TY - JOUR
T1 - An Overlapping Domain Decomposition Splitting Algorithm for Stochastic Nonlinear Schrödinger Equation
AU - Ji , Lihai
JO - Journal of Computational Mathematics
VL - 4
SP - 791
EP - 812
PY - 2025
DA - 2025/07
SN - 43
DO - http://doi.org/10.4208/jcm.2402-m2023-0104
UR - https://global-sci.org/intro/article_detail/jcm/24261.html
KW - Stochastic nonlinear Schrödinger equation, Domain decomposition method, Operator splitting, Overlapping domain decomposition splitting algorithm.
AB - <p style="text-align: justify;">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.</p>