Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients

doi:10.1016/j.apnum.2009.07.008

	Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients
	Dong, Qiao-Li; Cao, Li-Qun
	2009-12-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	59 期号:12 页码:3008-3032
摘要	In this paper, we discuss the multiscale analysis and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients. The formal multiscale asymptotic expansions of the solutions for these problems in four specific cases are presented. Higher order corrector methods are constructed and associated explicit convergence rates are obtained in some cases. A multiscale numerical method and a symplectic geometric scheme are introduced. Finally, some numerical results and unsolved problems are presented, and these numerical results support strongly the convergence theorem of this paper. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
关键词	Homogenization Multiscale asymptotic expansion The wave equation with rapidly oscillating coefficients Finite element method Symplectic geometric scheme
DOI	10.1016/j.apnum.2009.07.008
语种	英语
资助项目	National Natural Science Foundation of China[90405016] ; Special Funds for Major State Basic Research Projects[2006CB605102]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000270453100011
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8575
专题	计算数学与科学工程计算研究所
通讯作者	Dong, Qiao-Li
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Dong, Qiao-Li,Cao, Li-Qun. Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients[J]. APPLIED NUMERICAL MATHEMATICS,2009,59(12):3008-3032.
APA	Dong, Qiao-Li,&Cao, Li-Qun.(2009).Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients.APPLIED NUMERICAL MATHEMATICS,59(12),3008-3032.
MLA	Dong, Qiao-Li,et al."Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients".APPLIED NUMERICAL MATHEMATICS 59.12(2009):3008-3032.