[petsc-users] Accelerating eigenvalue computation / removing portion of spectrum

Lucas Banting bantingl at myumanitoba.ca
Tue May 31 12:28:33 CDT 2022


I have a general non hermitian eigenvalue problem arising from the 3D helmholtz equation.
The form of the helmholtz equaton is:

(S - k^2M)v = lambda k^2 M v

Where S is the stiffness/curl-curl matrix and M is the mass matrix associated with edge elements used to discretize the problem.
The helmholtz equation creates eigenvalues of -1.0, which I believe are eigenvectors that are part of the null space of the curl-curl operator S.

For my application, I would like to compute eigenvalues > -1.0, and avoid computation of eigenvalues of -1.0.
I am currently using shift invert ST with mumps LU direct solver. By increasing the shift away from lambda=-1.0. I get faster computation of eigenvectors, and the lambda=-1.0 eigenvectors appear to slow down the computation by about a factor of two.
Is there a way to avoid these lambda = -1.0 eigenpairs with a GNHEP problem type?


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