电子学报 ›› 2015, Vol. 43 ›› Issue (8): 1598-1603.DOI: 10.3969/j.issn.0372-2112.2015.08.019

• 学术论文 • 上一篇    下一篇

一种处理多极Davidson-Cole色散媒质的FDTD改进方案

刘广东, 张开银, 赵发勇   

  1. 阜阳师范学院物理与电子科学学院, 安徽阜阳 236037
  • 收稿日期:2014-01-23 修回日期:2014-07-07 出版日期:2015-08-25 发布日期:2015-08-25
  • 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 张开银 男,1973年生于山东曲阜.阜阳师范学院物电学院副教授、理学博士.研究方向为材料物理. E-mail:z.kaiyin@gmail.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)

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

LIU Guang-dong, ZHANG Kai-yin, ZHAO Fa-yong   

  1. School of Physics and Electronics, Fuyang Normal College, Fuyang, Anhui 236037, China
  • Received:2014-01-23 Revised:2014-07-07 Online:2015-08-25 Published:2015-08-25

摘要:

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(Padé)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.

关键词: 时域有限差分法, 帕德近似, 辅助微分方程, Davidson-Cole色散媒质

Abstract:

An improved finite-difference time-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 Padé polynomials;then, a set of auxiliary differential equations (ADEs) of integer order are derived by the inverse Fourier transform (IFM), this difficulty is thus circumvented.The feasibility and validity of the presented scheme is preliminarily demonstrated by the results and analyses of several examples.

Key words: finite-difference time-domain (FDTD) method, Padé, approximant, auxiliary differential equation (ADE), Davidson-Cole dispersive media

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