) pc->data;
812   PetscSection    cellCounts      = patch->cellCounts;
813   PetscSection    pointCounts     = patch->pointCounts;
814   PetscSection    gtolCounts;
815   IS              cells           = patch->cells;
816   IS              points          = patch->points;
817   PetscSection    cellNumbering   = patch->cellNumbering;
818   PetscInt        Nf              = patch->nsubspaces;
819   PetscInt        numCells, numPoints;
820   PetscInt        numDofs;
821   PetscInt        numGlobalDofs;
822   PetscInt        totalDofsPerCell = patch->totalDofsPerCell;
823   PetscInt        vStart, vEnd, v;
824   const PetscInt *cellsArray, *pointsArray;
825   PetscInt       *newCellsArray   = NULL;
826   PetscInt       *dofsArray       = NULL;
827   PetscInt       *offsArray       = NULL;
828   PetscInt       *asmArray        = NULL;
829   PetscInt       *globalDofsArray = NULL;
830   PetscInt        globalIndex     = 0;
831   PetscInt        key             = 0;
832   PetscInt        asmKey          = 0;
833   DM              dm              = NULL;
834   const PetscInt *bcNodes         = NULL;
835   PetscHMapI      ht;
836   PetscHSetI      globalBcs;
837   PetscInt        numBcs;
838   PetscHSetI      ownedpts, seenpts, owneddofs, seendofs, artificialbcs;
839   PetscInt        pStart, pEnd, p, i;
840   PetscErrorCode  ierr;
841 
842   PetscFunctionBegin;
843 
844   ierr = PCGetDM(pc, &dm); CHKERRQ(ierr);
845   /* dofcounts section is cellcounts section * dofPerCell */
846   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
847   ierr = PetscSectionGetStorageSize(patch->pointCounts, &numPoints);CHKERRQ(ierr);
848   numDofs = numCells * totalDofsPerCell;
849   ierr = PetscMalloc1(numDofs, &dofsArray);CHKERRQ(ierr);
850   ierr = PetscMalloc1(numPoints*Nf, &offsArray);CHKERRQ(ierr);
851   ierr = PetscMalloc1(numDofs, &asmArray);CHKERRQ(ierr);
852   ierr = PetscMalloc1(numCells, &newCellsArray);CHKERRQ(ierr);
853   ierr = PetscSectionGetChart(cellCounts, &vStart, &vEnd);CHKERRQ(ierr);
854   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->gtolCounts);CHKERRQ(ierr);
855   gtolCounts = patch->gtolCounts;
856   ierr = PetscSectionSetChart(gtolCounts, vStart, vEnd);CHKERRQ(ierr);
857   ierr = PetscObjectSetName((PetscObject) patch->gtolCounts, "Patch Global Index Section");CHKERRQ(ierr);
858 
859   /* Outside the patch loop, get the dofs that are globally-enforced Dirichlet
860    conditions */
861   ierr = PetscHSetICreate(&globalBcs);CHKERRQ(ierr);
862   ierr = ISGetIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
863   ierr = ISGetSize(patch->ghostBcNodes, &numBcs); CHKERRQ(ierr);
864   for (i = 0; i < numBcs; ++i) {
865     ierr = PetscHSetIAdd(globalBcs, bcNodes[i]);CHKERRQ(ierr); /* these are already in concatenated numbering */
866   }
867   ierr = ISRestoreIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
868   ierr = ISDestroy(&patch->ghostBcNodes); CHKERRQ(ierr); /* memory optimisation */
869 
870   /* Hash tables for artificial BC construction */
871   ierr = PetscHSetICreate(&ownedpts);CHKERRQ(ierr);
872   ierr = PetscHSetICreate(&seenpts);CHKERRQ(ierr);
873   ierr = PetscHSetICreate(&owneddofs);CHKERRQ(ierr);
874   ierr = PetscHSetICreate(&seendofs);CHKERRQ(ierr);
875   ierr = PetscHSetICreate(&artificialbcs);CHKERRQ(ierr);
876 
877   ierr = ISGetIndices(cells, &cellsArray);CHKERRQ(ierr);
878   ierr = ISGetIndices(points, &pointsArray);CHKERRQ(ierr);
879   ierr = PetscHMapICreate(&ht);CHKERRQ(ierr);
880   for (v = vStart; v < vEnd; ++v) {
881     PetscInt localIndex = 0;
882     PetscInt dof, off, i, j, k, l;
883 
884     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
885     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
886     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
887     if (dof <= 0) continue;
888 
889     /* Calculate the global numbers of the artificial BC dofs here first */
890     ierr = patch->patchconstructop((void*)patch, dm, v, ownedpts); CHKERRQ(ierr);
891     ierr = PCPatchCompleteCellPatch(pc, ownedpts, seenpts); CHKERRQ(ierr);
892     ierr = PCPatchGetPointDofs(pc, ownedpts, owneddofs, v, &patch->subspaces_to_exclude); CHKERRQ(ierr);
893     ierr = PCPatchGetPointDofs(pc, seenpts, seendofs, v, NULL); CHKERRQ(ierr);
894     ierr = PCPatchComputeSetDifference_Private(owneddofs, seendofs, artificialbcs); CHKERRQ(ierr);
895     if (patch->viewPatches) {
896       PetscHSetI globalbcdofs;
897       PetscHashIter hi;
898       MPI_Comm comm = PetscObjectComm((PetscObject)pc);
899 
900       ierr = PetscHSetICreate(&globalbcdofs);CHKERRQ(ierr);
901       ierr = PetscSynchronizedPrintf(comm, "Patch %d: owned dofs:\n", v); CHKERRQ(ierr);
902       PetscHashIterBegin(owneddofs, hi);
903       while (!PetscHashIterAtEnd(owneddofs, hi)) {
904         PetscInt globalDof;
905 
906         PetscHashIterGetKey(owneddofs, hi, globalDof);
907         PetscHashIterNext(owneddofs, hi);
908         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
909       }
910       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
911       ierr = PetscSynchronizedPrintf(comm, "Patch %d: seen dofs:\n", v); CHKERRQ(ierr);
912       PetscHashIterBegin(seendofs, hi);
913       while (!PetscHashIterAtEnd(seendofs, hi)) {
914         PetscInt globalDof;
915         PetscBool flg;
916 
917         PetscHashIterGetKey(seendofs, hi, globalDof);
918         PetscHashIterNext(seendofs, hi);
919         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
920 
921         ierr = PetscHSetIHas(globalBcs, globalDof, &flg);CHKERRQ(ierr);
922         if (flg) {ierr = PetscHSetIAdd(globalbcdofs, globalDof);CHKERRQ(ierr);}
923       }
924       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
925       ierr = PetscSynchronizedPrintf(comm, "Patch %d: global BCs:\n", v); CHKERRQ(ierr);
926       ierr = PetscHSetIGetSize(globalbcdofs, &numBcs);CHKERRQ(ierr);
927       if (numBcs > 0) {
928         PetscHashIterBegin(globalbcdofs, hi);
929         while (!PetscHashIterAtEnd(globalbcdofs, hi)) {
930           PetscInt globalDof;
931           PetscHashIterGetKey(globalbcdofs, hi, globalDof);
932           PetscHashIterNext(globalbcdofs, hi);
933           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof);CHKERRQ(ierr);
934         }
935       }
936       ierr = PetscSynchronizedPrintf(comm, "\n");CHKERRQ(ierr);
937       ierr = PetscSynchronizedPrintf(comm, "Patch %d: artificial BCs:\n", v);CHKERRQ(ierr);
938       ierr = PetscHSetIGetSize(artificialbcs, &numBcs);CHKERRQ(ierr);
939       if (numBcs > 0) {
