Multilevel preconditioners for solving eigenvalue problems occuring in the design of resonant cavities

Abstract

We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the JacobiDavidson algorithm and of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. We present numerical results of very large eigenvalue problems originating from the design of resonant cavities of particle accelerators.