BIT Numerical Mathematics

, Volume 37, Issue 2, pp 296–311 | Cite as

On the nonlinear domain decomposition method

  • M. Dryja
  • W. Hackbusch
Article

Abstract

Any domain decomposition or additive Schwarz method can be put into the abstract framework of subspace iteration. We consider generalizations of this method to the nonlinear case. The analysis shows under relatively weak assumptions that the nonlinear iteration converges locally with the same asymptotic speed as the corresponding linear iteration applied to the linearized problem.

AMS subject classification

65H10 65N55 

Key words

Domain decomposition nonlinear problems preconditioner nonlinear elliptic problems 

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Copyright information

© BIT Foundaton 1997

Authors and Affiliations

  • M. Dryja
    • 1
  • W. Hackbusch
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsUniversity of WarsawWarsawPoland
  2. 2.Lehrstuhl Praktische MathematikChristian-Albrechts-Universität zu KielKielGermany

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