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A novel overlapping domain decomposition splitting algorithm based on aCrank-Nisolson method is developed for the stochastic nonlinear Schroedingerequation driven by a multiplicative noise with non-periodic boundaryconditions. The proposed algorithm can significantly reduce the computationalcost while maintaining the similar conservation laws. Numerical experiments arededicated to illustrating the capability of the algorithm for different spatialdimensions, as well as the various initial conditions. In particular, wecompare the performance of the overlapping domain decomposition splittingalgorithm with the stochastic multi-symplectic method in [S. Jiang, L. Wang andJ. Hong, Commun. Comput. Phys., 2013] and the finite difference splittingscheme in [J. Cui, J. Hong, Z. Liu and W. Zhou, J. Differ. Equ., 2019]. Weobserve that our proposed algorithm has excellent computational efficiency andis highly competitive. It provides a useful tool for solving stochastic partialdifferential equations.

An overlapping domain decomposition splitting algorithm for stochastic nonlinear Schroedinger equation