An efficient multilevel solution scheme for large scale non‐linear systems

We present a new approach for the fast, efficient solution of large systems of non‐linear equations arising from the finite element discretization. The proposed non‐linear solver builds on the advantages of the popular methods of solution that are currently being employed, while eliminating most of their undesirable features. It combines the well‐known BFGS method with the FAS version of the multigrid method, introduced by Brandt, 1 to form a fast, efficient solution method for non‐linear problems. We present numerical performance studies that are indicative of the convergence properties as well as the stability of the new method.