Use of transmission-line modelling method in FEM for solution of nonlinear eddy-current problems

Classical numerical algorithms such as Runge-Kutta and trapezoidal methods are the most generally accepted techniques for the FEM solution of the nonlinear eddy-current problem in the time domain. To account for the nonlinearity, a new linear system is solved at each time step, which is not favourable with regard to the computation costs. The authors deal with a new solution method which is based on the transmission-line modelling (TLM) technique used for electric circuit analysis. The underlying idea is the analogy that exists between a finite element matrix and the node-admittance matrix of an equivalent network. An iterative scheme emerges in which the nonlinearity appears as a source term on the right-hand side of the linear system so that the stiffness matrix remains unchanged at all iterations. In that manner, substantial reduction in computation time is obtained. As an example, a nonlinear eddy-current problem is treated, and a comparison with the classical Crank-Nicholson technique shows the efficiency of the method