Stochastic Maxwell equations with additive noise are a system of stochasticHamiltonian partial differential equations intrinsically, possessing thestochastic multi-symplectic conservation law.It is shown that the averagedenergy increases linearly with respect to the evolution of time and the flow ofstochastic Maxwell equations with additive noise preserves the divergence inthe sense of expectation. Moreover, we propose three novel stochasticmulti-symplectic methods to discretize stochastic Maxwell equations in order toinvestigate the preservation of these properties numerically. We madetheoretical discussions and comparisons on all of the three methods to observethat all of them preserve the corresponding discrete version of the averageddivergence. Meanwhile, we obtain the corresponding dissipative property of thediscrete averaged energy satisfied by each method. Especially, the evolutionrates of the averaged energies for all of the three methods are derived whichare in accordance with the continuous case. Numerical experiments are performedto verify our theoretical results.
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