Actual source code: lcd.c
petsc-3.10.5 2019-03-28
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      2:  #include <../src/ksp/ksp/impls/lcd/lcdimpl.h>

      4: PetscErrorCode KSPSetUp_LCD(KSP ksp)
      5: {
      6:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;
      8:   PetscInt       restart = lcd->restart;

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

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

     20: /*     KSPSolve_LCD - This routine actually applies the left conjugate
     21:     direction method

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

     27:    Output Parameter:
     28: .     its - number of iterations used

     30: */
     31: PetscErrorCode  KSPSolve_LCD(KSP ksp)
     32: {
     34:   PetscInt       it,j,max_k;
     35:   PetscScalar    alfa, beta, num, den, mone;
     36:   PetscReal      rnorm;
     37:   Vec            X,B,R,Z;
     38:   KSP_LCD        *lcd;
     39:   Mat            Amat,Pmat;
     40:   PetscBool      diagonalscale;

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

     46:   lcd   = (KSP_LCD*)ksp->data;
     47:   X     = ksp->vec_sol;
     48:   B     = ksp->vec_rhs;
     49:   R     = ksp->work[0];
     50:   Z     = ksp->work[1];
     51:   max_k = lcd->restart;
     52:   mone  = -1;

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

     56:   ksp->its = 0;
     57:   if (!ksp->guess_zero) {
     58:     KSP_MatMult(ksp,Amat,X,Z);             /*   z <- b - Ax       */
     59:     VecAYPX(Z,mone,B);
     60:   } else {
     61:     VecCopy(B,Z);                         /*     z <- b (x is 0) */
     62:   }

     64:   KSP_PCApply(ksp,Z,R);                   /*     r <- M^-1z         */
     65:   VecNorm(R,NORM_2,&rnorm);
     66:   KSPLogResidualHistory(ksp,rnorm);
     67:   KSPMonitor(ksp,0,rnorm);
     68:   ksp->rnorm = rnorm;

     70:   /* test for convergence */
     71:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
     72:   if (ksp->reason) return(0);

     74:   VecCopy(R,lcd->P[0]);

     76:   while (!ksp->reason && ksp->its < ksp->max_it) {
     77:     it   = 0;
     78:     KSP_MatMult(ksp,Amat,lcd->P[it],Z);
     79:     KSP_PCApply(ksp,Z,lcd->Q[it]);

     81:     while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
     82:       ksp->its++;
     83:       VecDot(lcd->P[it],R,&num);
     84:       VecDot(lcd->P[it],lcd->Q[it], &den);
     85:       alfa = num/den;
     86:       VecAXPY(X,alfa,lcd->P[it]);
     87:       VecAXPY(R,-alfa,lcd->Q[it]);
     88:       VecNorm(R,NORM_2,&rnorm);

     90:       ksp->rnorm = rnorm;
     91:       KSPLogResidualHistory(ksp,rnorm);
     92:       KSPMonitor(ksp,ksp->its,rnorm);
     93:       (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);

     95:       if (ksp->reason) break;

     97:       VecCopy(R,lcd->P[it+1]);
     98:       KSP_MatMult(ksp,Amat,lcd->P[it+1],Z);
     99:       KSP_PCApply(ksp,Z,lcd->Q[it+1]);

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

    119: */
    120: PetscErrorCode KSPReset_LCD(KSP ksp)
    121: {
    122:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;

    126:   if (lcd->P) { VecDestroyVecs(lcd->restart+1,&lcd->P);}
    127:   if (lcd->Q) { VecDestroyVecs(lcd->restart+1,&lcd->Q);}
    128:   return(0);
    129: }

    132: PetscErrorCode KSPDestroy_LCD(KSP ksp)
    133: {

    137:   KSPReset_LCD(ksp);
    138:   PetscFree(ksp->data);
    139:   return(0);
    140: }

    142: /*
    143:      KSPView_LCD - Prints information about the current Krylov method being used

