Some Geometric and Algebraic Aspects of Domain Decomposition Methods

  • D. S. Butyugin
  • Y. L. Gurieva
  • V. P. Ilin
  • D. V. Perevozkin
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

Some geometric and algebraic aspects of various domain decomposition methods (DDMs) are considered. They are applied to a parallel solution of very large sparse SLAEs resulting from approximation of multi-dimensional mixed boundary value problems on non-structured grids. DDMs are used with parameterized overlapping of subdomains and various types of boundary conditions at the inner boundaries. An algorithm for automatic construction of a balancing domain decomposition for overlapping subdomains is presented. Subdomain SLAEs are solved by a direct or iterative preconditioned method in Krylov subspaces, whereas external iterations are performed by the FGMRES method. An experimental analysis of the algorithms is carried out on a set of model problems.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • D. S. Butyugin
    • 1
  • Y. L. Gurieva
    • 1
  • V. P. Ilin
    • 1
    • 2
  • D. V. Perevozkin
    • 1
  1. 1.Institute of Computational Mathematics and Mathematical Geophysics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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