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Symmetric coupling for eddy current problems. (English) Zbl 1010.78011

Summary: A novel symmetric finite element method-boundary element method-coupling for the \(\mathbf{E}\)-based eddy current model is derived in a rigorous fashion. To that end, the properties of potentials and boundary integral operators arising from a Stratton-Chu-type representation formula for the electric field in the nonconducting region are thoroughly analyzed in a Hilbert-space setting. It yields a variational problem with symmetric bilinear form that is coercive in the natural function spaces. Unknowns are the electric field inside the conductor and the equivalent surface current related to the magnetic field. Existence and uniqueness of solutions and the convergence of a conforming finite element/boundary element Galerkin discretization immediately follows. In particular, schemes based on curl-conforming edge elements and divergence-conforming surface elements are examined, and some aspects of implementation are discussed.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35C15 Integral representations of solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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