Actual source code: gasm.c

  1: /*
  2:   This file defines an "generalized" additive Schwarz preconditioner for any Mat implementation.
  3:   In this version each MPI rank may intersect multiple subdomains and any subdomain may
  4:   intersect multiple MPI ranks.  Intersections of subdomains with MPI ranks are called *local
  5:   subdomains*.

  7:        N    - total number of distinct global subdomains  (set explicitly in PCGASMSetTotalSubdomains() or implicitly PCGASMSetSubdomains() and then calculated in PCSetUp_GASM())
  8:        n    - actual number of local subdomains on this rank (set in PCGASMSetSubdomains() or calculated in PCGASMSetTotalSubdomains())
  9:        nmax - maximum number of local subdomains per rank    (calculated in PCSetUp_GASM())
 10: */
 11: #include <petsc/private/pcimpl.h>
 12: #include <petscdm.h>

 14: typedef struct {
 15:   PetscInt   N, n, nmax;
 16:   PetscInt   overlap;                /* overlap requested by user */
 17:   PCGASMType type;                   /* use reduced interpolation, restriction or both */
 18:   PetscBool  type_set;               /* if user set this value (so won't change it for symmetric problems) */
 19:   PetscBool  same_subdomain_solvers; /* flag indicating whether all local solvers are same */
 20:   PetscBool  sort_indices;           /* flag to sort subdomain indices */
 21:   PetscBool  user_subdomains;        /* whether the user set explicit subdomain index sets -- keep them on PCReset() */
 22:   PetscBool  dm_subdomains;          /* whether DM is allowed to define subdomains */
 23:   PetscBool  hierarchicalpartitioning;
 24:   IS        *ois;           /* index sets that define the outer (conceptually, overlapping) subdomains */
 25:   IS        *iis;           /* index sets that define the inner (conceptually, nonoverlapping) subdomains */
 26:   KSP       *ksp;           /* linear solvers for each subdomain */
 27:   Mat       *pmat;          /* subdomain block matrices */
 28:   Vec        gx, gy;        /* Merged work vectors */
 29:   Vec       *x, *y;         /* Split work vectors; storage aliases pieces of storage of the above merged vectors. */
 30:   VecScatter gorestriction; /* merged restriction to disjoint union of outer subdomains */
 31:   VecScatter girestriction; /* merged restriction to disjoint union of inner subdomains */
 32:   VecScatter pctoouter;
 33:   IS         permutationIS;
 34:   Mat        permutationP;
 35:   Mat        pcmat;
 36:   Vec        pcx, pcy;
 37: } PC_GASM;

 39: static PetscErrorCode PCGASMComputeGlobalSubdomainNumbering_Private(PC pc, PetscInt **numbering, PetscInt **permutation)
 40: {
 41:   PC_GASM *osm = (PC_GASM *)pc->data;
 42:   PetscInt i;

 44:   PetscFunctionBegin;
 45:   /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
 46:   PetscCall(PetscMalloc2(osm->n, numbering, osm->n, permutation));
 47:   PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->iis, NULL, *numbering));
 48:   for (i = 0; i < osm->n; ++i) (*permutation)[i] = i;
 49:   PetscCall(PetscSortIntWithPermutation(osm->n, *numbering, *permutation));
 50:   PetscFunctionReturn(PETSC_SUCCESS);
 51: }

 53: static PetscErrorCode PCGASMSubdomainView_Private(PC pc, PetscInt i, PetscViewer viewer)
 54: {
 55:   PC_GASM        *osm = (PC_GASM *)pc->data;
 56:   PetscInt        j, nidx;
 57:   const PetscInt *idx;
 58:   PetscViewer     sviewer;
 59:   char           *cidx;

 61:   PetscFunctionBegin;
 62:   PetscCheck(i >= 0 && i < osm->n, PetscObjectComm((PetscObject)viewer), PETSC_ERR_ARG_WRONG, "Invalid subdomain %" PetscInt_FMT ": must nonnegative and less than %" PetscInt_FMT, i, osm->n);
 63:   /* Inner subdomains. */
 64:   PetscCall(ISGetLocalSize(osm->iis[i], &nidx));
 65:   /*
 66:    No more than 15 characters per index plus a space.
 67:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
 68:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
 69:    For nidx == 0, the whole string 16 '\0'.
 70:    */
 71: #define len 16 * (nidx + 1) + 1
 72:   PetscCall(PetscMalloc1(len, &cidx));
 73:   PetscCall(PetscViewerStringOpen(PETSC_COMM_SELF, cidx, len, &sviewer));
 74: #undef len
 75:   PetscCall(ISGetIndices(osm->iis[i], &idx));
 76:   for (j = 0; j < nidx; ++j) PetscCall(PetscViewerStringSPrintf(sviewer, "%" PetscInt_FMT " ", idx[j]));
 77:   PetscCall(ISRestoreIndices(osm->iis[i], &idx));
 78:   PetscCall(PetscViewerDestroy(&sviewer));
 79:   PetscCall(PetscViewerASCIIPrintf(viewer, "Inner subdomain:\n"));
 80:   PetscCall(PetscViewerFlush(viewer));
 81:   PetscCall(PetscViewerASCIIPushSynchronized(viewer));
 82:   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx));
 83:   PetscCall(PetscViewerFlush(viewer));
 84:   PetscCall(PetscViewerASCIIPopSynchronized(viewer));
 85:   PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
 86:   PetscCall(PetscViewerFlush(viewer));
 87:   PetscCall(PetscFree(cidx));
 88:   /* Outer subdomains. */
 89:   PetscCall(ISGetLocalSize(osm->ois[i], &nidx));
 90:   /*
 91:    No more than 15 characters per index plus a space.
 92:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
 93:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
 94:    For nidx == 0, the whole string 16 '\0'.
 95:    */
 96: #define len 16 * (nidx + 1) + 1
 97:   PetscCall(PetscMalloc1(len, &cidx));
 98:   PetscCall(PetscViewerStringOpen(PETSC_COMM_SELF, cidx, len, &sviewer));
 99: #undef len
100:   PetscCall(ISGetIndices(osm->ois[i], &idx));
101:   for (j = 0; j < nidx; ++j) PetscCall(PetscViewerStringSPrintf(sviewer, "%" PetscInt_FMT " ", idx[j]));
102:   PetscCall(PetscViewerDestroy(&sviewer));
103:   PetscCall(ISRestoreIndices(osm->ois[i], &idx));
104:   PetscCall(PetscViewerASCIIPrintf(viewer, "Outer subdomain:\n"));
105:   PetscCall(PetscViewerFlush(viewer));
106:   PetscCall(PetscViewerASCIIPushSynchronized(viewer));
107:   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx));
108:   PetscCall(PetscViewerFlush(viewer));
109:   PetscCall(PetscViewerASCIIPopSynchronized(viewer));
110:   PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
111:   PetscCall(PetscViewerFlush(viewer));
112:   PetscCall(PetscFree(cidx));
113:   PetscFunctionReturn(PETSC_SUCCESS);
114: }

116: static PetscErrorCode PCGASMPrintSubdomains(PC pc)
117: {
118:   PC_GASM    *osm = (PC_GASM *)pc->data;
119:   const char *prefix;
120:   char        fname[PETSC_MAX_PATH_LEN + 1];
121:   PetscInt    l, d, count;
122:   PetscBool   found;
123:   PetscViewer viewer, sviewer = NULL;
124:   PetscInt   *numbering, *permutation; /* global numbering of locally-supported subdomains and the permutation from the local ordering */

126:   PetscFunctionBegin;
127:   PetscCall(PCGetOptionsPrefix(pc, &prefix));
128:   PetscCall(PetscOptionsHasName(NULL, prefix, "-pc_gasm_print_subdomains", &found));
129:   if (!found) PetscFunctionReturn(PETSC_SUCCESS);
130:   PetscCall(PetscOptionsGetString(NULL, prefix, "-pc_gasm_print_subdomains", fname, sizeof(fname), &found));
131:   if (!found) PetscCall(PetscStrncpy(fname, "stdout", sizeof(fname)));
132:   PetscCall(PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc), fname, &viewer));
133:   /*
134:    Make sure the viewer has a name. Otherwise this may cause a deadlock or other weird errors when creating a subcomm viewer:
135:    the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed collectively on the comm.
136:   */
137:   PetscCall(PetscObjectName((PetscObject)viewer));
138:   l = 0;
139:   PetscCall(PCGASMComputeGlobalSubdomainNumbering_Private(pc, &numbering, &permutation));
140:   for (count = 0; count < osm->N; ++count) {
141:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
142:     if (l < osm->n) {
143:       d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
144:       if (numbering[d] == count) {
145:         PetscCall(PetscViewerGetSubViewer(viewer, ((PetscObject)osm->ois[d])->comm, &sviewer));
146:         PetscCall(PCGASMSubdomainView_Private(pc, d, sviewer));
147:         PetscCall(PetscViewerRestoreSubViewer(viewer, ((PetscObject)osm->ois[d])->comm, &sviewer));
148:         ++l;
149:       }
150:     }
151:     PetscCallMPI(MPI_Barrier(PetscObjectComm((PetscObject)pc)));
152:   }
153:   PetscCall(PetscFree2(numbering, permutation));
154:   PetscCall(PetscViewerDestroy(&viewer));
155:   PetscFunctionReturn(PETSC_SUCCESS);
156: }

158: static PetscErrorCode PCView_GASM(PC pc, PetscViewer viewer)
159: {
160:   PC_GASM    *osm = (PC_GASM *)pc->data;
161:   const char *prefix;
162:   PetscMPIInt rank, size;
163:   PetscInt    bsz;
164:   PetscBool   iascii, view_subdomains = PETSC_FALSE;
165:   PetscViewer sviewer;
166:   PetscInt    count, l;
167:   char        overlap[256]     = "user-defined overlap";
168:   char        gsubdomains[256] = "unknown total number of subdomains";
169:   char        msubdomains[256] = "unknown max number of local subdomains";
170:   PetscInt   *numbering, *permutation; /* global numbering of locally-supported subdomains and the permutation from the local ordering */

172:   PetscFunctionBegin;
173:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
174:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));

176:   if (osm->overlap >= 0) PetscCall(PetscSNPrintf(overlap, sizeof(overlap), "requested amount of overlap = %" PetscInt_FMT, osm->overlap));
177:   if (osm->N != PETSC_DETERMINE) PetscCall(PetscSNPrintf(gsubdomains, sizeof(gsubdomains), "total number of subdomains = %" PetscInt_FMT, osm->N));
178:   if (osm->nmax != PETSC_DETERMINE) PetscCall(PetscSNPrintf(msubdomains, sizeof(msubdomains), "max number of local subdomains = %" PetscInt_FMT, osm->nmax));

180:   PetscCall(PCGetOptionsPrefix(pc, &prefix));
181:   PetscCall(PetscOptionsGetBool(NULL, prefix, "-pc_gasm_view_subdomains", &view_subdomains, NULL));

183:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
184:   if (iascii) {
185:     /*
186:      Make sure the viewer has a name. Otherwise this may cause a deadlock when creating a subcomm viewer:
187:      the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed
188:      collectively on the comm.
189:      */
190:     PetscCall(PetscObjectName((PetscObject)viewer));
191:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Restriction/interpolation type: %s\n", PCGASMTypes[osm->type]));
192:     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", overlap));
193:     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", gsubdomains));
194:     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", msubdomains));
195:     PetscCall(PetscViewerASCIIPushSynchronized(viewer));
196:     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "  [%d|%d] number of locally-supported subdomains = %" PetscInt_FMT "\n", rank, size, osm->n));
197:     PetscCall(PetscViewerFlush(viewer));
198:     PetscCall(PetscViewerASCIIPopSynchronized(viewer));
199:     /* Cannot take advantage of osm->same_subdomain_solvers without a global numbering of subdomains. */
200:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Subdomain solver info is as follows:\n"));
201:     PetscCall(PetscViewerASCIIPushTab(viewer));
202:     PetscCall(PetscViewerASCIIPrintf(viewer, "  - - - - - - - - - - - - - - - - - -\n"));
203:     /* Make sure that everybody waits for the banner to be printed. */
204:     PetscCallMPI(MPI_Barrier(PetscObjectComm((PetscObject)viewer)));
205:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
206:     PetscCall(PCGASMComputeGlobalSubdomainNumbering_Private(pc, &numbering, &permutation));
207:     l = 0;
208:     for (count = 0; count < osm->N; ++count) {
209:       PetscMPIInt srank, ssize;
210:       if (l < osm->n) {
211:         PetscInt d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
212:         if (numbering[d] == count) {
213:           PetscCallMPI(MPI_Comm_size(((PetscObject)osm->ois[d])->comm, &ssize));
214:           PetscCallMPI(MPI_Comm_rank(((PetscObject)osm->ois[d])->comm, &srank));
215:           PetscCall(PetscViewerGetSubViewer(viewer, ((PetscObject)osm->ois[d])->comm, &sviewer));
216:           PetscCall(ISGetLocalSize(osm->ois[d], &bsz));
217:           PetscCall(PetscViewerASCIISynchronizedPrintf(sviewer, "  [%d|%d] (subcomm [%d|%d]) local subdomain number %" PetscInt_FMT ", local size = %" PetscInt_FMT "\n", rank, size, srank, ssize, d, bsz));
218:           PetscCall(PetscViewerFlush(sviewer));
219:           if (view_subdomains) PetscCall(PCGASMSubdomainView_Private(pc, d, sviewer));
220:           if (!pc->setupcalled) {
221:             PetscCall(PetscViewerASCIIPrintf(sviewer, "  Solver not set up yet: PCSetUp() not yet called\n"));
222:           } else {
223:             PetscCall(KSPView(osm->ksp[d], sviewer));
224:           }
225:           PetscCall(PetscViewerASCIIPrintf(sviewer, "  - - - - - - - - - - - - - - - - - -\n"));
226:           PetscCall(PetscViewerFlush(sviewer));
227:           PetscCall(PetscViewerRestoreSubViewer(viewer, ((PetscObject)osm->ois[d])->comm, &sviewer));
228:           ++l;
229:         }
230:       }
231:       PetscCallMPI(MPI_Barrier(PetscObjectComm((PetscObject)pc)));
232:     }
233:     PetscCall(PetscFree2(numbering, permutation));
234:     PetscCall(PetscViewerASCIIPopTab(viewer));
235:     PetscCall(PetscViewerFlush(viewer));
236:     /* this line is needed to match the extra PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
237:     PetscCall(PetscViewerASCIIPopSynchronized(viewer));
238:   }
239:   PetscFunctionReturn(PETSC_SUCCESS);
240: }

242: PETSC_INTERN PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[]);

244: PetscErrorCode PCGASMSetHierarchicalPartitioning(PC pc)
245: {
246:   PC_GASM        *osm = (PC_GASM *)pc->data;
247:   MatPartitioning part;
248:   MPI_Comm        comm;
249:   PetscMPIInt     size;
250:   PetscInt        nlocalsubdomains, fromrows_localsize;
251:   IS              partitioning, fromrows, isn;
252:   Vec             outervec;

254:   PetscFunctionBegin;
255:   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
256:   PetscCallMPI(MPI_Comm_size(comm, &size));
257:   /* we do not need a hierarchical partitioning when
258:     * the total number of subdomains is consistent with
259:     * the number of MPI tasks.
260:     * For the following cases, we do not need to use HP
261:     * */
262:   if (osm->N == PETSC_DETERMINE || osm->N >= size || osm->N == 1) PetscFunctionReturn(PETSC_SUCCESS);
263:   PetscCheck(size % osm->N == 0, PETSC_COMM_WORLD, PETSC_ERR_ARG_INCOMP, "have to specify the total number of subdomains %" PetscInt_FMT " to be a factor of the number of ranks %d ", osm->N, size);
264:   nlocalsubdomains = size / osm->N;
265:   osm->n           = 1;
266:   PetscCall(MatPartitioningCreate(comm, &part));
267:   PetscCall(MatPartitioningSetAdjacency(part, pc->pmat));
268:   PetscCall(MatPartitioningSetType(part, MATPARTITIONINGHIERARCH));
269:   PetscCall(MatPartitioningHierarchicalSetNcoarseparts(part, osm->N));
270:   PetscCall(MatPartitioningHierarchicalSetNfineparts(part, nlocalsubdomains));
271:   PetscCall(MatPartitioningSetFromOptions(part));
272:   /* get new rank owner number of each vertex */
273:   PetscCall(MatPartitioningApply(part, &partitioning));
274:   PetscCall(ISBuildTwoSided(partitioning, NULL, &fromrows));
275:   PetscCall(ISPartitioningToNumbering(partitioning, &isn));
276:   PetscCall(ISDestroy(&isn));
277:   PetscCall(ISGetLocalSize(fromrows, &fromrows_localsize));
278:   PetscCall(MatPartitioningDestroy(&part));
279:   PetscCall(MatCreateVecs(pc->pmat, &outervec, NULL));
280:   PetscCall(VecCreateMPI(comm, fromrows_localsize, PETSC_DETERMINE, &(osm->pcx)));
281:   PetscCall(VecDuplicate(osm->pcx, &(osm->pcy)));
282:   PetscCall(VecScatterCreate(osm->pcx, NULL, outervec, fromrows, &(osm->pctoouter)));
283:   PetscCall(MatCreateSubMatrix(pc->pmat, fromrows, fromrows, MAT_INITIAL_MATRIX, &(osm->permutationP)));
284:   PetscCall(PetscObjectReference((PetscObject)fromrows));
285:   osm->permutationIS = fromrows;
286:   osm->pcmat         = pc->pmat;
287:   PetscCall(PetscObjectReference((PetscObject)osm->permutationP));
288:   pc->pmat = osm->permutationP;
289:   PetscCall(VecDestroy(&outervec));
290:   PetscCall(ISDestroy(&fromrows));
291:   PetscCall(ISDestroy(&partitioning));
292:   osm->n = PETSC_DETERMINE;
293:   PetscFunctionReturn(PETSC_SUCCESS);
294: }

296: static PetscErrorCode PCSetUp_GASM(PC pc)
297: {
298:   PC_GASM        *osm = (PC_GASM *)pc->data;
299:   PetscInt        i, nInnerIndices, nTotalInnerIndices;
300:   PetscMPIInt     rank, size;
301:   MatReuse        scall = MAT_REUSE_MATRIX;
302:   KSP             ksp;
303:   PC              subpc;
304:   const char     *prefix, *pprefix;
305:   Vec             x, y;
306:   PetscInt        oni;   /* Number of indices in the i-th local outer subdomain.               */
307:   const PetscInt *oidxi; /* Indices from the i-th subdomain local outer subdomain.             */
308:   PetscInt        on;    /* Number of indices in the disjoint union of local outer subdomains. */
309:   PetscInt       *oidx;  /* Indices in the disjoint union of local outer subdomains. */
310:   IS              gois;  /* Disjoint union the global indices of outer subdomains.             */
311:   IS              goid;  /* Identity IS of the size of the disjoint union of outer subdomains. */
312:   PetscScalar    *gxarray, *gyarray;
313:   PetscInt        gostart; /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
314:   PetscInt        num_subdomains  = 0;
315:   DM             *subdomain_dm    = NULL;
316:   char          **subdomain_names = NULL;
317:   PetscInt       *numbering;

319:   PetscFunctionBegin;
320:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
321:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
322:   if (!pc->setupcalled) {
323:     /* use a hierarchical partitioning */
324:     if (osm->hierarchicalpartitioning) PetscCall(PCGASMSetHierarchicalPartitioning(pc));
325:     if (osm->n == PETSC_DETERMINE) {
326:       if (osm->N != PETSC_DETERMINE) {
327:         /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
328:         PetscCall(PCGASMCreateSubdomains(pc->pmat, osm->N, &osm->n, &osm->iis));
329:       } else if (osm->dm_subdomains && pc->dm) {
330:         /* try pc->dm next, if allowed */
331:         PetscInt d;
332:         IS      *inner_subdomain_is, *outer_subdomain_is;
333:         PetscCall(DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm));
334:         if (num_subdomains) PetscCall(PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is));
335:         for (d = 0; d < num_subdomains; ++d) {
336:           if (inner_subdomain_is) PetscCall(ISDestroy(&inner_subdomain_is[d]));
337:           if (outer_subdomain_is) PetscCall(ISDestroy(&outer_subdomain_is[d]));
338:         }
339:         PetscCall(PetscFree(inner_subdomain_is));
340:         PetscCall(PetscFree(outer_subdomain_is));
341:       } else {
342:         /* still no subdomains; use one per rank */
343:         osm->nmax = osm->n = 1;
344:         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
345:         osm->N = size;
346:         PetscCall(PCGASMCreateLocalSubdomains(pc->pmat, osm->n, &osm->iis));
347:       }
348:     }
349:     if (!osm->iis) {
350:       /*
351:        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
352:        We create the requisite number of local inner subdomains and then expand them into
353:        out subdomains, if necessary.
354:        */
355:       PetscCall(PCGASMCreateLocalSubdomains(pc->pmat, osm->n, &osm->iis));
356:     }
357:     if (!osm->ois) {
358:       /*
359:             Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
360:             has been requested, copy the inner subdomains over so they can be modified.
361:       */
362:       PetscCall(PetscMalloc1(osm->n, &osm->ois));
363:       for (i = 0; i < osm->n; ++i) {
364:         if (osm->overlap > 0 && osm->N > 1) { /* With positive overlap, osm->iis[i] will be modified */
365:           PetscCall(ISDuplicate(osm->iis[i], (osm->ois) + i));
366:           PetscCall(ISCopy(osm->iis[i], osm->ois[i]));
367:         } else {
368:           PetscCall(PetscObjectReference((PetscObject)((osm->iis)[i])));
369:           osm->ois[i] = osm->iis[i];
370:         }
371:       }
372:       if (osm->overlap > 0 && osm->N > 1) {
373:         /* Extend the "overlapping" regions by a number of steps */
374:         PetscCall(MatIncreaseOverlapSplit(pc->pmat, osm->n, osm->ois, osm->overlap));
375:       }
376:     }

378:     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
379:     if (osm->nmax == PETSC_DETERMINE) {
380:       PetscMPIInt inwork, outwork;
381:       /* determine global number of subdomains and the max number of local subdomains */
382:       inwork = osm->n;
383:       PetscCall(MPIU_Allreduce(&inwork, &outwork, 1, MPI_INT, MPI_MAX, PetscObjectComm((PetscObject)pc)));
384:       osm->nmax = outwork;
385:     }
386:     if (osm->N == PETSC_DETERMINE) {
387:       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
388:       PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->ois, &osm->N, NULL));
389:     }

