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Re: [Getfem-users] GMM++ Preconditioner


From: Danesh Daroui
Subject: Re: [Getfem-users] GMM++ Preconditioner
Date: Mon, 13 Sep 2010 18:40:53 +0200
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Dear Umut,

I understand that in order to have an *efficient* iterative solver, an
appropriate preconditioner should be used. But, the thing is that when
I use a general preconditioner e.g. diagonal, the iterative solver seems
to get stuck in a loop and never ends! What I expect is that the
solution ends in a reasonable time without convergence (due to
inappropriate precond.) or ends in longer time but with convergence. By
long
I mean longer than direct solver. Then, I could work on preconditioner
to make it as efficient as possible. Again, I used GMRES and it never ended.

I have tested GMM++ using its direct solver and it was OK. Our code is
being ported to Intel MKL (partly). We have also used PETSc before.

Thanks,

Danesh


On 2010-09-13 11:14, Umut Tabak wrote:
> On 09/13/2010 11:01 AM, Danesh Daroui wrote:
>> Dear Renard,
>>
>> I have another question. When I run iterative solvers in GMM++, it takes
>> very very long time and sometimes (specially when ILU precond. is used)
>> the method
>> doesn't even converge. With ILUT and ILUTP I got the error "pivot is too
>> small" and i don't know why. But, with direct solvers, it is possible to
>> solve it in less time.
>> Is it because my matrix is not sparse enough? But I am wondering, if I
>> solve a dense system with iterative solver, shouldn't it take in worse
>> case, the time equal to
>> direct solver? I have run all my tests using GMRES solver. Do you think
>> that I may get better result with other iterative solvers in GMM++?
>>
>> Thanks,
>>
>> Danesh
>>    
> Hi Danesh,
>
> Iterative solvers, most of the time, do not work without a good 
> preconditioner set for them and finding good preconditioners is also 
> pretty hard, and problem specific most of the time.
>
> Apart from this, convergence properties are closely related to the 
> spectral properties of the operator matrix(the scattering of the 
> eigenvalues), using iterative solvers might need serious expertise and 
> knowing your problems in deep, so they are not sth like black box 
> routines, or a shot-in-the-dark like direct(LU factorization) solvers.
>
> And from my experience, if your matrices are really ill-conditioned and 
> you can not improve the condition numbers seriously by the application 
> of a preconditioner, the best bet is to rely on direct solvers, PETSc 
> has interfaces for MUMPS solver package, it seems to be the best option 
> most of the time.
>
> Hope this helps a bit,
> Umut
>
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-- 
Danesh Daroui
Ph.D Student
Lulea University of Technology
http://www.ltu.se

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