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

doi:10.1016/j.jcp.2020.109599

	Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations
	Chen, Chuchu 1,2; Hong, Jialin1,2 ; Sim, Chol 3; Sonwu, Kwang 3
	2020-10-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	418 页码:18
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.
关键词	Hamiltonian wave equations Energy preservation EQUIP multi-symplectic methods
DOI	10.1016/j.jcp.2020.109599
收录类别	SCI
语种	英语
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
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000561583600010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52050
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.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Acad Sci, Inst Math, Pyongyang, North Korea
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.