Implementational Aspects of Eigenmode Computation Based on Perturbation Theory∗

Geometry perturbations affect the eigenmodes of a resonant cavity and thereby can improve but also impair the performance characteristics of the cavity. To investigate the effects of both, intentional and inevitable geometry variations parameter studies are to be undertaken. Using common eigenmode solvers involves to perform a full eigenmode computation for each variation step, even if the geometry is only slightly altered. Therefore, such investigations tend to be computationally extensive and inefficient. Yet, the computational effort for parameter studies may be significantly reduced by using perturbative computation methods. Knowing a set of initial eigenmodes of the unperturbed geometry these allow for the expansion of the eigenmodes of the perturbed geometry in terms of the unperturbed modes. In this paper, we study the complexity of a numerical implementation of perturbative methods. An essential aspect is the computation and analysis of the unperturbed modes since the number and order of these modes determine the accuracy of the results.