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

For many technical devices large model parts are free of sources and consist of homogeneous, nonconductive materials. For these parts, spectral element techniques based on truncated Fourier series, are applied. Other model parts suffer from complicated geometries, ferromagnetic saturation, hysteresis and eddy-current effects and are discretised by the finite-element method. A hybrid finite-element, spectral-element formulation is developed for circular homogeneous inclusions and infinite domains. The hybrid formulation yields smaller models compared with conventional finite-element models. The system of equations, however, contains dense blocks which adversely affect the simulation time. Small solution times are retained by applying specialised iterative solution techniques based on matrix-free techniques and fast Fourier transforms.