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On the nonlinear domain decomposition method

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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.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    M. Dryja

  2. Lehrstuhl Praktische Mathematik, Christian-Albrechts-Universität zu Kiel, D-24098, Kiel, Germany

    W. Hackbusch

Authors
  1. M. Dryja
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  2. W. Hackbusch
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Dryja, M., Hackbusch, W. On the nonlinear domain decomposition method. Bit Numer Math 37, 296–311 (1997). https://doi.org/10.1007/BF02510214

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  • DOI: https://doi.org/10.1007/BF02510214

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