Global convergence of nonmonotone strategies in parallel methods for block-bordered nonlinear systems

In this paper we present a new method for solving block-bordered nonlinear systems of equations. This method is based on the modified Feng-Schnabel algorithm of G. Zanghirati (Global convergence extension of Feng-Schnabel algorithm for block bordered nonlinear systems, Technical report No. 252, Mathematics Department, University of Ferrara, 1997) for the selection of the search direction. The resulting technique is a nonmonotone strategy that we prove to be globally convergent. Furthermore, the multilevel Newton-like algorithm we propose maintains the intrinsic parallelism due to the sparsity structure of the problem, so it is very suitable for a parallel implementation on distributed memory multiprocessor architectures. A case study is given as a numerical example.