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Spectral theory and iterative methods for the Maxwell system in nonsmooth domains |
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| Authors: | Irina Mitrea Katharine Ott |
| Institution: | 1. Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester MA 01609‐2280, USA;2. Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506‐0027, USA;3. Phone: +1 859 257 6815, Fax: +1 859 257 4078 |
| 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 ? ?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 L2(?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) |
| Keywords: | Maxwell system magnetic dipole operator spectrum generalized Neumann series Faber polynomials |