xref: /petsc/src/ksp/pc/impls/patch/pcpatch.c (revision 1d36bdfd46c3877894678bf6fced88766689f9b6)
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, PetscInt exclude_subspace)
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 (k == exclude_subspace) {
589       /* only get this subspace dofs at the base entity, not any others */
590       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, base, &ldof, &loff);CHKERRQ(ierr);
591       if (0 == ldof) continue;
592       for (j = loff; j < ldof + loff; ++j) {
593         for (l = 0; l < bs; ++l) {
594           PetscInt dof = bs*j + l + subspaceOffset;
595           ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
596         }
597       }
598       continue; /* skip the other dofs of this subspace */
599     }
600 
601     PetscHashIterBegin(pts, hi);
602     while (!PetscHashIterAtEnd(pts, hi)) {
603       PetscHashIterGetKey(pts, hi, p);
604       PetscHashIterNext(pts, hi);
605       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, p, &ldof, &loff);CHKERRQ(ierr);
606       if (0 == ldof) continue;
607       for (j = loff; j < ldof + loff; ++j) {
608         for (l = 0; l < bs; ++l) {
609           PetscInt dof = bs*j + l + subspaceOffset;
610           ierr = PetscHSetIAdd(dofs, dof);CHKERRQ(ierr);
611         }
612       }
613     }
614   }
615   PetscFunctionReturn(0);
616 }
617 
618 /* Given two hash tables A and B, compute the keys in B that are not in A, and put them in C */
619 static PetscErrorCode PCPatchComputeSetDifference_Private(PetscHSetI A, PetscHSetI B, PetscHSetI C)
620 {
621   PetscHashIter  hi;
622   PetscInt       key;
623   PetscBool      flg;
624   PetscErrorCode ierr;
625 
626   PetscFunctionBegin;
627   ierr = PetscHSetIClear(C);CHKERRQ(ierr);
628   PetscHashIterBegin(B, hi);
629   while (!PetscHashIterAtEnd(B, hi)) {
630     PetscHashIterGetKey(B, hi, key);
631     PetscHashIterNext(B, hi);
632     ierr = PetscHSetIHas(A, key, &flg);CHKERRQ(ierr);
633     if (!flg) {ierr = PetscHSetIAdd(C, key);CHKERRQ(ierr);}
634   }
635   PetscFunctionReturn(0);
636 }
637 
638 /*
639  * PCPatchCreateCellPatches - create patches.
640  *
641  * Input Parameters:
642  * + dm - The DMPlex object defining the mesh
643  *
644  * Output Parameters:
645  * + cellCounts  - Section with counts of cells around each vertex
646  * . cells       - IS of the cell point indices of cells in each patch
647  * . pointCounts - Section with counts of cells around each vertex
648  * - point       - IS of the cell point indices of cells in each patch
649  */
650 static PetscErrorCode PCPatchCreateCellPatches(PC pc)
651 {
652   PC_PATCH       *patch = (PC_PATCH *) pc->data;
653   DMLabel         ghost = NULL;
654   DM              dm, plex;
655   PetscHSetI      ht, cht;
656   PetscSection    cellCounts,  pointCounts;
657   PetscInt       *cellsArray, *pointsArray;
658   PetscInt        numCells,    numPoints;
659   const PetscInt *leaves;
660   PetscInt        nleaves, pStart, pEnd, cStart, cEnd, vStart, vEnd, v;
661   PetscBool       isFiredrake;
662   PetscErrorCode  ierr;
663 
664   PetscFunctionBegin;
665   /* Used to keep track of the cells in the patch. */
666   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
667   ierr = PetscHSetICreate(&cht);CHKERRQ(ierr);
668 
669   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
670   if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONGSTATE, "DM not yet set on patch PC\n");
671   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
672   ierr = DMPlexGetChart(plex, &pStart, &pEnd);CHKERRQ(ierr);
673   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
674 
675   if (patch->user_patches) {
676     ierr = patch->userpatchconstructionop(pc, &patch->npatch, &patch->userIS, &patch->iterationSet, patch->userpatchconstructctx);CHKERRQ(ierr);
677     vStart = 0; vEnd = patch->npatch;
678   } else if (patch->codim < 0) {
679     if (patch->dim < 0) {ierr = DMPlexGetDepthStratum(plex,  0,            &vStart, &vEnd);CHKERRQ(ierr);}
680     else                {ierr = DMPlexGetDepthStratum(plex,  patch->dim,   &vStart, &vEnd);CHKERRQ(ierr);}
681   } else                {ierr = DMPlexGetHeightStratum(plex, patch->codim, &vStart, &vEnd);CHKERRQ(ierr);}
682   patch->npatch = vEnd - vStart;
683 
684   /* These labels mark the owned points.  We only create patches around points that this process owns. */
685   ierr = DMHasLabel(dm, "pyop2_ghost", &isFiredrake);CHKERRQ(ierr);
686   if (isFiredrake) {
687     ierr = DMGetLabel(dm, "pyop2_ghost", &ghost);CHKERRQ(ierr);
688     ierr = DMLabelCreateIndex(ghost, pStart, pEnd);CHKERRQ(ierr);
689   } else {
690     PetscSF sf;
691 
692     ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
693     ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
694     nleaves = PetscMax(nleaves, 0);
695   }
696 
697   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->cellCounts);CHKERRQ(ierr);
698   ierr = PetscObjectSetName((PetscObject) patch->cellCounts, "Patch Cell Layout");CHKERRQ(ierr);
699   cellCounts = patch->cellCounts;
700   ierr = PetscSectionSetChart(cellCounts, vStart, vEnd);CHKERRQ(ierr);
701   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->pointCounts);CHKERRQ(ierr);
702   ierr = PetscObjectSetName((PetscObject) patch->pointCounts, "Patch Point Layout");CHKERRQ(ierr);
703   pointCounts = patch->pointCounts;
704   ierr = PetscSectionSetChart(pointCounts, vStart, vEnd);CHKERRQ(ierr);
705   /* Count cells and points in the patch surrounding each entity */
706   for (v = vStart; v < vEnd; ++v) {
707     PetscHashIter hi;
708     PetscInt       chtSize, loc = -1;
709     PetscBool      flg;
710 
711     if (!patch->user_patches) {
712       if (ghost) {ierr = DMLabelHasPoint(ghost, v, &flg);CHKERRQ(ierr);}
713       else       {ierr = PetscFindInt(v, nleaves, leaves, &loc); flg = loc >=0 ? PETSC_TRUE : PETSC_FALSE;}
714       /* Not an owned entity, don't make a cell patch. */
715       if (flg) continue;
716     }
717 
718     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
719     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
720     ierr = PetscHSetIGetSize(cht, &chtSize);CHKERRQ(ierr);
721     /* empty patch, continue */
722     if (chtSize == 0) continue;
723 
724     /* safe because size(cht) > 0 from above */
725     PetscHashIterBegin(cht, hi);
726     while (!PetscHashIterAtEnd(cht, hi)) {
727       PetscInt point, pdof;
728 
729       PetscHashIterGetKey(cht, hi, point);
730       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
731       if (pdof)                            {ierr = PetscSectionAddDof(pointCounts, v, 1);CHKERRQ(ierr);}
732       if (point >= cStart && point < cEnd) {ierr = PetscSectionAddDof(cellCounts, v, 1);CHKERRQ(ierr);}
733       PetscHashIterNext(cht, hi);
734     }
735   }
736   if (isFiredrake) {ierr = DMLabelDestroyIndex(ghost);CHKERRQ(ierr);}
737 
738   ierr = PetscSectionSetUp(cellCounts);CHKERRQ(ierr);
739   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
740   ierr = PetscMalloc1(numCells, &cellsArray);CHKERRQ(ierr);
741   ierr = PetscSectionSetUp(pointCounts);CHKERRQ(ierr);
742   ierr = PetscSectionGetStorageSize(pointCounts, &numPoints);CHKERRQ(ierr);
743   ierr = PetscMalloc1(numPoints, &pointsArray);CHKERRQ(ierr);
744 
745   /* Now that we know how much space we need, run through again and actually remember the cells. */
746   for (v = vStart; v < vEnd; v++ ) {
747     PetscHashIter hi;
748     PetscInt       dof, off, cdof, coff, pdof, n = 0, cn = 0;
749 
750     ierr = PetscSectionGetDof(pointCounts, v, &dof);CHKERRQ(ierr);
751     ierr = PetscSectionGetOffset(pointCounts, v, &off);CHKERRQ(ierr);
752     ierr = PetscSectionGetDof(cellCounts, v, &cdof);CHKERRQ(ierr);
753     ierr = PetscSectionGetOffset(cellCounts, v, &coff);CHKERRQ(ierr);
754     if (dof <= 0) continue;
755     ierr = patch->patchconstructop((void *) patch, dm, v, ht);CHKERRQ(ierr);
756     ierr = PCPatchCompleteCellPatch(pc, ht, cht);CHKERRQ(ierr);
757     PetscHashIterBegin(cht, hi);
758     while (!PetscHashIterAtEnd(cht, hi)) {
759       PetscInt point;
760 
761       PetscHashIterGetKey(cht, hi, point);
762       ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, -1, patch->combined, point, &pdof, NULL);CHKERRQ(ierr);
763       if (pdof)                            {pointsArray[off + n++] = point;}
764       if (point >= cStart && point < cEnd) {cellsArray[coff + cn++] = point;}
765       PetscHashIterNext(cht, hi);
766     }
767     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);
768     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);
769   }
770   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
771   ierr = PetscHSetIDestroy(&cht);CHKERRQ(ierr);
772   ierr = DMDestroy(&plex);CHKERRQ(ierr);
773 
774   ierr = ISCreateGeneral(PETSC_COMM_SELF, numCells,  cellsArray,  PETSC_OWN_POINTER, &patch->cells);CHKERRQ(ierr);
775   ierr = PetscObjectSetName((PetscObject) patch->cells,  "Patch Cells");CHKERRQ(ierr);
776   if (patch->viewCells) {
777     ierr = ObjectView((PetscObject) patch->cellCounts, patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
778     ierr = ObjectView((PetscObject) patch->cells,      patch->viewerCells, patch->formatCells);CHKERRQ(ierr);
779   }
780   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, pointsArray, PETSC_OWN_POINTER, &patch->points);CHKERRQ(ierr);
781   ierr = PetscObjectSetName((PetscObject) patch->points, "Patch Points");CHKERRQ(ierr);
782   if (patch->viewPoints) {
783     ierr = ObjectView((PetscObject) patch->pointCounts, patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
784     ierr = ObjectView((PetscObject) patch->points,      patch->viewerPoints, patch->formatPoints);CHKERRQ(ierr);
785   }
786   PetscFunctionReturn(0);
787 }
788 
789 /*
790  * PCPatchCreateCellPatchDiscretisationInfo - Build the dof maps for cell patches
791  *
792  * Input Parameters:
793  * + dm - The DMPlex object defining the mesh
794  * . cellCounts - Section with counts of cells around each vertex
795  * . cells - IS of the cell point indices of cells in each patch
796  * . cellNumbering - Section mapping plex cell points to Firedrake cell indices.
