Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations

doi:10.1016/j.jcp.2020.109599

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations
	Chen, Chuchu 2,3; Hong, Jialin 2,3; Sim, Chol 1; Sonwu, Kwang 1
刊名	JOURNAL OF COMPUTATIONAL PHYSICS
	2020-10-01
卷号	418 页码:18
关键词	Hamiltonian wave equations Energy preservation EQUIP multi-symplectic methods
ISSN号	0021-9991
DOI	10.1016/j.jcp.2020.109599
英文摘要	It is well-known that a numerical method which is at the same time geometric structure -preserving and physical property-preserving cannot exist in general for Hamiltonian partial differential equations. Motivated by EQUIP methods proposed in Brugnano et al. (2012) [13], in this paper, we present a novel class of parametric multi-symplectic Runge-Kutta methods, called EQUIP multi-symplectic methods, for Hamiltonian wave equations, which can also conserve energy simultaneously in a weaker sense with a suitable parameter. The existence of such a parameter, which enforces the energy-preserving property, is proved under certain assumptions on the fixed step sizes and the fixed initial condition. We compare the proposed method with the classical multi-symplectic Runge-Kutta method in numerical experiments, which shows the remarkable energy-preserving property of the proposed method and illustrates the validity of theoretical results. These theoretical and numerical results show that EQUIP methods can be well adapted to handle Hamiltonian partial differential equations. (C) 2020 Elsevier Inc. All rights reserved.
资助项目	National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11711530017] ; National Natural Science Foundation of China[11871068] ; National Natural Science Foundation of China[11971470] ; Academy of Mathematics and Systems Science, Chinese Academy of Sciences
WOS研究方向	Computer Science ; Physics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000561583600010
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52049]
专题	计算数学与科学工程计算研究所
通讯作者	Chen, Chuchu
作者单位	1.Acad Sci, Inst Math, Pyongyang, North Korea 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chuchu,Hong, Jialin,Sim, Chol,et al. Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,418:18.
APA	Chen, Chuchu,Hong, Jialin,Sim, Chol,&Sonwu, Kwang.(2020).Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations.JOURNAL OF COMPUTATIONAL PHYSICS,418,18.
MLA	Chen, Chuchu,et al."Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations".JOURNAL OF COMPUTATIONAL PHYSICS 418(2020):18.