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

Roman Chapko and Leonidas Mindrinos
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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

Mathematics, 2022, vol. 10, issue 5, 1-11

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.

Keywords: boundary reconstruction; Laguerre transform; modified single layer potential; non-linear boundary integral equation; quadrature rules; Tikhonov regularization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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