  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 comparing to
conventional mesh-based numerical techniques. Both harmonic and pulse
excitations are considered via Fourier and Laplace transform, 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 (GPOF) method. Although being restricted to one dimensional
configurations, the present work provide the tools for the treatment of two and
three dimensional problems, whose study is under way.
