On backtracking failure in newton-GMRES methods with a demonstration for the navier-stokes equations

Authors:
Raymond S. Tuminaro;Homer F. Walker;John N. Shadid
Affiliations:
Sandia National Laboratories, MS 9214, P.O. Box 969, Livermore, California;Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts;Sandia National Laboratories, MS 1111, P.O. Box 5800, Albuquerque, New Mexico
Venue:
Journal of Computational Physics
Year:
2002

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Abstract

In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier-Stokes equations with heat and mass transport. Specifically, it was observed that a Newton-GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier-Stokes equations.