Hybrid Multigrid/Schwarz algorithms for the spectral element method

James W. Lottes, Paul F. Fischer

Research output: Contribution to journalArticlepeer-review


We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz methods based on restrictions of the originating SE matrices converge faster than FE-based methods and that weighting the Schwarz matrices by the inverse of the diagonal counting matrix is essential to effective Schwarz smoothing. Several of the methods considered achieve convergence rates comparable to those attained by classic multigrid on regular grids.

Original languageEnglish (US)
Pages (from-to)613-646
Number of pages34
JournalJournal of Scientific Computing
Issue number1
StatePublished - Jul 2005
Externally publishedYes


  • Domain decomposition
  • Multigrid
  • P-version finite element
  • Schwarz methods
  • Spectral element methods

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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