Padé近似下模拟一般色散媒质的FDTD改进方案

Improved FDTD Scheme Based on Padé Approximant Method for Modeling of Wave Propagation in General Dispersive Media

为了方便模拟不同媒质的色散特性,提出了一种时域有限差分(FDTD)改进方案,适用于统一处理几类各向同性、线性、有磁电色散媒质的电波传播问题:媒质类型可以是Havriliak-Negami(H-N)媒质、Davidson-Cole(D-C)媒质、Cole-Cole(C-C)媒质、Debye媒质、常规(非色散)媒质或其任意组合;媒质属性可以是单极或多极的、有电耗的或无电耗的。该方案利用帕德(Padé)近似法,导出了一组整数阶的辅助微分方程(ADEs),既克服了其中分数阶导数的主要困难,又展现了通用性好、复杂度低的优势。通过对一维及三维算例解析、数值结果之间的对比,初步证实了改进方案的可行性和有效性。

A modified finite-difference time-domain （FDTD） scheme is developed to simulate wave propagation in different electrically dispersive media with isotropic, linear and magnetic properties. The presented scheme is applicable to several types of general frequency-dependent media such as Havriliak-Negami （H-N）, Davidson-Cole （D-C）, Cole-Cole （C-C）, Debye dispersive media or nondispersive media, which are lossless or lossy, with single pole or multiple relaxation times. The main difficulty in this scheme is the appearance of fractional derivatives. Based on the Pade approximant method, a set of auxiliary differential equations （ADEs） of integer order are derived. Thus, this difficulty is circumvented, and its advantage in universality and complexity is also exhibited. The feasibility and validity of the presented scheme are preliminarily demonstrated by the comparisons between analytic and numerical results from several one-dimensional （1-D） and three-dimensional （3-D） examples.