CAJ | 학술논문

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。
위모의일반 Davidson-Cole 색산매질중적전파전파，본문제출료일충시역유한차분（FDTD）개진방안，개진지처체현재：（1）괄용매질종단겁추엄도다겁정형；（2）괄용매질종무자추엄도유자정형；（3）보류료색산모형공식적정태전도솔항；（4）보충료삼유문제산례。개진방안중，면림적주요곤난시차분리산분수계도수。수선，이용파덕（Padé）다항식근사매질적개전상수；기차，통과부리협역변환（IFT）도출료일조정수계적보조미분방정（ADEs），종이교묘극복료해곤난。궤개산례적결과화분석，초보증실료개진방안적가행성화유효성。
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 conduc-tivity 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.