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Related papers: Computing scattering resonances of rough obstacles

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The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…

Numerical Analysis · Mathematics 2023-02-15 Carlos Borges , Manas Rachh , Leslie Greengard

We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution…

Numerical Analysis · Mathematics 2016-09-21 Yuxiang Liu , Alex H. Barnett

We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of…

Analysis of PDEs · Mathematics 2026-01-13 Amandine Boucart , Sonia Fliss , Laure Giovangigli

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

Analysis of PDEs · Mathematics 2009-12-09 xiaodong Liu , Bo Zhang

The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles…

Numerical Analysis · Mathematics 2025-12-29 Jialei Li , Xiaodong Liu , Qingxiang Shi

This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…

Mathematical Physics · Physics 2025-09-30 Huaian Diao , Qingle Meng , Zhiying Sun

We propose a boundary element method for problems of time-harmonic acoustic scattering by multiple obstacles in two dimensions, at least one of which is a convex polygon. By combining a Hybrid Numerical Asymptotic (HNA) approximation space…

Numerical Analysis · Mathematics 2020-02-27 Andrew Gibbs , Simon Chandler-Wilde , Stephen Langdon , Andrea Moiola

We study time-harmonic scattering by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength…

Analysis of PDEs · Mathematics 2025-10-15 Yuxin Du , Xin Fu , Wenjia Jing

A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a…

Numerical Analysis · Mathematics 2017-09-29 Lehel Banjai , Alexander Rieder

We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in $\mathbb{R}^3$ by a single far-field measurement within polyhedral geometries. We are particularly interested in the case that the scattering…

Analysis of PDEs · Mathematics 2021-11-30 Xinlin cao , Huaian Diao , Hongyu Liu , Jun Zou

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…

Numerical Analysis · Mathematics 2018-05-01 Xiaoli Liu , Bo Zhang , Haiwen Zhang

In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…

Analysis of PDEs · Mathematics 2025-01-14 Bochao Chen , Yixian Gao , Peijun Li , Yuanchun Ren

The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative…

Computational Physics · Physics 2014-01-03 Sebastian Acosta , Vianey Villamizar , Bruce Malone

We consider the numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nystr\"{o}m method is proposed for the scattering problem based on the…

Numerical Analysis · Mathematics 2021-08-06 Jianliang Li , Xiaoli Liu , Bo Zhang , Haiwen Zhang

We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…

Numerical Analysis · Mathematics 2021-04-29 Carlos Borges , Manas Rachh

We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…

Numerical Analysis · Mathematics 2025-09-26 Tristan Goodwill , Shidong Jiang , Manas Rachh , Kosuke Sugita

For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…

Numerical Analysis · Mathematics 2018-05-24 Andrew Gibbs , Stephen Langdon , Andrea Moiola

The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…

Numerical Analysis · Mathematics 2014-09-17 Lexing Ying

We study the distribution of resonances for smooth strictly convex obstacles under general boundary conditions. We show that under a pinched curvature condition for the boundary of the obstacle, the resonances are separated into cubic bands…

Analysis of PDEs · Mathematics 2015-06-18 Long Jin