Re: [Getfem-users] GMM++ Preconditioner

[Umut Tabak]

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