Abstract
This paper studies numerical methods for time-harmonic eddy current problems in the case of homogeneous, isotropic, and linear materials. It provides a survey of approaches that entirely rely on boundary integral equations and their conforming Galerkin discretization. Starting point are both E- and H-based strong formulation, for which issues of gauging and topological constraints on the existence of potentials are discussed.
Direct boundary integral equations and the so-called symmetric coupling of the integral equations corresponding to the conductor and the non-conducting regions are employed. They give rise to coupled variational problems that are elliptic in suitable trace spaces. This implies quasi-optimal convergence of conforming Galerkin boundary element methods, which make use of divΓ-conforming trial spaces for surface currents.
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Hiptmair, R. (2007). Boundary Element Methods for Eddy Current Computation. In: Schanz, M., Steinbach, O. (eds) Boundary Element Analysis. Lecture Notes in Applied and Computational Mechanics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47533-0_9
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DOI: https://doi.org/10.1007/978-3-540-47533-0_9
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