The application of the finite element method to the calculation of non
linear periodic eddy current problems is discussed. Special attention
is paid to the case when specific conditions on the current or voltage
of several conductors have to be fulfilled. An efficient iterative pr
ocedure has been developed to satisfy these conditions in 2D problems
solved by a single component magnetic vector potential with the nonlin
earity taken into account. The total current condition can be fulfille
d in 3D with a noniterative scheme, but voltage conditions still requi
re a multistep approach. Additionally, a possibility of accelerating t
he time stepping algorithm in reaching steady state is presented for a
3D eddy current problem involving a single conductor.