# [SciPy-User] preconditioner for GMRES

Darcoux Christine bouloumag@gmail....
Mon Mar 29 17:59:37 CDT 2010

```Thnak you. I will look at these links.

I am using the finite volume method, with QUICK advection (maybe I will try
flux limiters in the future if there are too much oscillations).

2010/3/29 Joshua Stults <joshua.stults@gmail.com>

> On Mon, Mar 29, 2010 at 4:54 PM, Darcoux Christine <bouloumag@gmail.com>
> wrote:
> > I am developping a Jacobian-Free Newton-Krylov code to solve the Navier
> > Stokes equations. In this code, the product of the Jacobian matrix with a
> > given vector is represented by the matvec method of a "LinearOperator"
> > object. The scipy.sparse.linalg.isolve.gmres method can takes an optional
> > preconditioner as parameter which is either an object "LinearOperator" or
> a
> > matrix. However, the scipy documentation does not explain how one can
> form
> > this preconditioner in a (ideally) matrix-free manner given only the
> matvec
> > method of the jacobian.
> >
> > Any suggestions on this would be very appreciated.
> >
>
> A pretty straight-forward way to precondition these types of problems
> in a matrix-free way is with symmetric successive over relaxation (the
> symmetric part is important, you need to do a 'forward' and a
> 'backward' sweep or things won't converge):
> http://www.netlib.org/linalg/old_html_templates/subsection2.6.2.4.html
>
> You'll have to derive the update formulas yourself based on the type
> of discretization you are using;  if you are using a transform based
> method, then you can still precondition based on a low-order scheme.
> IIRC Boyd has a pretty decent discussion of this in his spectral
> methods book.
>
> Maybe you could construct one of the approximate factorization
> preconditioners using only the matvec of your Jacobian, but I've never
> gone with this approach, maybe someone else could chime in with
> recommendations along those lines?
> http://www.netlib.org/linalg/old_html_templates/chapter2.7.html
>
> What sort of spatial discretization are you using?
>
> > Thanks,
> >
> > Christine
> >
>
> HtH,
> --
> Joshua Stults
> Website: http://j-stults.blogspot.com
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