Parametric history analysis of resonance problems via step-by-step eigenvalue perturbation technique

The Galerkin procedure to solve Maxwell´s equations associated with a perturbed system approximately, yields a generalised eigenvalue perturbation problem. Instead of solving the generalised eigenvalue problem, perturbed eigenvalues and eigenvectors can be approximated in terms of unperturbed ones. Although solving the perturbed eigenvalue problem can be computationally attractive, the small perturbation requirement may be quite restrictive. This restriction can be relaxed using iterative perturbation techniques in which the problem is divided into small perturbation steps, and then each subsequent problem is solved depending on the solutions of the previous step. Besides, the step-by-step iterative solution also provides a parametric history of the system behaviour. In this study, the parametric history analysis of electromagnetic resonant structures has been accomplished using the step-by-step eigenvalue perturbation method. To illustrate the proposed method, the reanalysis of perturbation of a cylindrical cavity with a dielectric sample has been examined. The results obtained using the parametric history analysis are compared with the theoretical, the experimental and the results of the classical perturbation approach.