Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.
Aprogram applying an algorithm of finite-difference time-domain method is established that can be used to calculate the resonant frequencies of cavities of arbitrary modes, coupled with the discrete Fourier transform. Several coaxial resonators including the empty coaxial cavity, re-enrant coaxial cavity and partially stepped resonator are studied with this method, especially the spurious mode resonant frequencies of coaxial cavi- ties. The numerical results thus obtained are shown to be in excellent agreement with those obtainable through rigorous theoretical solutions and experiment results.
