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

Publikationstyp
Journal Article
Date Issued
2009-12-01
Sprache
English
Author(s)
Chandler-Wilde, Simon N.  
Graham, Ivan G.  
Langdon, Stephen  
Lindner, Marko  orcid-logo
TORE-URI
http://hdl.handle.net/11420/10570
Journal
Journal of integral equations and applications  
Volume
21
Issue
2
Start Page
229
End Page
279
Citation
Journal of Integral Equations and Applications 21 (2): 229-279 (2009-12-01)
Publisher DOI
10.1216/JIE-2009-21-2-229
Scopus ID
2-s2.0-75449087930
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. © 2009 Rocky Mountain Mathematics Consortium.
DDC Class
510: Mathematik