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: static 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(KSPSetNestLevel(ksp, pc->kspnestlevel));
516:       PetscCall(KSPSetErrorIfNotConverged(ksp, pc->erroriffailure));
517:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ksp, (PetscObject)pc, 1));
518:       PetscCall(KSPSetType(ksp, KSPPREONLY));
519:       PetscCall(KSPGetPC(ksp, &subpc)); /* Why do we need this here? */
520:       if (subdomain_dm) {
521:         PetscCall(KSPSetDM(ksp, subdomain_dm[i]));
522:         PetscCall(DMDestroy(subdomain_dm + i));
523:       }
524:       PetscCall(PCGetOptionsPrefix(pc, &prefix));
525:       PetscCall(KSPSetOptionsPrefix(ksp, prefix));
526:       if (subdomain_names && subdomain_names[i]) {
527:         PetscCall(PetscSNPrintf(subprefix, PETSC_MAX_PATH_LEN, "sub_%s_", subdomain_names[i]));
528:         PetscCall(KSPAppendOptionsPrefix(ksp, subprefix));
529:         PetscCall(PetscFree(subdomain_names[i]));
530:       }
531:       PetscCall(KSPAppendOptionsPrefix(ksp, "sub_"));
532:       osm->ksp[i] = ksp;
533:     }
534:     PetscCall(PetscFree(subdomain_dm));
535:     PetscCall(PetscFree(subdomain_names));
536:     scall = MAT_INITIAL_MATRIX;
537:   } else { /* if (pc->setupcalled) */
538:     /*
539:        Destroy the submatrices from the previous iteration
540:     */
541:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
542:       PetscCall(MatDestroyMatrices(osm->n, &osm->pmat));
543:       scall = MAT_INITIAL_MATRIX;
544:     }
545:     if (osm->permutationIS) {
546:       PetscCall(MatCreateSubMatrix(pc->pmat, osm->permutationIS, osm->permutationIS, scall, &osm->permutationP));
547:       PetscCall(PetscObjectReference((PetscObject)osm->permutationP));
548:       osm->pcmat = pc->pmat;
549:       pc->pmat   = osm->permutationP;
550:     }
551:   }

553:   /*
554:      Extract the submatrices.
555:   */
556:   if (size > 1) {
557:     PetscCall(MatCreateSubMatricesMPI(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
558:   } else {
559:     PetscCall(MatCreateSubMatrices(pc->pmat, osm->n, osm->ois, osm->ois, scall, &osm->pmat));
560:   }
561:   if (scall == MAT_INITIAL_MATRIX) {
562:     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)pc->pmat, &pprefix));
563:     for (i = 0; i < osm->n; i++) PetscCall(PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i], pprefix));
564:   }

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

570:   /*
571:      Loop over submatrices putting them into local ksps
572:   */
573:   for (i = 0; i < osm->n; i++) {
574:     PetscCall(KSPSetOperators(osm->ksp[i], osm->pmat[i], osm->pmat[i]));
575:     PetscCall(KSPGetOptionsPrefix(osm->ksp[i], &prefix));
576:     PetscCall(MatSetOptionsPrefix(osm->pmat[i], prefix));
577:     if (!pc->setupcalled) PetscCall(KSPSetFromOptions(osm->ksp[i]));
578:   }
579:   if (osm->pcmat) {
580:     PetscCall(MatDestroy(&pc->pmat));
581:     pc->pmat   = osm->pcmat;
582:     osm->pcmat = NULL;
583:   }
584:   PetscFunctionReturn(PETSC_SUCCESS);
585: }

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

592:   PetscFunctionBegin;
593:   for (i = 0; i < osm->n; i++) PetscCall(KSPSetUp(osm->ksp[i]));
594:   PetscFunctionReturn(PETSC_SUCCESS);
595: }

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

604:   PetscFunctionBegin;
605:   if (osm->pctoouter) {
606:     PetscCall(VecScatterBegin(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
607:     PetscCall(VecScatterEnd(osm->pctoouter, xin, osm->pcx, INSERT_VALUES, SCATTER_REVERSE));
608:     x = osm->pcx;
609:     y = osm->pcy;
610:   } else {
611:     x = xin;
612:     y = yout;
613:   }
614:   /*
615:      support for limiting the restriction or interpolation only to the inner
616:      subdomain values (leaving the other values 0).
617:   */
618:   if (!(osm->type & PC_GASM_RESTRICT)) {
619:     /* have to zero the work RHS since scatter may leave some slots empty */
620:     PetscCall(VecZeroEntries(osm->gx));
621:     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
622:   } else {
623:     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
624:   }
625:   PetscCall(VecZeroEntries(osm->gy));
626:   if (!(osm->type & PC_GASM_RESTRICT)) {
627:     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
628:   } else {
629:     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
630:   }
631:   /* do the subdomain solves */
632:   for (i = 0; i < osm->n; ++i) {
633:     PetscCall(KSPSolve(osm->ksp[i], osm->x[i], osm->y[i]));
634:     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
635:   }
636:   /* do we need to zero y? */
637:   PetscCall(VecZeroEntries(y));
638:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
639:     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
640:     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
641:   } else {
642:     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
643:     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
644:   }
645:   if (osm->pctoouter) {
646:     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
647:     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
648:   }
649:   PetscFunctionReturn(PETSC_SUCCESS);
650: }