940         PetscHashIterBegin(artificialbcs, hi);
941         while (!PetscHashIterAtEnd(artificialbcs, hi)) {
942           PetscInt globalDof;
943           PetscHashIterGetKey(artificialbcs, hi, globalDof);
944           PetscHashIterNext(artificialbcs, hi);
945           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
946         }
947       }
948       ierr = PetscSynchronizedPrintf(comm, "\n\n"); CHKERRQ(ierr);
949       ierr = PetscHSetIDestroy(&globalbcdofs);CHKERRQ(ierr);
950     }
951    for (k = 0; k < patch->nsubspaces; ++k) {
952       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
953       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
954       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
955       PetscInt        bs             = patch->bs[k];
956 
957       for (i = off; i < off + dof; ++i) {
958         /* Walk over the cells in this patch. */
959         const PetscInt c    = cellsArray[i];
960         PetscInt       cell = c;
961 
962         /* TODO Change this to an IS */
963         if (cellNumbering) {
964           ierr = PetscSectionGetDof(cellNumbering, c, &cell);CHKERRQ(ierr);
965           if (cell <= 0) SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_OUTOFRANGE, "Cell %D doesn't appear in cell numbering map", c);
966           ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);
967         }
968         newCellsArray[i] = cell;
969         for (j = 0; j < nodesPerCell; ++j) {
970           /* For each global dof, map it into contiguous local storage. */
971           const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + subspaceOffset;
972           /* finally, loop over block size */
973           for (l = 0; l < bs; ++l) {
974             PetscInt  localDof;
975             PetscBool isGlobalBcDof, isArtificialBcDof;
976 
977             /* first, check if this is either a globally enforced or locally enforced BC dof */
978             ierr = PetscHSetIHas(globalBcs, globalDof + l, &isGlobalBcDof);CHKERRQ(ierr);
979             ierr = PetscHSetIHas(artificialbcs, globalDof + l, &isArtificialBcDof);CHKERRQ(ierr);
980 
981             /* if it's either, don't ever give it a local dof number */
982             if (isGlobalBcDof || isArtificialBcDof) {
983               dofsArray[globalIndex++] = -1; /* don't use this in assembly in this patch */
984             } else {
985               ierr = PetscHMapIGet(ht, globalDof + l, &localDof);CHKERRQ(ierr);
986               if (localDof == -1) {
987                 localDof = localIndex++;
988                 ierr = PetscHMapISet(ht, globalDof + l, localDof);CHKERRQ(ierr);
989               }
990               if ( globalIndex >= numDofs ) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Found more dofs %D than expected %D", globalIndex+1, numDofs);
991               /* And store. */
992               dofsArray[globalIndex++] = localDof;
993             }
994           }
995         }
996       }
997     }
998     /* How many local dofs in this patch? */
999     ierr = PetscHMapIGetSize(ht, &dof);CHKERRQ(ierr);
1000     ierr = PetscSectionSetDof(gtolCounts, v, dof);CHKERRQ(ierr);
1001   }
1002   if (globalIndex != numDofs) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Expected number of dofs (%d) doesn't match found number (%d)", numDofs, globalIndex);
1003   ierr = PetscSectionSetUp(gtolCounts);CHKERRQ(ierr);
1004   ierr = PetscSectionGetStorageSize(gtolCounts, &numGlobalDofs);CHKERRQ(ierr);
1005   ierr = PetscMalloc1(numGlobalDofs, &globalDofsArray);CHKERRQ(ierr);
1006 
1007   /* Now populate the global to local map.  This could be merged into the above loop if we were willing to deal with reallocs. */
1008   for (v = vStart; v < vEnd; ++v) {
1009     PetscHashIter hi;
1010     PetscInt      dof, off, Np, ooff, i, j, k, l;
1011 
1012     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
1013     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
1014     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
1015     ierr = PetscSectionGetDof(pointCounts, v, &Np);CHKERRQ(ierr);
1016     ierr = PetscSectionGetOffset(pointCounts, v, &ooff);CHKERRQ(ierr);
1017     if (dof <= 0) continue;
1018 
1019     for (k = 0; k < patch->nsubspaces; ++k) {
1020       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1021       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1022       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1023       PetscInt        bs             = patch->bs[k];
1024       PetscInt        goff;
1025 
1026       for (i = off; i < off + dof; ++i) {
1027         /* Reconstruct mapping of global-to-local on this patch. */
1028         const PetscInt c    = cellsArray[i];
1029         PetscInt       cell = c;
1030 
1031         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1032         for (j = 0; j < nodesPerCell; ++j) {
1033           for (l = 0; l < bs; ++l) {
1034             const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1035             const PetscInt localDof  = dofsArray[key++];
1036 
1037             if (localDof >= 0) {ierr = PetscHMapISet(ht, globalDof, localDof);CHKERRQ(ierr);}
1038           }
1039         }
1040       }
1041 
1042       /* Shove it in the output data structure. */
1043       ierr = PetscSectionGetOffset(gtolCounts, v, &goff);CHKERRQ(ierr);
1044       PetscHashIterBegin(ht, hi);
1045       while (!PetscHashIterAtEnd(ht, hi)) {
1046         PetscInt globalDof, localDof;
1047 
1048         PetscHashIterGetKey(ht, hi, globalDof);
1049         PetscHashIterGetVal(ht, hi, localDof);
1050         if (globalDof >= 0) globalDofsArray[goff + localDof] = globalDof;
1051         PetscHashIterNext(ht, hi);
1052       }
1053 
1054       for (p = 0; p < Np; ++p) {
1055         const PetscInt point = pointsArray[ooff + p];
1056         PetscInt       globalDof, localDof;
1057 
1058         ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, point, NULL, &globalDof);CHKERRQ(ierr);
1059         ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1060         offsArray[(ooff + p)*Nf + k] = localDof;
1061       }
1062     }
1063 
1064     ierr = PetscHSetIDestroy(&globalBcs);CHKERRQ(ierr);
1065     ierr = PetscHSetIDestroy(&ownedpts);CHKERRQ(ierr);
1066     ierr = PetscHSetIDestroy(&seenpts);CHKERRQ(ierr);
1067     ierr = PetscHSetIDestroy(&owneddofs);CHKERRQ(ierr);
1068     ierr = PetscHSetIDestroy(&seendofs);CHKERRQ(ierr);
1069     ierr = PetscHSetIDestroy(&artificialbcs);CHKERRQ(ierr);
1070 
1071       /* At this point, we have a hash table ht built that maps globalDof -> localDof.
