A Nonlinear Effective Surface Impedance in a Magnetic Scalar Potential Formulation

The aim is to avoid expensive computations of eddy currents in large nonlinear problems where the characteristic size is large compared to the penetration depth of the electromagnetic fields. To this end a methodology is presented, where a nonlinear effective surface impedance is exploited. The effective surface impedance is determined by solving a suitable cell problem maintaining the apparent power for the case of time-harmonic eddy current problems. With this effective surface impedance an equivalent static magnetic field problem can be solved efficiently using a magnetic scalar potential in finite element models. The method with the effective material is cheap and accurate compared to the basic eddy current problem as shown by numerical simulations.