Parallel domain-decomposition preconditioning for computational fluid dynamics

Timothy J. Barth; Tony F. Chan; Wei Pai Tang

doi:10.1007/10703040_15

Parallel domain-decomposition preconditioning for computational fluid dynamics

Timothy J. Barth, Tony F. Chan, Wei Pai Tang

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Algebraic preconditioning algorithms suitable for computational fluid dynamics (CFD) based on overlapping and non-overlapping domain decomposition (DD) are considered. Specific distinction is given to techniques well-suited for time-dependent and steady-state computations of fluid flow. For time-dependent flow calculations, the overlapping Schwarz algorithm suggested by Wu et al. [28] together with stabilised (upwind) spatial discretisation shows acceptable scalability and parallel performance without requiring a coarse space correction. For steady-state flow computations, a family of non-overlapping Schur complement DD techniques are developed. In the Schur complement DD technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. The permutation of the mesh vertices based on subdomains and interfaces induces a natural 2 × 2 block partitioning of the discretisation matrix. Exact LU factorisation of this block system introduces a Schur complement matrix which couples subdomains and the interface together. A family of simplifying techniques for constructing the Schur complement and applying the 2 × 2 block system as a DD preconditioner are developed. Sample fluid flow calculations are presented to demonstrate performance characteristics of the simplified preconditioners.

Original language	English (US)
Title of host publication	Vector and Parallel Processing – VECPAR 1998 - 3rd International Conference, Selected Papers and Invited Talks
Editors	Jack J. Dongarra, José M.L.M. Palma, Jack J. Dongarra, Vicente Hernández
Publisher	Springer Verlag
Pages	176-202
Number of pages	27
ISBN (Print)	3540662286, 9783540662280
DOIs	https://doi.org/10.1007/10703040_15
State	Published - 1999
Externally published	Yes
Event	3rd International Meeting on Vector and Parallel Processing, VECPAR 1998 - Porto, Portugal Duration: Jun 21 1998 → Jun 23 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1573
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Meeting on Vector and Parallel Processing, VECPAR 1998
Country/Territory	Portugal
City	Porto
Period	06/21/98 → 06/23/98

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/10703040_15

Cite this

Barth, T. J., Chan, T. F., & Tang, W. P. (1999). Parallel domain-decomposition preconditioning for computational fluid dynamics. In J. J. Dongarra, J. M. L. M. Palma, J. J. Dongarra, & V. Hernández (Eds.), Vector and Parallel Processing – VECPAR 1998 - 3rd International Conference, Selected Papers and Invited Talks (pp. 176-202). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1573). Springer Verlag. https://doi.org/10.1007/10703040_15

Barth, Timothy J. ; Chan, Tony F. ; Tang, Wei Pai. / Parallel domain-decomposition preconditioning for computational fluid dynamics. Vector and Parallel Processing – VECPAR 1998 - 3rd International Conference, Selected Papers and Invited Talks. editor / Jack J. Dongarra ; José M.L.M. Palma ; Jack J. Dongarra ; Vicente Hernández. Springer Verlag, 1999. pp. 176-202 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Algebraic preconditioning algorithms suitable for computational fluid dynamics (CFD) based on overlapping and non-overlapping domain decomposition (DD) are considered. Specific distinction is given to techniques well-suited for time-dependent and steady-state computations of fluid flow. For time-dependent flow calculations, the overlapping Schwarz algorithm suggested by Wu et al. [28] together with stabilised (upwind) spatial discretisation shows acceptable scalability and parallel performance without requiring a coarse space correction. For steady-state flow computations, a family of non-overlapping Schur complement DD techniques are developed. In the Schur complement DD technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. The permutation of the mesh vertices based on subdomains and interfaces induces a natural 2 × 2 block partitioning of the discretisation matrix. Exact LU factorisation of this block system introduces a Schur complement matrix which couples subdomains and the interface together. A family of simplifying techniques for constructing the Schur complement and applying the 2 × 2 block system as a DD preconditioner are developed. Sample fluid flow calculations are presented to demonstrate performance characteristics of the simplified preconditioners.",

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Barth, TJ, Chan, TF & Tang, WP 1999, Parallel domain-decomposition preconditioning for computational fluid dynamics. in JJ Dongarra, JMLM Palma, JJ Dongarra & V Hernández (eds), Vector and Parallel Processing – VECPAR 1998 - 3rd International Conference, Selected Papers and Invited Talks. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1573, Springer Verlag, pp. 176-202, 3rd International Meeting on Vector and Parallel Processing, VECPAR 1998, Porto, Portugal, 06/21/98. https://doi.org/10.1007/10703040_15

Parallel domain-decomposition preconditioning for computational fluid dynamics. / Barth, Timothy J.; Chan, Tony F.; Tang, Wei Pai.
Vector and Parallel Processing – VECPAR 1998 - 3rd International Conference, Selected Papers and Invited Talks. ed. / Jack J. Dongarra; José M.L.M. Palma; Jack J. Dongarra; Vicente Hernández. Springer Verlag, 1999. p. 176-202 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1573).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Chan, Tony F.

AU - Tang, Wei Pai

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N2 - Algebraic preconditioning algorithms suitable for computational fluid dynamics (CFD) based on overlapping and non-overlapping domain decomposition (DD) are considered. Specific distinction is given to techniques well-suited for time-dependent and steady-state computations of fluid flow. For time-dependent flow calculations, the overlapping Schwarz algorithm suggested by Wu et al. [28] together with stabilised (upwind) spatial discretisation shows acceptable scalability and parallel performance without requiring a coarse space correction. For steady-state flow computations, a family of non-overlapping Schur complement DD techniques are developed. In the Schur complement DD technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. The permutation of the mesh vertices based on subdomains and interfaces induces a natural 2 × 2 block partitioning of the discretisation matrix. Exact LU factorisation of this block system introduces a Schur complement matrix which couples subdomains and the interface together. A family of simplifying techniques for constructing the Schur complement and applying the 2 × 2 block system as a DD preconditioner are developed. Sample fluid flow calculations are presented to demonstrate performance characteristics of the simplified preconditioners.

AB - Algebraic preconditioning algorithms suitable for computational fluid dynamics (CFD) based on overlapping and non-overlapping domain decomposition (DD) are considered. Specific distinction is given to techniques well-suited for time-dependent and steady-state computations of fluid flow. For time-dependent flow calculations, the overlapping Schwarz algorithm suggested by Wu et al. [28] together with stabilised (upwind) spatial discretisation shows acceptable scalability and parallel performance without requiring a coarse space correction. For steady-state flow computations, a family of non-overlapping Schur complement DD techniques are developed. In the Schur complement DD technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. The permutation of the mesh vertices based on subdomains and interfaces induces a natural 2 × 2 block partitioning of the discretisation matrix. Exact LU factorisation of this block system introduces a Schur complement matrix which couples subdomains and the interface together. A family of simplifying techniques for constructing the Schur complement and applying the 2 × 2 block system as a DD preconditioner are developed. Sample fluid flow calculations are presented to demonstrate performance characteristics of the simplified preconditioners.

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Barth TJ, Chan TF, Tang WP. Parallel domain-decomposition preconditioning for computational fluid dynamics. In Dongarra JJ, Palma JMLM, Dongarra JJ, Hernández V, editors, Vector and Parallel Processing – VECPAR 1998 - 3rd International Conference, Selected Papers and Invited Talks. Springer Verlag. 1999. p. 176-202. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/10703040_15

Parallel domain-decomposition preconditioning for computational fluid dynamics

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