Numerical problems in 3D FEM simulation Of harmonic magnetic fields

This paper deals with some numerical instabilities that could occur in the 3D time harmonic magnetic field FEM analysis. Because the electric conductivity σ of the air is 0 the ratio between the skin depths in the air and in the non ferromagnetic or ferromagnetic materials has a high value that affects the accuracy of the results. In order to attenuate this problem an artificial value of the electric conductivity σ of the air will be assigned. The evaluation of the artificial value was performed in two cases: with the gauge condition on and off. This approach was applied to the computation of the effectiveness of a spherical shield, made of steel and copper.