[petsc-users] Convergence problem with Krylov subspace methods

[Rui Emanuel Ferreira da Silva]

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?

Please forgive the intrussion if this question is not adequate in this  
email list.

Thank you very much in advance,
Rui Silva.


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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
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