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In this work, numerical analysis of nonlinear ferromagnetic problems is presented using the three-dimensional time-domain flnite element method (TDFEM). Formulated with the second- order nonlinear partial difierential equation (PDE) combined with the inverse Jiles-Atherton (J-A) vector hysteresis model, the nonlinear problems are solved in the time domain with the Newton- Raphson method. To solve the ordinary difierential equation (ODE) representing the magnetic hysteresis accurately and e-ciently, several ODE solvers are speciflcally designed and investigated. To improve the computational e-ciency of the Newton-Raphson method, the multi-dimensional secant methods, aka Broyden's methods, are incorporated in the nonlinear TDFEM solver. A nonuniform time-stepping scheme is also developed using the weighted residual approach to remove the requirement of a uniform time-step size during the simulation. The capability and the performance of the proposed methods are demonstrated by various numerical examples.

NUMERICAL STUDY OF A TIME-DOMAIN FINITE ELEMENT METHOD FOR NONLINEAR MAGNETIC PROBLEMS IN THREE DIMENSIONS (Invited Paper)