Maxwell方程特征值问题的谱方法  

The Spectral Method of Eigenvalue Problem of Maxwell’s Equation

作　　者：陈亚飞 茆晋晋 Chen Yafei;Mao Jinjin(School of Mathematical Science,Huaibei Normal University,Huaibei 235000,China;School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]中国矿业大学数学学院,江苏徐州221116

出　　处：《华东交通大学学报》2020年第4期136-142,共7页Journal of East China Jiaotong University

摘　　要：在传统微分方程求解中,多区域谱方法由于仅在局部单元独立构造方程的逼近格式,不同的单元通过惩罚边界或者边界上的数值流函数来进行信息交换,在基函数的选取和网格的剖分方面具有很好的灵活性和较高的精度。文章主要基于多区域谱方法对Maxwell微分方程的数值解进行研究,为了进一步降低求解方程的计算量,又引入了各种差分数值通量格式,当使用迎风通量时,格式支持的混杂模式的尺度被减小,尽管不能除去非物理特征值,但对谱得到了很清楚的分离,从而使得将物理模式与混合模式分离成为可能,使其适应于任意网格剖分的高精度、高效率算法,同时数值算例验证了该算法的有效性。In the traditional differential equation solution,the multi-region spectral method only constructs the approximation scheme of the equation independently in the local element,and different elements exchange information by penalizing the boundary or the numerical flow function on the boundary,which has good flexibility and high precision in the selection of the basis function and the generation of the grid.In this paper,the numerical solution of Maxwell Differential Equation is studied based on multi-region spectral method.In order to further reduce the computational cost of solving the equation,various difference numerical flux formats are introduced.By use of the upwind flux,the scale of the hybrid model supported by the format is reduced.The non-physical eigenvalues cannot be removed and the spectra are clearly separated,which makes it possible to separate the physical mode from the mixed mode.The algorithm is suitable for arbitrary mesh generation with high precision and high efficiency,and the effectiveness of the algorithm is verified by numerical examples.

关 键 词：MAXWELL方程 多区域谱方法 收敛阶 

分 类 号：O241.82[理学—计算数学]