Algebraic multigrid preconditioning of high-order spectral elements for elliptic problems on a simplicial mesh

Research output: Contribution to journalArticle

Abstract

Algebraic multigrid is investigated as a solver for linear systems that arise from high-order spectral element discretizations. An algorithm is introduced that utilizes the efficiency of low-order finite elements to precondition the high-order method in a multilevel setting. In particular, the efficacy of this approach is highlighted on simplexes in two and three dimensions with nodal spectral elements up to order n = 11. Additionally, a hybrid preconditioner is also developed for use with discontinuous spectral element methods. The latter approach is verified for the discontinuous Galerkin method on elliptic problems.

Original languageEnglish (US)
Pages (from-to)2189-2209
Number of pages21
JournalSIAM Journal on Scientific Computing
Volume29
Issue number5
DOIs
StatePublished - Dec 1 2007

Keywords

  • Algebraic multigrid
  • Discontinuous Galerkin
  • Spectral element

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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