Incompatibility of Finite Element Method Relations With Electromagnetic Continuity Conditions and Its Impact on Energy Conversion Calculations

Finite element method (FEM) is widely used in the modeling of electromagnetic systems and as a reliable method to verify analytical modeling of electromagnetic devices in design step. As the method is based on discretization of domains, the electromagnetic continuity conditions at the boundaries of elements should be confirmed. Electromagnetic continuity conditions in FEM modeling were investigated in this article. It was shown that the continuity of tangential component of magnetic field intensity is not guaranteed at the boundaries of elements. The inability of FEM to establish the continuity condition leads to some virtual surface current densities at the boundaries of adjacent elements which does not exist in reality. The existence of virtual surface currents is proved in an example. Then, with the help of a complicated example, it is shown that large number of elements and, consequently, the large number of boundaries between elements may cause great errors in FEM postprocess results, especially in calculating magnetic stored energy and electromagnetic forces acting on moving parts. It has been shown that it is very important to take into account the impact of these virtual current densities in energy conversion analysis by FEM.