Graphics Processing Unit Simulation of Magnetic Domains Under Alternating Field Excitation Including Iron Enhancement

Abstract

Predicting the magnetization of ferromagnetic materials in the presence of dc and ac background fields generated by current-carrying windings is a frequent requirement for important engineering applications in electrical machines and electromagnet design. Existing finite element techniques for the estimation of these effects are based on time-consuming, nonlinear iterative solvers. A novel mesh-free technique is proposed to overcome the issues related to coupled domain discretization, which also requires meshing the background media (air domain) of the control volume. In the proposed approach, the ferromagnetic domain is filled with small spherical subvolumes representing the complete magnetic domain. These spherical subvolumes are magnetized by the background magnetic field and their interaction with each other results in the cumulative field enhancing the ferromagnetic effect on the ferromagnetic element. Such an approach to modeling ferromagnetism presents a simple engineering solution that is on par, if not better, than conventional finite element methods. Although these methods do not model boundary effects between microscopic Weiss domains, the proposed method approximates this to a more reasonable extent than conventional finite element methods. Using this approach, the effect of each magnetic sphere can be concurrently calculated on general-purpose graphics processing units (GPUs), reducing computation time compared to by commercial finite element solvers while achieving comparable accuracy in the solution. With more powerful, state-of-the-art GPUs, the proposed mesh-free approach could be used to model complex domains and perform design space exploration of geometric constraints considered impractical with finite element methods. The proposed method is validated by comparing its performance against results obtained using a commercially available finite-element solver for a common iron geometry. This approach constitutes an approximate surrogate model for the fast optimization of complex systems, which would be relatively slow to implement with finite element methods.