基于帕德近似法模拟一般色散媒质电波传播的ADE-FDTD-CPML统一实现方案

为方便一站式处理常见几类各向同性、线性、无磁耗电色散媒质的电波传播问题,提出了一种ADE-FDTD-CPML统一实现方案:一是问题空间和吸收边界的统一处理;二是色散特性的统一建模:适用的媒质类型可以是单一的Havriliak-Negami(H-N)媒质、Davidson-Cole(D-C)媒质、Cole-Cole(C-C)媒质、Debye媒质、常规媒质或其任意组合;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,导出了一组整数阶辅助微分方程(ADEs),既克服了时域描述时遇到的分数阶导数困难,又展现了通用性好、复杂度低等优势.几个一维、三维算例解析、数值结果之间的对比,初步证实了统一实现方案的可行性和有效性.

Unified Implementation of ADE-FDTD-CPML Scheme Based on Padé Approximant Method for Simulation of EM Wave Propagation in General Dispersive Media

A unified ADE-FDTD-CPML scheme is proposed for one-stop simulation of electromagnetic (EM) wave propagation in different electrically dispersive media with isotropic,linear and nonmagnetic properties.This unification is manifested from two aspects.One aspect is unified FDTD treatment of problem space and its absorbing boundaries,the other is unified implementation of frequency-dependent properties for several types of media such as single Havriliak-Negami (H-N),Davidson-Cole (D-C),Cole-Cole (C-C),Debye dispersive media,ordinary media or their arbitrary combination,which are lossless or lossy with single pole or multiple relaxation times.The main difficulty in the presented scheme is appearance of fractional derivatives.This difficulty is overcomed by using the Padé approximant method,resulting in a set of auxiliary differential equations (ADEs) of integer order.The feasibility,validity,good generality and low complexity of the scheme is preliminarily demonstrated by the comparisons between analytic and calculated results from several one-dimensional (1-D) and three-dimensional (3-D) examples.