[petsc-users] precondition for matrix-free GMRES

[Matthew Knepley]

On Tue, Apr 3, 2012 at 4:40 PM, RenZhengYong <renzhengyong at gmail.com> wrote:

> Hi, Jed,
> Thanks for your quick reply and have a nice day.
>
> My problem is to solve a hybrid FEM-BEM problem, so one sub-matrix from
> BEM is fully dense and one from BEM-FEM is partially dense. I managed to
> used a multi-level fast multpole method to compute the product of my entire
> system matrix with a given vector. And I can find a quite good problem
> dependent approximation B to my system matrix *A*.
>
> My next purpose to speed up the convergence rate of GMRES using this
> operator *B*.  In my code, the expensive of storage of the far field
> interaction from BEM part is avoided. And I can explicitly form the sparse
> matrix *B*.  So, could I ask you:
> how to give the sparse matrix *B* to petsc?. Because *B* is sparse, I
> prefer to fully LU decomposition to solve the preconditioned problem *B*z=c.
>
>

Give B as the preconditioner matrix,

  KSPSetOperators(ksp, A, B, ...)

    Matt


> Best wishes
> Zhengyong
>
> On Tue, Apr 3, 2012 at 11:28 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>
>> On Tue, Apr 3, 2012 at 14:25, RenZhengYong <renzhengyong at gmail.com>wrote:
>>
>>> I have a question to ask for your suggestions which is to solve Ax=b
>>> using GMRES,
>>> here A is partially dense.  Using petsc, I successfully used the
>>> matrix-free approach to solve
>>> it so that the expensive storage of A is avoided.  My question is could
>>> I offer an matrix B
>>> (which is sparse matrix and good approximation to A) so that the
>>> convergence rate of
>>> GMRES can be speed up.
>>>
>>
>> Certainly, but the challenge is to find this other operator. You could
>> try sparse approximate methods to approximate either the operator or its
>> inverse. Other approaches would typically involve further knowledge of your
>> problem.
>>
>
>
>
> --
> Zhengyong Ren
> AUG Group, Institute of Geophysics
> Department of Geosciences, ETH Zurich
> NO H 47 Sonneggstrasse 5
> CH-8092, Zürich, Switzerland
> Tel: +41 44 633 37561
> e-mail: zhengyong.ren at aug.ig.erdw.ethz.ch
> Gmail: renzhengyong at gmail.com
>



-- 
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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