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We present Helmholtz or Helmholtz like equations for the approximation of the time-harmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models…

Analysis of PDEs · Mathematics 2019-05-22 Kersten Schmidt , Anastasia Thöns-Zueva

We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use…

Analysis of PDEs · Mathematics 2017-03-29 Georgi Vodev

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in…

Analysis of PDEs · Mathematics 2014-08-08 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella

This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space.The method constructs the interior Dirichlet-to-Neumann (DtN) map…

Numerical Analysis · Mathematics 2013-08-29 Adrianna Gillman , Alex Barnett , Per-Gunnar Martinsson

Suppose that a plane wave is incident onto an impenetrable grating profile of Dirichlet or Impedance type or a penetrable grating. The grating interface is assumed to be given by a Lipschitz function in two dimensions. We derive stability…

Analysis of PDEs · Mathematics 2023-04-11 Linlin Zhu , Guanghui Hu

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

Analysis of PDEs · Mathematics 2020-09-23 Anna Kirpichnikova , Jussi Korpela , Matti Lassas , Lauri Oksanen

The left-right operator splitting method is studied for the efficient calculation of acoustic fields scattered by arbitrary rough surfaces. Here the governing boundary integral is written as a sum of left- and right-going components, and…

Computational Physics · Physics 2017-08-25 Orsola Rath Spivack , Mark Spivack

This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations. We consider Galerkin and collocation…

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

The elastic neutron-${}^3\mathrm{H}$ scattering at intermediate energies is studied using rigorous integral equations solved in the momentum-space partial-wave basis. The four-particle transition operators are expanded into…

Nuclear Theory · Physics 2025-02-24 A. Deltuva

Scalar wave scattering by many small particles with impedance boundary condition and creating material with a desired refraction coefficient are studied. The acoustic wave scattering problem is solved asymptotically and numerically under…

Numerical Analysis · Mathematics 2017-10-17 Nhan Tran

We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant…

Numerical Analysis · Mathematics 2018-05-01 Heiko Gimperlein , Zouhair Nezhi , Ernst P. Stephan

The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two…

Exactly Solvable and Integrable Systems · Physics 2015-05-18 E Bogomolny , S Mashkevich , S Ouvry

Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…

Optics · Physics 2020-09-16 Masud Mansuripur

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

We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution…

Numerical Analysis · Mathematics 2016-09-21 Yuxiang Liu , Alex H. Barnett

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

In this article, high frequency stability estimates for the determination of the potential in the Schr\"odinger equation are studied when the boundary measurements are made on slightly more than half the boundary. The estimates reflect the…

Analysis of PDEs · Mathematics 2021-10-19 Anupam Pal Choudhury , Venkateswaran P. Krishnan

We present a method based on the scattering $\mathbb{T}$ operator, and conservation of net real and reactive power, to provide physical bounds on any electromagnetic design objective that can be framed as a net radiative emission,…

Optics · Physics 2020-08-12 Sean Molesky , Pengning Chao , Weiliang Jin , Alejandro W. Rodriguez

Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modeled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal…

Numerical Analysis · Mathematics 2022-07-05 Mame Gor Ngom , Ibrahima Faye , Diaraf Seck

Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…

Optics · Physics 2018-01-24 Andrey E. Miroshnichenko , Michael I. Tribelsky