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 hys teretic materials is presented. Taking into account the Coulomb gauge, and expressing the magnetic vector potential as a function of conduct ion currents and magnetizations, a nonlinear system in the magnetizati on unknowns and a differential set of equations in the conduction curr ent unknowns are obtained. The nonlinear system is derived imposing th e constitutive equation H(B) inside the ferromagnetic materials allowi ng the presence of anisotropic non-linear and hysteretic relations. Th e differential system is derived integrating Ohm's law inside the cond uctive 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 monotoni c non-linear time varying phenomenon, to which Newton-like methods can be applied. Numerical simulations comparing anisotropic non-linear re versible and hysteretic cases have shown the model capability to handl e 3-D anisotropic and hysteretic constitutive curves, and its numerica l robustness.