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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 paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…

Mathematical Physics · Physics 2015-06-12 Adrianna Gillman , Alex Barnett

This paper is concerned with the design of two different classes of Galerkin boundary element methods for the solution of high-frequency sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. Both…

Numerical Analysis · Mathematics 2020-11-10 Akash Anand , Yassine Boubendir , Fatih Ecevit , Souaad Lazergui

Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…

Numerical Analysis · Mathematics 2024-08-07 Carlos Borges , Leslie Greengard , Michael O'Neil , Manas Rachh

In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…

Computational Physics · Physics 2018-02-07 Andre Diatta , Muamer Kadic , Martin Wegener , Sebastien Guenneau

This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…

Numerical Analysis · Mathematics 2013-10-08 Yassine Boubendir , Oscar Bruno , David Levadoux , Catalin Turc

This paper devotes to developing novel boundary integral equation (BIE) solvers for the problem of thermoelastic scattering by open-arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the…

Numerical Analysis · Mathematics 2025-07-09 Yixuan X. Kong , José Pinto , Tao Yin

We present a new integral equation method for the calculation of two-dimensional scattering from periodic structures involving triple-points (multiple materials meeting at a single point). The combination of a robust and high-order accurate…

Numerical Analysis · Mathematics 2015-06-16 Leslie Greengard , Kenneth L. Ho , June-Yub Lee

Consider the elastic scattering of an incident wave by a rigid obstacle in three dimensions, which is formulated as an exterior problem for the Navier equation. By constructing a Dirichlet-to-Neumann (DtN) operator and introducing a…

Numerical Analysis · Mathematics 2021-01-18 Gang Bao , Peijun Li , Xiaokai Yuan

We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…

Numerical Analysis · Mathematics 2014-04-07 Y. Boubendir , V. Dominguez , C. Turc

A butterfly-based fast direct integral equation solver for analyzing high-frequency scattering from two-dimensional objects is presented. The solver leverages a randomized butterfly scheme to compress blocks corresponding to near- and…

Numerical Analysis · Mathematics 2017-06-07 Yang Liu , Han Guo , Eric Michielssen

This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a…

Numerical Analysis · Mathematics 2016-01-12 Adrianna Gillman

A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries…

Numerical Analysis · Mathematics 2014-06-03 Sijia Hao , Per-Gunnar Martinsson , Patrick Young

Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…

Numerical Analysis · Mathematics 2025-07-17 Felipe Vico , Leslie Greengard , Michael O'Neil , Manas Rachh

This paper proposes an $O(N)$ fast direct solver for two-dimensional elastic wave scattering problems. The proxy surface method is extended to elastodynamics to obtain shared coefficients for low-rank approximations from discretized…

Numerical Analysis · Mathematics 2025-03-05 Yasuhiro Matsumoto , Taizo Maruyama

A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…

Numerical Analysis · Mathematics 2025-08-19 Tonatiuh Sánchez-Vizuet

This manuscript is the second in a series presenting fast direct solution techniques for solving two-dimensional wave scattering problems from quasi-periodic multilayered structures. The fast direct solvers presented in the series are for…

Numerical Analysis · Mathematics 2022-04-15 Yabin Zhang , Adrianna Gillman

We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…

Spectral Theory · Mathematics 2022-04-11 Elena Kopylova , Gerald Teschl

This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…

Numerical Analysis · Mathematics 2023-08-14 Peijun Li , Xiaokai Yuan