Abstract In this paper, we present a time-explicit sparse grid discontinuous Galerkin method for solving the three-dimensional time-domain Maxwell equations. The conservation properties and convergence rates are established for different choices of numerical fluxes. The convergence rates are proved theoretically and then verified by several numerical examples. Even though our scheme does not preserve the divergence, but by implying the higher order polynomial, one can observe the same convergence rate as numerical solution. Several numerical tests are presented to validate these conclusions.

中文翻译：

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时域麦克斯韦方程组的不连续伽辽金稀疏网格方法

摘要 在本文中，我们提出了一种求解三维时域麦克斯韦方程组的时间显式稀疏网格不连续伽辽金方法。为不同的数值通量选择建立了守恒性质和收敛速度。从理论上证明了收敛速度，然后通过几个数值例子进行了验证。尽管我们的方案不保留发散性，但通过暗示高阶多项式，人们可以观察到与数值解相同的收敛速度。提出了几个数值试验来验证这些结论。