Actual source code: anderson.c

      1: #include <../src/snes/impls/ngmres/snesngmres.h>

      3: static PetscErrorCode SNESSetFromOptions_Anderson(PetscOptionItems *PetscOptionsObject,SNES snes)
      4: {
      5:   SNES_NGMRES    *ngmres = (SNES_NGMRES*) snes->data;
      7:   PetscBool      monitor = PETSC_FALSE;

     10:   PetscOptionsHead(PetscOptionsObject,"SNES NGMRES options");
     11:   PetscOptionsInt("-snes_anderson_m",            "Number of directions","SNES",ngmres->msize,&ngmres->msize,NULL);
     12:   PetscOptionsReal("-snes_anderson_beta",        "Mixing parameter","SNES",ngmres->andersonBeta,&ngmres->andersonBeta,NULL);
     13:   PetscOptionsInt("-snes_anderson_restart",      "Iterations before forced restart", "SNES",ngmres->restart_periodic,&ngmres->restart_periodic,NULL);
     14:   PetscOptionsInt("-snes_anderson_restart_it",   "Tolerance iterations before restart","SNES",ngmres->restart_it,&ngmres->restart_it,NULL);
     15:   PetscOptionsEnum("-snes_anderson_restart_type","Restart type","SNESNGMRESSetRestartType",SNESNGMRESRestartTypes,(PetscEnum)ngmres->restart_type,(PetscEnum*)&ngmres->restart_type,NULL);
     16:   PetscOptionsBool("-snes_anderson_monitor",     "Monitor steps of Anderson Mixing","SNES",ngmres->monitor ? PETSC_TRUE : PETSC_FALSE,&monitor,NULL);
     17:   if (monitor) {
     18:     ngmres->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
     19:   }
     20:   PetscOptionsTail();
     21:   return(0);
     22: }

     24: static PetscErrorCode SNESSolve_Anderson(SNES snes)
     25: {
     26:   SNES_NGMRES         *ngmres = (SNES_NGMRES*) snes->data;
     27:   /* present solution, residual, and preconditioned residual */
     28:   Vec                 X,F,B,D;
     29:   /* candidate linear combination answers */
     30:   Vec                 XA,FA,XM,FM;

     32:   /* coefficients and RHS to the minimization problem */
     33:   PetscReal           fnorm,fMnorm,fAnorm;
     34:   PetscReal           xnorm,ynorm;
     35:   PetscReal           dnorm,dminnorm=0.0,fminnorm;
     36:   PetscInt            restart_count=0;
     37:   PetscInt            k,k_restart,l,ivec;
     38:   PetscBool           selectRestart;
     39:   SNESConvergedReason reason;
     40:   PetscErrorCode      ierr;

     43:   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);

     45:   PetscCitationsRegister(SNESCitation,&SNEScite);
     46:   /* variable initialization */
     47:   snes->reason = SNES_CONVERGED_ITERATING;
     48:   X            = snes->vec_sol;
     49:   F            = snes->vec_func;
     50:   B            = snes->vec_rhs;
     51:   XA           = snes->vec_sol_update;
     52:   FA           = snes->work[0];
     53:   D            = snes->work[1];

     55:   /* work for the line search */
     56:   XM = snes->work[3];
     57:   FM = snes->work[4];

     59:   PetscObjectSAWsTakeAccess((PetscObject)snes);
     60:   snes->iter = 0;
     61:   snes->norm = 0.;
     62:   PetscObjectSAWsGrantAccess((PetscObject)snes);

     64:   /* initialization */

     66:   /* r = F(x) */

     68:   if (snes->npc && snes->npcside== PC_LEFT) {
     69:     SNESApplyNPC(snes,X,NULL,F);
     70:     SNESGetConvergedReason(snes->npc,&reason);
     71:     if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
     72:       snes->reason = SNES_DIVERGED_INNER;
     73:       return(0);
     74:     }
     75:     VecNorm(F,NORM_2,&fnorm);
     76:   } else {
     77:     if (!snes->vec_func_init_set) {
     78:       SNESComputeFunction(snes,X,F);
     79:     } else snes->vec_func_init_set = PETSC_FALSE;

