An Overlapping Domain Decomposition Splitting Algorithm for Stochastic Nonlinear Schrödinger Equation
Year: 2025
Author: Lihai Ji
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 791–812
Abstract
A novel overlapping domain decomposition splitting algorithm based on a Crank-Nicolson method is developed for the stochastic nonlinear Schrödinger 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 et al., Commun. Comput. Phys., 14 (2013), 393–411] and the finite difference splitting scheme in [J. Cui et al., J. Differ. Equ., 266 (2019), 5625–5663]. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2402-m2023-0104
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 791–812
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stochastic nonlinear Schrödinger equation Domain decomposition method Operator splitting Overlapping domain decomposition splitting algorithm.