Actual source code: asm.c

  1: /*
  2:   This file defines an additive Schwarz preconditioner for any Mat implementation.

  4:   Note that each processor may have any number of subdomains. But in order to 
  5:   deal easily with the VecScatter(), we treat each processor as if it has the
  6:   same number of subdomains.

  8:        n - total number of true subdomains on all processors
  9:        n_local_true - actual number of subdomains on this processor
 10:        n_local = maximum over all processors of n_local_true
 11: */
 12:  #include src/ksp/pc/pcimpl.h

 14: typedef struct {
 15:   PetscInt   n,n_local,n_local_true;
 16:   PetscTruth is_flg;              /* flg set to 1 if the IS created in pcsetup */
 17:   PetscInt   overlap;             /* overlap requested by user */
 18:   KSP       *ksp;               /* linear solvers for each block */
 19:   VecScatter *scat;               /* mapping to subregion */
 20:   Vec        *x,*y;
 21:   IS         *is;                 /* index set that defines each subdomain */
 22:   Mat        *mat,*pmat;          /* mat is not currently used */
 23:   PCASMType  type;                /* use reduced interpolation, restriction or both */
 24:   PetscTruth type_set;            /* if user set this value (so won't change it for symmetric problems) */
 25:   PetscTruth same_local_solves;   /* flag indicating whether all local solvers are same */
 26:   PetscTruth inplace;             /* indicates that the sub-matrices are deleted after 
 27:                                      PCSetUpOnBlocks() is done. Similar to inplace 
 28:                                      factorization in the case of LU and ILU */
 29: } PC_ASM;

 33: static PetscErrorCode PCView_ASM(PC pc,PetscViewer viewer)
 34: {
 35:   PC_ASM         *jac = (PC_ASM*)pc->data;
 37:   PetscMPIInt    rank;
 38:   PetscInt       i;
 39:   const char     *cstring = 0;
 40:   PetscTruth     iascii,isstring;
 41:   PetscViewer    sviewer;


 45:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
 46:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_STRING,&isstring);
 47:   if (iascii) {
 48:     PetscViewerASCIIPrintf(viewer,"  Additive Schwarz: total subdomain blocks = %D, amount of overlap = %D\n",jac->n,jac->overlap);
 49:     if (jac->type == PC_ASM_NONE)             cstring = "limited restriction and interpolation (PC_ASM_NONE)";
 50:     else if (jac->type == PC_ASM_RESTRICT)    cstring = "full restriction (PC_ASM_RESTRICT)";
 51:     else if (jac->type == PC_ASM_INTERPOLATE) cstring = "full interpolation (PC_ASM_INTERPOLATE)";
 52:     else if (jac->type == PC_ASM_BASIC)       cstring = "full restriction and interpolation (PC_ASM_BASIC)";
 53:     else                                      cstring = "Unknown ASM type";
 54:     PetscViewerASCIIPrintf(viewer,"  Additive Schwarz: type - %s\n",cstring);
 55:     MPI_Comm_rank(pc->comm,&rank);
 56:     if (jac->same_local_solves) {
 57:       PetscViewerASCIIPrintf(viewer,"  Local solve is same for all blocks, in the following KSP and PC objects:\n");
 58:       PetscViewerGetSingleton(viewer,&sviewer);
 59:       if (!rank && jac->ksp) {
 60:         PetscViewerASCIIPushTab(viewer);
 61:         KSPView(jac->ksp[0],sviewer);
 62:         PetscViewerASCIIPopTab(viewer);
 63:       }
 64:       PetscViewerRestoreSingleton(viewer,&sviewer);
 65:     } else {
 66:       PetscViewerASCIIPrintf(viewer,"  Local solve info for each block is in the following KSP and PC objects:\n");
 67:       PetscViewerASCIISynchronizedPrintf(viewer,"[%d] number of local blocks = %D\n",rank,jac->n_local);
 68:       PetscViewerASCIIPushTab(viewer);
 69:       for (i=0; i<jac->n_local; i++) {
 70:         PetscViewerASCIISynchronizedPrintf(viewer,"[%d] local block number %D\n",rank,i);
 71:         PetscViewerGetSingleton(viewer,&sviewer);
 72:         KSPView(jac->ksp[i],sviewer);
 73:         PetscViewerRestoreSingleton(viewer,&sviewer);
 74:         if (i != jac->n_local-1) {
 75:           PetscViewerASCIISynchronizedPrintf(viewer,"- - - - - - - - - - - - - - - - - -\n");
 76:         }
 77:       }
 78:       PetscViewerASCIIPopTab(viewer);
 79:       PetscViewerFlush(viewer);
 80:     }
 81:   } else if (isstring) {
 82:     PetscViewerStringSPrintf(viewer," blks=%D, overlap=%D, type=%D",jac->n,jac->overlap,jac->type);
 83:     PetscViewerGetSingleton(viewer,&sviewer);
 84:       if (jac->ksp) {KSPView(jac->ksp[0],sviewer);}
 85:     PetscViewerGetSingleton(viewer,&sviewer);
 86:   } else {
 87:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for PCASM",((PetscObject)viewer)->type_name);
 88:   }
 89:   return(0);
 90: }

