parpp3d++ - A Parallel HPC Code for the Incompressible Nonstationary Navier-Stokes Equations
Parallel multigrid methods belong to the most prominent tools for solving huge systems of (non-)linear equations arising from the discretisation of PDEs, as for instance in Computational Fluid Dynamics (CFD). However, the quality of (parallel) multigrid methods in regard of numerical and computational complexity mainly stands and falls with the smoothing algorithms (“smoother”) used. Since the inherent highly recursive character of many global smoothers (SOR, ILU) often impedes a direct parallelisation, the application of block smoothers is an alternative. However, due to the weakened recursive character, the resulting parallel efficiency may decrease in comparison to the sequential performance, due to a weaker total numerical efficiency. Within this paper, we show the consequences of such a strategy for the resulting total efficiency on the Hitachi SR8000-F1 if incorporated into the parallel CFD solver parpp3d++ for 3D incompressible flow. Moreover, we analyse the numerical losses of parallel efficiency due to communication costs and numerical efficiency on several modern parallel computer platforms.
KeywordsComputational Fluid Dynamics Acoustic Pressure Laplace Problem Algebraic Multigrid Method Additive Schwarz Method
Unable to display preview. Download preview PDF.
- 1.Buijssen, S.H.M. and Turek, S. Sources of parallel inefficiency for incompressible CFD simulation. In Monien, B. and Feldmann, R., editors, Proceedings 8th International Euro-Par Conference, LNCS. Springer, January 2002. Paderborn, Germany, August 27–30.Google Scholar
- 2.Buijssen, Sven H.M. Numerische Analyse eines parallelen 3-D-Navier-Stokes-Lösers. Master's thesis, Universität Heidelberg, October 2002. http://www.mathematik.uni-dortmund.de/lsiii/php/showpdffile.php?Buijssen2002.Google Scholar
- 3.HELICS — HEidelberg LInux Cluster System. http://www.helics.de/.Google Scholar
- 4.Karypis, G. and Kumar, V. METIS-A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices. http://www-users.cs.umn.edu/~karypis/metis/index.html, January 1998.Google Scholar
- 5.LRZ Munich. System Description. http://www.lrz-muenchen.de/services/compute/hlrb/system-en/.Google Scholar
- 6.Preis, R. and Diekmann, R. The PARTY Partitioning-Library, User Guide-Version 1.1. http://www.uni-paderborn.de/fachbereich/AG/monien/RESEARCH/PART/party.html, January 1996.Google Scholar
- 7.Turek, S. Efficient solvers for incompressible flow problems: An algorithmic and computational approach. Springer, 1999.Google Scholar
- 8.Turek, S., Becker, C., and Kilian, S. Hardware-oriented Numerics and cocepts for PDE software. Technical report, Universität Dortmund, Vogelpothsweg 87, 44227 Dortmund, June 2003. to appear in ICCS.Google Scholar
- 9.Turek, S. and Schäfer, M. Benchmark computations of laminar flow around cylinder. In E.H. Hirschel, editor, Flow Simulation with High-Performance Computers II, volume 52 of Notes on Numerical Fluid Mechanics. Vieweg, 1996. co. F. Durst, E. Krause, R. Rannacher.Google Scholar