[petsc-users] Motivation for default KSP solver and PC

[Matthew Knepley]

On Mon, Sep 21, 2020 at 10:20 AM Lawrence Mitchell <wence at gmx.li> wrote:

> > On 21 Sep 2020, at 14:03, Matthew Knepley <knepley at gmail.com> wrote:
> >
> > On Mon, Sep 21, 2020 at 8:51 AM Luciano Siqueira <
> luciano.siqueira at usp.br> wrote:
> > Hi *,
> >
> > I'm experimenting with different combinations of KSP solvers and PCs and
> > I don't know why GMRES/bjacobi are the default choices for CPU and
> >
> > GMRES is chosen because it is monotonic in the 2-norm, and also faster
> than any other
> > Krylov method in terms of iterates if you do not restart.
>
> Counterpoint: https://doi.org/10.1137/0613049


I was trying to be careful with "Krylov". What I meant by that is a method
that forms the solution from
the Krylov space

  {r, Ar, A^2r, ..., A^kr}

The other methods in the article use A^T as well. I don't think we can
generically call them Lanczos, but
maybe we need a word for methods going outside of the Krylov space above.

  Matt


>
> Lawrence
>
-- 
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.cse.buffalo.edu/~knepley/>
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