Step-by-Step Eigenvalue Perturbation Technique for Electromagnetic Resonance Problems

The Galerkin procedure to solve Maxwell's equations associated with a perturbed system approximately, yields a generalized eigenvalue perturbation problem. Instead of solving the generalized eigenvalue problem, perturbed eigenvalues and eigenvectors can be approximated in terms of unperturbed ones. However, 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. In this study, the parametric history analysis of electromagnetic resonant structures has been accomplished using the step-by-step eigenvalue perturbation method.