Space-time discontinuous Galerkin method for Maxwell's equations
Space-time discontinuous Galerkin method for Maxwell's equations
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DOI：
10.4208/cicp.230412.271212a
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发表时间：
2013-10
影响因子：
3.7
通讯作者：
Ziqing Xie;Bo Wang;Zhimin Zhang
中科院分区：
文献类型：
--
作者：
Ziqing Xie;Bo Wang;Zhimin Zhang
引入完全离散的不连续伽辽金方法来求解瞬态麦克斯韦方程组。与龙格-库塔间断伽辽金法（RKDG）和有限元时域法（FETD）不同，在我们的方案中，间断伽辽金法不仅用于空间域离散化，还用于时间域离散化。所提出的数值格式被证明是无条件稳定的，并且当次数至多为r和k的多项式分别用于时间和空间近似时，在L 2 范数下建立了收敛速率。提供 2D 和 3D 数值结果来验证理论预测。对于数值通量 w.r.t，在时间步长中观察到超收敛。网格点处的时间变量。
A fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell’s equations. Distinguished from the Runge-Kutta discontinuous Galerkin method (RKDG) and the finite element time domain method (FETD), in our scheme, discontinuous Galerkin methods are used to discretize not only the spatial domain but also the temporal domain. The proposed numerical scheme is proved to be unconditionally stable, and a convergent rate is established under the L 2 -norm when polynomials of degree atmost r and k are used for temporal and spatial approximation, respectively. Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction. An ultra-convergence of order in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points.