Scalable algebraic multilevel preconditioners with application to CFD. (English) Zbl 1398.76068

Tromeur-Dervout, Damien (ed.) et al., Parallel computational fluid dynamics 2008. Parallel numerical methods, software development and applications. Proceedings of the 20th international conference, Lyon, France, May 19–22, 2008. Berlin: Springer (ISBN 978-3-642-14437-0/hbk; 978-3-642-26515-0/pbk978-3-642-14438-7/ebook). Lecture Notes in Computational Science and Engineering 74, 15-27 (2010).
Summary: 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.
For the entire collection see [Zbl 1201.76012].


76F65 Direct numerical and large eddy simulation of turbulence
65F08 Preconditioners for iterative methods
65Y05 Parallel numerical computation
Full Text: DOI


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