A Multigrid Method Based On Shifted-Inverse Power Technique for Eigenvalue Problems

Abstract

A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of nonsingular solutions of boundary value problems on multilevel meshes. Since replacing the difficult eigenvalue solving by the easier solution of boundary value problems, the multigrid way can improve the overall efficiency of the eigenvalue problem solving. Some numerical experiments are presented to validate the efficiency of this new method.