391:     if (osm->sort_indices) {
392:       for (i = 0; i < osm->n; i++) {
393:         PetscCall(ISSort(osm->ois[i]));
394:         PetscCall(ISSort(osm->iis[i]));
395:       }
396:     }
397:     PetscCall(PCGetOptionsPrefix(pc, &prefix));
398:     PetscCall(PCGASMPrintSubdomains(pc));

400:     /*
401:        Merge the ISs, create merged vectors and restrictions.
402:      */
403:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
404:     on = 0;
405:     for (i = 0; i < osm->n; i++) {
406:       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
407:       on += oni;
408:     }
409:     PetscCall(PetscMalloc1(on, &oidx));
410:     on = 0;
411:     /* Merge local indices together */
412:     for (i = 0; i < osm->n; i++) {
413:       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
414:       PetscCall(ISGetIndices(osm->ois[i], &oidxi));
415:       PetscCall(PetscArraycpy(oidx + on, oidxi, oni));
416:       PetscCall(ISRestoreIndices(osm->ois[i], &oidxi));
417:       on += oni;
418:     }
419:     PetscCall(ISCreateGeneral(((PetscObject)(pc))->comm, on, oidx, PETSC_OWN_POINTER, &gois));
420:     nTotalInnerIndices = 0;
421:     for (i = 0; i < osm->n; i++) {
422:       PetscCall(ISGetLocalSize(osm->iis[i], &nInnerIndices));
423:       nTotalInnerIndices += nInnerIndices;
424:     }
425:     PetscCall(VecCreateMPI(((PetscObject)(pc))->comm, nTotalInnerIndices, PETSC_DETERMINE, &x));
426:     PetscCall(VecDuplicate(x, &y));

428:     PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)pc), on, PETSC_DECIDE, &osm->gx));
429:     PetscCall(VecDuplicate(osm->gx, &osm->gy));
430:     PetscCall(VecGetOwnershipRange(osm->gx, &gostart, NULL));
431:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), on, gostart, 1, &goid));
432:     /* gois might indices not on local */
433:     PetscCall(VecScatterCreate(x, gois, osm->gx, goid, &(osm->gorestriction)));
434:     PetscCall(PetscMalloc1(osm->n, &numbering));
435:     PetscCall(PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc), osm->n, (PetscObject *)osm->ois, NULL, numbering));
436:     PetscCall(VecDestroy(&x));
437:     PetscCall(ISDestroy(&gois));

439:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
440:     {
441:       PetscInt        ini;   /* Number of indices the i-th a local inner subdomain. */
442:       PetscInt        in;    /* Number of indices in the disjoint union of local inner subdomains. */
443:       PetscInt       *iidx;  /* Global indices in the merged local inner subdomain. */
444:       PetscInt       *ioidx; /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
445:       IS              giis;  /* IS for the disjoint union of inner subdomains. */
446:       IS              giois; /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
447:       PetscScalar    *array;
448:       const PetscInt *indices;
449:       PetscInt        k;
450:       on = 0;
451:       for (i = 0; i < osm->n; i++) {
452:         PetscCall(ISGetLocalSize(osm->ois[i], &oni));
453:         on += oni;
454:       }
455:       PetscCall(PetscMalloc1(on, &iidx));
456:       PetscCall(PetscMalloc1(on, &ioidx));
457:       PetscCall(VecGetArray(y, &array));
458:       /* set communicator id to determine where overlap is */
459:       in = 0;
460:       for (i = 0; i < osm->n; i++) {
461:         PetscCall(ISGetLocalSize(osm->iis[i], &ini));
462:         for (k = 0; k < ini; ++k) array[in + k] = numbering[i];
463:         in += ini;
464:       }
465:       PetscCall(VecRestoreArray(y, &array));
466:       PetscCall(VecScatterBegin(osm->gorestriction, y, osm->gy, INSERT_VALUES, SCATTER_FORWARD));
467:       PetscCall(VecScatterEnd(osm->gorestriction, y, osm->gy, INSERT_VALUES, SCATTER_FORWARD));
468:       PetscCall(VecGetOwnershipRange(osm->gy, &gostart, NULL));
469:       PetscCall(VecGetArray(osm->gy, &array));
470:       on = 0;
471:       in = 0;
472:       for (i = 0; i < osm->n; i++) {
473:         PetscCall(ISGetLocalSize(osm->ois[i], &oni));
474:         PetscCall(ISGetIndices(osm->ois[i], &indices));
475:         for (k = 0; k < oni; k++) {
476:           /*  skip overlapping indices to get inner domain */
477:           if (PetscRealPart(array[on + k]) != numbering[i]) continue;
478:           iidx[in]    = indices[k];
479:           ioidx[in++] = gostart + on + k;
480:         }
481:         PetscCall(ISRestoreIndices(osm->ois[i], &indices));
482:         on += oni;
483:       }
484:       PetscCall(VecRestoreArray(osm->gy, &array));
485:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, iidx, PETSC_OWN_POINTER, &giis));
486:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, ioidx, PETSC_OWN_POINTER, &giois));
487:       PetscCall(VecScatterCreate(y, giis, osm->gy, giois, &osm->girestriction));
488:       PetscCall(VecDestroy(&y));
489:       PetscCall(ISDestroy(&giis));
490:       PetscCall(ISDestroy(&giois));
491:     }
492:     PetscCall(ISDestroy(&goid));
493:     PetscCall(PetscFree(numbering));

495:     /* Create the subdomain work vectors. */
496:     PetscCall(PetscMalloc1(osm->n, &osm->x));
497:     PetscCall(PetscMalloc1(osm->n, &osm->y));
498:     PetscCall(VecGetArray(osm->gx, &gxarray));
499:     PetscCall(VecGetArray(osm->gy, &gyarray));
500:     for (i = 0, on = 0; i < osm->n; ++i, on += oni) {
501:       PetscInt oNi;
502:       PetscCall(ISGetLocalSize(osm->ois[i], &oni));
503:       /* on a sub communicator */
504:       PetscCall(ISGetSize(osm->ois[i], &oNi));
505:       PetscCall(VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm, 1, oni, oNi, gxarray + on, &osm->x[i]));
506:       PetscCall(VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm, 1, oni, oNi, gyarray + on, &osm->y[i]));
507:     }
508:     PetscCall(VecRestoreArray(osm->gx, &gxarray));
509:     PetscCall(VecRestoreArray(osm->gy, &gyarray));
510:     /* Create the subdomain solvers */
511:     PetscCall(PetscMalloc1(osm->n, &osm->ksp));
512:     for (i = 0; i < osm->n; i++) {
513:       char subprefix[PETSC_MAX_PATH_LEN + 1];
514:       PetscCall(KSPCreate(((PetscObject)(osm->ois[i]))->comm, &ksp));
515:       PetscCall(KSPSetErrorIfNotConverged(ksp, pc->erroriffailure));
516:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ksp, (PetscObject)pc, 1));
517:       PetscCall(KSPSetType(ksp, KSPPREONLY));
518:       PetscCall(KSPGetPC(ksp, &subpc)); /* Why do we need this here? */
519:       if (subdomain_dm) {
520:         PetscCall(KSPSetDM(ksp, subdomain_dm[i]));
521:         PetscCall(DMDestroy(subdomain_dm + i));
522:       }
523:       PetscCall(PCGetOptionsPrefix(pc, &prefix));
524:       PetscCall(KSPSetOptionsPrefix(ksp, prefix));
525:       if (subdomain_names && subdomain_names[i]) {
526:         PetscCall(PetscSNPrintf(subprefix, PETSC_MAX_PATH_LEN, "sub_%s_", subdomain_names[i]));
527:         PetscCall(KSPAppendOptionsPrefix(ksp, subprefix));
528:         PetscCall(PetscFree(subdomain_names[i]));
529:       }
530:       PetscCall(KSPAppendOptionsPrefix(ksp, "sub_"));
531:       osm->ksp[i] = ksp;
532:     }
533:     PetscCall(PetscFree(subdomain_dm));
534:     PetscCall(PetscFree(subdomain_names));
535:     scall = MAT_INITIAL_MATRIX;
536:   } else { /* if (pc->setupcalled) */
537:     /*
538:        Destroy the submatrices from the previous iteration
539:     */
540:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
541:       PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
542:       scall = MAT_INITIAL_MATRIX;
543:     }
544:     if (osm->permutationIS) {
545:       PetscCall(MatCreateSubMatrix(pc->pmat, osm->permutationIS, osm->permutationIS, scall, &osm->permutationP));
546:       PetscCall(PetscObjectReference((PetscObject)osm->permutationP));
547:       osm->pcmat = pc->pmat;
548:       pc->pmat   = osm->permutationP;
549:     }
550:   }

552:   /*
553:      Extract the submatrices.
554:   */
555:   if (size > 1) {
556:     PetscCall(MatCreateSubMatricesMPI(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
557:   } else {
558:     PetscCall(MatCreateSubMatrices(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
559:   }
560:   if (scall == MAT_INITIAL_MATRIX) {
561:     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)pc->pmat, &pprefix));
562:     for (i = 0; i < osm->n; i++) PetscCall(PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i], pprefix));
563:   }

565:   /* Return control to the user so that the submatrices can be modified (e.g., to apply
566:      different boundary conditions for the submatrices than for the global problem) */
567:   PetscCall(PCModifySubMatrices(pc, osm->n, osm->ois, osm->ois, osm->pmat, pc->modifysubmatricesP));

569:   /*
570:      Loop over submatrices putting them into local ksps
571:   */
572:   for (i = 0; i < osm->n; i++) {
573:     PetscCall(KSPSetOperators(osm->ksp[i], osm->pmat[i], osm->pmat[i]));
574:     PetscCall(KSPGetOptionsPrefix(osm->ksp[i], &prefix));
575:     PetscCall(MatSetOptionsPrefix(osm->pmat[i], prefix));
576:     if (!pc->setupcalled) PetscCall(KSPSetFromOptions(osm->ksp[i]));
577:   }
578:   if (osm->pcmat) {
579:     PetscCall(MatDestroy(&pc->pmat));
580:     pc->pmat   = osm->pcmat;
581:     osm->pcmat = NULL;
582:   }
583:   PetscFunctionReturn(PETSC_SUCCESS);
584: }

586: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
587: {
588:   PC_GASM *osm = (PC_GASM *)pc->data;
589:   PetscInt i;

591:   PetscFunctionBegin;
592:   for (i = 0; i < osm->n; i++) PetscCall(KSPSetUp(osm->ksp[i]));
593:   PetscFunctionReturn(PETSC_SUCCESS);
594: }

596: static PetscErrorCode PCApply_GASM(PC pc, Vec xin, Vec yout)
597: {
598:   PC_GASM    *osm = (PC_GASM *)pc->data;
599:   PetscInt    i;
600:   Vec         x, y;
601:   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;

