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

[Jose E. Roman]

> El 7 ago 2018, a las 12:01, Michael Werner <michael.werner at dlr.de> escribió:
> 
> Thank you for your reply and your explanations, I'll try it with a higher ksp tolerance. I chose this low value, because in the SLEPc manual it is mentioned that the Davidson solvers often work better with lower tolerances than with higher tolerances.
> 
> Is there also a way to improve convergence for the gd solver? As far as I know it doesn't use a ksp , so the only way I can think of to improve convergence would be using a higher quality preconditioner, right?

Yes, but "not too good". For instance an exact LU decomposition as a preconditioner may lead to stagnation in GD.

Jose


> 
> Kind regards,
> Michael
> 
> Jose E. Roman writes:
> 
>>> El 6 ago 2018, a las 14:44, Michael Werner <michael.werner at dlr.de> escribió:
>>> 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
>> 
>> You may need to enforce more accuracy on the KSP. Try replacing
>> -st_ksp_max_it 15 -st_ksp_rtol 1e-2 by
>> -st_ksp_rtol 1e-5
>> 
>> Normally, you don't need to set the -eps_mpd parameter, except if many eigenvalues (nev) are requested. The parameter jd_minv controls how the restart is done, keeping more or less information from previous restarts - it may affect convergece, but not too much. And yes, jd_plusk can be used for GNHEP problems.
>> 
>> Jose