 94: static PetscErrorCode PCSetUp_ASM(PC pc)
 95: {
 96:   PC_ASM         *osm  = (PC_ASM*)pc->data;
 98:   PetscInt       i,m,n_local = osm->n_local,n_local_true = osm->n_local_true;
 99:   PetscInt       start,start_val,end_val,sz,bs;
100:   PetscMPIInt    size;
101:   MatReuse       scall = MAT_REUSE_MATRIX;
102:   IS             isl;
103:   KSP            ksp;
104:   PC             subpc;
105:   char           *prefix,*pprefix;
106:   Vec            vec;

109:   MatGetVecs(pc->pmat,&vec,0);
110:   if (!pc->setupcalled) {
111:     if (osm->n == PETSC_DECIDE && osm->n_local_true == PETSC_DECIDE) {
112:       /* no subdomains given, use one per processor */
113:       osm->n_local_true = osm->n_local = 1;
114:       MPI_Comm_size(pc->comm,&size);
115:       osm->n = size;
116:     } else if (osm->n == PETSC_DECIDE) { /* determine global number of subdomains */
117:       PetscInt inwork[2],outwork[2];
118:       inwork[0] = inwork[1] = osm->n_local_true;
119:       MPI_Allreduce(inwork,outwork,1,MPIU_2INT,PetscMaxSum_Op,pc->comm);
120:       osm->n_local = outwork[0];
121:       osm->n       = outwork[1];
122:     }
123:     n_local      = osm->n_local;
124:     n_local_true = osm->n_local_true;
125:     if (!osm->is){ /* build the index sets */
126:       PetscMalloc((n_local_true+1)*sizeof(IS **),&osm->is);
127:       MatGetOwnershipRange(pc->pmat,&start_val,&end_val);
128:       MatGetBlockSize(pc->pmat,&bs);
129:       sz    = end_val - start_val;
130:       start = start_val;
131:       if (end_val/bs*bs != end_val || start_val/bs*bs != start_val) {
132:         SETERRQ(PETSC_ERR_ARG_WRONG,"Bad distribution for matrix block size");
133:       }
134:       for (i=0; i<n_local_true; i++){
135:         size       =  ((sz/bs)/n_local_true + (((sz/bs) % n_local_true) > i))*bs;
136:          ISCreateStride(PETSC_COMM_SELF,size,start,1,&isl);
137:         start      += size;
138:         osm->is[i] =  isl;
139:       }
140:       osm->is_flg = PETSC_TRUE;
141:     }

143:     PetscMalloc((n_local_true+1)*sizeof(KSP **),&osm->ksp);
144:     PetscMalloc(n_local*sizeof(VecScatter **),&osm->scat);
145:     PetscMalloc(2*n_local*sizeof(Vec **),&osm->x);
146:     osm->y = osm->x + n_local;

148:     /*  Extend the "overlapping" regions by a number of steps  */
149:     MatIncreaseOverlap(pc->pmat,n_local_true,osm->is,osm->overlap);
150:     for (i=0; i<n_local_true; i++) {
151:       ISSort(osm->is[i]);
152:     }

154:     /* create the local work vectors and scatter contexts */
155:     for (i=0; i<n_local_true; i++) {
156:       ISGetLocalSize(osm->is[i],&m);
157:       VecCreateSeq(PETSC_COMM_SELF,m,&osm->x[i]);
158:       VecDuplicate(osm->x[i],&osm->y[i]);
159:       ISCreateStride(PETSC_COMM_SELF,m,0,1,&isl);
160:       VecScatterCreate(vec,osm->is[i],osm->x[i],isl,&osm->scat[i]);
161:       ISDestroy(isl);
162:     }
163:     for (i=n_local_true; i<n_local; i++) {
164:       VecCreateSeq(PETSC_COMM_SELF,0,&osm->x[i]);
165:       VecDuplicate(osm->x[i],&osm->y[i]);
166:       ISCreateStride(PETSC_COMM_SELF,0,0,1,&isl);
167:       VecScatterCreate(vec,isl,osm->x[i],isl,&osm->scat[i]);
168:       ISDestroy(isl);
169:     }

171:    /* 
172:        Create the local solvers.
173:     */
174:     for (i=0; i<n_local_true; i++) {
175:       KSPCreate(PETSC_COMM_SELF,&ksp);
176:       PetscLogObjectParent(pc,ksp);
177:       KSPSetType(ksp,KSPPREONLY);
178:       KSPGetPC(ksp,&subpc);
179:       PCGetOptionsPrefix(pc,&prefix);
180:       KSPSetOptionsPrefix(ksp,prefix);
181:       KSPAppendOptionsPrefix(ksp,"sub_");
182:       osm->ksp[i] = ksp;
183:     }
184:     scall = MAT_INITIAL_MATRIX;
185:   } else {
186:     /* 
187:        Destroy the blocks from the previous iteration
188:     */
189:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
190:       MatDestroyMatrices(osm->n_local_true,&osm->pmat);
191:       scall = MAT_INITIAL_MATRIX;
192:     }
193:   }

195:   /* extract out the submatrices */
196:   MatGetSubMatrices(pc->pmat,osm->n_local_true,osm->is,osm->is,scall,&osm->pmat);

