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Parallel Domain-Decomposition Preconditioning for Computational Fluid Dynamics

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Vector and Parallel Processing – VECPAR’98 (VECPAR 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1573))

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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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Author information

Authors and Affiliations

  1. NASA Ames Research Center, Mail Stop T27A-1, Moffett Field, CA, 94035, USA

    Timothy J. Barth

  2. UCLA Department of Mathematics, Los Angeles, CA, 90095-1555, USA

    Tony F. Chan

  3. University of Waterloo Department of Computer Science, Waterloo, Ontario, N2L 3G1, Canada

    Wei-Pai Tang

Authors
  1. Timothy J. Barth
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  2. Tony F. Chan
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  3. Wei-Pai Tang
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Editor information

Editors and Affiliations

  1. EUIT Telecomunicación - DIATEL, Universidad Politécnica de Madrid, Ctra., Valencia, Km. 7, 28031, Madrid, Spain

    Vicente Hernández

  2. Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal

    José M. L. M. Palma

  3. Computer Science Department, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack J. Dongarra

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© 1999 Springer-Verlag Berlin Heidelberg

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Barth, T.J., Chan, T.F., Tang, WP. (1999). Parallel Domain-Decomposition Preconditioning for Computational Fluid Dynamics. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds) Vector and Parallel Processing – VECPAR’98. VECPAR 1998. Lecture Notes in Computer Science, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703040_15

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  • DOI: https://doi.org/10.1007/10703040_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66228-0

  • Online ISBN: 978-3-540-48516-2

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