[petsc-users] precondition for matrix-free GMRES

[RenZhengYong]

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.


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
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