Document Type

Article

Publication Date

12-1-2006

Publication Title

SIAM Review

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.

Volume

48

Issue

4

First Page Number

700

Last Page Number

721

DOI

10.1137/S0036144504443511

Publisher Statement

© 2006, SIAM Publications.

Included in

Mathematics Commons

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