Axially symmetric eigenvalue problem for a dielectric body

Dielectric resonators are used in a variety of application, including filters, oscillators, frequencies meters and tuned amplifiers. To date, a range of approximate semi-analytical methods have been used to model microwave dielectric resonators, namely magnetic wall method [1], variational method [2], and various integral equation methods [3,4]. Of special interest are the contour IE methods that use the Muller IEs and the Method of Analytical Regularisation (MAR) [5,6] to convert the original equations set to the matrix equations with more favourable features, namely to the Fredholm type equations of the second kind.conditions imposed on the disk median section [7]. Our main objective is to extend the Muller IEs to the full 3D case without making any approximating assumptions. In this paper we present a valuable intermediate step, namely method based on the combination of Muller IE and the Body of Revolution (BOR) approach [4]. The BOR method is IE based method that is applicable to bodies that possess axial (rotational) symmetry and can thus be obtained by rotating a so-called generic arc around the axis of symmetry.