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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Spectral properties for the magnetization integral operator


Authors: Mark J. Friedman and Joseph E. Pasciak
Journal: Math. Comp. 43 (1984), 447-453
MSC: Primary 78A30; Secondary 47G05
MathSciNet review: 758193
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Abstract: We analyze the spectrum of a certain singular integral operator on the space $ {({L^2}(\Omega ))^3}$ where $ \Omega $ is contained in three dimensional Euclidean space and has a Lipschitz continuous boundary. This operator arises in the integral formulation of the magnetostatic field problem. We decompose $ {({L^2}(\Omega ))^3}$ into invariant subspaces: in one where the operator is the zero map; in one, the identity map; and in one where the operator is positive definite and bounded. These results give rise to the formulation of new efficient numerical techniques for approximating nonlinear magnetostatic field problems [5], [6], [12].


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DOI: http://dx.doi.org/10.1090/S0025-5718-1984-0758193-1
PII: S 0025-5718(1984)0758193-1
Article copyright: © Copyright 1984 American Mathematical Society