This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, we first prove that the strong order of the numerical approximation is $\frac{1}{2}$ for general multiplicative noise. Combining a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be 1 for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings.

本文介绍了由乘法噪声和加性噪声驱动的随机麦克斯韦方程组的显式指数积分器。通过利用温和解的正则估计，我们首先证明数值逼近的强阶为$\frac{\mathrm{1个}}{2}$用于一般的乘法噪声。将适当的分解与随机Fubini定理结合起来，对于加性噪声，该方案的强阶显示为1。此外，对于带有加性噪声的线性随机麦克斯韦方程，拟议的时间积分器在期望的意义上可以精确地保留辛结构，能量的演化以及发散的演化。为了验证我们的理论发现，提出了一些数值实验。