Date: 2015-10-02T22:21:31+00:00

Actual source code: tfqmr.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/kspimpl.h>

      6: static PetscErrorCode KSPSetUp_TFQMR(KSP ksp)
      7: {

     11:   if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"no symmetric preconditioning for KSPTFQMR");
     12:   KSPSetWorkVecs(ksp,9);
     13:   return(0);
     14: }

     18: static PetscErrorCode  KSPSolve_TFQMR(KSP ksp)
     19: {
     21:   PetscInt       i,m;
     22:   PetscScalar    rho,rhoold,a,s,b,eta,etaold,psiold,cf;
     23:   PetscReal      dp,dpold,w,dpest,tau,psi,cm;
     24:   Vec            X,B,V,P,R,RP,T,T1,Q,U,D,AUQ;

     27:   X   = ksp->vec_sol;
     28:   B   = ksp->vec_rhs;
     29:   R   = ksp->work[0];
     30:   RP  = ksp->work[1];
     31:   V   = ksp->work[2];
     32:   T   = ksp->work[3];
     33:   Q   = ksp->work[4];
     34:   P   = ksp->work[5];
     35:   U   = ksp->work[6];
     36:   D   = ksp->work[7];
     37:   T1  = ksp->work[8];
     38:   AUQ = V;

     40:   /* Compute initial preconditioned residual */
     41:   KSPInitialResidual(ksp,X,V,T,R,B);

     43:   /* Test for nothing to do */
     44:   VecNorm(R,NORM_2,&dp);
     45:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
     46:   ksp->rnorm = dp;
     47:   ksp->its   = 0;
     48:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
     49:   KSPMonitor(ksp,0,dp);
     50:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
     51:   if (ksp->reason) return(0);

     53:   /* Make the initial Rp == R */
     54:   VecCopy(R,RP);

     56:   /* Set the initial conditions */
     57:   etaold = 0.0;
     58:   psiold = 0.0;
     59:   tau    = dp;
     60:   dpold  = dp;

     62:   VecDot(R,RP,&rhoold);       /* rhoold = (r,rp)     */
     63:   VecCopy(R,U);
     64:   VecCopy(R,P);
     65:   KSP_PCApplyBAorAB(ksp,P,V,T);
     66:   VecSet(D,0.0);

     68:   i=0;
     69:   do {
     70:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
     71:     ksp->its++;
     72:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
     73:     VecDot(V,RP,&s);          /* s <- (v,rp)          */
     74:     a    = rhoold / s;                              /* a <- rho / s         */
     75:     VecWAXPY(Q,-a,V,U);  /* q <- u - a v         */
     76:     VecWAXPY(T,1.0,U,Q);     /* t <- u + q           */
     77:     KSP_PCApplyBAorAB(ksp,T,AUQ,T1);
     78:     VecAXPY(R,-a,AUQ);      /* r <- r - a K (u + q) */
     79:     VecNorm(R,NORM_2,&dp);
     80:     for (m=0; m<2; m++) {
     81:       if (!m) w = PetscSqrtReal(dp*dpold);
     82:       else w = dp;
     83:       psi = w / tau;
     84:       cm  = 1.0 / PetscSqrtReal(1.0 + psi * psi);
     85:       tau = tau * psi * cm;
     86:       eta = cm * cm * a;
     87:       cf  = psiold * psiold * etaold / a;
     88:       if (!m) {
     89:         VecAYPX(D,cf,U);
     90:       } else {
     91:         VecAYPX(D,cf,Q);
     92:       }
     93:       VecAXPY(X,eta,D);

     95:       dpest      = PetscSqrtReal(m + 1.0) * tau;
     96:       PetscObjectSAWsTakeAccess((PetscObject)ksp);
     97:       ksp->rnorm = dpest;
     98:       PetscObjectSAWsGrantAccess((PetscObject)ksp);
     99:       KSPLogResidualHistory(ksp,dpest);
    100:       KSPMonitor(ksp,i+1,dpest);
    101:       (*ksp->converged)(ksp,i+1,dpest,&ksp->reason,ksp->cnvP);
    102:       if (ksp->reason) break;

    104:       etaold = eta;
    105:       psiold = psi;
    106:     }
    107:     if (ksp->reason) break;

    109:     VecDot(R,RP,&rho);        /* rho <- (r,rp)       */
    110:     b    = rho / rhoold;                            /* b <- rho / rhoold   */
    111:     VecWAXPY(U,b,Q,R);       /* u <- r + b q        */
    112:     VecAXPY(Q,b,P);
    113:     VecWAXPY(P,b,Q,U);       /* p <- u + b(q + b p) */
    114:     KSP_PCApplyBAorAB(ksp,P,V,Q); /* v <- K p  */

    116:     rhoold = rho;
    117:     dpold  = dp;

    119:     i++;
    120:   } while (i<ksp->max_it);
    121:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;

    123:   KSPUnwindPreconditioner(ksp,X,T);
    124:   return(0);
    125: }

    127: /*MC
    128:      KSPTFQMR - A transpose free QMR (quasi minimal residual),

    130:    Options Database Keys:
    131: .   see KSPSolve()

    133:    Level: beginner

    135:    Notes: Supports left and right preconditioning, but not symmetric

    137:           The "residual norm" computed in this algorithm is actually just an upper bound on the actual residual norm.
    138:           That is for left preconditioning it is a bound on the preconditioned residual and for right preconditioning
    139:           it is a bound on the true residual.

    141:    References: Freund, 1993

    143: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPTCQMR
    144: M*/
    147: PETSC_EXTERN PetscErrorCode KSPCreate_TFQMR(KSP ksp)
    148: {

    152:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    153:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

    155:   ksp->data                = (void*)0;
    156:   ksp->ops->setup          = KSPSetUp_TFQMR;
    157:   ksp->ops->solve          = KSPSolve_TFQMR;
    158:   ksp->ops->destroy        = KSPDestroyDefault;
    159:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    160:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    161:   ksp->ops->setfromoptions = 0;
    162:   ksp->ops->view           = 0;
    163:   return(0);
    164: }