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Numerical Analysis of Systems of Singular Integral Equations of the First Kind with an Indefinable Index in the Problem of Diffraction of Plane Waves on a Rigid Inclusion

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Abstract

By reducing the systems of singular integral equations (SIE) to two types, we carry out a numerical analysis of the problem of mathematical physics about interaction of stationary plane strain waves with a rigid inclusion (cavity with a clamped contour) located in an infinite isotropic elastic medium. The problem is solved using the systems of SIEs of the 1st and 2nd kinds, where the latter has an indefinable index. The conditionality of the models is analyzed using cluster high-precision computational schemes.

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Authors and Affiliations

  1. A. S. Popov National Academy of Communication, Odessa, Ukraine

    B. E. Panchenko & Yu. D. Kovalev

  2. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    I. N. Saiko

Authors
  1. B. E. Panchenko
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  2. Yu. D. Kovalev
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  3. I. N. Saiko
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Corresponding author

Correspondence to B. E. Panchenko.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2020, pp. 3–17.

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Panchenko, B.E., Kovalev, Y.D. & Saiko, I.N. Numerical Analysis of Systems of Singular Integral Equations of the First Kind with an Indefinable Index in the Problem of Diffraction of Plane Waves on a Rigid Inclusion. Cybern Syst Anal 56, 521–533 (2020). https://doi.org/10.1007/s10559-020-00268-z

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  • DOI: https://doi.org/10.1007/s10559-020-00268-z

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