Actual source code: fas.c
petsc-3.13.6 2020-09-29
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      1: /* Defines the basic SNES object */
      2:  #include <../src/snes/impls/fas/fasimpls.h>

      4: const char *const SNESFASTypes[] = {"MULTIPLICATIVE","ADDITIVE","FULL","KASKADE","SNESFASType","SNES_FAS",0};

      6: static PetscErrorCode SNESReset_FAS(SNES snes)
      7: {
      8:   SNES_FAS       *fas = (SNES_FAS*)snes->data;

     12:   SNESDestroy(&fas->smoothu);
     13:   SNESDestroy(&fas->smoothd);
     14:   MatDestroy(&fas->inject);
     15:   MatDestroy(&fas->interpolate);
     16:   MatDestroy(&fas->restrct);
     17:   VecDestroy(&fas->rscale);
     18:   VecDestroy(&fas->Xg);
     19:   VecDestroy(&fas->Fg);
     20:   if (fas->next) {SNESReset(fas->next);}
     21:   return(0);
     22: }

     24: static PetscErrorCode SNESDestroy_FAS(SNES snes)
     25: {
     26:   SNES_FAS       *fas = (SNES_FAS*)snes->data;

     30:   /* recursively resets and then destroys */
     31:   SNESReset_FAS(snes);
     32:   SNESDestroy(&fas->next);
     33:   PetscFree(fas);
     34:   return(0);
     35: }

     37: static PetscErrorCode SNESFASSetUpLineSearch_Private(SNES snes, SNES smooth)
     38: {
     39:   SNESLineSearch linesearch;
     40:   SNESLineSearch slinesearch;
     41:   void           *lsprectx,*lspostctx;
     42:   PetscErrorCode (*precheck)(SNESLineSearch,Vec,Vec,PetscBool*,void*);
     43:   PetscErrorCode (*postcheck)(SNESLineSearch,Vec,Vec,Vec,PetscBool*,PetscBool*,void*);

     47:   if (!snes->linesearch) return(0);
     48:   SNESGetLineSearch(snes,&linesearch);
     49:   SNESGetLineSearch(smooth,&slinesearch);
     50:   SNESLineSearchGetPreCheck(linesearch,&precheck,&lsprectx);
     51:   SNESLineSearchGetPostCheck(linesearch,&postcheck,&lspostctx);
     52:   SNESLineSearchSetPreCheck(slinesearch,precheck,lsprectx);
     53:   SNESLineSearchSetPostCheck(slinesearch,postcheck,lspostctx);
     54:   PetscObjectCopyFortranFunctionPointers((PetscObject)linesearch, (PetscObject)slinesearch);
     55:   return(0);
     56: }

     58: static PetscErrorCode SNESFASCycleSetUpSmoother_Private(SNES snes, SNES smooth)
     59: {
     60:   SNES_FAS       *fas = (SNES_FAS*) snes->data;

     64:   PetscObjectCopyFortranFunctionPointers((PetscObject)snes, (PetscObject)smooth);
     65:   SNESSetFromOptions(smooth);
     66:   SNESFASSetUpLineSearch_Private(snes, smooth);

     68:   PetscObjectReference((PetscObject)snes->vec_sol);
     69:   PetscObjectReference((PetscObject)snes->vec_sol_update);
     70:   PetscObjectReference((PetscObject)snes->vec_func);
     71:   smooth->vec_sol        = snes->vec_sol;
     72:   smooth->vec_sol_update = snes->vec_sol_update;
     73:   smooth->vec_func       = snes->vec_func;

     75:   if (fas->eventsmoothsetup) {PetscLogEventBegin(fas->eventsmoothsetup,smooth,0,0,0);}
     76:   SNESSetUp(smooth);
     77:   if (fas->eventsmoothsetup) {PetscLogEventEnd(fas->eventsmoothsetup,smooth,0,0,0);}
     78:   return(0);
     79: }

     81: static PetscErrorCode SNESSetUp_FAS(SNES snes)
     82: {
     83:   SNES_FAS       *fas = (SNES_FAS*) snes->data;
     85:   PetscInt       dm_levels;
     86:   SNES           next;
     87:   PetscBool      isFine, hasCreateRestriction, hasCreateInjection;

     90:   SNESFASCycleIsFine(snes, &isFine);
     91:   if (fas->usedmfornumberoflevels && isFine) {
     92:     DMGetRefineLevel(snes->dm,&dm_levels);
     93:     dm_levels++;
     94:     if (dm_levels > fas->levels) {
     95:       /* reset the number of levels */
     96:       SNESFASSetLevels(snes,dm_levels,NULL);
     97:       SNESSetFromOptions(snes);
     98:     }
     99:   }
    100:   SNESFASCycleGetCorrection(snes, &next);
    101:   if (!isFine) snes->gridsequence = 0; /* no grid sequencing inside the multigrid hierarchy! */

    103:   SNESSetWorkVecs(snes, 2); /* work vectors used for intergrid transfers */

    105:   /* set up the smoothers if they haven't already been set up */
    106:   if (!fas->smoothd) {
    107:     SNESFASCycleCreateSmoother_Private(snes, &fas->smoothd);
    108:   }