797  * . nodesPerCell - number of nodes per cell.
798  * - cellNodeMap - map from cells to node indices (nodesPerCell * numCells)
799  *
800  * Output Parameters:
801  * + dofs - IS of local dof numbers of each cell in the patch, where local is a patch local numbering
802  * . gtolCounts - Section with counts of dofs per cell patch
803  * - gtol - IS mapping from global dofs to local dofs for each patch.
804  */
805 static PetscErrorCode PCPatchCreateCellPatchDiscretisationInfo(PC pc)
806 {
807   PC_PATCH       *patch           = (PC_PATCH *) pc->data;
808   PetscSection    cellCounts      = patch->cellCounts;
809   PetscSection    pointCounts     = patch->pointCounts;
810   PetscSection    gtolCounts;
811   IS              cells           = patch->cells;
812   IS              points          = patch->points;
813   PetscSection    cellNumbering   = patch->cellNumbering;
814   PetscInt        Nf              = patch->nsubspaces;
815   PetscInt        numCells, numPoints;
816   PetscInt        numDofs;
817   PetscInt        numGlobalDofs;
818   PetscInt        totalDofsPerCell = patch->totalDofsPerCell;
819   PetscInt        vStart, vEnd, v;
820   const PetscInt *cellsArray, *pointsArray;
821   PetscInt       *newCellsArray   = NULL;
822   PetscInt       *dofsArray       = NULL;
823   PetscInt       *offsArray       = NULL;
824   PetscInt       *asmArray        = NULL;
825   PetscInt       *globalDofsArray = NULL;
826   PetscInt        globalIndex     = 0;
827   PetscInt        key             = 0;
828   PetscInt        asmKey          = 0;
829   DM              dm              = NULL;
830   const PetscInt *bcNodes         = NULL;
831   PetscHMapI      ht;
832   PetscHSetI      globalBcs;
833   PetscInt        numBcs;
834   PetscHSetI      ownedpts, seenpts, owneddofs, seendofs, artificialbcs;
835   PetscInt        pStart, pEnd, p, i;
836   PetscErrorCode  ierr;
837 
838   PetscFunctionBegin;
839 
840   ierr = PCGetDM(pc, &dm); CHKERRQ(ierr);
841   /* dofcounts section is cellcounts section * dofPerCell */
842   ierr = PetscSectionGetStorageSize(cellCounts, &numCells);CHKERRQ(ierr);
843   ierr = PetscSectionGetStorageSize(patch->pointCounts, &numPoints);CHKERRQ(ierr);
844   numDofs = numCells * totalDofsPerCell;
845   ierr = PetscMalloc1(numDofs, &dofsArray);CHKERRQ(ierr);
846   ierr = PetscMalloc1(numPoints*Nf, &offsArray);CHKERRQ(ierr);
847   ierr = PetscMalloc1(numDofs, &asmArray);CHKERRQ(ierr);
848   ierr = PetscMalloc1(numCells, &newCellsArray);CHKERRQ(ierr);
849   ierr = PetscSectionGetChart(cellCounts, &vStart, &vEnd);CHKERRQ(ierr);
850   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->gtolCounts);CHKERRQ(ierr);
851   gtolCounts = patch->gtolCounts;
852   ierr = PetscSectionSetChart(gtolCounts, vStart, vEnd);CHKERRQ(ierr);
853   ierr = PetscObjectSetName((PetscObject) patch->gtolCounts, "Patch Global Index Section");CHKERRQ(ierr);
854 
855   /* Outside the patch loop, get the dofs that are globally-enforced Dirichlet
856    conditions */
857   ierr = PetscHSetICreate(&globalBcs);CHKERRQ(ierr);
858   ierr = ISGetIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
859   ierr = ISGetSize(patch->ghostBcNodes, &numBcs); CHKERRQ(ierr);
860   for (i = 0; i < numBcs; ++i) {
861     ierr = PetscHSetIAdd(globalBcs, bcNodes[i]);CHKERRQ(ierr); /* these are already in concatenated numbering */
862   }
863   ierr = ISRestoreIndices(patch->ghostBcNodes, &bcNodes); CHKERRQ(ierr);
864   ierr = ISDestroy(&patch->ghostBcNodes); CHKERRQ(ierr); /* memory optimisation */
865 
866   /* Hash tables for artificial BC construction */
867   ierr = PetscHSetICreate(&ownedpts);CHKERRQ(ierr);
868   ierr = PetscHSetICreate(&seenpts);CHKERRQ(ierr);
869   ierr = PetscHSetICreate(&owneddofs);CHKERRQ(ierr);
870   ierr = PetscHSetICreate(&seendofs);CHKERRQ(ierr);
871   ierr = PetscHSetICreate(&artificialbcs);CHKERRQ(ierr);
872 
873   ierr = ISGetIndices(cells, &cellsArray);CHKERRQ(ierr);
874   ierr = ISGetIndices(points, &pointsArray);CHKERRQ(ierr);
875   ierr = PetscHMapICreate(&ht);CHKERRQ(ierr);
876   for (v = vStart; v < vEnd; ++v) {
877     PetscInt localIndex = 0;
878     PetscInt dof, off, i, j, k, l;
879 
880     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
881     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
882     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
883     if (dof <= 0) continue;
884 
885     /* Calculate the global numbers of the artificial BC dofs here first */
886     ierr = patch->patchconstructop((void*)patch, dm, v, ownedpts); CHKERRQ(ierr);
887     ierr = PCPatchCompleteCellPatch(pc, ownedpts, seenpts); CHKERRQ(ierr);
888     ierr = PCPatchGetPointDofs(pc, ownedpts, owneddofs, v, patch->exclude_subspace); CHKERRQ(ierr);
889     ierr = PCPatchGetPointDofs(pc, seenpts, seendofs, v, -1); CHKERRQ(ierr);
890     ierr = PCPatchComputeSetDifference_Private(owneddofs, seendofs, artificialbcs); CHKERRQ(ierr);
891     if (patch->viewPatches) {
892       PetscHSetI globalbcdofs;
893       PetscHashIter hi;
894       MPI_Comm comm = PetscObjectComm((PetscObject)pc);
895 
896       ierr = PetscHSetICreate(&globalbcdofs);CHKERRQ(ierr);
897       ierr = PetscSynchronizedPrintf(comm, "Patch %d: owned dofs:\n", v); CHKERRQ(ierr);
898       PetscHashIterBegin(owneddofs, hi);
899       while (!PetscHashIterAtEnd(owneddofs, hi)) {
900         PetscInt globalDof;
901 
902         PetscHashIterGetKey(owneddofs, hi, globalDof);
903         PetscHashIterNext(owneddofs, hi);
904         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
905       }
906       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
907       ierr = PetscSynchronizedPrintf(comm, "Patch %d: seen dofs:\n", v); CHKERRQ(ierr);
908       PetscHashIterBegin(seendofs, hi);
909       while (!PetscHashIterAtEnd(seendofs, hi)) {
910         PetscInt globalDof;
911         PetscBool flg;
912 
913         PetscHashIterGetKey(seendofs, hi, globalDof);
914         PetscHashIterNext(seendofs, hi);
915         ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
916 
917         ierr = PetscHSetIHas(globalBcs, globalDof, &flg);CHKERRQ(ierr);
918         if (flg) {ierr = PetscHSetIAdd(globalbcdofs, globalDof);CHKERRQ(ierr);}
919       }
920       ierr = PetscSynchronizedPrintf(comm, "\n"); CHKERRQ(ierr);
921       ierr = PetscSynchronizedPrintf(comm, "Patch %d: global BCs:\n", v); CHKERRQ(ierr);
922       ierr = PetscHSetIGetSize(globalbcdofs, &numBcs);CHKERRQ(ierr);
923       if (numBcs > 0) {
924         PetscHashIterBegin(globalbcdofs, hi);
925         while (!PetscHashIterAtEnd(globalbcdofs, hi)) {
926           PetscInt globalDof;
927           PetscHashIterGetKey(globalbcdofs, hi, globalDof);
928           PetscHashIterNext(globalbcdofs, hi);
929           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof);CHKERRQ(ierr);
930         }
931       }
