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Bridging the gap between geometric and algebraic multi-grid methods

  • D. Feuchter
  • I. Heppner
  • S.A. Sauter
  • G. Wittum
Regular article

Abstract.

In this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains will be developed. The algorithm requires as input only the given discretisation instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations will be generated in a black-box fashion and will be employed to define purely algebraic intergrid transfer operators. The geometric interpretation of the algorithm allows one to use the framework of geometric multigrid methods to prove its convergence. The focus of this paper is on the formulation of the algorithm and the demonstration of its efficiency by numerical experiments while the analysis is carried out for some model problems.

Keywords

Differential Equation Partial Differential Equation Numerical Experiment Model Problem Coarse Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • D. Feuchter
    • 1
  • I. Heppner
    • 1
  • S.A. Sauter
    • 2
  • G. Wittum
    • 1
  1. 1.IWR, Universität Heidelberg, 69120 Heidelberg, Germany (e-mail: {Dirk.Feuchter, Ingo.Heppner, Wittum}@iwr.uni-heidelberg.de)DE
  2. 2.Institut für Mathematik, Universität Zürich, 8057 Zürich, Switzerland (e-mail: stas@amath.unizh.ch)CH

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