Combining the treatment of the field nonlinearity by using the polarization fixed point technique with the application of the superposition allows a matrix formulation relating the magnetic induction to the coil fluxes and to the polarizations in the actual nonlinear media. Since the linear medium used in the adopted model has the same permeability at each iteration, the matrices involved are computed only once, before the start of the iterative procedure. The method is illustrated for two-dimensional fields. In the case of a periodic regime produced by coils with sinusoidal voltages, each harmonic of the magnetic field can be analyzed independently. It is shown that the proposed method is convergent.

Keywords: Computational electromagnetics, Integral equations, Iterative algorithms, Nonlinear magnetics