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

660:   PetscFunctionBegin;
661:   PetscCheck(osm->n == 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not yet implemented");
662:   PetscCall(MatGetSize(Xin, NULL, &N));
663:   if (osm->pctoouter) {
664:     PetscCall(VecGetLocalSize(osm->pcx, &m));
665:     PetscCall(VecGetSize(osm->pcx, &M));
666:     PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &O));
667:     for (i = 0; i < N; ++i) {
668:       PetscCall(MatDenseGetColumnVecRead(Xin, i, &x));
669:       PetscCall(MatDenseGetColumnVecWrite(O, i, &y));
670:       PetscCall(VecScatterBegin(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
671:       PetscCall(VecScatterEnd(osm->pctoouter, x, y, INSERT_VALUES, SCATTER_REVERSE));
672:       PetscCall(MatDenseRestoreColumnVecWrite(O, i, &y));
673:       PetscCall(MatDenseRestoreColumnVecRead(Xin, i, &x));
674:     }
675:     X = Y = O;
676:   } else {
677:     X = Xin;
678:     Y = Yout;
679:   }
680:   /*
681:      support for limiting the restriction or interpolation only to the inner
682:      subdomain values (leaving the other values 0).
683:   */
684:   PetscCall(VecGetLocalSize(osm->x[0], &m));
685:   PetscCall(VecGetSize(osm->x[0], &M));
686:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &Z));
687:   for (i = 0; i < N; ++i) {
688:     PetscCall(MatDenseGetColumnVecRead(X, i, &x));
689:     PetscCall(MatDenseGetColumnVecWrite(Z, i, &y));
690:     if (!(osm->type & PC_GASM_RESTRICT)) {
691:       /* have to zero the work RHS since scatter may leave some slots empty */
692:       PetscCall(VecZeroEntries(y));
693:       PetscCall(VecScatterBegin(osm->girestriction, x, y, INSERT_VALUES, forward));
694:       PetscCall(VecScatterEnd(osm->girestriction, x, y, INSERT_VALUES, forward));
695:     } else {
696:       PetscCall(VecScatterBegin(osm->gorestriction, x, y, INSERT_VALUES, forward));
697:       PetscCall(VecScatterEnd(osm->gorestriction, x, y, INSERT_VALUES, forward));
698:     }
699:     PetscCall(MatDenseRestoreColumnVecWrite(Z, i, &y));
700:     PetscCall(MatDenseRestoreColumnVecRead(X, i, &x));
701:   }
702:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]), m, PETSC_DECIDE, M, N, NULL, &W));
703:   PetscCall(MatSetOption(Z, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
704:   PetscCall(MatAssemblyBegin(Z, MAT_FINAL_ASSEMBLY));
705:   PetscCall(MatAssemblyEnd(Z, MAT_FINAL_ASSEMBLY));
706:   /* do the subdomain solve */
707:   PetscCall(KSPMatSolve(osm->ksp[0], Z, W));
708:   PetscCall(KSPCheckSolve(osm->ksp[0], pc, NULL));
709:   PetscCall(MatDestroy(&Z));
710:   /* do we need to zero y? */
711:   PetscCall(MatZeroEntries(Y));
712:   for (i = 0; i < N; ++i) {
713:     PetscCall(MatDenseGetColumnVecWrite(Y, i, &y));
714:     PetscCall(MatDenseGetColumnVecRead(W, i, &x));
715:     if (!(osm->type & PC_GASM_INTERPOLATE)) {
716:       PetscCall(VecScatterBegin(osm->girestriction, x, y, ADD_VALUES, reverse));
717:       PetscCall(VecScatterEnd(osm->girestriction, x, y, ADD_VALUES, reverse));
718:     } else {
719:       PetscCall(VecScatterBegin(osm->gorestriction, x, y, ADD_VALUES, reverse));
720:       PetscCall(VecScatterEnd(osm->gorestriction, x, y, ADD_VALUES, reverse));
721:     }
722:     PetscCall(MatDenseRestoreColumnVecRead(W, i, &x));
723:     if (osm->pctoouter) {
724:       PetscCall(MatDenseGetColumnVecWrite(Yout, i, &x));
725:       PetscCall(VecScatterBegin(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
726:       PetscCall(VecScatterEnd(osm->pctoouter, y, x, INSERT_VALUES, SCATTER_FORWARD));
727:       PetscCall(MatDenseRestoreColumnVecRead(Yout, i, &x));
728:     }
729:     PetscCall(MatDenseRestoreColumnVecWrite(Y, i, &y));
730:   }
731:   PetscCall(MatDestroy(&W));
732:   PetscCall(MatDestroy(&O));
733:   PetscFunctionReturn(PETSC_SUCCESS);
734: }

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

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

757:      Note: these are reversed from the PCApply_GASM() because we are applying the
758:      transpose of the three terms
759:   */
760:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
761:     /* have to zero the work RHS since scatter may leave some slots empty */
762:     PetscCall(VecZeroEntries(osm->gx));
763:     PetscCall(VecScatterBegin(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
764:   } else {
765:     PetscCall(VecScatterBegin(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
766:   }
767:   PetscCall(VecZeroEntries(osm->gy));
768:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
769:     PetscCall(VecScatterEnd(osm->girestriction, x, osm->gx, INSERT_VALUES, forward));
770:   } else {
771:     PetscCall(VecScatterEnd(osm->gorestriction, x, osm->gx, INSERT_VALUES, forward));
772:   }
773:   /* do the local solves */
774:   for (i = 0; i < osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
775:     PetscCall(KSPSolveTranspose(osm->ksp[i], osm->x[i], osm->y[i]));
776:     PetscCall(KSPCheckSolve(osm->ksp[i], pc, osm->y[i]));
777:   }
778:   PetscCall(VecZeroEntries(y));
779:   if (!(osm->type & PC_GASM_RESTRICT)) {
780:     PetscCall(VecScatterBegin(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
781:     PetscCall(VecScatterEnd(osm->girestriction, osm->gy, y, ADD_VALUES, reverse));
782:   } else {
783:     PetscCall(VecScatterBegin(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
784:     PetscCall(VecScatterEnd(osm->gorestriction, osm->gy, y, ADD_VALUES, reverse));
785:   }
786:   if (osm->pctoouter) {
787:     PetscCall(VecScatterBegin(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
788:     PetscCall(VecScatterEnd(osm->pctoouter, y, yout, INSERT_VALUES, SCATTER_FORWARD));
789:   }
790:   PetscFunctionReturn(PETSC_SUCCESS);
791: }

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

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

823:   PetscCall(VecScatterDestroy(&osm->gorestriction));
824:   PetscCall(VecScatterDestroy(&osm->girestriction));
825:   if (!osm->user_subdomains) {
826:     PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
827:     osm->N    = PETSC_DETERMINE;
828:     osm->nmax = PETSC_DETERMINE;
829:   }
830:   if (osm->pctoouter) PetscCall(VecScatterDestroy(&(osm->pctoouter)));
831:   if (osm->permutationIS) PetscCall(ISDestroy(&(osm->permutationIS)));
832:   if (osm->pcx) PetscCall(VecDestroy(&(osm->pcx)));
833:   if (osm->pcy) PetscCall(VecDestroy(&(osm->pcy)));
834:   if (osm->permutationP) PetscCall(MatDestroy(&(osm->permutationP)));
835:   if (osm->pcmat) PetscCall(MatDestroy(&osm->pcmat));
836:   PetscFunctionReturn(PETSC_SUCCESS);
837: }

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

844:   PetscFunctionBegin;
845:   PetscCall(PCReset_GASM(pc));
846:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
847:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->ois, &osm->iis));
848:   if (osm->ksp) {
849:     for (i = 0; i < osm->n; i++) PetscCall(KSPDestroy(&osm->ksp[i]));
850:     PetscCall(PetscFree(osm->ksp));
851:   }
852:   PetscCall(PetscFree(osm->x));
853:   PetscCall(PetscFree(osm->y));
854:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", NULL));
855:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", NULL));
856:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", NULL));
857:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", NULL));
858:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", NULL));
859:   PetscCall(PetscFree(pc->data));
860:   PetscFunctionReturn(PETSC_SUCCESS);
861: }

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

870:   PetscFunctionBegin;
871:   PetscOptionsHeadBegin(PetscOptionsObject, "Generalized additive Schwarz options");
872:   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));
873:   PetscCall(PetscOptionsInt("-pc_gasm_total_subdomains", "Total number of subdomains across communicator", "PCGASMSetTotalSubdomains", osm->N, &blocks, &flg));
874:   if (flg) PetscCall(PCGASMSetTotalSubdomains(pc, blocks));
875:   PetscCall(PetscOptionsInt("-pc_gasm_overlap", "Number of overlapping degrees of freedom", "PCGASMSetOverlap", osm->overlap, &ovl, &flg));
876:   if (flg) {
877:     PetscCall(PCGASMSetOverlap(pc, ovl));
878:     osm->dm_subdomains = PETSC_FALSE;
879:   }
880:   flg = PETSC_FALSE;
881:   PetscCall(PetscOptionsEnum("-pc_gasm_type", "Type of restriction/extension", "PCGASMSetType", PCGASMTypes, (PetscEnum)osm->type, (PetscEnum *)&gasmtype, &flg));
882:   if (flg) PetscCall(PCGASMSetType(pc, gasmtype));
883:   PetscCall(PetscOptionsBool("-pc_gasm_use_hierachical_partitioning", "use hierarchical partitioning", NULL, osm->hierarchicalpartitioning, &osm->hierarchicalpartitioning, &flg));
884:   PetscOptionsHeadEnd();
885:   PetscFunctionReturn(PETSC_SUCCESS);
886: }