1072      We need to create the dof table laid out cellwise first, then by subspace,
1073      as the assembler assembles cell-wise and we need to stuff the different
1074      contributions of the different function spaces to the right places. So we loop
1075      over cells, then over subspaces. */
1076     if (patch->nsubspaces > 1) { /* for nsubspaces = 1, data we need is already in dofsArray */
1077       for (i = off; i < off + dof; ++i) {
1078         const PetscInt c    = cellsArray[i];
1079         PetscInt       cell = c;
1080 
1081         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1082         for (k = 0; k < patch->nsubspaces; ++k) {
1083           const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1084           PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1085           PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1086           PetscInt        bs             = patch->bs[k];
1087 
1088           for (j = 0; j < nodesPerCell; ++j) {
1089             for (l = 0; l < bs; ++l) {
1090               const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1091               PetscInt       localDof;
1092 
1093               ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1094               /* If it's not in the hash table, i.e. is a BC dof,
1095                then the PetscHSetIMap above gives -1, which matches
1096                exactly the convention for PETSc's matrix assembly to
1097                ignore the dof. So we don't need to do anything here */
1098               asmArray[asmKey++] = localDof;
1099             }
1100           }
1101         }
1102       }
1103     }
1104   }
1105   if (1 == patch->nsubspaces) {ierr = PetscMemcpy(asmArray, dofsArray, numDofs * sizeof(PetscInt));CHKERRQ(ierr);}
1106 
1107   ierr = PetscHMapIDestroy(&ht);CHKERRQ(ierr);
1108   ierr = ISRestoreIndices(cells, &cellsArray);CHKERRQ(ierr);
1109   ierr = ISRestoreIndices(points, &pointsArray);CHKERRQ(ierr);
1110   ierr = PetscFree(dofsArray);CHKERRQ(ierr);
1111   /* Create placeholder section for map from points to patch dofs */
1112   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->patchSection);CHKERRQ(ierr);
1113   ierr = PetscSectionSetNumFields(patch->patchSection, patch->nsubspaces);CHKERRQ(ierr);
1114   if (patch->combined) {
1115     PetscInt numFields;
1116     ierr = PetscSectionGetNumFields(patch->dofSection[0], &numFields);CHKERRQ(ierr);
1117     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);
1118     ierr = PetscSectionGetChart(patch->dofSection[0], &pStart, &pEnd);CHKERRQ(ierr);
1119     ierr = PetscSectionSetChart(patch->patchSection, pStart, pEnd);CHKERRQ(ierr);
1120     for (p = pStart; p < pEnd; ++p) {
1121       PetscInt dof, fdof, f;
1122 
1123       ierr = PetscSectionGetDof(patch->dofSection[0], p, &dof);CHKERRQ(ierr);
1124       ierr = PetscSectionSetDof(patch->patchSection, p, dof);CHKERRQ(ierr);
1125       for (f = 0; f < patch->nsubspaces; ++f) {
1126         ierr = PetscSectionGetFieldDof(patch->dofSection[0], p, f, &fdof);CHKERRQ(ierr);
1127         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, fdof);CHKERRQ(ierr);
1128       }
1129     }
1130   } else {
1131     PetscInt pStartf, pEndf, f;
1132     pStart = PETSC_MAX_INT;
1133     pEnd = PETSC_MIN_INT;
1134     for (f = 0; f < patch->nsubspaces; ++f) {
1135       ierr = PetscSectionGetChart(patch->dofSection[f], &pStartf, &pEndf);CHKERRQ(ierr);
1136       pStart = PetscMin(pStart, pStartf);
1137       pEnd = PetscMax(pEnd, pEndf);
1138     }
1139     ierr = PetscSectionSetChart(patch->patchSection, pStart, pEnd);CHKERRQ(ierr);
1140     for (f = 0; f < patch->nsubspaces; ++f) {
1141       ierr = PetscSectionGetChart(patch->dofSection[f], &pStartf, &pEndf);CHKERRQ(ierr);
1142       for (p = pStartf; p < pEndf; ++p) {
1143         PetscInt fdof;
1144         ierr = PetscSectionGetDof(patch->dofSection[f], p, &fdof);CHKERRQ(ierr);
1145         ierr = PetscSectionAddDof(patch->patchSection, p, fdof);CHKERRQ(ierr);
1146         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, fdof);CHKERRQ(ierr);
1147       }
1148     }
1149   }
1150   ierr = PetscSectionSetUp(patch->patchSection);CHKERRQ(ierr);
1151   ierr = PetscSectionSetUseFieldOffsets(patch->patchSection, PETSC_TRUE);CHKERRQ(ierr);
1152   /* Replace cell indices with firedrake-numbered ones. */
1153   ierr = ISGeneralSetIndices(cells, numCells, (const PetscInt *) newCellsArray, PETSC_OWN_POINTER);CHKERRQ(ierr);
1154   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalDofs, globalDofsArray, PETSC_OWN_POINTER, &patch->gtol);CHKERRQ(ierr);
1155   ierr = PetscObjectSetName((PetscObject) patch->gtol, "Global Indices");CHKERRQ(ierr);
1156   ierr = PetscSectionViewFromOptions(patch->gtolCounts, (PetscObject) pc, "-pc_patch_g2l_view");CHKERRQ(ierr);
1157   ierr = ISViewFromOptions(patch->gtol, (PetscObject) pc, "-pc_patch_g2l_view");CHKERRQ(ierr);
1158   ierr = ISCreateGeneral(PETSC_COMM_SELF, numDofs, asmArray, PETSC_OWN_POINTER, &patch->dofs);CHKERRQ(ierr);
1159   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints*Nf, offsArray, PETSC_OWN_POINTER, &patch->offs);CHKERRQ(ierr);
1160   PetscFunctionReturn(0);
1161 }
1162 
1163 static PetscErrorCode PCPatchZeroFillMatrix_Private(Mat mat, const PetscInt ncell, const PetscInt ndof, const PetscInt *dof)
1164 {
1165   PetscScalar    *values = NULL;
1166   PetscInt        rows, c, i;
1167   PetscErrorCode  ierr;
1168 
1169   PetscFunctionBegin;
1170   ierr = PetscCalloc1(ndof*ndof, &values);CHKERRQ(ierr);
1171   for (c = 0; c < ncell; ++c) {
1172     const PetscInt *idx = &dof[ndof*c];
1173     ierr = MatSetValues(mat, ndof, idx, ndof, idx, values, INSERT_VALUES);CHKERRQ(ierr);
1174   }
1175   ierr = MatGetLocalSize(mat, &rows, NULL);CHKERRQ(ierr);
1176   for (i = 0; i < rows; ++i) {
1177     ierr = MatSetValues(mat, 1, &i, 1, &i, values, INSERT_VALUES);CHKERRQ(ierr);
1178   }
1179   ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1180   ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1181   ierr = PetscFree(values);CHKERRQ(ierr);
1182   PetscFunctionReturn(0);
1183 }
1184 
1185 static PetscErrorCode PCPatchCreateMatrix_Private(PC pc, PetscInt point, Mat *mat)
1186 {
1187   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1188   Vec            x, y;
1189   PetscBool      flg;
1190   PetscInt       csize, rsize;
1191   const char    *prefix = NULL;
1192   PetscErrorCode ierr;
1193 
1194   PetscFunctionBegin;
1195   x = patch->patchX[point];
1196   y = patch->patchY[point];
1197   ierr = VecGetSize(x, &csize);CHKERRQ(ierr);
1198   ierr = VecGetSize(y, &rsize);CHKERRQ(ierr);
1199   ierr = MatCreate(PETSC_COMM_SELF, mat);CHKERRQ(ierr);
1200   ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1201   ierr = MatSetOptionsPrefix(*mat, prefix);CHKERRQ(ierr);
1202   ierr = MatAppendOptionsPrefix(*mat, "pc_patch_sub_");CHKERRQ(ierr);
1203   if (patch->sub_mat_type)       {ierr = MatSetType(*mat, patch->sub_mat_type);CHKERRQ(ierr);}
1204   else if (!patch->sub_mat_type) {ierr = MatSetType(*mat, MATDENSE);CHKERRQ(ierr);}
1205   ierr = MatSetSizes(*mat, rsize, csize, rsize, csize);CHKERRQ(ierr);
1206   ierr = PetscObjectTypeCompare((PetscObject) *mat, MATDENSE, &flg);CHKERRQ(ierr);
1207   if (!flg) {ierr = PetscObjectTypeCompare((PetscObject)*mat, MATSEQDENSE, &flg);CHKERRQ(ierr);}
1208   /* Sparse patch matrices */
1209   if (!flg) {
1210     PetscBT         bt;
1211     PetscInt       *dnnz      = NULL;
1212     const PetscInt *dofsArray = NULL;
1213     PetscInt        pStart, pEnd, ncell, offset, c, i, j;
1214 
1215     ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1216     ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1217     point += pStart;
1218     if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1219     ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1220     ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1221     ierr = PetscCalloc1(rsize, &dnnz);CHKERRQ(ierr);
1222     ierr = PetscLogEventBegin(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1223     /* XXX: This uses N^2 bits to store the sparsity pattern on a
1224      * patch.  This is probably OK if the patches are not too big,
1225      * but could use quite a bit of memory for planes in 3D.
