On an energy minimizing basis for algebraic multigrid methods

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Abstract

This paper is devoted to the study of an energy minimizing basis first introduced in Wan, Chan and Smith (2000) for algebraic multigrid methods. The basis will be first obtained in an explicit and compact form in terms of certain local and global operators. The basis functions are then proved to be locally harmonic functions on each coarse grid "element". Using these new results, it is illustrated that this basis can be numerically obtained in an optimal fashion. In addition to the intended application for algebraic multigrid method, the energy minimizing basis may also be applied for numerical homogenization.

Original languageEnglish (US)
Pages (from-to)121-127
Number of pages7
JournalComputing and Visualization in Science
Volume7
Issue number3-4
DOIs
Publication statusPublished - Oct 2004

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

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