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The inverse elastic scattering problem in the cavity with impedance boundary
Abstract
In this paper, we investigate the elastic inverse scattering problem in a two-dimensional cavity with an impedance boundary condition. We prove that the scattered fields inside the cavity satisfy a reciprocity relation, and prove that both the shape of cavity and the impedance parameter on the boundary can be uniquely determined from the scattered fields measured on an interior curve. Numerically, we first employ the linear sampling method to reconstruct the shape, and then recover the impedance parameter by combining potential theory with the least squares method. Several numerical experiments are presented to demonstrate the feasibility and effectiveness of our methods.
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BibTeX
@misc{xu2026inverse,
title = {{The inverse elastic scattering problem in the cavity with impedance boundary}},
author = {Shiyu Xu and Huiling Zheng and Fang Zeng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25858},
eprint = {2609.25858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25858},
}
RIS
TY - UNPB
TI - The inverse elastic scattering problem in the cavity with impedance boundary
AU - Shiyu Xu
AU - Huiling Zheng
AU - Fang Zeng
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25858
UR - https://arxiv.org/abs/2609.25858
AB - In this paper, we investigate the elastic inverse scattering problem in a two-dimensional cavity with an impedance boundary condition. We prove that the scattered fields inside the cavity satisfy a reciprocity relation, and prove that both the shape of cavity and the impedance parameter on the boundary can be uniquely determined from the scattered fields measured on an interior curve. Numerically, we first employ the linear sampling method to reconstruct the shape, and then recover the impedance parameter by combining potential theory with the least squares method. Several numerical experiments are presented to demonstrate the feasibility and effectiveness of our methods.
ER -