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

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, 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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/1615
Identification Number/DOI	10.1216/JIE-2009-21-2-229
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Rocky Mountain Mathematics Consortium
Download/View statistics	View download statistics for this item