A PWDG method for the Maxwell system in anisotropic media with piecewise constant coefficient matrix

Long Yuan, Qiya Hu
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引用次数: 0

Abstract

In this paper we are concerned with plane wave discontinuous Galerkin (PWDG) methods for time-harmonic Maxwell equations in three-dimensional anisotropic media, for which the coefficients of the equations are piecewise constant symmetric matrices, where each constant symmetric matrix is defined on a medium (subdomain). By using suitable scaling transformations and coordinate (complex) transformations on every subdomain, the original Maxwell equation in anisotropic media is transformed into a Maxwell equation in isotropic media occupying a union domain of specific subdomains of complex Euclidean space. Based on these transformations, we define anisotropic plane wave basis functions and discretize the considered Maxwell equations by PWDG method with the proposed plane wave basis functions.  We derive error estimates of the resulting approximate solutions, and further introduce a practically feasible local $hp-$refinement algorithm, which substantially improves accuracies of the approximate solutions. Numerical results indicate that the approximate solutions generated by the proposed PWDG methods possess high accuracy for the case of strong discontinuity media.
各向异性介质中麦克斯韦系统的 PWDG 方法,系数矩阵为片断常数
本文涉及三维各向异性介质中时谐麦克斯韦方程的平面波非连续伽勒金(PWDG)方法,方程的系数为片断常数对称矩阵,其中每个常数对称矩阵都定义在一个介质(子域)上。通过在每个子域上使用适当的缩放变换和坐标(复数)变换,各向异性介质中的原始麦克斯韦方程被转换为各向同性介质中的麦克斯韦方程,该方程占据复欧几里得空间特定子域的联合域。基于这些转换,我们定义了各向异性平面波基函数,并利用所提出的平面波基函数通过 PWDG 方法对所考虑的麦克斯韦方程进行离散化。 我们得出了所得到的近似解的误差估计值,并进一步引入了一种实际可行的局部$hp-$细化算法,该算法大大提高了近似解的精确度。数值结果表明,所提出的 PWDG 方法生成的近似解在强不连续介质情况下具有很高的精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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