    110:   if (snes->dm) {
    111:     /* set the smoother DMs properly */
    112:     if (fas->smoothu) {SNESSetDM(fas->smoothu, snes->dm);}
    113:     SNESSetDM(fas->smoothd, snes->dm);
    114:     /* construct EVERYTHING from the DM -- including the progressive set of smoothers */
    115:     if (next) {
    116:       /* for now -- assume the DM and the evaluation functions have been set externally */
    117:       if (!next->dm) {
    118:         DMCoarsen(snes->dm, PetscObjectComm((PetscObject)next), &next->dm);
    119:         SNESSetDM(next, next->dm);
    120:       }
    121:       /* set the interpolation and restriction from the DM */
    122:       if (!fas->interpolate) {
    123:         DMCreateInterpolation(next->dm, snes->dm, &fas->interpolate, &fas->rscale);
    124:         if (!fas->restrct) {
    125:           DMHasCreateRestriction(next->dm, &hasCreateRestriction);
    126:           /* DM can create restrictions, use that */
    127:           if (hasCreateRestriction) {
    128:             DMCreateRestriction(next->dm, snes->dm, &fas->restrct);
    129:           } else {
    130:             PetscObjectReference((PetscObject)fas->interpolate);
    131:             fas->restrct = fas->interpolate;
    132:           }
    133:         }
    134:       }
    135:       /* set the injection from the DM */
    136:       if (!fas->inject) {
    137:         DMHasCreateInjection(next->dm, &hasCreateInjection);
    138:         if (hasCreateInjection) {
    139:           DMCreateInjection(next->dm, snes->dm, &fas->inject);
    140:         }
    141:       }
    142:     }
    143:   }

    145:   /*pass the smoother, function, and jacobian up to the next level if it's not user set already */
    146:   if (fas->galerkin) {
    147:     if (next) {
    148:       SNESSetFunction(next, NULL, SNESFASGalerkinFunctionDefault, next);
    149:     }
    150:     if (fas->smoothd && fas->level != fas->levels - 1) {
    151:       SNESSetFunction(fas->smoothd, NULL, SNESFASGalerkinFunctionDefault, snes);
    152:     }
    153:     if (fas->smoothu && fas->level != fas->levels - 1) {
    154:       SNESSetFunction(fas->smoothu, NULL, SNESFASGalerkinFunctionDefault, snes);
    155:     }
    156:   }

    158:   /* sets the down (pre) smoother's default norm and sets it from options */
    159:   if (fas->smoothd) {
    160:     if (fas->level == 0 && fas->levels != 1) {
    161:       SNESSetNormSchedule(fas->smoothd, SNES_NORM_NONE);
    162:     } else {
    163:       SNESSetNormSchedule(fas->smoothd, SNES_NORM_FINAL_ONLY);
    164:     }
    165:     SNESFASCycleSetUpSmoother_Private(snes, fas->smoothd);
    166:   }

    168:   /* sets the up (post) smoother's default norm and sets it from options */
    169:   if (fas->smoothu) {
    170:     if (fas->level != fas->levels - 1) {
    171:       SNESSetNormSchedule(fas->smoothu, SNES_NORM_NONE);
    172:     } else {
    173:       SNESSetNormSchedule(fas->smoothu, SNES_NORM_FINAL_ONLY);
    174:     }
    175:     SNESFASCycleSetUpSmoother_Private(snes, fas->smoothu);
    176:   }

    178:   if (next) {
    179:     /* gotta set up the solution vector for this to work */
    180:     if (!next->vec_sol) {SNESFASCreateCoarseVec(snes,&next->vec_sol);}
    181:     if (!next->vec_rhs) {SNESFASCreateCoarseVec(snes,&next->vec_rhs);}
    182:     PetscObjectCopyFortranFunctionPointers((PetscObject)snes, (PetscObject)next);
    183:     SNESFASSetUpLineSearch_Private(snes, next);
    184:     SNESSetUp(next);
    185:   }

    187:   /* setup FAS work vectors */
    188:   if (fas->galerkin) {
    189:     VecDuplicate(snes->vec_sol, &fas->Xg);
    190:     VecDuplicate(snes->vec_sol, &fas->Fg);
    191:   }
    192:   return(0);
    193: }

    195: static PetscErrorCode SNESSetFromOptions_FAS(PetscOptionItems *PetscOptionsObject,SNES snes)
    196: {
    197:   SNES_FAS       *fas   = (SNES_FAS*) snes->data;
    198:   PetscInt       levels = 1;
    199:   PetscBool      flg    = PETSC_FALSE, upflg = PETSC_FALSE, downflg = PETSC_FALSE, monflg = PETSC_FALSE, galerkinflg = PETSC_FALSE,continuationflg = PETSC_FALSE;
    201:   SNESFASType    fastype;
    202:   const char     *optionsprefix;
    203:   SNESLineSearch linesearch;
    204:   PetscInt       m, n_up, n_down;
    205:   SNES           next;
    206:   PetscBool      isFine;

    209:   SNESFASCycleIsFine(snes, &isFine);
    210:   PetscOptionsHead(PetscOptionsObject,"SNESFAS Options-----------------------------------");

    212:   /* number of levels -- only process most options on the finest level */
    213:   if (isFine) {
    214:     PetscOptionsInt("-snes_fas_levels", "Number of Levels", "SNESFASSetLevels", levels, &levels, &flg);
    215:     if (!flg && snes->dm) {
    216:       DMGetRefineLevel(snes->dm,&levels);
    217:       levels++;
    218:       fas->usedmfornumberoflevels = PETSC_TRUE;
    219:     }
    220:     SNESFASSetLevels(snes, levels, NULL);
    221:     fastype = fas->fastype;
    222:     PetscOptionsEnum("-snes_fas_type","FAS correction type","SNESFASSetType",SNESFASTypes,(PetscEnum)fastype,(PetscEnum*)&fastype,&flg);
    223:     if (flg) {
    224:       SNESFASSetType(snes, fastype);
    225:     }

