Theoretical study of transient nonlinear magnetic field simulation by a complex frequency domain finite element method with Laplace transform

A complex frequency domain finite element (FE) method is proposed to simulate transient nonlinear magnetic fields. In this method, the transient exciting signal is converted into the complex frequency domain by the Laplace transform and discretized by limited numbers of the considered harmonic orders. With the implementation of the fixed-point technique and the secant method, the algorithm is applicable for the computation of nonlinear magnetization. Besides, it is found that the value of the damping factor of the Laplace transform is sensitive to the convergence and the accuracy of this complex frequency domain method. Thus, a numerical technique optimally determining the damping factor is proposed and verified by comparing it to other strategies for setting the damping factor. As a validation, the simulation results of the proposed method are compared to the results of the time-stepping FE method and the harmonic balance (HB) FE method with Fourier transform using an eddy current model under the transient nonlinear magnetization. The results show that the proposed complex frequency domain method can accurately simulate the transient nonlinear magnetic field with a speed-up ratio of up to 4 to the time-stepping method in certain cases.