Multi-Scale Finite Element Method Applied in 3D Nonlinear Problem

Numerical calculation of electromagnetic fields plays an important role in the design of electrical equipment. However, due to the special structure of certain equipment, traditional numerical calculation methods often meet great difficulties when dealing with such problems. For example, in the design process of the transformer core, it is difficult to calculate the electromagnetic field around the core due to the nonlinearity of the material, the huge size difference between the silicon steel sheet and the core, and the complexity of the air gap distribution. Taking the widely used commercial numerical calculation software as an example, the finite element method is used in the numerical calculation process, and many elements and nodes are used in the process. This will lead to a complex mesh and cost a lot of computing resources and a long computing time. This paper improves on the widely used conventional finite element method (CFEM) and proposes a multi-scale finite element method (MSFEM). Using a special interpolation built with an enrichment function, the elements are not restricted by media or geometry. Taking Team Workshop problem 10 as a numerical example, the accuracy of this method and the saving of computational costs have been proved.