198:   /* Return control to the user so that the submatrices can be modified (e.g., to apply
199:      different boundary conditions for the submatrices than for the global problem) */
200:   PCModifySubMatrices(pc,osm->n_local,osm->is,osm->is,osm->pmat,pc->modifysubmatricesP);

202:   /* loop over subdomains putting them into local ksp */
203:   PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
204:   for (i=0; i<n_local_true; i++) {
205:     PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
206:     PetscLogObjectParent(pc,osm->pmat[i]);
207:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i],pc->flag);
208:     KSPSetFromOptions(osm->ksp[i]);
209:   }
210:   VecDestroy(vec);
211:   return(0);
212: }

216: static PetscErrorCode PCSetUpOnBlocks_ASM(PC pc)
217: {
218:   PC_ASM         *osm = (PC_ASM*)pc->data;
220:   PetscInt       i;

223:   for (i=0; i<osm->n_local_true; i++) {
224:     KSPSetUp(osm->ksp[i]);
225:   }
226:   /* 
227:      If inplace flag is set, then destroy the matrix after the setup
228:      on blocks is done.
229:   */
230:   if (osm->inplace && osm->n_local_true > 0) {
231:     MatDestroyMatrices(osm->n_local_true,&osm->pmat);
232:   }
233:   return(0);
234: }

238: static PetscErrorCode PCApply_ASM(PC pc,Vec x,Vec y)
239: {
240:   PC_ASM         *osm = (PC_ASM*)pc->data;
242:   PetscInt       i,n_local = osm->n_local,n_local_true = osm->n_local_true;
243:   PetscScalar    zero = 0.0;
244:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

247:   /*
248:        Support for limiting the restriction or interpolation to only local 
249:      subdomain values (leaving the other values 0). 
250:   */
251:   if (!(osm->type & PC_ASM_RESTRICT)) {
252:     forward = SCATTER_FORWARD_LOCAL;
253:     /* have to zero the work RHS since scatter may leave some slots empty */
254:     for (i=0; i<n_local; i++) {
255:       VecSet(&zero,osm->x[i]);
256:     }
257:   }
258:   if (!(osm->type & PC_ASM_INTERPOLATE)) {
259:     reverse = SCATTER_REVERSE_LOCAL;
260:   }

262:   for (i=0; i<n_local; i++) {
263:     VecScatterBegin(x,osm->x[i],INSERT_VALUES,forward,osm->scat[i]);
264:   }
265:   VecSet(&zero,y);
266:   /* do the local solves */
267:   for (i=0; i<n_local_true; i++) {
268:     VecScatterEnd(x,osm->x[i],INSERT_VALUES,forward,osm->scat[i]);
269:     KSPSolve(osm->ksp[i],osm->x[i],osm->y[i]);
270:     VecScatterBegin(osm->y[i],y,ADD_VALUES,reverse,osm->scat[i]);
271:   }
272:   /* handle the rest of the scatters that do not have local solves */
273:   for (i=n_local_true; i<n_local; i++) {
274:     VecScatterEnd(x,osm->x[i],INSERT_VALUES,forward,osm->scat[i]);
275:     VecScatterBegin(osm->y[i],y,ADD_VALUES,reverse,osm->scat[i]);
276:   }
277:   for (i=0; i<n_local; i++) {
278:     VecScatterEnd(osm->y[i],y,ADD_VALUES,reverse,osm->scat[i]);
279:   }
280:   return(0);
281: }

285: static PetscErrorCode PCApplyTranspose_ASM(PC pc,Vec x,Vec y)
286: {
287:   PC_ASM         *osm = (PC_ASM*)pc->data;
289:   PetscInt       i,n_local = osm->n_local,n_local_true = osm->n_local_true;
290:   PetscScalar    zero = 0.0;
291:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

294:   /*
295:        Support for limiting the restriction or interpolation to only local 
296:      subdomain values (leaving the other values 0).

298:        Note: these are reversed from the PCApply_ASM() because we are applying the 
299:      transpose of the three terms 
300:   */
301:   if (!(osm->type & PC_ASM_INTERPOLATE)) {
302:     forward = SCATTER_FORWARD_LOCAL;
303:     /* have to zero the work RHS since scatter may leave some slots empty */
304:     for (i=0; i<n_local; i++) {
305:       VecSet(&zero,osm->x[i]);
306:     }
307:   }
308:   if (!(osm->type & PC_ASM_RESTRICT)) {
309:     reverse = SCATTER_REVERSE_LOCAL;
310:   }

312:   for (i=0; i<n_local; i++) {
313:     VecScatterBegin(x,osm->x[i],INSERT_VALUES,forward,osm->scat[i]);
314:   }
315:   VecSet(&zero,y);
316:   /* do the local solves */
317:   for (i=0; i<n_local_true; i++) {
318:     VecScatterEnd(x,osm->x[i],INSERT_VALUES,forward,osm->scat[i]);
319:     KSPSolveTranspose(osm->ksp[i],osm->x[i],osm->y[i]);
320:     VecScatterBegin(osm->y[i],y,ADD_VALUES,reverse,osm->scat[i]);
321:   }
322:   /* handle the rest of the scatters that do not have local solves */
323:   for (i=n_local_true; i<n_local; i++) {
324:     VecScatterEnd(x,osm->x[i],INSERT_VALUES,forward,osm->scat[i]);
325:     VecScatterBegin(osm->y[i],y,ADD_VALUES,reverse,osm->scat[i]);
326:   }
327:   for (i=0; i<n_local; i++) {
328:     VecScatterEnd(osm->y[i],y,ADD_VALUES,reverse,osm->scat[i]);
329:   }
330:   return(0);
331: }

