[petsc-users] precondition for matrix-free GMRES

[RenZhengYong]

Hi, Matt,
Thanks for the help. I got it.

Have a nice day
Best wishes
Zhengyong

On Tue, Apr 3, 2012 at 11:44 PM, Matthew Knepley <knepley at gmail.com> wrote:

> 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
>



-- 
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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