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Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure

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Abstract

This paper discusses the spectral properties and numerical simulation for the second order elliptic operators with rapidly oscillating coefficients in the domains which may contain small cavities distributed periodically with period ε. A multiscale asymptotic analysis formula for this problem is obtained by constructing properly the boundary layer. Finally, numerical results are given, which provide a strong support for the analytical estimates

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Authors and Affiliations

  1. Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Cao Liqun & Cui Junzhi

  2. Center of Solid Research, Beijing University of Aeronautics and Astronautics, 100083, Beijing, China

    Zhu Dechao

  3. Department of Applied Physics, Beijing University of Aeronautics and Astronautics, 100083, Beijing, China

    Luo Jianlan

Authors
  1. Cao Liqun
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  2. Cui Junzhi
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  3. Zhu Dechao
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  4. Luo Jianlan
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Correspondence to Cao Liqun.

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Liqun, C., Junzhi, C., Dechao, Z. et al. Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure. Sci. China Ser. A-Math. 45, 1588–1602 (2002). https://doi.org/10.1360/02ys9171

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  • DOI: https://doi.org/10.1360/02ys9171

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