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The inverse scattering problem by an elastic inclusion

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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.

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Lviv, Ukraine

    Roman Chapko

  2. Department of Mathematics, National Technical University of Athens, Zografou, Greece

    Drossos Gintides

  3. Computational Science Center, University of Vienna, Vienna, Austria

    Leonidas Mindrinos

Authors
  1. Roman Chapko
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  2. Drossos Gintides
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  3. Leonidas Mindrinos
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Corresponding author

Correspondence to Leonidas Mindrinos.

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Communicated by: Karsten Urban

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Chapko, R., Gintides, D. & Mindrinos, L. The inverse scattering problem by an elastic inclusion. Adv Comput Math 44, 453–476 (2018). https://doi.org/10.1007/s10444-017-9550-z

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  • DOI: https://doi.org/10.1007/s10444-017-9550-z

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