On Generalizing the Algebraic Multigrid Framework

We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation met...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 42; no. 4; pp. 1669 - 1693
Main Authors Falgout, Robert D., Vassilevski, Panayot S.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2004
Subjects
Algebra
Algorithms
Approximation
Laboratories
Methods
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Summary:We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation methods and give theoretical justification for their use as tools for measuring the quality of coarse grids.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142903429742