Hybrid Discretization Based on Finite Elements and Harmonic Functions for the Simulation of Technical Models Exhibiting Partial Symmetry

Many technical devices such as transformers, electrical machines and particle accelerator magnets feature large differences in geometric dimensions. In that case, the construction of a 3D mesh for the overall geometry may fail or may give rise to unacceptably large numbers of elements. Even though a structure does not feature an overall symmetry, the symmetries of certain parts can be exploited by appropriate 2D models. The field distribution along the boundaries of those submodels does not remain symmetric but if it is expected to be smooth, the asymmetry of the fields is well approximated by a set of orthogonal functions along the third dimension. For the discretization of the remaining model parts standard finite elements (FEs) are used. By applying the proposed hybrid discretization, the number of unknowns in the numerical model is reduced significantly while maintaining a high accuracy