Low frequency plane eddy currents in conductors with various cross-sections — A hybrid analytical-numerical boundary integral equation approach

Various solutions to plane low frequency eddy current problems can be found in the literature, nearly all of which employ numerical methods like finite element or finite difference methods, and solve the problem on a mesh by evaluating the equations governing fields or potentials at discrete observation points. Yet, for the kind of problem under investigation in this paper, there is an approach which involves numerical approximations only for calculating the integrals involved (in those cases that can not be treated analytically) and for solving the resulting system of linear equations. This hybrid analytical-numerical approach combines a BIE formulation and a separation of the differential equation of an appropriate vector potential and can be useful to evaluate quality, residuals and covergence of numerical solutions. Since the in-depth discussion of the single terms in the formulation is beyond the scope of a conference paper, we will focus on the governing equations, the kernel functions of the BIE and on appropriate series representations expressions that faciliate the calculation.