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Spectral theory and iterative methods for the Maxwell system in nonsmooth domains

✍ Scribed by Irina Mitrea; Katharine Ott

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 250 KB
Volume: 283
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200910226

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✦ Synopsis

Abstract

We study spectral properties of boundary integral operators which naturally arise in the study of the Maxwell system of equations in a Lipschitz domain Ω ⊆ ℝ^3^. By employing Rellich‐type identities we show that the spectrum of the magnetic dipole boundary integral operator (composed with an appropriate projection) acting on L^2^(∂Ω) lies in the exterior of a hyperbola whose shape depends only on the Lipschitz constant of Ω. These spectral theory results are then used to construct generalized Neumann series solutions for boundary value problems associated with the Maxwell system and to study their rates of convergence (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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