Direct BIE formulation for skin and proximity effect calculation with and without the use of the surface impedance approximation

The authors illustrate a new, direct BIE (boundary integral equation) formulation for skin and proximity effect calculations. The main advantage of the present formulation is that it is a logical extension of the well-known TM (transverse magnetic) induction formulation. The authors introduce the impedance boundary condition (IBC) approximation of the skin and proximity effect problems in terms of the conventional Fredholm boundary integral equations. Unlike previous formulations, the IBC approximation can be used with the external electric field equation, so the skin and proximity effect problem is formulated as an exterior problem. The method has been applied to test problems; reliable results were obtained both with and without the use of the IBC approximation