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Numerical Algorithm for Solving the Inverse Problem for the Helmholtz Equation

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Computational and Information Technologies in Science, Engineering and Education (CITech 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 998))

Abstract

In this paper we consider acoustic equation. The equation by separation of variables is reduced to a boundary value problem for the Helmholtz equation. We consider problem for the Helmholtz equation. We reduce the solution of the operator equation to the problem of minimizing the functional. And we build numerical algorithm for solving the inverse problem. At the end of the article is given the numerical calculations of this problem.

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Acknowledgement

This work was supported by the grant of the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (AP05134121 “Numerical methods of identifiability of inverse and ill-posed problems of natural science”.

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

    M. A. Shishlenin

  2. Novosibirsk State University, Novosibirsk, Russia

    M. A. Shishlenin

  3. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. A. Shishlenin

  4. Al-Farabi Kazakh National University, Almaty, Kazakhstan

    S. E. Kasenov & Zh. A. Askerbekova

Authors
  1. M. A. Shishlenin
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  2. S. E. Kasenov
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  3. Zh. A. Askerbekova
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Corresponding author

Correspondence to M. A. Shishlenin .

Editor information

Editors and Affiliations

  1. RAS, Institute of Computational Technologies, Novosibirsk, Russia

    Yuri Shokin

  2. D. Serikbayev East Kazakhstan State Technical University, Ust-Kamenogorsk, Kazakhstan

    Zhassulan Shaimardanov

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Shishlenin, M.A., Kasenov, S.E., Askerbekova, Z.A. (2019). Numerical Algorithm for Solving the Inverse Problem for the Helmholtz Equation. In: Shokin, Y., Shaimardanov, Z. (eds) Computational and Information Technologies in Science, Engineering and Education. CITech 2018. Communications in Computer and Information Science, vol 998. Springer, Cham. https://doi.org/10.1007/978-3-030-12203-4_20

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  • DOI: https://doi.org/10.1007/978-3-030-12203-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12202-7

  • Online ISBN: 978-3-030-12203-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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