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

Jed Brown jed at jedbrown.org
Sun Mar 18 19:02:27 CDT 2018

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.

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

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