In this article, we investigate a stochastic Galerkin method for the Maxwell equations with random inputs. The generalized Polynomial Chaos (gPC) expansion technique is used to obtain a deterministic system of the gPC expansion coefficients. The regularity of the solution with respect to the random is analyzed. On the basis of the regularity results, the optimal convergence rate of the stochastic Galerkin approach for Maxwell equations with random inputs is proved. Numerical examples are presented to support the theoretical analysis.

中文翻译：

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具有不确定性的麦克斯韦方程组的一种随机伽辽金方法

在本文中，我们研究了具有随机输入的麦克斯韦方程组的随机伽辽金方法。广义多项式混沌 (gPC) 展开技术用于获得 gPC 展开系数的确定性系统。分析了解相对于随机的规律性。在规律性结果的基础上，证明了具有随机输入的麦克斯韦方程组的随机Galerkin方法的最优收敛速度。给出了数值例子来支持理论分析。