Maxwell方程的高阶间断有限元数值解法

High-Order Discontinuous Galerkin Solution of Maxwell′s Equations

采用高精度方法求解时域Maxwell方程,方程的空间离散采用基于计算流体力学(Computational fluid dynamics,CFD)领域的高阶间断有限元格式,非定常时间迭代采用四步龙格-库塔格式。为了提高计算效率,本文采用了Quadrature-free implementation和网格分区并行技术。数值结果表明,采用高阶格式的情况下,采用稀疏网格便可以得到高精度数值解。另外由于本文的方法基于非结构网格,因此非常适合计算复杂外形的情况。

A highly-accurate numerical method is used to solve the two-dimensional Maxwell＇s equations,where a computational fluid dynamics（CFD） based discontinuous galerkin（DG） method is employed for the spatial discretization and the four-step Runge-Kutta is used for time-stepping.In order to improve the efficiency,the quadrature-free implementation and the parallel computing based on mesh partitioning are used.Numerical tests indicate that highly-accurate solutions can be obtained when using high orders even on very coarse grids.More importantly,this CFD-based high-order DG method for the Maxwell＇s equations is very suitable for complex geometries since it is implemented on unstructured mesh.