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Splitting K-symplectic methods for non-canonical separable Hamiltonian problems
Zhu, Beibei1; Zhang, Ruili2; Tang, Yifa1; Tu, Xiongbiao1; Zhao, Yue1
2016-10-01
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume322Pages:387-399
AbstractNon-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems; for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generating function technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent. (C) 2016 Elsevier Inc. All rights reserved.
KeywordK-symplectic methods Splitting algorithms Gauss' methods Generating function methods
DOI10.1016/j.jcp.2016.06.044
Language英语
Funding ProjectNational Natural Science Foundation of China[11371357] ; ITER-China Program[2014GB124005]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000381585100020
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23353
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.Univ Sci & Technol China, Ctr Adv Fus Energy & Plasma Sci, Dept Modern Phys & Collaborat Innovat, Hefei 230026, Anhui, Peoples R China
Recommended Citation
GB/T 7714
Zhu, Beibei,Zhang, Ruili,Tang, Yifa,et al. Splitting K-symplectic methods for non-canonical separable Hamiltonian problems[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2016,322:387-399.
APA Zhu, Beibei,Zhang, Ruili,Tang, Yifa,Tu, Xiongbiao,&Zhao, Yue.(2016).Splitting K-symplectic methods for non-canonical separable Hamiltonian problems.JOURNAL OF COMPUTATIONAL PHYSICS,322,387-399.
MLA Zhu, Beibei,et al."Splitting K-symplectic methods for non-canonical separable Hamiltonian problems".JOURNAL OF COMPUTATIONAL PHYSICS 322(2016):387-399.
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