Adaptive Algebraic Multigrid Methods

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Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null ... continued below

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PDF-file: 22 pages; size: 0.2 Mbytes

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Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S & Ruge, J April 9, 2004.

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Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

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PDF-file: 22 pages; size: 0.2 Mbytes

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  • Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 27; Journal Issue: 4

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  • Report No.: UCRL-JRNL-203501
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 875948
  • Archival Resource Key: ark:/67531/metadc878260

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  • April 9, 2004

Added to The UNT Digital Library

  • Sept. 21, 2016, 2:29 a.m.

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  • Dec. 6, 2016, 6:46 p.m.

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Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S & Ruge, J. Adaptive Algebraic Multigrid Methods, article, April 9, 2004; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc878260/: accessed August 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.