A Boundary Integral Method for Computing Eddy Currents in Thin Conductors of Arbitrary Topology

We present an effective technique to solve eddy current problems in thin conductors of arbitrary topology by a boundary element method based on a stream function. By considering a mesh of the thin conductor, which we assume to be a surface (i.e., an orientable combinatorial two-manifold embedded in $\mathbb {R}^{3}$ ), the aim of this paper is to introduce a novel technique to render the stream function single valued when the thin conductor is not topologically trivial. In particular, a novel combinatorial algorithm to compute the appropriate cohomology generators in linear time worst case complexity is introduced, providing an effective and rigorous solution for the required topological preprocessing.