Date: 2013-07-02T14:48:23+00:00

Actual source code: lcd.c
petsc-3.4.2 2013-07-02

      2: #include <../src/ksp/ksp/impls/lcd/lcdimpl.h>

      6: PetscErrorCode KSPSetUp_LCD(KSP ksp)
      7: {
      8:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;
     10:   PetscInt       restart = lcd->restart;

     13:   /* get work vectors needed by LCD */
     14:   KSPSetWorkVecs(ksp,2);

     16:   VecDuplicateVecs(ksp->work[0],restart+1,&lcd->P);
     17:   VecDuplicateVecs(ksp->work[0], restart + 1, &lcd->Q);
     18:   PetscLogObjectMemory(ksp,2*(restart+2)*sizeof(Vec));
     19:   return(0);
     20: }

     22: /*     KSPSolve_LCD - This routine actually applies the left conjugate
     23:     direction method

     25:    Input Parameter:
     26: .     ksp - the Krylov space object that was set to use LCD, by, for
     27:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPLCD);

     29:    Output Parameter:
     30: .     its - number of iterations used

     32: */
     35: PetscErrorCode  KSPSolve_LCD(KSP ksp)
     36: {
     38:   PetscInt       it,j,max_k;
     39:   PetscScalar    alfa, beta, num, den, mone;
     40:   PetscReal      rnorm;
     41:   Vec            X,B,R,Z;
     42:   KSP_LCD        *lcd;
     43:   Mat            Amat,Pmat;
     44:   MatStructure   pflag;
     45:   PetscBool      diagonalscale;

     48:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
     49:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

     51:   lcd   = (KSP_LCD*)ksp->data;
     52:   X     = ksp->vec_sol;
     53:   B     = ksp->vec_rhs;
     54:   R     = ksp->work[0];
     55:   Z     = ksp->work[1];
     56:   max_k = lcd->restart;
     57:   mone  = -1;

     59:   PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);

     61:   ksp->its = 0;
     62:   if (!ksp->guess_zero) {
     63:     KSP_MatMult(ksp,Amat,X,Z);             /*   z <- b - Ax       */
     64:     VecAYPX(Z,mone,B);
     65:   } else {
     66:     VecCopy(B,Z);                         /*     z <- b (x is 0) */
     67:   }

     69:   KSP_PCApply(ksp,Z,R);                   /*     r <- M^-1z         */
     70:   VecNorm(R,NORM_2,&rnorm);
     71:   KSPLogResidualHistory(ksp,rnorm);
     72:   KSPMonitor(ksp,0,rnorm);
     73:   ksp->rnorm = rnorm;

     75:   /* test for convergence */
     76:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
     77:   if (ksp->reason) return(0);

     79:   it = 0;
     80:   VecCopy(R,lcd->P[0]);

     82:   while (!ksp->reason && ksp->its < ksp->max_it) {
     83:     it   = 0;
     84:     KSP_MatMult(ksp,Amat,lcd->P[it],Z);
     85:     KSP_PCApply(ksp,Z,lcd->Q[it]);

     87:     while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
     88:       ksp->its++;
     89:       VecDot(lcd->P[it],R,&num);
     90:       VecDot(lcd->P[it],lcd->Q[it], &den);
     91:       alfa = num/den;
     92:       VecAXPY(X,alfa,lcd->P[it]);
     93:       VecAXPY(R,-alfa,lcd->Q[it]);
     94:       VecNorm(R,NORM_2,&rnorm);

     96:       ksp->rnorm = rnorm;
     97:       KSPLogResidualHistory(ksp,rnorm);
     98:       KSPMonitor(ksp,ksp->its,rnorm);
     99:       (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);

    101:       if (ksp->reason) break;

    103:       VecCopy(R,lcd->P[it+1]);
    104:       KSP_MatMult(ksp,Amat,lcd->P[it+1],Z);
    105:       KSP_PCApply(ksp,Z,lcd->Q[it+1]);

    107:       for (j = 0; j <= it; j++) {
    108:         VecDot(lcd->P[j],lcd->Q[it+1],&num);
    109:         VecDot(lcd->P[j],lcd->Q[j],&den);
    110:         beta = -num/den;
    111:         VecAXPY(lcd->P[it+1],beta,lcd->P[j]);
    112:         VecAXPY(lcd->Q[it+1],beta,lcd->Q[j]);
    113:       }
    114:       it++;
    115:     }
    116:     VecCopy(lcd->P[it],lcd->P[0]);
    117:   }
    118:   if (ksp->its >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    119:   VecCopy(X,ksp->vec_sol);
    120:   return(0);
    121: }
    122: /*
    123:        KSPDestroy_LCD - Frees all memory space used by the Krylov method

    125: */
    128: PetscErrorCode KSPReset_LCD(KSP ksp)
    129: {
    130:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;

    134:   if (lcd->P) { VecDestroyVecs(lcd->restart+1,&lcd->P);}
    135:   if (lcd->Q) { VecDestroyVecs(lcd->restart+1,&lcd->Q);}
    136:   return(0);
    137: }

    142: PetscErrorCode KSPDestroy_LCD(KSP ksp)
    143: {

    147:   KSPReset_LCD(ksp);
    148:   PetscFree(ksp->data);
    149:   return(0);
    150: }

    152: /*
    153:      KSPView_LCD - Prints information about the current Krylov method being used

    155:       Currently this only prints information to a file (or stdout) about the
    156:       symmetry of the problem. If your Krylov method has special options or
    157:       flags that information should be printed here.

