Comparison of Time Integration Methods in Magnetomechanical Problems

This paper makes a survey of several popular time integration methods, including the backward Euler, central difference, Crank-Nicolson, Newmark, weighted residual finite element, and time-discontinuous Galerkin methods, and comparisons are made by applying some of the methods to the vibration analysis of a stator-housing structure as well as to the transient response analysis of an electromagnet. The comparison of vibration analysis shows that with an acceptably small step-size, the Newmark method gives result as accurate as the Euler method does, with half the cost. In the transient analysis of the electromagnet, however, it was observed that applying the Euler method to the magnetic equation performs much better compared with the Crank-Nicolson method even though the theoretical accuracy of the latter is higher.