The Time-Harmonic Eddy-Current Problem in General Domains: Solvability via Scalar Potentials
The eddy-current problem for the time-harmonic Maxwell equations in domains of general topology is solved by introducing a scalar “potential” for the magnetic field in the insulator part of the domain. Indeed, since in general the insulator Ω I is multiply-connected, the magnetic field differs from the gradient of a potential by a harmonic field. We rewrite the problem in a two-domain formulation, in term of a scalar magnetic potential and a harmonic field in Ω I . Then the finite element numerical approximation based on this two-domain formulation is presented, using edge elements in the conductor and nodal elements in the insulator, and an optimal error estimate is proved. An iteration-by-sub domain procedure for the solution of the problem is also proposed.
KeywordsGeneral Domain Duality Pairing Mixed Finite Element Finite Element Space Optimal Error Estimate
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