Dual simple-layer source formulation for two-dimensional eddy current and skin effect problems

Abstract

The integrodifferential expression resulting from a reformulation of the time-harmonic diffusion equation to accommodate skin effect problems is further transformed, via an approximate average potential A0, to allow solution using a boundary integral technique. Conducting and nonconducting regions are initially separated into subregions. On each subregion boundary a simple-layer distribution of sources is prescribed resulting in a first kind Fredholm integral equation. Dual simple-layer sources are therefore distributed on subregion interfaces. The 2n equations derived from enforcing continuity of normal B̄ and tangential H̄, using point collocation, are added to the current conservation equation for direct solution of the 2n+1 unknowns. This method allows subregion solutions to be decoupled once the sources are determined since the fields in any subregion are adequately prescribed by the corresponding source layer. Curved interfaces are modeled accurately by fourth-order boundary elements. Numerical results, including vector potential distributions and loss ratio and inductance variation with frequency, for a single conductor of circular cross section modeled by four quartic elements are compared with the exact solution. The extension of this technique to noncontacting multiconductor geometries is discussed. It is shown that asymmetric block-sparse matrices are generated for problems made up of more than two subregions.