TY - JOUR
T1 - Structure-Preserving Numerical Methods for Stochastic Poisson Systems
AU - Hong , Jialin
AU - Ruan , Jialin
AU - Sun , Liying
AU - Wang , Lijin
JO - Communications in Computational Physics
VL - 3
SP - 802
EP - 830
PY - 2021
DA - 2021/01
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2019-0084
UR - https://global-sci.org/intro/article_detail/cicp/18567.html
KW - Stochastic Poisson systems, Poisson structure, Casimir functions, Poisson integrators,
symplectic integrators, generating functions, stochastic rigid body system.
AB - <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>