Actual source code: anderson.c
petsc-3.7.1 2016-05-15
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      1: #include <../src/snes/impls/ngmres/snesngmres.h> /*I "petscsnes.h" I*/

      3: extern PetscErrorCode SNESDestroy_NGMRES(SNES);
      4: extern PetscErrorCode SNESReset_NGMRES(SNES);
      5: extern PetscErrorCode SNESSetUp_NGMRES(SNES);
      6: extern PetscErrorCode SNESView_NGMRES(SNES,PetscViewer);

      8: PETSC_EXTERN const char *const SNESNGMRESRestartTypes[];

     12: PetscErrorCode SNESSetFromOptions_Anderson(PetscOptionItems *PetscOptionsObject,SNES snes)
     13: {
     14:   SNES_NGMRES    *ngmres = (SNES_NGMRES*) snes->data;
     16:   PetscBool      debug;
     17:   SNESLineSearch linesearch;

     20:   PetscOptionsHead(PetscOptionsObject,"SNES NGMRES options");
     21:   PetscOptionsInt("-snes_anderson_m",            "Number of directions","SNES",ngmres->msize,&ngmres->msize,NULL);
     22:   PetscOptionsReal("-snes_anderson_beta",        "Mixing parameter","SNES",ngmres->andersonBeta,&ngmres->andersonBeta,NULL);
     23:   PetscOptionsBool("-snes_anderson_monitor",     "Monitor steps of Anderson Mixing","SNES",ngmres->monitor ? PETSC_TRUE : PETSC_FALSE,&debug,NULL);
     24:   PetscOptionsInt("-snes_anderson_restart",      "Iterations before forced restart", "SNES",ngmres->restart_periodic,&ngmres->restart_periodic,NULL);
     25:   PetscOptionsInt("-snes_anderson_restart_it",   "Tolerance iterations before restart","SNES",ngmres->restart_it,&ngmres->restart_it,NULL);
     26:   PetscOptionsEnum("-snes_anderson_restart_type","Restart type","SNESNGMRESSetRestartType",SNESNGMRESRestartTypes,
     27:                           (PetscEnum)ngmres->restart_type,(PetscEnum*)&ngmres->restart_type,NULL);
     28:   if (debug) {
     29:     ngmres->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
     30:   }
     31:   PetscOptionsTail();
     32:   /* set the default type of the line search if the user hasn't already. */
     33:   if (!snes->linesearch) {
     34:     SNESGetLineSearch(snes,&linesearch);
     35:     SNESLineSearchSetType(linesearch,SNESLINESEARCHBASIC);
     36:   }
     37:   return(0);
     38: }

     42: PetscErrorCode SNESSolve_Anderson(SNES snes)
     43: {
     44:   SNES_NGMRES         *ngmres = (SNES_NGMRES*) snes->data;
     45:   /* present solution, residual, and preconditioned residual */
     46:   Vec                 X,F,B,D;
     47:   /* candidate linear combination answers */
     48:   Vec                 XA,FA,XM,FM;

     50:   /* coefficients and RHS to the minimization problem */
     51:   PetscReal           fnorm,fMnorm,fAnorm;
     52:   PetscReal           xnorm,ynorm;
     53:   PetscReal           dnorm,dminnorm=0.0,fminnorm;
     54:   PetscInt            restart_count=0;
     55:   PetscInt            k,k_restart,l,ivec;
     56:   PetscBool           selectRestart;
     57:   SNESConvergedReason reason;
     58:   PetscErrorCode      ierr;

     61:   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);

     63:   PetscCitationsRegister(SNESCitation,&SNEScite);
     64:   /* variable initialization */
     65:   snes->reason = SNES_CONVERGED_ITERATING;
     66:   X            = snes->vec_sol;
     67:   F            = snes->vec_func;
     68:   B            = snes->vec_rhs;
     69:   XA           = snes->vec_sol_update;
     70:   FA           = snes->work[0];
     71:   D            = snes->work[1];

     73:   /* work for the line search */
     74:   XM = snes->work[3];
     75:   FM = snes->work[4];

