Parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise

TL;DR

This paper analyzes the convergence of parareal algorithms applied to stochastic Maxwell equations with damping and additive noise, demonstrating their effectiveness through theoretical proofs and numerical experiments.

Contribution

It introduces and analyzes new parareal algorithms for stochastic Maxwell equations with damping, establishing their convergence properties and practical performance.

Findings

Convergence order linearly depends on iteration number.

Algorithms perform well with different damping coefficients.

Numerical results confirm theoretical convergence.

Abstract

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 of the parareal algorithms for different choices of the iteration number and the damping coefficient.