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

891:   Logically Collective

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

897:   Level: beginner

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

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

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

914:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
915:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
916:   osm->N             = N;
917:   osm->n             = PETSC_DETERMINE;
918:   osm->nmax          = PETSC_DETERMINE;
919:   osm->dm_subdomains = PETSC_FALSE;
920:   PetscFunctionReturn(PETSC_SUCCESS);
921: }

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

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

932:   PetscCall(PCGASMDestroySubdomains(osm->n, &osm->iis, &osm->ois));
933:   osm->iis = osm->ois = NULL;
934:   osm->n              = n;
935:   osm->N              = PETSC_DETERMINE;
936:   osm->nmax           = PETSC_DETERMINE;
937:   if (ois) {
938:     PetscCall(PetscMalloc1(n, &osm->ois));
939:     for (i = 0; i < n; i++) {
940:       PetscCall(PetscObjectReference((PetscObject)ois[i]));
941:       osm->ois[i] = ois[i];
942:     }
943:     /*
944:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
945:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
946:     */
947:     osm->overlap = -1;
948:     /* inner subdomains must be provided  */
949:     PetscCheck(iis, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "inner indices have to be provided ");
950:   } /* end if */
951:   if (iis) {
952:     PetscCall(PetscMalloc1(n, &osm->iis));
953:     for (i = 0; i < n; i++) {
954:       PetscCall(PetscObjectReference((PetscObject)iis[i]));
955:       osm->iis[i] = iis[i];
956:     }
957:     if (!ois) {
958:       osm->ois = NULL;
959:       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
960:     }
961:   }
962:   if (PetscDefined(USE_DEBUG)) {
963:     PetscInt        j, rstart, rend, *covered, lsize;
964:     const PetscInt *indices;
965:     /* check if the inner indices cover and only cover the local portion of the preconditioning matrix */
966:     PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
967:     PetscCall(PetscCalloc1(rend - rstart, &covered));
968:     /* check if the current MPI rank owns indices from others */
969:     for (i = 0; i < n; i++) {
970:       PetscCall(ISGetIndices(osm->iis[i], &indices));
971:       PetscCall(ISGetLocalSize(osm->iis[i], &lsize));
972:       for (j = 0; j < lsize; j++) {
973:         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]);
974:         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]);
975:         covered[indices[j] - rstart] = 1;
976:       }
977:       PetscCall(ISRestoreIndices(osm->iis[i], &indices));
978:     }
979:     /* check if we miss any indices */
980:     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);
981:     PetscCall(PetscFree(covered));
982:   }
983:   if (iis) osm->user_subdomains = PETSC_TRUE;
984:   PetscFunctionReturn(PETSC_SUCCESS);
985: }

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

991:   PetscFunctionBegin;
992:   PetscCheck(ovl >= 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap value requested");
993:   PetscCheck(!pc->setupcalled || ovl == osm->overlap, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "PCGASMSetOverlap() should be called before PCSetUp().");
994:   if (!pc->setupcalled) osm->overlap = ovl;
995:   PetscFunctionReturn(PETSC_SUCCESS);
996: }

998: static PetscErrorCode PCGASMSetType_GASM(PC pc, PCGASMType type)
999: {
1000:   PC_GASM *osm = (PC_GASM *)pc->data;

1002:   PetscFunctionBegin;
1003:   osm->type     = type;
1004:   osm->type_set = PETSC_TRUE;
1005:   PetscFunctionReturn(PETSC_SUCCESS);
1006: }

1008: static PetscErrorCode PCGASMSetSortIndices_GASM(PC pc, PetscBool doSort)
1009: {
1010:   PC_GASM *osm = (PC_GASM *)pc->data;

1012:   PetscFunctionBegin;
1013:   osm->sort_indices = doSort;
1014:   PetscFunctionReturn(PETSC_SUCCESS);
1015: }

1017: /*
1018:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
1019:         In particular, it would upset the global subdomain number calculation.
1020: */
1021: static PetscErrorCode PCGASMGetSubKSP_GASM(PC pc, PetscInt *n, PetscInt *first, KSP **ksp)
1022: {
1023:   PC_GASM *osm = (PC_GASM *)pc->data;

1025:   PetscFunctionBegin;
1026:   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");

1028:   if (n) *n = osm->n;
1029:   if (first) {
1030:     PetscCallMPI(MPI_Scan(&osm->n, first, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));
1031:     *first -= osm->n;
1032:   }
1033:   if (ksp) {
1034:     /* Assume that local solves are now different; not necessarily
1035:        true, though!  This flag is used only for PCView_GASM() */
1036:     *ksp                        = osm->ksp;
1037:     osm->same_subdomain_solvers = PETSC_FALSE;
1038:   }
1039:   PetscFunctionReturn(PETSC_SUCCESS);
1040: } /* PCGASMGetSubKSP_GASM() */

1042: /*@C
1043:   PCGASMSetSubdomains - Sets the subdomains for this MPI rank
1044:   for the additive Schwarz preconditioner with multiple MPI ranks per subdomain, `PCGASM`

1046:   Collective

1048:   Input Parameters:
1049: + pc  - the preconditioner object
1050: . n   - the number of subdomains for this MPI rank
1051: . iis - the index sets that define the inner subdomains (or `NULL` for PETSc to determine subdomains)
1052: - ois - the index sets that define the outer subdomains (or `NULL` to use the same as `iis`, or to construct by expanding `iis` by
1053:           the requested overlap)

1055:   Level: advanced

1057:   Notes:
1058:   The `IS` indices use the parallel, global numbering of the vector entries.

1060:   Inner subdomains are those where the correction is applied.

1062:   Outer subdomains are those where the residual necessary to obtain the
1063:   corrections is obtained (see `PCGASMType` for the use of inner/outer subdomains).

1065:   Both inner and outer subdomains can extend over several MPI ranks.
1066:   This rank's portion of a subdomain is known as a local subdomain.

1068:   Inner subdomains can not overlap with each other, do not have any entities from remote ranks,
1069:   and  have to cover the entire local subdomain owned by the current rank. The index sets on each
1070:   rank should be ordered such that the ith local subdomain is connected to the ith remote subdomain
1071:   on another MPI rank.

1073:   By default the `PGASM` preconditioner uses 1 (local) subdomain per MPI rank.

1075:   The `iis` and `ois` arrays may be freed after this call using `PCGASMDestroySubdomains()`

1077: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMDestroySubdomains()`,
1078:           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1079: @*/
1080: PetscErrorCode PCGASMSetSubdomains(PC pc, PetscInt n, IS iis[], IS ois[])
1081: {
1082:   PC_GASM *osm = (PC_GASM *)pc->data;

1084:   PetscFunctionBegin;
1086:   PetscTryMethod(pc, "PCGASMSetSubdomains_C", (PC, PetscInt, IS[], IS[]), (pc, n, iis, ois));
1087:   osm->dm_subdomains = PETSC_FALSE;
1088:   PetscFunctionReturn(PETSC_SUCCESS);
1089: }

1091: /*@
1092:   PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
1093:   additive Schwarz preconditioner `PCGASM`.  Either all or no MPI ranks in the
1094:   pc communicator must call this routine.

