[petsc-users] Deflated GMRES in PETSc

[Jed Brown]

[Cc'ing petsc-users since people may be interested.]

Matteo Parsani <parsani.matteo at gmail.com> writes:

> Hi Jed,
> do you know if in PETSc we can start a Krylov iteration with problematic
> eigenmodes in the Krylov subspace at the beginning of the iteration?

Deflation is identical to a Galerkin coarse grid correction.  I would
use PCMG to create a two-level method.  Write your deflation space into
the prolongation operator and use Galerkin.  You can compose a PCMG with
other preconditioners.  I would leave DGMRES to only deal with adaptive
identification of those problematic modes.  Note that the DGMRES basis
vectors will be global, but when you provide vectors a priori, you are
free to localize them.

> Machinery should be there already because we see that this is used when
> GMRES stagnates.
>
> Thanks,
>
> -- 
> Matteo