A novel overlapping domain decomposition splitting algorithm based on a Crank-Nisolson method is developed for the stochastic nonlinear Schroedinger equation driven by a multiplicative noise with non-periodic boundary conditions. The proposed algorithm can significantly reduce the computational cost while maintaining the similar conservation laws. Numerical experiments are dedicated to illustrating the capability of the algorithm for different spatial dimensions, as well as the various initial conditions. In particular, we compare the performance of the overlapping domain decomposition splitting algorithm with the stochastic multi-symplectic method in [S. Jiang, L. Wang and J. Hong, Commun. Comput. Phys., 2013] and the finite difference splitting scheme in [J. Cui, J. Hong, Z. Liu and W. Zhou, J. Differ. Equ., 2019]. We observe that our proposed algorithm has excellent computational efficiency and is highly competitive. It provides a useful tool for solving stochastic partial differential equations.

翻译：针对由乘性噪声驱动、具有非周期边界条件的随机非线性薛定谔方程，本文提出了一种基于Crank-Nicolson格式的新型重叠区域分解分裂算法。该算法在保持相似守恒律的同时，能够显著降低计算成本。数值实验验证了该算法在不同空间维度及多种初始条件下的适用性。特别地，我们将所提算法与文献[S. Jiang, L. Wang and J. Hong, Commun. Comput. Phys., 2013]中的随机多辛方法以及[J. Cui, J. Hong, Z. Liu and W. Zhou, J. Differ. Equ., 2019]中的有限差分分裂方案进行了性能对比。结果表明，所提算法具有卓越的计算效率与高度竞争力，为求解随机偏微分方程提供了有效工具。