Partially-Filled Rectangular Cavity Resonator with Chebyshev-FDTD Method

Abstract

In this study, electromagnetic analysis of a three-dimensional rectangular cavity resonator, which has perfectly conducting walls, is performed with the Chebyshev grid using Finite Difference Time Domain (FDTD) method.
The resonance behavior of the magnetic and electric field equations of the three dimensional homogeneously air-filled rectangular resonator is observed. The analytically proven resonance frequency equation, which is well known in the literature, has been investigated whether is included in the field equations. In the case of the resonance behavior is not observed, the resonance behavior is shown by solving the inhomogeneous Helmholtz equation including the source term with the help of the Green function instead of the field equations found by the source-less homogeneous Helmholtz equation.
Besides the equidistant Yee collocation grid which is commonly used in the classical Finite Difference Time Domain method, the Chebyshev grid type is created by using the roots of the function of Chebyshev (Chebyshev-Gauss-Lobatto points), which is dense in the middle and sparse at the edges.
Firstly, the three-dimensional cavity resonator is filled homogeneously with air. The field equations of this resonator are numerically solved and compared by using the Finite Difference Time Domain method at the calculation points on the Yee and Chebyshev grid. Then, the air-filled cavity resonator is filled with a dielectric material until half of its height, and the results are compared by making numerical analysis again on the mentioned two different grids. The average method is then applied to the compared results to correct the transition region. Field distributions and time domain results are re-collected and compared by doing the same procedures for average method.