[SciPy-User] preconditioner for GMRES

Daniel Wheeler daniel.wheeler2@gmail....
Wed Mar 31 08:51:46 CDT 2010


You might want to look at fipy <http://www.ctcms.nist.gov/fipy>, it
has the Van Leer flux limiting schemes for convection terms as well as
other options. Also, it uses either pysparse or trilinos, which both
have a number or preconditioning options.

On Mon, Mar 29, 2010 at 6:59 PM, Darcoux Christine <bouloumag@gmail.com> wrote:
> 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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>
>
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-- 
Daniel Wheeler


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