    159: */
    162: PetscErrorCode KSPView_LCD(KSP ksp,PetscViewer viewer)
    163: {

    165:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;
    167:   PetscBool      iascii;

    170:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    171:   if (iascii) {
    172:     PetscViewerASCIIPrintf(viewer,"  LCD: restart=%d\n",lcd->restart);
    173:     PetscViewerASCIIPrintf(viewer,"  LCD: happy breakdown tolerance %g\n",lcd->haptol);
    174:   }
    175:   return(0);
    176: }

    178: /*
    179:     KSPSetFromOptions_LCD - Checks the options database for options related to the
    180:                             LCD method.
    181: */
    184: PetscErrorCode KSPSetFromOptions_LCD(KSP ksp)
    185: {
    187:   PetscBool      flg;
    188:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;

    191:   PetscOptionsHead("KSP LCD options");
    192:   PetscOptionsInt("-ksp_lcd_restart","Number of vectors conjugate","KSPLCDSetRestart",lcd->restart,&lcd->restart,&flg);
    193:   if (flg && lcd->restart < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
    194:   PetscOptionsReal("-ksp_lcd_haptol","Tolerance for exact convergence (happy ending)","KSPLCDSetHapTol",lcd->haptol,&lcd->haptol,&flg);
    195:   if (flg && lcd->haptol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
    196:   return(0);
    197: }

    199: /*MC
    200:      KSPLCD -  Implements the LCD (left conjugate direction) method in PETSc.

    202:    Options Database Keys:
    203: +   -ksp_lcd_restart - number of vectors conjudate
    204: -   -ksp_lcd_haptol - tolerance for exact convergence (happing ending)

    206:    Level: beginner

    208:     Notes: Support only for left preconditioning

    210:     References:
    211:    - J.Y. Yuan, G.H.Golub, R.J. Plemmons, and W.A.G. Cecilio. Semiconjugate
    212:      direction methods for real positive definite system. BIT Numerical
    213:      Mathematics, 44(1):189-207,2004.
    214:    - Y. Dai and J.Y. Yuan. Study on semi-conjugate direction methods for
    215:      non-symmetric systems. International Journal for Numerical Methods in
    216:      Engineering, 60:1383-1399,2004.
    217:    - L. Catabriga, A.L.G.A. Coutinho, and L.P.Franca. Evaluating the LCD
    218:      algorithm for solving linear systems of equations arising from implicit
    219:      SUPG formulation of compressible flows. International Journal for
    220:      Numerical Methods in Engineering, 60:1513-1534,2004
    221:    - L. Catabriga, A. M. P. Valli, B. Z. Melotti, L. M. Pessoa,
    222:      A. L. G. A. Coutinho, Performance of LCD iterative method in the finite
    223:      element and finite difference solution of convection-diffusion
    224:      equations,  Communications in Numerical Methods in Engineering, (Early
    225:      View).

    227:   Contributed by: Lucia Catabriga <luciac@ices.utexas.edu>

    230: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
    231:            KSPCGSetType(), KSPLCDSetRestart(), KSPLCDSetHapTol()

    233: M*/

    237: PETSC_EXTERN PetscErrorCode KSPCreate_LCD(KSP ksp)
    238: {
    240:   KSP_LCD        *lcd;

    243:   PetscNewLog(ksp,KSP_LCD,&lcd);
    244:   ksp->data    = (void*)lcd;
    245:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    246:   lcd->restart = 30;
    247:   lcd->haptol  = 1.0e-30;

    249:   /*
    250:        Sets the functions that are associated with this data structure
    251:        (in C++ this is the same as defining virtual functions)
    252:   */
    253:   ksp->ops->setup          = KSPSetUp_LCD;
    254:   ksp->ops->solve          = KSPSolve_LCD;
    255:   ksp->ops->reset          = KSPReset_LCD;
    256:   ksp->ops->destroy        = KSPDestroy_LCD;
    257:   ksp->ops->view           = KSPView_LCD;
    258:   ksp->ops->setfromoptions = KSPSetFromOptions_LCD;
    259:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    260:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    261:   return(0);
    262: }