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