Vector Finite Elements and the Step by Step Eigenvalue Perturbation Methods

The electromagnetic resonant structures and their perturbations have been found their way in many applications in microwave engineering. Analysis of these structures using finite element method results in a generalized eigenvalue problem, where the eigenvalues correspond to the resonant frequencies, and the eigenvectors correspond to the resonant modes. The perturbations of resonant structures yield perturbed eigenvalue problem and can be solved by eigenvalue perturbation methods, effectively. Combining finite element method with step by step eigenvalue perturbation method yields parametric history with respect to perturbation parameter. In this study perturbation of a microwave ring resonator placed in a metalic enclosure has been examined, combining the vector finite element and the step-by-step generalized eigenvalue perturbation methods.