932       ierr = PetscSynchronizedPrintf(comm, "\n");CHKERRQ(ierr);
933       ierr = PetscSynchronizedPrintf(comm, "Patch %d: artificial BCs:\n", v);CHKERRQ(ierr);
934       ierr = PetscHSetIGetSize(artificialbcs, &numBcs);CHKERRQ(ierr);
935       if (numBcs > 0) {
936         PetscHashIterBegin(artificialbcs, hi);
937         while (!PetscHashIterAtEnd(artificialbcs, hi)) {
938           PetscInt globalDof;
939           PetscHashIterGetKey(artificialbcs, hi, globalDof);
940           PetscHashIterNext(artificialbcs, hi);
941           ierr = PetscSynchronizedPrintf(comm, "%d ", globalDof); CHKERRQ(ierr);
942         }
943       }
944       ierr = PetscSynchronizedPrintf(comm, "\n\n"); CHKERRQ(ierr);
945       ierr = PetscHSetIDestroy(&globalbcdofs);CHKERRQ(ierr);
946     }
947    for (k = 0; k < patch->nsubspaces; ++k) {
948       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
949       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
950       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
951       PetscInt        bs             = patch->bs[k];
952 
953       for (i = off; i < off + dof; ++i) {
954         /* Walk over the cells in this patch. */
955         const PetscInt c    = cellsArray[i];
956         PetscInt       cell = c;
957 
958         /* TODO Change this to an IS */
959         if (cellNumbering) {
960           ierr = PetscSectionGetDof(cellNumbering, c, &cell);CHKERRQ(ierr);
961           if (cell <= 0) SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_OUTOFRANGE, "Cell %D doesn't appear in cell numbering map", c);
962           ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);
963         }
964         newCellsArray[i] = cell;
965         for (j = 0; j < nodesPerCell; ++j) {
966           /* For each global dof, map it into contiguous local storage. */
967           const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + subspaceOffset;
968           /* finally, loop over block size */
969           for (l = 0; l < bs; ++l) {
970             PetscInt  localDof;
971             PetscBool isGlobalBcDof, isArtificialBcDof;
972 
973             /* first, check if this is either a globally enforced or locally enforced BC dof */
974             ierr = PetscHSetIHas(globalBcs, globalDof + l, &isGlobalBcDof);CHKERRQ(ierr);
975             ierr = PetscHSetIHas(artificialbcs, globalDof + l, &isArtificialBcDof);CHKERRQ(ierr);
976 
977             /* if it's either, don't ever give it a local dof number */
978             if (isGlobalBcDof || isArtificialBcDof) {
979               dofsArray[globalIndex++] = -1; /* don't use this in assembly in this patch */
980             } else {
981               ierr = PetscHMapIGet(ht, globalDof + l, &localDof);CHKERRQ(ierr);
982               if (localDof == -1) {
983                 localDof = localIndex++;
984                 ierr = PetscHMapISet(ht, globalDof + l, localDof);CHKERRQ(ierr);
985               }
986               if ( globalIndex >= numDofs ) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Found more dofs %D than expected %D", globalIndex+1, numDofs);
987               /* And store. */
988               dofsArray[globalIndex++] = localDof;
989             }
990           }
991         }
992       }
993     }
994     /* How many local dofs in this patch? */
995     ierr = PetscHMapIGetSize(ht, &dof);CHKERRQ(ierr);
996     ierr = PetscSectionSetDof(gtolCounts, v, dof);CHKERRQ(ierr);
997   }
998   if (globalIndex != numDofs) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Expected number of dofs (%d) doesn't match found number (%d)", numDofs, globalIndex);
999   ierr = PetscSectionSetUp(gtolCounts);CHKERRQ(ierr);
1000   ierr = PetscSectionGetStorageSize(gtolCounts, &numGlobalDofs);CHKERRQ(ierr);
1001   ierr = PetscMalloc1(numGlobalDofs, &globalDofsArray);CHKERRQ(ierr);
1002 
1003   /* Now populate the global to local map.  This could be merged into the above loop if we were willing to deal with reallocs. */
1004   for (v = vStart; v < vEnd; ++v) {
1005     PetscHashIter hi;
1006     PetscInt      dof, off, Np, ooff, i, j, k, l;
1007 
1008     ierr = PetscHMapIClear(ht);CHKERRQ(ierr);
1009     ierr = PetscSectionGetDof(cellCounts, v, &dof);CHKERRQ(ierr);
1010     ierr = PetscSectionGetOffset(cellCounts, v, &off);CHKERRQ(ierr);
1011     ierr = PetscSectionGetDof(pointCounts, v, &Np);CHKERRQ(ierr);
1012     ierr = PetscSectionGetOffset(pointCounts, v, &ooff);CHKERRQ(ierr);
1013     if (dof <= 0) continue;
1014 
1015     for (k = 0; k < patch->nsubspaces; ++k) {
1016       const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1017       PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1018       PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1019       PetscInt        bs             = patch->bs[k];
1020       PetscInt        goff;
1021 
1022       for (i = off; i < off + dof; ++i) {
1023         /* Reconstruct mapping of global-to-local on this patch. */
1024         const PetscInt c    = cellsArray[i];
1025         PetscInt       cell = c;
1026 
1027         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1028         for (j = 0; j < nodesPerCell; ++j) {
1029           for (l = 0; l < bs; ++l) {
1030             const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1031             const PetscInt localDof  = dofsArray[key++];
1032 
1033             if (localDof >= 0) {ierr = PetscHMapISet(ht, globalDof, localDof);CHKERRQ(ierr);}
1034           }
1035         }
1036       }
1037 
1038       /* Shove it in the output data structure. */
1039       ierr = PetscSectionGetOffset(gtolCounts, v, &goff);CHKERRQ(ierr);
1040       PetscHashIterBegin(ht, hi);
1041       while (!PetscHashIterAtEnd(ht, hi)) {
1042         PetscInt globalDof, localDof;
1043 
1044         PetscHashIterGetKey(ht, hi, globalDof);
1045         PetscHashIterGetVal(ht, hi, localDof);
1046         if (globalDof >= 0) globalDofsArray[goff + localDof] = globalDof;
1047         PetscHashIterNext(ht, hi);
1048       }
1049 
1050       for (p = 0; p < Np; ++p) {
1051         const PetscInt point = pointsArray[ooff + p];
1052         PetscInt       globalDof, localDof;
1053 
1054         ierr = PCPatchGetGlobalDofs(pc, patch->dofSection, k, patch->combined, point, NULL, &globalDof);CHKERRQ(ierr);
1055         ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1056         offsArray[(ooff + p)*Nf + k] = localDof;
1057       }
1058     }
1059 
1060     ierr = PetscHSetIDestroy(&globalBcs);CHKERRQ(ierr);
1061     ierr = PetscHSetIDestroy(&ownedpts);CHKERRQ(ierr);
1062     ierr = PetscHSetIDestroy(&seenpts);CHKERRQ(ierr);
1063     ierr = PetscHSetIDestroy(&owneddofs);CHKERRQ(ierr);
1064     ierr = PetscHSetIDestroy(&seendofs);CHKERRQ(ierr);
1065     ierr = PetscHSetIDestroy(&artificialbcs);CHKERRQ(ierr);
1066 
1067       /* At this point, we have a hash table ht built that maps globalDof -> localDof.
