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Related papers: A Galerkin BEM for high-frequency scattering probl…

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We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…

Numerical Analysis · Mathematics 2016-03-01 D. C. Antonopoulos , V. A. Dougalis

We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft…

Numerical Analysis · Mathematics 2023-06-21 Jürgen Dölz , Helmut Harbrecht , Michael Multerer

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…

Computational Engineering, Finance, and Science · Computer Science 2024-12-13 Benjamin Marussig , Thomas Rüberg , Jürgen Zechner , Lars Kielhorn , Thomas-Peter Fries

Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application of the boundary element method (BEM) where each BEM basis…

Numerical Analysis · Mathematics 2024-04-23 António M. Caetano , Simon N. Chandler-Wilde , Andrew Gibbs , David P. Hewett , Andrea Moiola

We propose a time stepping scheme for the space-time systems obtained from Galerkin time-domain boundary element methods for the wave equation. Based on extrapolation, the method proves stable, becomes exact for increasing degrees of…

Numerical Analysis · Mathematics 2020-03-06 Heiko Gimperlein , David Stark

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…

Numerical Analysis · Mathematics 2022-01-14 Anton Arnold , Sjoerd Geevers , Ilaria Perugia , Dmitry Ponomarev

This paper presents a boundary element method (BEM) for computing the energy transmittance of a singly-periodic grating in 2D for a wide frequency band, which is of engineering interest in various fields with possible applications to…

Numerical Analysis · Mathematics 2023-05-16 Yuta Honshuku , Hiroshi Isakari

Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…

Analysis of PDEs · Mathematics 2018-12-03 Peijun Li , Lei Zhang

The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…

Numerical Analysis · Mathematics 2025-03-25 Bin Han , Michelle Michelle

We propose and analyse a hybrid numerical-asymptotic $hp$ boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation…

Numerical Analysis · Mathematics 2014-08-12 David P. Hewett , Stephen Langdon , Simon N. Chandler-Wilde

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the…

Numerical Analysis · Mathematics 2019-02-25 Jeffrey Galkowski , Eike H. Müller , Euan A. Spence

We propose a boundary element method for problems of time-harmonic acoustic scattering by multiple obstacles in two dimensions, at least one of which is a convex polygon. By combining a Hybrid Numerical Asymptotic (HNA) approximation space…

Numerical Analysis · Mathematics 2020-02-27 Andrew Gibbs , Simon Chandler-Wilde , Stephen Langdon , Andrea Moiola

A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…

Numerical Analysis · Mathematics 2026-05-22 Benedikt Gräßle , Stefan A. Sauter

Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…

Numerical Analysis · Mathematics 2015-09-09 Eric T. Chung , Wing Tat Leung

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 propose and analyze a fully discrete method for a direct boundary integral formulation of the scattering of a transient acoustic wave by a sound-soft obstacle. The method uses Galerkin-BEM in the space variables and three…

Numerical Analysis · Mathematics 2013-01-03 Lehel Banjai , Antonio Laliena , Francisco-Javier Sayas

We present a Fourier--Galerkin framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we project the operator onto…

Numerical Analysis · Mathematics 2026-05-25 Jinghao Cao

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

Numerical Analysis · Mathematics 2026-05-08 Siyu Cen , Bangti Jin , Yavar Kian , Zhi Zhou

Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…

Numerical Analysis · Mathematics 2024-07-29 Martin Eigel , Nando Hegemann

We propose and analyse a numerical method for time-harmonic acoustic scattering in $\mathbb{R}^n$, $n=2,3$, by a class of inhomogeneities (penetrable scatterers) with fractal boundary. Our method is based on a Galerkin discretisation of the…

Numerical Analysis · Mathematics 2026-02-06 Joshua Bannister , David P. Hewett , Andrew Gibbs