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This paper considers an inverse shape problem for recovering an unknown clamped obstacle in two dimensions from far--field measurements generated by a single incident wave or just a few incident waves for the biharmonic (flexural) wave…

Analysis of PDEs · Mathematics 2026-05-13 Isaac Harris , General Ozochiawaeze

In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…

Numerical Analysis · Mathematics 2026-01-23 Shutong Hou , Mourad Sini , Haibing Wang

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

Numerical Analysis · Mathematics 2017-10-13 Ernesto De Vito , Massimo Fornasier , Valeriya Naumova

Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Qian Liu , Xingkang He , Haitao Fang

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…

Mathematical Physics · Physics 2015-05-20 Michael Carley

Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow quadratically with the wavenumber $k$. Here, we describe a solver which applies only when the scattering potential is…

Numerical Analysis · Mathematics 2020-04-22 James Bremer

This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…

Numerical Analysis · Mathematics 2026-01-01 Qiling Gu , Wenlong Zhang , Zhidong Zhang

Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…

Analysis of PDEs · Mathematics 2016-12-21 Gang Bao , Guanghui Hu , Jiguang Sun , Tao Yin

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

Mathematical Physics · Physics 2025-10-13 Xinwei Hu , Jingrun Chen , Haijun Yu

We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…

Computational Physics · Physics 2011-09-27 Peter Schwander , Chun Hong Yoon , Abbas Ourmazd , Dimitrios Giannakis

We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…

Analysis of PDEs · Mathematics 2020-10-05 Yves Capdeboscq , Roland Griesmaier , Marvin Knöller

Estimating the sound absorption in situ relies on accurately describing the measured sound field. Evidence suggests that modeling the reflection of impinging spherical waves is important, especially for compact measurement systems. This…

Audio and Speech Processing · Electrical Eng. & Systems 2024-04-18 Eric Brandao , William Fonseca , Paulo Mareze , Carlos Resende , Gabriel Azzuz , Joao Pontalti , Efren Fernandez-Grande

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…

Numerical Analysis · Mathematics 2015-06-22 Jun Lai , Motoki Kobayashi , Leslie Greengard

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born…

Numerical Analysis · Mathematics 2024-01-22 Lorenzo Audibert , Shixu Meng

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…

Numerical Analysis · Mathematics 2015-05-30 Bangti Jin

We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…

Numerical Analysis · Mathematics 2016-09-21 Lauri Mustonen

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

Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…

Numerical Analysis · Mathematics 2022-07-27 Vladimir Druskin , Shari Moskow , Mikhail Zaslavsky

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…

Numerical Analysis · Mathematics 2024-01-02 Hongxia Guo , Guanghui Hu

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

Analysis of PDEs · Mathematics 2025-02-21 Zhenhao Li , Jian Wang , Jared Wunsch