A numerical study of globalizations of Newton-GMRES methods

by Simonis, Joseph P.

Newton’s method is at the core of many algorithms used for solving nonlinear equations. A globalized Newton method is an implementation of Newton’s method augmented with “globalization procedures” intended to enhance the likelihood of convergence to a solution from an arbitrary initial guess. A Newton-GMRES method is an implementation of Newton’s method in which the iterative linear algebra method GMRES is used to solve approximately the linear system that characterizes the Newton step. A globalized Newton-GMRES method combines both globalization procedures and the GMRES scheme to develop robust and efficient algorithms for solving nonlinear equations. The aim of this project is to describe the development of some globalized Newton-GMRES methods and to compare their performances on a few benchmark fluid flow problems. i