[petsc-users] Preconditioned residuals for FGMRES

[Jed Brown]

It's a very different algorithm, but FBCGS is a flexible method that
supports preconditioned norm (though I don't how meaningful it is since
the preconditioner is changing).

Nishant Nangia <nishantnangia329 at gmail.com> writes:

> Hi,
>
> I am solving a saddle point system using a shell preconditioner (which
> itself uses Krylov solvers, hence the use of FGMRES). I had added the
> option to re-scale parts of the saddle point system to minimize loss of
> floating point precision for cases where there are varying orders of
> magnitude in the system/unknowns.
>
> I wanted to show that re-scaling can alleviate large differences between
> the preconditioned and unpreconditioned residual norms. However, I notice
> that FGMRES only supports right preconditioning, meaning the preconditioned
> residual is never formed/used (I think).
>
> Is there any way to form the preconditioned norm for FGMRES, or does it
> just not make sense in the context of right-preconditioned iterative
> solvers? Is there any way to show that the re-scaling is improving the
> solver convergence (i.e. showing that it ensures that the true and relative
> residual are close to each other)?
>
> *Nishant Nangia*
> Northwestern University
> Ph.D. Candidate | Engineering Sciences and Applied Mathematics
> Tech L386