A 3-D integral equation method for electromagnetic field analysis in anisotropic materials

In this paper a method for non linear three dimensional eddy currents and magnetodynamic analysis handling of anisotropic non-linear and hysteretic materials is presented. Taking into account the Coulomb gauge, and expressing the magnetic vector potential as a function of conduction currents and magnetizations, a nonlinear system in the magnetization unknowns and a differential set of equations in the conduction current unknowns are obtained. The nonlinear system is derived imposing the constitutive equation H(B) inside the ferromagnetic materials allowing the presence of anisotropic non-linear and hysteretic relations. The differential system is derived integrating Ohm's law inside the conductive materials. Considering an hysteretic model characterized by an internal state, like the Preisach one, we know the 'actual' branch in the magnetization loop, and we can schematize hysteresis as a monotonic non-linear time varying phenomenon, to which Newton-like methods can be applied. Numerical simulations comparing anisotropic non-linear reversible and hysteretic cases have shown the model capability to handle 3-D anisotropic and hysteretic constitutive curves, and its numerical robustness.