static PetscErrorCode KSPSolve_AGMRES(KSP ksp)
{
PetscErrorCode ierr;
PetscInt its;
KSP_AGMRES *agmres = (KSP_AGMRES*)ksp->data;
PetscBool guess_zero = ksp->guess_zero;
PetscReal res_old, res;
PetscInt test;
PetscFunctionBegin;
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->reason = KSP_CONVERGED_ITERATING;
if (!agmres->HasShifts) { /* Compute Shifts for the Newton basis */
ierr = KSPComputeShifts_DGMRES(ksp);CHKERRQ(ierr);
}
/* NOTE: At this step, the initial guess is not equal to zero since one cycle of the classical GMRES is performed to compute the shifts */
ierr = (*ksp->converged)(ksp,0,ksp->rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
while (!ksp->reason) {
ierr = KSPInitialResidual(ksp,ksp->vec_sol,VEC_TMP,VEC_TMP_MATOP,VEC_V(0),ksp->vec_rhs);CHKERRQ(ierr);
if ((ksp->pc_side == PC_LEFT) && agmres->r && agmres->DeflPrecond) {
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_V(0), VEC_TMP);CHKERRQ(ierr);
ierr = VecCopy(VEC_TMP, VEC_V(0));CHKERRQ(ierr);
agmres->matvecs += 1;
}
ierr = VecNormalize(VEC_V(0),&(ksp->rnorm));CHKERRQ(ierr);
KSPCheckNorm(ksp,ksp->rnorm);
res_old = ksp->rnorm; /* Record the residual norm to test if deflation is needed */
ksp->ops->buildsolution = KSPBuildSolution_AGMRES;
ierr = KSPAGMRESCycle(&its,ksp);CHKERRQ(ierr);
if (ksp->its >= ksp->max_it) {
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
break;
}
/* compute the eigenvectors to augment the subspace : use an adaptive strategy */
res = ksp->rnorm;
if (!ksp->reason && agmres->neig > 0) {
test = agmres->max_k * PetscLogReal(ksp->rtol/res) / PetscLogReal(res/res_old); /* estimate the remaining number of steps */
if ((test > agmres->smv*(ksp->max_it-ksp->its)) || agmres->force) {
if (!agmres->force && ((test > agmres->bgv*(ksp->max_it-ksp->its)) && ((agmres->r + 1) < agmres->max_neig))) {
agmres->neig += 1; /* Augment the number of eigenvalues to deflate if the convergence is too slow */
}
ierr = KSPDGMRESComputeDeflationData_DGMRES(ksp,&agmres->neig);CHKERRQ(ierr);
}
}
ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
}
ksp->guess_zero = guess_zero; /* restore if user has provided nonzero initial guess */
PetscFunctionReturn(0);
}
PetscErrorCode KSPComputeShifts_DGMRES(KSP ksp)
{
PetscErrorCode ierr;
KSP_AGMRES *agmres = (KSP_AGMRES*)(ksp->data);
PetscInt max_k = agmres->max_k; /* size of the (non augmented) Krylov subspace */
PetscInt Neig = 0;
PetscInt max_it = ksp->max_it;
/* Perform one cycle of dgmres to find the eigenvalues and compute the first approximations of the eigenvectors */
PetscFunctionBegin;
ierr = PetscLogEventBegin(KSP_AGMRESComputeShifts, ksp, 0,0,0);CHKERRQ(ierr);
/* Send the size of the augmented basis to DGMRES */
ksp->max_it = max_k; /* set this to have DGMRES performing only one cycle */
ksp->ops->buildsolution = KSPBuildSolution_DGMRES;
ierr = KSPSolve_DGMRES(ksp);
ksp->guess_zero = PETSC_FALSE;
if (ksp->reason == KSP_CONVERGED_RTOL) {
ierr = PetscLogEventEnd(KSP_AGMRESComputeShifts, ksp, 0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
} else ksp->reason = KSP_CONVERGED_ITERATING;
if ((agmres->r == 0) && (agmres->neig > 0)) { /* Compute the eigenvalues for the shifts and the eigenvectors (to augment the Newton basis) */
agmres->HasSchur = PETSC_FALSE;
ierr = KSPDGMRESComputeDeflationData_DGMRES (ksp, &Neig);CHKERRQ (ierr);
Neig = max_k;
} else { /* From DGMRES, compute only the eigenvalues needed as Shifts for the Newton Basis */
ierr = KSPDGMRESComputeSchurForm_DGMRES(ksp, &Neig);CHKERRQ(ierr);
}
/* It may happen that the Ritz values from one cycle of GMRES are not accurate enough to provide a good stability. In this case, another cycle of GMRES is performed. The two sets of values thus generated are sorted and the most accurate are kept as shifts */
PetscBool flg;
ierr = PetscOptionsHasName(NULL, "-ksp_agmres_ImproveShifts", &flg);CHKERRQ(ierr);
if (!flg) {
ierr = KSPAGMRESLejaOrdering(agmres->wr, agmres->wi, agmres->Rshift, agmres->Ishift, max_k);CHKERRQ(ierr);
} else { /* Perform another cycle of DGMRES to find another set of eigenvalues */
PetscInt i;
PetscScalar *wr, *wi,*Rshift, *Ishift;
ierr = PetscMalloc4(2*max_k, &wr, 2*max_k, &wi, 2*max_k, &Rshift, 2*max_k, &Ishift);CHKERRQ(ierr);
for (i = 0; i < max_k; i++) {
wr[i] = agmres->wr[i];
wi[i] = agmres->wi[i];
}
ierr = KSPSolve_DGMRES(ksp);
ksp->guess_zero = PETSC_FALSE;
if (ksp->reason == KSP_CONVERGED_RTOL) PetscFunctionReturn(0);
else ksp->reason = KSP_CONVERGED_ITERATING;
if (agmres->neig > 0) { /* Compute the eigenvalues for the shifts) and the eigenvectors (to augment the Newton basis */
agmres->HasSchur = PETSC_FALSE;
ierr = KSPDGMRESComputeDeflationData_DGMRES(ksp, &Neig);CHKERRQ(ierr);
Neig = max_k;
} else { /* From DGMRES, compute only the eigenvalues needed as Shifts for the Newton Basis */
ierr = KSPDGMRESComputeSchurForm_DGMRES(ksp, &Neig);CHKERRQ(ierr);
}
for (i = 0; i < max_k; i++) {
wr[max_k+i] = agmres->wr[i];
wi[max_k+i] = agmres->wi[i];
}
ierr = KSPAGMRESLejaOrdering(wr, wi, Rshift, Ishift, 2*max_k);CHKERRQ(ierr);
for (i = 0; i< max_k; i++) {
agmres->Rshift[i] = Rshift[i];
agmres->Ishift[i] = Ishift[i];
}
ierr = PetscFree(Rshift);CHKERRQ(ierr);
ierr = PetscFree(wr);CHKERRQ(ierr);
ierr = PetscFree(Ishift);CHKERRQ(ierr);
ierr = PetscFree(wi);CHKERRQ(ierr);
}
agmres->HasShifts = PETSC_TRUE;
ksp->max_it = max_it;
ierr = PetscLogEventEnd(KSP_AGMRESComputeShifts, ksp, 0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
