The transmission line modeling (TLM) method as a new iterative technique in nonlinear 2-D magnetostatics

Nonlinear magnetostatic analysis generally involves an iterative approach such as direct iteration, the Newton-Raphson method, or a combination of both. However, those techniques always require the solution of a new linear system at each iteration that is CPU time consuming. Some acceleration can be carried out in order to partially overcome this drawback, but this may lead to a loss of convergence. In this paper, it is shown that the 2-D nonlinear magnetostatic problem may be solved by using the transmission-line modeling (TLM) method that is usually exploited for the solution of electrical networks. The fundamental mechanism of this method is the modeling of the nonlinearity as fictitious sources so that the stiffness matrix of the problem remains unchanged at all iterations. Substantial reduction in execution time is obtained with excellent convergence properties. Numerical results are presented, and a comparison to the classical Newton-Raphson algorithm points out the efficiency of our method