    227:     SNESGetOptionsPrefix(snes, &optionsprefix);
    228:     PetscOptionsInt("-snes_fas_cycles","Number of cycles","SNESFASSetCycles",fas->n_cycles,&m,&flg);
    229:     if (flg) {
    230:       SNESFASSetCycles(snes, m);
    231:     }
    232:     PetscOptionsBool("-snes_fas_continuation","Corrected grid-sequence continuation","SNESFASSetContinuation",fas->continuation,&continuationflg,&flg);
    233:     if (flg) {
    234:       SNESFASSetContinuation(snes,continuationflg);
    235:     }

    237:     PetscOptionsBool("-snes_fas_galerkin", "Form coarse problems with Galerkin","SNESFASSetGalerkin",fas->galerkin,&galerkinflg,&flg);
    238:     if (flg) {
    239:       SNESFASSetGalerkin(snes, galerkinflg);
    240:     }

    242:     if (fas->fastype == SNES_FAS_FULL) {
    243:       PetscOptionsBool("-snes_fas_full_downsweep","Smooth on the initial down sweep for full FAS cycles","SNESFASFullSetDownSweep",fas->full_downsweep,&fas->full_downsweep,&flg);
    244:       if (flg) {SNESFASFullSetDownSweep(snes,fas->full_downsweep);}
    245:     }

    247:     PetscOptionsInt("-snes_fas_smoothup","Number of post-smoothing steps","SNESFASSetNumberSmoothUp",fas->max_up_it,&n_up,&upflg);

    249:     PetscOptionsInt("-snes_fas_smoothdown","Number of pre-smoothing steps","SNESFASSetNumberSmoothDown",fas->max_down_it,&n_down,&downflg);

    251:     {
    252:       PetscViewer viewer;
    253:       PetscViewerFormat format;
    254:       PetscOptionsGetViewer(PetscObjectComm((PetscObject)snes),((PetscObject) snes)->options,((PetscObject)snes)->prefix,"-snes_fas_monitor",&viewer,&format,&monflg);
    255:       if (monflg) {
    256:         PetscViewerAndFormat *vf;
    257:         PetscViewerAndFormatCreate(viewer,format,&vf);
    258:         PetscObjectDereference((PetscObject)viewer);
    259:         SNESFASSetMonitor(snes,vf,PETSC_TRUE);
    260:       }
    261:     }
    262:     flg    = PETSC_FALSE;
    263:     monflg = PETSC_TRUE;
    264:     PetscOptionsBool("-snes_fas_log","Log times for each FAS level","SNESFASSetLog",monflg,&monflg,&flg);
    265:     if (flg) {SNESFASSetLog(snes,monflg);}
    266:   }

    268:   PetscOptionsTail();

    270:   /* setup from the determined types if there is no pointwise procedure or smoother defined */
    271:   if (upflg) {
    272:     SNESFASSetNumberSmoothUp(snes,n_up);
    273:   }
    274:   if (downflg) {
    275:     SNESFASSetNumberSmoothDown(snes,n_down);
    276:   }

    278:   /* set up the default line search for coarse grid corrections */
    279:   if (fas->fastype == SNES_FAS_ADDITIVE) {
    280:     if (!snes->linesearch) {
    281:       SNESGetLineSearch(snes, &linesearch);
    282:       SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);
    283:     }
    284:   }

    286:   /* recursive option setting for the smoothers */
    287:   SNESFASCycleGetCorrection(snes, &next);
    288:   if (next) {SNESSetFromOptions(next);}
    289:   return(0);
    290: }

    292:  #include <petscdraw.h>
    293: static PetscErrorCode SNESView_FAS(SNES snes, PetscViewer viewer)
    294: {
    295:   SNES_FAS       *fas = (SNES_FAS*) snes->data;
    296:   PetscBool      isFine,iascii,isdraw;
    297:   PetscInt       i;
    299:   SNES           smoothu, smoothd, levelsnes;

