On the use of the impedance boundary conditions in eddy current problems

The paper examines the use of the Impedance Boundary Condition (IBC) for the reduction of the field problem encountered in the computation of eddy currents in non-magnetic and magnetic conductors with small penetration depths to a simpler exterior problem. A brief review of the various IBC's for linear and nonlinear problems and their limits is presented. The formulations of the original field problem and the approximate IBC problem in terms of boundary integral equations are developed for two dimensional and three dimensional linear problems. These formulations are used to analyze the eddy currents in conducting magnetic cylinders with circular or rectangular crosssection when subjected to transverse-magnetic time-harmonic fields. The results are used to identify the conditions under which the IBC formulation gives acceptable results. The computational requirements of the two formulations are compared. Problems associated with edges are discussed.