335: static PetscErrorCode PCDestroy_ASM(PC pc)
336: {
337:   PC_ASM         *osm = (PC_ASM*)pc->data;
339:   PetscInt       i;

342:   for (i=0; i<osm->n_local; i++) {
343:     VecScatterDestroy(osm->scat[i]);
344:     VecDestroy(osm->x[i]);
345:     VecDestroy(osm->y[i]);
346:   }
347:   if (osm->n_local_true > 0 && !osm->inplace && osm->pmat) {
348:     MatDestroyMatrices(osm->n_local_true,&osm->pmat);
349:   }
350:   if (osm->ksp) {
351:     for (i=0; i<osm->n_local_true; i++) {
352:       KSPDestroy(osm->ksp[i]);
353:     }
354:   }
355:   if (osm->is_flg) {
356:     for (i=0; i<osm->n_local_true; i++) {ISDestroy(osm->is[i]);}
357:     PetscFree(osm->is);
358:   }
359:   if (osm->ksp) {PetscFree(osm->ksp);}
360:   if (osm->scat) {PetscFree(osm->scat);}
361:   if (osm->x) {PetscFree(osm->x);}
362:   PetscFree(osm);
363:   return(0);
364: }

368: static PetscErrorCode PCSetFromOptions_ASM(PC pc)
369: {
370:   PC_ASM         *osm = (PC_ASM*)pc->data;
372:   PetscInt       blocks,ovl,indx;
373:   PetscTruth     flg,set,sym;
374:   const char     *type[] = {"none","restrict","interpolate","basic"};

377:   /* set the type to symmetric if matrix is symmetric */
378:   if (pc->pmat && !osm->type_set) {
379:     MatIsSymmetricKnown(pc->pmat,&set,&sym);
380:     if (set && sym) {
381:       osm->type = PC_ASM_BASIC;
382:     }
383:   }
384:   PetscOptionsHead("Additive Schwarz options");
385:     PetscOptionsInt("-pc_asm_blocks","Number of subdomains","PCASMSetTotalSubdomains",osm->n,&blocks,&flg);
386:     if (flg) {PCASMSetTotalSubdomains(pc,blocks,PETSC_NULL); }
387:     PetscOptionsInt("-pc_asm_overlap","Number of grid points overlap","PCASMSetOverlap",osm->overlap,&ovl,&flg);
388:     if (flg) {PCASMSetOverlap(pc,ovl); }
389:     PetscOptionsName("-pc_asm_in_place","Perform matrix factorization inplace","PCASMSetUseInPlace",&flg);
390:     if (flg) {PCASMSetUseInPlace(pc); }
391:     PetscOptionsEList("-pc_asm_type","Type of restriction/extension","PCASMSetType",type,4,type[1],&indx,&flg);
392:     if (flg) {
393:       PCASMSetType(pc,(PCASMType)indx);
394:     }
395:   PetscOptionsTail();
396:   return(0);
397: }

399: /*------------------------------------------------------------------------------------*/

404: PetscErrorCode PCASMSetLocalSubdomains_ASM(PC pc,PetscInt n,IS is[])
405: {
406:   PC_ASM *osm = (PC_ASM*)pc->data;

409:   if (n < 0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Each process must have 0 or more blocks");

411:   if (pc->setupcalled && n != osm->n_local_true) {
412:     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"PCASMSetLocalSubdomains() should be called before calling PCSetup().");
413:   }
414:   if (!pc->setupcalled){
415:     osm->n_local_true = n;
416:     osm->is           = is;
417:   }
418:   return(0);
419: }

425: PetscErrorCode PCASMSetTotalSubdomains_ASM(PC pc,PetscInt N,IS *is)
426: {
427:   PC_ASM         *osm = (PC_ASM*)pc->data;
429:   PetscMPIInt    rank,size;
430:   PetscInt       n;


434:   if (is) SETERRQ(PETSC_ERR_SUP,"Use PCASMSetLocalSubdomains() to set specific index sets\n\
435: they cannot be set globally yet.");

437:   /*
438:      Split the subdomains equally amoung all processors 
439:   */
440:   MPI_Comm_rank(pc->comm,&rank);
441:   MPI_Comm_size(pc->comm,&size);
442:   n = N/size + ((N % size) > rank);
443:   if (pc->setupcalled && n != osm->n_local_true) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"PCASMSetTotalSubdomains() should be called before PCSetup().");
444:   if (!pc->setupcalled){
445:     osm->n_local_true = n;
446:     osm->is           = 0;
447:   }
448:   return(0);
449: }

455: PetscErrorCode PCASMSetOverlap_ASM(PC pc,PetscInt ovl)
456: {
457:   PC_ASM *osm;

