UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Boundary element methods for acoustic scattering by fractal screens

Chandler-Wilde, SN; Hewett, DP; Moiola, A; Besson, J; (2021) Boundary element methods for acoustic scattering by fractal screens. Numerische Mathematik 10.1007/s00211-021-01182-y. (In press). Green open access

[thumbnail of Hewett_Boundary element methods for acoustic scattering by fractal screens_AOP.pdf]
Preview
Text
Hewett_Boundary element methods for acoustic scattering by fractal screens_AOP.pdf - Published Version

Download (4MB) | Preview

Abstract

We study boundary element methods for time-harmonic scattering in R^{n} (n= 2 , 3) by a fractal planar screen, assumed to be a non-empty bounded subset Γ of the hyperplane Γ ∞= R^{n-1} x {0}. We consider two distinct cases: (i) Γ is a relatively open subset of Γ ∞ with fractal boundary (e.g. the interior of the Koch snowflake in the case n= 3); (ii) Γ is a compact fractal subset of Γ ∞ with empty interior (e.g. the Sierpinski triangle in the case n= 3). In both cases our numerical simulation strategy involves approximating the fractal screen Γ by a sequence of smoother “prefractal” screens, for which we compute the scattered field using boundary element methods that discretise the associated first kind boundary integral equations. We prove sufficient conditions on the mesh sizes guaranteeing convergence to the limiting fractal solution, using the framework of Mosco convergence. We also provide numerical examples illustrating our theoretical results.

Type: Article
Title: Boundary element methods for acoustic scattering by fractal screens
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-021-01182-y
Publisher version: https://doi.org/10.1007/s00211-021-01182-y
Language: English
Additional information: © 2021 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
Keywords: 28A80 Fractals, 65R20 Numerical methods for integral equations, 65N38 Boundary element methods for boundary value problems involving PDEs, 78A45 Diffraction scattering, 78M15 Boundary element methods applied to problems in optics and electromagnetic theory
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10124089
Downloads since deposit
25Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item