English
Related papers

Related papers: Well-posedness for the biharmonic scattering probl…

200 papers

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

A perturbation approach is used for analysis of a near-cloak in shielding a finite scatterer from an incident flexural wave. The effect of the boundary conditions on the interior surface of the cloaking layer is analysed in detail, based on…

Classical Physics · Physics 2015-01-28 I. S. Jones , M. Brun , N. V. Movchan , A. B. Movchan

We consider time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens embedded in $\mathbb{R}^n$ for $n = 2$ or $3$. In contrast to previous studies in which the screen is assumed to be a bounded…

Analysis of PDEs · Mathematics 2017-09-28 Simon N. Chandler-Wilde , David P. Hewett

We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to…

Quantum Physics · Physics 2009-11-13 Gursoy B. Akguc , Thomas H. Seligman

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…

Computational Physics · Physics 2018-08-01 Johan Helsing , Anders Karlsson

We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a…

Analysis of PDEs · Mathematics 2025-07-21 Narek Hovsepyan , Michael S. Vogelius

The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with…

Computational Physics · Physics 2019-12-04 Juan D. González , Edmundo F. Lavia , Silvia Blanc

The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new…

Analysis of PDEs · Mathematics 2015-05-30 Habib Ammari , Hyeonbae Kang , Hyundae Lee , Mikyoung Lim

Motivated by the study and simulation of long, coiled optical fibers we consider in this article a simplified model that is prevalent in the engineering community. Mathematically, the problem is specified as follows: Time-harmonic wave…

Analysis of PDEs · Mathematics 2026-03-17 Leszek Demkowicz , Martin Halla , Jens Markus Melenk

The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh…

Analysis of PDEs · Mathematics 2024-02-20 Guanghui Hu , Andreas Kirsch

We study the inverse problem of qualitatively recovering a supported cavity in a thin elastic plate governed by the flexural (biharmonic) wave equation, using far-field pattern measurements. We derive a reciprocity principle and a…

Numerical Analysis · Mathematics 2026-03-24 Carlos Borges , Rafael Ceja Ayala , Peter Nekrasov

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather…

Fluid Dynamics · Physics 2020-11-03 M. J. A. Smith , M. A. Peter , I. D. Abrahams , M. H. Meylan

We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…

Numerical Analysis · Mathematics 2015-07-14 Kui Du

We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…

Analysis of PDEs · Mathematics 2021-02-19 Zhengjian Bai , Huaian Diao , Hongyu Liu , Qingle Meng

Consider the interaction of biharmonic waves with a periodic array of cavities, characterized by the Kirchhoff--Love model. This paper investigates the perfectly matched layer (PML) formulation and its numerical soution to the governing…

Numerical Analysis · Mathematics 2024-04-23 Peijun Li , Xiaokai Yuan

We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve. The scattering problem is equivalently reformulated as an initial-boundary value problem of…

Numerical Analysis · Mathematics 2023-01-18 Hongxia Guo , Guanghui Hu

We formulate a problem that can be viewed as a natural variation of the so-called Pompeiu or Schiffer problem in the context of scattering of plane waves for the Linear Helmholtz equation. For the two dimensional version of this variation,…

Analysis of PDEs · Mathematics 2025-09-25 Narek Hovsepyan , Michael S. Vogelius

We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…

Analysis of PDEs · Mathematics 2017-01-10 Agnes Lamacz , Ben Schweizer