[SciPy-User] preconditioner for GMRES
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 <firstname.lastname@example.org>
> On Mon, Mar 29, 2010 at 4:54 PM, Darcoux Christine <email@example.com>
> > 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
> > matrix. However, the scipy documentation does not explain how one can
> > this preconditioner in a (ideally) matrix-free manner given only the
> > 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):
> 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?
> What sort of spatial discretization are you using?
> > Thanks,
> > Christine
> Joshua Stults
> Website: http://j-stults.blogspot.com
> SciPy-User mailing list
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