1226      * Should we switch based on the value of rsize to a
1227      * hash-table (slower, but more memory efficient) approach? */
1228     ierr = PetscBTCreate(rsize*rsize, &bt);CHKERRQ(ierr);
1229     for (c = 0; c < ncell; ++c) {
1230       const PetscInt *idx = dofsArray + (offset + c)*patch->totalDofsPerCell;
1231       for (i = 0; i < patch->totalDofsPerCell; ++i) {
1232         const PetscInt row = idx[i];
1233         if (row < 0) continue;
1234         for (j = 0; j < patch->totalDofsPerCell; ++j) {
1235           const PetscInt col = idx[j];
1236           const PetscInt key = row*rsize + col;
1237           if (col < 0) continue;
1238           if (!PetscBTLookupSet(bt, key)) ++dnnz[row];
1239         }
1240       }
1241     }
1242     ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
1243     ierr = MatXAIJSetPreallocation(*mat, 1, dnnz, NULL, NULL, NULL);CHKERRQ(ierr);
1244     ierr = PetscFree(dnnz);CHKERRQ(ierr);
1245     ierr = PCPatchZeroFillMatrix_Private(*mat, ncell, patch->totalDofsPerCell, &dofsArray[offset*patch->totalDofsPerCell]);CHKERRQ(ierr);
1246     ierr = PetscLogEventEnd(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1247     ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1248   }
1249   ierr = MatSetUp(*mat);CHKERRQ(ierr);
1250   PetscFunctionReturn(0);
1251 }
1252 
1253 static PetscErrorCode PCPatchComputeOperator_DMPlex_Private(PC pc, PetscInt patchNum, Mat J, IS cellIS, PetscInt n, const PetscInt *l2p, void *ctx)
1254 {
1255   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1256   DM              dm;
1257   PetscSection    s;
1258   const PetscInt *parray, *oarray;
1259   PetscInt        Nf = patch->nsubspaces, Np, poff, p, f;
1260   PetscErrorCode  ierr;
1261 
1262   PetscFunctionBegin;
1263   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1264   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1265   /* Set offset into patch */
1266   ierr = PetscSectionGetDof(patch->pointCounts, patchNum, &Np);CHKERRQ(ierr);
1267   ierr = PetscSectionGetOffset(patch->pointCounts, patchNum, &poff);CHKERRQ(ierr);
1268   ierr = ISGetIndices(patch->points, &parray);CHKERRQ(ierr);
1269   ierr = ISGetIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1270   for (f = 0; f < Nf; ++f) {
1271     for (p = 0; p < Np; ++p) {
1272       const PetscInt point = parray[poff+p];
1273       PetscInt       dof;
1274 
1275       ierr = PetscSectionGetFieldDof(patch->patchSection, point, f, &dof);CHKERRQ(ierr);
1276       ierr = PetscSectionSetFieldOffset(patch->patchSection, point, f, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);
1277       if (patch->nsubspaces == 1) {ierr = PetscSectionSetOffset(patch->patchSection, point, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);}
1278       else                        {ierr = PetscSectionSetOffset(patch->patchSection, point, -1);CHKERRQ(ierr);}
1279     }
1280   }
1281   ierr = ISRestoreIndices(patch->points, &parray);CHKERRQ(ierr);
1282   ierr = ISRestoreIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1283   if (patch->viewSection) {ierr = ObjectView((PetscObject) patch->patchSection, patch->viewerSection, patch->formatSection);CHKERRQ(ierr);}
1284   /* TODO Shut off MatViewFromOptions() in MatAssemblyEnd() here */
1285   ierr = DMPlexComputeJacobian_Patch_Internal(pc->dm, patch->patchSection, patch->patchSection, cellIS, 0.0, 0.0, NULL, NULL, J, J, ctx);CHKERRQ(ierr);
1286   PetscFunctionReturn(0);
1287 }
1288 
1289 static PetscErrorCode PCPatchComputeOperator_Private(PC pc, Mat mat, PetscInt point)
1290 {
1291   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1292   const PetscInt *dofsArray;
1293   const PetscInt *cellsArray;
1294   PetscInt        ncell, offset, pStart, pEnd;
1295   PetscErrorCode  ierr;
1296 
1297   PetscFunctionBegin;
1298   ierr = PetscLogEventBegin(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1299   if (!patch->usercomputeop) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call PCPatchSetComputeOperator() to set user callback\n");
1300   ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1301   ierr = ISGetIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1302   ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1303 
1304   point += pStart;
1305   if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1306 
1307   ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1308   ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1309   if (ncell <= 0) {
1310     ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1311     PetscFunctionReturn(0);
1312   }
1313   PetscStackPush("PCPatch user callback");
1314   /* Cannot reuse the same IS because the geometry info is being cached in it */
1315   ierr = ISCreateGeneral(PETSC_COMM_SELF, ncell, cellsArray + offset, PETSC_USE_POINTER, &patch->cellIS);CHKERRQ(ierr);
1316   ierr = patch->usercomputeop(pc, point, mat, patch->cellIS, ncell*patch->totalDofsPerCell, dofsArray + offset*patch->totalDofsPerCell, patch->usercomputectx);CHKERRQ(ierr);
1317   PetscStackPop;
1318   ierr = ISDestroy(&patch->cellIS);CHKERRQ(ierr);
1319   ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1320   ierr = ISRestoreIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1321   if (patch->viewMatrix) {
1322     char name[PETSC_MAX_PATH_LEN];
1323 
1324     ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN-1, "Patch matrix for Point %D", point);CHKERRQ(ierr);
1325     ierr = PetscObjectSetName((PetscObject) mat, name);CHKERRQ(ierr);
1326     ierr = ObjectView((PetscObject) mat, patch->viewerMatrix, patch->formatMatrix);CHKERRQ(ierr);
1327   }
1328   ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1329   PetscFunctionReturn(0);
1330 }
1331 
1332 static PetscErrorCode PCPatch_ScatterLocal_Private(PC pc, PetscInt p, Vec x, Vec y, InsertMode mode, ScatterMode scat)
1333 {
1334   PC_PATCH          *patch     = (PC_PATCH *) pc->data;
1335   const PetscScalar *xArray    = NULL;
1336   PetscScalar       *yArray    = NULL;
1337   const PetscInt    *gtolArray = NULL;
1338   PetscInt           dof, offset, lidx;
1339   PetscErrorCode     ierr;
1340 
1341   PetscFunctionBeginHot;
1342   ierr = PetscLogEventBegin(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1343   ierr = VecGetArrayRead(x, &xArray);CHKERRQ(ierr);
1344   ierr = VecGetArray(y, &yArray);CHKERRQ(ierr);
1345   ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1346   ierr = PetscSectionGetOffset(patch->gtolCounts, p, &offset);CHKERRQ(ierr);
1347   ierr = ISGetIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1348   if (mode == INSERT_VALUES && scat != SCATTER_FORWARD) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't insert if not scattering forward\n");
1349   if (mode == ADD_VALUES    && scat != SCATTER_REVERSE) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't add if not scattering reverse\n");
1350   for (lidx = 0; lidx < dof; ++lidx) {
1351     const PetscInt gidx = gtolArray[offset+lidx];
1352 
1353     if (mode == INSERT_VALUES) yArray[lidx]  = xArray[gidx]; /* Forward */
