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数值计算与计算机应用  2018, Vol. 39 Issue (4): 288-298    DOI:
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一维Maxwell方程间断解的多区域Legendre tau方法
方丹丹, 马和平
上海大学 理学院, 上海 200444
MULTIDOMAIN LEGENDRE TAU METHOD FOR THE 1-D MAXWELL EQUATION WITH DISCONTINUOUS SOLUTIONS
Fang Dandan, Ma Heping
College of Sciences, Shanghai University, Shanghai 200444, China
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摘要 以一维非一致介质Maxwell方程的间断问题为模型,建立了多区域Legendre tau方法.不同于Galerkin方法,对电场和磁场的逼近采用不同的多项式次数,使电场和磁场的计算可以解耦.同时改进了精度,对于半离散情况证明了格式的稳定性和最优阶误差估计.数值算例验证了多区域Legendre tau方法对于该间断问题的有效性.
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关键词Maxwell方程   间断问题   多区域Legendre tau方法     
Abstract: A multidomain Legendre tau method is established for the 1-D Maxwell's equations of nonhomogeneous media with discontinuous solutions. Unlike the Galerkin method, polynomials of different degrees are used to approximate the electric and magnetic fields, respectively, so that they can be decoupled in computation. Also, the method improves the accuracy, and the stability and optimal error estimates of the semi-discrete scheme are given. Numerical examples show the effectiveness of the method without being affected by the discontinuity of the solutions.
Key wordsMaxwell's equation   discontinuous solution   multidomain Legendre tau method   
收稿日期: 2018-05-02;
基金资助:

国家自然科学基金(11571224).

引用本文:   
. 一维Maxwell方程间断解的多区域Legendre tau方法[J]. 数值计算与计算机应用, 2018, 39(4): 288-298.
. MULTIDOMAIN LEGENDRE TAU METHOD FOR THE 1-D MAXWELL EQUATION WITH DISCONTINUOUS SOLUTIONS[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(4): 288-298.
 
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