Meshless structure-preserving GRBF collocation methods for stochastic Maxwell equations with multiplicative noise

In this paper, motivated by the principle that numerical methods should preserve the intrinsic properties of the original system as much as possible, we propose two novel classes of structure-preserving methods for the stochastic Maxwell equations with multiplicative noise. More precisely, due to the advantages of high-order accuracy and the simplicity to deal with high-dimensional problems, the meshless global radial basis function (GRBF) collocation method is firstly utilized to discretize the stochastic Maxwell equations in space, the resulting semi-discretization preserves energy and symplectic structure. Then we apply Padé approximation, the splitting technique and the Runge–Kutta method to propose two kinds of efficient fully-discrete methods that are proved to be symplectic, multi-symplectic and energy-preserving simultaneously. Numerical experiments are given to indicate the validity of the proposed methods.