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Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using…

Atomic Physics · Physics 2015-05-27 M. V. Volkov , N. Elander , E. Yarevsky , S. L. Yakovlev

We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…

Numerical Analysis · Mathematics 2013-10-11 T. P. Barrios , R. Bustinza , V. Dominguez

This paper proposes a collocation boundary element method based on the Burton--Miller method for solving transmission problems, which is rapidly convergent within the Krylov subspace solver framework. Our study enhances Burton--Miller-type…

Numerical Analysis · Mathematics 2025-01-17 Yasuhiro Matsumoto , Akihiro Yoshiki , Hiroshi Isakari

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…

Numerical Analysis · Mathematics 2012-03-19 Martin Costabel , Frédérique Le Louër

This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…

Numerical Analysis · Mathematics 2010-04-08 Lothar Nannen , Achim Schädle

We deal with the general problem of scattering by open-arcs in two-dimensional space. We show that this problem can be solved by means of certain second-kind integral equations of the form $\tilde{N} \tilde{S}[\varphi] = f$, where…

Analysis of PDEs · Mathematics 2013-06-07 Stephane K. Lintner , Oscar P. Bruno

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and…

Numerical Analysis · Mathematics 2026-03-24 Jeffrey Galkowski , Euan A. Spence

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

The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…

Numerical Analysis · Mathematics 2022-04-19 Elwin van 't Wout , Seyyed R. Haqshenas , Pierre Gélat , Timo Betcke , Nader Saffari

In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering…

Numerical Analysis · Mathematics 2012-10-12 Oscar P. Bruno , Victor Dominguez , Francisco-Javier Sayas

In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…

Numerical Analysis · Mathematics 2025-10-20 Tristan Goodwill , Leslie Greengard , Jeremy Hoskins , Manas Rachh , Yuguan Wang

In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a…

Mathematical Physics · Physics 2020-06-23 Juan Carlos Araujo Cabarcas , Christian Engström

We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized…

Numerical Analysis · Mathematics 2020-11-06 José Pinto , Rubén Aylwin , Carlos Jerez-Hanckes

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…

High Energy Physics - Theory · Physics 2009-10-06 M. G. Garcia , A. S. de Castro

A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…

Mathematical Physics · Physics 2016-06-21 Subhasis Panda , S. Pratik Khastgir

We construct new spin singular integral equations for solving scattering problems for Maxwell's equations, both against perfect conductors and in media with piecewise constant permittivity, permeability and conductivity, improving and…

Analysis of PDEs · Mathematics 2018-03-20 Andreas Rosén

This paper introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects based on the time-domain PMCHWT equation. To address dense-mesh breakdown, a multiplicative Calderon…

Systems and Control · Electrical Eng. & Systems 2025-10-10 Van Chien Le , Cedric Munger , Francesco P. Andriulli , Kristof Cools

The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative…

Computational Physics · Physics 2014-01-03 Sebastian Acosta , Vianey Villamizar , Bruce Malone

Existence and uniqueness of the scattering solutions is proved for a class of bounded rough obstacles which is much larger than the class of Lipschitz obstacles. Integral equations method is not used. The approach is based on the…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm , M. Sammartino