On geometric multigrid methods for triangular grids using three-coarsening strategy

This paper deals with the design of efficient geometric multigrid methods on hierarchical triangular grids using a three-coarsening strategy. In [F.J. Gaspar, J.L. Gracia, F.J. Lisbona, Fourier analysis for multigrid methods on triangular grids, SIAM J. Sci. Comput., in press], a Local Fourier Analy...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 59; no. 7; pp. 1693 - 1708
Main Authors: Gaspar, F.J., Gracia, J.L., Lisbona, F.J., Rodrigo, C.
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.07.2009
Elsevier
Subjects:
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
Fourier analysis
Mathematical analysis
Mathematics
Multigrid
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Three-coarsening
Three-color smoother
Triangular grids
65N12
65F10
Multigrid
Three-coarsening
Triangular grids
Fourier analysis
65N55
Three-color smoother
Laplace operator
Fourier transformation
Decomposition method
Triangular finite element
Triangle
Linear operator
Partial differential equation
Finite element method
Smoothing methods
Grid pattern
Initial value problem
Algorithm
Numerical analysis
Boundary value problem
Smoothing
Applied mathematics
Domain decomposition
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary:This paper deals with the design of efficient geometric multigrid methods on hierarchical triangular grids using a three-coarsening strategy. In [F.J. Gaspar, J.L. Gracia, F.J. Lisbona, Fourier analysis for multigrid methods on triangular grids, SIAM J. Sci. Comput., in press], a Local Fourier Analysis (LFA) for multigrid methods with standard coarsening on triangular grids has been proposed. It is based on an expression of the Fourier transform in new coordinate systems. LFA is applied to the new coarsening strategy to design components for an efficient multigrid algorithm. The definition of low and high frequencies, and therefore the spaces of harmonics, are adapted according to the new situation. Appropriate smoothing methods, in particular a three-color smoother with optimal relaxation parameter, are proposed and analyzed for the discrete Laplace operator obtained with linear finite elements. Moreover, special inter-grid transfer operators are designed. These methods are compared with standard coarsening algorithms in terms of the computational work required. Independently of the shape of the triangles, we show that the three-coarsening strategy is a good computational alternative to standard coarsening.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2009.01.003