Integral equations for the current density in thin conductors and their solution by the finite-element method

The current density and magnetic field distributions in thin conductors are important for several applications, and they can be computed by solving integral equations. This paper describes the implementation of a one-dimensional (1D) integral equation in a finite-element model. This numerical method does not require the use of ad hoc assumptions to avoid logarithmic divergences of the current density at the conductor's edges and, by using a coupling with 2D electromagnetic models, it can be used to solve cases of increasing complexity. With respect to commonly used 2D models, it overcomes the typical problems linked to the mesh of conductors with high aspect ratio, such as the use of large memory and long computing times.