守恒无伪解麦克斯韦方程间断元研究:(Ⅰ)一维和二维情况  

Non-dissipative and spurious-free discontinuous Galerkin method for solving Maxwell equations:(Ⅰ)One-and two-dimensional cases

作　　者：齐红新 张杰[1] 王向晖[1] 王建国[2] 

机构地区：[1]华东师范大学物理系,上海200241 [2]西北核技术研究所,西安710024

出　　处：《强激光与粒子束》2013年第11期2931-2938,共8页High Power Laser and Particle Beams

基　　金：国家自然科学基金项目(61231003);国家重点基础研究发展计划项目(2011CB503701)

摘　　要：考察了电、磁场分量分别基于不同近似函数空间展开的一维和二维Maxwell方程间断元求解方法。结合中心数值通量和电、磁场分量近似函数空间的不同组合,构造了各种间断元算子。通过用这些算子在规则和不规则网格上编码分析一维和二维金属腔的谐振模式,详细考察了算子的收敛和伪解支持性,并据此对基函数进行了优选。算子在时域和频域对谐振模式的计算结果彼此符合良好。优选的Maxwell方程间断元算子不仅同时具备能量守恒和免于伪解的特性,且无需引入辅助变量,为设计高品质Maxwell方程间断元算法和研发相关电磁场模拟软件提供了支撑。One and two-dimensional discontinuous Galerkin finite-element （DGFE） operators for solving Maxwell＇s equations are investigated in this paper.These operators are based on unconventional spaces of approximation functions.Unlike in the existing DGFE method where the field components E and H are expanded with the same family of basis functions,in our scheme,it is attempted to compose various discontinuous Galerkin operators by approximating each of the two components in different function spaces and employing center numerical fluxes.With the combination of various basis function spaces for E and H,we build a series of operators.Through the calculation of the resonant modes of one-and two-dimensional PEC cavities on regular and irregular meshes,the convergence and spuriousness supporting properties of these operators are examined,and based on which a selection of the optimal spaces of basis functions is made.Resonant modes calculated in time-domain and frequency-domain agree well with each other.It is shown not only that the proposed scheme is both non-dissipative and spurious-free,but also that no additional auxiliary variables are required,thus providing a new way to develop high quality algorithm for the Maxwell＇s equations and the corresponding electromagnetic field simulating software.

关 键 词：伽辽金间断元 麦克斯韦方程 伪解 基函数 

分 类 号：O441.4[理学—电磁学]