research-article

On Red-Black SOR Smoothing in Multigrid

Author:

Irad YavnehAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 17, Issue 1

Pages 180 - 192

https://doi.org/10.1137/0917013

Published: 01 January 1996 Publication History

Abstract

Optimal relaxation parameters are obtained for red-black Gauss–Seidel relaxation in multigrid solvers of a family of elliptic equations. The resulting relaxation schemes are found to retain very high efficiency over an appreciable range of coefficients of the elliptic differential operator, yielding simple, inexpensive, and fully parallelizable smoothers in many situations where less cost-effective block- and alternating-direction schemes are commonly used.

References

[1]

Achi Brandt, W. Hackbusch, U. Trottenberg, Guide to multigrid developmentMultigrid methods (Cologne, 1981), Lecture Notes in Math., Vol. 960, Springer, Berlin, 1982, 220–312

Google Scholar

[2]

Rob Kettler, W. Hackbusch, U. Trottenberg, Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methodsMultigrid methods (Cologne, 1981), Lecture Notes in Math., Vol. 960, Springer, Berlin, 1982, 502–534

Google Scholar

[3]

C.-C. Jay Kuo, Bernard C. Levy, Two-color Fourier analysis of the multigrid method with red-black Gauss-Seidel smoothing, Appl. Math. Comput., 29 (1989), 69–87

Digital Library

Google Scholar

[4]

J. Ruge, Y. Li, S. F. McCormick, A. Brandt, J. R. Bates, A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based barotropic model on the sphere, SIAM J. Sci. Comput., submitted

Google Scholar

[5]

Klaus Stüben, Ulrich Trottenberg, W. Hackbusch, U. Trottenberg, Multigrid methods: fundamental algorithms, model problem analysis and applicationsMultigrid methods (Cologne, 1981), Lecture Notes in Math., Vol. 960, Springer, Berlin, 1982, 1–176

Google Scholar

[6]

Richard S. Varga, Matrix iterative analysis, Prentice-Hall Inc., Englewood Cliffs, N.J., 1962xiii+322

Google Scholar

[7]

Pieter Wesseling, An introduction to multigrid methods, Pure and Applied Mathematics, John Wiley & Sons Ltd., Chichester, 1992viii+284

Google Scholar

[8]

P. Wesseling, W. Hackbusch, U. Trottenberg, A survey of Fourier smoothing analysis resultsMultigrid methods, III (Bonn, 1990), Internat. Ser. Numer. Math., Vol. 98, Birkhäuser, Basel, 1991, 105–127

Google Scholar

[9]

P. Wesseling, W. Hackbusch, U. Trottenberg, A robust and efficient multigrid methodMultigrid methods (Cologne, 1981), Lecture Notes in Math., Vol. 960, Springer, Berlin, 1982, 614–630

Google Scholar

[10]

Irad Yavneh, Multigrid smoothing factors for red-black Gauss-Seidel relaxation applied to a class of elliptic operators, SIAM J. Numer. Anal., 32 (1995), 1126–1138

Digital Library

Google Scholar

Cited By

View all

Liu CHenshaw W(2023)Multigrid with Nonstandard Coarse-Level Operators and Coarsening FactorsJournal of Scientific Computing10.1007/s10915-023-02103-x94:3Online publication date: 31-Jan-2023
https://dl.acm.org/doi/10.1007/s10915-023-02103-x
Wan FYin YZhang S(2018)3D Parallel Multigrid Methods for Real-Time Fluid Simulation3D Research10.1007/s13319-018-0157-z9:1(1-12)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s13319-018-0157-z
Garain SBalsara DReid J(2015)Comparing Coarray Fortran (CAF) with MPI for several structured mesh PDE applicationsJournal of Computational Physics10.1016/j.jcp.2015.05.020297:C(237-253)Online publication date: 15-Sep-2015
https://dl.acm.org/doi/10.1016/j.jcp.2015.05.020
Show More Cited By

Index Terms

On Red-Black SOR Smoothing in Multigrid

Index terms have been assigned to the content through auto-classification.

