Computing cavity resonances using eigenvalues displacement

The numerical discretization of the field inside a cavity by means of edge elements, results in a generalized algebraic eigenvalues problem which contains several undesired null eigenvalues. This occurrence prevents the effective use of iterative eigensolvers. To overcome this difficulty, a complementary eigenproblem has been proposed in the literature. The present paper extends this method by introducing a family of algebraically built complementary eigenproblems, and determines by numerical experiments and heuristics which complementary eigenproblems are best suited for the preconditioned inverse iteration eigensolver and the Lanczos method.