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Structure-Preserving Numerical Methods for Stochastic Poisson Systems

文献类型：期刊论文

作者Hong, Jialin1; Ruan, Jialin2; Sun, Liying1; Wang, Lijin2
刊名COMMUNICATIONS IN COMPUTATIONAL PHYSICS
出版日期2021-03-01
卷号29期号:3页码:802-830
ISSN号1815-2406
关键词Stochastic Poisson systems Poisson structure Casimir functions Poisson integrators symplectic integrators generating functions stochastic rigid body system
DOI10.4208/cicp.OA-2019-0084
英文摘要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.
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
语种英语
出版者GLOBAL SCIENCE PRESS
WOS记录号WOS:000614555300006
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58149]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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