A new efficient operator splitting method for stochastic Maxwell equations

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.