In order to model thin conductive non-magnetic shells, an original surface integral formulation is proposed. The method is based on a surface impedance condition which takes into account the field variation through depth due to skin effect. It is general and enables the modeling of various problems whatever their skin depth and avoiding the meshing of the air region. The formulation is compared with another integral formulation recently proposed by authors and is validated thanks to an axisymmetric finite-element method (FEM). Advantages and drawbacks of this new formulation are discussed.

In order to reduce the computation time of a quasi-static problem solved by the finite element method, methods of model order reduction can be applied. In this context, two approaches, the proper orthogonal decomposition and the proper generalized decomposition, are applied to the vector poten-tial formulation used to solve the quasi-static problem. The developed methods are compared on an academic example.

This paper calculates the electric and magnetic fields and the Poynting vector around two infinitely long parallel cylindrical conductors, carrying a DC current. Also the charges on the surface of the wire are calculated, and their distribution is visualized. The wire is assumed to be perfectly electrically conducting. Furthermore, the Hall effect is ignored. In the literature [S.J. Orfanidis, Electromagnetic waves and antennas, 2008], the problem of determining the electric field is usually tackled using an equivalent model consisting of two line charge densities, producing the same electric field. In this work, the Laplace equation is rigorously solved. The authors found no work explaining the solution of the Laplace equation with boundary conditions for this problem and hence thought it was useful to dedicate a paper to this topic. The method of separation of variables is employed and a bipolar coordinate system is used. After solving the appropriate Sturm-Liouville problems, the scalar potential is obtained. Taking the gradient yields the electric field.

A subproblem h-conformal eddy current finite element method is proposed for correcting the inaccuracies inherent to thin shell models. Such models replace volume thin regions by surfaces but neglect border effects in the vicinity of their edges and corners. The developed surface-to-volume correction problem is defined as a step of the multiple subproblems that can split a complete problem, consisting of inductors and magnetic or conducting regions, some of these being thin regions. The general case of multiply connected thin regions is considered.

This paper presents 2D and 3D homogenization techniques for laminated iron cores in the frequency domain. In 2D, two approaches (analytical and numerical) are compared in terms of complex reluctivity considering tangential magnetic field to laminations. The analytical approach is generalized to 3D problems. The validation performed on homogenized block gives satisfactory results only in case of closed-core or thin air gap open-core. Thus, we have a correct approximation only when the magnetic field is essentially parallel to laminations. In order to remediate the poor approximation of losses due to non parallel magnetic field component and model large air gap devices, we propose an alternative to block homogenization. A validation is done on a laminated open-core inductance.