     81:     VecNorm(F,NORM_2,&fnorm);
     82:     SNESCheckFunctionNorm(snes,fnorm);
     83:   }
     84:   fminnorm = fnorm;

     86:   PetscObjectSAWsTakeAccess((PetscObject)snes);
     87:   snes->norm = fnorm;
     88:   PetscObjectSAWsGrantAccess((PetscObject)snes);
     89:   SNESLogConvergenceHistory(snes,fnorm,0);
     90:   SNESMonitor(snes,0,fnorm);
     91:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
     92:   if (snes->reason) return(0);

     94:   k_restart = 0;
     95:   l         = 0;
     96:   ivec      = 0;
     97:   for (k=1; k < snes->max_its+1; k++) {
     98:     /* select which vector of the stored subspace will be updated */
     99:     if (snes->npc && snes->npcside== PC_RIGHT) {
    100:       VecCopy(X,XM);
    101:       SNESSetInitialFunction(snes->npc,F);

    103:       PetscLogEventBegin(SNES_NPCSolve,snes->npc,XM,B,0);
    104:       SNESSolve(snes->npc,B,XM);
    105:       PetscLogEventEnd(SNES_NPCSolve,snes->npc,XM,B,0);

    107:       SNESGetConvergedReason(snes->npc,&reason);
    108:       if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    109:         snes->reason = SNES_DIVERGED_INNER;
    110:         return(0);
    111:       }
    112:       SNESGetNPCFunction(snes,FM,&fMnorm);
    113:       if (ngmres->andersonBeta != 1.0) {
    114:         VecAXPBY(XM,(1.0 - ngmres->andersonBeta),ngmres->andersonBeta,X);
    115:       }
    116:     } else {
    117:       VecCopy(F,FM);
    118:       VecCopy(X,XM);
    119:       VecAXPY(XM,-ngmres->andersonBeta,FM);
    120:       fMnorm = fnorm;
    121:     }

    123:     SNESNGMRESFormCombinedSolution_Private(snes,ivec,l,XM,FM,fMnorm,X,XA,FA);
    124:     ivec = k_restart % ngmres->msize;
    125:     if (ngmres->restart_type == SNES_NGMRES_RESTART_DIFFERENCE) {
    126:       SNESNGMRESNorms_Private(snes,l,X,F,XM,FM,XA,FA,D,&dnorm,&dminnorm,NULL,NULL,NULL,&xnorm,&fAnorm,&ynorm);
    127:       SNESNGMRESSelectRestart_Private(snes,l,fMnorm,fnorm,dnorm,fminnorm,dminnorm,&selectRestart);
    128:       /* if the restart conditions persist for more than restart_it iterations, restart. */
    129:       if (selectRestart) restart_count++;
    130:       else restart_count = 0;
    131:     } else if (ngmres->restart_type == SNES_NGMRES_RESTART_PERIODIC) {
    132:       SNESNGMRESNorms_Private(snes,l,X,F,XM,FM,XA,FA,D,NULL,NULL,NULL,NULL,NULL,&xnorm,&fAnorm,&ynorm);
    133:       if (k_restart > ngmres->restart_periodic) {
    134:         if (ngmres->monitor) PetscViewerASCIIPrintf(ngmres->monitor,"periodic restart after %D iterations\n",k_restart);
    135:         restart_count = ngmres->restart_it;
    136:       }
    137:     } else {
    138:       SNESNGMRESNorms_Private(snes,l,X,F,XM,FM,XA,FA,D,NULL,NULL,NULL,NULL,NULL,&xnorm,&fAnorm,&ynorm);
    139:     }
    140:     /* restart after restart conditions have persisted for a fixed number of iterations */
    141:     if (restart_count >= ngmres->restart_it) {
    142:       if (ngmres->monitor) {
    143:         PetscViewerASCIIPrintf(ngmres->monitor,"Restarted at iteration %d\n",k_restart);
    144:       }
    145:       restart_count = 0;
    146:       k_restart     = 0;
    147:       l             = 0;
    148:       ivec          = 0;
    149:     } else {
    150:       if (l < ngmres->msize) l++;
    151:       k_restart++;
    152:       SNESNGMRESUpdateSubspace_Private(snes,ivec,l,FM,fnorm,XM);
    153:     }

