Referent: Dr. Gerhard Unger, Graz University of Technology
We consider Galerkin boundary element methods for the approximation of different kinds of electromagnetic resonance problems. Examples are the cavity resonance problem, the scattering resonance problem and the plasmonic resonance problem. An analysis of the used boundary integral formulations and their numerical approximations is presented in the framework of eigenvalue problems for holomorphic Fredholmoperator-valued functions. We use recent abstract results to show that the Galerkin approximations with Raviart-Thomas elements provide a so-called regular approximation of the underlying operators of the eigenvalue problems. This enables us to apply classical results of the numerical analysis of eigenvalue problems for holomorphic Fredholm operator-valued functions which implies convergence of the approximations and quasi-optimal error estimates.
We also address practical issues of the numerical computations of resonances and modes as the application of the contour integral method and of Newton-type methods for eigenvalue tracking.