[petsc-users] [petsc-maint] the role of field split pressure inner solver

Matthew Knepley knepley at gmail.com
Sun Mar 18 19:14:52 CDT 2018

On Sun, Mar 18, 2018 at 8:02 PM, Jed Brown <jed at jedbrown.org> wrote:

> The inner solver matters in practice, but that paper is predicated on
> the assumption that a scalable inner solver is available and is
> practical to apply exactly (e.g., converge to a tight tolerance).
> In practice, it often occupies most of the time and sometimes is the
> greatest robustness challenge.  But there isn't a clean theory for how
> its inexactness affects the coupled solve.

Yes, there is no theory that I know of. It is easy to see that relaxing the
here kills the outer convergence by experimenting however. Theory so often


> John <johnlucassaturday at gmail.com> writes:
> > Hello:
> >
> > I just have a very general question with regard to the Schur complement.
> In
> > the literature (e.g. H. Elman, et al. A taxonomy and comparison of
> parallel
> > block multi-level preconditioners for the incompressible Navier-Stokes
> > equations), people discuss the preconditioner for the Schur (SIMPLE, PCD,
> > LSC etc.), the role of the inner solver in the exact Schur is rarely
> > mentioned. My limited numerical experience is that the inner solver
> affects
> > the convergence rate (hence robustness) at least.
> >
> > My general question is that why do most people ignore the inner solver
> > inside Schur? Is it non-important, or is it bad for parallel scaling?
> >
> > Thanks!
> >
> > John

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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