[petsc-users] Preconditioned residuals for FGMRES

[Boyce Griffith]

> On Jun 22, 2018, at 4:49 PM, Matthew Knepley <knepley at gmail.com> wrote:
> 
>> 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?

Yes that is it.

I think we default to FGMRES for robustness, because the preconditioner can easily be configured to be nonlinear, but unless you have made some big changes to the algorithm that I think you are using, I think it should be possible to set it up as a stationary linear operator.

>   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/
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