Boundary integral equation analysis on the sphere

Felipe Vico, Leslie Greengard, Zydrunas Gimbutas

Research output: Contribution to journalArticle

Abstract

We present a systematic analysis of the integral operators of potential theory that arise when solving the Helmholtz or Maxwell equations in the exterior (or interior) of a sphere in the frequency domain. After obtaining expressions for the signatures of layer potentials in the spherical harmonic or vector spherical harmonic basis, we turn to a consideration of various integral equations that have been proposed in the literature for problems of acoustic and electromagnetic scattering. The selection of certain parameters in “combined field” and “Calderon-preconditioned” formulations is shown to have a significant impact on condition number, extending earlier work by Kress and others.

Original languageEnglish (US)
Pages (from-to)463-487
Number of pages25
JournalNumerische Mathematik
Volume128
Issue number3
DOIs
StatePublished - Oct 15 2014

Keywords

  • 31B10
  • 35Q60
  • 35Q61
  • 45B05
  • 65R20
  • 78A45
  • 78M05

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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