Quasi-3-D Finite-Element Method for Cylindrically Symmetric Models With Small Eccentricities

A model with a cylindrically symmetric geometry and excitation is commonly simulated by a 2-D axisymmetric finite-element (FE) solver. When one part of the geometry is, however, not aligned with the remaining parts, the resulting magnetic field is no longer cylindrically symmetric and 3-D FE simulation seems unavoidable. Here, a more efficient quasi-3-D FE solver is constructed by selecting dedicated shape functions and by applying elementary toroidal coordinates in a tilted air region between different parts.