  In this paper, it is shown that three-dimensional stochastic Maxwell
equations with multiplicative noise are stochastic Hamiltonian partial
differential equations possessing a geometric structure (i.e. stochastic
mutli-symplectic conservation law), and the energy of system is a conservative
quantity almost surely. We propose a stochastic multi-symplectic
energy-conserving method for the equations by using the wavelet collocation
method in space and stochastic symplectic method in time. Numerical experiments
are performed to verify the excellent abilities of the proposed method in
providing accurate solution and preserving energy. The mean square convergence
result of the method in temporal direction is tested numerically, and numerical
comparisons with finite difference method are also investigated.
