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The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that…

Computational Physics · Physics 2024-12-16 Xiaoxu Li , Huajie Chen

We present a new computational approach to simulate linear sweep and cyclic voltammetry experiments that does not require a discretized grid in space to quantify diffusion. By using a Green's function solution coupled to a standard implicit…

Chemical Physics · Physics 2021-05-05 Alec J. Coffman , Jianfeng Lu , Joseph E. Subotnik

We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

Analysis of PDEs · Mathematics 2018-12-03 Jianliang Li , Tapio Helin , Peijun Li

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

Numerical Analysis · Mathematics 2026-05-08 Siyu Cen , Bangti Jin , Yavar Kian , Zhi Zhou

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

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…

Analysis of PDEs · Mathematics 2020-04-22 Xiaoli Feng , Peijun Li , Xu Wang

In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…

Analysis of PDEs · Mathematics 2023-05-16 Hongyu Liu , Shiqi Ma

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…

Probability · Mathematics 2007-10-02 Francesco Mainardi

An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…

Mathematical Physics · Physics 2019-01-01 Michael V. Klibanov , Jingzhi Li , Wenlong Zhang

In this paper, direct sampling method is considered for determining the location of a set of small, linear perfectly conducting cracks from the collected far-field data corresponding to an incident field. To show the feasibility of the…

Numerical Analysis · Mathematics 2018-09-18 Won-Kwang Park

We consider the problem of determining the shape and location of an unknown penetrable object in a perfectly conducting electromagnetic waveguide. The inverse problem is posed in the frequency domain and uses multistatic data in the near…

Numerical Analysis · Mathematics 2019-09-04 Peter Monk , Virginia Selgas , Fan Yang

Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to…

Optics · Physics 2017-04-17 O. V. Belai , L. L. Frumin , S. V. Perminov , D. A. Shapiro

This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way.…

Numerical Analysis · Mathematics 2023-05-09 Isaac Harris , Thu Le , Dinh-Liem Nguyen

This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges,…

Numerical Analysis · Mathematics 2024-07-08 Yunwen Yin , Liang Yan

In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…

Analysis of PDEs · Mathematics 2019-11-27 Peijun Li , Xu Wang

This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two-spatial dimensions. The…

Computational Physics · Physics 2019-10-02 Ignacio Labarca , Luiz M. Faria , Carlos Pérez-Arancibia

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

Analysis of PDEs · Mathematics 2012-10-22 G. Giorgi , M. Brignone , R. Aramini , M. Piana

A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…

Numerical Analysis · Mathematics 2023-05-24 Sergei M. Grudsky , Vladislav V. Kravchenko , Sergii M. Torba

Inverse scattering transform method of the heat equation is developed for a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Extended…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 M. Boiti , F. Pempinelli , A. K. Pogrebkov , B. Prinari