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In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…

Plasma Physics · Physics 2023-01-20 Vladimir V. Gorin

This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…

Numerical Analysis · Mathematics 2025-11-07 Riley Fisher , Fruzsina Agocs , Adrianna Gillman

We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…

Numerical Analysis · Mathematics 2015-06-23 Min Hyung Cho , Alex H. Barnett

We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate…

Numerical Analysis · Mathematics 2011-01-25 Anil Zenginoglu

It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resolved by any grid-based method. In this paper, we intend to…

Numerical Analysis · Mathematics 2024-01-30 Jiangxing Wang , Lilian Wang , Bo Wang

We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding to "existence and uniqueness of…

General Relativity and Quantum Cosmology · Physics 2018-06-28 Mihalis Dafermos , Igor Rodnianski , Yakov Shlapentokh-Rothman

This paper investigates the scattering of biharmonic waves by a one-dimensional periodic array of cavities embedded in an infinite elastic thin plate. The transparent boundary conditions are introduced to formulate the problem from an…

Analysis of PDEs · Mathematics 2023-11-21 Gang Bao , Peijun Li , Xiaokai Yuan

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, 1) A multiple scattering strategy that decomposes a…

Numerical Analysis · Mathematics 2023-02-07 Oscar P. Bruno , Tao Yin

In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…

Numerical Analysis · Mathematics 2025-11-17 Maryna Kachanovska , Adrian Savchuk

In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…

Analysis of PDEs · Mathematics 2021-02-23 Junxiong Jia , Shigang Yu , Jigen Peng , Jinghuai Gao

This paper develops a finite-difference analogue of the boundary integral/element method for the numerical solution of two-dimensional exterior scattering from scatterers of arbitrary shapes. The discrete fundamental solution, known as the…

Numerical Analysis · Mathematics 2025-11-19 Siyuan Wang , Qing Xia

A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a…

Numerical Analysis · Mathematics 2017-09-29 Lehel Banjai , Alexander Rieder

We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.

Analysis of PDEs · Mathematics 2024-03-26 Pu-Zhao Kow , Mikko Salo , Henrik Shahgholian

We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…

Analysis of PDEs · Mathematics 2021-03-01 Roland Griesmaier , Bastian Harrach

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

Numerical Analysis · Mathematics 2020-05-29 Lehel Banjai , Christian Lubich , Joerg Nick

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

This article introduces a novel "bootstrap domain-of-dependence" concept, according to which, for all time following a given illumination period of arbitrary duration, the wave field scattered by an obstacle is encoded in the history of…

Analysis of PDEs · Mathematics 2022-11-28 Thomas G. Anderson , Oscar P. Bruno

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this…

Optics · Physics 2018-05-23 Chris King , Simon Horsley , Thomas Philbin

Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…

Numerical Analysis · Mathematics 2021-10-26 Christiaan C. Stolk

We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…

Classical Physics · Physics 2015-06-16 Stephen C Creagh , Hanya Ben Hamdin , Gregor Tanner