Actual source code: tfqmr.c

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

      3: static PetscErrorCode KSPSetUp_TFQMR(KSP ksp)
      4: {
      5:   PetscFunctionBegin;
      6:   PetscCheck(ksp->pc_side != PC_SYMMETRIC, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "no symmetric preconditioning for KSPTFQMR");
      7:   PetscCall(KSPSetWorkVecs(ksp, 9));
      8:   PetscFunctionReturn(PETSC_SUCCESS);
      9: }

     11: static PetscErrorCode KSPSolve_TFQMR(KSP ksp)
     12: {
     13:   PetscInt    i, m;
     14:   PetscScalar rho, rhoold, a, s, b, eta, etaold, psiold, cf;
     15:   PetscReal   dp, dpold, w, dpest, tau, psi, cm;
     16:   Vec         X, B, V, P, R, RP, T, T1, Q, U, D, AUQ;

     18:   PetscFunctionBegin;
     19:   X   = ksp->vec_sol;
     20:   B   = ksp->vec_rhs;
     21:   R   = ksp->work[0];
     22:   RP  = ksp->work[1];
     23:   V   = ksp->work[2];
     24:   T   = ksp->work[3];
     25:   Q   = ksp->work[4];
     26:   P   = ksp->work[5];
     27:   U   = ksp->work[6];
     28:   D   = ksp->work[7];
     29:   T1  = ksp->work[8];
     30:   AUQ = V;

     32:   /* Compute initial preconditioned residual */
     33:   PetscCall(KSPInitialResidual(ksp, X, V, T, R, B));

     35:   /* Test for nothing to do */
     36:   PetscCall(VecNorm(R, NORM_2, &dp));
     37:   KSPCheckNorm(ksp, dp);
     38:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
     39:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = dp;
     40:   else ksp->rnorm = 0.0;
     41:   ksp->its = 0;
     42:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
     43:   PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
     44:   PetscCall(KSPMonitor(ksp, 0, ksp->rnorm));
     45:   PetscCall((*ksp->converged)(ksp, 0, ksp->rnorm, &ksp->reason, ksp->cnvP));
     46:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

     48:   /* Make the initial Rp == R */
     49:   PetscCall(VecCopy(R, RP));

     51:   /* Set the initial conditions */
     52:   etaold = 0.0;
     53:   psiold = 0.0;
     54:   tau    = dp;
     55:   dpold  = dp;

     57:   PetscCall(VecDot(R, RP, &rhoold)); /* rhoold = (r,rp)     */
     58:   PetscCall(VecCopy(R, U));
     59:   PetscCall(VecCopy(R, P));
     60:   PetscCall(KSP_PCApplyBAorAB(ksp, P, V, T));
     61:   PetscCall(VecSet(D, 0.0));

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

     92:       dpest = PetscSqrtReal(2 * i + m + 2.0) * tau;
     93:       PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
     94:       if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = dpest;
     95:       else ksp->rnorm = 0.0;
     96:       PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
     97:       PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
     98:       PetscCall(KSPMonitor(ksp, i + 1, ksp->rnorm));
     99:       PetscCall((*ksp->converged)(ksp, i + 1, ksp->rnorm, &ksp->reason, ksp->cnvP));
    100:       if (ksp->reason) break;

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

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

    114:     rhoold = rho;
    115:     dpold  = dp;

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

    121:   PetscCall(KSPUnwindPreconditioner(ksp, X, T));
    122:   PetscFunctionReturn(PETSC_SUCCESS);
    123: }

    125: /*MC
    126:    KSPTFQMR - An implementation of transpose-free QMR (quasi minimal residual) {cite}`f:93`.

    128:    Level: intermediate

    130:    Notes:
    131:    Transpose-free QMR is an algorithm somewhat similar to QMR, but unlike QMR it does not need the application
    132:    of the transpose of the matrix or preconditioner.

    134:    Supports left and right preconditioning, but not symmetric

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

    140:    The solver has a two-step inner iteration, each of which computes and updates the solution and the residual norm.
    141:    Hence the values from `KSPGetResidualHistory()` and `KSPGetIterationNumber()` will differ.

    143: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPTCQMR`
    144: M*/
    145: PETSC_EXTERN PetscErrorCode KSPCreate_TFQMR(KSP ksp)
    146: {
    147:   PetscFunctionBegin;
    148:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
    149:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
    150:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));
    151:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

    153:   ksp->data                = NULL;
    154:   ksp->ops->setup          = KSPSetUp_TFQMR;
    155:   ksp->ops->solve          = KSPSolve_TFQMR;
    156:   ksp->ops->destroy        = KSPDestroyDefault;
    157:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    158:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    159:   ksp->ops->setfromoptions = NULL;
    160:   ksp->ops->view           = NULL;
    161:   PetscFunctionReturn(PETSC_SUCCESS);
    162: }