| 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 often
"globalized," that is, augmented with auxiliary procedures ("globalizations")
that improve the likelihood of convergence from a poor starting point. In
recent years, globalized NewtonKrylov methods have been used increasingly
for the fully coupled solution of large-scale CFD problems. In this talk, I
will review several representative globalizations, discuss their properties,
and report on a numerical study aimed at evaluating their relative merits
on large-scale 2D and 3D problems involving the steady-state Navier-Stokes
equations. This is joint work with John Shadid and Roger Pawlowski at
Sandia
National Laboratories and Joseph Simonis at WPI.
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