Non-linear additive Schwarz preconditioners and application in computational fluid dynamics

Xiao Chuan Cai*, David Elliot Keyes, Leszek Marcinkowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


The focus of this paper is on the numerical solution of large sparse non-linear systems of algebraic equations on parallel computers. Such non-linear systems often arise from the discretization of non-linear partial differential equations, such as the Navier-Stokes equations for fluid flows, using finite element or finite difference methods. A traditional inexact Newton method, applied directly to the discretized system, does not work well when the non-linearities in the algebraic system become unbalanced. In this paper, we study some preconditioned inexact Newton algorithms, including the single-level and multilevel non-linear additive Schwarz preconditioners. Some results for solving the high Reynolds number incompressible Navier-Stokes equations are reported.

Original languageEnglish (US)
Pages (from-to)1463-1470
Number of pages8
JournalInternational Journal for Numerical Methods in Fluids
Issue number12
StatePublished - Dec 30 2002


  • Domain decomposition
  • Inexact Newton methods
  • Multilevel methods
  • Non-linear additive Schwarz
  • Non-linear equations
  • Non-linear preconditioning

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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