Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations

When microwave structures are perturbed by the presence of an external material, the resonant frequencies shift depending on the location and the electrical properties of the perturber. Such a shift can be used to determine the properties of the perturber, as well as variations with respect to an additional parameter such as the temperature. The finite-element method can be used to study these effects numerically. When the electrical parameters of the perturber are changed in an attempt to fine tuning or optimization of the structure, the numerical analysis requires resulting finite-element equations to be solved for each value of the perturbation parameter, repetitively. In this paper, we present the step-by-step eigenvalue perturbation technique to reduce the computational cost of such analysis significantly. The arising generalized eigenvalue problem is solved by successive iterations of eigenvalue perturbations. The step size of the sequential perturbations is chosen adaptively such that corresponding generalized eigenvalue problem is valid physically. The technique is especially effective when used with finite-element methods due to the characteristic symmetric structure of the matrices of the associated generalized eigenvalue problem.