460:   if (ovl < 0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");

462:   osm               = (PC_ASM*)pc->data;
463:   osm->overlap      = ovl;
464:   return(0);
465: }

471: PetscErrorCode PCASMSetType_ASM(PC pc,PCASMType type)
472: {
473:   PC_ASM *osm;

476:   osm           = (PC_ASM*)pc->data;
477:   osm->type     = type;
478:   osm->type_set = PETSC_TRUE;
479:   return(0);
480: }

486: PetscErrorCode PCASMGetSubKSP_ASM(PC pc,PetscInt *n_local,PetscInt *first_local,KSP **ksp)
487: {
488:   PC_ASM         *jac = (PC_ASM*)pc->data;

492:   if (jac->n_local_true < 0) {
493:     SETERRQ(PETSC_ERR_ORDER,"Need to call PCSetUP() on PC (or KSPSetUp() on the outer KSP object) before calling here");
494:   }

496:   if (n_local)     *n_local     = jac->n_local_true;
497:   if (first_local) {
498:     MPI_Scan(&jac->n_local_true,first_local,1,MPIU_INT,MPI_SUM,pc->comm);
499:     *first_local -= jac->n_local_true;
500:   }
501:   *ksp                         = jac->ksp;
502:   jac->same_local_solves        = PETSC_FALSE; /* Assume that local solves are now different;
503:                                       not necessarily true though!  This flag is 
504:                                       used only for PCView_ASM() */
505:   return(0);
506: }

512: PetscErrorCode PCASMSetUseInPlace_ASM(PC pc)
513: {
514:   PC_ASM *dir;

517:   dir          = (PC_ASM*)pc->data;
518:   dir->inplace = PETSC_TRUE;
519:   return(0);
520: }

523: /*----------------------------------------------------------------------------*/
526: /*@
527:    PCASMSetUseInPlace - Tells the system to destroy the matrix after setup is done.

529:    Collective on PC

531:    Input Parameters:
532: .  pc - the preconditioner context

534:    Options Database Key:
535: .  -pc_asm_in_place - Activates in-place factorization

537:    Note:
538:    PCASMSetUseInplace() can only be used with the KSP method KSPPREONLY, and
539:    when the original matrix is not required during the Solve process.
540:    This destroys the matrix, early thus, saving on memory usage.

542:    Level: intermediate

544: .keywords: PC, set, factorization, direct, inplace, in-place, ASM

546: .seealso: PCILUSetUseInPlace(), PCLUSetUseInPlace ()
547: @*/
548: PetscErrorCode PCASMSetUseInPlace(PC pc)
549: {
550:   PetscErrorCode ierr,(*f)(PC);

554:   PetscObjectQueryFunction((PetscObject)pc,"PCASMSetUseInPlace_C",(void (**)(void))&f);
555:   if (f) {
556:     (*f)(pc);
557:   }
558:   return(0);
559: }
560: /*----------------------------------------------------------------------------*/

564: /*@C
565:     PCASMSetLocalSubdomains - Sets the local subdomains (for this processor
566:     only) for the additive Schwarz preconditioner. 

568:     Collective on PC 

570:     Input Parameters:
571: +   pc - the preconditioner context
572: .   n - the number of subdomains for this processor (default value = 1)
573: -   is - the index sets that define the subdomains for this processor
574:          (or PETSC_NULL for PETSc to determine subdomains)

576:     Notes:
577:     The IS numbering is in the parallel, global numbering of the vector.

579:     By default the ASM preconditioner uses 1 block per processor.  

581:     These index sets cannot be destroyed until after completion of the
582:     linear solves for which the ASM preconditioner is being used.

584:     Use PCASMSetTotalSubdomains() to set the subdomains for all processors.

586:     Level: advanced

588: .keywords: PC, ASM, set, local, subdomains, additive Schwarz

590: .seealso: PCASMSetTotalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
591:           PCASMCreateSubdomains2D(), PCASMGetLocalSubdomains()
592: @*/
593: PetscErrorCode PCASMSetLocalSubdomains(PC pc,PetscInt n,IS is[])
594: {
595:   PetscErrorCode ierr,(*f)(PC,PetscInt,IS[]);

599:   PetscObjectQueryFunction((PetscObject)pc,"PCASMSetLocalSubdomains_C",(void (**)(void))&f);
600:   if (f) {
601:     (*f)(pc,n,is);
602:   }
603:   return(0);
604: }

608: /*@C
609:     PCASMSetTotalSubdomains - Sets the subdomains for all processor for the 
610:     additive Schwarz preconditioner.  Either all or no processors in the
611:     PC communicator must call this routine, with the same index sets.

613:     Collective on PC

615:     Input Parameters:
616: +   pc - the preconditioner context
617: .   n - the number of subdomains for all processors
618: -   is - the index sets that define the subdomains for all processor
619:          (or PETSC_NULL for PETSc to determine subdomains)

621:     Options Database Key:
622:     To set the total number of subdomain blocks rather than specify the
623:     index sets, use the option
624: .    -pc_asm_blocks <blks> - Sets total blocks

626:     Notes:
627:     Currently you cannot use this to set the actual subdomains with the argument is.

629:     By default the ASM preconditioner uses 1 block per processor.  

