KMS Of Academy of mathematics and systems sciences, CAS
| Structure-Preserving Numerical Methods for Stochastic Poisson Systems | |
| Hong, Jialin1; Ruan, Jialin2; Sun, Liying1; Wang, Lijin2 | |
| 2021-03-01 | |
| Source Publication | COMMUNICATIONS IN COMPUTATIONAL PHYSICS
 |
| ISSN | 1815-2406 |
| Volume | 29Issue:3Pages: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 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. |
| Keyword | Stochastic Poisson systems Poisson structure Casimir functions Poisson integrators symplectic integrators generating functions stochastic rigid body system |
| DOI | 10.4208/cicp.OA-2019-0084 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Physics |
| WOS Subject | Physics, Mathematical |
| WOS ID | WOS:000614555300006 |
| Publisher | GLOBAL SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58150 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Lijin |
| Affiliation | 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 |
| 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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