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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 Publication APPLIED MATHEMATICS AND COMPUTATION ISSN 0096-3003 Volume 298Pages:201-220 Abstract In 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. Keyword Multiscale asymptotic analysis Damped wave equations Quasi-periodic structure Second-order two-scale numerical method Newmark scheme DOI 10.1016/j.amc.2016.11.023 Language 英语 Funding Project National 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 Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000392785400016 Publisher ELSEVIER SCIENCE INC Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/24649 Collection 计算数学与科学工程计算研究所 Corresponding Author Nie, Yufeng Affiliation 1.Northwestern Polytech Univ, Sch Sci, Dept Math Appl, Xian 710129, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/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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