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

Fuente: arXiv
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Autori principali: Xu, Xiaoxu, Hu, Guanghui
Natura: Preprint
Pubblicazione: 2025
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author Xu, Xiaoxu
Hu, Guanghui
author_facet Xu, Xiaoxu
Hu, Guanghui
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_21023
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation
Xu, Xiaoxu
Hu, Guanghui
Analysis of PDEs
65N21, 35R30, 35R25, 35J25
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.
title Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation
topic Analysis of PDEs
65N21, 35R30, 35R25, 35J25
url https://arxiv.org/abs/2511.21023