631:     These index sets cannot be destroyed until after completion of the
632:     linear solves for which the ASM preconditioner is being used.

634:     Use PCASMSetLocalSubdomains() to set local subdomains.

636:     Level: advanced

638: .keywords: PC, ASM, set, total, global, subdomains, additive Schwarz

640: .seealso: PCASMSetLocalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
641:           PCASMCreateSubdomains2D()
642: @*/
643: PetscErrorCode PCASMSetTotalSubdomains(PC pc,PetscInt N,IS *is)
644: {
645:   PetscErrorCode ierr,(*f)(PC,PetscInt,IS *);

649:   PetscObjectQueryFunction((PetscObject)pc,"PCASMSetTotalSubdomains_C",(void (**)(void))&f);
650:   if (f) {
651:     (*f)(pc,N,is);
652:   }
653:   return(0);
654: }

658: /*@
659:     PCASMSetOverlap - Sets the overlap between a pair of subdomains for the
660:     additive Schwarz preconditioner.  Either all or no processors in the
661:     PC communicator must call this routine. 

663:     Collective on PC

665:     Input Parameters:
666: +   pc  - the preconditioner context
667: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 1)

669:     Options Database Key:
670: .   -pc_asm_overlap <ovl> - Sets overlap

672:     Notes:
673:     By default the ASM preconditioner uses 1 block per processor.  To use
674:     multiple blocks per perocessor, see PCASMSetTotalSubdomains() and
675:     PCASMSetLocalSubdomains() (and the option -pc_asm_blocks <blks>).

677:     The overlap defaults to 1, so if one desires that no additional
678:     overlap be computed beyond what may have been set with a call to
679:     PCASMSetTotalSubdomains() or PCASMSetLocalSubdomains(), then ovl
680:     must be set to be 0.  In particular, if one does not explicitly set
681:     the subdomains an application code, then all overlap would be computed
682:     internally by PETSc, and using an overlap of 0 would result in an ASM 
683:     variant that is equivalent to the block Jacobi preconditioner.  

685:     Note that one can define initial index sets with any overlap via
686:     PCASMSetTotalSubdomains() or PCASMSetLocalSubdomains(); the routine
687:     PCASMSetOverlap() merely allows PETSc to extend that overlap further
688:     if desired.

690:     Level: intermediate

692: .keywords: PC, ASM, set, overlap

694: .seealso: PCASMSetTotalSubdomains(), PCASMSetLocalSubdomains(), PCASMGetSubKSP(),
695:           PCASMCreateSubdomains2D(), PCASMGetLocalSubdomains()
696: @*/
697: PetscErrorCode PCASMSetOverlap(PC pc,PetscInt ovl)
698: {
699:   PetscErrorCode ierr,(*f)(PC,PetscInt);

703:   PetscObjectQueryFunction((PetscObject)pc,"PCASMSetOverlap_C",(void (**)(void))&f);
704:   if (f) {
705:     (*f)(pc,ovl);
706:   }
707:   return(0);
708: }

712: /*@
713:     PCASMSetType - Sets the type of restriction and interpolation used
714:     for local problems in the additive Schwarz method.

716:     Collective on PC

718:     Input Parameters:
719: +   pc  - the preconditioner context
720: -   type - variant of ASM, one of
721: .vb
722:       PC_ASM_BASIC       - full interpolation and restriction
723:       PC_ASM_RESTRICT    - full restriction, local processor interpolation
724:       PC_ASM_INTERPOLATE - full interpolation, local processor restriction
725:       PC_ASM_NONE        - local processor restriction and interpolation
726: .ve

728:     Options Database Key:
729: .   -pc_asm_type [basic,restrict,interpolate,none] - Sets ASM type

731:     Level: intermediate

733: .keywords: PC, ASM, set, type

735: .seealso: PCASMSetTotalSubdomains(), PCASMSetTotalSubdomains(), PCASMGetSubKSP(),
736:           PCASMCreateSubdomains2D()
737: @*/
738: PetscErrorCode PCASMSetType(PC pc,PCASMType type)
739: {
740:   PetscErrorCode ierr,(*f)(PC,PCASMType);

744:   PetscObjectQueryFunction((PetscObject)pc,"PCASMSetType_C",(void (**)(void))&f);
745:   if (f) {
746:     (*f)(pc,type);
747:   }
748:   return(0);
749: }

753: /*@C
754:    PCASMGetSubKSP - Gets the local KSP contexts for all blocks on
755:    this processor.
756:    
757:    Collective on PC iff first_local is requested

759:    Input Parameter:
760: .  pc - the preconditioner context

762:    Output Parameters:
763: +  n_local - the number of blocks on this processor or PETSC_NULL
764: .  first_local - the global number of the first block on this processor or PETSC_NULL,
765:                  all processors must request or all must pass PETSC_NULL
766: -  ksp - the array of KSP contexts

768:    Note:  
769:    After PCASMGetSubKSP() the array of KSPes is not to be freed

771:    Currently for some matrix implementations only 1 block per processor 
772:    is supported.
773:    
774:    You must call KSPSetUp() before calling PCASMGetSubKSP().

