Numerical solution of eddy current problems in bounded domains using realistic boundary conditions

Abstract The aim of this paper is to analyze a finite element method to solve the low-frequency harmonic Maxwell equations in a bounded domain containing conductors and dielectrics, and using realistic boundary conditions in that they can be easily measured. These equations provide a model for the so-called eddy currents. The problem is formulated in terms of the magnetic field. This formulation is discretized by using Nedelec edge finite elements on a tetrahedral mesh. Error estimates are easily obtained when the curl-free condition is imposed explicitly on the elements in the dielectric domain. A multivalued magnetic scalar potential is introduced then to impose this curl-free condition. The discrete counterpart of this formulation leads to an important saving in computational effort. Problems related to the topology are also considered, more precisely, the possibility of having a non-simply connected dielectric domain is taken into account. Finally, the method is applied to solve two three-dimensional model problems: a test with a known analytical solution and the computation of the electromagnetic field in a metallurgical arc furnace.

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