On the numerical solution of the direct scattering problem for an open sound-hard arc
type: Item
instance of: scholarly article
title: On the numerical solution of the direct scattering problem for an open sound-hard arc
zbMATH Open document ID: 0854.65106
DOI: 10.1016/0377-0427(95)00230-8
author: Lars Mönch
published in: Journal of Computational and Applied Mathematics
publication date: 1997-01-22T00:00:00Z
review text: A boundary integral equation approach is used to solve the (Neumann) boundary value problem for the Helmholtz equation in \(\mathbb{R}^2 \setminus \Gamma\) modelling the scattering phenomena for time-harmonic acoustic waves by a sound-hard open arc \(\Gamma\). (Such problems arise also in the analysis of cracks.) Using the so-called cosine substitution the integral equation is found to be essentially the same as that for a closed boundary, considered e.g. by \textit{R. Kress} [J. Comput. Appl. Math. 61, No. 3, 345-360 (1995; Zbl 0839.65119)]. Hence, the integral equation is solved approximately by a quadrature formula method, and error estimates in Hölder norms are found by standard techniques, cf. \textit{S. G. Michlin, S. Prößdorf} [Singuläre Integraloperatoren, Akademie-Verlag Berlin (1980; Zbl 0442.47027)]. A numerical example (bowl-shaped open arc) shows exponential convergence.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76M15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 910321
zbMATH Keywords: Neumann boundary value problem
zbMATH Keywords: boundary integral equation
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: scattering
zbMATH Keywords: time-harmonic acoustic waves
zbMATH Keywords: cosine substitution
zbMATH Keywords: quadrature formula method
zbMATH Keywords: error estimates
zbMATH Keywords: numerical example
zbMATH Keywords: exponential convergence
reviewed by: E. Lanckau
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00230-8
OpenAlex ID: W2077697588
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description: scientific article; zbMATH DE number 910321