1354     else                       yArray[gidx] += xArray[lidx]; /* Reverse */
1355   }
1356   ierr = ISRestoreIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1357   ierr = VecRestoreArrayRead(x, &xArray);CHKERRQ(ierr);
1358   ierr = VecRestoreArray(y, &yArray);CHKERRQ(ierr);
1359   ierr = PetscLogEventEnd(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1360   PetscFunctionReturn(0);
1361 }
1362 
1363 static PetscErrorCode PCSetUp_PATCH(PC pc)
1364 {
1365   PC_PATCH       *patch   = (PC_PATCH *) pc->data;
1366   PetscInt        i;
1367   const char     *prefix;
1368   PetscErrorCode  ierr;
1369 
1370   PetscFunctionBegin;
1371   if (!pc->setupcalled) {
1372     PetscInt pStart, pEnd, p;
1373     PetscInt localSize;
1374 
1375     ierr = PetscLogEventBegin(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1376 
1377     if (!patch->nsubspaces) {
1378       DM           dm;
1379       PetscDS      prob;
1380       PetscSection s;
1381       PetscInt     cStart, cEnd, c, Nf, f, numGlobalBcs = 0, *globalBcs, *Nb, totNb = 0, **cellDofs;
1382 
1383       ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1384       if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONG, "Must set DM for PCPATCH or call PCPatchSetDiscretisationInfo()");
1385       ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1386       ierr = PetscSectionGetNumFields(s, &Nf);CHKERRQ(ierr);
1387       ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
1388       for (p = pStart; p < pEnd; ++p) {
1389         PetscInt cdof;
1390         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1391         numGlobalBcs += cdof;
1392       }
1393       ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1394       ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1395       ierr = PetscMalloc3(Nf, &Nb, Nf, &cellDofs, numGlobalBcs, &globalBcs);CHKERRQ(ierr);
1396       for (f = 0; f < Nf; ++f) {
1397         PetscFE        fe;
1398         PetscDualSpace sp;
1399         PetscInt       cdoff = 0;
1400 
1401         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1402         /* ierr = PetscFEGetNumComponents(fe, &Nc[f]);CHKERRQ(ierr); */
1403         ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
1404         ierr = PetscDualSpaceGetDimension(sp, &Nb[f]);CHKERRQ(ierr);
1405         totNb += Nb[f];
1406 
1407         ierr = PetscMalloc1((cEnd-cStart)*Nb[f], &cellDofs[f]);CHKERRQ(ierr);
1408         for (c = cStart; c < cEnd; ++c) {
1409           PetscInt *closure = NULL;
1410           PetscInt  clSize  = 0, cl;
1411 
1412           ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1413           for (cl = 0; cl < clSize*2; cl += 2) {
1414             const PetscInt p = closure[cl];
1415             PetscInt       fdof, d, foff;
1416 
1417             ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
1418             ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
1419             for (d = 0; d < fdof; ++d, ++cdoff) cellDofs[f][cdoff] = foff + d;
1420           }
1421           ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1422         }
1423         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]);
1424       }
1425       numGlobalBcs = 0;
1426       for (p = pStart; p < pEnd; ++p) {
1427         const PetscInt *ind;
1428         PetscInt        off, cdof, d;
1429 
1430         ierr = PetscSectionGetOffset(s, p, &off);CHKERRQ(ierr);
1431         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1432         ierr = PetscSectionGetConstraintIndices(s, p, &ind);CHKERRQ(ierr);
1433         for (d = 0; d < cdof; ++d) globalBcs[numGlobalBcs++] = off + ind[d];
1434       }
1435 
1436       ierr = PCPatchSetDiscretisationInfoCombined(pc, dm, Nb, (const PetscInt **) cellDofs, numGlobalBcs, globalBcs, numGlobalBcs, globalBcs);CHKERRQ(ierr);
1437       for (f = 0; f < Nf; ++f) {
1438         ierr = PetscFree(cellDofs[f]);CHKERRQ(ierr);
1439       }
1440       ierr = PetscFree3(Nb, cellDofs, globalBcs);CHKERRQ(ierr);
1441       ierr = PCPatchSetComputeOperator(pc, PCPatchComputeOperator_DMPlex_Private, NULL);CHKERRQ(ierr);
1442     }
1443 
1444     localSize = patch->subspaceOffsets[patch->nsubspaces];
1445     ierr = VecCreateSeq(PETSC_COMM_SELF, localSize, &patch->localX);CHKERRQ(ierr);
1446     ierr = VecSetUp(patch->localX);CHKERRQ(ierr);
1447     ierr = VecDuplicate(patch->localX, &patch->localY);CHKERRQ(ierr);
1448     ierr = PCPatchCreateCellPatches(pc);CHKERRQ(ierr);
1449     ierr = PCPatchCreateCellPatchDiscretisationInfo(pc);CHKERRQ(ierr);
1450 
1451     /* OK, now build the work vectors */
1452     ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, &pEnd);CHKERRQ(ierr);
1453     ierr = PetscMalloc1(patch->npatch, &patch->patchX);CHKERRQ(ierr);
1454     ierr = PetscMalloc1(patch->npatch, &patch->patchY);CHKERRQ(ierr);
1455     for (p = pStart; p < pEnd; ++p) {
1456       PetscInt dof;
1457 
1458       ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1459       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchX[p-pStart]);CHKERRQ(ierr);
1460       ierr = VecSetUp(patch->patchX[p-pStart]);CHKERRQ(ierr);
1461       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchY[p-pStart]);CHKERRQ(ierr);
1462       ierr = VecSetUp(patch->patchY[p-pStart]);CHKERRQ(ierr);
1463     }
1464     ierr = PetscMalloc1(patch->npatch, &patch->ksp);CHKERRQ(ierr);
1465     ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1466     for (i = 0; i < patch->npatch; ++i) {
1467       PC subpc;
1468 
1469       ierr = KSPCreate(PETSC_COMM_SELF, &patch->ksp[i]);CHKERRQ(ierr);
1470       ierr = KSPSetOptionsPrefix(patch->ksp[i], prefix);CHKERRQ(ierr);
1471       ierr = KSPAppendOptionsPrefix(patch->ksp[i], "sub_");CHKERRQ(ierr);
1472       ierr = PetscObjectIncrementTabLevel((PetscObject) patch->ksp[i], (PetscObject) pc, 1);CHKERRQ(ierr);
1473       ierr = KSPGetPC(patch->ksp[i], &subpc);CHKERRQ(ierr);
1474       ierr = PetscObjectIncrementTabLevel((PetscObject) subpc, (PetscObject) pc, 1);CHKERRQ(ierr);
1475       ierr = PetscLogObjectParent((PetscObject) pc, (PetscObject) patch->ksp[i]);CHKERRQ(ierr);
1476     }
1477     if (patch->save_operators) {
1478       ierr = PetscMalloc1(patch->npatch, &patch->mat);CHKERRQ(ierr);
1479       for (i = 0; i < patch->npatch; ++i) {
1480         ierr = PCPatchCreateMatrix_Private(pc, i, &patch->mat[i]);CHKERRQ(ierr);
1481       }
1482     }
1483     ierr = PetscLogEventEnd(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1484 
1485     /* If desired, calculate weights for dof multiplicity */
1486     if (patch->partition_of_unity) {
1487       ierr = VecDuplicate(patch->localX, &patch->dof_weights);CHKERRQ(ierr);
1488       for (i = 0; i < patch->npatch; ++i) {
1489         PetscInt dof;
1490 
1491         ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &dof);CHKERRQ(ierr);
1492         if (dof <= 0) continue;
1493         ierr = VecSet(patch->patchX[i], 1.0);CHKERRQ(ierr);
1494         ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchX[i], patch->dof_weights, ADD_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