    155:     fnorm = fAnorm;
    156:     if (fminnorm > fnorm) fminnorm = fnorm;

    158:     VecCopy(XA,X);
    159:     VecCopy(FA,F);

    161:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    162:     snes->iter = k;
    163:     snes->norm = fnorm;
    164:     snes->xnorm = xnorm;
    165:     snes->ynorm = ynorm;
    166:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    167:     SNESLogConvergenceHistory(snes,snes->norm,snes->iter);
    168:     SNESMonitor(snes,snes->iter,snes->norm);
    169:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
    170:     if (snes->reason) return(0);
    171:   }
    172:   snes->reason = SNES_DIVERGED_MAX_IT;
    173:   return(0);
    174: }

    176: /*MC
    177:   SNESANDERSON - Anderson Mixing method.

    179:    Level: beginner

    181:    Options Database:
    182: +  -snes_anderson_m                - Number of stored previous solutions and residuals
    183: .  -snes_anderson_beta             - Anderson mixing parameter
    184: .  -snes_anderson_restart_type     - Type of restart (see SNESNGMRES)
    185: .  -snes_anderson_restart_it       - Number of iterations of restart conditions before restart
    186: .  -snes_anderson_restart          - Number of iterations before periodic restart
    187: -  -snes_anderson_monitor          - Prints relevant information about the ngmres iteration

    189:    Notes:

    191:    The Anderson Mixing method combines m previous solutions into a minimum-residual solution by solving a small linearized
    192:    optimization problem at each iteration.

    194:    Very similar to the SNESNGMRES algorithm.

    196:    References:
    197: +  1. -  D. G. Anderson. Iterative procedures for nonlinear integral equations.
    198:     J. Assoc. Comput. Mach., 12, 1965."
    199: -  2. - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
    200:    SIAM Review, 57(4), 2015

    203: .seealso: SNESNGMRES, SNESCreate(), SNES, SNESSetType(), SNESType (for list of available types)
    204: M*/

    206: PETSC_EXTERN PetscErrorCode SNESCreate_Anderson(SNES snes)
    207: {
    208:   SNES_NGMRES    *ngmres;
    210:   SNESLineSearch linesearch;

    213:   snes->ops->destroy        = SNESDestroy_NGMRES;
    214:   snes->ops->setup          = SNESSetUp_NGMRES;
    215:   snes->ops->setfromoptions = SNESSetFromOptions_Anderson;
    216:   snes->ops->view           = SNESView_NGMRES;
    217:   snes->ops->solve          = SNESSolve_Anderson;
    218:   snes->ops->reset          = SNESReset_NGMRES;

    220:   snes->usesnpc = PETSC_TRUE;
    221:   snes->usesksp = PETSC_FALSE;
    222:   snes->npcside = PC_RIGHT;

    224:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

    226:   PetscNewLog(snes,&ngmres);
    227:   snes->data    = (void*) ngmres;
    228:   ngmres->msize = 30;

    230:   if (!snes->tolerancesset) {
    231:     snes->max_funcs = 30000;
    232:     snes->max_its   = 10000;
    233:   }

    235:   SNESGetLineSearch(snes,&linesearch);
    236:   if (!((PetscObject)linesearch)->type_name) {
    237:     SNESLineSearchSetType(linesearch,SNESLINESEARCHBASIC);
    238:   }

    240:   ngmres->additive_linesearch = NULL;
    241:   ngmres->approxfunc       = PETSC_FALSE;
    242:   ngmres->restart_type     = SNES_NGMRES_RESTART_NONE;
    243:   ngmres->restart_it       = 2;
    244:   ngmres->restart_periodic = 30;
    245:   ngmres->gammaA           = 2.0;
    246:   ngmres->gammaC           = 2.0;
    247:   ngmres->deltaB           = 0.9;
    248:   ngmres->epsilonB         = 0.1;

    250:   ngmres->andersonBeta = 1.0;
    251:   return(0);
    252: }