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

S N Chandler-Wilde, I G Graham, S Langdon, M Lindner

Research output: Contribution to journalArticle

44 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)229-279
Number of pages51
JournalJournal of Integral Equations and Applications
Volume21
Issue number2
DOIs
Publication statusPublished - Jul 2009

Fingerprint Dive into the research topics of 'Condition number estimates for combined potential boundary integral operators in acoustic scattering'. Together they form a unique fingerprint.

  • Projects

  • Cite this