Parareal Algorithms for Stochastic Maxwell Equations with the Damping Term Driven by Additive Noise

Abstract

In this paper, we propose the parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed algorithms proceed as two-level temporal parallelizable integrators with the stochastic exponential integrator as the coarse $\mathscr{G}$-propagator and both the exact solution integrator and the stochastic exponential integrator as the fine $\mathscr{F}$-propagator. The mean-square convergence order of the proposed algorithms consistently increases to $k,$ regardless of whether the exact solution integrator or the stochastic exponential integrator is chosen as the fine $\mathscr{F}$-propagator. Several numerical experiments are illustrated in order to verify our theoretical findings for different choices of the iteration number k and the damping coefficient $σ.$