Fast and stable non-linear converging method

In this paper, a non-linear converging method in the finite element analysis for magnetic field problems is proposed. Two types of materials with different saturation characteristics are considered. One has a gradual saturation characteristic called gradual saturaion, the other has a quick saturaion characteristic called quick saturation. A simple model, in which the value of magnetic flux density B for the applied magnetic field H can be evaluated analytically, is used for the numerical calculation. It is known that for materials with gradual saturation, the Newton-Raphson method is efficient for non-linear converging. For the materials with quick saturation there are some examples in which it does not work well. Conditions for the Newton-Raphson method to be applicable are studied both theoretically and numerically. A new, fast and stable iterative method with some sort of relaxation is proposed. Using some numerical examples, it is shown that the fast and stable convergence in the numerical analysis for material with gradual saturation and that with quick saturation is obtained.