Computation of resonant modes for axisymmetric Maxwell cavities using hp-version edge finite elements

The computation of the resonant frequencies for closed cavities is not a trivial task: Multi-materials and sharp corners all give rise to highly singular eigenfunctions. However, an approach using hp-finite elements is well suited to such problems and, with the correct combination of h- and p-refinements, it yields the theoretically predicated exponential rates of convergence. In this paper, we present a novel approach to the solution of axisymmetric cavity problems which uses a hierarchic H1 and H(curl) conforming finite element basis. A selection of numerical examples is included and these demonstrate that the exponential rates of convergence are achieved in practice