电子科技大学学报
電子科技大學學報
전자과기대학학보
Journal of University of Electronic Science and Technology of China
2015年
6期
845-850
,共6页
辅助微分方程%时域有限差分法%色散媒质%帕德近似法
輔助微分方程%時域有限差分法%色散媒質%帕德近似法
보조미분방정%시역유한차분법%색산매질%파덕근사법
auxiliary differential equation (ADE)%finite-difference time-domain (FDTD) method%frequency-dependent media%Padé approximant method
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。
為瞭方便模擬不同媒質的色散特性，提齣瞭一種時域有限差分(FDTD)改進方案，適用于統一處理幾類各嚮同性、線性、有磁電色散媒質的電波傳播問題：媒質類型可以是Havriliak-Negami(H-N)媒質、Davidson-Cole(D-C)媒質、Cole-Cole(C-C)媒質、Debye媒質、常規(非色散)媒質或其任意組閤；媒質屬性可以是單極或多極的、有電耗的或無電耗的。該方案利用帕德(Padé)近似法，導齣瞭一組整數階的輔助微分方程(ADEs)，既剋服瞭其中分數階導數的主要睏難，又展現瞭通用性好、複雜度低的優勢。通過對一維及三維算例解析、數值結果之間的對比，初步證實瞭改進方案的可行性和有效性。
위료방편모의불동매질적색산특성，제출료일충시역유한차분(FDTD)개진방안，괄용우통일처리궤류각향동성、선성、유자전색산매질적전파전파문제：매질류형가이시Havriliak-Negami(H-N)매질、Davidson-Cole(D-C)매질、Cole-Cole(C-C)매질、Debye매질、상규(비색산)매질혹기임의조합；매질속성가이시단겁혹다겁적、유전모적혹무전모적。해방안이용파덕(Padé)근사법，도출료일조정수계적보조미분방정(ADEs)，기극복료기중분수계도수적주요곤난，우전현료통용성호、복잡도저적우세。통과대일유급삼유산예해석、수치결과지간적대비，초보증실료개진방안적가행성화유효성。
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 Padé 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.