1495       }
1496       ierr = VecReciprocal(patch->dof_weights);CHKERRQ(ierr);
1497     }
1498   }
1499   if (patch->save_operators) {
1500     for (i = 0; i < patch->npatch; ++i) {
1501       ierr = MatZeroEntries(patch->mat[i]);CHKERRQ(ierr);
1502       ierr = PCPatchComputeOperator_Private(pc, patch->mat[i], i);CHKERRQ(ierr);
1503       ierr = KSPSetOperators(patch->ksp[i], patch->mat[i], patch->mat[i]);CHKERRQ(ierr);
1504     }
1505   }
1506   if (!pc->setupcalled && patch->optionsSet) for (i = 0; i < patch->npatch; ++i) {ierr = KSPSetFromOptions(patch->ksp[i]);CHKERRQ(ierr);}
1507   PetscFunctionReturn(0);
1508 }
1509 
1510 static PetscErrorCode PCApply_PATCH(PC pc, Vec x, Vec y)
1511 {
1512   PC_PATCH          *patch    = (PC_PATCH *) pc->data;
1513   const PetscScalar *globalX  = NULL;
1514   PetscScalar       *localX   = NULL;
1515   PetscScalar       *globalY  = NULL;
1516   const PetscInt    *bcNodes  = NULL;
1517   PetscInt           nsweep   = patch->symmetrise_sweep ? 2 : 1;
1518   PetscInt           start[2] = {0, 0};
1519   PetscInt           end[2]   = {-1, -1};
1520   const PetscInt     inc[2]   = {1, -1};
1521   const PetscScalar *localY;
1522   const PetscInt    *iterationSet;
1523   PetscInt           pStart, numBcs, n, sweep, bc, j;
1524   PetscErrorCode     ierr;
1525 
1526   PetscFunctionBegin;
1527   ierr = PetscLogEventBegin(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
1528   ierr = PetscOptionsPushGetViewerOff(PETSC_TRUE);CHKERRQ(ierr);
1529   end[0]   = patch->npatch;
1530   start[1] = patch->npatch-1;
1531   if (patch->user_patches) {
1532     ierr = ISGetLocalSize(patch->iterationSet, &end[0]);CHKERRQ(ierr);
1533     start[1] = end[0] - 1;
1534     ierr = ISGetIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);
1535   }
1536   /* Scatter from global space into overlapped local spaces */
1537   ierr = VecGetArrayRead(x, &globalX);CHKERRQ(ierr);
1538   ierr = VecGetArray(patch->localX, &localX);CHKERRQ(ierr);
1539   ierr = PetscSFBcastBegin(patch->defaultSF, MPIU_SCALAR, globalX, localX);CHKERRQ(ierr);
1540   ierr = PetscSFBcastEnd(patch->defaultSF, MPIU_SCALAR, globalX, localX);CHKERRQ(ierr);
1541   ierr = VecRestoreArrayRead(x, &globalX);CHKERRQ(ierr);
1542   ierr = VecRestoreArray(patch->localX, &localX);CHKERRQ(ierr);
1543 
1544   ierr = VecSet(patch->localY, 0.0);CHKERRQ(ierr);
1545   ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, NULL);CHKERRQ(ierr);
1546   for (sweep = 0; sweep < nsweep; sweep++) {
1547     for (j = start[sweep]; j*inc[sweep] < end[sweep]*inc[sweep]; j += inc[sweep]) {
1548       PetscInt i       = patch->user_patches ? iterationSet[j] : j;
1549       PetscInt start, len;
1550 
1551       ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &len);CHKERRQ(ierr);
1552       ierr = PetscSectionGetOffset(patch->gtolCounts, i+pStart, &start);CHKERRQ(ierr);
1553       /* TODO: Squash out these guys in the setup as well. */
1554       if (len <= 0) continue;
1555       /* TODO: Do we need different scatters for X and Y? */
1556       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->localX, patch->patchX[i], INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
1557       if (!patch->save_operators) {
1558         Mat mat;
1559 
1560         ierr = PCPatchCreateMatrix_Private(pc, i, &mat);CHKERRQ(ierr);
1561         /* Populate operator here. */
1562         ierr = PCPatchComputeOperator_Private(pc, mat, i);CHKERRQ(ierr);
1563         ierr = KSPSetOperators(patch->ksp[i], mat, mat);CHKERRQ(ierr);
1564         /* Drop reference so the KSPSetOperators below will blow it away. */
1565         ierr = MatDestroy(&mat);CHKERRQ(ierr);
1566       }
1567       ierr = PetscLogEventBegin(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
1568       ierr = KSPSolve(patch->ksp[i], patch->patchX[i], patch->patchY[i]);CHKERRQ(ierr);
1569       ierr = PetscLogEventEnd(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
1570 
1571       if (!patch->save_operators) {
1572         PC pc;
1573         ierr = KSPSetOperators(patch->ksp[i], NULL, NULL);CHKERRQ(ierr);
1574         ierr = KSPGetPC(patch->ksp[i], &pc);CHKERRQ(ierr);
1575         /* Destroy PC context too, otherwise the factored matrix hangs around. */
1576         ierr = PCReset(pc);CHKERRQ(ierr);
1577       }
1578 
1579       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchY[i], patch->localY, ADD_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
1580     }
1581   }
1582   if (patch->user_patches) {ierr = ISRestoreIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);}
1583   /* XXX: should we do this on the global vector? */
1584   if (patch->partition_of_unity) {
1585     ierr = VecPointwiseMult(patch->localY, patch->localY, patch->dof_weights);CHKERRQ(ierr);
1586   }
1587   /* Now patch->localY contains the solution of the patch solves, so we need to combine them all. */
1588   ierr = VecSet(y, 0.0);CHKERRQ(ierr);
1589   ierr = VecGetArray(y, &globalY);CHKERRQ(ierr);
1590   ierr = VecGetArrayRead(patch->localY, &localY);CHKERRQ(ierr);
1591   ierr = PetscSFReduceBegin(patch->defaultSF, MPIU_SCALAR, localY, globalY, MPI_SUM);CHKERRQ(ierr);
1592   ierr = PetscSFReduceEnd(patch->defaultSF, MPIU_SCALAR, localY, globalY, MPI_SUM);CHKERRQ(ierr);
1593   ierr = VecRestoreArrayRead(patch->localY, &localY);CHKERRQ(ierr);
1594 
1595   /* Now we need to send the global BC values through */
1596   ierr = VecGetArrayRead(x, &globalX);CHKERRQ(ierr);
1597   ierr = ISGetSize(patch->globalBcNodes, &numBcs);CHKERRQ(ierr);
1598   ierr = ISGetIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
1599   ierr = VecGetLocalSize(x, &n);CHKERRQ(ierr);
1600   for (bc = 0; bc < numBcs; ++bc) {
1601     const PetscInt idx = bcNodes[bc];
1602     if (idx < n) globalY[idx] = globalX[idx];
1603   }
1604 
1605   ierr = ISRestoreIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
1606   ierr = VecRestoreArrayRead(x, &globalX);CHKERRQ(ierr);
1607   ierr = VecRestoreArray(y, &globalY);CHKERRQ(ierr);
1608 
1609   ierr = PetscOptionsPopGetViewerOff();CHKERRQ(ierr);
1610   ierr = PetscLogEventEnd(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
1611   PetscFunctionReturn(0);
1612 }
1613 
1614 static PetscErrorCode PCReset_PATCH(PC pc)
1615 {
1616   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1617   PetscInt       i;
1618   PetscErrorCode ierr;
1619 
1620   PetscFunctionBegin;
1621   /* TODO: Get rid of all these ifs */
1622   ierr = PetscSFDestroy(&patch->defaultSF);CHKERRQ(ierr);
1623   ierr = PetscSectionDestroy(&patch->cellCounts);CHKERRQ(ierr);
1624   ierr = PetscSectionDestroy(&patch->pointCounts);CHKERRQ(ierr);
1625   ierr = PetscSectionDestroy(&patch->cellNumbering);CHKERRQ(ierr);
1626   ierr = PetscSectionDestroy(&patch->gtolCounts);CHKERRQ(ierr);
1627   ierr = ISDestroy(&patch->gtol);CHKERRQ(ierr);
1628   ierr = ISDestroy(&patch->cells);CHKERRQ(ierr);
1629   ierr = ISDestroy(&patch->points);CHKERRQ(ierr);
1630   ierr = ISDestroy(&patch->dofs);CHKERRQ(ierr);
