> On Jun 22, 2018, at 3:33 PM, Nishant Nangia <[email protected]>
> wrote:
>
> 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).
Yes, FGMRES doesn't make sense with left preconditioning.
>
> 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?
It doesn't make sense for right preconditioning.
> 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)?
I don't think so. I think the only thing you could hope to show is that the
rescaling requires fewer FGMRES iterations.
Barry
>
> Nishant Nangia
> Northwestern University
> Ph.D. Candidate | Engineering Sciences and Applied Mathematics
> Tech L386