776:    Level: advanced

778: .keywords: PC, ASM, additive Schwarz, get, sub, KSP, context

780: .seealso: PCASMSetTotalSubdomains(), PCASMSetTotalSubdomains(), PCASMSetOverlap(),
781:           PCASMCreateSubdomains2D(),
782: @*/
783: PetscErrorCode PCASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
784: {
785:   PetscErrorCode ierr,(*f)(PC,PetscInt*,PetscInt*,KSP **);

790:   PetscObjectQueryFunction((PetscObject)pc,"PCASMGetSubKSP_C",(void (**)(void))&f);
791:   if (f) {
792:     (*f)(pc,n_local,first_local,ksp);
793:   } else {
794:     SETERRQ(PETSC_ERR_ARG_WRONG,"Cannot get subksp for this type of PC");
795:   }

797:  return(0);
798: }

800: /* -------------------------------------------------------------------------------------*/
801: /*MC
802:    PCASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with 
803:            its own KSP object.

805:    Options Database Keys:
806: +  -pc_asm_truelocal - Activates PCASMSetUseTrueLocal()
807: .  -pc_asm_in_place - Activates in-place factorization
808: .  -pc_asm_blocks <blks> - Sets total blocks
809: .  -pc_asm_overlap <ovl> - Sets overlap
810: -  -pc_asm_type [basic,restrict,interpolate,none] - Sets ASM type

812:      IMPORTANT: If you run with, for example, 3 blocks on 1 processor or 3 blocks on 3 processors you 
813:       will get a different convergence rate due to the default option of -pc_asm_type restrict. Use
814:       -pc_asm_type basic to use the standard ASM. 

816:    Notes: Each processor can have one or more blocks, but a block cannot be shared by more
817:      than one processor. Defaults to one block per processor.

819:      To set options on the solvers for each block append -sub_ to all the KSP, and PC
820:         options database keys. For example, -sub_pc_type ilu -sub_pc_ilu_levels 1 -sub_ksp_type preonly
821:         
822:      To set the options on the solvers seperate for each block call PCASMGetSubKSP()
823:          and set the options directly on the resulting KSP object (you can access its PC
824:          with KSPGetPC())


827:    Level: beginner

829:    Concepts: additive Schwarz method

831: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
832:            PCBJACOBI, PCASMSetUseTrueLocal(), PCASMGetSubKSP(), PCASMSetLocalSubdomains(),
833:            PCASMSetTotalSubdomains(), PCSetModifySubmatrices(), PCASMSetOverlap(), PCASMSetType(),
834:            PCASMSetUseInPlace()
835: M*/

840: PetscErrorCode PCCreate_ASM(PC pc)
841: {
843:   PC_ASM         *osm;

846:   PetscNew(PC_ASM,&osm);
847:   PetscLogObjectMemory(pc,sizeof(PC_ASM));
848:   PetscMemzero(osm,sizeof(PC_ASM));
849:   osm->n                 = PETSC_DECIDE;
850:   osm->n_local           = 0;
851:   osm->n_local_true      = PETSC_DECIDE;
852:   osm->overlap           = 1;
853:   osm->is_flg            = PETSC_FALSE;
854:   osm->ksp              = 0;
855:   osm->scat              = 0;
856:   osm->is                = 0;
857:   osm->mat               = 0;
858:   osm->pmat              = 0;
859:   osm->type              = PC_ASM_RESTRICT;
860:   osm->same_local_solves = PETSC_TRUE;
861:   osm->inplace           = PETSC_FALSE;
862:   pc->data               = (void*)osm;

864:   pc->ops->apply             = PCApply_ASM;
865:   pc->ops->applytranspose    = PCApplyTranspose_ASM;
866:   pc->ops->setup             = PCSetUp_ASM;
867:   pc->ops->destroy           = PCDestroy_ASM;
868:   pc->ops->setfromoptions    = PCSetFromOptions_ASM;
869:   pc->ops->setuponblocks     = PCSetUpOnBlocks_ASM;
870:   pc->ops->view              = PCView_ASM;
871:   pc->ops->applyrichardson   = 0;

873:   PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASMSetLocalSubdomains_C","PCASMSetLocalSubdomains_ASM",
874:                     PCASMSetLocalSubdomains_ASM);
875:   PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASMSetTotalSubdomains_C","PCASMSetTotalSubdomains_ASM",
876:                     PCASMSetTotalSubdomains_ASM);
877:   PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASMSetOverlap_C","PCASMSetOverlap_ASM",
878:                     PCASMSetOverlap_ASM);
879:   PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASMSetType_C","PCASMSetType_ASM",
880:                     PCASMSetType_ASM);
881:   PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASMGetSubKSP_C","PCASMGetSubKSP_ASM",
882:                     PCASMGetSubKSP_ASM);
883: PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASMSetUseInPlace_C","PCASMSetUseInPlace_ASM",
884:                     PCASMSetUseInPlace_ASM);
885:   return(0);
886: }


892: /*@
893:    PCASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz 
894:    preconditioner for a two-dimensional problem on a regular grid.

