Scalable algebraic multilevel preconditioners with application to CFD

  • Andrea Aprovitola
  • Pasqua D’Ambra
  • Filippo Denaro
  • Daniela di Serafino
  • Salvatore Filippone
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 74)


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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Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Andrea Aprovitola
    • 1
  • Pasqua D’Ambra
    • 2
  • Filippo Denaro
    • 1
  • Daniela di Serafino
    • 3
  • Salvatore Filippone
    • 4
  1. 1.Department of Aerospace and Mechanical EngineeringSecond University of NaplesAversaItaly
  2. 2.Institute for High-Performance Computing and Networking (ICAR)CNRNaplesItaly
  3. 3.Department of MathematicsSecond University of NaplesCasertaItaly
  4. 4.Department of Mechanical EngineeringUniversity of Rome “Tor Vergata”RomeItaly

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