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


Reference:

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.

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Official URL:

http://dx.doi.org/10.1216/JIE-2009-21-2-229

Abstract

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/Panič, 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.

Details

Item Type Articles
CreatorsChandler-Wilde, S. N., Graham, I. G., Langdon, S. and Lindner, M.
DOI10.1216/JIE-2009-21-2-229
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code17374

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