On Some Versions of the Element Agglomeration AMGe Method

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The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. 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 element based AMG 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 (dofs) is based on solving large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive ... continued below

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Lashuk, I & Vassilevski, P August 9, 2007.

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Description

The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. 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 element based AMG 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 (dofs) is based on solving 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.

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PDF-file: 29 pages; size: 1.9 Mbytes

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  • Journal Name: Numerical Linear Algebra with Applications, vol. 15, n/a, February 21, 2008, DOI: 10.1002/nla.585; Journal Volume: 15

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  • Report No.: UCRL-JRNL-233772
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 942043
  • Archival Resource Key: ark:/67531/metadc898154

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  • August 9, 2007

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 30, 2016, 2:13 p.m.

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Lashuk, I & Vassilevski, P. On Some Versions of the Element Agglomeration AMGe Method, article, August 9, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc898154/: accessed September 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.