[petsc-users] Preconditioned residuals for FGMRES

[Matthew Knepley]

On Fri, Jun 22, 2018 at 1:47 PM Boyce Griffith <griffith at cims.nyu.edu>
wrote:

> Can you set up the preconditioner so that you can just use GMRES?
>

So I think what Boyce is saying is, can't you fix the number of iterates in
the inner Krylov solvers so that it becomes a linear
operator and you can use GMRES?

  Thanks,

     Matt


> On Jun 22, 2018, at 4:33 PM, Nishant Nangia <nishantnangia329 at gmail.com>
> 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).
>
> 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
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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