English
Related papers

Related papers: A null infinity layer for wave scattering

200 papers

We consider a transmission problem for the Helmholtz equation across the boundary of an extension domain. A such boundary can be Lipschitz, fractal, or of varying Hausdorff dimension for instance. We generalise the notions of layer…

Analysis of PDEs · Mathematics 2026-01-22 Gabriel Claret

The "flexible boundary condition" method, introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic…

Numerical Analysis · Mathematics 2021-10-15 M. Hodapp

We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…

Numerical Analysis · Mathematics 2025-05-20 Tonatiuh Sánchez-Vizuet

We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…

Analysis of PDEs · Mathematics 2025-01-14 Manuel Cañizares

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz…

Computational Physics · Physics 2023-12-27 Tao Yin , Lu Zhang , Weiying Zheng , Xiaopeng Zhu

We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both…

Numerical Analysis · Mathematics 2015-04-01 Thorsten Hohage , Lothar Nannen

We present a general construction of semiglobal scattering solutions to quasilinear wave equations in a neighbourhood of spacelike infinity including past and future null infinity, where the scattering data are posed on an ingoing null cone…

Analysis of PDEs · Mathematics 2025-12-22 Istvan Kadar , Lionor Kehrberger

This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical…

Numerical Analysis · Mathematics 2025-12-16 Wangtao Lu , Kuanrong Shen , Ruming Zhang

We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null condition appear in many equations in…

Analysis of PDEs · Mathematics 2021-02-24 Hans Lindblad , Volker Schlue

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…

Numerical Analysis · Mathematics 2014-06-23 Giulio Ciraolo , Francesco Gargano , Vincenzo Sciacca

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

Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity…

Numerical Analysis · Mathematics 2020-04-24 Xiaokai Yuan , Gang Bao , Peijun Li

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…

Numerical Analysis · Mathematics 2025-07-29 Zhiqi Sun , Yiwen Lin

Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…

Numerical Analysis · Mathematics 2025-10-29 Oscar P. Bruno , Manuel A. Santana

The radiation condition is the key question in the mathematical modelling for scattering problems in unbounded domains. Mathematically, it plays the role as the "boundary condition" at the infinity, which guarantees the well-posedness of…

Analysis of PDEs · Mathematics 2024-10-03 Ruming Zhang

This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…

Numerical Analysis · Mathematics 2026-04-17 Bo Gong , Jiguang Sun

In this paper, we consider the scattering of a time-dependent electromagnetic wave by an elastic body immersed in the lower half-space of a two-layered background medium which is separated by an unbounded rough surface. By proposing two…

Analysis of PDEs · Mathematics 2021-02-04 Changkun Wei , Jiaqing Yang , Bo Zhang

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first…

Numerical Analysis · Mathematics 2011-09-27 Li-Lian Wang , Bo Wang , Xiaodan Zhao

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

Numerical Analysis · Mathematics 2020-07-20 Heping Dong , Jun Lai , Peijun Li