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The paper presents and compares three potential formulations to solve nonlinear static magnetic field problems by applying the fixed point technique and the Newton-Raphson scheme. Nonlinear characteristics are handled by the polarization method in both algorithms. The proposed combination of the Newton-Raphson scheme and the polarization formulation results in a very effective nonlinear solver, because only the derivate of the characteristics, i.e., only the permeability or the reluctivity has to be used. Therefore, this method can be used to solve nonlinear problems with hysteresis, and it is faster than the classical fixed point method.