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Condition number estimates for combined potential boundary integral operators in acoustic scattering

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Chandler-Wilde, S. N., Graham, I. G., Langdon, S. and Lindner, M. (2009) Condition number estimates for combined potential boundary integral operators in acoustic scattering. Journal of Integral Equations and Applications, 21 (2). pp. 229-279. ISSN 0897-3962

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To link to this article DOI: 10.1216/JIE-2009-21-2-229

Abstract/Summary

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:1615
Publisher:Rocky Mountain Mathematics Consortium

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