Accuracy Analyses of FDTD Resonance Frequency Calculations for a Partially Dielectric-Filled Cavity

Abstract

In this study, accuracy analyses of resonance frequency calculations for a three-dimensional partially dielectric-filled cavity are investigated by using finite difference time domain (FDTD) method. The calculations are performed for low- and high-contrast lossless dielectric materials. In order to excite multicavity modes, the cavity is driven by a Gaussian pulse source. The main error sources for the numerical resonance frequency calculations of the partially dielectric-filled cavity are (i) applied technique for treatment of a dielectric interface between free space and material medium and (ii) numerical dispersion of the FDTD method. The effects of these errors are analyzed both in detail. A no averaging (without any averaging), a proper averaging technique for the low-/high-contrast case, and the dielectric functioning technique with three different distances of $3∆z,5∆z,\text{and}7∆z$ are applied for the treatment of dielectric interface. Additionally, four spatial resolutions of $\lambda ⁄10$, $\lambda ⁄20$, $\lambda ⁄30$, and $\lambda ⁄40$ are used for the numerical dispersion analyses. The calculated results are compared with a semianalytical solution for the accuracy evaluations. Specially, in order to explain ordering of numerical errors for each case, a technique based on electromotor force $\mathrm{emf}$ calculation is proposed with good success. The computational advantages of the applied techniques are also shown over no averaging case.