Using Symmetries and Antisymmetries to Analyze a Parallel Multigrid Algorithm: The Elliptic Boundary Value Problem Case

Symmetry and antisymmetry properties of a class of elliptic partial differential equations are exploited to prove when a particular parallel multilevel algorithm is a direct method rather than the usual iterative method. No smoothing is required for this result. Examples are presented, including var...

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Veröffentlicht in:SIAM journal on numerical analysis Jg. 26; H. 6; S. 1439 - 1461
Hauptverfasser: Douglas, Craig C., Smith, Barry F.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.12.1989
Schlagworte:
Algorithms
Antisymmetry
Applied mathematics
Boundary value problems
Data smoothing
Decomposition
Decomposition methods
Exact sciences and technology
Iterative methods
Mathematics
Multigrid methods
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Symmetry
Total costs
Wall clocks
Parallel algorithm
Numerical analysis
Elliptic equation
Boundary value problem
Multigrid
Convergence rate
Numerical convergence
Partial differential equation
ISSN:0036-1429, 1095-7170
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Abstract Symmetry and antisymmetry properties of a class of elliptic partial differential equations are exploited to prove when a particular parallel multilevel algorithm is a direct method rather than the usual iterative method. No smoothing is required for this result. Examples are presented, including variable coefficient ones. A connection between the algorithm in this article and domain decomposition is established, even though this algorithm is more general and different. The parallel algorithm is also analyzed when it is iterative and it is shown how to increase processor utilization. Hackbusch's robust multigrid algorithm ["A new approach to robust multi-grid solvers," in ICIAM '87: Proceedings of the First International Conference on Industrial and Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1988, pp. 111-126] is analyzed for some model problems and it is shown that the parallel algorithm in this article uses much less computer time with at most the same amount of storage.
AbstractList Symmetry and antisymmetry properties of a class of elliptic partial differential equations are exploited to prove when a particular parallel multilevel algorithm is a direct method rather than the usual iterative method. No smoothing is required for this result. Examples are presented, including variable coefficient ones. A connection between the algorithm in this article and domain decomposition is established, even though this algorithm is more general and different. The parallel algorithm is also analyzed when it is iterative and it is shown how to increase processor utilization. Hackbusch's robust multigrid algorithm ["A new approach to robust multi-grid solvers," in ICIAM '87: Proceedings of the First International Conference on Industrial and Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1988, pp. 111-126] is analyzed for some model problems and it is shown that the parallel algorithm in this article uses much less computer time with at most the same amount of storage.
Author Smith, Barry F.
Douglas, Craig C.
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Cites_doi 10.1002/num.1690050304
10.1016/0167-8191(89)90114-2
10.1016/B978-0-12-632620-8.50027-9
10.1137/0610004
10.1007/BFb0072643
10.1137/0722038
10.1137/0902035
10.1137/0721017
10.1137/0725026
10.1137/1.9781611971057.ch4
10.1016/0168-9274(85)90033-9
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Issue 6
Keywords Parallel algorithm
Numerical analysis
Elliptic equation
Boundary value problem
Multigrid
Convergence rate
Numerical convergence
Partial differential equation
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References R2
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Snippet Symmetry and antisymmetry properties of a class of elliptic partial differential equations are exploited to prove when a particular parallel multilevel...
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SubjectTerms Algorithms
Antisymmetry
Applied mathematics
Boundary value problems
Data smoothing
Decomposition
Decomposition methods
Exact sciences and technology
Iterative methods
Mathematics
Multigrid methods
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Symmetry
Total costs
Wall clocks
Title Using Symmetries and Antisymmetries to Analyze a Parallel Multigrid Algorithm: The Elliptic Boundary Value Problem Case
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