Globalization Techniques for Newton–Krylov Methods and Applications to the Fully-Coupled

Abstract. A Newton–Krylov method is an implementation of Newton’s method in which a Krylov subspace method is used to solve approximately the linear subproblems that determine Newton steps. To enhance robustness when good initial approximate solutions are not available, these methods are usually globalized, i.e., augmented with auxiliary procedures (globalizations) that improve the likelihood of convergence from a starting point that is not near a solution. In recent years, globalized Newton–Krylov methods have been used increasingly for the fully coupled solution of large-scale problems. In this paper, we review several representative globalizations, discuss their properties, and report on a numerical study aimed at evaluating their relative merits on large-scale two- and three-dimensional problems involving the steady-state Navier–Stokes equations. Key words. Newton’s method, inexact Newton methods, Newton iterative methods, Newton–Krylov methods, globalized Newton methods, backtracking, line search, trust-region methods, dogleg methods, fully coupled solution methods, Navier–Stokes equation