Thin Layers in Electrical Engineering. Example of Shell models in Analysing Eddy-Currents by Boundary and Finite Element Methods

Summary from only given, as follows. During last years, several numerical formulations have been developed by us to modelize physical problems like: conducting film effects over the surface of insulators (pollution) [1], high frequency eddy-currents [2], earth field effects on the hull of a ship [3]. The physical effects being at stake are completely different, but in each of these examples, they originate from a region thin in regard with the other geometrical dimensions. An efficient numerical approach consists on using a surfacic representation with special boundary conditions expressing the solution inside the thin region. We propose in that paper a didactical approach to thin regions in electromanetics and, as an example, the boundary conditions and surfacic equation for eddy currents flowing inside a thin ferromagnetic shell. The numerical tests are done using the BEM software PH13D, but the results could easily be transposed in a FEM context. The practical applications may concern the computation of losses (shield of electrical machines or transformers) or low frequency electromagnetic perturbations (screen effects, EMC) as well as special domains like optimization of the induction heating of pans (french art culinaire).