[petsc-users] difference between left and right pc

[Klaij, Christiaan]

> > > > 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

Thanks Matt. But don't you mean *left* preconditioning would do
nothing at all? If P^{-1} has a null space and b fits into it
then P^{-1} A x = P^{-1} b => A x = 0 => x = 0. That's not what
I'm seeing.

Chris


dr. ir. Christiaan Klaij
CFD Researcher
Research & Development
E mailto:C.Klaij at marin.nl
T +31 317 49 33 44

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