Two-Dimensional Elastic Scattering Coefficients and Enhancement of Nearly Elastic Cloaking

  • Tasawar Abbas
  • Habib Ammari
  • Guanghui Hu
  • Abdul Wahab
  • Jong Chul Ye
Article

DOI: 10.1007/s10659-017-9624-7

Cite this article as:
Abbas, T., Ammari, H., Hu, G. et al. J Elast (2017). doi:10.1007/s10659-017-9624-7
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Abstract

The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to mathematical imaging and elastic cloaking, the notion of elastic scattering coefficients of an inclusion is presented from the perspective of boundary layer potentials and a few properties are discussed. A reconstruction algorithm is developed and analyzed for extracting the elastic scattering coefficients from multi-static response measurements of the scattered field in order to cater to inverse scattering problems. The decay rate, stability and error analyses, and the estimate of maximal resolving order in terms of the signal-to-noise ratio are discussed. Moreover, scattering-coefficients-vanishing structures are designed and their utility for enhancement of nearly elastic cloaking is elucidated.

Keywords

Elastic scattering Scattering coefficients Elastic cloaking Inverse scattering 

Mathematics Subject Classification

35L05 35R30 74B05 74J20 78A46 

Funding information

Funder NameGrant NumberFunding Note
National Research Foundation of Korea
  • NRF-2015H1D3A106240
  • NRF-2016R1A2B3008104
  • NRF-2016R1A2B3008104
  • NRF-2014R1A2A1A11052491
  • NRF-2014R1A2A1A11052491
National Research Council of Science and Technology of Korea
  • CAP-13-3-KERI
  • CAP-13-3-KERI
National Natural Science Foundation of China (CN)
  • 11671028
1000-Talent Program of Young Scientists in China

    Copyright information

    © Springer Science+Business Media Dordrecht 2017

    Authors and Affiliations

    1. 1.Department of Mathematics and Statistics, Faculty of Basic and Applied SciencesInternational Islamic UniversityIslamabadPakistan
    2. 2.Department of MathematicsETH ZürichZürichSwitzerland
    3. 3.Beijing Computational Science Research CenterBeijingChina
    4. 4.Bio Imaging and Signal Processing Laboratory, Department of Bio and Brain EngineeringKorea Advanced Institute of Science and TechnologyYuseong-gu, DaejeonKorea

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