1096:   Logically Collective

1098:   Input Parameters:
1099: + pc  - the preconditioner context
1100: - ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

1102:   Options Database Key:
1103: . -pc_gasm_overlap <overlap> - Sets overlap

1105:   Level: intermediate

1107:   Notes:
1108:   By default the `PCGASM` preconditioner uses 1 subdomain per rank.  To use
1109:   multiple subdomain per perocessor or "straddling" subdomains that intersect
1110:   multiple ranks use `PCGASMSetSubdomains()` (or option `-pc_gasm_total_subdomains` <n>).

1112:   The overlap defaults to 0, so if one desires that no additional
1113:   overlap be computed beyond what may have been set with a call to
1114:   `PCGASMSetSubdomains()`, then `ovl` must be set to be 0.  In particular, if one does
1115:   not explicitly set the subdomains in application code, then all overlap would be computed
1116:   internally by PETSc, and using an overlap of 0 would result in an `PCGASM`
1117:   variant that is equivalent to the block Jacobi preconditioner.

1119:   One can define initial index sets with any overlap via
1120:   `PCGASMSetSubdomains()`; the routine `PCGASMSetOverlap()` merely allows
1121:   PETSc to extend that overlap further, if desired.

1123: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1124:           `PCGASMCreateSubdomains2D()`, `PCGASMGetSubdomains()`
1125: @*/
1126: PetscErrorCode PCGASMSetOverlap(PC pc, PetscInt ovl)
1127: {
1128:   PC_GASM *osm = (PC_GASM *)pc->data;

1130:   PetscFunctionBegin;
1133:   PetscTryMethod(pc, "PCGASMSetOverlap_C", (PC, PetscInt), (pc, ovl));
1134:   osm->dm_subdomains = PETSC_FALSE;
1135:   PetscFunctionReturn(PETSC_SUCCESS);
1136: }

1138: /*@
1139:   PCGASMSetType - Sets the type of restriction and interpolation used
1140:   for local problems in the `PCGASM` additive Schwarz method.

1142:   Logically Collective

1144:   Input Parameters:
1145: + pc   - the preconditioner context
1146: - type - variant of `PCGASM`, one of
1147: .vb
1148:       `PC_GASM_BASIC`       - full interpolation and restriction
1149:       `PC_GASM_RESTRICT`    - full restriction, local MPI rank interpolation
1150:       `PC_GASM_INTERPOLATE` - full interpolation, local MPI rank restriction
1151:       `PC_GASM_NONE`        - local MPI rank restriction and interpolation
1152: .ve

1154:   Options Database Key:
1155: . -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASM` type

1157:   Level: intermediate

1159: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1160:           `PCGASMCreateSubdomains2D()`, `PCASM`, `PCASMSetType()`
1161: @*/
1162: PetscErrorCode PCGASMSetType(PC pc, PCGASMType type)
1163: {
1164:   PetscFunctionBegin;
1167:   PetscTryMethod(pc, "PCGASMSetType_C", (PC, PCGASMType), (pc, type));
1168:   PetscFunctionReturn(PETSC_SUCCESS);
1169: }

1171: /*@
1172:   PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

1174:   Logically Collective

1176:   Input Parameters:
1177: + pc     - the preconditioner context
1178: - doSort - sort the subdomain indices

1180:   Level: intermediate

1182: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`,
1183:           `PCGASMCreateSubdomains2D()`
1184: @*/
1185: PetscErrorCode PCGASMSetSortIndices(PC pc, PetscBool doSort)
1186: {
1187:   PetscFunctionBegin;
1190:   PetscTryMethod(pc, "PCGASMSetSortIndices_C", (PC, PetscBool), (pc, doSort));
1191:   PetscFunctionReturn(PETSC_SUCCESS);
1192: }

1194: /*@C
1195:   PCGASMGetSubKSP - Gets the local `KSP` contexts for all subdomains on
1196:   this MPI rank.

1198:   Collective iff first_local is requested

1200:   Input Parameter:
1201: . pc - the preconditioner context

1203:   Output Parameters:
1204: + n_local     - the number of blocks on this MPI rank or `NULL`
1205: . first_local - the global number of the first block on this rank or `NULL`,
1206:                  all ranks must request or all must pass `NULL`
1207: - ksp         - the array of `KSP` contexts

1209:   Level: advanced

1211:   Note:
1212:   After `PCGASMGetSubKSP()` the array of `KSP`es is not to be freed

1214:   Currently for some matrix implementations only 1 block per MPI process
1215:   is supported.

1217:   You must call `KSPSetUp()` before calling `PCGASMGetSubKSP()`.

1219: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`,
1220:           `PCGASMCreateSubdomains2D()`,
1221: @*/
1222: PetscErrorCode PCGASMGetSubKSP(PC pc, PetscInt *n_local, PetscInt *first_local, KSP *ksp[])
1223: {
1224:   PetscFunctionBegin;
1226:   PetscUseMethod(pc, "PCGASMGetSubKSP_C", (PC, PetscInt *, PetscInt *, KSP **), (pc, n_local, first_local, ksp));
1227:   PetscFunctionReturn(PETSC_SUCCESS);
1228: }

1230: /*MC
1231:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1232:            its own `KSP` object on a subset of MPI processes

1234:    Options Database Keys:
1235: +  -pc_gasm_total_subdomains <n>                   - Sets total number of local subdomains to be distributed among the MPI processes
1236: .  -pc_gasm_view_subdomains                        - activates the printing of subdomain indices in `PCView()`, -ksp_view or -snes_view
1237: .  -pc_gasm_print_subdomains                       - activates the printing of subdomain indices in `PCSetUp()`
1238: .  -pc_gasm_overlap <ovl>                          - Sets overlap by which to (automatically) extend local subdomains
1239: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets `PCGASMType`

1241:    Level: beginner

1243:    Notes:
1244:    To set options on the solvers for each block append `-sub_` to all the `KSP`, and `PC`
1245:    options database keys. For example, `-sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly`

1247:    To set the options on the solvers separate for each block call `PCGASMGetSubKSP()`
1248:    and set the options directly on the resulting `KSP` object (you can access its `PC`
1249:    with `KSPGetPC()`)

1251:    See {cite}`dryja1987additive` and {cite}`1sbg` for details on additive Schwarz algorithms

1253: .seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCASM`, `PCGASMType`, `PCGASMSetType()`,
1254:           `PCBJACOBI`, `PCGASMGetSubKSP()`, `PCGASMSetSubdomains()`,
1255:           `PCSetModifySubMatrices()`, `PCGASMSetOverlap()`, `PCGASMSetType()`
1256: M*/

1258: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1259: {
1260:   PC_GASM *osm;

1262:   PetscFunctionBegin;
1263:   PetscCall(PetscNew(&osm));

