An Edge-Based Smoothed Finite Element Method for Magnetic Field Analysis in Permanent Magnet Motors

This article presents an edge-based smoothed finite element method (ES-FEM) aiming to enhance the accuracy of magnetic field simulations in permanent magnet motors (PMMs). ES-FEM constructs cross-mesh smooth domains while retaining the traditional finite element mesh. The global stiffness matrix is assembled based on the gradient fields associated with these smooth domains, providing an appropriate stiffness for obtaining more precise results. Utilizing the ES-FEM, this article formulates a smoothed Galerkin weak form for the magnetic field of permanent magnets. Numerical examples, employing a Halbach array, have been carried out. The results indicate that the ES-FEM demonstrates superior accuracy and cost-effectiveness compared to the traditional finite element method (FEM) with low-order triangular and quadrilateral elements. Moreover, the ES-FEM exhibits better tolerance to mesh distortion, thereby improving its utility in simulations of motor magnetic fields.