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 <mpovo...@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@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. >>> >
