h- and a-Formulations for the Time-Domain Modelling of Thin Electromagnetic Shells

Thin conductive magnetic shells are accounted for by means of two different time-domain magnetodynamic finite-element formulations, namely the magnetic field formulation and the magnetic vector potential formulation. Both approaches are an extension of the classical linear frequency-domain thin-shell approximation. The interface conditions for the magnetic field formulation and the vector potential formulation are expressed in terms of the average current density and the average flux density, respectively, together with a number of higher-order components of these quantities. The proposed time-domain thin-shell approaches are validated by means of a 3D magnetodynamic problem. The results are shown to agree well with those obtained with a fine model, whereas the computation time is significantly reduced.