Modification and Numerical Method for the Jiles-Atherton Hysteresis Model (Communications in Computational Physics, 2018)
The Jiles-Atherton (J-A) model is a commonly used physics-based modelin describing the hysteresis characteristics of ferromagnetic materials. However, citationsand interpretation of this model in literature have been non-uniform. Solutionmethods for solving numerically this model has not been studied adequately. In thispaper, through analyzing the mathematical properties of equations and the physicalmechanism of energy conservation, we point out some unreasonable descriptions ofthis model and develop a relatively more accurate, modified J-A model together withits numerical solution method. Our method employs a fixed point method to computeanhysteretic magnetization. We obtain the susceptibility value of the anhystereticmagnetization analytically and apply the 4th order Runge-Kutta method to the solutionof total magnetization. Computational errors are estimated and then precisionsof the solving method in describing various materials are verified. At last, throughanalyzing the effects of the accelerating method, iterative error and step size on thecomputational errors, we optimize the numerical method to achieve the effects of highprecision and short computing time. From analysis, we determine the range of bestvalues of some key parameters for fast and accurate computation.