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

    149: */
    150: PetscErrorCode KSPView_LCD(KSP ksp,PetscViewer viewer)
    151: {

    153:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;
    155:   PetscBool      iascii;

    158:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    159:   if (iascii) {
    160:     PetscViewerASCIIPrintf(viewer,"  restart=%d\n",lcd->restart);
    161:     PetscViewerASCIIPrintf(viewer,"  happy breakdown tolerance %g\n",lcd->haptol);
    162:   }
    163:   return(0);
    164: }

    166: /*
    167:     KSPSetFromOptions_LCD - Checks the options database for options related to the
    168:                             LCD method.
    169: */
    170: PetscErrorCode KSPSetFromOptions_LCD(PetscOptionItems *PetscOptionsObject,KSP ksp)
    171: {
    173:   PetscBool      flg;
    174:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;

    177:   PetscOptionsHead(PetscOptionsObject,"KSP LCD options");
    178:   PetscOptionsInt("-ksp_lcd_restart","Number of vectors conjugate","KSPLCDSetRestart",lcd->restart,&lcd->restart,&flg);
    179:   if (flg && lcd->restart < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
    180:   PetscOptionsReal("-ksp_lcd_haptol","Tolerance for exact convergence (happy ending)","KSPLCDSetHapTol",lcd->haptol,&lcd->haptol,&flg);
    181:   if (flg && lcd->haptol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
    182:   return(0);
    183: }

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

    188:    Options Database Keys:
    189: +   -ksp_lcd_restart - number of vectors conjudate
    190: -   -ksp_lcd_haptol - tolerance for exact convergence (happing ending)

    192:    Level: beginner

    194:     Notes:
    195:     Support only for left preconditioning

    197:     References:
    198: +    1. - J.Y. Yuan, G.H.Golub, R.J. Plemmons, and W.A.G. Cecilio. Semiconjugate
    199:      direction methods for real positive definite system. BIT Numerical
    200:      Mathematics, 44(1),2004.
    201: .    2. - Y. Dai and J.Y. Yuan. Study on semiconjugate direction methods for
    202:      nonsymmetric systems. International Journal for Numerical Methods in
    203:      Engineering, 60, 2004.
    204: .    3. - L. Catabriga, A.L.G.A. Coutinho, and L.P.Franca. Evaluating the LCD
    205:      algorithm for solving linear systems of equations arising from implicit
    206:      SUPG formulation of compressible flows. International Journal for
    207:      Numerical Methods in Engineering, 60, 2004
    208: -    4. - L. Catabriga, A. M. P. Valli, B. Z. Melotti, L. M. Pessoa,
    209:      A. L. G. A. Coutinho, Performance of LCD iterative method in the finite
    210:      element and finite difference solution of convection diffusion
    211:      equations,  Communications in Numerical Methods in Engineering, (Early
    212:      View).

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

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

    220: M*/

    222: PETSC_EXTERN PetscErrorCode KSPCreate_LCD(KSP ksp)
    223: {
    225:   KSP_LCD        *lcd;

    228:   PetscNewLog(ksp,&lcd);
    229:   ksp->data    = (void*)lcd;
    230:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    231:   lcd->restart = 30;
    232:   lcd->haptol  = 1.0e-30;

    234:   /*
    235:        Sets the functions that are associated with this data structure
    236:        (in C++ this is the same as defining virtual functions)
    237:   */
    238:   ksp->ops->setup          = KSPSetUp_LCD;
    239:   ksp->ops->solve          = KSPSolve_LCD;
    240:   ksp->ops->reset          = KSPReset_LCD;
    241:   ksp->ops->destroy        = KSPDestroy_LCD;
    242:   ksp->ops->view           = KSPView_LCD;
    243:   ksp->ops->setfromoptions = KSPSetFromOptions_LCD;
    244:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    245:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    246:   return(0);
    247: }