603:   PetscFunctionBegin;
604:   if (osm->pctoouter) {
605:     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
606:     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
607:     x = osm->pcx;
608:     y = osm->pcy;
609:   } else {
610:     x = xin;
611:     y = yout;
612:   }
613:   /*
614:      support for limiting the restriction or interpolation only to the inner
615:      subdomain values (leaving the other values 0).
616:   */
617:   if (!(osm->type & PC_GASM_RESTRICT)) {
618:     /* have to zero the work RHS since scatter may leave some slots empty */
619:     PetscCall(VecZeroEntries(osm->gx));
620:     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
621:   } else {
622:     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
623:   }
624:   PetscCall(VecZeroEntries(osm->gy));
625:   if (!(osm->type & PC_GASM_RESTRICT)) {
626:     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
627:   } else {
628:     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
629:   }
630:   /* do the subdomain solves */
631:   for (i = 0; i < osm->n; ++i) {
632:     PetscCall(KSPSolve(osm->ksp[i], osm->x[i], osm->y[i]));
633:     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
634:   }
635:   /* do we need to zero y? */
636:   PetscCall(VecZeroEntries(y));
637:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
638:     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
639:     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
640:   } else {
641:     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
642:     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
643:   }
644:   if (osm->pctoouter) {
645:     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
646:     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
647:   }
648:   PetscFunctionReturn(PETSC_SUCCESS);
649: }

651: static PetscErrorCode PCMatApply_GASM(PC pc, Mat Xin, Mat Yout)
652: {
653:   PC_GASM    *osm = (PC_GASM *)pc->data;
654:   Mat         X, Y, O = NULL, Z, W;
655:   Vec         x, y;
656:   PetscInt    i, m, M, N;
657:   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;

659:   PetscFunctionBegin;
660:   PetscCheck(osm->n == 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not yet implemented");
661:   PetscCall(MatGetSize(Xin, NULL, &N));
662:   if (osm->pctoouter) {
663:     PetscCall(VecGetLocalSize(osm->pcx, &m));
664:     PetscCall(VecGetSize(osm->pcx, &M));
665:     PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &O));
666:     for (i = 0; i < N; ++i) {
667:       PetscCall(MatDenseGetColumnVecRead(Xin, i, &x));
668:       PetscCall(MatDenseGetColumnVecWrite(O, i, &y));
669:       PetscCall(VecScatterBegin(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
670:       PetscCall(VecScatterEnd(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
671:       PetscCall(MatDenseRestoreColumnVecWrite(O, i, &y));
672:       PetscCall(MatDenseRestoreColumnVecRead(Xin, i, &x));
673:     }
674:     X = Y = O;
675:   } else {
676:     X = Xin;
677:     Y = Yout;
678:   }
679:   /*
680:      support for limiting the restriction or interpolation only to the inner
681:      subdomain values (leaving the other values 0).
682:   */
683:   PetscCall(VecGetLocalSize(osm->x[0], &m));
684:   PetscCall(VecGetSize(osm->x[0], &M));
685:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &Z));
686:   for (i = 0; i < N; ++i) {
687:     PetscCall(MatDenseGetColumnVecRead(X, i, &x));
688:     PetscCall(MatDenseGetColumnVecWrite(Z, i, &y));
689:     if (!(osm->type & PC_GASM_RESTRICT)) {
690:       /* have to zero the work RHS since scatter may leave some slots empty */
691:       PetscCall(VecZeroEntries(y));
692:       PetscCall(VecScatterBegin(osm->girestriction, x, y, INSERT_VALUES, forward));
693:       PetscCall(VecScatterEnd(osm->girestriction, x, y, INSERT_VALUES, forward));
694:     } else {
695:       PetscCall(VecScatterBegin(osm->gorestriction, x, y, INSERT_VALUES, forward));
696:       PetscCall(VecScatterEnd(osm->gorestriction, x, y, INSERT_VALUES, forward));
697:     }
698:     PetscCall(MatDenseRestoreColumnVecWrite(Z, i, &y));
699:     PetscCall(MatDenseRestoreColumnVecRead(X, i, &x));
700:   }
701:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &W));
702:   PetscCall(MatSetOption(Z, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
703:   PetscCall(MatAssemblyBegin(Z, MAT_FINAL_ASSEMBLY));
704:   PetscCall(MatAssemblyEnd(Z, MAT_FINAL_ASSEMBLY));
705:   /* do the subdomain solve */
706:   PetscCall(KSPMatSolve(osm->ksp[0], Z, W));
707:   PetscCall(KSPCheckSolve(osm->ksp[0], pc, NULL));
708:   PetscCall(MatDestroy(&Z));
709:   /* do we need to zero y? */
710:   PetscCall(MatZeroEntries(Y));
711:   for (i = 0; i < N; ++i) {
712:     PetscCall(MatDenseGetColumnVecWrite(Y, i, &y));
713:     PetscCall(MatDenseGetColumnVecRead(W, i, &x));
714:     if (!(osm->type & PC_GASM_INTERPOLATE)) {
715:       PetscCall(VecScatterBegin(osm->girestriction, x, y, ADD_VALUES, reverse));
716:       PetscCall(VecScatterEnd(osm->girestriction, x, y, ADD_VALUES, reverse));
717:     } else {
718:       PetscCall(VecScatterBegin(osm->gorestriction, x, y, ADD_VALUES, reverse));
719:       PetscCall(VecScatterEnd(osm->gorestriction, x, y, ADD_VALUES, reverse));
720:     }
721:     PetscCall(MatDenseRestoreColumnVecRead(W, i, &x));
722:     if (osm->pctoouter) {
723:       PetscCall(MatDenseGetColumnVecWrite(Yout, i, &x));
724:       PetscCall(VecScatterBegin(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
725:       PetscCall(VecScatterEnd(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
726:       PetscCall(MatDenseRestoreColumnVecRead(Yout, i, &x));
727:     }
728:     PetscCall(MatDenseRestoreColumnVecWrite(Y, i, &y));
729:   }
730:   PetscCall(MatDestroy(&W));
731:   PetscCall(MatDestroy(&O));
732:   PetscFunctionReturn(PETSC_SUCCESS);
733: }

735: static PetscErrorCode PCApplyTranspose_GASM(PC pc, Vec xin, Vec yout)
736: {
737:   PC_GASM    *osm = (PC_GASM *)pc->data;
738:   PetscInt    i;
739:   Vec         x, y;
740:   ScatterMode forward = SCATTER_FORWARD, reverse = SCATTER_REVERSE;

742:   PetscFunctionBegin;
743:   if (osm->pctoouter) {
744:     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
745:     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
746:     x = osm->pcx;
747:     y = osm->pcy;
748:   } else {
749:     x = xin;
750:     y = yout;
751:   }
752:   /*
753:      Support for limiting the restriction or interpolation to only local
754:      subdomain values (leaving the other values 0).

756:      Note: these are reversed from the PCApply_GASM() because we are applying the
757:      transpose of the three terms
758:   */
759:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
760:     /* have to zero the work RHS since scatter may leave some slots empty */
761:     PetscCall(VecZeroEntries(osm->gx));
762:     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
763:   } else {
764:     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
765:   }
766:   PetscCall(VecZeroEntries(osm->gy));
767:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
768:     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
769:   } else {
770:     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
771:   }
772:   /* do the local solves */
773:   for (i = 0; i < osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
774:     PetscCall(KSPSolveTranspose(osm->ksp[i], osm->x[i], osm->y[i]));
775:     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
776:   }
777:   PetscCall(VecZeroEntries(y));
778:   if (!(osm->type & PC_GASM_RESTRICT)) {
779:     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
780:     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
781:   } else {
782:     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
783:     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
784:   }
785:   if (osm->pctoouter) {
786:     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
787:     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
788:   }
789:   PetscFunctionReturn(PETSC_SUCCESS);
790: }

792: static PetscErrorCode PCReset_GASM(PC pc)
793: {
794:   PC_GASM *osm = (PC_GASM *)pc->data;
795:   PetscInt i;

797:   PetscFunctionBegin;
798:   if (osm->ksp) {
799:     for (i = 0; i < osm->n; i++) PetscCall(KSPReset(osm->ksp[i]));
800:   }
801:   if (osm->pmat) {
802:     if (osm->n > 0) {
803:       PetscMPIInt size;
804:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
805:       if (size > 1) {
806:         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
807:         PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
808:       } else {
809:         PetscCall(MatDestroySubMatrices(osm->n, &osm->pmat));
810:       }
811:     }
812:   }
813:   if (osm->x) {
814:     for (i = 0; i < osm->n; i++) {
815:       PetscCall(VecDestroy(&osm->x[i]));
816:       PetscCall(VecDestroy(&osm->y[i]));
817:     }
818:   }
819:   PetscCall(VecDestroy(&osm->gx));
820:   PetscCall(VecDestroy(&osm->gy));

822:   PetscCall(VecScatterDestroy(&osm->gorestriction));
823:   PetscCall(VecScatterDestroy(&osm->girestriction));
824:   if (!osm->user_subdomains) {
825:     PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
826:     osm->N    = PETSC_DETERMINE;
827:     osm->nmax = PETSC_DETERMINE;
828:   }
829:   if (osm->pctoouter) PetscCall(VecScatterDestroy(&(osm->pctoouter)));
830:   if (osm->permutationIS) PetscCall(ISDestroy(&(osm->permutationIS)));
831:   if (osm->pcx) PetscCall(VecDestroy(&(osm->pcx)));
832:   if (osm->pcy) PetscCall(VecDestroy(&(osm->pcy)));
833:   if (osm->permutationP) PetscCall(MatDestroy(&(osm->permutationP)));
834:   if (osm->pcmat) PetscCall(MatDestroy(&osm->pcmat));
835:   PetscFunctionReturn(PETSC_SUCCESS);
836: }

838: static PetscErrorCode PCDestroy_GASM(PC pc)
839: {
840:   PC_GASM *osm = (PC_GASM *)pc->data;
841:   PetscInt i;

843:   PetscFunctionBegin;
844:   PetscCall(PCReset_GASM(pc));
845:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
846:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
847:   if (osm->ksp) {
848:     for (i = 0; i < osm->n; i++) PetscCall(KSPDestroy(&osm->ksp[i]));
849:     PetscCall(PetscFree(osm->ksp));
850:   }
851:   PetscCall(PetscFree(osm->x));
852:   PetscCall(PetscFree(osm->y));
853:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", NULL));
854:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", NULL));
855:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", NULL));
856:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", NULL));
857:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", NULL));
858:   PetscCall(PetscFree(pc->data));
859:   PetscFunctionReturn(PETSC_SUCCESS);
860: }

862: static PetscErrorCode PCSetFromOptions_GASM(PC pc, PetscOptionItems *PetscOptionsObject)
863: {
864:   PC_GASM   *osm = (PC_GASM *)pc->data;
865:   PetscInt   blocks, ovl;
866:   PetscBool  flg;
867:   PCGASMType gasmtype;

869:   PetscFunctionBegin;
870:   PetscOptionsHeadBegin(PetscOptionsObject, "Generalized additive Schwarz options");
871:   PetscCall(PetscOptionsBool("-pc_gasm_use_dm_subdomains", "If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.", "PCGASMSetUseDMSubdomains", osm->dm_subdomains, &osm->dm_subdomains, &flg));
872:   PetscCall(PetscOptionsInt("-pc_gasm_total_subdomains", "Total number of subdomains across communicator", "PCGASMSetTotalSubdomains", osm->N, &blocks, &flg));
873:   if (flg) PetscCall(PCGASMSetTotalSubdomains(pc, blocks));
874:   PetscCall(PetscOptionsInt("-pc_gasm_overlap", "Number of overlapping degrees of freedom", "PCGASMSetOverlap", osm->overlap, &ovl, &flg));
875:   if (flg) {
876:     PetscCall(PCGASMSetOverlap(pc, ovl));
877:     osm->dm_subdomains = PETSC_FALSE;
878:   }
879:   flg = PETSC_FALSE;
880:   PetscCall(PetscOptionsEnum("-pc_gasm_type", "Type of restriction/extension", "PCGASMSetType", PCGASMTypes, (PetscEnum)osm->type, (PetscEnum *)&gasmtype, &flg));
881:   if (flg) PetscCall(PCGASMSetType(pc, gasmtype));
882:   PetscCall(PetscOptionsBool("-pc_gasm_use_hierachical_partitioning", "use hierarchical partitioning", NULL, osm->hierarchicalpartitioning, &osm->hierarchicalpartitioning, &flg));
883:   PetscOptionsHeadEnd();
884:   PetscFunctionReturn(PETSC_SUCCESS);
885: }