    302:   SNESFASCycleIsFine(snes, &isFine);
    303:   if (isFine) {
    304:     PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    305:     PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);
    306:     if (iascii) {
    307:       PetscViewerASCIIPrintf(viewer, "  type is %s, levels=%D, cycles=%D\n",  SNESFASTypes[fas->fastype], fas->levels, fas->n_cycles);
    308:       if (fas->galerkin) {
    309:         PetscViewerASCIIPrintf(viewer,"  Using Galerkin computed coarse grid function evaluation\n");
    310:       } else {
    311:         PetscViewerASCIIPrintf(viewer,"  Not using Galerkin computed coarse grid function evaluation\n");
    312:       }
    313:       for (i=0; i<fas->levels; i++) {
    314:         SNESFASGetCycleSNES(snes, i, &levelsnes);
    315:         SNESFASCycleGetSmootherUp(levelsnes, &smoothu);
    316:         SNESFASCycleGetSmootherDown(levelsnes, &smoothd);
    317:         if (!i) {
    318:           PetscViewerASCIIPrintf(viewer,"  Coarse grid solver -- level %D -------------------------------\n",i);
    319:         } else {
    320:           PetscViewerASCIIPrintf(viewer,"  Down solver (pre-smoother) on level %D -------------------------------\n",i);
    321:         }
    322:         PetscViewerASCIIPushTab(viewer);
    323:         if (smoothd) {
    324:           SNESView(smoothd,viewer);
    325:         } else {
    326:           PetscViewerASCIIPrintf(viewer,"Not yet available\n");
    327:         }
    328:         PetscViewerASCIIPopTab(viewer);
    329:         if (i && (smoothd == smoothu)) {
    330:           PetscViewerASCIIPrintf(viewer,"  Up solver (post-smoother) same as down solver (pre-smoother)\n");
    331:         } else if (i) {
    332:           PetscViewerASCIIPrintf(viewer,"  Up solver (post-smoother) on level %D -------------------------------\n",i);
    333:           PetscViewerASCIIPushTab(viewer);
    334:           if (smoothu) {
    335:             SNESView(smoothu,viewer);
    336:           } else {
    337:             PetscViewerASCIIPrintf(viewer,"Not yet available\n");
    338:           }
    339:           PetscViewerASCIIPopTab(viewer);
    340:         }
    341:       }
    342:     } else if (isdraw) {
    343:       PetscDraw draw;
    344:       PetscReal x,w,y,bottom,th,wth;
    345:       SNES_FAS  *curfas = fas;
    346:       PetscViewerDrawGetDraw(viewer,0,&draw);
    347:       PetscDrawGetCurrentPoint(draw,&x,&y);
    348:       PetscDrawStringGetSize(draw,&wth,&th);
    349:       bottom = y - th;
    350:       while (curfas) {
    351:         if (!curfas->smoothu) {
    352:           PetscDrawPushCurrentPoint(draw,x,bottom);
    353:           if (curfas->smoothd) SNESView(curfas->smoothd,viewer);
    354:           PetscDrawPopCurrentPoint(draw);
    355:         } else {
    356:           w    = 0.5*PetscMin(1.0-x,x);
    357:           PetscDrawPushCurrentPoint(draw,x-w,bottom);
    358:           if (curfas->smoothd) SNESView(curfas->smoothd,viewer);
    359:           PetscDrawPopCurrentPoint(draw);
    360:           PetscDrawPushCurrentPoint(draw,x+w,bottom);
    361:           if (curfas->smoothu) SNESView(curfas->smoothu,viewer);
    362:           PetscDrawPopCurrentPoint(draw);
    363:         }
    364:         /* this is totally bogus but we have no way of knowing how low the previous one was draw to */
    365:         bottom -= 5*th;
    366:         if (curfas->next) curfas = (SNES_FAS*)curfas->next->data;
    367:         else curfas = NULL;
    368:       }
    369:     }
    370:   }
    371:   return(0);
    372: }

    374: /*
    375: Defines the action of the downsmoother
    376:  */
    377: static PetscErrorCode SNESFASDownSmooth_Private(SNES snes, Vec B, Vec X, Vec F, PetscReal *fnorm)
    378: {
    379:   PetscErrorCode      ierr;
    380:   SNESConvergedReason reason;
    381:   Vec                 FPC;
    382:   SNES                smoothd;
    383:   PetscBool           flg;
    384:   SNES_FAS            *fas = (SNES_FAS*) snes->data;

    387:   SNESFASCycleGetSmootherDown(snes, &smoothd);
    388:   SNESSetInitialFunction(smoothd, F);
    389:   if (fas->eventsmoothsolve) {PetscLogEventBegin(fas->eventsmoothsolve,smoothd,B,X,0);}
    390:   SNESSolve(smoothd, B, X);
    391:   if (fas->eventsmoothsolve) {PetscLogEventEnd(fas->eventsmoothsolve,smoothd,B,X,0);}
    392:   /* check convergence reason for the smoother */
    393:   SNESGetConvergedReason(smoothd,&reason);
    394:   if (reason < 0 && !(reason == SNES_DIVERGED_MAX_IT || reason == SNES_DIVERGED_LOCAL_MIN || reason == SNES_DIVERGED_LINE_SEARCH)) {
    395:     snes->reason = SNES_DIVERGED_INNER;
    396:     return(0);
    397:   }

    399:   SNESGetFunction(smoothd, &FPC, NULL, NULL);
    400:   SNESGetAlwaysComputesFinalResidual(smoothd, &flg);
    401:   if (!flg) {
    402:     SNESComputeFunction(smoothd, X, FPC);
    403:   }
    404:   VecCopy(FPC, F);
    405:   if (fnorm) {VecNorm(F,NORM_2,fnorm);}
    406:   return(0);
    407: }

    410: /*
    411: Defines the action of the upsmoother
    412:  */
    413: static PetscErrorCode SNESFASUpSmooth_Private(SNES snes, Vec B, Vec X, Vec F, PetscReal *fnorm)
    414: {
    415:   PetscErrorCode      ierr;
    416:   SNESConvergedReason reason;
    417:   Vec                 FPC;
    418:   SNES                smoothu;
    419:   PetscBool           flg;
    420:   SNES_FAS            *fas = (SNES_FAS*) snes->data;

    423:   SNESFASCycleGetSmootherUp(snes, &smoothu);
    424:   if (fas->eventsmoothsolve) {PetscLogEventBegin(fas->eventsmoothsolve,smoothu,0,0,0);}
    425:   SNESSolve(smoothu, B, X);
    426:   if (fas->eventsmoothsolve) {PetscLogEventEnd(fas->eventsmoothsolve,smoothu,0,0,0);}
    427:   /* check convergence reason for the smoother */
    428:   SNESGetConvergedReason(smoothu,&reason);
    429:   if (reason < 0 && !(reason == SNES_DIVERGED_MAX_IT || reason == SNES_DIVERGED_LOCAL_MIN || reason == SNES_DIVERGED_LINE_SEARCH)) {
    430:     snes->reason = SNES_DIVERGED_INNER;
    431:     return(0);
    432:   }
    433:   SNESGetFunction(smoothu, &FPC, NULL, NULL);
    434:   SNESGetAlwaysComputesFinalResidual(smoothu, &flg);
    435:   if (!flg) {
    436:     SNESComputeFunction(smoothu, X, FPC);
    437:   }
    438:   VecCopy(FPC, F);
    439:   if (fnorm) {VecNorm(F,NORM_2,fnorm);}
    440:   return(0);
    441: }

