Memory efficient harmonic method for electromagnetic models using scattering matrices

In design and optimization of electrical machines, accurate models of the electromagnetic fields are important to predict the performance of the machine. The finite element method (FEM) is often used, because of its ability to produce accurate results when it is correctly utilized. However, the method can be demanding in terms of memory and relatively slow in terms of computation time. Therefore, semi-analytical models have been proposed over the years for increasingly complex structures in both 2D and 3D. One of the semi-analytical models is the harmonic modeling technique [1], [2], [3], which uses a Fourier bases to describe the solutions to electromagnetic field quantities. In many electromagnetic configurations, accurate results are obtained using a relatively low number of harmonics. However, for more complex structures, the number of harmonics has to be increased to retain accuracy. This leads to a proportional increase in the required memory. As a result, especially in 3D models, the advantage in terms of memory of the harmonic model in comparison to FEM is reducing. In this paper an alternative solving method for 3D harmonic models with position dependent material properties is presented. Using the scattering matrix approach, the memory required to obtain the solutions of the model is significantly reduced