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

Author

Listed:
  • Dong, Hao
  • Nie, Yufeng
  • Cui, Junzhi
  • Wu, Yatao
  • Yang, Zihao

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.

Suggested Citation

  • 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, Elsevier, vol. 298(C), pages 201-220.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:201-220
    DOI: 10.1016/j.amc.2016.11.023
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    References listed on IDEAS

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    1. Huang, Jizu & Cao, Liqun & Yang, Chao, 2015. "A multiscale algorithm for radiative heat transfer equation with rapidly oscillating coefficients," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 149-168.
    2. Dong, Qiao-Li & Cao, Li-Qun, 2014. "Multiscale asymptotic expansions methods and numerical algorithms for the wave equations in perforated domains," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 872-887.
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    Cited by:

    1. Dong, Qiao-li & Cao, Li-qun & Wang, Xin & Huang, Ji-zu, 2018. "Multiscale numerical algorithms for elastic wave equations with rapidly oscillating coefficients," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 16-35.

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