@Article{CiCP-29-3,
author = {Jialin, Hong and Ruan, Jialin and Sun, Liying and Wang, Lijin},
title = {Structure-Preserving Numerical Methods for Stochastic Poisson Systems},
journal = {Communications in Computational Physics},
year = {2021},
volume = {29},
number = {3},
pages = {802--830},
abstract = {<p style="text-align: justify;">We propose a numerical integration methodology for stochastic Poisson systems (SPSs) of arbitrary dimensions and multiple noises with different Hamiltonians
in diffusion coefficients, which can provide numerical schemes preserving both the
Poisson structure and the Casimir functions of the SPSs, based on the Darboux-Lie theorem. We first transform the SPSs to their canonical form, the generalized stochastic
Hamiltonian systems (SHSs), via canonical coordinate transformations found by solving certain PDEs defined by the Poisson brackets of the SPSs. An $α$-generating function approach with $α∈[0,1]$ is then constructed and used to create symplectic schemes
for the SHSs, which are then transformed back by the inverse coordinate transformation to become stochastic Poisson integrators of the original SPSs. Numerical tests on a
three-dimensional stochastic rigid body system illustrate the efficiency of the proposed
methods.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0084},
url = {https://global-sci.com/article/79652/structure-preserving-numerical-methods-for-stochastic-poisson-systems}
}