Boundary integral equation analysis on the sphere

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...

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Bibliographic Details
Published inNumerische Mathematik Vol. 128; no. 3; pp. 463 - 487
Main Authors Vico, Felipe, Greengard, Leslie, Gimbutas, Zydrunas
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
78M05
78A45
65R20
45B05
31B10
35Q61
35Q60
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Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-014-0619-z