887: /*@
888:     PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the communicator for `PCGASM`

890:     Logically Collective

892:     Input Parameters:
893: +   pc  - the preconditioner
894: -   N   - total number of subdomains

896:     Level: beginner

898: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`
899:           `PCGASMCreateSubdomains2D()`
900: @*/
901: PetscErrorCode PCGASMSetTotalSubdomains(PC pc, PetscInt N)
902: {
903:   PC_GASM    *osm = (PC_GASM *)pc->data;
904:   PetscMPIInt size, rank;

906:   PetscFunctionBegin;
907:   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Total number of subdomains must be 1 or more, got N = %" PetscInt_FMT, N);
908:   PetscCheck(!pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetTotalSubdomains() should be called before calling PCSetUp().");

910:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
911:   osm->ois = osm->iis = NULL;

913:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
914:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
915:   osm->N             = N;
916:   osm->n             = PETSC_DETERMINE;
917:   osm->nmax          = PETSC_DETERMINE;
918:   osm->dm_subdomains = PETSC_FALSE;
919:   PetscFunctionReturn(PETSC_SUCCESS);
920: }

922: static PetscErrorCode PCGASMSetSubdomains_GASM(PC pc, PetscInt n, IS iis[], IS ois[])
923: {
924:   PC_GASM *osm = (PC_GASM *)pc->data;
925:   PetscInt i;

927:   PetscFunctionBegin;
928:   PetscCheck(n >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Each MPI rank must have 1 or more subdomains, got n = %" PetscInt_FMT, n);
929:   PetscCheck(!pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetSubdomains() should be called before calling PCSetUp().");

931:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
932:   osm->iis = osm->ois = NULL;
933:   osm->n              = n;
934:   osm->N              = PETSC_DETERMINE;
935:   osm->nmax           = PETSC_DETERMINE;
936:   if (ois) {
937:     PetscCall(PetscMalloc1(n, &osm->ois));
938:     for (i = 0; i < n; i++) {
939:       PetscCall(PetscObjectReference((PetscObject)ois[i]));
940:       osm->ois[i] = ois[i];
941:     }
942:     /*
943:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
944:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
945:     */
946:     osm->overlap = -1;
947:     /* inner subdomains must be provided  */
948:     PetscCheck(iis, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "inner indices have to be provided ");
949:   } /* end if */
950:   if (iis) {
951:     PetscCall(PetscMalloc1(n, &osm->iis));
952:     for (i = 0; i < n; i++) {
953:       PetscCall(PetscObjectReference((PetscObject)iis[i]));
954:       osm->iis[i] = iis[i];
955:     }
956:     if (!ois) {
957:       osm->ois = NULL;
958:       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
959:     }
960:   }
961:   if (PetscDefined(USE_DEBUG)) {
962:     PetscInt        j, rstart, rend, *covered, lsize;
963:     const PetscInt *indices;
964:     /* check if the inner indices cover and only cover the local portion of the preconditioning matrix */
965:     PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
966:     PetscCall(PetscCalloc1(rend - rstart, &covered));
967:     /* check if the current MPI rank owns indices from others */
968:     for (i = 0; i < n; i++) {
969:       PetscCall(ISGetIndices(osm->iis[i], &indices));
970:       PetscCall(ISGetLocalSize(osm->iis[i], &lsize));
971:       for (j = 0; j < lsize; j++) {
972:         PetscCheck(indices[j] >= rstart && indices[j] < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "inner subdomains can not own an index %" PetscInt_FMT " from other ranks", indices[j]);
973:         PetscCheck(covered[indices[j] - rstart] != 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "inner subdomains can not have an overlapping index %" PetscInt_FMT " ", indices[j]);
974:         covered[indices[j] - rstart] = 1;
975:       }
976:       PetscCall(ISRestoreIndices(osm->iis[i], &indices));
977:     }
978:     /* check if we miss any indices */
979:     for (i = rstart; i < rend; i++) PetscCheck(covered[i - rstart], PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "local entity %" PetscInt_FMT " was not covered by inner subdomains", i);
980:     PetscCall(PetscFree(covered));
981:   }
982:   if (iis) osm->user_subdomains = PETSC_TRUE;
983:   PetscFunctionReturn(PETSC_SUCCESS);
984: }

986: static PetscErrorCode PCGASMSetOverlap_GASM(PC pc, PetscInt ovl)
987: {
988:   PC_GASM *osm = (PC_GASM *)pc->data;

990:   PetscFunctionBegin;
991:   PetscCheck(ovl >= 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap value requested");
992:   PetscCheck(!pc->setupcalled || ovl == osm->overlap, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetOverlap() should be called before PCSetUp().");
993:   if (!pc->setupcalled) osm->overlap = ovl;
994:   PetscFunctionReturn(PETSC_SUCCESS);
995: }

997: static PetscErrorCode PCGASMSetType_GASM(PC pc, PCGASMType type)
998: {
999:   PC_GASM *osm = (PC_GASM *)pc->data;

1001:   PetscFunctionBegin;
1002:   osm->type     = type;
1003:   osm->type_set = PETSC_TRUE;
1004:   PetscFunctionReturn(PETSC_SUCCESS);
1005: }

1007: static PetscErrorCode PCGASMSetSortIndices_GASM(PC pc, PetscBool doSort)
1008: {
1009:   PC_GASM *osm = (PC_GASM *)pc->data;

1011:   PetscFunctionBegin;
1012:   osm->sort_indices = doSort;
1013:   PetscFunctionReturn(PETSC_SUCCESS);
1014: }

1016: /*
1017:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
1018:         In particular, it would upset the global subdomain number calculation.
1019: */
1020: static PetscErrorCode PCGASMGetSubKSP_GASM(PC pc, PetscInt *n, PetscInt *first, KSP **ksp)
1021: {
1022:   PC_GASM *osm = (PC_GASM *)pc->data;

1024:   PetscFunctionBegin;
1025:   PetscCheck(osm->n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Need to call PCSetUp() on PC (or KSPSetUp() on the outer KSP object) before calling here");

1027:   if (n) *n = osm->n;
1028:   if (first) {
1029:     PetscCallMPI(MPI_Scan(&osm->n, first, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));
1030:     *first -= osm->n;
1031:   }
1032:   if (ksp) {
1033:     /* Assume that local solves are now different; not necessarily
1034:        true, though!  This flag is used only for PCView_GASM() */
1035:     *ksp                        = osm->ksp;
1036:     osm->same_subdomain_solvers = PETSC_FALSE;
1037:   }
1038:   PetscFunctionReturn(PETSC_SUCCESS);
1039: } /* PCGASMGetSubKSP_GASM() */

1041: /*@C
1042:     PCGASMSetSubdomains - Sets the subdomains for this MPI rank
1043:     for the additive Schwarz preconditioner with multiple MPI ranks per subdomain, `PCGASM`

1045:     Collective

1047:     Input Parameters:
1048: +   pc  - the preconditioner object
1049: .   n   - the number of subdomains for this MPI rank
1050: .   iis - the index sets that define the inner subdomains (or `NULL` for PETSc to determine subdomains)
1051: -   ois - the index sets that define the outer subdomains (or `NULL` to use the same as `iis`, or to construct by expanding `iis` by
1052:           the requested overlap)

1054:     Level: advanced

1056:     Notes:
1057:     The `IS` indices use the parallel, global numbering of the vector entries.

1059:     Inner subdomains are those where the correction is applied.

1061:     Outer subdomains are those where the residual necessary to obtain the
1062:     corrections is obtained (see `PCGASMType` for the use of inner/outer subdomains).

1064:     Both inner and outer subdomains can extend over several MPI ranks.
1065:     This rank's portion of a subdomain is known as a local subdomain.

1067:     Inner subdomains can not overlap with each other, do not have any entities from remote ranks,
1068:     and  have to cover the entire local subdomain owned by the current rank. The index sets on each
1069:     rank should be ordered such that the ith local subdomain is connected to the ith remote subdomain
1070:     on another MPI rank.

1072:     By default the `PGASM` preconditioner uses 1 (local) subdomain per MPI rank.

1074:     The `iis` and `ois` arrays may be freed after this call using `PCGASMDestroySubdomains()`

1076: .seealso: `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMDestroySubdomains()`,
1077:           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1078: @*/
1079: PetscErrorCode PCGASMSetSubdomains(PC pc, PetscInt n, IS iis[], IS ois[])
1080: {
1081:   PC_GASM *osm = (PC_GASM *)pc->data;

1083:   PetscFunctionBegin;
1085:   PetscTryMethod(pc, "PCGASMSetSubdomains_C", (PC, PetscInt, IS[], IS[]), (pc, n, iis, ois));
1086:   osm->dm_subdomains = PETSC_FALSE;
1087:   PetscFunctionReturn(PETSC_SUCCESS);
1088: }

1090: /*@
1091:     PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
1092:     additive Schwarz preconditioner `PCGASM`.  Either all or no MPI ranks in the
1093:     pc communicator must call this routine.

1095:     Logically Collective

1097:     Input Parameters:
1098: +   pc  - the preconditioner context
1099: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

1101:     Options Database Key:
1102: .   -pc_gasm_overlap <overlap> - Sets overlap

1104:     Level: intermediate

1106:     Notes:
1107:     By default the `PCGASM` preconditioner uses 1 subdomain per rank.  To use
1108:     multiple subdomain per perocessor or "straddling" subdomains that intersect
1109:     multiple ranks use `PCGASMSetSubdomains()` (or option `-pc_gasm_total_subdomains` <n>).

1111:     The overlap defaults to 0, so if one desires that no additional
1112:     overlap be computed beyond what may have been set with a call to
1113:     `PCGASMSetSubdomains()`, then `ovl` must be set to be 0.  In particular, if one does
1114:     not explicitly set the subdomains in application code, then all overlap would be computed
1115:     internally by PETSc, and using an overlap of 0 would result in an `PCGASM`
1116:     variant that is equivalent to the block Jacobi preconditioner.

1118:     One can define initial index sets with any overlap via
1119:     `PCGASMSetSubdomains()`; the routine `PCGASMSetOverlap()` merely allows
1120:     PETSc to extend that overlap further, if desired.

1122: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1123:           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1124: @*/
1125: PetscErrorCode PCGASMSetOverlap(PC pc, PetscInt ovl)
1126: {
1127:   PC_GASM *osm = (PC_GASM *)pc->data;

1129:   PetscFunctionBegin;
1132:   PetscTryMethod(pc, "PCGASMSetOverlap_C", (PC, PetscInt), (pc, ovl));
1133:   osm->dm_subdomains = PETSC_FALSE;
1134:   PetscFunctionReturn(PETSC_SUCCESS);
1135: }

1137: /*@
1138:     PCGASMSetType - Sets the type of restriction and interpolation used
1139:     for local problems in the `PCGASM` additive Schwarz method.

