Re: [Getfem-users] GMM++ Preconditioner

[Yves Renard]

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.
> >>>> 
> >>>> 
> >>>> 
> >>>> 
> >>>> 
> >>>> _______________________________________________
> >>>> Getfem-users mailing list
> >>>> address@hidden
> >>>> https://mail.gna.org/listinfo/getfem-users
> >>> 
> >>> _______________________________________________
> >>> Getfem-users mailing list
> >>> address@hidden
> >>> https://mail.gna.org/listinfo/getfem-users


-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
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  http://math.univ-lyon1.fr/~renard

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