Finite Formulation of Surface Impedance Boundary Condition

In several electromagnetic applications field quantities are confined in layers which are thin with respect to other geometrical dimensions. The numerical solution of these phenomena has led to the development of special formulations. Among these, the surface impedance boundary conditions has been extensively developed in the past decades, often coupling it to other techniques for the analysis of volumes like finite elements or boundary elements method. In this paper a finite formulation of the surface impedance boundary condition is presented and its application to the analysis of induction heating problems is proposed. The novelty of the paper lies in the definition of the operative quantities present in the formulation and in its development toward an iterative technique which takes into account magnetic nonlinearity.