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Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures
Dong, Hao1; Nie, Yufeng1; Cui, Junzhi2; Wu, Yatao1; Yang, Zihao1
2017-04-01
Source PublicationAPPLIED MATHEMATICS AND COMPUTATION
ISSN0096-3003
Volume298Pages:201-220
AbstractIn this paper, we perform a second-order two-scale analysis and introduce a numerical algorithm for the damped wave equations of composite materials with a quasi-periodic structure. Firstly, second-order two-scale asymptotic expansion solutions for these problems are constructed by a multiscale asymptotic analysis. In addition, we explain the importance of the second-order two-scale solutions by the error analysis in the pointwise sense. Moreover, explicit convergence rates of these second-order two-scale solutions are obtained in the integral sense. Then a second-order two-scale numerical method based on a Newmark scheme is presented to solve these multiscale problems. Finally, some numerical examples show the effectiveness and efficiency of the multiscale numerical method we proposed. (C) 2016 Elsevier Inc. All rights reserved.
KeywordMultiscale asymptotic analysis Damped wave equations Quasi-periodic structure Second-order two-scale numerical method Newmark scheme
DOI10.1016/j.amc.2016.11.023
Language英语
Funding ProjectNational Natural Science Foundation of China[11471262] ; National Natural Science Foundation of China[11501449] ; National Basic Research Program of China[2012CB025904] ; Center for high performance computing of Northwestern Polytechnical University
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000392785400016
PublisherELSEVIER SCIENCE INC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24649
Collection计算数学与科学工程计算研究所
Corresponding AuthorNie, Yufeng
Affiliation1.Northwestern Polytech Univ, Sch Sci, Dept Math Appl, Xian 710129, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Dong, Hao,Nie, Yufeng,Cui, Junzhi,et al. Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures[J]. APPLIED MATHEMATICS AND COMPUTATION,2017,298:201-220.
APA Dong, Hao,Nie, Yufeng,Cui, Junzhi,Wu, Yatao,&Yang, Zihao.(2017).Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures.APPLIED MATHEMATICS AND COMPUTATION,298,201-220.
MLA Dong, Hao,et al."Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures".APPLIED MATHEMATICS AND COMPUTATION 298(2017):201-220.
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