Convergence Analysis of SEM and FEM to an analytical field distribution in the airgap.

The optimisation routines and the validation models for the Electrical Machines(EM) are often based on Finite Element Method (FEM) models. However, their computation time is manifestly high, and are often replaced by semi-analytical models, which approximate the essential performance of EM with reduced computational cost. Therefore, the trade-off between the model accuracy and the size of the problem leads to the appropriate choice of the modelling technique [1]. Recently, Spectral Element Method (SEM) which uses higher order mesh elements compared to FEM, has been implemented for EM [2]. The latter benefits from higher convergence rate, resulting in a smaller size of the problem. Therefore, SEM is considered a potential option for building low-cost EM models. However, complex EM geometries are challenging for any technique, limiting their accuracy by the high aspect ratio and shapes with sharp corners. Consequently, the performance analysis must be thoroughly checked before making the choice. In this paper, the performance analysis of both SEM and FEM is discussed. An analytical solution for the magnetic field is used for the reference which is generated by the Harmonic Model (HM) [3] using a finite number of harmonics.