一维Maxwell方程间断解的多区域Legendre tau方法  

MULTIDOMAIN LEGENDRE TAU METHOD FOR THE 1-D MAXWELL EQUATION WITH DISCONTINUOUS SOLUTIONS

作　　者：方丹丹 马和平[1] Fang Dandan;Ma Heping(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院

出　　处：《数值计算与计算机应用》2018年第4期288-298,共11页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11571224)

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.A multidomain Legendre tau method is established for the 1-D Maxwell's equation- s 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.

关 键 词：MAXWELL方程 间断问题 多区域Legendre tau方法 

分 类 号：O241.8[理学—计算数学] M12[理学—数学]