Harmonic Balance Method and Convergence of the 2-D Nonlinear Eddy Current Problem

A nonlinear model and the simulation method of the periodic magnetic field in a homogeneous conductive ferromagnetic medium is presented. The method is based on the simultaneous use of the harmonic balance method and the finite element method. The case of a magnetic field excitation by an alternating current source is considered. To solve the obtained system of the nonlinear equations the modified Newton's method was adopted. To accelerate the convergence of the iteration process the special optimization algorithm of a damping factor was used. The convergence of the algorithm is compared with COMSOL simulation. The convergence of harmonic balance finite element method is illustrated by samples with 3 odd harmonics. The resulting magnetic flux density of the presented approaches is compared too.