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Structure-Preserving Numerical Methods for Stochastic Poisson Systems
Hong, Jialin1; Ruan, Jialin2; Sun, Liying1; Wang, Lijin2
2021-03-01
Source PublicationCOMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN1815-2406
Volume29Issue:3Pages:802-830
AbstractWe 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.
KeywordStochastic Poisson systems Poisson structure Casimir functions Poisson integrators symplectic integrators generating functions stochastic rigid body system
DOI10.4208/cicp.OA-2019-0084
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000614555300006
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58150
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWang, Lijin
Affiliation1.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
Recommended Citation
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.
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