     77:   PetscObjectSAWsTakeAccess((PetscObject)snes);
     78:   snes->iter = 0;
     79:   snes->norm = 0.;
     80:   PetscObjectSAWsGrantAccess((PetscObject)snes);

     82:   /* initialization */

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

     86:   if (snes->pc && snes->pcside == PC_LEFT) {
     87:     SNESApplyNPC(snes,X,NULL,F);
     88:     SNESGetConvergedReason(snes->pc,&reason);
     89:     if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
     90:       snes->reason = SNES_DIVERGED_INNER;
     91:       return(0);
     92:     }
     93:     VecNorm(F,NORM_2,&fnorm);
     94:   } else {
     95:     if (!snes->vec_func_init_set) {
     96:       SNESComputeFunction(snes,X,F);
     97:     } else snes->vec_func_init_set = PETSC_FALSE;

     99:     VecNorm(F,NORM_2,&fnorm);
    100:     SNESCheckFunctionNorm(snes,fnorm);
    101:   }
    102:   fminnorm = fnorm;

    104:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    105:   snes->norm = fnorm;
    106:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    107:   SNESLogConvergenceHistory(snes,fnorm,0);
    108:   SNESMonitor(snes,0,fnorm);
    109:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    110:   if (snes->reason) return(0);

    112:   k_restart = 0;
    113:   l         = 0;
    114:   ivec      = 0;
    115:   for (k=1; k < snes->max_its+1; k++) {
    116:     /* select which vector of the stored subspace will be updated */
    117:     if (snes->pc && snes->pcside == PC_RIGHT) {
    118:       VecCopy(X,XM);
    119:       SNESSetInitialFunction(snes->pc,F);

    121:       PetscLogEventBegin(SNES_NPCSolve,snes->pc,XM,B,0);
    122:       SNESSolve(snes->pc,B,XM);
    123:       PetscLogEventEnd(SNES_NPCSolve,snes->pc,XM,B,0);

    125:       SNESGetConvergedReason(snes->pc,&reason);
    126:       if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    127:         snes->reason = SNES_DIVERGED_INNER;
    128:         return(0);
    129:       }
    130:       SNESGetNPCFunction(snes,FM,&fMnorm);
    131:       if (ngmres->andersonBeta != 1.0) {
    132:         VecAXPBY(XM,(1.0 - ngmres->andersonBeta),ngmres->andersonBeta,X);
    133:       }
    134:     } else {
    135:       VecCopy(F,FM);
    136:       VecCopy(X,XM);
    137:       VecAXPY(XM,-ngmres->andersonBeta,FM);
    138:       fMnorm = fnorm;
    139:     }

    141:     SNESNGMRESFormCombinedSolution_Private(snes,ivec,l,XM,FM,fMnorm,X,XA,FA);
    142:     ivec = k_restart % ngmres->msize;
    143:     if (ngmres->restart_type == SNES_NGMRES_RESTART_DIFFERENCE) {
    144:       SNESNGMRESNorms_Private(snes,l,X,F,XM,FM,XA,FA,D,&dnorm,&dminnorm,NULL,NULL,NULL,&xnorm,&fAnorm,&ynorm);
    145:       SNESNGMRESSelectRestart_Private(snes,l,fMnorm,fnorm,dnorm,fminnorm,dminnorm,&selectRestart);
    146:       /* if the restart conditions persist for more than restart_it iterations, restart. */
    147:       if (selectRestart) restart_count++;
    148:       else restart_count = 0;
    149:     } else if (ngmres->restart_type == SNES_NGMRES_RESTART_PERIODIC) {
    150:       SNESNGMRESNorms_Private(snes,l,X,F,XM,FM,XA,FA,D,NULL,NULL,NULL,NULL,NULL,&xnorm,&fAnorm,&ynorm);
    151:       if (k_restart > ngmres->restart_periodic) {
    152:         if (ngmres->monitor) PetscViewerASCIIPrintf(ngmres->monitor,"periodic restart after %D iterations\n",k_restart);
    153:         restart_count = ngmres->restart_it;
    154:       }
    155:     } else {
    156:       SNESNGMRESNorms_Private(snes,l,X,F,XM,FM,XA,FA,D,NULL,NULL,NULL,NULL,NULL,&xnorm,&fAnorm,&ynorm);
    157:     }
    158:     /* restart after restart conditions have persisted for a fixed number of iterations */
    159:     if (restart_count >= ngmres->restart_it) {
    160:       if (ngmres->monitor) {
    161:         PetscViewerASCIIPrintf(ngmres->monitor,"Restarted at iteration %d\n",k_restart);
    162:       }
    163:       restart_count = 0;
    164:       k_restart     = 0;
    165:       l             = 0;
    166:       ivec          = 0;
    167:     } else {
    168:       if (l < ngmres->msize) l++;
    169:       k_restart++;
    170:       SNESNGMRESUpdateSubspace_Private(snes,ivec,l,FM,fnorm,XM);
    171:     }

