Computing Eddy Currents in Thin Shells of Arbitrary Topology by Mesh Analysis

A novel 3-D integral formulation for solving eddy currents in thin conducting structures with complex topology is presented. As in discrete approaches field problem variables are cochains, dual to chains defined on a pair of interlocked cell complexes. So the discretized problem can be cast in a circuit-like manner. The proposed method is formulated in terms of mesh currents on a triangulated surface in order to reduce computing requirements compared to edge element formulations. The basic idea is to use homology generators of the triangulated surface to compute the additional cochains needed by mesh analysis.