In this paper, we investigate the strong convergence analysis of parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed parareal algorithms proceed as two-level temporal parallelizable integrators with the stochastic exponential integrator as the coarse propagator and both the exact solution integrator and the stochastic exponential integrator as the fine propagator. It is proved that the convergence order of the proposed algorithms linearly depends on the iteration number. Numerical experiments are performed to illustrate the convergence order of the algorithms for different choices of the iteration number, the damping coefficient and the scale of noise.

翻译：本文研究了带有阻尼项的随机Maxwell方程在加性噪声驱动下Parareal算法的强收敛性分析。所提出的Parareal算法作为两级时间并行积分器实现，其中粗传播子采用随机指数积分器，细传播子则同时采用精确解积分器与随机指数积分器。理论证明表明，所提算法的收敛阶数与迭代次数呈线性依赖关系。通过数值实验验证了算法在不同迭代次数、阻尼系数及噪声尺度下的收敛阶数表现。