1068      We need to create the dof table laid out cellwise first, then by subspace,
1069      as the assembler assembles cell-wise and we need to stuff the different
1070      contributions of the different function spaces to the right places. So we loop
1071      over cells, then over subspaces. */
1072     if (patch->nsubspaces > 1) { /* for nsubspaces = 1, data we need is already in dofsArray */
1073       for (i = off; i < off + dof; ++i) {
1074         const PetscInt c    = cellsArray[i];
1075         PetscInt       cell = c;
1076 
1077         if (cellNumbering) {ierr = PetscSectionGetOffset(cellNumbering, c, &cell);CHKERRQ(ierr);}
1078         for (k = 0; k < patch->nsubspaces; ++k) {
1079           const PetscInt *cellNodeMap    = patch->cellNodeMap[k];
1080           PetscInt        nodesPerCell   = patch->nodesPerCell[k];
1081           PetscInt        subspaceOffset = patch->subspaceOffsets[k];
1082           PetscInt        bs             = patch->bs[k];
1083 
1084           for (j = 0; j < nodesPerCell; ++j) {
1085             for (l = 0; l < bs; ++l) {
1086               const PetscInt globalDof = cellNodeMap[cell*nodesPerCell + j]*bs + l + subspaceOffset;
1087               PetscInt       localDof;
1088 
1089               ierr = PetscHMapIGet(ht, globalDof, &localDof);CHKERRQ(ierr);
1090               /* If it's not in the hash table, i.e. is a BC dof,
1091                then the PetscHSetIMap above gives -1, which matches
1092                exactly the convention for PETSc's matrix assembly to
1093                ignore the dof. So we don't need to do anything here */
1094               asmArray[asmKey++] = localDof;
1095             }
1096           }
1097         }
1098       }
1099     }
1100   }
1101   if (1 == patch->nsubspaces) {ierr = PetscMemcpy(asmArray, dofsArray, numDofs * sizeof(PetscInt));CHKERRQ(ierr);}
1102 
1103   ierr = PetscHMapIDestroy(&ht);CHKERRQ(ierr);
1104   ierr = ISRestoreIndices(cells, &cellsArray);CHKERRQ(ierr);
1105   ierr = ISRestoreIndices(points, &pointsArray);CHKERRQ(ierr);
1106   ierr = PetscFree(dofsArray);CHKERRQ(ierr);
1107   /* Create placeholder section for map from points to patch dofs */
1108   ierr = PetscSectionCreate(PETSC_COMM_SELF, &patch->patchSection);CHKERRQ(ierr);
1109   ierr = PetscSectionSetNumFields(patch->patchSection, patch->nsubspaces);CHKERRQ(ierr);
1110   ierr = PetscSectionGetChart(patch->dofSection[0], &pStart, &pEnd);CHKERRQ(ierr);
1111   ierr = PetscSectionSetChart(patch->patchSection, pStart, pEnd);CHKERRQ(ierr);
1112   for (p = pStart; p < pEnd; ++p) {
1113     PetscInt dof, fdof, f;
1114 
1115     ierr = PetscSectionGetDof(patch->dofSection[0], p, &dof);CHKERRQ(ierr);
1116     ierr = PetscSectionSetDof(patch->patchSection, p, dof);CHKERRQ(ierr);
1117     for (f = 0; f < patch->nsubspaces; ++f) {
1118       ierr = PetscSectionGetFieldDof(patch->dofSection[0], p, f, &fdof);
1119       if (ierr == 0) {
1120         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, fdof);CHKERRQ(ierr);
1121       }
1122       else {
1123         /* assume only one field */
1124         ierr = PetscSectionSetFieldDof(patch->patchSection, p, f, dof);CHKERRQ(ierr);
1125       }
1126     }
1127   }
1128   ierr = PetscSectionSetUp(patch->patchSection);CHKERRQ(ierr);
1129   ierr = PetscSectionSetUseFieldOffsets(patch->patchSection, PETSC_TRUE);CHKERRQ(ierr);
1130   /* Replace cell indices with firedrake-numbered ones. */
1131   ierr = ISGeneralSetIndices(cells, numCells, (const PetscInt *) newCellsArray, PETSC_OWN_POINTER);CHKERRQ(ierr);
1132   ierr = ISCreateGeneral(PETSC_COMM_SELF, numGlobalDofs, globalDofsArray, PETSC_OWN_POINTER, &patch->gtol);CHKERRQ(ierr);
1133   ierr = PetscObjectSetName((PetscObject) patch->gtol, "Global Indices");CHKERRQ(ierr);
1134   ierr = PetscSectionViewFromOptions(patch->gtolCounts, (PetscObject) pc, "-pc_patch_g2l_view");CHKERRQ(ierr);
1135   ierr = ISViewFromOptions(patch->gtol, (PetscObject) pc, "-pc_patch_g2l_view");CHKERRQ(ierr);
1136   ierr = ISCreateGeneral(PETSC_COMM_SELF, numDofs, asmArray, PETSC_OWN_POINTER, &patch->dofs);CHKERRQ(ierr);
1137   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints*Nf, offsArray, PETSC_OWN_POINTER, &patch->offs);CHKERRQ(ierr);
1138   PetscFunctionReturn(0);
1139 }
1140 
1141 static PetscErrorCode PCPatchZeroFillMatrix_Private(Mat mat, const PetscInt ncell, const PetscInt ndof, const PetscInt *dof)
1142 {
1143   PetscScalar    *values = NULL;
1144   PetscInt        rows, c, i;
1145   PetscErrorCode  ierr;
1146 
1147   PetscFunctionBegin;
1148   ierr = PetscCalloc1(ndof*ndof, &values);CHKERRQ(ierr);
1149   for (c = 0; c < ncell; ++c) {
1150     const PetscInt *idx = &dof[ndof*c];
1151     ierr = MatSetValues(mat, ndof, idx, ndof, idx, values, INSERT_VALUES);CHKERRQ(ierr);
1152   }
1153   ierr = MatGetLocalSize(mat, &rows, NULL);CHKERRQ(ierr);
1154   for (i = 0; i < rows; ++i) {
1155     ierr = MatSetValues(mat, 1, &i, 1, &i, values, INSERT_VALUES);CHKERRQ(ierr);
1156   }
1157   ierr = MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1158   ierr = MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1159   ierr = PetscFree(values);CHKERRQ(ierr);
1160   PetscFunctionReturn(0);
1161 }
1162 
1163 static PetscErrorCode PCPatchCreateMatrix_Private(PC pc, PetscInt point, Mat *mat)
1164 {
1165   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1166   Vec            x, y;
1167   PetscBool      flg;
1168   PetscInt       csize, rsize;
1169   const char    *prefix = NULL;
1170   PetscErrorCode ierr;
1171 
1172   PetscFunctionBegin;
1173   x = patch->patchX[point];
1174   y = patch->patchY[point];
1175   ierr = VecGetSize(x, &csize);CHKERRQ(ierr);
1176   ierr = VecGetSize(y, &rsize);CHKERRQ(ierr);
1177   ierr = MatCreate(PETSC_COMM_SELF, mat);CHKERRQ(ierr);
1178   ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1179   ierr = MatSetOptionsPrefix(*mat, prefix);CHKERRQ(ierr);
1180   ierr = MatAppendOptionsPrefix(*mat, "pc_patch_sub_");CHKERRQ(ierr);
1181   if (patch->sub_mat_type)       {ierr = MatSetType(*mat, patch->sub_mat_type);CHKERRQ(ierr);}
1182   else if (!patch->sub_mat_type) {ierr = MatSetType(*mat, MATDENSE);CHKERRQ(ierr);}
1183   ierr = MatSetSizes(*mat, rsize, csize, rsize, csize);CHKERRQ(ierr);
1184   ierr = PetscObjectTypeCompare((PetscObject) *mat, MATDENSE, &flg);CHKERRQ(ierr);
1185   if (!flg) {ierr = PetscObjectTypeCompare((PetscObject)*mat, MATSEQDENSE, &flg);CHKERRQ(ierr);}
1186   /* Sparse patch matrices */
1187   if (!flg) {
1188     PetscBT         bt;
1189     PetscInt       *dnnz      = NULL;
1190     const PetscInt *dofsArray = NULL;
1191     PetscInt        pStart, pEnd, ncell, offset, c, i, j;
1192 
1193     ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1194     ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1195     point += pStart;
1196     if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1197     ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1198     ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1199     ierr = PetscCalloc1(rsize, &dnnz);CHKERRQ(ierr);
1200     ierr = PetscLogEventBegin(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1201     /* XXX: This uses N^2 bits to store the sparsity pattern on a
1202      * patch.  This is probably OK if the patches are not too big,
1203      * but could use quite a bit of memory for planes in 3D.
1204      * Should we switch based on the value of rsize to a
1205      * hash-table (slower, but more memory efficient) approach? */
1206     ierr = PetscBTCreate(rsize*rsize, &bt);CHKERRQ(ierr);
1207     for (c = 0; c < ncell; ++c) {
1208       const PetscInt *idx = dofsArray + (offset + c)*patch->totalDofsPerCell;
1209       for (i = 0; i < patch->totalDofsPerCell; ++i) {
1210         const PetscInt row = idx[i];
1211         if (row < 0) continue;
1212         for (j = 0; j < patch->totalDofsPerCell; ++j) {
1213           const PetscInt col = idx[j];
1214           const PetscInt key = row*rsize + col;
1215           if (col < 0) continue;
1216           if (!PetscBTLookupSet(bt, key)) ++dnnz[row];
1217         }
1218       }
1219     }
1220     ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
1221     ierr = MatXAIJSetPreallocation(*mat, 1, dnnz, NULL, NULL, NULL);CHKERRQ(ierr);
1222     ierr = PetscFree(dnnz);CHKERRQ(ierr);
