[petsc-users] Advise on choice of iterative solver

[Klaus Zimmermann]

Hi,

I want to extract the most relevant eigenstates from a quadratic, 
complex symmetric generalized eigenvalue problem Ax = \lambda Bx. A is 
complex symmetric with 3*36 non-zeros per row, B is real with 36 
non-zeros per row (subpattern), both with dimension of the order of up 
to 1e7. We use Krylov-Schur with shift-and-invert from slepc. With a 
direct solver for the inner part (at the moment mumps) everything works 
fine. To circumvent memory problems and improve parallelizability I 
would like to use an iterative solver for the inner part, but was unable 
to actually get one to work.
What is also strange is that the setup as it is now works fine only with 
out true residuals. If we use the command line switch for true residuals 
the Krylov-Schur does not seem to convert.
So my questions are:
1) Do you have any idea on why true residuals would work worse than the 
Krylov estimate?
2) What iterative solver/preconditioner would you suggest?

Thanks in advance!
Klaus