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Journal of Elasticity

, Volume 137, Issue 2, pp 177–217 | Cite as

Leading and Second Order Homogenization of an Elastic Scattering Problem for Highly Oscillating Anisotropic Medium

  • Yi-Hsuan Lin
  • Shixu MengEmail author
Article

Abstract

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or overall wave field. We further pursue a higher-order homogenization with the help of complimentary boundary correctors and provide a detailed analysis on the rate of higher-order convergence. Finally we provide preliminary numerical examples to demonstrate the higher-order homogenization.

Keywords

Second-order homogenization Elastic scattering Periodic media Wave dispersion Two-scale homogenization 

Mathematics Subject Classification

35B27 74J20 74B05 

Notes

Acknowledgements

The work was initiated when the authors participated the annual program on “Mathematics and Optics” (2017–2018) at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. Y.-H. Lin would like to thank the support from IMA for his stay at the University of Minnesota. S. Meng was partially supported by the Air Force Office of Scientific Research under award FA9550-18-1-0131.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute for Advanced StudyThe Hong Kong University Science and TechnologyKowloonHong Kong
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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