Spectral properties for the magnetization integral operator
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- by Mark J. Friedman and Joseph E. Pasciak PDF
- Math. Comp. 43 (1984), 447-453 Request permission
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].References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 43 (1984), 447-453
- MSC: Primary 78A30; Secondary 47G05
- DOI: https://doi.org/10.1090/S0025-5718-1984-0758193-1
- MathSciNet review: 758193