1265:   osm->N                        = PETSC_DETERMINE;
1266:   osm->n                        = PETSC_DECIDE;
1267:   osm->nmax                     = PETSC_DETERMINE;
1268:   osm->overlap                  = 0;
1269:   osm->ksp                      = NULL;
1270:   osm->gorestriction            = NULL;
1271:   osm->girestriction            = NULL;
1272:   osm->pctoouter                = NULL;
1273:   osm->gx                       = NULL;
1274:   osm->gy                       = NULL;
1275:   osm->x                        = NULL;
1276:   osm->y                        = NULL;
1277:   osm->pcx                      = NULL;
1278:   osm->pcy                      = NULL;
1279:   osm->permutationIS            = NULL;
1280:   osm->permutationP             = NULL;
1281:   osm->pcmat                    = NULL;
1282:   osm->ois                      = NULL;
1283:   osm->iis                      = NULL;
1284:   osm->pmat                     = NULL;
1285:   osm->type                     = PC_GASM_RESTRICT;
1286:   osm->same_subdomain_solvers   = PETSC_TRUE;
1287:   osm->sort_indices             = PETSC_TRUE;
1288:   osm->dm_subdomains            = PETSC_FALSE;
1289:   osm->hierarchicalpartitioning = PETSC_FALSE;

1291:   pc->data                 = (void *)osm;
1292:   pc->ops->apply           = PCApply_GASM;
1293:   pc->ops->matapply        = PCMatApply_GASM;
1294:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1295:   pc->ops->setup           = PCSetUp_GASM;
1296:   pc->ops->reset           = PCReset_GASM;
1297:   pc->ops->destroy         = PCDestroy_GASM;
1298:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1299:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1300:   pc->ops->view            = PCView_GASM;
1301:   pc->ops->applyrichardson = NULL;

1303:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSubdomains_C", PCGASMSetSubdomains_GASM));
1304:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetOverlap_C", PCGASMSetOverlap_GASM));
1305:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetType_C", PCGASMSetType_GASM));
1306:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMSetSortIndices_C", PCGASMSetSortIndices_GASM));
1307:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGASMGetSubKSP_C", PCGASMGetSubKSP_GASM));
1308:   PetscFunctionReturn(PETSC_SUCCESS);
1309: }

1311: PetscErrorCode PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1312: {
1313:   MatPartitioning mpart;
1314:   const char     *prefix;
1315:   PetscInt        i, j, rstart, rend, bs;
1316:   PetscBool       hasop, isbaij = PETSC_FALSE, foundpart = PETSC_FALSE;
1317:   Mat             Ad = NULL, adj;
1318:   IS              ispart, isnumb, *is;

1320:   PetscFunctionBegin;
1321:   PetscCheck(nloc >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "number of local subdomains must > 0, got nloc = %" PetscInt_FMT, nloc);

1323:   /* Get prefix, row distribution, and block size */
1324:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1325:   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
1326:   PetscCall(MatGetBlockSize(A, &bs));
1327:   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);

1329:   /* Get diagonal block from matrix if possible */
1330:   PetscCall(MatHasOperation(A, MATOP_GET_DIAGONAL_BLOCK, &hasop));
1331:   if (hasop) PetscCall(MatGetDiagonalBlock(A, &Ad));
1332:   if (Ad) {
1333:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQBAIJ, &isbaij));
1334:     if (!isbaij) PetscCall(PetscObjectBaseTypeCompare((PetscObject)Ad, MATSEQSBAIJ, &isbaij));
1335:   }
1336:   if (Ad && nloc > 1) {
1337:     PetscBool match, done;
1338:     /* Try to setup a good matrix partitioning if available */
1339:     PetscCall(MatPartitioningCreate(PETSC_COMM_SELF, &mpart));
1340:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mpart, prefix));
1341:     PetscCall(MatPartitioningSetFromOptions(mpart));
1342:     PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGCURRENT, &match));
1343:     if (!match) PetscCall(PetscObjectTypeCompare((PetscObject)mpart, MATPARTITIONINGSQUARE, &match));
1344:     if (!match) { /* assume a "good" partitioner is available */
1345:       PetscInt        na;
1346:       const PetscInt *ia, *ja;
1347:       PetscCall(MatGetRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1348:       if (done) {
1349:         /* Build adjacency matrix by hand. Unfortunately a call to
1350:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1351:            remove the block-aij structure and we cannot expect
1352:            MatPartitioning to split vertices as we need */
1353:         PetscInt        i, j, len, nnz, cnt, *iia = NULL, *jja = NULL;
1354:         const PetscInt *row;
1355:         nnz = 0;
1356:         for (i = 0; i < na; i++) { /* count number of nonzeros */
1357:           len = ia[i + 1] - ia[i];
1358:           row = ja + ia[i];
1359:           for (j = 0; j < len; j++) {
1360:             if (row[j] == i) { /* don't count diagonal */
1361:               len--;
1362:               break;
1363:             }
1364:           }
1365:           nnz += len;
1366:         }
1367:         PetscCall(PetscMalloc1(na + 1, &iia));
1368:         PetscCall(PetscMalloc1(nnz, &jja));
1369:         nnz    = 0;
1370:         iia[0] = 0;
1371:         for (i = 0; i < na; i++) { /* fill adjacency */
1372:           cnt = 0;
1373:           len = ia[i + 1] - ia[i];
1374:           row = ja + ia[i];
1375:           for (j = 0; j < len; j++) {
1376:             if (row[j] != i) jja[nnz + cnt++] = row[j]; /* if not diagonal */
1377:           }
1378:           nnz += cnt;
1379:           iia[i + 1] = nnz;
1380:         }
1381:         /* Partitioning of the adjacency matrix */
1382:         PetscCall(MatCreateMPIAdj(PETSC_COMM_SELF, na, na, iia, jja, NULL, &adj));
1383:         PetscCall(MatPartitioningSetAdjacency(mpart, adj));
1384:         PetscCall(MatPartitioningSetNParts(mpart, nloc));
1385:         PetscCall(MatPartitioningApply(mpart, &ispart));
1386:         PetscCall(ISPartitioningToNumbering(ispart, &isnumb));
1387:         PetscCall(MatDestroy(&adj));
1388:         foundpart = PETSC_TRUE;
1389:       }
1390:       PetscCall(MatRestoreRowIJ(Ad, 0, PETSC_TRUE, isbaij, &na, &ia, &ja, &done));
1391:     }
1392:     PetscCall(MatPartitioningDestroy(&mpart));
1393:   }
1394:   PetscCall(PetscMalloc1(nloc, &is));
1395:   if (!foundpart) {
1396:     /* Partitioning by contiguous chunks of rows */

1398:     PetscInt mbs   = (rend - rstart) / bs;
1399:     PetscInt start = rstart;
1400:     for (i = 0; i < nloc; i++) {
1401:       PetscInt count = (mbs / nloc + ((mbs % nloc) > i)) * bs;
1402:       PetscCall(ISCreateStride(PETSC_COMM_SELF, count, start, 1, &is[i]));
1403:       start += count;
1404:     }

1406:   } else {
1407:     /* Partitioning by adjacency of diagonal block  */

1409:     const PetscInt *numbering;
1410:     PetscInt       *count, nidx, *indices, *newidx, start = 0;
1411:     /* Get node count in each partition */
1412:     PetscCall(PetscMalloc1(nloc, &count));
1413:     PetscCall(ISPartitioningCount(ispart, nloc, count));
1414:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1415:       for (i = 0; i < nloc; i++) count[i] *= bs;
1416:     }
1417:     /* Build indices from node numbering */
1418:     PetscCall(ISGetLocalSize(isnumb, &nidx));
1419:     PetscCall(PetscMalloc1(nidx, &indices));
1420:     for (i = 0; i < nidx; i++) indices[i] = i; /* needs to be initialized */
1421:     PetscCall(ISGetIndices(isnumb, &numbering));
1422:     PetscCall(PetscSortIntWithPermutation(nidx, numbering, indices));
1423:     PetscCall(ISRestoreIndices(isnumb, &numbering));
1424:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1425:       PetscCall(PetscMalloc1(nidx * bs, &newidx));
1426:       for (i = 0; i < nidx; i++) {
1427:         for (j = 0; j < bs; j++) newidx[i * bs + j] = indices[i] * bs + j;
1428:       }
1429:       PetscCall(PetscFree(indices));
1430:       nidx *= bs;
1431:       indices = newidx;
1432:     }
1433:     /* Shift to get global indices */
1434:     for (i = 0; i < nidx; i++) indices[i] += rstart;

