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Reducing complexity of algebraic multigrid by aggregation
Author(s) -
Gratton Serge,
Hé Pascal,
Jiránek Pavel,
Vasseur Xavier
Publication year - 2016
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2036
Subject(s) - multigrid method , preconditioner , interpolation (computer graphics) , solver , convergence (economics) , benchmark (surveying) , mathematics , mathematical optimization , rate of convergence , algebraic number , iterative method , algorithm , computer science , partial differential equation , channel (broadcasting) , mathematical analysis , animation , computer network , computer graphics (images) , geodesy , geography , economics , economic growth
Summary A typical approach to decrease computational costs and memory requirements of classical algebraic multigrid methods is to replace a conservative coarsening algorithm and short‐distance interpolation on a fixed number of fine levels by an aggressive coarsening with a long‐distance interpolation. Although the quality of the resulting algebraic multigrid grid preconditioner often deteriorates in terms of convergence rates and iteration counts of the preconditioned iterative solver, the overall performance can improve substantially. We investigate here, as an alternative, a possibility to replace the classical aggressive coarsening by aggregation, which is motivated by the fact that the convergence of aggregation methods can be independent of the problem size provided that the number of levels is fixed. The relative simplicity of aggregation can lead to improved solution and setup costs. The numerical experiments show the relevance of the proposed combination on both academic and benchmark problems in reservoir simulation from oil industry. Copyright © 2016 John Wiley & Sons, Ltd.