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Mathematics of Computation

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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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Article copyright: © Copyright 1984 American Mathematical Society

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