论文标题
随机Maxwell方程完全离散的符合性不连续的Galerkin
A symplectic discontinuous Galerkin full discretization for stochastic Maxwell equations
论文作者
论文摘要
本文提出了一种完全离散的方法，称为随机噪声驱动的随机麦克斯韦方程完全离散化，基于随机的随机符号方法和不连续的Galerkin（DG）方法，并具有太空中的逆风磁通量。提出了先验的$ h^k $ - regularity（$ k \ in \ {1,2 \} $），用于介绍随机Maxwell方程的解决方案，这是我们最大程度地报告的。这些$ h^k $ - 规范性对于在初始字段，噪声和介质系数上进行均方体收敛分析的假设至关重要，但在解决方案本身上却不重要。符号DG完全离散化的收敛顺序显示为$ k/2 $在时间方向上，$ k-1/2 $在空间方向上。同时，我们通过大偏差原理揭示了精确和数值解决方案的噪声渐近行为，并表明完全离散的方法在薄弱的意义上保留了差异关系。
This paper proposes a fully discrete method called the symplectic dG full discretization for stochastic Maxwell equations driven by additive noises, based on a stochastic symplectic method in time and a discontinuous Galerkin (dG) method with the upwind fluxes in space. A priori $H^k$-regularity ($k\in\{1,2\}$) estimates for the solution of stochastic Maxwell equations are presented, which have not been reported before to the best of our knowledge. These $H^k$-regularities are vital to make the assumptions of the mean-square convergence analysis on the initial fields, the noise and the medium coefficients, but not on the solution itself. The convergence order of the symplectic dG full discretization is shown to be $k/2$ in the temporal direction and $k-1/2$ in the spatial direction. Meanwhile we reveal the small noise asymptotic behaviors of the exact and numerical solutions via the large deviation principle, and show that the fully discrete method preserves the divergence relations in a weak sense.
