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We prove that in contrast to the free wave equation in $\R^3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming…

Mathematical Physics · Physics 2010-11-18 Ferruccio Colombini , Vesselin Petkov , Jeffrey Rauch

We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis,…

Mathematical Physics · Physics 2008-06-04 D. L. Foulis

This paper introduces a new Windowed Green Function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in presence of dielectric or conducting half-planes. The WGF method, which…

Computational Physics · Physics 2015-08-05 Oscar Bruno , Mark Lyon , Carlos Perez-Arancibia , Catalin Turc

A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…

Numerical Analysis · Mathematics 2015-07-23 Jun Lai , Leslie Greengard , Michael O'Neil

Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…

Computational Engineering, Finance, and Science · Computer Science 2014-10-14 Nicolás Guarín-Zapata , Juan Gómez , Juan Jaramillo

In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…

Numerical Analysis · Mathematics 2025-01-03 Travis Askham , Jeremy G. Hoskins , Peter Nekrasov , Manas Rachh

In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…

Mathematical Physics · Physics 2007-05-23 T. Dolinszky

This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…

Numerical Analysis · Mathematics 2023-07-12 Maximilian Harmel , Roger Andrew Sauer

Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…

Numerical Analysis · Mathematics 2023-09-08 Edward Caunt , Rhodri Nelson , Fabio Luporini , Gerard Gorman

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…

Numerical Analysis · Mathematics 2022-04-01 Carlos Jerez-Hanckes , Ignacio Labarca

We consider a model case for a strictly convex domain of dimension $d\geq 2$ with smooth boundary and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay…

Analysis of PDEs · Mathematics 2021-08-23 Oana Ivanovici , Gilles Lebeau , Fabrice Planchon

This paper presents a theoretical discussion as well as novel solution algorithms for problems of scattering on smooth two-dimensional domains under Zaremba boundary conditions for which Dirichlet and Neumann conditions are specified on…

Analysis of PDEs · Mathematics 2015-08-17 Eldar Akhmetgaliyev , Oscar Bruno

We develop a framework for the multiple scattering of a polarized wave. We consider particles with spin propagating in a medium filled with scatterers. We write the amplitudes of each spin eigenstate in a local, mobile frame. One of the…

Other Condensed Matter · Physics 2010-07-20 Vincent Rossetto

We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…

Numerical Analysis · Mathematics 2025-01-14 Alireza Daneshyar , Stefan Kollmannsberger

We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…

Numerical Analysis · Mathematics 2018-04-23 George C. Hsiao , Tonatiuh Sanchez-Vizuet , Francisco--Javier Sayas

Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…

General Relativity and Quantum Cosmology · Physics 2015-06-04 Olivier Sarbach , Manuel Tiglio

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

Numerical Analysis · Mathematics 2022-10-26 Siyang Wang , Gunilla Kreiss

Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution…

Numerical Analysis · Mathematics 2025-10-20 David De Wit

In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower…

Mathematical Physics · Physics 2023-11-28 Hisashi Morioka , Naotaka Shoji

The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…

Numerical Analysis · Mathematics 2021-04-28 Yanli Chen , Xue Jiang , Jun Lai , Peijun Li