1223     ierr = PCPatchZeroFillMatrix_Private(*mat, ncell, patch->totalDofsPerCell, &dofsArray[offset*patch->totalDofsPerCell]);CHKERRQ(ierr);
1224     ierr = PetscLogEventEnd(PC_Patch_Prealloc, pc, 0, 0, 0);CHKERRQ(ierr);
1225     ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1226   }
1227   ierr = MatSetUp(*mat);CHKERRQ(ierr);
1228   PetscFunctionReturn(0);
1229 }
1230 
1231 static PetscErrorCode PCPatchComputeOperator_DMPlex_Private(PC pc, PetscInt patchNum, Mat J, IS cellIS, PetscInt n, const PetscInt *l2p, void *ctx)
1232 {
1233   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1234   DM              dm;
1235   PetscSection    s;
1236   const PetscInt *parray, *oarray;
1237   PetscInt        Nf = patch->nsubspaces, Np, poff, p, f;
1238   PetscErrorCode  ierr;
1239 
1240   PetscFunctionBegin;
1241   ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1242   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1243   /* Set offset into patch */
1244   ierr = PetscSectionGetDof(patch->pointCounts, patchNum, &Np);CHKERRQ(ierr);
1245   ierr = PetscSectionGetOffset(patch->pointCounts, patchNum, &poff);CHKERRQ(ierr);
1246   ierr = ISGetIndices(patch->points, &parray);CHKERRQ(ierr);
1247   ierr = ISGetIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1248   for (f = 0; f < Nf; ++f) {
1249     for (p = 0; p < Np; ++p) {
1250       const PetscInt point = parray[poff+p];
1251       PetscInt       dof;
1252 
1253       ierr = PetscSectionGetFieldDof(patch->patchSection, point, f, &dof);CHKERRQ(ierr);
1254       ierr = PetscSectionSetFieldOffset(patch->patchSection, point, f, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);
1255       if (patch->nsubspaces == 1) {ierr = PetscSectionSetOffset(patch->patchSection, point, oarray[(poff+p)*Nf+f]);CHKERRQ(ierr);}
1256       else                        {ierr = PetscSectionSetOffset(patch->patchSection, point, -1);CHKERRQ(ierr);}
1257     }
1258   }
1259   ierr = ISRestoreIndices(patch->points, &parray);CHKERRQ(ierr);
1260   ierr = ISRestoreIndices(patch->offs,   &oarray);CHKERRQ(ierr);
1261   if (patch->viewSection) {ierr = ObjectView((PetscObject) patch->patchSection, patch->viewerSection, patch->formatSection);CHKERRQ(ierr);}
1262   /* TODO Shut off MatViewFromOptions() in MatAssemblyEnd() here */
1263   ierr = DMPlexComputeJacobian_Patch_Internal(pc->dm, patch->patchSection, patch->patchSection, cellIS, 0.0, 0.0, NULL, NULL, J, J, ctx);CHKERRQ(ierr);
1264   PetscFunctionReturn(0);
1265 }
1266 
1267 static PetscErrorCode PCPatchComputeOperator_Private(PC pc, Mat mat, PetscInt point)
1268 {
1269   PC_PATCH       *patch = (PC_PATCH *) pc->data;
1270   const PetscInt *dofsArray;
1271   const PetscInt *cellsArray;
1272   PetscInt        ncell, offset, pStart, pEnd;
1273   PetscErrorCode  ierr;
1274 
1275   PetscFunctionBegin;
1276   ierr = PetscLogEventBegin(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1277   if (!patch->usercomputeop) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call PCPatchSetComputeOperator() to set user callback\n");
1278   ierr = ISGetIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1279   ierr = ISGetIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1280   ierr = PetscSectionGetChart(patch->cellCounts, &pStart, &pEnd);CHKERRQ(ierr);
1281 
1282   point += pStart;
1283   if (point >= pEnd) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Operator point %D not in [%D, %D)\n", point, pStart, pEnd);CHKERRQ(ierr);
1284 
1285   ierr = PetscSectionGetDof(patch->cellCounts, point, &ncell);CHKERRQ(ierr);
1286   ierr = PetscSectionGetOffset(patch->cellCounts, point, &offset);CHKERRQ(ierr);
1287   if (ncell <= 0) {
1288     ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1289     PetscFunctionReturn(0);
1290   }
1291   PetscStackPush("PCPatch user callback");
1292   /* Cannot reuse the same IS because the geometry info is being cached in it */
1293   ierr = ISCreateGeneral(PETSC_COMM_SELF, ncell, cellsArray + offset, PETSC_USE_POINTER, &patch->cellIS);CHKERRQ(ierr);
1294   ierr = patch->usercomputeop(pc, point, mat, patch->cellIS, ncell*patch->totalDofsPerCell, dofsArray + offset*patch->totalDofsPerCell, patch->usercomputectx);CHKERRQ(ierr);
1295   PetscStackPop;
1296   ierr = ISDestroy(&patch->cellIS);CHKERRQ(ierr);
1297   ierr = ISRestoreIndices(patch->dofs, &dofsArray);CHKERRQ(ierr);
1298   ierr = ISRestoreIndices(patch->cells, &cellsArray);CHKERRQ(ierr);
1299   if (patch->viewMatrix) {
1300     char name[PETSC_MAX_PATH_LEN];
1301 
1302     ierr = PetscSNPrintf(name, PETSC_MAX_PATH_LEN-1, "Patch matrix for Point %D", point);CHKERRQ(ierr);
1303     ierr = PetscObjectSetName((PetscObject) mat, name);CHKERRQ(ierr);
1304     ierr = ObjectView((PetscObject) mat, patch->viewerMatrix, patch->formatMatrix);CHKERRQ(ierr);
1305   }
1306   ierr = PetscLogEventEnd(PC_Patch_ComputeOp, pc, 0, 0, 0);CHKERRQ(ierr);
1307   PetscFunctionReturn(0);
1308 }
1309 
1310 static PetscErrorCode PCPatch_ScatterLocal_Private(PC pc, PetscInt p, Vec x, Vec y, InsertMode mode, ScatterMode scat)
1311 {
1312   PC_PATCH          *patch     = (PC_PATCH *) pc->data;
1313   const PetscScalar *xArray    = NULL;
1314   PetscScalar       *yArray    = NULL;
1315   const PetscInt    *gtolArray = NULL;
1316   PetscInt           dof, offset, lidx;
1317   PetscErrorCode     ierr;
1318 
1319   PetscFunctionBeginHot;
1320   ierr = PetscLogEventBegin(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1321   ierr = VecGetArrayRead(x, &xArray);CHKERRQ(ierr);
1322   ierr = VecGetArray(y, &yArray);CHKERRQ(ierr);
1323   ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1324   ierr = PetscSectionGetOffset(patch->gtolCounts, p, &offset);CHKERRQ(ierr);
1325   ierr = ISGetIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1326   if (mode == INSERT_VALUES && scat != SCATTER_FORWARD) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't insert if not scattering forward\n");
1327   if (mode == ADD_VALUES    && scat != SCATTER_REVERSE) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Can't add if not scattering reverse\n");
1328   for (lidx = 0; lidx < dof; ++lidx) {
1329     const PetscInt gidx = gtolArray[offset+lidx];
1330 
1331     if (mode == INSERT_VALUES) yArray[lidx]  = xArray[gidx]; /* Forward */
1332     else                       yArray[gidx] += xArray[lidx]; /* Reverse */
1333   }
1334   ierr = ISRestoreIndices(patch->gtol, &gtolArray);CHKERRQ(ierr);
1335   ierr = VecRestoreArrayRead(x, &xArray);CHKERRQ(ierr);
1336   ierr = VecRestoreArray(y, &yArray);CHKERRQ(ierr);
1337   ierr = PetscLogEventEnd(PC_Patch_Scatter, pc, 0, 0, 0);CHKERRQ(ierr);
1338   PetscFunctionReturn(0);
1339 }
1340 
1341 static PetscErrorCode PCSetUp_PATCH(PC pc)
1342 {
1343   PC_PATCH       *patch   = (PC_PATCH *) pc->data;
1344   PetscInt        i;
1345   const char     *prefix;
1346   PetscErrorCode  ierr;
1347 
1348   PetscFunctionBegin;
1349   if (!pc->setupcalled) {
1350     PetscInt pStart, pEnd, p;
1351     PetscInt localSize;
1352 
1353     ierr = PetscLogEventBegin(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1354 
1355     if (!patch->nsubspaces) {
1356       DM           dm;
1357       PetscDS      prob;
1358       PetscSection s;
1359       PetscInt     cStart, cEnd, c, Nf, f, numGlobalBcs = 0, *globalBcs, *Nb, totNb = 0, **cellDofs;
1360 
1361       ierr = PCGetDM(pc, &dm);CHKERRQ(ierr);
1362       if (!dm) SETERRQ(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONG, "Must set DM for PCPATCH or call PCPatchSetDiscretisationInfo()");
1363       ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
1364       ierr = PetscSectionGetNumFields(s, &Nf);CHKERRQ(ierr);
1365       ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
1366       for (p = pStart; p < pEnd; ++p) {
1367         PetscInt cdof;
1368         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1369         numGlobalBcs += cdof;
1370       }
1371       ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1372       ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1373       ierr = PetscMalloc3(Nf, &Nb, Nf, &cellDofs, numGlobalBcs, &globalBcs);CHKERRQ(ierr);
1374       for (f = 0; f < Nf; ++f) {
1375         PetscFE        fe;
1376         PetscDualSpace sp;
1377         PetscInt       cdoff = 0;
1378 
