Nonlinearly preconditioned inexact Newton algorithms

Xiao Chuan Cai*, David Elliot Keyes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

150 Scopus citations

Abstract

Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations F(u*) = 0 arising, for example, from the discretization of partial differential equations. Even with global strategies such as linesearch or trust region, the methods often stagnate at local minima of ∥F∥, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u*, one may want to solve instead and equivalent nonlinearly preconditioned system F(u*) = 0 whose nonlinearities are more balanced. In this paper, we propose and study a nonlinear additive Schwarz-based parallel nonlinear preconditioner and show numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, where a traditional inexact Newton method fails.

Original languageEnglish (US)
Pages (from-to)183-200
Number of pages18
JournalSIAM Journal on Scientific Computing
Volume24
Issue number1
DOIs
StatePublished - Apr 15 2003

Keywords

  • Domain decomposition
  • Incompressible flows
  • Inexact Newton methods
  • Krylov subspace methods
  • Nonlinear additive Schwarz
  • Nonlinear equations
  • Nonlinear preconditioning
  • Parallel computing

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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