Reducing Complexity in Parallel Algebraic Multigrid Preconditioners

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Algebraic multigrid (AMG) is a very efficient iterative solver and preconditioner for large unstructured linear systems. Traditional coarsening schemes for AMG can, however, lead to computational complexity growth as problem size increases, resulting in increased memory use and execution time, and diminished scalability. Two new parallel AMG coarsening schemes are proposed, that are based on solely enforcing a maximum independent set property, resulting in sparser coarse grids. The new coarsening techniques remedy memory and execution time complexity growth for various large three-dimensional (3D) problems. If used within AMG as a preconditioner for Krylov subspace methods, the resulting iterative methods tend ... continued below

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De Sterck, H; Yang, U M & Heys, J September 21, 2004.

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Algebraic multigrid (AMG) is a very efficient iterative solver and preconditioner for large unstructured linear systems. Traditional coarsening schemes for AMG can, however, lead to computational complexity growth as problem size increases, resulting in increased memory use and execution time, and diminished scalability. Two new parallel AMG coarsening schemes are proposed, that are based on solely enforcing a maximum independent set property, resulting in sparser coarse grids. The new coarsening techniques remedy memory and execution time complexity growth for various large three-dimensional (3D) problems. If used within AMG as a preconditioner for Krylov subspace methods, the resulting iterative methods tend to converge fast. This paper discusses complexity issues that can arise in AMG, describes the new coarsening schemes and examines the performance of the new preconditioners for various large 3D problems.

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PDF-file: 22 pages; size: 0.7 Mbytes

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  • Journal Name: SIAM (Society for Industrial and Applied Mathematics) Journal on Matrix Analysis and Applications; Journal Volume: 27; Journal Issue: 4

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  • Report No.: UCRL-JRNL-206780
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 883821
  • Archival Resource Key: ark:/67531/metadc891614

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  • September 21, 2004

Added to The UNT Digital Library

  • Sept. 23, 2016, 2:42 p.m.

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  • Dec. 1, 2016, 1:43 p.m.

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De Sterck, H; Yang, U M & Heys, J. Reducing Complexity in Parallel Algebraic Multigrid Preconditioners, article, September 21, 2004; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc891614/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.