General formulation for the Newton-Raphson method and the fixed-point method in finite-element programs

This paper proposes a general formulation for implementing the fixed-point method (FPM) and the Newton-Raphson method (NRM) in finite-element (FE) analysis of nonlinear magnetic problems. As the NRM and FPM have advantages and disadvantages, the aim is to make both of the methods available in FE programs and use them in a convenient manner. It is shown in the paper that the FPM can be implemented using the same formulation of the NRM that is commonly applied in FE programs. The idea is simple and straightforward, and can be applied to a wide variety of magnetic problems. As an example, the proposed scheme is applied here to a magnetic field problem formulated by the magnetic vector potential where numerical results for two types of electrical machines are carried out using two-dimensional FE simulations.