1631   ierr = ISDestroy(&patch->offs);CHKERRQ(ierr);
1632   ierr = PetscSectionDestroy(&patch->patchSection);CHKERRQ(ierr);
1633   ierr = ISDestroy(&patch->ghostBcNodes);CHKERRQ(ierr);
1634   ierr = ISDestroy(&patch->globalBcNodes);CHKERRQ(ierr);
1635 
1636   if (patch->dofSection) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscSectionDestroy(&patch->dofSection[i]);CHKERRQ(ierr);}
1637   ierr = PetscFree(patch->dofSection);CHKERRQ(ierr);
1638   ierr = PetscFree(patch->bs);CHKERRQ(ierr);
1639   ierr = PetscFree(patch->nodesPerCell);CHKERRQ(ierr);
1640   if (patch->cellNodeMap) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscFree(patch->cellNodeMap[i]);CHKERRQ(ierr);}
1641   ierr = PetscFree(patch->cellNodeMap);CHKERRQ(ierr);
1642   ierr = PetscFree(patch->subspaceOffsets);CHKERRQ(ierr);
1643 
1644   if (patch->ksp) {
1645     for (i = 0; i < patch->npatch; ++i) {ierr = KSPReset(patch->ksp[i]);CHKERRQ(ierr);}
1646   }
1647 
1648   if (patch->subspaces_to_exclude) {
1649     PetscHSetIDestroy(&patch->subspaces_to_exclude);
1650   }
1651 
1652   ierr = VecDestroy(&patch->localX);CHKERRQ(ierr);
1653   ierr = VecDestroy(&patch->localY);CHKERRQ(ierr);
1654   if (patch->patchX) {
1655     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchX[i]);CHKERRQ(ierr);}
1656     ierr = PetscFree(patch->patchX);CHKERRQ(ierr);
1657   }
1658   if (patch->patchY) {
1659     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchY[i]);CHKERRQ(ierr);}
1660     ierr = PetscFree(patch->patchY);CHKERRQ(ierr);
1661   }
1662   ierr = VecDestroy(&patch->dof_weights);CHKERRQ(ierr);
1663   if (patch->patch_dof_weights) {
1664     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patch_dof_weights[i]);CHKERRQ(ierr);}
1665     ierr = PetscFree(patch->patch_dof_weights);CHKERRQ(ierr);
1666   }
1667   if (patch->mat) {
1668     for (i = 0; i < patch->npatch; ++i) {ierr = MatDestroy(&patch->mat[i]);CHKERRQ(ierr);}
1669     ierr = PetscFree(patch->mat);CHKERRQ(ierr);
1670   }
1671   ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);
1672   if (patch->userIS) {
1673     for (i = 0; i < patch->npatch; ++i) {ierr = ISDestroy(&patch->userIS[i]);CHKERRQ(ierr);}
1674     ierr = PetscFree(patch->userIS);CHKERRQ(ierr);
1675   }
1676   patch->bs          = 0;
1677   patch->cellNodeMap = NULL;
1678   patch->nsubspaces  = 0;
1679   ierr = ISDestroy(&patch->iterationSet);CHKERRQ(ierr);
1680 
1681   ierr = PetscViewerDestroy(&patch->viewerSection);CHKERRQ(ierr);
1682   PetscFunctionReturn(0);
1683 }
1684 
1685 static PetscErrorCode PCDestroy_PATCH(PC pc)
1686 {
1687   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1688   PetscInt       i;
1689   PetscErrorCode ierr;
1690 
1691   PetscFunctionBegin;
1692   ierr = PCReset_PATCH(pc);CHKERRQ(ierr);
1693   if (patch->ksp) {
1694     for (i = 0; i < patch->npatch; ++i) {ierr = KSPDestroy(&patch->ksp[i]);CHKERRQ(ierr);}
1695     ierr = PetscFree(patch->ksp);CHKERRQ(ierr);
1696   }
1697   ierr = PetscFree(pc->data);CHKERRQ(ierr);
1698   PetscFunctionReturn(0);
1699 }
1700 
1701 static PetscErrorCode PCSetFromOptions_PATCH(PetscOptionItems *PetscOptionsObject, PC pc)
1702 {
1703   PC_PATCH            *patch = (PC_PATCH *) pc->data;
1704   PCPatchConstructType patchConstructionType = PC_PATCH_STAR;
1705   char                 sub_mat_type[PETSC_MAX_PATH_LEN];
1706   const char          *prefix;
1707   PetscBool            flg, dimflg, codimflg;
1708   MPI_Comm             comm;
1709   PetscInt            *ifields, nfields, k;
1710   PetscErrorCode       ierr;
1711 
1712   PetscFunctionBegin;
1713   ierr = PetscObjectGetComm((PetscObject) pc, &comm);CHKERRQ(ierr);
1714   ierr = PetscObjectGetOptionsPrefix((PetscObject) pc, &prefix);CHKERRQ(ierr);
1715   ierr = PetscOptionsHead(PetscOptionsObject, "Vertex-patch Additive Schwarz options");CHKERRQ(ierr);
1716   ierr = PetscOptionsBool("-pc_patch_save_operators",  "Store all patch operators for lifetime of PC?", "PCPatchSetSaveOperators", patch->save_operators, &patch->save_operators, &flg);CHKERRQ(ierr);
1717   ierr = PetscOptionsBool("-pc_patch_partition_of_unity", "Weight contributions by dof multiplicity?", "PCPatchSetPartitionOfUnity", patch->partition_of_unity, &patch->partition_of_unity, &flg);CHKERRQ(ierr);
1718   ierr = PetscOptionsInt("-pc_patch_construct_dim", "What dimension of mesh point to construct patches by? (0 = vertices)", "PCPATCH", patch->dim, &patch->dim, &dimflg);CHKERRQ(ierr);
1719   ierr = PetscOptionsInt("-pc_patch_construct_codim", "What co-dimension of mesh point to construct patches by? (0 = cells)", "PCPATCH", patch->codim, &patch->codim, &codimflg);CHKERRQ(ierr);
1720   if (dimflg && codimflg) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Can only set one of dimension or co-dimension");CHKERRQ(ierr);
1721   ierr = PetscOptionsEnum("-pc_patch_construct_type", "How should the patches be constructed?", "PCPatchSetConstructType", PCPatchConstructTypes, (PetscEnum) patchConstructionType, (PetscEnum *) &patchConstructionType, &flg);CHKERRQ(ierr);
1722   if (flg) {ierr = PCPatchSetConstructType(pc, patchConstructionType, NULL, NULL);CHKERRQ(ierr);}
1723   ierr = PetscOptionsInt("-pc_patch_vanka_dim", "Topological dimension of entities for Vanka to ignore", "PCPATCH", patch->vankadim, &patch->vankadim, &flg);CHKERRQ(ierr);
1724   ierr = PetscOptionsInt("-pc_patch_ignore_dim", "Topological dimension of entities for completion to ignore", "PCPATCH", patch->ignoredim, &patch->ignoredim, &flg);CHKERRQ(ierr);
1725   ierr = PetscOptionsFList("-pc_patch_sub_mat_type", "Matrix type for patch solves", "PCPatchSetSubMatType", MatList, NULL, sub_mat_type, PETSC_MAX_PATH_LEN, &flg);CHKERRQ(ierr);
1726   if (flg) {ierr = PCPatchSetSubMatType(pc, sub_mat_type);CHKERRQ(ierr);}
1727   ierr = PetscOptionsBool("-pc_patch_symmetrise_sweep", "Go start->end, end->start?", "PCPATCH", patch->symmetrise_sweep, &patch->symmetrise_sweep, &flg);CHKERRQ(ierr);
1728 
1729   /* If the user has set the number of subspaces, use that for the buffer size,
1730      otherwise use a large number */
1731   if (patch->nsubspaces <= 0) {
1732     nfields = 128;
1733   } else {
1734     nfields = patch->nsubspaces;
1735   }
1736   ierr = PetscMalloc1(nfields, &ifields);CHKERRQ(ierr);
1737   ierr = PetscOptionsGetIntArray(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_patch_exclude_subspaces",ifields,&nfields,&flg);CHKERRQ(ierr);
1738   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");
1739   if (flg) {
1740     PetscHSetIClear(patch->subspaces_to_exclude);
1741     for (k = 0; k < nfields; k++) {
1742       PetscHSetIAdd(patch->subspaces_to_exclude, ifields[k]);
1743     }
1744   }
1745   ierr = PetscFree(ifields);CHKERRQ(ierr);
1746 
1747   ierr = PetscOptionsBool("-pc_patch_patches_view", "Print out information during patch construction", "PCPATCH", patch->viewPatches, &patch->viewPatches, &flg);CHKERRQ(ierr);
1748   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_cells_view",   &patch->viewerCells,   &patch->formatCells,   &patch->viewCells);CHKERRQ(ierr);
