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On the Numerical Solution of a Hyperbolic Inverse Boundary Value Problem in Bounded Domains

Author

Listed:
  • Roman Chapko

    (Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine)

  • Leonidas Mindrinos

    (Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria)

Abstract

We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation method and we reduce the inverse problem to a system of boundary integral equations. We propose an iterative scheme that linearizes the equation using the Fréchet derivative of the forward operator. The application of special quadrature rules results to an ill-conditioned linear system which we solve using Tikhonov regularization. The numerical results show that the proposed method produces accurate and stable reconstructions.

Suggested Citation

  • Roman Chapko & Leonidas Mindrinos, 2022. "On the Numerical Solution of a Hyperbolic Inverse Boundary Value Problem in Bounded Domains," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:750-:d:759426
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    References listed on IDEAS

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    1. Fagueye Ndiaye & Idrissa Ly & Remi Léandre, 2021. "Inverse Problem Related to Boundary Shape Identification for a Hyperbolic Differential Equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2021, pages 1-12, October.
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