[petsc-users] SLEPc - Davidson-type solvers options

[Michael Werner]

Michael Werner writes:

> Hello, I want to use a Davidson-type solver (probably jd) to 
> find 
> the eigenvalues with the smallest real part, but so far I'm 
> strugglung to get them to converge. So I was hoping to get some 
> advice on the various  options available for those solvers.
>
> For my test case, I know the smallest eigenvalue is -0.04+0.71i 
> (calculated with shift-and-invert and lu 
> preconditioner). However, 
> when I try to use jd or gd, the eigensolver never 
> converges. After 
> a few iterations, the "first unconverged value" is more or less 
> as 
> expected, but it fluctuates around the correct value, and the 
> residual never drops below 1e-2. The best results so far were 
> achieved with the following set of commandline options:
>
> -st_type precond -st_pc_type asm -st_sub_pc_type ilu 
>  -st_sub_pc_factor_levels 2 -st_ksp_max_it 15 -st_ksp_rtol 1e-2 
>  -eps_type jd -eps_tol 1e-4 -eps_monitor -eps_nev 5 -eps_target 
>  -0.08 -eps_target_real -eps_harmonic_largest
>
> I also tried using more ksp iterations or different 
> st_sub_pc_factor_levels. I also tried using eps_smallest_real 
> instead of a target value, without any success. So far, I 
> noticed 
> that the extraction type had the largest influence. Only for 
> eps_harmonic_largest could I observe any eigenvalues with 
> negative 
> real part, for all the other extraction types I only got 
> eigenvalues with positive real parts.
>
> I also had a look at the available options for the Davidson 
> solvers, but I couldn't find a good explanation for 

Sorry, I didn't mean to send it already. What I wanted to say:

I also had a look at the available options for the Davidson 
solvers, but I couldn't find a good explanation for many of the 
additional options. Is there any recommendation to chose -eps_mpd 
or -eps_jd_minv? And can -eps_jd_plusk be used for GNHEP-type 
problems? I already had a look at the paper of E. Romero and 
J. E. Roman concerning the implementation of the Davidson-type 
solvers in SLEPc, but it didn't answer all my questions.

Kind regards,
Michael