Abstract
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 language | English (US) |
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Pages (from-to) | 613-646 |
Number of pages | 34 |
Journal | Journal of Scientific Computing |
Volume | 24 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2005 |
Externally published | Yes |
Keywords
- 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