[petsc-users] difference between left and right pc

[Matthew Knepley]

On Thu, Sep 20, 2012 at 2:11 AM, Klaij, Christiaan <C.Klaij at marin.nl> wrote:

> > > I'm solving a system with GMRES using the same preconditioner either on
> > > the left or on the right.
> > > For left preconditioning I get two orders of reduction for the
> > > preconditioned residual in 20 its:
> > >
> >
> > Notice here that your "preconditioner" is far from one. It manages to
> blow
> > up the true residual by
> > 5 orders of magnitude, from which it never recovers. The right
> > preconditioning just avoids being
> > so screwed up.
> >
> >    Matt
>
> Yes, I noticed that. It does recover 2 orders in 20 its, and it
> can recover 5 orders and beyond in a few hundred its. What I
> don't understand is how the same preconditioner applied to the
> right "just avoids being so screwed up".
>

Suppose that your preconditioner has a huge null space, and b fits
into it. Then right preconditioning would do nothing at all. Some tiny
bit would creep through since Ab is not entirely in it, but there would
be a small preconditioned residual with large true residual.

    Matt


> Chris
>
>
> dr. ir. Christiaan Klaij
> CFD Researcher
> Research & Development
> E mailto:C.Klaij at marin.nl
> T +31 317 49 33 44
>
> MARIN
> 2, Haagsteeg, P.O. Box 28, 6700 AA Wageningen, The Netherlands
> T +31 317 49 39 11, F +31 317 49 32 45, I www.marin.nl
>
>


-- 
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
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