Finite-element network models and their application to eddy-current problems

The finite-element method is less easily applied to eddy-current than to other field problems, because the dissipation of energy affects the variational formulation. Of the various ways of overcoming the difficulty, the simplest is to separate the geometric from the physical properties of the magnetic-field region by forming a network model of the linked current and flux paths. This illustrates the geometric relationships and, in particular, the linkages, associated with the lst-order finite-element analysis. The network is common to wave-propagation problems in which the electric and magnetic quantities are coupled, and its components can either store or dissipate energy. The network model of eddy-current problems differs from the conventional finite-difference equivalent in that the magnetic components have negative conductances in parallel with them. In a test calculation, these produce a substantial improvement in accuracy. They can be added to the finite-difference network.