1436:     /* Build the index sets for each block */
1437:     for (i = 0; i < nloc; i++) {
1438:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count[i], &indices[start], PETSC_COPY_VALUES, &is[i]));
1439:       PetscCall(ISSort(is[i]));
1440:       start += count[i];
1441:     }

1443:     PetscCall(PetscFree(count));
1444:     PetscCall(PetscFree(indices));
1445:     PetscCall(ISDestroy(&isnumb));
1446:     PetscCall(ISDestroy(&ispart));
1447:   }
1448:   *iis = is;
1449:   PetscFunctionReturn(PETSC_SUCCESS);
1450: }

1452: PETSC_INTERN PetscErrorCode PCGASMCreateStraddlingSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1453: {
1454:   PetscFunctionBegin;
1455:   PetscCall(MatSubdomainsCreateCoalesce(A, N, n, iis));
1456:   PetscFunctionReturn(PETSC_SUCCESS);
1457: }

1459: /*@C
1460:   PCGASMCreateSubdomains - Creates `n` index sets defining `n` nonoverlapping subdomains on this MPI process for the `PCGASM` additive
1461:   Schwarz preconditioner for a any problem based on its matrix.

1463:   Collective

1465:   Input Parameters:
1466: + A - The global matrix operator
1467: - N - the number of global subdomains requested

1469:   Output Parameters:
1470: + n   - the number of subdomains created on this MPI rank
1471: - iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

1473:   Level: advanced

1475:   Notes:
1476:   When `N` >= A's communicator size, each subdomain is local -- contained within a single MPI process.
1477:   When `N` < size, the subdomains are 'straddling' (rank boundaries) and are no longer local.
1478:   The resulting subdomains can be use in `PCGASMSetSubdomains`(pc,n,iss,`NULL`).  The overlapping
1479:   outer subdomains will be automatically generated from these according to the requested amount of
1480:   overlap; this is currently supported only with local subdomains.

1482:   Use `PCGASMDestroySubdomains()` to free the array and the list of index sets.

1484: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMDestroySubdomains()`
1485: @*/
1486: PetscErrorCode PCGASMCreateSubdomains(Mat A, PetscInt N, PetscInt *n, IS *iis[])
1487: {
1488:   PetscMPIInt size;

1490:   PetscFunctionBegin;
1492:   PetscAssertPointer(iis, 4);

1494:   PetscCheck(N >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of subdomains must be > 0, N = %" PetscInt_FMT, N);
1495:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
1496:   if (N >= size) {
1497:     *n = N / size + (N % size);
1498:     PetscCall(PCGASMCreateLocalSubdomains(A, *n, iis));
1499:   } else {
1500:     PetscCall(PCGASMCreateStraddlingSubdomains(A, N, n, iis));
1501:   }
1502:   PetscFunctionReturn(PETSC_SUCCESS);
1503: }

1505: /*@C
1506:   PCGASMDestroySubdomains - Destroys the index sets created with
1507:   `PCGASMCreateSubdomains()` or `PCGASMCreateSubdomains2D()`. Should be
1508:   called after setting subdomains with `PCGASMSetSubdomains()`.

1510:   Collective

1512:   Input Parameters:
1513: + n   - the number of index sets
1514: . iis - the array of inner subdomains
1515: - ois - the array of outer subdomains, can be `NULL`

1517:   Level: intermediate

1519:   Note:
1520:   This is a convenience subroutine that walks each list,
1521:   destroys each `IS` on the list, and then frees the list. At the end the
1522:   list pointers are set to `NULL`.

1524: .seealso: [](ch_ksp), `PCGASM`, `PCGASMCreateSubdomains()`, `PCGASMSetSubdomains()`
1525: @*/
1526: PetscErrorCode PCGASMDestroySubdomains(PetscInt n, IS **iis, IS **ois)
1527: {
1528:   PetscInt i;

1530:   PetscFunctionBegin;
1531:   if (n <= 0) PetscFunctionReturn(PETSC_SUCCESS);
1532:   if (ois) {
1533:     PetscAssertPointer(ois, 3);
1534:     if (*ois) {
1535:       PetscAssertPointer(*ois, 3);
1536:       for (i = 0; i < n; i++) PetscCall(ISDestroy(&(*ois)[i]));
1537:       PetscCall(PetscFree((*ois)));
1538:     }
1539:   }
1540:   if (iis) {
1541:     PetscAssertPointer(iis, 2);
1542:     if (*iis) {
1543:       PetscAssertPointer(*iis, 2);
1544:       for (i = 0; i < n; i++) PetscCall(ISDestroy(&(*iis)[i]));
1545:       PetscCall(PetscFree((*iis)));
1546:     }
1547:   }
1548:   PetscFunctionReturn(PETSC_SUCCESS);
1549: }

1551: #define PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, xleft_loc, ylow_loc, xright_loc, yhigh_loc, n) \
1552:   do { \
1553:     PetscInt first_row = first / M, last_row = last / M + 1; \
1554:     /*                                                                                                    \
1555:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1556:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1557:      subdomain).                                                                                          \
1558:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1559:      of the intersection.                                                                                 \
1560:     */ \
1561:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */ \
1562:     *ylow_loc = PetscMax(first_row, ylow); \
1563:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1564:     *xleft_loc = *ylow_loc == first_row ? PetscMax(first % M, xleft) : xleft; \
1565:     /* yhigh_loc is the grid row above the last local subdomain element */ \
1566:     *yhigh_loc = PetscMin(last_row, yhigh); \
1567:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */ \
1568:     *xright_loc = *yhigh_loc == last_row ? PetscMin(xright, last % M) : xright; \
1569:     /* Now compute the size of the local subdomain n. */ \
1570:     *n = 0; \
1571:     if (*ylow_loc < *yhigh_loc) { \
1572:       PetscInt width = xright - xleft; \
1573:       *n += width * (*yhigh_loc - *ylow_loc - 1); \
1574:       *n += PetscMin(PetscMax(*xright_loc - xleft, 0), width); \
1575:       *n -= PetscMin(PetscMax(*xleft_loc - xleft, 0), width); \
1576:     } \
1577:   } while (0)

1579: /*@C
1580:   PCGASMCreateSubdomains2D - Creates the index sets for the `PCGASM` overlapping Schwarz
1581:   preconditioner for a two-dimensional problem on a regular grid.