    443: /*@
    444:    SNESFASCreateCoarseVec - create Vec corresponding to a state vector on one level coarser than current level

    446:    Collective

    448:    Input Arguments:
    449: .  snes - SNESFAS

    451:    Output Arguments:
    452: .  Xcoarse - vector on level one coarser than snes

    454:    Level: developer

    456: .seealso: SNESFASSetRestriction(), SNESFASRestrict()
    457: @*/
    458: PetscErrorCode SNESFASCreateCoarseVec(SNES snes,Vec *Xcoarse)
    459: {
    461:   SNES_FAS       *fas;

    466:   fas = (SNES_FAS*)snes->data;
    467:   if (fas->rscale) {
    468:     VecDuplicate(fas->rscale,Xcoarse);
    469:   } else if (fas->inject) {
    470:     MatCreateVecs(fas->inject,Xcoarse,NULL);
    471:   } else SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE,"Must set restriction or injection");
    472:   return(0);
    473: }

    475: /*@
    476:    SNESFASRestrict - restrict a Vec to the next coarser level

    478:    Collective

    480:    Input Arguments:
    481: +  fine - SNES from which to restrict
    482: -  Xfine - vector to restrict

    484:    Output Arguments:
    485: .  Xcoarse - result of restriction

    487:    Level: developer

    489: .seealso: SNESFASSetRestriction(), SNESFASSetInjection()
    490: @*/
    491: PetscErrorCode SNESFASRestrict(SNES fine,Vec Xfine,Vec Xcoarse)
    492: {
    494:   SNES_FAS       *fas;

    500:   fas = (SNES_FAS*)fine->data;
    501:   if (fas->inject) {
    502:     MatRestrict(fas->inject,Xfine,Xcoarse);
    503:   } else {
    504:     MatRestrict(fas->restrct,Xfine,Xcoarse);
    505:     VecPointwiseMult(Xcoarse,fas->rscale,Xcoarse);
    506:   }
    507:   return(0);
    508: }

    510: /*

    512: Performs the FAS coarse correction as:

    514: fine problem:   F(x) = b
    515: coarse problem: F^c(x^c) = b^c

    517: b^c = F^c(Rx) - R(F(x) - b)

    519:  */
    520: PetscErrorCode SNESFASCoarseCorrection(SNES snes, Vec X, Vec F, Vec X_new)
    521: {
    522:   PetscErrorCode      ierr;
    523:   Vec                 X_c, Xo_c, F_c, B_c;
    524:   SNESConvergedReason reason;
    525:   SNES                next;
    526:   Mat                 restrct, interpolate;
    527:   SNES_FAS            *fasc;

    530:   SNESFASCycleGetCorrection(snes, &next);
    531:   if (next) {
    532:     fasc = (SNES_FAS*)next->data;

    534:     SNESFASCycleGetRestriction(snes, &restrct);
    535:     SNESFASCycleGetInterpolation(snes, &interpolate);

    537:     X_c  = next->vec_sol;
    538:     Xo_c = next->work[0];
    539:     F_c  = next->vec_func;
    540:     B_c  = next->vec_rhs;

    542:     if (fasc->eventinterprestrict) {PetscLogEventBegin(fasc->eventinterprestrict,snes,0,0,0);}
    543:     SNESFASRestrict(snes, X, Xo_c);
    544:     /* restrict the defect: R(F(x) - b) */
    545:     MatRestrict(restrct, F, B_c);
    546:     if (fasc->eventinterprestrict) {PetscLogEventEnd(fasc->eventinterprestrict,snes,0,0,0);}

    548:     if (fasc->eventresidual) {PetscLogEventBegin(fasc->eventresidual,next,0,0,0);}
    549:     /* F_c = F^c(Rx) - R(F(x) - b) since the second term was sitting in next->vec_rhs */
    550:     SNESComputeFunction(next, Xo_c, F_c);
    551:     if (fasc->eventresidual) {PetscLogEventEnd(fasc->eventresidual,next,0,0,0);}

    553:     /* solve the coarse problem corresponding to F^c(x^c) = b^c = F^c(Rx) - R(F(x) - b) */
    554:     VecCopy(B_c, X_c);
    555:     VecCopy(F_c, B_c);
    556:     VecCopy(X_c, F_c);
    557:     /* set initial guess of the coarse problem to the projected fine solution */
    558:     VecCopy(Xo_c, X_c);

    560:     /* recurse to the next level */
    561:     SNESSetInitialFunction(next, F_c);
    562:     SNESSolve(next, B_c, X_c);
    563:     SNESGetConvergedReason(next,&reason);
    564:     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    565:       snes->reason = SNES_DIVERGED_INNER;
    566:       return(0);
    567:     }
    568:     /* correct as x <- x + I(x^c - Rx)*/
    569:     VecAXPY(X_c, -1.0, Xo_c);

    571:     if (fasc->eventinterprestrict) {PetscLogEventBegin(fasc->eventinterprestrict,snes,0,0,0);}
    572:     MatInterpolateAdd(interpolate, X_c, X, X_new);
    573:     PetscObjectSetName((PetscObject) X_c, "Coarse correction");
    574:     VecViewFromOptions(X_c, NULL, "-fas_coarse_solution_view");
    575:     PetscObjectSetName((PetscObject) X_new, "Updated Fine solution");
    576:     VecViewFromOptions(X_new, NULL, "-fas_levels_1_solution_view");
    577:     if (fasc->eventinterprestrict) {PetscLogEventEnd(fasc->eventinterprestrict,snes,0,0,0);}
    578:   }
    579:   return(0);
    580: }

    582: /*

    584: The additive cycle looks like:

    586: xhat = x
    587: xhat = dS(x, b)
    588: x = coarsecorrection(xhat, b_d)
    589: x = x + nu*(xhat - x);
    590: (optional) x = uS(x, b)

    592: With the coarse RHS (defect correction) as below.

