> El 7 ago 2018, a las 12:01, Michael Werner <[email protected]> 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 <[email protected]> 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
