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 - A transpose-free QMR (quasi minimal residual) {cite}`f:93`

128:    Level: beginner

130:    Notes:
131:    Supports left and right preconditioning, but not symmetric

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

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

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

150:   ksp->data                = (void *)0;
151:   ksp->ops->setup          = KSPSetUp_TFQMR;
152:   ksp->ops->solve          = KSPSolve_TFQMR;
153:   ksp->ops->destroy        = KSPDestroyDefault;
154:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
155:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
156:   ksp->ops->setfromoptions = NULL;
157:   ksp->ops->view           = NULL;
158:   PetscFunctionReturn(PETSC_SUCCESS);
159: }