Hello, 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? Regards, Lucas
