The pole condition as transparent boundary condition for resonance problems: detection of spurious modes

In many implementations of transparent boundary conditions for resonance problems, spurious modes arise. We have developed a transparent boundary condition based on the pole condition that has one complex tuning parameter. Numerical experiments suggest that the artificial eigenvalues are due to badly converged solutions in the exterior domain and thus are strongly dependent on variations of this parameter while physical solutions are well converged and thus almost invariant. Hence it is possible to differentiate between spurious and physical solutions by doing a sensitivity analysis of the eigenvalues.