Spectral Element-Based Multi-Physical Modeling Framework for Axisymmetric Wireless Power Transfer Systems

This paper concerns a multi-physical modeling framework based on the spectral element method (SEM) for axisymmetric wireless power transfer systems. The modeling framework consists of an electromagnetic and a thermal model. The electromagnetic model allows for eddy currents in source- and non-source regions to be included in the analysis. The SEM is a numerical method, which is particularly advantageous in 2D problems for which the skin-depth is several orders of magnitude smaller compared to the object dimensions and complex geometrical shapes are absent. The SEM applies high-order trial functions to obtain the approximate solution to a boundary-value problem. To that end, the approximation is expressed as an interpolation at a set of nodal points, i.e., the nodal representation. The trial functions are Legendre polynomials, which reduces the complexity of the formulation. Furthermore, numerical integration is performed through Gaussian quadratures. In order to verify the SEM, a benchmark system is modeled using both the SEM and a finite element-based commercial software. The differences in the SEM solutions, i.e., magnetic vector potential and temperature distribution, and the discrepancies in essential post-processing quantities are assessed with respect to the finite element solutions. Additionally, the computational efforts of both methods are evaluated in terms of the sparsity, number of degrees of freedom, and non-zero elements.