Journal of Scientific Computing

, Volume 24, Issue 1, pp 45–78 | Cite as

Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method

  • James W. Lottes
  • Paul F. FischerEmail author


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.


Multigrid Schwarz methods domain decomposition spectral element methods p-version finite element 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbanaUSA
  2. 2.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA

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