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

摘要

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.