An Adaptive Fixed-Point Iteration Algorithm for Finite-Element Analysis With Magnetic Hysteresis Materials

Abstract

In this paper, an adaptive fixed-point iteration algorithm for 2-D/3-D finite-element analysis with hysteresis is proposed. The iteration starts with the $B$ -correction scheme. If the solution is not converged to a given accuracy after a certain number of iterations, the iteration will be continued by switching to the $H$ -correction scheme. Based on the combined use of the two correction schemes during the whole iteration process, the solution with the minimum error together with the scheme type is recorded and will be used as the final solution at the current time step. At the same time, the recorded scheme type will be used as the initial scheme type for the next time step. The numerical validation shows that the proposed algorithm not only has very fast convergence rate, but is also very stable.