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arXiv · 2112.10976

A Linearized Boundary Control Method for the Acoustic Inverse Boundary Value Problem

Lauri Oksanen·Tianyu Yang·Yang Yang
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Abstract

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.

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Lauri Oksanen, Tianyu Yang, Yang Yang. 2021-12-21. A Linearized Boundary Control Method for the Acoustic Inverse Boundary Value Problem. https://doi.org/10.1088/1361-6420%2Fac91eb

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