Modified nonlinear algorithm for solving time stepping finite element system equations

In order to reduce numerical error of nonlinear iterations and noisy spikes of the derivative quantities the backward Euler's method was used to solve the time stepping finite element system equations, and a modified algorithm which can reduce the numerical error of the discrete variables and the noisy spikes of the derivative quantities was presented. According to the deformed matrix format of the time stepping finite element system equations of the transient process for electromagnetic devices, the new coefficient matrix of the system equations and the recurrence formulation of the nonlinear iterations were derived, and the calculation formula of the nonlinear iteration error was also deduced. The proposed method is applied to simulate an induction motor. Computed results of the back emf and eddy-current loss obtained by the traditional method and the proposed method are compared and reported. All the results show that the new method can successfully remove the spikes in the calculated waveforms.