Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures

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• 作者：Hao Dong^a ; ^{donghao@mail.nwpu.edu.cn} ; Yufeng Nie ; ^a ; ^{yfnie@nwpu.edu.cn} ; Junzhi Cui^b ; Yatao Wu^a ; Zihao Yang^a
• 关键词：Multiscale asymptotic analysis ; Damped wave equations ; Quasi-periodic structure ; Second-order two-scale numerical method ; Newmark scheme
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：298
• 期：Complete
• 页码：201-220
• 全文大小：2546 K
• 卷排序：298

文摘

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.