1141:     Logically Collective

1143:     Input Parameters:
1144: +   pc  - the preconditioner context
1145: -   type - variant of `PCGASM`, one of
1146: .vb
1147:       `PC_GASM_BASIC`       - full interpolation and restriction
1148:       `PC_GASM_RESTRICT`    - full restriction, local MPI rank interpolation
1149:       `PC_GASM_INTERPOLATE` - full interpolation, local MPI rank restriction
1150:       `PC_GASM_NONE`        - local MPI rank restriction and interpolation
1151: .ve

1153:     Options Database Key:
1154: .   -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASM` type

1156:     Level: intermediate

1158: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1159:           `PCGASMCreateSubdomains2D()`, `PCASM`, `PCASMSetType()`
1160: @*/
1161: PetscErrorCode PCGASMSetType(PC pc, PCGASMType type)
1162: {
1163:   PetscFunctionBegin;
1166:   PetscTryMethod(pc, "PCGASMSetType_C", (PC, PCGASMType), (pc, type));
1167:   PetscFunctionReturn(PETSC_SUCCESS);
1168: }

1170: /*@
1171:     PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

1173:     Logically Collective

1175:     Input Parameters:
1176: +   pc  - the preconditioner context
1177: -   doSort - sort the subdomain indices

1179:     Level: intermediate

1181: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1182:           `PCGASMCreateSubdomains2D()`
1183: @*/
1184: PetscErrorCode PCGASMSetSortIndices(PC pc, PetscBool doSort)
1185: {
1186:   PetscFunctionBegin;
1189:   PetscTryMethod(pc, "PCGASMSetSortIndices_C", (PC, PetscBool), (pc, doSort));
1190:   PetscFunctionReturn(PETSC_SUCCESS);
1191: }

1193: /*@C
1194:    PCGASMGetSubKSP - Gets the local `KSP` contexts for all subdomains on
1195:    this MPI rank.

1197:    Collective iff first_local is requested

1199:    Input Parameter:
1200: .  pc - the preconditioner context

1202:    Output Parameters:
1203: +  n_local - the number of blocks on this MPI rank or `NULL`
1204: .  first_local - the global number of the first block on this rank or `NULL`,
1205:                  all ranks must request or all must pass `NULL`
1206: -  ksp - the array of `KSP` contexts

1208:    Level: advanced

1210:    Note:
1211:    After `PCGASMGetSubKSP()` the array of `KSP`es is not to be freed

1213:    Currently for some matrix implementations only 1 block per MPI process
1214:    is supported.

1216:    You must call `KSPSetUp()` before calling `PCGASMGetSubKSP()`.

1218: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`,
1219:           `PCGASMCreateSubdomains2D()`,
1220: @*/
1221: PetscErrorCode PCGASMGetSubKSP(PC pc, PetscInt *n_local, PetscInt *first_local, KSP *ksp[])
1222: {
1223:   PetscFunctionBegin;
1225:   PetscUseMethod(pc, "PCGASMGetSubKSP_C", (PC, PetscInt *, PetscInt *, KSP **), (pc, n_local, first_local, ksp));
1226:   PetscFunctionReturn(PETSC_SUCCESS);
1227: }

1229: /*MC
1230:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1231:            its own `KSP` object on a subset of MPI ranks

1233:    Options Database Keys:
1234: +  -pc_gasm_total_subdomains <n>  - Sets total number of local subdomains to be distributed among MPI ranks
1235: .  -pc_gasm_view_subdomains       - activates the printing of subdomain indices in `PCView()`, -ksp_view or -snes_view
1236: .  -pc_gasm_print_subdomains      - activates the printing of subdomain indices in `PCSetUp()`
1237: .  -pc_gasm_overlap <ovl>         - Sets overlap by which to (automatically) extend local subdomains
1238: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASMType`

1240:    Level: beginner

1242:    Notes:
1243:    To set options on the solvers for each block append `-sub_` to all the `KSP`, and `PC`
1244:    options database keys. For example, `-sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly`

1246:    To set the options on the solvers separate for each block call `PCGASMGetSubKSP()`
1247:    and set the options directly on the resulting `KSP` object (you can access its `PC`
1248:    with `KSPGetPC()`)

1250:     References:
1251: +   * - M Dryja, OB Widlund, An additive variant of the Schwarz alternating method for the case of many subregions
1252:      Courant Institute, New York University Technical report
1253: -   * - Barry Smith, Petter Bjorstad, and William Gropp, Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
1254:     Cambridge University Press.

1256: .seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCASM`, `PCGASMType`, `PCGASMSetType()`,
1257:           `PCBJACOBI`, `PCGASMGetSubKSP()`, `PCGASMSetSubdomains()`,
1258:           `PCSetModifySubMatrices()`, `PCGASMSetOverlap()`, `PCGASMSetType()`
1259: M*/

1261: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1262: {
1263:   PC_GASM *osm;

1265:   PetscFunctionBegin;
1266:   PetscCall(PetscNew(&osm));

1268:   osm->N                        = PETSC_DETERMINE;
1269:   osm->n                        = PETSC_DECIDE;
1270:   osm->nmax                     = PETSC_DETERMINE;
1271:   osm->overlap                  = 0;
1272:   osm->ksp                      = NULL;
1273:   osm->gorestriction            = NULL;
1274:   osm->girestriction            = NULL;
1275:   osm->pctoouter                = NULL;
1276:   osm->gx                       = NULL;
1277:   osm->gy                       = NULL;
1278:   osm->x                        = NULL;
1279:   osm->y                        = NULL;
1280:   osm->pcx                      = NULL;
1281:   osm->pcy                      = NULL;
1282:   osm->permutationIS            = NULL;
1283:   osm->permutationP             = NULL;
1284:   osm->pcmat                    = NULL;
1285:   osm->ois                      = NULL;
1286:   osm->iis                      = NULL;
1287:   osm->pmat                     = NULL;
1288:   osm->type                     = PC_GASM_RESTRICT;
1289:   osm->same_subdomain_solvers   = PETSC_TRUE;
1290:   osm->sort_indices             = PETSC_TRUE;
1291:   osm->dm_subdomains            = PETSC_FALSE;
1292:   osm->hierarchicalpartitioning = PETSC_FALSE;

1294:   pc->data                 = (void *)osm;
1295:   pc->ops->apply           = PCApply_GASM;
1296:   pc->ops->matapply        = PCMatApply_GASM;
1297:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1298:   pc->ops->setup           = PCSetUp_GASM;
1299:   pc->ops->reset           = PCReset_GASM;
1300:   pc->ops->destroy         = PCDestroy_GASM;
1301:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1302:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1303:   pc->ops->view            = PCView_GASM;
1304:   pc->ops->applyrichardson = NULL;

1306:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", PCGASMSetSubdomains_GASM));
1307:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", PCGASMSetOverlap_GASM));
1308:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", PCGASMSetType_GASM));
1309:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", PCGASMSetSortIndices_GASM));
1310:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", PCGASMGetSubKSP_GASM));
1311:   PetscFunctionReturn(PETSC_SUCCESS);
1312: }

1314: PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1315: {
1316:   MatPartitioning mpart;
1317:   const char     *prefix;
1318:   PetscInt        i, j, rstart, rend, bs;
1319:   PetscBool       hasop, isbaij = PETSC_FALSE, foundpart = PETSC_FALSE;
1320:   Mat             Ad = NULL, adj;
1321:   IS              ispart, isnumb, *is;

1323:   PetscFunctionBegin;
1324:   PetscCheck(nloc >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "number of local subdomains must > 0, got nloc = %" PetscInt_FMT, nloc);

1326:   /* Get prefix, row distribution, and block size */
1327:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1328:   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
1329:   PetscCall(MatGetBlockSize(A, &bs));
1330:   PetscCheck(rstart / bs * bs == rstart && rend / bs * bs == rend, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "bad row distribution [%" PetscInt_FMT ",%" PetscInt_FMT ") for matrix block size %" PetscInt_FMT, rstart, rend, bs);

1332:   /* Get diagonal block from matrix if possible */
1333:   PetscCall(MatHasOperation(A, MATOP_GET_DIAGONAL_BLOCK, &hasop));
1334:   if (hasop) PetscCall(MatGetDiagonalBlock(A, &Ad));
1335:   if (Ad) {
1336:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQBAIJ, &isbaij));
1337:     if (!isbaij) PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQSBAIJ, &isbaij));
1338:   }
1339:   if (Ad && nloc > 1) {
1340:     PetscBool match, done;
1341:     /* Try to setup a good matrix partitioning if available */
1342:     PetscCall(MatPartitioningCreate(PETSC_COMM_SELF, &mpart));
1343:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mpart, prefix));
1344:     PetscCall(MatPartitioningSetFromOptions(mpart));
1345:     PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGCURRENT, &match));
1346:     if (!match) PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGSQUARE, &match));
1347:     if (!match) { /* assume a "good" partitioner is available */
1348:       PetscInt        na;
1349:       const PetscInt *ia, *ja;
1350:       PetscCall(MatGetRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1351:       if (done) {
1352:         /* Build adjacency matrix by hand. Unfortunately a call to
1353:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1354:            remove the block-aij structure and we cannot expect
1355:            MatPartitioning to split vertices as we need */
1356:         PetscInt        i, j, len, nnz, cnt, *iia = NULL, *jja = NULL;
1357:         const PetscInt *row;
1358:         nnz = 0;
1359:         for (i = 0; i < na; i++) { /* count number of nonzeros */
1360:           len = ia[i + 1] - ia[i];
1361:           row = ja + ia[i];
1362:           for (j = 0; j < len; j++) {
1363:             if (row[j] == i) { /* don't count diagonal */
1364:               len--;
1365:               break;
1366:             }
1367:           }
1368:           nnz += len;
1369:         }
1370:         PetscCall(PetscMalloc1(na + 1, &iia));
1371:         PetscCall(PetscMalloc1(nnz, &jja));
1372:         nnz    = 0;
1373:         iia[0] = 0;
1374:         for (i = 0; i < na; i++) { /* fill adjacency */
1375:           cnt = 0;
1376:           len = ia[i + 1] - ia[i];
1377:           row = ja + ia[i];
1378:           for (j = 0; j < len; j++) {
1379:             if (row[j] != i) jja[nnz + cnt++] = row[j]; /* if not diagonal */
1380:           }
1381:           nnz += cnt;
1382:           iia[i + 1] = nnz;
1383:         }
1384:         /* Partitioning of the adjacency matrix */
1385:         PetscCall(MatCreateMPIAdj(PETSC_COMM_SELF, na, na, iia, jja, NULL, &adj));
1386:         PetscCall(MatPartitioningSetAdjacency(mpart, adj));
1387:         PetscCall(MatPartitioningSetNParts(mpart, nloc));
1388:         PetscCall(MatPartitioningApply(mpart, &ispart));
1389:         PetscCall(ISPartitioningToNumbering(ispart, &isnumb));
1390:         PetscCall(MatDestroy(&adj));
1391:         foundpart = PETSC_TRUE;
1392:       }
1393:       PetscCall(MatRestoreRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1394:     }
1395:     PetscCall(MatPartitioningDestroy(&mpart));
1396:   }
1397:   PetscCall(PetscMalloc1(nloc, &is));
1398:   if (!foundpart) {
1399:     /* Partitioning by contiguous chunks of rows */

