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Numerical Solution of a Three-Dimensional Coefficient Inverse Problem for the Wave Equation with Integral Data in a Cylindrical Domain

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Abstract

A three-dimensional coefficient inverse problem for the wave equation (with losses) in a cylindrical domain is considered. The data given for its solution are special time integrals of a wave field measured in a cylindrical layer. We present and substantiate an efficient algorithm for solving this three-dimensional problem based on the fast Fourier transform. The algorithm makes it possible to obtain a solution on 512× 512×512 grids in about 1.4 hours on a typical PC without paralleling the calculations. The results of numerical experiments of model inverse problem solving are presented.

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Funding

This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00039) and by the Competitiveness Project (agreement no. 02.a03.21.0005 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and the National Research Nuclear University (Moscow Engineering Physics Institute).

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Authors and Affiliations

  1. Institute of System Analysis. Federal Research Center “Informatics and Control,”, Russian Academy of Sciences, ul. Vavilova 44, b. 2, Moscow, 119333, Russia

    A. B. Bakushinsky

  2. National Research Nuclear University (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow, 115409, Russia

    A. S. Leonov

Authors
  1. A. B. Bakushinsky
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  2. A. S. Leonov
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Corresponding authors

Correspondence to A. B. Bakushinsky or A. S. Leonov.

Additional information

Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2019, Vol. 22, No. 4, pp. 381–396.

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Bakushinsky, A.B., Leonov, A.S. Numerical Solution of a Three-Dimensional Coefficient Inverse Problem for the Wave Equation with Integral Data in a Cylindrical Domain. Numer. Analys. Appl. 12, 311–325 (2019). https://doi.org/10.1134/S1995423919040013

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  • DOI: https://doi.org/10.1134/S1995423919040013

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