    594:  */
    595: static PetscErrorCode SNESFASCycle_Additive(SNES snes, Vec X)
    596: {
    597:   Vec                  F, B, Xhat;
    598:   Vec                  X_c, Xo_c, F_c, B_c;
    599:   PetscErrorCode       ierr;
    600:   SNESConvergedReason  reason;
    601:   PetscReal            xnorm, fnorm, ynorm;
    602:   SNESLineSearchReason lsresult;
    603:   SNES                 next;
    604:   Mat                  restrct, interpolate;
    605:   SNES_FAS             *fas = (SNES_FAS*)snes->data,*fasc;

    608:   SNESFASCycleGetCorrection(snes, &next);
    609:   F    = snes->vec_func;
    610:   B    = snes->vec_rhs;
    611:   Xhat = snes->work[1];
    612:   VecCopy(X, Xhat);
    613:   /* recurse first */
    614:   if (next) {
    615:     fasc = (SNES_FAS*)next->data;
    616:     SNESFASCycleGetRestriction(snes, &restrct);
    617:     SNESFASCycleGetInterpolation(snes, &interpolate);
    618:     if (fas->eventresidual) {PetscLogEventBegin(fas->eventresidual,snes,0,0,0);}
    619:     SNESComputeFunction(snes, Xhat, F);
    620:     if (fas->eventresidual) {PetscLogEventEnd(fas->eventresidual,snes,0,0,0);}
    621:     VecNorm(F, NORM_2, &fnorm);
    622:     X_c  = next->vec_sol;
    623:     Xo_c = next->work[0];
    624:     F_c  = next->vec_func;
    625:     B_c  = next->vec_rhs;

    627:     SNESFASRestrict(snes,Xhat,Xo_c);
    628:     /* restrict the defect */
    629:     MatRestrict(restrct, F, B_c);

    631:     /* solve the coarse problem corresponding to F^c(x^c) = b^c = Rb + F^c(Rx) - RF(x) */
    632:     if (fasc->eventresidual) {PetscLogEventBegin(fasc->eventresidual,next,0,0,0);}
    633:     SNESComputeFunction(next, Xo_c, F_c);
    634:     if (fasc->eventresidual) {PetscLogEventEnd(fasc->eventresidual,next,0,0,0);}
    635:     VecCopy(B_c, X_c);
    636:     VecCopy(F_c, B_c);
    637:     VecCopy(X_c, F_c);
    638:     /* set initial guess of the coarse problem to the projected fine solution */
    639:     VecCopy(Xo_c, X_c);

    641:     /* recurse */
    642:     SNESSetInitialFunction(next, F_c);
    643:     SNESSolve(next, B_c, X_c);

    645:     /* smooth on this level */
    646:     SNESFASDownSmooth_Private(snes, B, X, F, &fnorm);

    648:     SNESGetConvergedReason(next,&reason);
    649:     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    650:       snes->reason = SNES_DIVERGED_INNER;
    651:       return(0);
    652:     }

    654:     /* correct as x <- x + I(x^c - Rx)*/
    655:     VecAYPX(X_c, -1.0, Xo_c);
    656:     MatInterpolate(interpolate, X_c, Xhat);

    658:     /* additive correction of the coarse direction*/
    659:     SNESLineSearchApply(snes->linesearch, X, F, &fnorm, Xhat);
    660:     SNESLineSearchGetReason(snes->linesearch, &lsresult);
    661:     SNESLineSearchGetNorms(snes->linesearch, &xnorm, &snes->norm, &ynorm);
    662:     if (lsresult) {
    663:       if (++snes->numFailures >= snes->maxFailures) {
    664:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
    665:         return(0);
    666:       }
    667:     }
    668:   } else {
    669:     SNESFASDownSmooth_Private(snes, B, X, F, &snes->norm);
    670:   }
    671:   return(0);
    672: }

    674: /*

    676: Defines the FAS cycle as:

    678: fine problem: F(x) = b
    679: coarse problem: F^c(x) = b^c

    681: b^c = F^c(Rx) - R(F(x) - b)

    683: correction:

    685: x = x + I(x^c - Rx)

    687:  */
    688: static PetscErrorCode SNESFASCycle_Multiplicative(SNES snes, Vec X)
    689: {

    692:   Vec            F,B;
    693:   SNES           next;

    696:   F = snes->vec_func;
    697:   B = snes->vec_rhs;
    698:   /* pre-smooth -- just update using the pre-smoother */
    699:   SNESFASCycleGetCorrection(snes, &next);
    700:   SNESFASDownSmooth_Private(snes, B, X, F, &snes->norm);
    701:   if (next) {
    702:     SNESFASCoarseCorrection(snes, X, F, X);
    703:     SNESFASUpSmooth_Private(snes, B, X, F, &snes->norm);
    704:   }
    705:   return(0);
    706: }

