Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method

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 GM...

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Bibliographic Details
Published in:Journal of scientific computing 2005-07, Vol.24 (1), p.45-78
Main Authors: Lottes, James W., Fischer, Paul F.
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Helmholtz equations
Multigrid methods
Spectral element method
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-004-4787-3