Globalization Techniques for Newton-Krylov Methods and Applications to the Fully Coupled Solution of the Navier-Stokes Equations

• Published in: SIAM review Vol. 48; no. 4; pp. 700 - 721
• Main Authors: Pawlowski, Roger P., Shadid, John N., Simonis, Joseph P., Walker, Homer F.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01-12-2006
• Subjects: Algorithms; Boundary conditions; Exact sciences and technology; Free convection; Globalization; Jacobians; Linear equations; Linear systems; Mathematical analysis; Mathematics; Methods; Navier Stokes equation; Navier-Stokes equations; Newton approximation methods; Newtons method; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Partial differential equations; Perceptron convergence procedure; Problems and Techniques; Sciences and techniques of general use; Studies; Krylov subspace method; Iterative method; Navier-Stokes equations 65H10; fully coupled solution methods; Convergence; inexact Newton methods; Backtracking; Newton iterative methods; 65F10; Navier Stokes equation; Robustness; Newton method; globalized Newton methods; Newton-Krylov methods; dogleg methods; Fully coupled solution method; Steady state; Confidence interval; Line search; trust-region methods; Applied mathematics; Dogleg method; Newton's method; Two-dimensional calculations; Approximate solution
• ISSN: 0036-1445; 1095-7200
• DOI: 10.1137/S0036144504443511

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.