    173:     fnorm = fAnorm;
    174:     if (fminnorm > fnorm) fminnorm = fnorm;

    176:     VecCopy(XA,X);
    177:     VecCopy(FA,F);

    179:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    180:     snes->iter = k;
    181:     snes->norm = fnorm;
    182:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    183:     SNESLogConvergenceHistory(snes,snes->norm,snes->iter);
    184:     SNESMonitor(snes,snes->iter,snes->norm);
    185:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
    186:     if (snes->reason) return(0);
    187:   }
    188:   snes->reason = SNES_DIVERGED_MAX_IT;
    189:   return(0);
    190: }

    192: /*MC
    193:   SNESANDERSON - Anderson Mixing method.

    195:    Level: beginner

    197:    Options Database:
    198: +  -snes_anderson_m                - Number of stored previous solutions and residuals
    199: .  -snes_anderson_beta             - Relaxation parameter; X_{update} = X + \beta F
    200: .  -snes_anderson_restart_type     - Type of restart (see SNESNGMRES)
    201: .  -snes_anderson_restart_it       - Number of iterations of restart conditions before restart
    202: .  -snes_anderson_restart          - Number of iterations before periodic restart
    203: -  -snes_anderson_monitor          - Prints relevant information about the ngmres iteration

    205:    Notes:

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

    210:    Very similar to the SNESNGMRES algorithm.

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

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

    224: PETSC_EXTERN PetscErrorCode SNESCreate_Anderson(SNES snes)
    225: {
    226:   SNES_NGMRES    *ngmres;

    230:   snes->ops->destroy        = SNESDestroy_NGMRES;
    231:   snes->ops->setup          = SNESSetUp_NGMRES;
    232:   snes->ops->setfromoptions = SNESSetFromOptions_Anderson;
    233:   snes->ops->view           = SNESView_NGMRES;
    234:   snes->ops->solve          = SNESSolve_Anderson;
    235:   snes->ops->reset          = SNESReset_NGMRES;

    237:   snes->usespc  = PETSC_TRUE;
    238:   snes->usesksp = PETSC_FALSE;
    239:   snes->pcside  = PC_RIGHT;

    241:   PetscNewLog(snes,&ngmres);
    242:   snes->data    = (void*) ngmres;
    243:   ngmres->msize = 30;

    245:   if (!snes->tolerancesset) {
    246:     snes->max_funcs = 30000;
    247:     snes->max_its   = 10000;
    248:   }

    250:   ngmres->additive_linesearch = NULL;
    251:   ngmres->approxfunc       = PETSC_FALSE;
    252:   ngmres->restart_type     = SNES_NGMRES_RESTART_NONE;
    253:   ngmres->restart_it       = 2;
    254:   ngmres->restart_periodic = 30;
    255:   ngmres->gammaA           = 2.0;
    256:   ngmres->gammaC           = 2.0;
    257:   ngmres->deltaB           = 0.9;
    258:   ngmres->epsilonB         = 0.1;

    260:   ngmres->andersonBeta = 1.0;
    261:   return(0);
    262: }