1379         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1380         /* ierr = PetscFEGetNumComponents(fe, &Nc[f]);CHKERRQ(ierr); */
1381         ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
1382         ierr = PetscDualSpaceGetDimension(sp, &Nb[f]);CHKERRQ(ierr);
1383         totNb += Nb[f];
1384 
1385         ierr = PetscMalloc1((cEnd-cStart)*Nb[f], &cellDofs[f]);CHKERRQ(ierr);
1386         for (c = cStart; c < cEnd; ++c) {
1387           PetscInt *closure = NULL;
1388           PetscInt  clSize  = 0, cl;
1389 
1390           ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1391           for (cl = 0; cl < clSize*2; cl += 2) {
1392             const PetscInt p = closure[cl];
1393             PetscInt       fdof, d, foff;
1394 
1395             ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
1396             ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
1397             for (d = 0; d < fdof; ++d, ++cdoff) cellDofs[f][cdoff] = foff + d;
1398           }
1399           ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure);CHKERRQ(ierr);
1400         }
1401         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]);
1402       }
1403       numGlobalBcs = 0;
1404       for (p = pStart; p < pEnd; ++p) {
1405         const PetscInt *ind;
1406         PetscInt        off, cdof, d;
1407 
1408         ierr = PetscSectionGetOffset(s, p, &off);CHKERRQ(ierr);
1409         ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
1410         ierr = PetscSectionGetConstraintIndices(s, p, &ind);CHKERRQ(ierr);
1411         for (d = 0; d < cdof; ++d) globalBcs[numGlobalBcs++] = off + ind[d];
1412       }
1413 
1414       ierr = PCPatchSetDiscretisationInfoCombined(pc, dm, Nb, (const PetscInt **) cellDofs, numGlobalBcs, globalBcs, numGlobalBcs, globalBcs);CHKERRQ(ierr);
1415       for (f = 0; f < Nf; ++f) {
1416         ierr = PetscFree(cellDofs[f]);CHKERRQ(ierr);
1417       }
1418       ierr = PetscFree3(Nb, cellDofs, globalBcs);CHKERRQ(ierr);
1419       ierr = PCPatchSetComputeOperator(pc, PCPatchComputeOperator_DMPlex_Private, NULL);CHKERRQ(ierr);
1420     }
1421 
1422     localSize = patch->subspaceOffsets[patch->nsubspaces];
1423     ierr = VecCreateSeq(PETSC_COMM_SELF, localSize, &patch->localX);CHKERRQ(ierr);
1424     ierr = VecSetUp(patch->localX);CHKERRQ(ierr);
1425     ierr = VecDuplicate(patch->localX, &patch->localY);CHKERRQ(ierr);
1426     ierr = PCPatchCreateCellPatches(pc);CHKERRQ(ierr);
1427     ierr = PCPatchCreateCellPatchDiscretisationInfo(pc);CHKERRQ(ierr);
1428 
1429     /* OK, now build the work vectors */
1430     ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, &pEnd);CHKERRQ(ierr);
1431     ierr = PetscMalloc1(patch->npatch, &patch->patchX);CHKERRQ(ierr);
1432     ierr = PetscMalloc1(patch->npatch, &patch->patchY);CHKERRQ(ierr);
1433     for (p = pStart; p < pEnd; ++p) {
1434       PetscInt dof;
1435 
1436       ierr = PetscSectionGetDof(patch->gtolCounts, p, &dof);CHKERRQ(ierr);
1437       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchX[p-pStart]);CHKERRQ(ierr);
1438       ierr = VecSetUp(patch->patchX[p-pStart]);CHKERRQ(ierr);
1439       ierr = VecCreateSeq(PETSC_COMM_SELF, dof, &patch->patchY[p-pStart]);CHKERRQ(ierr);
1440       ierr = VecSetUp(patch->patchY[p-pStart]);CHKERRQ(ierr);
1441     }
1442     ierr = PetscMalloc1(patch->npatch, &patch->ksp);CHKERRQ(ierr);
1443     ierr = PCGetOptionsPrefix(pc, &prefix);CHKERRQ(ierr);
1444     for (i = 0; i < patch->npatch; ++i) {
1445       PC subpc;
1446 
1447       ierr = KSPCreate(PETSC_COMM_SELF, &patch->ksp[i]);CHKERRQ(ierr);
1448       ierr = KSPSetOptionsPrefix(patch->ksp[i], prefix);CHKERRQ(ierr);
1449       ierr = KSPAppendOptionsPrefix(patch->ksp[i], "sub_");CHKERRQ(ierr);
1450       ierr = PetscObjectIncrementTabLevel((PetscObject) patch->ksp[i], (PetscObject) pc, 1);CHKERRQ(ierr);
1451       ierr = KSPGetPC(patch->ksp[i], &subpc);CHKERRQ(ierr);
1452       ierr = PetscObjectIncrementTabLevel((PetscObject) subpc, (PetscObject) pc, 1);CHKERRQ(ierr);
1453       ierr = PetscLogObjectParent((PetscObject) pc, (PetscObject) patch->ksp[i]);CHKERRQ(ierr);
1454     }
1455     if (patch->save_operators) {
1456       ierr = PetscMalloc1(patch->npatch, &patch->mat);CHKERRQ(ierr);
1457       for (i = 0; i < patch->npatch; ++i) {
1458         ierr = PCPatchCreateMatrix_Private(pc, i, &patch->mat[i]);CHKERRQ(ierr);
1459       }
1460     }
1461     ierr = PetscLogEventEnd(PC_Patch_CreatePatches, pc, 0, 0, 0);CHKERRQ(ierr);
1462 
1463     /* If desired, calculate weights for dof multiplicity */
1464     if (patch->partition_of_unity) {
1465       ierr = VecDuplicate(patch->localX, &patch->dof_weights);CHKERRQ(ierr);
1466       for (i = 0; i < patch->npatch; ++i) {
1467         PetscInt dof;
1468 
1469         ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &dof);CHKERRQ(ierr);
1470         if (dof <= 0) continue;
1471         ierr = VecSet(patch->patchX[i], 1.0);CHKERRQ(ierr);
1472         ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchX[i], patch->dof_weights, ADD_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
1473       }
1474       ierr = VecReciprocal(patch->dof_weights);CHKERRQ(ierr);
1475     }
1476   }
1477   if (patch->save_operators) {
1478     for (i = 0; i < patch->npatch; ++i) {
1479       ierr = MatZeroEntries(patch->mat[i]);CHKERRQ(ierr);
1480       ierr = PCPatchComputeOperator_Private(pc, patch->mat[i], i);CHKERRQ(ierr);
1481       ierr = KSPSetOperators(patch->ksp[i], patch->mat[i], patch->mat[i]);CHKERRQ(ierr);
1482     }
1483   }
1484   if (!pc->setupcalled && patch->optionsSet) for (i = 0; i < patch->npatch; ++i) {ierr = KSPSetFromOptions(patch->ksp[i]);CHKERRQ(ierr);}
1485   PetscFunctionReturn(0);
1486 }
1487 
1488 static PetscErrorCode PCApply_PATCH(PC pc, Vec x, Vec y)
1489 {
1490   PC_PATCH          *patch    = (PC_PATCH *) pc->data;
1491   const PetscScalar *globalX  = NULL;
1492   PetscScalar       *localX   = NULL;
1493   PetscScalar       *globalY  = NULL;
1494   const PetscInt    *bcNodes  = NULL;
1495   PetscInt           nsweep   = patch->symmetrise_sweep ? 2 : 1;
1496   PetscInt           start[2] = {0, 0};
1497   PetscInt           end[2]   = {-1, -1};
1498   const PetscInt     inc[2]   = {1, -1};
1499   const PetscScalar *localY;
1500   const PetscInt    *iterationSet;
1501   PetscInt           pStart, numBcs, n, sweep, bc, j;
1502   PetscErrorCode     ierr;
1503 
1504   PetscFunctionBegin;
1505   ierr = PetscLogEventBegin(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
1506   ierr = PetscOptionsPushGetViewerOff(PETSC_TRUE);CHKERRQ(ierr);
1507   end[0]   = patch->npatch;
1508   start[1] = patch->npatch-1;
1509   if (patch->user_patches) {
1510     ierr = ISGetLocalSize(patch->iterationSet, &end[0]);CHKERRQ(ierr);
1511     start[1] = end[0] - 1;
1512     ierr = ISGetIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);
1513   }
1514   /* Scatter from global space into overlapped local spaces */
1515   ierr = VecGetArrayRead(x, &globalX);CHKERRQ(ierr);
1516   ierr = VecGetArray(patch->localX, &localX);CHKERRQ(ierr);
1517   ierr = PetscSFBcastBegin(patch->defaultSF, MPIU_SCALAR, globalX, localX);CHKERRQ(ierr);
1518   ierr = PetscSFBcastEnd(patch->defaultSF, MPIU_SCALAR, globalX, localX);CHKERRQ(ierr);
1519   ierr = VecRestoreArrayRead(x, &globalX);CHKERRQ(ierr);
1520   ierr = VecRestoreArray(patch->localX, &localX);CHKERRQ(ierr);
1521 
1522   ierr = VecSet(patch->localY, 0.0);CHKERRQ(ierr);
1523   ierr = PetscSectionGetChart(patch->gtolCounts, &pStart, NULL);CHKERRQ(ierr);
1524   for (sweep = 0; sweep < nsweep; sweep++) {
1525     for (j = start[sweep]; j*inc[sweep] < end[sweep]*inc[sweep]; j += inc[sweep]) {
1526       PetscInt i       = patch->user_patches ? iterationSet[j] : j;
1527       PetscInt start, len;
1528 
1529       ierr = PetscSectionGetDof(patch->gtolCounts, i+pStart, &len);CHKERRQ(ierr);
1530       ierr = PetscSectionGetOffset(patch->gtolCounts, i+pStart, &start);CHKERRQ(ierr);
1531       /* TODO: Squash out these guys in the setup as well. */
1532       if (len <= 0) continue;
1533       /* TODO: Do we need different scatters for X and Y? */
1534       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->localX, patch->patchX[i], INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
1535       if (!patch->save_operators) {
1536         Mat mat;
1537 
