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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

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected each other through homogeneous linear…

Materials Science · Physics 2017-04-05 Andrea Bacigalupo , Luigi Gambarotta

The structure of an optical waveguide determines the characteristics of its guided modes, such as their spatial profile and group index. General features are shared by modes regardless of the waveguiding structure; for example, modal…

Optics · Physics 2021-11-05 Abbas Shiri , Ayman F. Abouraddy

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…

Analysis of PDEs · Mathematics 2024-03-14 Ibtissem Ben Aïcha , Guanghui Hu , Suliang Si

Modal expansions are useful to understand wave propagation in an infinite electromagnetic transmission line or waveguide. They can also be used to construct generalized Dirichlet-to-Neumann maps that can be used to provide artificial…

Analysis of PDEs · Mathematics 2023-02-24 Martin Halla , Peter Monk

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

We propose a novel on-surface radiation condition to approximate the outgoing solution to the Helmholtz equation in the exterior of several impenetrable convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann operator…

Computational Physics · Physics 2021-02-01 Sebastian Acosta

We are interested in the Helmholtz equation in a junction of two periodic half-spaces. When the overall medium is periodic in the direction of the interface, Fliss and Joly (2019) proposed a method which consists in applying a partial…

Analysis of PDEs · Mathematics 2025-05-07 Pierre Amenoagbadji , Sonia Fliss , Patrick Joly

A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a…

Numerical Analysis · Mathematics 2021-03-03 Daniel Appelo , Fortino Garcia , Olof Runborg

We study time-harmonic scattering by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength…

Analysis of PDEs · Mathematics 2025-10-15 Yuxin Du , Xin Fu , Wenjia Jing

The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…

Analysis of PDEs · Mathematics 2015-12-24 Andrey V. Shanin , Andrey I. Korolkov

We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO$_{3}$ waveguides with…

In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…

Analysis of PDEs · Mathematics 2023-10-13 Wafa Ahmedi , Akram Ben Aissa

Propagation of high amplitude acoustic pulses is studied in a 1D waveguide connected to a lattice of Helmholtz resonators. An homogenized model has been proposed by Sugimoto (J. Fluid. Mech., \textbf{244} (1992)), taking into account both…

Classical Physics · Physics 2017-04-06 Jean-François Mercier , Bruno Lombard

We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter $\a>0$. The high-frequency (or: semi-classical) parameter is $\eps>0$. We let $\eps$ and $\a$ go to zero simultaneously. We assume…

Analysis of PDEs · Mathematics 2007-05-23 François Castella

At a horizontally homogeneous isothermal atmosphere approximation, we derive an ordinary six-order differential equation describing linear disturbances with consideration for heat conductivity and viscosity of medium. The wave problem may…

Atmospheric and Oceanic Physics · Physics 2013-07-30 G. V. Rudenko

This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…

Analysis of PDEs · Mathematics 2020-11-25 Peijun Li , Jian Zhai , Yue Zhao

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

Analysis of PDEs · Mathematics 2022-02-09 Victor Isakov , Shuai Lu , Boxi Xu

In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height $H$. The perforations are…

Analysis of PDEs · Mathematics 2023-02-24 Delfina Gómez , Sergei A. Nazarov , Rafael Orive-Illera , Maria-Eugenia Pérez-Martínez

The time derivative of the charge density is linked to the current density by the continuity equation. However, it features only the longitudinal part of a current density, which is known to produce no radiation. This fact usually remains…

Optics · Physics 2022-01-21 Nikita Nemkov , Vassili Fedotov