[petsc-users] Preconditioned residuals for FGMRES

[Nishant Nangia]

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
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