[petsc-users] Preconditioned residuals for FGMRES

[Smith, Barry F.]

> On Jun 22, 2018, at 3:33 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).

  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