电子学报 ›› 2015, Vol. 43 ›› Issue (7): 1382-1387.DOI: 10.3969/j.issn.0372-2112.2015.07.020

• 学术论文 • 上一篇    下一篇

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

刘广东   

  1. 阜阳师范学院物理与电子工程学院, 安徽阜阳 236037
  • 收稿日期:2014-04-02 修回日期:2014-09-04 出版日期:2015-07-25 发布日期:2015-07-25
  • 作者简介:刘广东 男,1972年生于江苏灌云.阜阳师范学院物电学院副教授、工学博士.研究方向为微波医学成像. E-mail:liu_guang_dong@126.com
  • 基金资助:

    国家自然科学基金(No.61071022);安徽高校省级自然科学研究重点项目(No.KJ2014A193);安徽省科技计划项目(No.12010302080);阜阳师范学院自然科学研究项目(No.2014FSKJ14)

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

LIU Guang-dong   

  1. School of Physics and Electronic Engineering, Fuyang Normal College, Fuyang, Anhui 236037, China
  • Received:2014-04-02 Revised:2014-09-04 Online:2015-07-25 Published:2015-07-25

摘要:

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.

关键词: 色散媒质, 时域有限差分法, 卷积完全匹配层, 帕德近似法

Abstract:

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.

Key words: frequency-dependent media, finite-difference time-domain (FDTD) method, convolutional perfectly matched layer (CPML), Padé, approximant method

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