[petsc-users] Solving tridiagonal hermitian generalized eigenvalue problem with SLEPC

[Barry Smith]

   I would recommend just using AIJ matrices and not worry about SBAIJ at this stage. SBAIJ can save you memory but not operations and unless memory is really tight is not likely a useful optimization.

   What eigensolvers have you tried and which eigenvalues do you want?

   Barry

On Aug 18, 2014, at 5:46 AM, Toon Weyens <tweyens at fis.uc3m.es> wrote:

> Dear all,
> 
> I am using PETSC and SLEPC to simulate a problem in MHD, described in http://scitation.aip.org/content/aip/journal/pop/21/4/10.1063/1.4871859.
> 
> I have a bit of experience with MPI but not too much with PETSC and SLEPC. So after reading both user manuals and also the relevant chapters of the PETSC developers manual, I still can't get it to work.
> 
> The problem that I have to solve is a large generalized eigenvalue system where the matrices are both Hermitian by blocks and tridiagonal, e.g.:
> 
> ( A11  A12    0     0       0   )                      ( B11  B12    0     0       0   )
> ( A12* A22  A23   0      0   )                       ( B12* B22  B23   0      0   )
> (   0    A23* A33  A34   0   )   =   lambda    (   0    B23* B33  B34   0   ) 
> (   0      0    A34* A44  A45)                       (   0      0    B34* B44  B45)
> (   0      0    A45* A55    0  )                       (   0      0    B45* B55    0  )
> 
> where Aii = Aii*, with * the Hermitian conjugate. I apologize for the ugly representation. 
> 
> The dimensions of both A and B are around 50 to 100 blocks (as there is a block per discretized point) and the blocks themselves can vary from 1 to more than 100x100 as well (as they correspond to a spectral decomposition).
> 
> Now, my question is: how to solve this economically?
> 
> What I have been trying to do is to make use of the fact that the matrices are Hermitian and by using matcreatesbaij and through the recommended matcreate, matsettype(matsbaij), etc.
> 
> Could someone help me out? All help would be greatly appreciated!
> 
> Thank you in advance,
> Toon
> UC3M