Comparison of the Finite Element Method and High-Order Isogeometric Analysis for Modeling Magnetic Vector Hysteresis

This work presents a generic dynamically scaling memory layout, applicable to model a large amount of anisotropic vector hysteresis models in a structured manner, while aiming for efficiency. Contrary to other works, concerned with coupling vector hysteresis to finite element analysis, where limited implementation insight is provided, this work provides extensive details on this procedure. The library Nutils was used as the finite element analysis framework, which supports a wide variety of bases, including the low-order finite element method, and high-order isogeometric analysis. These low and high order bases were applied in conjunction with an anisotropic vector hysteresis model to simulate the magnetic behavior of a T-joint of NO27-1450H steel, including iron loss, while recording the required solving time. The isogeometric analysis was able to outperform the finite element method on superior convergence and better loss modeling, except for a very low number of degrees of freedom, where the 2nd order finite element method was superior, albeit with limited accuracy. Hence, isogeometric analysis can be exploited to model magnetic vector hysteresis effectively, as its higher-order approximation ensures accurate solutions for a reduced computational burden, and it yields satisfactory results with less required simulation time versus the finite element method.