Reducing the computation time of nonlinear problems by an adaptive linear system tolerance

Within the finite-element framework, nonlinear magnetic problems are often solved by an iterative line search strategy. The efforts to achieve convergence concentrate on the selection of an adequate relaxation factor. The line search is performed along a direction obtained by solving a system of linear equations. However, it is not required to compute this intermediate solution with a high accuracy, to ensure convergence. This paper shows how the accuracy of the solver can be modified at each nonlinear iteration, in order to reduce the overall computation time.