    708: static PetscErrorCode SNESFASCycleSetupPhase_Full(SNES snes)
    709: {
    710:   SNES           next;
    711:   SNES_FAS       *fas = (SNES_FAS*)snes->data;
    712:   PetscBool      isFine;

    716:   /* pre-smooth -- just update using the pre-smoother */
    717:   SNESFASCycleIsFine(snes,&isFine);
    718:   SNESFASCycleGetCorrection(snes,&next);
    719:   fas->full_stage = 0;
    720:   if (next) {SNESFASCycleSetupPhase_Full(next);}
    721:   return(0);
    722: }

    724: static PetscErrorCode SNESFASCycle_Full(SNES snes, Vec X)
    725: {
    727:   Vec            F,B;
    728:   SNES_FAS       *fas = (SNES_FAS*)snes->data;
    729:   PetscBool      isFine;
    730:   SNES           next;

    733:   F = snes->vec_func;
    734:   B = snes->vec_rhs;
    735:   SNESFASCycleIsFine(snes,&isFine);
    736:   SNESFASCycleGetCorrection(snes,&next);

    738:   if (isFine) {
    739:     SNESFASCycleSetupPhase_Full(snes);
    740:   }

    742:   if (fas->full_stage == 0) {
    743:     /* downsweep */
    744:     if (next) {
    745:       if (fas->level != 1) next->max_its += 1;
    746:       if (fas->full_downsweep) {SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);}
    747:       fas->full_downsweep = PETSC_TRUE;
    748:       SNESFASCoarseCorrection(snes,X,F,X);
    749:       SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);
    750:       if (fas->level != 1) next->max_its -= 1;
    751:     } else {
    752:       /* The smoother on the coarse level is the coarse solver */
    753:       SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);
    754:     }
    755:     fas->full_stage = 1;
    756:   } else if (fas->full_stage == 1) {
    757:     if (snes->iter == 0) {SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);}
    758:     if (next) {
    759:       SNESFASCoarseCorrection(snes,X,F,X);
    760:       SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);
    761:     }
    762:   }
    763:   /* final v-cycle */
    764:   if (isFine) {
    765:     if (next) {
    766:       SNESFASCoarseCorrection(snes,X,F,X);
    767:       SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);
    768:     }
    769:   }
    770:   return(0);
    771: }

    773: static PetscErrorCode SNESFASCycle_Kaskade(SNES snes, Vec X)
    774: {
    776:   Vec            F,B;
    777:   SNES           next;

    780:   F = snes->vec_func;
    781:   B = snes->vec_rhs;
    782:   SNESFASCycleGetCorrection(snes,&next);
    783:   if (next) {
    784:     SNESFASCoarseCorrection(snes,X,F,X);
    785:     SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);
    786:   } else {
    787:     SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);
    788:   }
    789:   return(0);
    790: }

    792: PetscBool SNEScite = PETSC_FALSE;
    793: const char SNESCitation[] = "@techreport{pbmkbsxt2012,\n"
    794:                             "  title = {Composing Scalable Nonlinear Algebraic Solvers},\n"
    795:                             "  author = {Peter Brune and Mathew Knepley and Barry Smith and Xuemin Tu},\n"
    796:                             "  year = 2013,\n"
    797:                             "  type = Preprint,\n"
    798:                             "  number = {ANL/MCS-P2010-0112},\n"
    799:                             "  institution = {Argonne National Laboratory}\n}\n";

    801: static PetscErrorCode SNESSolve_FAS(SNES snes)
    802: {
    804:   PetscInt       i;
    805:   Vec            X, F;
    806:   PetscReal      fnorm;
    807:   SNES_FAS       *fas = (SNES_FAS*)snes->data,*ffas;
    808:   DM             dm;
    809:   PetscBool      isFine;

    812:   if (snes->xl || snes->xu || snes->ops->computevariablebounds) SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

    814:   PetscCitationsRegister(SNESCitation,&SNEScite);
    815:   snes->reason = SNES_CONVERGED_ITERATING;
    816:   X            = snes->vec_sol;
    817:   F            = snes->vec_func;

    819:   SNESFASCycleIsFine(snes, &isFine);
    820:   /* norm setup */
    821:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    822:   snes->iter = 0;
    823:   snes->norm = 0;
    824:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    825:   if (!snes->vec_func_init_set) {
    826:     if (fas->eventresidual) {PetscLogEventBegin(fas->eventresidual,snes,0,0,0);}
    827:     SNESComputeFunction(snes,X,F);
    828:     if (fas->eventresidual) {PetscLogEventEnd(fas->eventresidual,snes,0,0,0);}
    829:   } else snes->vec_func_init_set = PETSC_FALSE;

    831:   VecNorm(F, NORM_2, &fnorm); /* fnorm <- ||F||  */
    832:   SNESCheckFunctionNorm(snes,fnorm);
    833:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    834:   snes->norm = fnorm;
    835:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    836:   SNESLogConvergenceHistory(snes,fnorm,0);
    837:   SNESMonitor(snes,snes->iter,fnorm);

    839:   /* test convergence */
    840:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    841:   if (snes->reason) return(0);

    844:   if (isFine) {
    845:     /* propagate scale-dependent data up the hierarchy */
    846:     SNESGetDM(snes,&dm);
    847:     for (ffas=fas; ffas->next; ffas=(SNES_FAS*)ffas->next->data) {
    848:       DM dmcoarse;
    849:       SNESGetDM(ffas->next,&dmcoarse);
    850:       DMRestrict(dm,ffas->restrct,ffas->rscale,ffas->inject,dmcoarse);
    851:       dm   = dmcoarse;
    852:     }
    853:   }

