一种处理多极Davidson-Cole色散媒质的FDTD改进方案

A Modified FDTD Scheme for Multi-Pole Davidson-Cole Dispersive Media

为模拟一般Davidson-Cole色散媒质中的电波传播,本文提出了一种时域有限差分(FDTD)改进方案,改进之处体现在:(1)适用媒质从单极推广到多极情形;(2)适用媒质从无磁推广到有磁情形;(3)保留了色散模型公式的静态电导率项;(4)补充了三维问题算例.改进方案中,面临的主要困难是差分离散分数阶导数.首先,利用帕德(Pade)多项式近似媒质的介电常数;其次,通过傅里叶逆变换(IFT)导出了一组整数阶的辅助微分方程(ADEs),从而巧妙克服了该困难.几个算例的结果和分析,初步证实了改进方案的可行性和有效性.

An improved finite-difference tirne-domain （FDTD） scheme is presented to simulate wave propagation in general Davidson-Cole media. Four improvements are made in this paper： （ 1 ） extending to media with multiple relaxation times from ones with single relaxation time; （2）extending to magnetic media from nonmagnetic ones; （3）preserving the term of static ionic conductivity in the Davidson-Cole model; （4）supplementing an example for a three-dimensional （3D） problem. The main difficulty in this scheme is appearance of fractional derivatives. Firstly, the complex permittivity of the medium may be approximated by the Pade polynomials;then,a set of auxiliary differential equations （ADEs） of integer order are derived by the inverse Fourier transform （IPM）, this difficulty is thus circumvented. The feasibility and validity of the presented scheme is preliminarily demonstrated by the results and analyses of several examples.