Re: [Getfem-users] GMM++ Preconditioner

[Danesh Daroui]

Dear Renard,

Well I am just testing and the problem (convergence is not an issue
before it is solved) is that the solver never ends! It seems that it is
stuck in a loop!
I mean can it be due to ill-conditioned (not sparse enough) matrix?

Thanks,

Danesh


On 2010-09-13 11:16, Yves Renard wrote:
>
> Dear Danesh,
>
> A priori, it is not a good idea to use sparse preconditionners on nearly 
> dense 
> matrices because it will correspond more or less to a full (not optimized at 
> all) decomposition. So it will be less efficient than a direct solver. A 
> sparse 
> preconditionner should be used when the number of non-zero components on a 
> row 
> is more or less independent of the problem size. In your case, you probably 
> have to adapt some specific preconditionners if you want to use iterative 
> solvers.
>
> Yves.
>
>
>
> On lundi 13 septembre 2010, 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
>>
>> On 2010-09-13 08:51, Yves Renard wrote:
>>> Dear Danesh
>>>
>>> If your matrix is nearly dense (if I understand well, in your case, you
>>> have more than 30% of nonzero components) the dense format is the better
>>> because the linear algebra operations are far more optimized for dense
>>> matrices (using blas) than for sparse matrices.
>>>
>>> Yves.
>>>
>>> On dimanche 12 septembre 2010, Danesh Daroui wrote:
>>>> Dear Renard,
>>>>
>>>> Thanks for your answer. Yes you are right. In principle, using iterative
>>>> solvers for a dense matrix is not a good idea. Maybe for special cases,
>>>> but not in general. Please correct me if I am wrong. The reason that I
>>>> am using a dense matrix type is that I am using a very large matrix
>>>> where I fill each quarter separately. Two of quarters are dense and the
>>>> others are very sparse. It is also possible to make the dense quarters
>>>> more sparse that I am working on it. For this purpose I thought maybe it
>>>> is better to use a dense matrix, however I leave mane zero cells in the
>>>> memory. Do you have any suggestion? Is it possible to reference each
>>>> quarter using a sparse format matrix like dense format in GMM++?
>>>>
>>>> Regards,
>>>>
>>>> D.
>>>>
>>>> On 2010-09-12 17:09, Renard Yves wrote:
>>>>> Dear Danesh,
>>>>>
>>>>> The template argument for the preconditionner is the matrix type. So
>>>>> you should declare
>>>>>
>>>>> gmm::dense_matrix<double> A(100, 100);
>>>>>
>>>>> filling the matrix
>>>>>
>>>>> gmm::ilu_precond<gmm::dense_matrix<double> > P1(A);
>>>>>
>>>>>
>>>>>
>>>>> Of course, this is not very satisfactory because an incomplete LU
>>>>> decomposition on a dense matrix is a complete LU decomposition. You
>>>>> should work with sparse matrices instead.
>>>>>
>>>>> You can see on the following page of the documentation how to declare
>>>>> each preconditionner :
>>>>>
>>>>> http://download.gna.org/getfem/html/homepage/gmm/iter.html#precondition
>>>>> er s
>>>>>
>>>>> Yves.
>>>>>
>>>>> Danesh Daroui <address@hidden> a écrit :
>>>>>> Dear all,
>>>>>>
>>>>>> I would like to use GMM++ iterative solvers. The problem is that I can
>>>>>> not use for example incomplete LU factorization preconditioner. Let
>>>>>> say that I have the equation Ax=b. The I define the preconditioner
>>>>>> as:
>>>>>>
>>>>>> gmm::dense_matrix<double> A(100, 100);
>>>>>>
>>>>>> // filling the matrix
>>>>>>
>>>>>> gmm::ilu_precond<double> P1(A);
>>>>>>
>>>>>> but I get compilation errors. It just compiled successfullt when I
>>>>>> define:
>>>>>>
>>>>>> gmm::ilu_precond<double> P1;
>>>>>>
>>>>>> but there is no hint and neither sample code to show which function
>>>>>> should I call to create the preconditioner.
>>>>>>
>>>>>> Can anybody help?
>>>>>>
>>>>>> Regards,
>>>>>>
>>>>>> D.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
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>


-- 
Danesh Daroui
Ph.D Student
Lulea University of Technology
http://www.ltu.se

address@hidden
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