1749   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_points_view",  &patch->viewerPoints,  &patch->formatPoints,  &patch->viewPoints);CHKERRQ(ierr);
1750   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_section_view", &patch->viewerSection, &patch->formatSection, &patch->viewSection);CHKERRQ(ierr);
1751   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_mat_view",     &patch->viewerMatrix,  &patch->formatMatrix,  &patch->viewMatrix);CHKERRQ(ierr);
1752   ierr = PetscOptionsTail();CHKERRQ(ierr);
1753   patch->optionsSet = PETSC_TRUE;
1754   PetscFunctionReturn(0);
1755 }
1756 
1757 static PetscErrorCode PCSetUpOnBlocks_PATCH(PC pc)
1758 {
1759   PC_PATCH          *patch = (PC_PATCH*) pc->data;
1760   KSPConvergedReason reason;
1761   PetscInt           i;
1762   PetscErrorCode     ierr;
1763 
1764   PetscFunctionBegin;
1765   for (i = 0; i < patch->npatch; ++i) {
1766     ierr = KSPSetUp(patch->ksp[i]);CHKERRQ(ierr);
1767     ierr = KSPGetConvergedReason(patch->ksp[i], &reason);CHKERRQ(ierr);
1768     if (reason == KSP_DIVERGED_PCSETUP_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1769   }
1770   PetscFunctionReturn(0);
1771 }
1772 
1773 static PetscErrorCode PCView_PATCH(PC pc, PetscViewer viewer)
1774 {
1775   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1776   PetscViewer    sviewer;
1777   PetscBool      isascii;
1778   PetscMPIInt    rank;
1779   PetscErrorCode ierr;
1780 
1781   PetscFunctionBegin;
1782   /* TODO Redo tabbing with set tbas in new style */
1783   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
1784   if (!isascii) PetscFunctionReturn(0);
1785   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) pc), &rank);CHKERRQ(ierr);
1786   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1787   ierr = PetscViewerASCIIPrintf(viewer, "Subspace Correction preconditioner with %d patches\n", patch->npatch);CHKERRQ(ierr);
1788   ierr = PetscViewerASCIIPrintf(viewer, "Schwarz type: additive\n");CHKERRQ(ierr);
1789   if (patch->partition_of_unity) {ierr = PetscViewerASCIIPrintf(viewer, "Weighting by partition of unity\n");CHKERRQ(ierr);}
1790   else                           {ierr = PetscViewerASCIIPrintf(viewer, "Not weighting by partition of unity\n");CHKERRQ(ierr);}
1791   if (patch->symmetrise_sweep) {ierr = PetscViewerASCIIPrintf(viewer, "Symmetrising sweep (start->end, then end->start)\n");CHKERRQ(ierr);}
1792   else                         {ierr = PetscViewerASCIIPrintf(viewer, "Not symmetrising sweep\n");CHKERRQ(ierr);}
1793   if (!patch->save_operators) {ierr = PetscViewerASCIIPrintf(viewer, "Not saving patch operators (rebuilt every PCApply)\n");CHKERRQ(ierr);}
1794   else                        {ierr = PetscViewerASCIIPrintf(viewer, "Saving patch operators (rebuilt every PCSetUp)\n");CHKERRQ(ierr);}
1795   if (patch->patchconstructop == PCPatchConstruct_Star)       {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: star\n");CHKERRQ(ierr);}
1796   else if (patch->patchconstructop == PCPatchConstruct_Vanka) {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: Vanka\n");CHKERRQ(ierr);}
1797   else if (patch->patchconstructop == PCPatchConstruct_User)  {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: user-specified\n");CHKERRQ(ierr);}
1798   else                                                        {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: unknown\n");CHKERRQ(ierr);}
1799   ierr = PetscViewerASCIIPrintf(viewer, "KSP on patches (all same):\n");CHKERRQ(ierr);
1800   if (patch->ksp) {
1801     ierr = PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
1802     if (!rank) {
1803       ierr = PetscViewerASCIIPushTab(sviewer);CHKERRQ(ierr);
1804       ierr = KSPView(patch->ksp[0], sviewer);CHKERRQ(ierr);
1805       ierr = PetscViewerASCIIPopTab(sviewer);CHKERRQ(ierr);
1806     }
1807     ierr = PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
1808   } else {
1809     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1810     ierr = PetscViewerASCIIPrintf(viewer, "KSP not yet set.\n");CHKERRQ(ierr);
1811     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1812   }
1813   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1814   PetscFunctionReturn(0);
1815 }
1816 
1817 /*MC
1818   PCPATCH - A PC object that encapsulates flexible definition of blocks for overlapping and non-overlapping
1819             small block additive preconditioners. Block definition is based on topology from
1820             a DM and equation numbering from a PetscSection.
1821 
1822   Options Database Keys:
1823 + -pc_patch_cells_view   - Views the process local cell numbers for each patch
1824 . -pc_patch_points_view  - Views the process local mesh point numbers for each patch
1825 . -pc_patch_g2l_view     - Views the map between global dofs and patch local dofs for each patch
1826 . -pc_patch_patches_view - Views the global dofs associated with each patch and its boundary
1827 - -pc_patch_sub_mat_view - Views the matrix associated with each patch
1828 
1829   Level: intermediate
1830 
1831 .seealso: PCType, PCCreate(), PCSetType()
1832 M*/
1833 PETSC_EXTERN PetscErrorCode PCCreate_Patch(PC pc)
1834 {
1835   PC_PATCH      *patch;
1836   PetscErrorCode ierr;
1837 
1838   PetscFunctionBegin;
1839   ierr = PetscNewLog(pc, &patch);CHKERRQ(ierr);
1840 
1841   if (patch->subspaces_to_exclude) {
1842     PetscHSetIDestroy(&patch->subspaces_to_exclude);
1843   }
1844   PetscHSetICreate(&patch->subspaces_to_exclude);
1845 
1846   /* Set some defaults */
1847   patch->combined           = PETSC_FALSE;
1848   patch->save_operators     = PETSC_TRUE;
1849   patch->partition_of_unity = PETSC_FALSE;
1850   patch->codim              = -1;
1851   patch->dim                = -1;
1852   patch->vankadim           = -1;
1853   patch->ignoredim          = -1;
1854   patch->patchconstructop   = PCPatchConstruct_Star;
1855   patch->symmetrise_sweep   = PETSC_FALSE;
1856   patch->npatch             = 0;
1857   patch->userIS             = NULL;
1858   patch->optionsSet         = PETSC_FALSE;
1859   patch->iterationSet       = NULL;
1860   patch->user_patches       = PETSC_FALSE;
1861   ierr = PetscStrallocpy(MATDENSE, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
1862   patch->viewPatches        = PETSC_FALSE;
1863   patch->viewCells          = PETSC_FALSE;
1864   patch->viewPoints         = PETSC_FALSE;
1865   patch->viewSection        = PETSC_FALSE;
1866   patch->viewMatrix         = PETSC_FALSE;
1867 
1868   pc->data                 = (void *) patch;
1869   pc->ops->apply           = PCApply_PATCH;
1870   pc->ops->applytranspose  = 0; /* PCApplyTranspose_PATCH; */
1871   pc->ops->setup           = PCSetUp_PATCH;
1872   pc->ops->reset           = PCReset_PATCH;
1873   pc->ops->destroy         = PCDestroy_PATCH;
1874   pc->ops->setfromoptions  = PCSetFromOptions_PATCH;
1875   pc->ops->setuponblocks   = PCSetUpOnBlocks_PATCH;
1876   pc->ops->view            = PCView_PATCH;
1877   pc->ops->applyrichardson = 0;
1878 
1879   PetscFunctionReturn(0);
1880 }
1881