Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation

Xiaoxu Xu; Guanghui Hu

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arXiv · 2511.21023

Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation

Xiaoxu Xu·Guanghui Hu

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Abstract

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from a single pair of Cauchy data. Uniqueness results are verified under some a priori assumptions and the one-wave factorization method has been adapted to recover the polygonal obstacle as well as the two coefficients. A modified factorization using the Dirichlet-to-Neumann operator is employed to overcome difficulties arising from possible eigenvalues. Intensive numerical examples indicate that our method is efficient.

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Xiaoxu Xu, Guanghui Hu. 2025-11-26. Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation. https://arxiv.org/abs/2511.21023

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