The Harmonic-Balanced Finite Element Method with Laplace Transform for Transient State Nonlinear Problems

A harmonic-balanced finite element method (FEM) with the Laplace transform is proposed for transient state nonlinear problems. Different from the conventional harmonic-balanced method applying the Fourier transform, the implementation of the Laplace transform can make sure the simulation is accurate and more efficient for the convergence of transient state nonlinear problems. The strategies of taking the damping factor of the Laplace transform and the fixed-point reluctivity are investigated for the algorithm. To validate the method on problems with saturated magnetization, the simulation results are compared to the results of the conventional harmonic-balanced FEM with the Fourier transform in a 3D eddy current model under different exciting sources.