A new efficient operator splitting method for stochastic Maxwell equations

TL;DR

This paper introduces an operator splitting method for stochastic Maxwell equations driven by additive noise, which is efficient, preserves key geometric properties, and achieves a convergence order of one in mean square sense.

Contribution

It presents a novel operator splitting technique that decomposes stochastic Maxwell equations into local subsystems, preserving symplectic properties and providing rigorous error analysis.

Findings

Method is numerically efficient.

Preserves symplectic and multi-symplectic structures.

Achieves convergence order one in mean square sense.

Abstract

This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional system into some local one-dimensional subsystems, but also separates the deterministic and stochastic parts. This method is numerically efficient, and preserves the symplecticity, the multi-symplecticity as well as the growth rate of the averaged energy. A detailed $H^2$-regularity analysis of stochastic Maxwell equations is obtained, which is a crucial prerequisite of the error analysis. Under the regularity assumptions of the initial data and the noise, the convergence order one in mean square sense of the operator splitting method is established.