Higher-Order Frequency Derivatives of Electroquasistatic System

Frequency sensitivity analysis (FSA) aimed to evaluate the reaction of electromagnetic field with respect to frequency variation. This study proposed a higher-order FSA of electroquasistatic (EQS) system. A variational formulation for the first-order FSA was obtained by differentiating a time-harmonic EQS system with respect to angular frequency. The higher-order formulation was sequentially derived from the lower-order formulation by repeating the differentiation. A continuum approach was taken so that the frequency sensitivity was expressed in an analytical form. Since the frequency sensitivity was evaluated prior to the discretization process of the finite element method (FEM), it could be readily and accurately calculated using commercial FEM software. The theoretical validity and numerical feasibility of this study were demonstrated in two examples.