1401:     PetscInt mbs   = (rend - rstart) / bs;
1402:     PetscInt start = rstart;
1403:     for (i = 0; i < nloc; i++) {
1404:       PetscInt count = (mbs / nloc + ((mbs % nloc) > i)) * bs;
1405:       PetscCall(ISCreateStride(PETSC_COMM_SELF, count, start, 1, &is[i]));
1406:       start += count;
1407:     }

1409:   } else {
1410:     /* Partitioning by adjacency of diagonal block  */

1412:     const PetscInt *numbering;
1413:     PetscInt       *count, nidx, *indices, *newidx, start = 0;
1414:     /* Get node count in each partition */
1415:     PetscCall(PetscMalloc1(nloc, &count));
1416:     PetscCall(ISPartitioningCount(ispart, nloc, count));
1417:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1418:       for (i = 0; i < nloc; i++) count[i] *= bs;
1419:     }
1420:     /* Build indices from node numbering */
1421:     PetscCall(ISGetLocalSize(isnumb, &nidx));
1422:     PetscCall(PetscMalloc1(nidx, &indices));
1423:     for (i = 0; i < nidx; i++) indices[i] = i; /* needs to be initialized */
1424:     PetscCall(ISGetIndices(isnumb, &numbering));
1425:     PetscCall(PetscSortIntWithPermutation(nidx, numbering, indices));
1426:     PetscCall(ISRestoreIndices(isnumb, &numbering));
1427:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1428:       PetscCall(PetscMalloc1(nidx * bs, &newidx));
1429:       for (i = 0; i < nidx; i++) {
1430:         for (j = 0; j < bs; j++) newidx[i * bs + j] = indices[i] * bs + j;
1431:       }
1432:       PetscCall(PetscFree(indices));
1433:       nidx *= bs;
1434:       indices = newidx;
1435:     }
1436:     /* Shift to get global indices */
1437:     for (i = 0; i < nidx; i++) indices[i] += rstart;

1439:     /* Build the index sets for each block */
1440:     for (i = 0; i < nloc; i++) {
1441:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count[i], &indices[start], PETSC_COPY_VALUES, &is[i]));
1442:       PetscCall(ISSort(is[i]));
1443:       start += count[i];
1444:     }

1446:     PetscCall(PetscFree(count));
1447:     PetscCall(PetscFree(indices));
1448:     PetscCall(ISDestroy(&isnumb));
1449:     PetscCall(ISDestroy(&ispart));
1450:   }
1451:   *iis = is;
1452:   PetscFunctionReturn(PETSC_SUCCESS);
1453: }

1455: PETSC_INTERN PetscErrorCode PCGASMCreateStraddlingSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1456: {
1457:   PetscFunctionBegin;
1458:   PetscCall(MatSubdomainsCreateCoalesce(A, N, n, iis));
1459:   PetscFunctionReturn(PETSC_SUCCESS);
1460: }

1462: /*@C
1463:    PCGASMCreateSubdomains - Creates `n` index sets defining `n` nonoverlapping subdomains on this MPI process for the `PCGASM` additive
1464:    Schwarz preconditioner for a any problem based on its matrix.

1466:    Collective

1468:    Input Parameters:
1469: +  A       - The global matrix operator
1470: -  N       - the number of global subdomains requested

1472:    Output Parameters:
1473: +  n   - the number of subdomains created on this MPI rank
1474: -  iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

1476:    Level: advanced

1478:    Notes:
1479:    When `N` >= A's communicator size, each subdomain is local -- contained within a single MPI process.
1480:          When `N` < size, the subdomains are 'straddling' (rank boundaries) and are no longer local.
1481:          The resulting subdomains can be use in `PCGASMSetSubdomains`(pc,n,iss,`NULL`).  The overlapping
1482:          outer subdomains will be automatically generated from these according to the requested amount of
1483:          overlap; this is currently supported only with local subdomains.

1485:    Use `PCGASMDestroySubdomains()` to free the array and the list of index sets.

1487: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMDestroySubdomains()`
1488: @*/
1489: PetscErrorCode PCGASMCreateSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1490: {
1491:   PetscMPIInt size;

1493:   PetscFunctionBegin;

1497:   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of subdomains must be > 0, N = %" PetscInt_FMT, N);
1498:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
1499:   if (N >= size) {
1500:     *n = N / size + (N % size);
1501:     PetscCall(PCGASMCreateLocalSubdomains(A, *n, iis));
1502:   } else {
1503:     PetscCall(PCGASMCreateStraddlingSubdomains(A, N, n, iis));
1504:   }
1505:   PetscFunctionReturn(PETSC_SUCCESS);
1506: }

1508: /*@C
1509:    PCGASMDestroySubdomains - Destroys the index sets created with
1510:    `PCGASMCreateSubdomains()` or `PCGASMCreateSubdomains2D()`. Should be
1511:    called after setting subdomains with `PCGASMSetSubdomains()`.

1513:    Collective

1515:    Input Parameters:
1516: +  n   - the number of index sets
1517: .  iis - the array of inner subdomains
1518: -  ois - the array of outer subdomains, can be `NULL`

1520:    Level: intermediate

1522:    Note:
1523:    This is a convenience subroutine that walks each list,
1524:    destroys each `IS` on the list, and then frees the list. At the end the
1525:    list pointers are set to `NULL`.

1527: .seealso: `PCGASM`, `PCGASMCreateSubdomains()`, `PCGASMSetSubdomains()`, `PCGASMSetSubdomains()`
1528: @*/
1529: PetscErrorCode PCGASMDestroySubdomains(PetscInt n, IS **iis, IS **ois)
1530: {
1531:   PetscInt i;

1533:   PetscFunctionBegin;
1534:   if (n <= 0) PetscFunctionReturn(PETSC_SUCCESS);
1535:   if (ois) {
1537:     if (*ois) {
1539:       for (i = 0; i < n; i++) PetscCall(ISDestroy(&(*ois)[i]));
1540:       PetscCall(PetscFree((*ois)));
1541:     }
1542:   }
1543:   if (iis) {
1545:     if (*iis) {
1547:       for (i = 0; i < n; i++) PetscCall(ISDestroy(&(*iis)[i]));
1548:       PetscCall(PetscFree((*iis)));
1549:     }
1550:   }
1551:   PetscFunctionReturn(PETSC_SUCCESS);
1552: }

1554: #define PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, xleft_loc, ylow_loc, xright_loc, yhigh_loc, n) \
1555:   { \
1556:     PetscInt first_row = first / M, last_row = last / M + 1; \
1557:     /*                                                                                                    \
1558:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1559:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1560:      subdomain).                                                                                          \
1561:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1562:      of the intersection.                                                                                 \
1563:     */ \
1564:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */ \
1565:     *ylow_loc = PetscMax(first_row, ylow); \
1566:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1567:     *xleft_loc = *ylow_loc == first_row ? PetscMax(first % M, xleft) : xleft; \
1568:     /* yhigh_loc is the grid row above the last local subdomain element */ \
1569:     *yhigh_loc = PetscMin(last_row, yhigh); \
1570:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */ \
1571:     *xright_loc = *yhigh_loc == last_row ? PetscMin(xright, last % M) : xright; \
1572:     /* Now compute the size of the local subdomain n. */ \
1573:     *n = 0; \
1574:     if (*ylow_loc < *yhigh_loc) { \
1575:       PetscInt width = xright - xleft; \
1576:       *n += width * (*yhigh_loc - *ylow_loc - 1); \
1577:       *n += PetscMin(PetscMax(*xright_loc - xleft, 0), width); \
1578:       *n -= PetscMin(PetscMax(*xleft_loc - xleft, 0), width); \
1579:     } \
1580:   }

1582: /*@C
1583:    PCGASMCreateSubdomains2D - Creates the index sets for the `PCGASM` overlapping Schwarz
1584:    preconditioner for a two-dimensional problem on a regular grid.

1586:    Collective

1588:    Input Parameters:
1589: +  pc       - the preconditioner context
1590: .  M        - the global number of grid points in the x direction
1591: .  N        - the global number of grid points in the y direction
1592: .  Mdomains - the global number of subdomains in the x direction
1593: .  Ndomains - the global number of subdomains in the y direction
1594: .  dof      - degrees of freedom per node
1595: -  overlap  - overlap in mesh lines

1597:    Output Parameters:
1598: +  Nsub - the number of local subdomains created
1599: .  iis  - array of index sets defining inner (nonoverlapping) subdomains
1600: -  ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains

1602:    Level: advanced

1604:    Note:
1605:    Use `PCGASMDestroySubdomains()` to free the index sets and the arrays

1607:    Fortran Note:
1608:    The `IS` must be declared as an array of length long enough to hold `Nsub` entries

1610: .seealso: `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`, `PCGASMSetOverlap()`, `PCASMCreateSubdomains2D()`,
1611:           `PCGASMDestroySubdomains()`
1612: @*/
1613: PetscErrorCode PCGASMCreateSubdomains2D(PC pc, PetscInt M, PetscInt N, PetscInt Mdomains, PetscInt Ndomains, PetscInt dof, PetscInt overlap, PetscInt *nsub, IS **iis, IS **ois)
1614: {
1615:   PetscMPIInt size, rank;
1616:   PetscInt    i, j;
1617:   PetscInt    maxheight, maxwidth;
1618:   PetscInt    xstart, xleft, xright, xleft_loc, xright_loc;
1619:   PetscInt    ystart, ylow, yhigh, ylow_loc, yhigh_loc;
1620:   PetscInt    x[2][2], y[2][2], n[2];
1621:   PetscInt    first, last;
1622:   PetscInt    nidx, *idx;
1623:   PetscInt    ii, jj, s, q, d;
1624:   PetscInt    k, kk;
1625:   PetscMPIInt color;
1626:   MPI_Comm    comm, subcomm;
1627:   IS        **xis = NULL, **is = ois, **is_local = iis;

1629:   PetscFunctionBegin;
1630:   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
1631:   PetscCallMPI(MPI_Comm_size(comm, &size));
1632:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1633:   PetscCall(MatGetOwnershipRange(pc->pmat, &first, &last));
1634:   PetscCheck((first % dof) == 0 && (last % dof) == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE,
1635:              "Matrix row partitioning unsuitable for domain decomposition: local row range (%" PetscInt_FMT ",%" PetscInt_FMT ") "
1636:              "does not respect the number of degrees of freedom per grid point %" PetscInt_FMT,
1637:              first, last, dof);

1639:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1640:   s      = 0;
1641:   ystart = 0;
1642:   for (j = 0; j < Ndomains; ++j) {
1643:     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1644:     PetscCheck(maxheight >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the vertical direction for mesh height %" PetscInt_FMT, Ndomains, N);
1645:     /* Vertical domain limits with an overlap. */
1646:     ylow   = PetscMax(ystart - overlap, 0);
1647:     yhigh  = PetscMin(ystart + maxheight + overlap, N);
1648:     xstart = 0;
1649:     for (i = 0; i < Mdomains; ++i) {
1650:       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1651:       PetscCheck(maxwidth >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the horizontal direction for mesh width %" PetscInt_FMT, Mdomains, M);
1652:       /* Horizontal domain limits with an overlap. */
1653:       xleft  = PetscMax(xstart - overlap, 0);
1654:       xright = PetscMin(xstart + maxwidth + overlap, M);
1655:       /*
1656:          Determine whether this subdomain intersects this rank's ownership range of pc->pmat.
1657:       */
1658:       PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1659:       if (nidx) ++s;
1660:       xstart += maxwidth;
1661:     } /* for (i = 0; i < Mdomains; ++i) */
1662:     ystart += maxheight;
1663:   } /* for (j = 0; j < Ndomains; ++j) */

