Coupled finite element-spectral element discretization for models with circular inclusions and far field domains

In many technical models, large parts are source-free and consist of a homogeneous material. An analytical solution is found as linear combination of harmonic functions. In this paper, a finite set of harmonic functions is selected as basis in a spectral element method. Other model parts, suffering from complicated geometries, ferromagnetic saturation, hysteresis and eddy current effects, are discretized by finite elements. In this paper, the properties of spectral element, finite element coupled systems of equations are studied and specialized solution algorithms are developed. Although generally applicable, for simplicity, the methods are explained using a 2D magnetostatic example.