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Multigrid methods: from geometrical to algebraic versions

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Modern Methods in Scientific Computing and Applications

Part of the book series: NATO Science Series ((NAII,volume 75))

Abstract

Nowadays the multigrid technique is one of the most efficient methods for solving a large class of problems including elliptic boundary value problems for partial differential equations (PDEs) or systems of PDEs. Our lecture notes start with a motivation for the multigrid idea and a brief review of the multigrid history, its situation and the perspectives. The next part of our paper is devoted to the algorithmical aspects of the construction of multigrid methods including also algebraic approaches and parallelization techniques. Algebraic multigrid methods are now quite popular in practical applications because they can be included in conventional finite element packages without changing the data structure of the package. In the theoretical part of our lecture, we present some general approaches to the convergence and efficiency analysis of multigrid methods. Finally, we discuss implementation issues and present some numerical results obtained from the application of our algebraic multigrid package PEBBLES to large-scale problems in medicine and engineering.

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Authors and Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University of Linz, A-4040, Linz, Austria

    Gundolf Haase & Ulrich Langer

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  1. Gundolf Haase
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  2. Ulrich Langer
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Editors and Affiliations

  1. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada

    Anne Bourlioux  & Gert Sabidussi  & 

  2. Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada

    Martin J. Gander

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Haase, G., Langer, U. (2002). Multigrid methods: from geometrical to algebraic versions. In: Bourlioux, A., Gander, M.J., Sabidussi, G. (eds) Modern Methods in Scientific Computing and Applications. NATO Science Series, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0510-4_4

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  • DOI: https://doi.org/10.1007/978-94-010-0510-4_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0782-8

  • Online ISBN: 978-94-010-0510-4

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