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First order finite element or finite difference approximations to the electric and magnetic scalar potential Poisson equations are represented by network models. The resulting linked-circuit problem is solved using nodal variables for the larger, magnetic part of the problem and mesh variables for the smaller, conducting region. This method of solution is shown to compare favourably, in terms of number of variables, with conventional finite element techniques. A surface impedance model is also presented for the solution of saturated eddy-current problems. This model uses actual iron B/H curves rather than the approximations usually employed. Both calculation methods are verified using experimental results.