    855:   for (i = 0; i < snes->max_its; i++) {
    856:     /* Call general purpose update function */
    857:     if (snes->ops->update) {
    858:       (*snes->ops->update)(snes, snes->iter);
    859:     }

    861:     if (fas->fastype == SNES_FAS_MULTIPLICATIVE) {
    862:       SNESFASCycle_Multiplicative(snes, X);
    863:     } else if (fas->fastype == SNES_FAS_ADDITIVE) {
    864:       SNESFASCycle_Additive(snes, X);
    865:     } else if (fas->fastype == SNES_FAS_FULL) {
    866:       SNESFASCycle_Full(snes, X);
    867:     } else if (fas->fastype == SNES_FAS_KASKADE) {
    868:       SNESFASCycle_Kaskade(snes, X);
    869:     } else SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE,"Unsupported FAS type");

    871:     /* check for FAS cycle divergence */
    872:     if (snes->reason != SNES_CONVERGED_ITERATING) return(0);

    874:     /* Monitor convergence */
    875:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    876:     snes->iter = i+1;
    877:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    878:     SNESLogConvergenceHistory(snes,snes->norm,0);
    879:     SNESMonitor(snes,snes->iter,snes->norm);
    880:     /* Test for convergence */
    881:     if (isFine) {
    882:       (*snes->ops->converged)(snes,snes->iter,0.0,0.0,snes->norm,&snes->reason,snes->cnvP);
    883:       if (snes->reason) break;
    884:     }
    885:   }
    886:   if (i == snes->max_its) {
    887:     PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", i);
    888:     if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
    889:   }
    890:   return(0);
    891: }

    893: /*MC

    895: SNESFAS - Full Approximation Scheme nonlinear multigrid solver.

    897:    The nonlinear problem is solved by correction using coarse versions
    898:    of the nonlinear problem.  This problem is perturbed so that a projected
    899:    solution of the fine problem elicits no correction from the coarse problem.

    901: Options Database:
    902: +   -snes_fas_levels -  The number of levels
    903: .   -snes_fas_cycles<1> -  The number of cycles -- 1 for V, 2 for W
    904: .   -snes_fas_type<additive,multiplicative,full,kaskade>  -  Additive or multiplicative cycle
    905: .   -snes_fas_galerkin<PETSC_FALSE> -  Form coarse problems by projection back upon the fine problem
    906: .   -snes_fas_smoothup<1> -  The number of iterations of the post-smoother
    907: .   -snes_fas_smoothdown<1> -  The number of iterations of the pre-smoother
    908: .   -snes_fas_monitor -  Monitor progress of all of the levels
    909: .   -snes_fas_full_downsweep<PETSC_FALSE> - call the downsmooth on the initial downsweep of full FAS
    910: .   -fas_levels_snes_ -  SNES options for all smoothers
    911: .   -fas_levels_cycle_snes_ -  SNES options for all cycles
    912: .   -fas_levels_i_snes_ -  SNES options for the smoothers on level i
    913: .   -fas_levels_i_cycle_snes_ - SNES options for the cycle on level i
    914: -   -fas_coarse_snes_ -  SNES options for the coarsest smoother

    916: Notes:
    917:    The organization of the FAS solver is slightly different from the organization of PCMG
    918:    As each level has smoother SNES instances(down and potentially up) and a cycle SNES instance.
    919:    The cycle SNES instance may be used for monitoring convergence on a particular level.

    921: Level: beginner

    923:    References:
    924: . 1. -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers",
    925:    SIAM Review, 57(4), 2015

    927: .seealso: PCMG, SNESCreate(), SNES, SNESSetType(), SNESType (for list of available types)
    928: M*/

    930: PETSC_EXTERN PetscErrorCode SNESCreate_FAS(SNES snes)
    931: {
    932:   SNES_FAS       *fas;

    936:   snes->ops->destroy        = SNESDestroy_FAS;
    937:   snes->ops->setup          = SNESSetUp_FAS;
    938:   snes->ops->setfromoptions = SNESSetFromOptions_FAS;
    939:   snes->ops->view           = SNESView_FAS;
    940:   snes->ops->solve          = SNESSolve_FAS;
    941:   snes->ops->reset          = SNESReset_FAS;

    943:   snes->usesksp = PETSC_FALSE;
    944:   snes->usesnpc = PETSC_FALSE;

    946:   if (!snes->tolerancesset) {
    947:     snes->max_funcs = 30000;
    948:     snes->max_its   = 10000;
    949:   }

    951:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

    953:   PetscNewLog(snes,&fas);

    955:   snes->data                  = (void*) fas;
    956:   fas->level                  = 0;
    957:   fas->levels                 = 1;
    958:   fas->n_cycles               = 1;
    959:   fas->max_up_it              = 1;
    960:   fas->max_down_it            = 1;
    961:   fas->smoothu                = NULL;
    962:   fas->smoothd                = NULL;
    963:   fas->next                   = NULL;
    964:   fas->previous               = NULL;
    965:   fas->fine                   = snes;
    966:   fas->interpolate            = NULL;
    967:   fas->restrct                = NULL;
    968:   fas->inject                 = NULL;
    969:   fas->usedmfornumberoflevels = PETSC_FALSE;
    970:   fas->fastype                = SNES_FAS_MULTIPLICATIVE;
    971:   fas->full_downsweep         = PETSC_FALSE;

    973:   fas->eventsmoothsetup    = 0;
    974:   fas->eventsmoothsolve    = 0;
    975:   fas->eventresidual       = 0;
    976:   fas->eventinterprestrict = 0;
    977:   return(0);
    978: }