[petsc-users] question about CISS

[Jose E. Roman]

I am not an expert in contour integral eigensolvers. I think difficulties come with corners, so ellipses are the best choice. I don't think ring regions are relevant here.

Have you considered using ScaLAPACK. Some time ago we were able to address problems of size up to 400k   https://doi.org/10.1017/jfm.2016.208

Jose


> El 29 ago 2019, a las 21:55, Povolotskyi, Mykhailo <mpovolot at purdue.edu> escribió:
> 
> Thank you, Jose,
> 
> what about rings? Are they better than rectangles?
> 
> Michael.
> 
> 
> On 08/29/2019 03:44 PM, Jose E. Roman wrote:
>> The CISS solver is supposed to estimate the number of eigenvalues contained in the contour. My impression is that the estimation is less accurate in case of rectangular contours, compared to elliptic ones. But of course, with ellipses it is not possible to fully cover the complex plane unless there is some overlap.
>> 
>> Jose
>> 
>> 
>>> El 29 ago 2019, a las 20:56, Povolotskyi, Mykhailo via petsc-users <petsc-users at mcs.anl.gov> escribió:
>>> 
>>> Hello everyone,
>>> 
>>> this is a question about  SLEPc.
>>> 
>>> The problem that I need to solve is as follows.
>>> 
>>> I have a matrix and I need a full spectrum of it (both eigenvalues and
>>> eigenvectors).
>>> 
>>> The regular way is to use Lapack, but it is slow. I decided to try the
>>> following:
>>> 
>>> a) compute the bounds of the spectrum using Krylov Schur approach.
>>> 
>>> b) divide the complex eigenvalue plane into rectangular areas, then
>>> apply CISS to each area in parallel.
>>> 
>>> However, I found that the solver is missing some eigenvalues, even if my
>>> rectangles cover the whole spectral area.
>>> 
>>> My question: can this approach work in principle? If yes, how one can
>>> set-up CISS solver to not loose the eigenvalues?
>>> 
>>> Thank you,
>>> 
>>> Michael.
>>> 
>