Solving nonlinear magnetic problems using Newton trust region methods

In this paper, a Newton trust region method is presented as an alternative to the Newton-Raphson method for solving nonlinear magnetic problems. Instead of underrelaxing the Newton step in a line search algorithm, the step is determined by minimizing a local quadratic model of the functional within a trust region. If the Newton step lies outside the trust region, a step with a smaller norm and different direction is computed. The size of the trust region plays a similar role as the relaxation factor in the line search approach. To ensure that the method converges, the trust region size is automatically adjusted from one iteration to the next one, depending on the local accuracy of the quadratic model. The trust region approach is applied to the simulation of an 8/6 switched reluctance motor.