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This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…

Numerical Analysis · Mathematics 2022-12-12 Hongxia Guo , Guanghui Hu , Mengjie 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

In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…

Analysis of PDEs · Mathematics 2024-11-08 Suliang Si

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…

Discrete Mathematics · Computer Science 2014-06-03 Christoph Gugg , Matthew Harker , Paul O'Leary , Gerhard Rath

A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…

Numerical Analysis · Mathematics 2017-12-04 Nicholas Hale , Sheehan Olver

In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…

Numerical Analysis · Mathematics 2022-11-22 Erik Schnaubelt , Nicolas Marsic , Herbert De Gersem

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…

Optimization and Control · Mathematics 2022-09-28 William W. Symes

The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…

Numerical Analysis · Mathematics 2025-04-29 Xin Liu , Yong Zhang

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

In this paper, we theoretically propose a new hashing scheme to establish the sparse Fourier transform in high-dimensional space. The estimation of the algorithm complexity shows that this sparse Fourier transform can overcome the curse of…

Data Structures and Algorithms · Computer Science 2022-05-03 Liang Chen

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes or the fast Fourier transform can efficiently treat the…

Numerical Analysis · Mathematics 2025-01-31 Daniel Fortunato , David B. Stein , Alex H. Barnett

We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…

Numerical Analysis · Mathematics 2025-06-17 Trong D. Dang , Chanh V. Le , Khoa D. Luu , Loc H Nguyen

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without…

Computational Physics · Physics 2020-04-20 Victorita Dolean , Pierre Jolivet , Stéphane Operto , Pierre-Henri Tournier

We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…

Analysis of PDEs · Mathematics 2020-04-17 Mtthias Eller , Philip Hoskins , Leonid Kunyansky

This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…

Analysis of PDEs · Mathematics 2021-11-12 Masaru Ikehata

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