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In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…

Numerical Analysis · Mathematics 2020-10-28 Carlos Borges , Jun Lai

This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is…

Numerical Analysis · Mathematics 2019-02-13 Gang Bao , Tao Yin , Fang Zeng

This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…

Analysis of PDEs · Mathematics 2025-10-16 Chengyu Wu , Jiaqing Yang

This paper concerns the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the point-interaction model for the Lam\'{e} operator…

Mathematical Physics · Physics 2019-11-26 Guanghui Hu , Andrea Mantile , Mourad Sini , Tao Yin

In this work we shall review the (phased) inverse scattering problem and then pursue the phaseless reconstruction from far-field data with the help of the concept of scattering coefficients. We perform sensitivity, resolution and stability…

Numerical Analysis · Mathematics 2015-10-15 Habib Ammari , Yat Tin Chow , Jun Zou

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…

Numerical Analysis · Mathematics 2018-03-14 Xia Ji , Xiaodong Liu , Yingxia Xi

Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…

Analysis of PDEs · Mathematics 2026-04-15 Huaian Diao , Hongyu Liu , Longyue Tao

The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…

Numerical Analysis · Mathematics 2026-05-05 Tielei Zhu , Zhihao Ge , Bangmin Wu

We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…

Numerical Analysis · Mathematics 2025-08-18 Sarah Eberle-Blick , Bastian Harrach , Xianchao Wang

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…

Analysis of PDEs · Mathematics 2015-02-05 Jingzhi Li , Hongyu Liu

This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration…

Numerical Analysis · Mathematics 2017-06-06 Bo Zhang , Haiwen Zhang

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang

We propose a deep learning framework based on an encoder-decoder architecture for the design and evaluation of cloaking devices, demonstrated in this work for two-dimensional wave propagation governed by the Helmholtz equation. The cloaks…

Computational Physics · Physics 2026-05-22 Camille Carvalho , Elsie Cortes , Chrysoula Tsogka , Symeon Papadimitropoulos

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…

Numerical Analysis · Mathematics 2023-07-05 Youzi He , Hongyu Liu , Xianchao Wang

This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…

Numerical Analysis · Mathematics 2025-06-03 Xiaoli Liu , Shixu Meng , Jialu Tian , Bo Zhang

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…

Analysis of PDEs · Mathematics 2017-05-24 Hongyu Liu , Xiaodong Liu

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang