Date: 2022-08-02T03:14:42+00:00

Actual source code: bicg.c

      2: #include <petsc/private/kspimpl.h>

      4: static PetscErrorCode KSPSetUp_BiCG(KSP ksp)
      5: {
      6:   /* check user parameters and functions */
      9:   KSPSetWorkVecs(ksp,6);
     10:   return 0;
     11: }

     13: static PetscErrorCode  KSPSolve_BiCG(KSP ksp)
     14: {
     15:   PetscInt       i;
     16:   PetscBool      diagonalscale;
     17:   PetscScalar    dpi,a=1.0,beta,betaold=1.0,b,ma;
     18:   PetscReal      dp;
     19:   Vec            X,B,Zl,Zr,Rl,Rr,Pl,Pr;
     20:   Mat            Amat,Pmat;

     22:   PCGetDiagonalScale(ksp->pc,&diagonalscale);

     25:   X  = ksp->vec_sol;
     26:   B  = ksp->vec_rhs;
     27:   Rl = ksp->work[0];
     28:   Zl = ksp->work[1];
     29:   Pl = ksp->work[2];
     30:   Rr = ksp->work[3];
     31:   Zr = ksp->work[4];
     32:   Pr = ksp->work[5];

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

     36:   if (!ksp->guess_zero) {
     37:     KSP_MatMult(ksp,Amat,X,Rr);      /*   r <- b - Ax       */
     38:     VecAYPX(Rr,-1.0,B);
     39:   } else {
     40:     VecCopy(B,Rr);           /*     r <- b (x is 0) */
     41:   }
     42:   VecCopy(Rr,Rl);
     43:   KSP_PCApply(ksp,Rr,Zr);     /*     z <- Br         */
     44:   KSP_PCApplyHermitianTranspose(ksp,Rl,Zl);
     45:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
     46:     VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
     47:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
     48:     VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
     49:   } else dp = 0.0;

     51:   KSPCheckNorm(ksp,dp);
     52:   KSPMonitor(ksp,0,dp);
     53:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
     54:   ksp->its   = 0;
     55:   ksp->rnorm = dp;
     56:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
     57:   KSPLogResidualHistory(ksp,dp);
     58:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
     59:   if (ksp->reason) return 0;

     61:   i = 0;
     62:   do {
     63:     VecDot(Zr,Rl,&beta);       /*     beta <- r'z     */
     64:     KSPCheckDot(ksp,beta);
     65:     if (!i) {
     66:       if (beta == 0.0) {
     67:         ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
     68:         return 0;
     69:       }
     70:       VecCopy(Zr,Pr);       /*     p <- z          */
     71:       VecCopy(Zl,Pl);
     72:     } else {
     73:       b    = beta/betaold;
     74:       VecAYPX(Pr,b,Zr);  /*     p <- z + b* p   */
     75:       b    = PetscConj(b);
     76:       VecAYPX(Pl,b,Zl);
     77:     }
     78:     betaold = beta;
     79:     KSP_MatMult(ksp,Amat,Pr,Zr); /*     z <- Kp         */
     80:     KSP_MatMultHermitianTranspose(ksp,Amat,Pl,Zl);
     81:     VecDot(Zr,Pl,&dpi);            /*     dpi <- z'p      */
     82:     KSPCheckDot(ksp,dpi);
     83:     a       = beta/dpi;                           /*     a = beta/p'z    */
     84:     VecAXPY(X,a,Pr);    /*     x <- x + ap     */
     85:     ma      = -a;
     86:     VecAXPY(Rr,ma,Zr);
     87:     ma      = PetscConj(ma);
     88:     VecAXPY(Rl,ma,Zl);
     89:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
     90:       KSP_PCApply(ksp,Rr,Zr);  /*     z <- Br         */
     91:       KSP_PCApplyHermitianTranspose(ksp,Rl,Zl);
     92:       VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
     93:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
     94:       VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
     95:     } else dp = 0.0;

     97:     KSPCheckNorm(ksp,dp);
     98:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
     99:     ksp->its   = i+1;
    100:     ksp->rnorm = dp;
    101:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
    102:     KSPLogResidualHistory(ksp,dp);
    103:     KSPMonitor(ksp,i+1,dp);
    104:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    105:     if (ksp->reason) break;
    106:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    107:       KSP_PCApply(ksp,Rr,Zr);  /* z <- Br  */
    108:       KSP_PCApplyHermitianTranspose(ksp,Rl,Zl);
    109:     }
    110:     i++;
    111:   } while (i<ksp->max_it);
    112:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    113:   return 0;
    114: }

    116: /*MC
    117:      KSPBICG - Implements the Biconjugate gradient method (similar to running the conjugate
    118:          gradient on the normal equations).

    120:    Options Database Keys:
    121:    see KSPSolve()

    123:    Level: beginner

    125:    Notes:
    126:     this method requires that one be apply to apply the transpose of the preconditioner and operator
    127:          as well as the operator and preconditioner.
    128:          Supports only left preconditioning

    130:          See KSPCGNE for code that EXACTLY runs the preconditioned conjugate gradient method on the
    131:          normal equations

    133: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBCGS, KSPCGNE

    135: M*/
    136: PETSC_EXTERN PetscErrorCode KSPCreate_BiCG(KSP ksp)
    137: {
    138:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    139:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    140:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    142:   ksp->ops->setup          = KSPSetUp_BiCG;
    143:   ksp->ops->solve          = KSPSolve_BiCG;
    144:   ksp->ops->destroy        = KSPDestroyDefault;
    145:   ksp->ops->view           = NULL;
    146:   ksp->ops->setfromoptions = NULL;
    147:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    148:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    149:   return 0;
    150: }