1583:   Collective

1585:   Input Parameters:
1586: + pc       - the preconditioner context
1587: . M        - the global number of grid points in the x direction
1588: . N        - the global number of grid points in the y direction
1589: . Mdomains - the global number of subdomains in the x direction
1590: . Ndomains - the global number of subdomains in the y direction
1591: . dof      - degrees of freedom per node
1592: - overlap  - overlap in mesh lines

1594:   Output Parameters:
1595: + nsub - the number of local subdomains created
1596: . iis  - array of index sets defining inner (nonoverlapping) subdomains
1597: - ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains

1599:   Level: advanced

1601:   Note:
1602:   Use `PCGASMDestroySubdomains()` to free the index sets and the arrays

1604:   Fortran Notes:
1605:   The `IS` must be declared as an array of length long enough to hold `Nsub` entries

1607: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetSubdomains()`, `PCGASMGetSubKSP()`, `PCGASMSetOverlap()`, `PCASMCreateSubdomains2D()`,
1608:           `PCGASMDestroySubdomains()`
1609: @*/
1610: PetscErrorCode PCGASMCreateSubdomains2D(PC pc, PetscInt M, PetscInt N, PetscInt Mdomains, PetscInt Ndomains, PetscInt dof, PetscInt overlap, PetscInt *nsub, IS **iis, IS **ois)
1611: {
1612:   PetscMPIInt size, rank;
1613:   PetscInt    i, j;
1614:   PetscInt    maxheight, maxwidth;
1615:   PetscInt    xstart, xleft, xright, xleft_loc, xright_loc;
1616:   PetscInt    ystart, ylow, yhigh, ylow_loc, yhigh_loc;
1617:   PetscInt    x[2][2], y[2][2], n[2];
1618:   PetscInt    first, last;
1619:   PetscInt    nidx, *idx;
1620:   PetscInt    ii, jj, s, q, d;
1621:   PetscInt    k, kk;
1622:   PetscMPIInt color;
1623:   MPI_Comm    comm, subcomm;
1624:   IS        **xis = NULL, **is = ois, **is_local = iis;

1626:   PetscFunctionBegin;
1627:   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
1628:   PetscCallMPI(MPI_Comm_size(comm, &size));
1629:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1630:   PetscCall(MatGetOwnershipRange(pc->pmat, &first, &last));
1631:   PetscCheck((first % dof) == 0 && (last % dof) == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE,
1632:              "Matrix row partitioning unsuitable for domain decomposition: local row range (%" PetscInt_FMT ",%" PetscInt_FMT ") "
1633:              "does not respect the number of degrees of freedom per grid point %" PetscInt_FMT,
1634:              first, last, dof);

1636:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1637:   s      = 0;
1638:   ystart = 0;
1639:   for (j = 0; j < Ndomains; ++j) {
1640:     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1641:     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);
1642:     /* Vertical domain limits with an overlap. */
1643:     ylow   = PetscMax(ystart - overlap, 0);
1644:     yhigh  = PetscMin(ystart + maxheight + overlap, N);
1645:     xstart = 0;
1646:     for (i = 0; i < Mdomains; ++i) {
1647:       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1648:       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);
1649:       /* Horizontal domain limits with an overlap. */
1650:       xleft  = PetscMax(xstart - overlap, 0);
1651:       xright = PetscMin(xstart + maxwidth + overlap, M);
1652:       /*
1653:          Determine whether this subdomain intersects this rank's ownership range of pc->pmat.
1654:       */
1655:       PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1656:       if (nidx) ++s;
1657:       xstart += maxwidth;
1658:     } /* for (i = 0; i < Mdomains; ++i) */
1659:     ystart += maxheight;
1660:   } /* for (j = 0; j < Ndomains; ++j) */

1662:   /* Now we can allocate the necessary number of ISs. */
1663:   *nsub = s;
1664:   PetscCall(PetscMalloc1(*nsub, is));
1665:   PetscCall(PetscMalloc1(*nsub, is_local));
1666:   s      = 0;
1667:   ystart = 0;
1668:   for (j = 0; j < Ndomains; ++j) {
1669:     maxheight = N / Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1670:     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);
1671:     /* Vertical domain limits with an overlap. */
1672:     y[0][0] = PetscMax(ystart - overlap, 0);
1673:     y[0][1] = PetscMin(ystart + maxheight + overlap, N);
1674:     /* Vertical domain limits without an overlap. */
1675:     y[1][0] = ystart;
1676:     y[1][1] = PetscMin(ystart + maxheight, N);
1677:     xstart  = 0;
1678:     for (i = 0; i < Mdomains; ++i) {
1679:       maxwidth = M / Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1680:       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);
1681:       /* Horizontal domain limits with an overlap. */
1682:       x[0][0] = PetscMax(xstart - overlap, 0);
1683:       x[0][1] = PetscMin(xstart + maxwidth + overlap, M);
1684:       /* Horizontal domain limits without an overlap. */
1685:       x[1][0] = xstart;
1686:       x[1][1] = PetscMin(xstart + maxwidth, M);
1687:       /*
1688:          Determine whether this domain intersects this rank's ownership range of pc->pmat.
1689:          Do this twice: first for the domains with overlaps, and once without.
1690:          During the first pass create the subcommunicators, and use them on the second pass as well.
1691:       */
1692:       for (q = 0; q < 2; ++q) {
1693:         PetscBool split = PETSC_FALSE;
1694:         /*
1695:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1696:           according to whether the domain with an overlap or without is considered.
1697:         */
1698:         xleft  = x[q][0];
1699:         xright = x[q][1];
1700:         ylow   = y[q][0];
1701:         yhigh  = y[q][1];
1702:         PCGASMLocalSubdomainBounds2D(M, N, xleft, ylow, xright, yhigh, first, last, (&xleft_loc), (&ylow_loc), (&xright_loc), (&yhigh_loc), (&nidx));
1703:         nidx *= dof;
1704:         n[q] = nidx;
1705:         /*
1706:          Based on the counted number of indices in the local domain *with an overlap*,
1707:          construct a subcommunicator of all the MPI ranks supporting this domain.
1708:          Observe that a domain with an overlap might have nontrivial local support,
1709:          while the domain without an overlap might not.  Hence, the decision to participate
1710:          in the subcommunicator must be based on the domain with an overlap.
1711:          */
1712:         if (q == 0) {
1713:           if (nidx) color = 1;
1714:           else color = MPI_UNDEFINED;
1715:           PetscCallMPI(MPI_Comm_split(comm, color, rank, &subcomm));
1716:           split = PETSC_TRUE;
1717:         }
1718:         /*
1719:          Proceed only if the number of local indices *with an overlap* is nonzero.
1720:          */
1721:         if (n[0]) {
1722:           if (q == 0) xis = is;
1723:           if (q == 1) {
1724:             /*
1725:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1726:              Moreover, if the overlap is zero, the two ISs are identical.
1727:              */
1728:             if (overlap == 0) {
1729:               (*is_local)[s] = (*is)[s];
1730:               PetscCall(PetscObjectReference((PetscObject)(*is)[s]));
1731:               continue;
1732:             } else {
1733:               xis     = is_local;
1734:               subcomm = ((PetscObject)(*is)[s])->comm;
1735:             }
1736:           } /* if (q == 1) */
1737:           idx = NULL;
1738:           PetscCall(PetscMalloc1(nidx, &idx));
1739:           if (nidx) {
1740:             k = 0;
1741:             for (jj = ylow_loc; jj < yhigh_loc; ++jj) {
1742:               PetscInt x0 = (jj == ylow_loc) ? xleft_loc : xleft;
1743:               PetscInt x1 = (jj == yhigh_loc - 1) ? xright_loc : xright;
1744:               kk          = dof * (M * jj + x0);
1745:               for (ii = x0; ii < x1; ++ii) {
1746:                 for (d = 0; d < dof; ++d) idx[k++] = kk++;
1747:               }
1748:             }
1749:           }
1750:           PetscCall(ISCreateGeneral(subcomm, nidx, idx, PETSC_OWN_POINTER, (*xis) + s));
1751:           if (split) PetscCallMPI(MPI_Comm_free(&subcomm));
1752:         } /* if (n[0]) */
1753:       }   /* for (q = 0; q < 2; ++q) */
1754:       if (n[0]) ++s;
1755:       xstart += maxwidth;
1756:     } /* for (i = 0; i < Mdomains; ++i) */
1757:     ystart += maxheight;
1758:   } /* for (j = 0; j < Ndomains; ++j) */
1759:   PetscFunctionReturn(PETSC_SUCCESS);
1760: }

1762: /*@C
1763:   PCGASMGetSubdomains - Gets the subdomains supported on this MPI rank
1764:   for the `PCGASM` additive Schwarz preconditioner.

