Oliver Axel Ruebenacker wrote:
>
>
> Hello!
>
> > I have an application that spends nearly all its time in a generalize
> > eigenvalue problem with very large (say 10-20 million rows)
> > and very sparse (either ~16 or ~44 non zeros per row) matrices.
>
> Excuse my curiousity, but what applications are there out there that use
> such matrices? Are you actually able to directly diagonalize such a
> matrix?
> Thanks for the information.
>
> Take care
> Oliver
The application is a parallel distributed memory finite-element
code for solving electromagnetics in the frequency domain for
complex 3D geometries. Accelerator structures tend to be
curvy and have small details so we represent the geometry
with an unstructured tetrahedral mesh. In the generalized
eigenvalue problem that arises from the formulation (K x =
lambda M x), x is related to the electric fields and
lambda is related to frequency.
We are usually interested in only a very small number
of eigenmodes (in most cases only the first non-zero mode).
So this makes the problem much easier. Our eigensolver is based
on the shift-invert Lanczos method. Also, in most cases
we have a pretty good idea of what frequency range the modes
of interest are in, and so we know how to set the shift parameter.
Brian
Stanford Linear Accelerator Center
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