Structure-Preserving Numerical Methods for Stochastic Poisson Systems

doi:10.4208/cicp.OA-2019-0084

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	Structure-Preserving Numerical Methods for Stochastic Poisson Systems
	Hong, Jialin 1; Ruan, Jialin 2; Sun, Liying 1; Wang, Lijin 2
	2021-03-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	29 期号:3 页码:802-830
摘要	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 alpha-generating function approach with alpha is an element of [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.
关键词	Stochastic Poisson systems Poisson structure Casimir functions Poisson integrators symplectic integrators generating functions stochastic rigid body system
DOI	10.4208/cicp.OA-2019-0084
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11971458] ; National Natural Science Foundation of China[11471310] ; National Natural Science Foundation of China[11071251]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000614555300006
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58150
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Lijin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, 19 YuQuan Rd, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Ruan, Jialin,Sun, Liying,et al. Structure-Preserving Numerical Methods for Stochastic Poisson Systems[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2021,29(3):802-830.
APA	Hong, Jialin,Ruan, Jialin,Sun, Liying,&Wang, Lijin.(2021).Structure-Preserving Numerical Methods for Stochastic Poisson Systems.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,29(3),802-830.
MLA	Hong, Jialin,et al."Structure-Preserving Numerical Methods for Stochastic Poisson Systems".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 29.3(2021):802-830.