The inverse scattering problem by an elastic inclusion

  • Roman Chapko
  • Drossos Gintides
  • Leonidas Mindrinos
Article

Abstract

In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti’s formula (direct method), is equivalent to a system of four integral equations that are non linear with respect to the unknown boundary. Two equations are on the boundary and two on the unit circle where the far-field patterns of the scattered waves lie. We solve iteratively the system of integral equations by linearising only the far-field equations. Numerical results are presented that illustrate the feasibility of the proposed method.

Keywords

Linear elasticity Inverse scattering problem Integral equation method 

Mathematics Subject Classification (2010)

35P25 35R30 45G05 65N35 74J20 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Faculty of Applied Mathematics and InformaticsIvan Franko National University of LvivLvivUkraine
  2. 2.Department of MathematicsNational Technical University of AthensZografouGreece
  3. 3.Computational Science CenterUniversity of ViennaViennaAustria

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