1538         ierr = PCPatchCreateMatrix_Private(pc, i, &mat);CHKERRQ(ierr);
1539         /* Populate operator here. */
1540         ierr = PCPatchComputeOperator_Private(pc, mat, i);CHKERRQ(ierr);
1541         ierr = KSPSetOperators(patch->ksp[i], mat, mat);
1542         /* Drop reference so the KSPSetOperators below will blow it away. */
1543         ierr = MatDestroy(&mat);CHKERRQ(ierr);
1544       }
1545       ierr = PetscLogEventBegin(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
1546       ierr = KSPSolve(patch->ksp[i], patch->patchX[i], patch->patchY[i]);CHKERRQ(ierr);
1547       ierr = PetscLogEventEnd(PC_Patch_Solve, pc, 0, 0, 0);CHKERRQ(ierr);
1548 
1549       if (!patch->save_operators) {
1550         PC pc;
1551         ierr = KSPSetOperators(patch->ksp[i], NULL, NULL);CHKERRQ(ierr);
1552         ierr = KSPGetPC(patch->ksp[i], &pc);CHKERRQ(ierr);
1553         /* Destroy PC context too, otherwise the factored matrix hangs around. */
1554         ierr = PCReset(pc);CHKERRQ(ierr);
1555       }
1556 
1557       ierr = PCPatch_ScatterLocal_Private(pc, i+pStart, patch->patchY[i], patch->localY, ADD_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
1558     }
1559   }
1560   if (patch->user_patches) {ierr = ISRestoreIndices(patch->iterationSet, &iterationSet);CHKERRQ(ierr);}
1561   /* XXX: should we do this on the global vector? */
1562   if (patch->partition_of_unity) {
1563     ierr = VecPointwiseMult(patch->localY, patch->localY, patch->dof_weights);CHKERRQ(ierr);
1564   }
1565   /* Now patch->localY contains the solution of the patch solves, so we need to combine them all. */
1566   ierr = VecSet(y, 0.0);CHKERRQ(ierr);
1567   ierr = VecGetArray(y, &globalY);CHKERRQ(ierr);
1568   ierr = VecGetArrayRead(patch->localY, &localY);CHKERRQ(ierr);
1569   ierr = PetscSFReduceBegin(patch->defaultSF, MPIU_SCALAR, localY, globalY, MPI_SUM);CHKERRQ(ierr);
1570   ierr = PetscSFReduceEnd(patch->defaultSF, MPIU_SCALAR, localY, globalY, MPI_SUM);CHKERRQ(ierr);
1571   ierr = VecRestoreArrayRead(patch->localY, &localY);CHKERRQ(ierr);
1572 
1573   /* Now we need to send the global BC values through */
1574   ierr = VecGetArrayRead(x, &globalX);CHKERRQ(ierr);
1575   ierr = ISGetSize(patch->globalBcNodes, &numBcs);CHKERRQ(ierr);
1576   ierr = ISGetIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
1577   ierr = VecGetLocalSize(x, &n);CHKERRQ(ierr);
1578   for (bc = 0; bc < numBcs; ++bc) {
1579     const PetscInt idx = bcNodes[bc];
1580     if (idx < n) globalY[idx] = globalX[idx];
1581   }
1582 
1583   ierr = ISRestoreIndices(patch->globalBcNodes, &bcNodes);CHKERRQ(ierr);
1584   ierr = VecRestoreArrayRead(x, &globalX);CHKERRQ(ierr);
1585   ierr = VecRestoreArray(y, &globalY);CHKERRQ(ierr);
1586 
1587   ierr = PetscOptionsPopGetViewerOff();CHKERRQ(ierr);
1588   ierr = PetscLogEventEnd(PC_Patch_Apply, pc, 0, 0, 0);CHKERRQ(ierr);
1589   PetscFunctionReturn(0);
1590 }
1591 
1592 static PetscErrorCode PCReset_PATCH(PC pc)
1593 {
1594   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1595   PetscInt       i;
1596   PetscErrorCode ierr;
1597 
1598   PetscFunctionBegin;
1599   /* TODO: Get rid of all these ifs */
1600   ierr = PetscSFDestroy(&patch->defaultSF);CHKERRQ(ierr);
1601   ierr = PetscSectionDestroy(&patch->cellCounts);CHKERRQ(ierr);
1602   ierr = PetscSectionDestroy(&patch->pointCounts);CHKERRQ(ierr);
1603   ierr = PetscSectionDestroy(&patch->cellNumbering);CHKERRQ(ierr);
1604   ierr = PetscSectionDestroy(&patch->gtolCounts);CHKERRQ(ierr);
1605   ierr = ISDestroy(&patch->gtol);CHKERRQ(ierr);
1606   ierr = ISDestroy(&patch->cells);CHKERRQ(ierr);
1607   ierr = ISDestroy(&patch->points);CHKERRQ(ierr);
1608   ierr = ISDestroy(&patch->dofs);CHKERRQ(ierr);
1609   ierr = ISDestroy(&patch->offs);CHKERRQ(ierr);
1610   ierr = PetscSectionDestroy(&patch->patchSection);CHKERRQ(ierr);
1611   ierr = ISDestroy(&patch->ghostBcNodes);CHKERRQ(ierr);
1612   ierr = ISDestroy(&patch->globalBcNodes);CHKERRQ(ierr);
1613 
1614   if (patch->dofSection) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscSectionDestroy(&patch->dofSection[i]);CHKERRQ(ierr);}
1615   ierr = PetscFree(patch->dofSection);CHKERRQ(ierr);
1616   ierr = PetscFree(patch->bs);CHKERRQ(ierr);
1617   ierr = PetscFree(patch->nodesPerCell);CHKERRQ(ierr);
1618   if (patch->cellNodeMap) for (i = 0; i < patch->nsubspaces; i++) {ierr = PetscFree(patch->cellNodeMap[i]);CHKERRQ(ierr);}
1619   ierr = PetscFree(patch->cellNodeMap);CHKERRQ(ierr);
1620   ierr = PetscFree(patch->subspaceOffsets);CHKERRQ(ierr);
1621 
1622   if (patch->ksp) {
1623     for (i = 0; i < patch->npatch; ++i) {ierr = KSPReset(patch->ksp[i]);CHKERRQ(ierr);}
1624   }
1625 
1626   ierr = VecDestroy(&patch->localX);CHKERRQ(ierr);
1627   ierr = VecDestroy(&patch->localY);CHKERRQ(ierr);
1628   if (patch->patchX) {
1629     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchX[i]);CHKERRQ(ierr);}
1630     ierr = PetscFree(patch->patchX);CHKERRQ(ierr);
1631   }
1632   if (patch->patchY) {
1633     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patchY[i]);CHKERRQ(ierr);}
1634     ierr = PetscFree(patch->patchY);CHKERRQ(ierr);
1635   }
1636   ierr = VecDestroy(&patch->dof_weights);CHKERRQ(ierr);
1637   if (patch->patch_dof_weights) {
1638     for (i = 0; i < patch->npatch; ++i) {ierr = VecDestroy(&patch->patch_dof_weights[i]);CHKERRQ(ierr);}
1639     ierr = PetscFree(patch->patch_dof_weights);CHKERRQ(ierr);
1640   }
1641   if (patch->mat) {
1642     for (i = 0; i < patch->npatch; ++i) {ierr = MatDestroy(&patch->mat[i]);CHKERRQ(ierr);}
1643     ierr = PetscFree(patch->mat);CHKERRQ(ierr);
1644   }
1645   ierr = PetscFree(patch->sub_mat_type);CHKERRQ(ierr);
1646   if (patch->userIS) {
1647     for (i = 0; i < patch->npatch; ++i) {ierr = ISDestroy(&patch->userIS[i]);CHKERRQ(ierr);}
1648     ierr = PetscFree(patch->userIS);CHKERRQ(ierr);
1649   }
1650   patch->bs          = 0;
1651   patch->cellNodeMap = NULL;
1652   patch->nsubspaces  = 0;
1653   ierr = ISDestroy(&patch->iterationSet);CHKERRQ(ierr);
1654 
1655   ierr = PetscViewerDestroy(&patch->viewerSection);CHKERRQ(ierr);
1656   PetscFunctionReturn(0);
1657 }
1658 
1659 static PetscErrorCode PCDestroy_PATCH(PC pc)
1660 {
1661   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1662   PetscInt       i;
1663   PetscErrorCode ierr;
1664 
1665   PetscFunctionBegin;
1666   ierr = PCReset_PATCH(pc);CHKERRQ(ierr);
1667   if (patch->ksp) {
1668     for (i = 0; i < patch->npatch; ++i) {ierr = KSPDestroy(&patch->ksp[i]);CHKERRQ(ierr);}
1669     ierr = PetscFree(patch->ksp);CHKERRQ(ierr);
1670   }
1671   ierr = PetscFree(pc->data);CHKERRQ(ierr);
1672   PetscFunctionReturn(0);
1673 }
1674 
1675 static PetscErrorCode PCSetFromOptions_PATCH(PetscOptionItems *PetscOptionsObject, PC pc)
1676 {
1677   PC_PATCH            *patch = (PC_PATCH *) pc->data;
1678   PCPatchConstructType patchConstructionType = PC_PATCH_STAR;
1679   char                 sub_mat_type[PETSC_MAX_PATH_LEN];
1680   const char          *prefix;
1681   PetscBool            flg, dimflg, codimflg;
1682   MPI_Comm             comm;
1683   PetscErrorCode       ierr;
1684 
1685   PetscFunctionBegin;
1686   ierr = PetscObjectGetComm((PetscObject) pc, &comm);CHKERRQ(ierr);
1687   ierr = PetscObjectGetOptionsPrefix((PetscObject) pc, &prefix);CHKERRQ(ierr);
1688   ierr = PetscOptionsHead(PetscOptionsObject, "Vertex-patch Additive Schwarz options");CHKERRQ(ierr);
1689   ierr = PetscOptionsBool("-pc_patch_save_operators",  "Store all patch operators for lifetime of PC?", "PCPatchSetSaveOperators", patch->save_operators, &patch->save_operators, &flg);CHKERRQ(ierr);
1690   ierr = PetscOptionsBool("-pc_patch_partition_of_unity", "Weight contributions by dof multiplicity?", "PCPatchSetPartitionOfUnity", patch->partition_of_unity, &patch->partition_of_unity, &flg);CHKERRQ(ierr);
1691   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);
1692   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);
1693   if (dimflg && codimflg) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Can only set one of dimension or co-dimension");CHKERRQ(ierr);
1694   ierr = PetscOptionsEnum("-pc_patch_construct_type", "How should the patches be constructed?", "PCPatchSetConstructType", PCPatchConstructTypes, (PetscEnum) patchConstructionType, (PetscEnum *) &patchConstructionType, &flg);CHKERRQ(ierr);
