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 Qu?mica, M?dulo 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>
