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Parallel Computational Fluid Dynamics 2008 pp 15–27Cite as

Scalable algebraic multilevel preconditioners with application to CFD

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Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 74)

Abstract

The solution of large and sparse linear systems is one of the main computational kernels in CFD applications and is often a very time-consuming task, thus requiring the use of effective algorithms on high-performance computers. Preconditioned Krylov solvers are the methods of choice for these systems, but the availability of “good” preconditioners is crucial to achieve efficiency and robustness. In this paper we discuss some issues concerning the design and the implementation of scalable algebraic multilevel preconditioners, that have shown to be able to enhance the performance of Krylov solvers in parallel settings. In this context, we outline the main objectives and the related design choices of MLD2P4, a package of multilevel preconditioners based on Schwarz methods and on the smoothed aggregation technique, that has been developed to provide scalable and easy-to-use preconditioners in the Parallel Sparse BLAS computing framework. Results concerning the application of various MLD2P4 preconditioners within a large eddy simulation of a turbulent channel flow are discussed.

Key words

  • Preconditioning technique
  • Schwarz domain decomposition
  • Krylov methods

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Author information

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, Second University of Naples, via Roma 29, I-81031, Aversa, Italy

    Andrea Aprovitola & Filippo Denaro

  2. Institute for High-Performance Computing and Networking (ICAR), CNR, via Pietro Castellino 111, I-80131, Naples, Italy

    Pasqua D’Ambra

  3. Department of Mathematics, Second University of Naples, via Vivaldi 43, I-81100, Caserta, Italy

    Daniela di Serafino

  4. Department of Mechanical Engineering, University of Rome “Tor Vergata”, viale del Politecnico 1, I-00133, Rome, Italy

    Salvatore Filippone

Authors
  1. Andrea Aprovitola
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  2. Pasqua D’Ambra
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  3. Filippo Denaro
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  4. Daniela di Serafino
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  5. Salvatore Filippone
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Corresponding author

Correspondence to Andrea Aprovitola .

Editor information

Editors and Affiliations

  1. , Institut Camille Jordan, Université Lyon 1 - CNRS, Bd du 11 Novembre 1918 43, Villeurbanne, 69622, France

    Damien Tromeur-Dervout

  2. , Institut für Technische Mechanik, TU Clausthal, Adolph-Roemer-Str. 2A2a, Clausthal-Zellerfeld, 38678, Germany

    Gunther Brenner

  3. Daresbury Laboratory, Daresbury Science & Innovation Campus, Science & Technology Facilities Council, Warrington, WA4 4AD, Cheshire, United Kingdom

    David R. Emerson

  4. INRIA - SAGE, Campus de Beaulieu, Rennes, 35042, France

    Jocelyne Erhel

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Aprovitola, A., D’Ambra, P., Denaro, F., di Serafino, D., Filippone, S. (2010). Scalable algebraic multilevel preconditioners with application to CFD. In: Tromeur-Dervout, D., Brenner, G., Emerson, D., Erhel, J. (eds) Parallel Computational Fluid Dynamics 2008. Lecture Notes in Computational Science and Engineering, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14438-7_2

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