Solution of transient hysteretic magnetic field problems with hybrid Newton-polarization methods

This paper presents two hybrid Newton-polarization methods for transient magnetoquasistatic field simulation, including hysteretic ferromagnetic materials, in conjunction with the finite integration implicit time-domain formulation. The hybrid techniques are based on the combination of the polarization method and the Newton method. The first hybrid technique uses the magnetic polarization obtained from the polarization method instead of the modified reluctivity for hysteretic material in the Newton method at each iteration. The second hybrid technique combines the solutions from the overrelaxed polarization method and the underrelaxed Newton method at each iteration. The purpose of the two hybrid algorithms is to increase the robustness of the nonlinear iteration, without loosing the quadratic speed of convergence in the vicinity of the solution.