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In this paper, we propose a stochastic conformal multi-symplectic method fora class of damped stochastic Hamiltonian partial differential equations inorder to inherit the intrinsic properties, and apply the numerical method tosolve a kind of damped stochastic nonlinear Schrodinger equation withmultiplicative noise. It is shown that the stochastic conformalmulti-symplectic method preserves the discrete stochastic conformalmulti-symplectic conservation law, the discrete charge exponential dissipationlaw almost surely, and we also deduce the recurrence relation of the discreteglobal energy. Numerical experiments are preformed to verify the goodperformance of the proposed stochastic conformal multi-symplectic method,compared with a Crank-Nicolson type method. Finally, we present the mean squareconvergence result of the proposed numerical method in temporal directionnumerically.

Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrodinger equation