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Multilevel Preconditioning of 2D Rannacher-Turek FE Problems; Additive and Multiplicative Methods

  • Ivan Georgiev
  • Johannes Kraus
  • Svetozar Margenov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)

Abstract

In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested (in general). To handle this, a proper two-level basis is required in order to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the methods to the multilevel case.

The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. As will be shown, the obtained bounds – in particular – give rise to optimal order AMLI methods of additive type. The presented numerical tests fully confirm the theoretical estimates.

Keywords

Hierarchical Basis Coarse Partition Multiplicative Variant Nodal Basis Function Multilevel Precondition 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Ivan Georgiev
    • 1
  • Johannes Kraus
    • 2
  • Svetozar Margenov
    • 3
  1. 1.Institute of Mathematics and Informatics and Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Bl. 25A, 1113 SofiaBulgaria
  2. 2.Johann Radon Institute for Computational and Applied Mathematics, Altenbergerstraße 69, A-4040 LinzAustria
  3. 3.Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Bl. 25A, 1113 SofiaBulgaria

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