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;
      6:   PetscBool      monitor = PETSC_FALSE;

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

     22: static PetscErrorCode SNESSolve_Anderson(SNES snes)
     23: {
     24:   SNES_NGMRES         *ngmres = (SNES_NGMRES*) snes->data;
     25:   /* present solution, residual, and preconditioned residual */
     26:   Vec                 X,F,B,D;
     27:   /* candidate linear combination answers */
     28:   Vec                 XA,FA,XM,FM;

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

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

     51:   /* work for the line search */
     52:   XM = snes->work[3];
     53:   FM = snes->work[4];

     55:   PetscObjectSAWsTakeAccess((PetscObject)snes);
     56:   snes->iter = 0;
     57:   snes->norm = 0.;
     58:   PetscObjectSAWsGrantAccess((PetscObject)snes);

     60:   /* initialization */

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

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

     77:     VecNorm(F,NORM_2,&fnorm);
     78:     SNESCheckFunctionNorm(snes,fnorm);
     79:   }
     80:   fminnorm = fnorm;

     82:   PetscObjectSAWsTakeAccess((PetscObject)snes);
     83:   snes->norm = fnorm;
     84:   PetscObjectSAWsGrantAccess((PetscObject)snes);
     85:   SNESLogConvergenceHistory(snes,fnorm,0);
     86:   SNESMonitor(snes,0,fnorm);
     87:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
     88:   if (snes->reason) return 0;

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

     99:       PetscLogEventBegin(SNES_NPCSolve,snes->npc,XM,B,0);
    100:       SNESSolve(snes->npc,B,XM);
    101:       PetscLogEventEnd(SNES_NPCSolve,snes->npc,XM,B,0);

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

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

    151:     fnorm = fAnorm;
    152:     if (fminnorm > fnorm) fminnorm = fnorm;

    154:     VecCopy(XA,X);
    155:     VecCopy(FA,F);

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

    172: /*MC
    173:   SNESANDERSON - Anderson Mixing method.

    175:    Level: beginner

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

    185:    Notes:

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

    190:    Very similar to the SNESNGMRES algorithm.

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

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

    201: PETSC_EXTERN PetscErrorCode SNESCreate_Anderson(SNES snes)
    202: {
    203:   SNES_NGMRES    *ngmres;
    204:   SNESLineSearch linesearch;

    206:   snes->ops->destroy        = SNESDestroy_NGMRES;
    207:   snes->ops->setup          = SNESSetUp_NGMRES;
    208:   snes->ops->setfromoptions = SNESSetFromOptions_Anderson;
    209:   snes->ops->view           = SNESView_NGMRES;
    210:   snes->ops->solve          = SNESSolve_Anderson;
    211:   snes->ops->reset          = SNESReset_NGMRES;

    213:   snes->usesnpc = PETSC_TRUE;
    214:   snes->usesksp = PETSC_FALSE;
    215:   snes->npcside = PC_RIGHT;

    217:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

    219:   PetscNewLog(snes,&ngmres);
    220:   snes->data    = (void*) ngmres;
    221:   ngmres->msize = 30;

    223:   if (!snes->tolerancesset) {
    224:     snes->max_funcs = 30000;
    225:     snes->max_its   = 10000;
    226:   }

    228:   SNESGetLineSearch(snes,&linesearch);
    229:   if (!((PetscObject)linesearch)->type_name) {
    230:     SNESLineSearchSetType(linesearch,SNESLINESEARCHBASIC);
    231:   }

    233:   ngmres->additive_linesearch = NULL;
    234:   ngmres->approxfunc       = PETSC_FALSE;
    235:   ngmres->restart_type     = SNES_NGMRES_RESTART_NONE;
    236:   ngmres->restart_it       = 2;
    237:   ngmres->restart_periodic = 30;
    238:   ngmres->gammaA           = 2.0;
    239:   ngmres->gammaC           = 2.0;
    240:   ngmres->deltaB           = 0.9;
    241:   ngmres->epsilonB         = 0.1;

    243:   ngmres->andersonBeta = 1.0;
    244:   return 0;
    245: }