  We consider the scattering of time periodic electro-magnetic fields by
metallic obstacles, the eddy current problem. In this interface problem
different sets of Maxwell equations must be solved in the obstacle and outside,
while the tangential components of both electric and magnetic fields are
continuous across the interface. We describe an asymptotic procedure, which
applies for large conductivity and reflects the skin effect in metals. The key
to our method is to introduce a special integral equation procedure for the
exterior boundary value problem corresponding to perfect conductors. The
asymptotic procedure leads to a great reduction in complexity for the numerical
solution since it involves solving only the exterior boundary value problem.
Furthermore we introduce a new fem/bem coupling procedure for the transmission
problem and consider the implementation of the Galerkin elements for the
perfect conductor problem and present numerical experiments.
