[petsc-users] Convergence problem with Krylov subspace methods

[Matthew Knepley]

On Wed, Jan 9, 2013 at 9:04 AM, Rui Emanuel Ferreira da Silva <
rui.silva at uam.es> wrote:

> To whom it may concern,
>
> I am writing to you to ask some technical problems that I am dealing with
> the use of PETSc.
>
> The problem that I need to solve is a system of linear equations (Ax=b).
> The matrix A is a banded matrix (five-point matrix) resulting from the
> discretization of a second derivative in a 2D space.  In other words, it is
> a pentadiagonal matrix, but the two outer bands are separated from the
> three central bands.
>
> This matrix is complex and is not hermitian (its actual shape is A= H - E
> - i*delta, where H is a hermitian five-point matrix and E and delta a real
> scalar). Its size is 1.8e7 x 1.8e7, thus the problem cannot be solved with
> direct methods but with iterative methods.
>
> For negative values of E, I have been able to solve the system using PETSc
> with a Krylov subspace method, with no problems.
> But for positive values, where the spectrum is quasi-degenerate, I cannot
> solve it. I have tried the following iterative methods:
>
> --> GMRES with the ILU preconditioner
> --> BICG
> --> BCGS
>
> and convergence was not reached in any of the cases.
>
> I have run out of ideas, so my question is: is it possible that you
> suggest me any method which I could use to deal with such a problem?
>

Helmholtz is very difficult for iterative methods:

http://www.maths.dur.ac.uk/events/Meetings/LMS/2010/NAMP/Talks/gander.pdf
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDUQFjAA&url=http%3A%2F%2Fwww.unige.ch%2F~gander%2FPreprints%2FHelmholtzReview.ps.gz&ei=rZXtUJqwFaOs2wXsoIHYBw&usg=AFQjCNEhaFnD7CrzZKF16IZWWQ1nVtdUGg&bvm=bv.1357316858,d.b2I

First, you ought to try MUMPS for your problem in case it fits in the
memory you have.

   Thanks,

       Matt


> Please forgive the intrussion if this question is not adequate in this
> email list.
>
> Thank you very much in advance,
> Rui Silva.
>
>
> -------------------
> Rui Silva
> EMTCCM (European Master in Theoretical Chemistry and Computational
> Modelling)
> UAM, Departamento de Química, Módulo 13
> CAMPUS http://www.uam.es/**departamentos/ciencias/**
> quimica/spline/index.html<http://www.uam.es/departamentos/ciencias/quimica/spline/index.html>
> -------------------
>
>


-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20130109/1d2e93e7/attachment.html>