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An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…

Mathematical Physics · Physics 2007-05-23 A. S. Blagovestchenskii , Y. Kurylev , V. Zalipaev

This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first show that the point sources in both $\mathbb{R}^2$ and…

Analysis of PDEs · Mathematics 2025-03-11 Xiaodong Liu , Qingxiang Shi , Jing Wang

Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined…

Analysis of PDEs · Mathematics 2022-04-06 Jiaqing Yang , Jianliang Li , Bo Zhang

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

For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…

Numerical Analysis · Mathematics 2024-03-06 A. Gibbs , S. Langdon

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…

Analysis of PDEs · Mathematics 2026-01-19 Emilia L. K. Blåsten , Tapio Helin , Antti Kujanpää , Lauri Oksanen , Jesse Railo

This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a random potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian…

Analysis of PDEs · Mathematics 2021-03-23 Jianliang Li , Peijun Li , Xu Wang

A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problems with the initial condition the delta function concentrated at a single plane (i.e. the plane…

Analysis of PDEs · Mathematics 2022-03-23 Michael V. Klibanov , Vladimir G. Romanov

We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…

Numerical Analysis · Mathematics 2018-05-22 Michael V. Klibanov , Aleksandr E. Kolesov , Dinh-Liem Nguyen

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 work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated…

Numerical Analysis · Mathematics 2025-10-27 Marvin Knöller , Jörg Nick

We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…

Numerical Analysis · Mathematics 2018-11-30 Xiao Liu , Yuanzhe Xi , Yousef Saad , Maarten V. de Hoop

This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…

Numerical Analysis · Mathematics 2024-01-08 Yan Chang , Yukun Guo , Yue Zhao

This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…

Analysis of PDEs · Mathematics 2020-08-05 Jianliang Li , Jiaqing Yang , Bo Zhang

This paper presents a solution to an initial value problem for the 1-dimensional wave equation on time scales through the application of a Fourier transform and its inverse via contour integrals. The time scale of the spatial dimension is…

Analysis of PDEs · Mathematics 2024-09-26 Davis Funk , Charis Tsikkou

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

Numerical Analysis · Mathematics 2025-11-04 Hao Gu , Tianjiao Wang , Xiang Xu , Yue Zhao

This paper is concerned with the inverse acoustic scattering problem with phaseless total-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the…

Numerical Analysis · Mathematics 2020-10-15 Bo Zhang , Haiwen Zhang

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse…

Analysis of PDEs · Mathematics 2018-01-11 Xianchao Wang , Minghui Song , Yukun Guo , Hongjie Li , Hongyu Liu

This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…

Numerical Analysis · Mathematics 2020-08-13 Gang Bao , Yiwen Lin , Xiang Xu

We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations…

Numerical Analysis · Mathematics 2020-10-29 Jürgen Dölz , Helmut Harbrecht , Carlos Jerez-Hanckes , Michael Multerer