A Modal Approach for the Solution of the Non-Linear Induction Problem in Ferromagnetic Media

The non-linear induction problem in ferromagnetic media is solved using the fixed-point iteration method, where the linearized problem at each iteration is treated by means of a modal approach. The proposed approach does not require meshing of the solution domain, which results in fast computations compared with the conventional mesh-based numerical techniques. Both harmonic and pulse excitations are considered via Fourier and Laplace transforms, respectively. An efficient method for the fast computation of the inverse Laplace transform of the magnetic polarization signals is also devised based on the generalized pencil-of-function method. Although being restricted to 1-D configurations, this paper provides the tools for the treatment of 2-D and 3-D problems, whose study is under way.