1766:   Not Collective

1768:   Input Parameter:
1769: . pc - the preconditioner context

1771:   Output Parameters:
1772: + n   - the number of subdomains for this MPI rank (default value = 1)
1773: . iis - the index sets that define the inner subdomains (without overlap) supported on this rank (can be `NULL`)
1774: - ois - the index sets that define the outer subdomains (with overlap) supported on this rank (can be `NULL`)

1776:   Level: advanced

1778:   Notes:
1779:   The user is responsible for destroying the `IS`s and freeing the returned arrays, this can be done with
1780:   `PCGASMDestroySubdomains()`

1782:   The `IS` numbering is in the parallel, global numbering of the vector.

1784: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`, `PCGASMCreateSubdomains2D()`,
1785:           `PCGASMSetSubdomains()`, `PCGASMGetSubmatrices()`, `PCGASMDestroySubdomains()`
1786: @*/
1787: PetscErrorCode PCGASMGetSubdomains(PC pc, PetscInt *n, IS *iis[], IS *ois[])
1788: {
1789:   PC_GASM  *osm;
1790:   PetscBool match;
1791:   PetscInt  i;

1793:   PetscFunctionBegin;
1795:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1796:   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1797:   osm = (PC_GASM *)pc->data;
1798:   if (n) *n = osm->n;
1799:   if (iis) PetscCall(PetscMalloc1(osm->n, iis));
1800:   if (ois) PetscCall(PetscMalloc1(osm->n, ois));
1801:   if (iis || ois) {
1802:     for (i = 0; i < osm->n; ++i) {
1803:       if (iis) (*iis)[i] = osm->iis[i];
1804:       if (ois) (*ois)[i] = osm->ois[i];
1805:     }
1806:   }
1807:   PetscFunctionReturn(PETSC_SUCCESS);
1808: }

1810: /*@C
1811:   PCGASMGetSubmatrices - Gets the local submatrices (for this MPI rank
1812:   only) for the `PCGASM` additive Schwarz preconditioner.

1814:   Not Collective

1816:   Input Parameter:
1817: . pc - the preconditioner context

1819:   Output Parameters:
1820: + n   - the number of matrices for this MPI rank (default value = 1)
1821: - mat - the matrices

1823:   Level: advanced

1825:   Note:
1826:   Matrices returned by this routine have the same communicators as the index sets (`IS`)
1827:   used to define subdomains in `PCGASMSetSubdomains()`

1829: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetOverlap()`, `PCGASMGetSubKSP()`,
1830:           `PCGASMCreateSubdomains2D()`, `PCGASMSetSubdomains()`, `PCGASMGetSubdomains()`
1831: @*/
1832: PetscErrorCode PCGASMGetSubmatrices(PC pc, PetscInt *n, Mat *mat[])
1833: {
1834:   PC_GASM  *osm;
1835:   PetscBool match;

1837:   PetscFunctionBegin;
1839:   PetscAssertPointer(n, 2);
1840:   if (mat) PetscAssertPointer(mat, 3);
1841:   PetscCheck(pc->setupcalled, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call after KSPSetUp() or PCSetUp().");
1842:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1843:   PetscCheck(match, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1844:   osm = (PC_GASM *)pc->data;
1845:   if (n) *n = osm->n;
1846:   if (mat) *mat = osm->pmat;
1847:   PetscFunctionReturn(PETSC_SUCCESS);
1848: }

1850: /*@
1851:   PCGASMSetUseDMSubdomains - Indicates whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible for `PCGASM`

1853:   Logically Collective

1855:   Input Parameters:
1856: + pc  - the preconditioner
1857: - flg - boolean indicating whether to use subdomains defined by the `DM`

1859:   Options Database Key:
1860: + -pc_gasm_dm_subdomains    - configure subdomains
1861: . -pc_gasm_overlap          - set overlap
1862: - -pc_gasm_total_subdomains - set number of subdomains

1864:   Level: intermediate

1866:   Note:
1867:   `PCGASMSetSubdomains()`, `PCGASMSetTotalSubdomains()` or `PCGASMSetOverlap()` take precedence over `PCGASMSetUseDMSubdomains()`,
1868:   so setting `PCGASMSetSubdomains()` with nontrivial subdomain ISs or any of `PCGASMSetTotalSubdomains()` and `PCGASMSetOverlap()`
1869:   automatically turns the latter off.

1871: .seealso: [](ch_ksp), `PCGASM`, `PCGASMGetUseDMSubdomains()`, `PCGASMSetSubdomains()`, `PCGASMSetOverlap()`
1872:           `PCGASMCreateSubdomains2D()`
1873: @*/
1874: PetscErrorCode PCGASMSetUseDMSubdomains(PC pc, PetscBool flg)
1875: {
1876:   PC_GASM  *osm = (PC_GASM *)pc->data;
1877:   PetscBool match;

1879:   PetscFunctionBegin;
1882:   PetscCheck(!pc->setupcalled, ((PetscObject)pc)->comm, PETSC_ERR_ARG_WRONGSTATE, "Not for a setup PC.");
1883:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1884:   if (match) {
1885:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) osm->dm_subdomains = flg;
1886:   }
1887:   PetscFunctionReturn(PETSC_SUCCESS);
1888: }

1890: /*@
1891:   PCGASMGetUseDMSubdomains - Returns flag indicating whether to use `DMCreateDomainDecomposition()` to define the subdomains, whenever possible with `PCGASM`

1893:   Not Collective

1895:   Input Parameter:
1896: . pc - the preconditioner

1898:   Output Parameter:
1899: . flg - boolean indicating whether to use subdomains defined by the `DM`

1901:   Level: intermediate

1903: .seealso: [](ch_ksp), `PCGASM`, `PCGASMSetUseDMSubdomains()`, `PCGASMSetOverlap()`
1904:           `PCGASMCreateSubdomains2D()`
1905: @*/
1906: PetscErrorCode PCGASMGetUseDMSubdomains(PC pc, PetscBool *flg)
1907: {
1908:   PC_GASM  *osm = (PC_GASM *)pc->data;
1909:   PetscBool match;

1911:   PetscFunctionBegin;
1913:   PetscAssertPointer(flg, 2);
1914:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCGASM, &match));
1915:   if (match) {
1916:     if (flg) *flg = osm->dm_subdomains;
1917:   }
1918:   PetscFunctionReturn(PETSC_SUCCESS);
1919: }