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This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…

Analysis of PDEs · Mathematics 2019-04-30 Frank Osterbrink , Dirk Pauly

Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially-varying density - a limitation that restricts applications in biomedical…

Computational Physics · Physics 2025-07-23 Antonio Stanziola , Simon R. Arridge , Bradley E. Treeby , Benjamin T. Cox

In this work, we develop a novel hybrid Schwarz method, termed as edge multiscale space based hybrid Schwarz (EMs-HS), for solving the Helmholtz problem with large wavenumbers. The problem is discretized using $H^1$-conforming nodal finite…

Numerical Analysis · Mathematics 2024-08-16 Shubin Fu , Shihua Gong , Guanglian Li , Yueqi Wang

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be…

Mathematical Physics · Physics 2025-03-28 Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes

In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media…

Numerical Analysis · Mathematics 2020-12-02 Bo Wang , Wen Zhong Zhang , Wei Cai

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…

Numerical Analysis · Mathematics 2018-05-15 Lise-Marie Imbert-Gerard , Felipe Vico , Leslie Greengard , Miguel Ferrando

We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…

Instrumentation and Methods for Astrophysics · Physics 2014-10-20 Keigo Nitadori

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

The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…

Mathematical Physics · Physics 2019-10-23 P. Zhevandrov , A. Merzon , M. I. Romero Rodríguez , J. E. de la Paz Méndez

Wave propagation and scattering problems in acoustics are often solved with boundary element methods. They lead to a discretization matrix that is typically dense and large: its size and condition number grow with increasing frequency. Yet,…

Numerical Analysis · Mathematics 2018-01-16 Daan Huybrechs , Peter Opsomer

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

Analysis of PDEs · Mathematics 2017-09-07 Peijun Li , Xiaokai Yuan

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…

Numerical Analysis · Mathematics 2022-08-15 Yassine Boubendir , Fatih Ecevit

In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…

Analysis of PDEs · Mathematics 2016-06-08 Drossos Gintides , Leonidas Mindrinos

Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their…

Mesoscale and Nanoscale Physics · Physics 2023-07-26 Wojciech Śmigaj , Krzysztof Sobucki , Paweł Gruszecki , Maciej Krawczyk

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…

Plasma Physics · Physics 2024-02-27 Nils W. Schween , Brian Reville

Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for…

Mathematical Physics · Physics 2011-02-07 Jean-Marc Conoir , Andrew N. Norris

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

A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…

Atomic Physics · Physics 2023-08-23 V. A. Gradusov , S. L. Yakovlev

We present an efficient matrix-free geometric multigrid method for the elastic Helmholtz equation, and a suitable discretization. Many discretization methods had been considered in the literature for the Helmholtz equations, as well as many…

Numerical Analysis · Mathematics 2023-12-05 Rachel Yovel , Eran Treister

This paper presents a boundary element formulation for the solution of the Mild-Slope equation in wave propagation problems with variable water depth in one direction. Based on the Green's function approximation proposed by Belibassakis…

Numerical Analysis · Mathematics 2025-02-04 Antonio Cerrato , José A. González , Luis Rodríguez-Temblequer