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On some versions of the element agglomeration AMGe method
Author(s) -
Lashuk Ilya,
Vassilevski Panayot S.
Publication year - 2008
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.585
Subject(s) - multigrid method , mathematics , conjugate gradient method , finite element method , interpolation (computer graphics) , eigenvalues and eigenvectors , topology (electrical circuits) , partial differential equation , mathematical optimization , algorithm , computer science , mathematical analysis , animation , physics , computer graphics (images) , quantum mechanics , combinatorics , thermodynamics
Abstract The present paper deals with element‐based algebraic multigrid (AMGe) methods that target linear systems of equations coming from finite element discretizations of elliptic partial differential equations. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate AMGe method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom is based on solving a large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V ‐cycle utilizing simple interpolation matrices and nested conjugate gradient (CG)‐based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods. Copyright © 2008 John Wiley & Sons, Ltd.