Electrical steel sheets are crucial magnetic materials that constitute the magnetic circuit structure of power equipment, such as transformers. Their hysteresis and magnetostrictive properties have a profound impact on the loss and vibration performance of devices like transformers and motors. In addition, in order to develop iron core materials with lower costs and a better match between magnetic characteristics and the performance requirements of devices, magnetic powder cores have been attracting increasing attention. At the same time, as the complexity of the models and the nonlinearity of materials increase, improving the computational efficiency of electromagnetic fields becomes of great significance. In the presentation, the domain wall movement of electrical steel sheets is observed and modeled. The magnetic characteristics within a certain temperature range and under external stress are measured and estimated. Additionally, a microstructural model of magnetic powder cores is constructed based on the simulation data of the powder densification process. The effect of the regulation degree of inter-particle metallic insulation on the eddy current loss is studied. Finally, to reflect the physical characteristics of in-service electrical equipment in real-time through simulation, an adaptive model order reduction algorithm for three-dimensional nonlinear magnetic fields and a GPU-based parallel computation method are proposed.