1695   if (flg) {ierr = PCPatchSetConstructType(pc, patchConstructionType, NULL, NULL);CHKERRQ(ierr);}
1696   ierr = PetscOptionsInt("-pc_patch_vanka_dim", "Topological dimension of entities for Vanka to ignore", "PCPATCH", patch->vankadim, &patch->vankadim, &flg);CHKERRQ(ierr);
1697   ierr = PetscOptionsInt("-pc_patch_ignore_dim", "Topological dimension of entities for completion to ignore", "PCPATCH", patch->ignoredim, &patch->ignoredim, &flg);CHKERRQ(ierr);
1698   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);
1699   if (flg) {ierr = PCPatchSetSubMatType(pc, sub_mat_type);CHKERRQ(ierr);}
1700   ierr = PetscOptionsBool("-pc_patch_symmetrise_sweep", "Go start->end, end->start?", "PCPATCH", patch->symmetrise_sweep, &patch->symmetrise_sweep, &flg);CHKERRQ(ierr);
1701   ierr = PetscOptionsInt("-pc_patch_exclude_subspace", "What subspace (if any) to exclude in construction?", "PCPATCH", patch->exclude_subspace, &patch->exclude_subspace, &flg);CHKERRQ(ierr);
1702   if (patch->exclude_subspace && (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");
1703 
1704   ierr = PetscOptionsBool("-pc_patch_patches_view", "Print out information during patch construction", "PCPATCH", patch->viewPatches, &patch->viewPatches, &flg);CHKERRQ(ierr);
1705   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_cells_view",   &patch->viewerCells,   &patch->formatCells,   &patch->viewCells);CHKERRQ(ierr);
1706   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_points_view",  &patch->viewerPoints,  &patch->formatPoints,  &patch->viewPoints);CHKERRQ(ierr);
1707   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_section_view", &patch->viewerSection, &patch->formatSection, &patch->viewSection);CHKERRQ(ierr);
1708   ierr = PetscOptionsGetViewer(comm, prefix, "-pc_patch_mat_view",     &patch->viewerMatrix,  &patch->formatMatrix,  &patch->viewMatrix);CHKERRQ(ierr);
1709   ierr = PetscOptionsTail();CHKERRQ(ierr);
1710   patch->optionsSet = PETSC_TRUE;
1711   PetscFunctionReturn(0);
1712 }
1713 
1714 static PetscErrorCode PCSetUpOnBlocks_PATCH(PC pc)
1715 {
1716   PC_PATCH          *patch = (PC_PATCH*) pc->data;
1717   KSPConvergedReason reason;
1718   PetscInt           i;
1719   PetscErrorCode     ierr;
1720 
1721   PetscFunctionBegin;
1722   for (i = 0; i < patch->npatch; ++i) {
1723     ierr = KSPSetUp(patch->ksp[i]);CHKERRQ(ierr);
1724     ierr = KSPGetConvergedReason(patch->ksp[i], &reason);CHKERRQ(ierr);
1725     if (reason == KSP_DIVERGED_PCSETUP_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1726   }
1727   PetscFunctionReturn(0);
1728 }
1729 
1730 static PetscErrorCode PCView_PATCH(PC pc, PetscViewer viewer)
1731 {
1732   PC_PATCH      *patch = (PC_PATCH *) pc->data;
1733   PetscViewer    sviewer;
1734   PetscBool      isascii;
1735   PetscMPIInt    rank;
1736   PetscErrorCode ierr;
1737 
1738   PetscFunctionBegin;
1739   /* TODO Redo tabbing with set tbas in new style */
1740   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
1741   if (!isascii) PetscFunctionReturn(0);
1742   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) pc), &rank);CHKERRQ(ierr);
1743   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1744   ierr = PetscViewerASCIIPrintf(viewer, "Subspace Correction preconditioner with %d patches\n", patch->npatch);CHKERRQ(ierr);
1745   ierr = PetscViewerASCIIPrintf(viewer, "Schwarz type: additive\n");CHKERRQ(ierr);
1746   if (patch->partition_of_unity) {ierr = PetscViewerASCIIPrintf(viewer, "Weighting by partition of unity\n");CHKERRQ(ierr);}
1747   else                           {ierr = PetscViewerASCIIPrintf(viewer, "Not weighting by partition of unity\n");CHKERRQ(ierr);}
1748   if (patch->symmetrise_sweep) {ierr = PetscViewerASCIIPrintf(viewer, "Symmetrising sweep (start->end, then end->start)\n");CHKERRQ(ierr);}
1749   else                         {ierr = PetscViewerASCIIPrintf(viewer, "Not symmetrising sweep\n");CHKERRQ(ierr);}
1750   if (!patch->save_operators) {ierr = PetscViewerASCIIPrintf(viewer, "Not saving patch operators (rebuilt every PCApply)\n");CHKERRQ(ierr);}
1751   else                        {ierr = PetscViewerASCIIPrintf(viewer, "Saving patch operators (rebuilt every PCSetUp)\n");CHKERRQ(ierr);}
1752   if (patch->patchconstructop == PCPatchConstruct_Star)       {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: star\n");CHKERRQ(ierr);}
1753   else if (patch->patchconstructop == PCPatchConstruct_Vanka) {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: Vanka\n");CHKERRQ(ierr);}
1754   else if (patch->patchconstructop == PCPatchConstruct_User)  {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: user-specified\n");CHKERRQ(ierr);}
1755   else                                                        {ierr = PetscViewerASCIIPrintf(viewer, "Patch construction operator: unknown\n");CHKERRQ(ierr);}
1756   ierr = PetscViewerASCIIPrintf(viewer, "KSP on patches (all same):\n");CHKERRQ(ierr);
1757   if (patch->ksp) {
1758     ierr = PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
1759     if (!rank) {
1760       ierr = PetscViewerASCIIPushTab(sviewer);CHKERRQ(ierr);
1761       ierr = KSPView(patch->ksp[0], sviewer);CHKERRQ(ierr);
1762       ierr = PetscViewerASCIIPopTab(sviewer);CHKERRQ(ierr);
1763     }
1764     ierr = PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer);CHKERRQ(ierr);
1765   } else {
1766     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1767     ierr = PetscViewerASCIIPrintf(viewer, "KSP not yet set.\n");CHKERRQ(ierr);
1768     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1769   }
1770   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1771   PetscFunctionReturn(0);
1772 }
1773 
1774 /*MC
1775   PCPATCH - A PC object that encapsulates flexible definition of blocks for overlapping and non-overlapping
1776             small block additive preconditioners. Block definition is based on topology from
1777             a DM and equation numbering from a PetscSection.
1778 
1779   Options Database Keys:
1780 + -pc_patch_cells_view   - Views the process local cell numbers for each patch
1781 . -pc_patch_points_view  - Views the process local mesh point numbers for each patch
1782 . -pc_patch_g2l_view     - Views the map between global dofs and patch local dofs for each patch
1783 . -pc_patch_patches_view - Views the global dofs associated with each patch and its boundary
1784 - -pc_patch_sub_mat_view - Views the matrix associated with each patch
1785 
1786   Level: intermediate
1787 
1788 .seealso: PCType, PCCreate(), PCSetType()
1789 M*/
1790 PETSC_EXTERN PetscErrorCode PCCreate_Patch(PC pc)
1791 {
1792   PC_PATCH      *patch;
1793   PetscErrorCode ierr;
1794 
1795   PetscFunctionBegin;
1796   ierr = PetscNewLog(pc, &patch);CHKERRQ(ierr);
1797 
1798   /* Set some defaults */
1799   patch->combined           = PETSC_FALSE;
1800   patch->save_operators     = PETSC_TRUE;
1801   patch->partition_of_unity = PETSC_FALSE;
1802   patch->codim              = -1;
1803   patch->dim                = -1;
1804   patch->exclude_subspace   = -1;
1805   patch->vankadim           = -1;
1806   patch->ignoredim          = -1;
1807   patch->patchconstructop   = PCPatchConstruct_Star;
1808   patch->symmetrise_sweep   = PETSC_FALSE;
1809   patch->npatch             = 0;
1810   patch->userIS             = NULL;
1811   patch->optionsSet         = PETSC_FALSE;
1812   patch->iterationSet       = NULL;
1813   patch->user_patches       = PETSC_FALSE;
1814   ierr = PetscStrallocpy(MATDENSE, (char **) &patch->sub_mat_type);CHKERRQ(ierr);
1815   patch->viewPatches        = PETSC_FALSE;
1816   patch->viewCells          = PETSC_FALSE;
1817   patch->viewPoints         = PETSC_FALSE;
1818   patch->viewSection        = PETSC_FALSE;
1819   patch->viewMatrix         = PETSC_FALSE;
1820 
1821   pc->data                 = (void *) patch;
1822   pc->ops->apply           = PCApply_PATCH;
1823   pc->ops->applytranspose  = 0; /* PCApplyTranspose_PATCH; */
1824   pc->ops->setup           = PCSetUp_PATCH;
1825   pc->ops->reset           = PCReset_PATCH;
1826   pc->ops->destroy         = PCDestroy_PATCH;
1827   pc->ops->setfromoptions  = PCSetFromOptions_PATCH;
1828   pc->ops->setuponblocks   = PCSetUpOnBlocks_PATCH;
1829   pc->ops->view            = PCView_PATCH;
1830   pc->ops->applyrichardson = 0;
1831 
1832   PetscFunctionReturn(0);
1833 }
1834