Year: 2021
Author: Jialin Hong, Jialin Ruan, Liying Sun, Lijin Wang
Communications in Computational Physics, Vol. 29 (2021), Iss. 3 : pp. 802–830
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0084
Communications in Computational Physics, Vol. 29 (2021), Iss. 3 : pp. 802–830
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Stochastic Poisson systems Poisson structure Casimir functions Poisson integrators symplectic integrators generating functions stochastic rigid body system.
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