—In this work, numerical analysis of nonlinear ferromagnetic problems is presented using the three-dimensional time-domain-nite element method (TDFEM). Formulated with the second- order nonlinear partial differential 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 differential equation (ODE) representing the magnetic hysteresis accurately and effciently, several ODE solvers are specically designed and investigated. To improve the computational effciency 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.
ASJC Scopus subject areas
- Condensed Matter Physics
- Electrical and Electronic Engineering