Recommendations

Multigrid preconditioning of linear systems for semi-smooth Newton methods applied to optimization problems constrained by smoothing operators

This article is concerned with the question of constructing efficient multigrid preconditioners for the linear systems arising when applying semi-smooth Newton methods to large-scale linear-quadratic optimization problems constrained by smoothing ...
A modulus-based cascadic multigrid method for elliptic variational inequality problems
Abstract
In this paper, by using a modulus-based matrix splitting method as a smoother, a new modulus-based cascadic multigrid method is presented for solving elliptic variational inequality problems. Convergence of the new method is analyzed. Numerical ...
An Algebraic Multigrid Method for a Class of Elliptic Differential Systems

The development, numerical investigation, and analysis of an algebraic multigrid (AMG) method for the numerical solution of a representative class of elliptic differential systems are presented. Our AMG scheme is based on the AMG strategy of Brandt, Ruge, ...

Comments

Information & Contributors

Information

Published In

cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 17, Issue 1

^* Special Issue on Iterative Methods in Numerical Linear Algebra

Jan 1996

305 pages

ISSN:1064-8275

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 1996

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

19
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 17 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Liu CHenshaw W(2023)Multigrid with Nonstandard Coarse-Level Operators and Coarsening FactorsJournal of Scientific Computing10.1007/s10915-023-02103-x94:3Online publication date: 31-Jan-2023
https://dl.acm.org/doi/10.1007/s10915-023-02103-x
Wan FYin YZhang S(2018)3D Parallel Multigrid Methods for Real-Time Fluid Simulation3D Research10.1007/s13319-018-0157-z9:1(1-12)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s13319-018-0157-z
Garain SBalsara DReid J(2015)Comparing Coarray Fortran (CAF) with MPI for several structured mesh PDE applicationsJournal of Computational Physics10.1016/j.jcp.2015.05.020297:C(237-253)Online publication date: 15-Sep-2015
https://dl.acm.org/doi/10.1016/j.jcp.2015.05.020
Dai QYang XWang CMagnenat-Thalmann NPan Z(2013)Interactive smoke simulation and rendering on the GPUProceedings of the 12th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry10.1145/2534329.2534358(177-182)Online publication date: 17-Nov-2013
https://dl.acm.org/doi/10.1145/2534329.2534358
Gmeiner BGradl TGaspar FRüDe U(2013)Optimization of the multigrid-convergence rate on semi-structured meshes by local Fourier analysisComputers & Mathematics with Applications10.1016/j.camwa.2012.12.00665:4(694-711)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1016/j.camwa.2012.12.006
Epicoco IMocavero SAloisio G(2012)The performance model for a parallel SOR algorithm using the red-black schemeInternational Journal of High Performance Systems Architecture10.1504/IJHPSA.2012.0509894:2(101-109)Online publication date: 1-Dec-2012
https://dl.acm.org/doi/10.1504/IJHPSA.2012.050989
Epicoco IMocavero S(2012)The performance model of an enhanced parallel algorithm for the SOR methodProceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I10.1007/978-3-642-31125-3_4(44-56)Online publication date: 18-Jun-2012
https://dl.acm.org/doi/10.1007/978-3-642-31125-3_4
Cohen JTariq SGreen SAliaga DOliveira MVarshney AWyman C(2010)Interactive fluid-particle simulation using translating Eulerian gridsProceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games10.1145/1730804.1730807(15-22)Online publication date: 19-Feb-2010
https://dl.acm.org/doi/10.1145/1730804.1730807
Molemaker JCohen JPatel SNoh JFiume ETessendorf JGross MJames D(2008)Low viscosity flow simulations for animationProceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation10.5555/1632592.1632595(9-18)Online publication date: 7-Jul-2008
https://dl.acm.org/doi/10.5555/1632592.1632595
Xie D(2006)A New Block Parallel SOR Method and Its AnalysisSIAM Journal on Scientific Computing10.1137/04060477727:5(1513-1533)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.1137/040604777
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

Multigrid preconditioning of linear systems for semi-smooth Newton methods applied to optimization problems constrained by smoothing operators

A modulus-based cascadic multigrid method for elliptic variational inequality problems

An Algebraic Multigrid Method for a Class of Elliptic Differential Systems

Comments

Information

Published In

Publisher

Publication History

Author Tags

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations