Fast Time-Domain Finite Element Analysis of 3-D Nonlinear Time-Periodic Eddy Current Problems With ${\rm T},\Phi-\Phi$ Formulation

A method is presented for obtaining the steady-state solution of three-dimensional eddy current problems with nonlinear material properties and periodic excitations using the T, Φ-Φ formulation. The problem is formulated in the time-domain and the application of a fixed-point approach combined with a discrete Fourier-transformation technique ensures that, during one nonlinear iteration step, there is no coupling between the time-steps within one period. The steady-state result is hence obtained by solving half as many time steps as their number in one period. Since the time steps are decoupled, their computation can be readily parallelized resulting in a fast method. Comparison with results obtained by a transient time-stepping technique is presented.