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Recovering Density and Speed of Sound Coefficients in the 2D Hyperbolic System of Acoustic Equations of the First Order by a Finite Number of Observations

Author

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  • Dmitriy Klyuchinskiy

    (Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia
    Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Nikita Novikov

    (Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia
    Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia
    Mathematical Center in Akademgorodok, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Maxim Shishlenin

    (Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia
    Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia
    Mathematical Center in Akademgorodok, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

Abstract

We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.

Suggested Citation

  • Dmitriy Klyuchinskiy & Nikita Novikov & Maxim Shishlenin, 2021. "Recovering Density and Speed of Sound Coefficients in the 2D Hyperbolic System of Acoustic Equations of the First Order by a Finite Number of Observations," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:199-:d:483168
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    Citations

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    Cited by:

    1. Maxim Shishlenin & Nikita Savchenko & Nikita Novikov & Dmitriy Klyuchinskiy, 2022. "Modeling of 2D Acoustic Radiation Patterns as a Control Problem," Mathematics, MDPI, vol. 10(7), pages 1-14, March.
    2. Nikita Novikov & Maxim Shishlenin, 2023. "Direct Method for Identification of Two Coefficients of Acoustic Equation," Mathematics, MDPI, vol. 11(13), pages 1-16, July.

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