Solution of plane transient eddy current problems by analytical treatment of the time-dependency

Our paper describes different alternatives for the solution of the plane transient eddy current problem of a system of conductors. By separation of time the problem is transformed into an eigenvalue problem which we solve with the help of volume and boundary integral equations or by a hybrid method which combines the separation of differential equations inside the conductors with boundary integral formulations for their exterior. As an important result it is shown that the eigenfunctions form an orthogonal set throughout the cross-sections of all conductors of the system, even if the permeability varies from conductor to conductor. Numerical results for a strip-line demonstrate the usefulness of our approach.