896:    Not Collective

898:    Input Parameters:
899: +  m, n - the number of mesh points in the x and y directions
900: .  M, N - the number of subdomains in the x and y directions
901: .  dof - degrees of freedom per node
902: -  overlap - overlap in mesh lines

904:    Output Parameters:
905: +  Nsub - the number of subdomains created
906: -  is - the array of index sets defining the subdomains

908:    Note:
909:    Presently PCAMSCreateSubdomains2d() is valid only for sequential
910:    preconditioners.  More general related routines are
911:    PCASMSetTotalSubdomains() and PCASMSetLocalSubdomains().

913:    Level: advanced

915: .keywords: PC, ASM, additive Schwarz, create, subdomains, 2D, regular grid

917: .seealso: PCASMSetTotalSubdomains(), PCASMSetLocalSubdomains(), PCASMGetSubKSP(),
918:           PCASMSetOverlap()
919: @*/
920: PetscErrorCode PCASMCreateSubdomains2D(PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt dof,PetscInt overlap,PetscInt *Nsub,IS **is)
921: {
922:   PetscInt       i,j,height,width,ystart,xstart,yleft,yright,xleft,xright,loc_outter;
924:   PetscInt       nidx,*idx,loc,ii,jj,count;

927:   if (dof != 1) SETERRQ(PETSC_ERR_SUP," ");

929:   *Nsub = N*M;
930:   PetscMalloc((*Nsub)*sizeof(IS **),is);
931:   ystart = 0;
932:   loc_outter = 0;
933:   for (i=0; i<N; i++) {
934:     height = n/N + ((n % N) > i); /* height of subdomain */
935:     if (height < 2) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Too many N subdomains for mesh dimension n");
936:     yleft  = ystart - overlap; if (yleft < 0) yleft = 0;
937:     yright = ystart + height + overlap; if (yright > n) yright = n;
938:     xstart = 0;
939:     for (j=0; j<M; j++) {
940:       width = m/M + ((m % M) > j); /* width of subdomain */
941:       if (width < 2) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Too many M subdomains for mesh dimension m");
942:       xleft  = xstart - overlap; if (xleft < 0) xleft = 0;
943:       xright = xstart + width + overlap; if (xright > m) xright = m;
944:       nidx   = (xright - xleft)*(yright - yleft);
945:       PetscMalloc(nidx*sizeof(int),&idx);
946:       loc    = 0;
947:       for (ii=yleft; ii<yright; ii++) {
948:         count = m*ii + xleft;
949:         for (jj=xleft; jj<xright; jj++) {
950:           idx[loc++] = count++;
951:         }
952:       }
953:       ISCreateGeneral(PETSC_COMM_SELF,nidx,idx,(*is)+loc_outter++);
954:       PetscFree(idx);
955:       xstart += width;
956:     }
957:     ystart += height;
958:   }
959:   for (i=0; i<*Nsub; i++) { ISSort((*is)[i]); }
960:   return(0);
961: }

965: /*@C
966:     PCASMGetLocalSubdomains - Gets the local subdomains (for this processor
967:     only) for the additive Schwarz preconditioner. 

969:     Collective on PC 

971:     Input Parameter:
972: .   pc - the preconditioner context

974:     Output Parameters:
975: +   n - the number of subdomains for this processor (default value = 1)
976: -   is - the index sets that define the subdomains for this processor
977:          

979:     Notes:
980:     The IS numbering is in the parallel, global numbering of the vector.

982:     Level: advanced

984: .keywords: PC, ASM, set, local, subdomains, additive Schwarz

986: .seealso: PCASMSetTotalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
987:           PCASMCreateSubdomains2D(), PCASMSetLocalSubdomains(), PCASMGetLocalSubmatrices()
988: @*/
989: PetscErrorCode PCASMGetLocalSubdomains(PC pc,PetscInt *n,IS *is[])
990: {
991:   PC_ASM *osm;

996:   if (!pc->setupcalled) {
997:     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUP() or PCSetUp().");
998:   }

1000:   osm = (PC_ASM*)pc->data;
1001:   if (n)  *n = osm->n_local_true;
1002:   if (is) *is = osm->is;
1003:   return(0);
1004: }

1008: /*@C
1009:     PCASMGetLocalSubmatrices - Gets the local submatrices (for this processor
1010:     only) for the additive Schwarz preconditioner. 

1012:     Collective on PC 

1014:     Input Parameter:
1015: .   pc - the preconditioner context

1017:     Output Parameters:
1018: +   n - the number of matrices for this processor (default value = 1)
1019: -   mat - the matrices
1020:          

1022:     Level: advanced

1024: .keywords: PC, ASM, set, local, subdomains, additive Schwarz, block Jacobi

1026: .seealso: PCASMSetTotalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
1027:           PCASMCreateSubdomains2D(), PCASMSetLocalSubdomains(), PCASMGetLocalSubdomains()
1028: @*/
1029: PetscErrorCode PCASMGetLocalSubmatrices(PC pc,PetscInt *n,Mat *mat[])
1030: {
1031:   PC_ASM *osm;

1036:   if (!pc->setupcalled) {
1037:     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUP() or PCSetUp().");
1038:   }

1040:   osm = (PC_ASM*)pc->data;
1041:   if (n)   *n   = osm->n_local_true;
1042:   if (mat) *mat = osm->pmat;
1043:   return(0);
1044: }