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We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…

Numerical Analysis · Mathematics 2021-07-27 Juan A. Barceló , Carlos Castro

In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…

Numerical Analysis · Mathematics 2024-02-23 Drossos Gintides , Leonidas Mindrinos

Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…

Numerical Analysis · Mathematics 2020-08-17 Jun Lai , Peijun Li

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…

Numerical Analysis · Mathematics 2022-05-11 Carlos Jerez-Hanckes , Jose Pinto , Tao Yin

The Nystr\"om method for the numerical solution of Fredholm integral equations of the second kind is generalized by decoupling the set of solution nodes from the set of quadrature nodes. The accuracy and efficiency of the new method is…

Numerical Analysis · Mathematics 2025-10-21 Bruno Degli Esposti , Alessandra Sestini

We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…

Analysis of PDEs · Mathematics 2019-04-09 Thomas Baden-Riess

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral…

We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…

Analysis of PDEs · Mathematics 2014-01-28 Anel Esquivel Navarrete , Anatoli Merzon

The authors consider the interior Dirichlet problem for Laplace's equation on planar domains with corners. In order to approximate the solution of the corresponding double layer boundary integral equation, they propose a numerical method of…

Numerical Analysis · Mathematics 2015-04-15 Luisa Fermo , Concetta Laurita

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

In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…

Numerical Analysis · Mathematics 2018-07-04 Aihua Lin , Anastasiia Kuzmina , Per Kristen Jakobsen

This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…

Computational Physics · Physics 2021-02-03 Oscar P. Bruno , Tao Yin

Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…

Classical Physics · Physics 2022-10-18 Omer Haq , Sergei Shabanov

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is…

Numerical Analysis · Mathematics 2024-12-20 Fenglong Qu , Bo Zhang , Haiwen Zhang

This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lam\'e equations and the problem with a compactly supported inhomogeneity is…

Numerical Analysis · Mathematics 2023-12-27 Xiaojuan Liu , Maojun Li , Tao Yin

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

We present three high-order Nystrom discretization strategies of various boundary integral equation formulations of the impenetrable time-harmonic Navier equations in two dimensions. One class of such formulations is based on the four…

Numerical Analysis · Mathematics 2022-06-27 Victor Dominguez , Catalin Turc

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…

Classical Physics · Physics 2016-06-29 Mathieu Chekroun , Loïc Le Marrec , Bruno Lombard , Joël Piraux

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller (\cite{BM71}) boundary integral…

Numerical Analysis · Mathematics 2017-08-15 Gang Bao , Liwei Xu , Tao Yin