1665:   /* Now we can allocate the necessary number of ISs. */
1666:   *nsub = s;
1667:   PetscCall(PetscMalloc1(*nsub, is));
1668:   PetscCall(PetscMalloc1(*nsub, is_local));
1669:   s      = 0;
1670:   ystart = 0;
1671:   for (j = 0; j < Ndomains; ++j) {
1672:     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1673:     PetscCheck(maxheight >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the vertical direction for mesh height %" PetscInt_FMT, Ndomains, N);
1674:     /* Vertical domain limits with an overlap. */
1675:     y[0][0] = PetscMax(ystart - overlap, 0);
1676:     y[0][1] = PetscMin(ystart + maxheight + overlap, N);
1677:     /* Vertical domain limits without an overlap. */
1678:     y[1][0] = ystart;
1679:     y[1][1] = PetscMin(ystart + maxheight, N);
1680:     xstart  = 0;
1681:     for (i = 0; i < Mdomains; ++i) {
1682:       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1683:       PetscCheck(maxwidth >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Too many %" PetscInt_FMT " subdomains in the horizontal direction for mesh width %" PetscInt_FMT, Mdomains, M);
1684:       /* Horizontal domain limits with an overlap. */
1685:       x[0][0] = PetscMax(xstart - overlap, 0);
1686:       x[0][1] = PetscMin(xstart + maxwidth + overlap, M);
1687:       /* Horizontal domain limits without an overlap. */
1688:       x[1][0] = xstart;
1689:       x[1][1] = PetscMin(xstart + maxwidth, M);
1690:       /*
1691:          Determine whether this domain intersects this rank's ownership range of pc->pmat.
1692:          Do this twice: first for the domains with overlaps, and once without.
1693:          During the first pass create the subcommunicators, and use them on the second pass as well.
1694:       */
1695:       for (q = 0; q < 2; ++q) {
1696:         PetscBool split = PETSC_FALSE;
1697:         /*
1698:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1699:           according to whether the domain with an overlap or without is considered.
1700:         */
1701:         xleft  = x[q][0];
1702:         xright = x[q][1];
1703:         ylow   = y[q][0];
1704:         yhigh  = y[q][1];
1705:         PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1706:         nidx *= dof;
1707:         n[q] = nidx;
1708:         /*
1709:          Based on the counted number of indices in the local domain *with an overlap*,
1710:          construct a subcommunicator of all the MPI ranks supporting this domain.
1711:          Observe that a domain with an overlap might have nontrivial local support,
1712:          while the domain without an overlap might not.  Hence, the decision to participate
1713:          in the subcommunicator must be based on the domain with an overlap.
1714:          */
1715:         if (q == 0) {
1716:           if (nidx) color = 1;
1717:           else color = MPI_UNDEFINED;
1718:           PetscCallMPI(MPI_Comm_split(comm, color, rank, &subcomm));
1719:           split = PETSC_TRUE;
1720:         }
1721:         /*
1722:          Proceed only if the number of local indices *with an overlap* is nonzero.
1723:          */
1724:         if (n[0]) {
1725:           if (q == 0) xis = is;
1726:           if (q == 1) {
1727:             /*
1728:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1729:              Moreover, if the overlap is zero, the two ISs are identical.
1730:              */
1731:             if (overlap == 0) {
1732:               (*is_local)[s] = (*is)[s];
1733:               PetscCall(PetscObjectReference((PetscObject)(*is)[s]));
1734:               continue;
1735:             } else {
1736:               xis     = is_local;
1737:               subcomm = ((PetscObject)(*is)[s])->comm;
1738:             }
1739:           } /* if (q == 1) */
1740:           idx = NULL;
1741:           PetscCall(PetscMalloc1(nidx, &idx));
1742:           if (nidx) {
1743:             k = 0;
1744:             for (jj = ylow_loc; jj < yhigh_loc; ++jj) {
1745:               PetscInt x0 = (jj == ylow_loc) ? xleft_loc : xleft;
1746:               PetscInt x1 = (jj == yhigh_loc - 1) ? xright_loc : xright;
1747:               kk          = dof * (M * jj + x0);
1748:               for (ii = x0; ii < x1; ++ii) {
1749:                 for (d = 0; d < dof; ++d) idx[k++] = kk++;
1750:               }
1751:             }
1752:           }
1753:           PetscCall(ISCreateGeneral(subcomm, nidx, idx, PETSC_OWN_POINTER, (*xis) + s));
1754:           if (split) PetscCallMPI(MPI_Comm_free(&subcomm));
1755:         } /* if (n[0]) */
1756:       }   /* for (q = 0; q < 2; ++q) */
1757:       if (n[0]) ++s;
1758:       xstart += maxwidth;
1759:     } /* for (i = 0; i < Mdomains; ++i) */
1760:     ystart += maxheight;
1761:   } /* for (j = 0; j < Ndomains; ++j) */
1762:   PetscFunctionReturn(PETSC_SUCCESS);
1763: }

1765: /*@C
1766:     PCGASMGetSubdomains - Gets the subdomains supported on this MPI rank
1767:     for the `PCGASM` additive Schwarz preconditioner.

1769:     Not Collective

1771:     Input Parameter:
1772: .   pc - the preconditioner context

1774:     Output Parameters:
1775: +   n   - the number of subdomains for this MPI rank (default value = 1)
1776: .   iis - the index sets that define the inner subdomains (without overlap) supported on this rank (can be `NULL`)
1777: -   ois - the index sets that define the outer subdomains (with overlap) supported on this rank (can be `NULL`)

1779:     Level: advanced

1781:     Notes:
1782:     The user is responsible for destroying the `IS`s and freeing the returned arrays, this can be done with
1783:     `PCGASMDestroySubdomains()`

1785:     The `IS` numbering is in the parallel, global numbering of the vector.

1787: .seealso: `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMCreateSubdomains2D()`,
1788:           `PCGASMSetSubdomains()`, `PCGASMGetSubmatrices()`, `PCGASMDestroySubdomains()`
1789: @*/
1790: PetscErrorCode PCGASMGetSubdomains(PC pc, PetscInt *n, IS *iis[], IS *ois[])
1791: {
1792:   PC_GASM  *osm;
1793:   PetscBool match;
1794:   PetscInt  i;

1796:   PetscFunctionBegin;
1798:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1799:   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1800:   osm = (PC_GASM *)pc->data;
1801:   if (n) *n = osm->n;
1802:   if (iis) PetscCall(PetscMalloc1(osm->n, iis));
1803:   if (ois) PetscCall(PetscMalloc1(osm->n, ois));
1804:   if (iis || ois) {
1805:     for (i = 0; i < osm->n; ++i) {
1806:       if (iis) (*iis)[i] = osm->iis[i];
1807:       if (ois) (*ois)[i] = osm->ois[i];
1808:     }
1809:   }
1810:   PetscFunctionReturn(PETSC_SUCCESS);
1811: }

1813: /*@C
1814:     PCGASMGetSubmatrices - Gets the local submatrices (for this MPI rank
1815:     only) for the `PCGASM` additive Schwarz preconditioner.

1817:     Not Collective

1819:     Input Parameter:
1820: .   pc - the preconditioner context

1822:     Output Parameters:
1823: +   n   - the number of matrices for this MPI rank (default value = 1)
1824: -   mat - the matrices

1826:     Level: advanced

1828:     Note:
1829:     Matrices returned by this routine have the same communicators as the index sets (`IS`)
1830:            used to define subdomains in `PCGASMSetSubdomains()`

1832: .seealso: `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`,
1833:           `PCGASMCreateSubdomains2D()`, `PCGASMSetSubdomains()`, `PCGASMGetSubdomains()`
1834: @*/
1835: PetscErrorCode PCGASMGetSubmatrices(PC pc, PetscInt *n, Mat *mat[])
1836: {
1837:   PC_GASM  *osm;
1838:   PetscBool match;

1840:   PetscFunctionBegin;
1844:   PetscCheck(pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call after KSPSetUp() or PCSetUp().");
1845:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1846:   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1847:   osm = (PC_GASM *)pc->data;
1848:   if (n) *n = osm->n;
1849:   if (mat) *mat = osm->pmat;
1850:   PetscFunctionReturn(PETSC_SUCCESS);
1851: }

1853: /*@
1854:     PCGASMSetUseDMSubdomains - Indicates whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible for `PCGASM`

1856:     Logically Collective

1858:     Input Parameters:
1859: +   pc  - the preconditioner
1860: -   flg - boolean indicating whether to use subdomains defined by the `DM`

1862:     Options Database Key:
1863: .   -pc_gasm_dm_subdomains -pc_gasm_overlap -pc_gasm_total_subdomains

1865:     Level: intermediate

1867:     Note:
1868:     `PCGASMSetSubdomains()`, `PCGASMSetTotalSubdomains()` or `PCGASMSetOverlap()` take precedence over `PCGASMSetUseDMSubdomains()`,
1869:     so setting `PCGASMSetSubdomains()` with nontrivial subdomain ISs or any of `PCGASMSetTotalSubdomains()` and `PCGASMSetOverlap()`
1870:     automatically turns the latter off.

1872: .seealso: `PCGASM`, `PCGASMGetUseDMSubdomains()`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`
1873:           `PCGASMCreateSubdomains2D()`
1874: @*/
1875: PetscErrorCode PCGASMSetUseDMSubdomains(PC pc, PetscBool flg)
1876: {
1877:   PC_GASM  *osm = (PC_GASM *)pc->data;
1878:   PetscBool match;

1880:   PetscFunctionBegin;
1883:   PetscCheck(!pc->setupcalled, ((PetscObject)pc)->comm, PETSC_ERR_ARG_WRONGSTATE, "Not for a setup PC.");
1884:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1885:   if (match) {
1886:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) osm->dm_subdomains = flg;
1887:   }
1888:   PetscFunctionReturn(PETSC_SUCCESS);
1889: }

1891: /*@
1892:     PCGASMGetUseDMSubdomains - Returns flag indicating whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible with `PCGASM`

1894:     Not Collective

1896:     Input Parameter:
1897: .   pc  - the preconditioner

1899:     Output Parameter:
1900: .   flg - boolean indicating whether to use subdomains defined by the `DM`

1902:     Level: intermediate

1904: .seealso: `PCGASM`, `PCGASMSetUseDMSubdomains()`, `PCGASMSetOverlap()`
1905:           `PCGASMCreateSubdomains2D()`
1906: @*/
1907: PetscErrorCode PCGASMGetUseDMSubdomains(PC pc, PetscBool *flg)
1908: {
1909:   PC_GASM  *osm = (PC_GASM *)pc->data;
1910:   PetscBool match;

1912:   PetscFunctionBegin;
1915:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1916:   if (match) {
1917:     if (flg) *flg = osm->dm_subdomains;
1918:   }
1919:   PetscFunctionReturn(PETSC_SUCCESS);
1920: }