  In this paper, we consider stochastic Runge-Kutta methods for stochastic
Hamiltonian partial differential equations and present some sufficient
conditions for multisymplecticity of stochastic Runge-Kutta methods of
stochastic Hamiltonian partial differential equations. Particularly, we apply
these ideas to stochastic Maxwell equations with multiplicative noise,
possessing the stochastic multi-symplectic conservation law and energy
conservation law. Theoretical analysis shows that the methods can preserve both
the discrete stochastic multi-symplectic conservation law and discrete energy
conservation law almost surely.
