Abstract
The paper deals with the efficient parallelization of leastsquares spectral element methods for incompressible flows. The parallelization of this sort of problems requires two different strategies. On the one hand, the spectral element discretization benefits from an element-by-element parallelization strategy. On the other hand, an efficient strategy to solve the large sparse global systems benefits from a row-wise distribution of data. This requires two different kinds of data distributions and the conversion between them is rather complicated. In the present paper, the different strategies together with its conversion are discussed. Moreover, some results obtained on a distributed memory machine (Cray T3E) and on a virtual shared memory machine (SGI Origin 3800) are presented.
Funding for this work was provided by the National Computing Facilities Foundation (NCF), under project numbers NRG-2000.07 and MP-068. Computing time was also provided by HPαC, Centre for High Performance Applied Computing at the Delft University of Technology.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M. I. Gerritsma and T.N. Phillips. Discontinuous spectral element approximations for the velocity-pressure-stress formulation of the Stokes problem. Int. J. Numer. Meth. Eng., 43:1401–1419, 1998. 47
M. Nool and M. M. J. Proot. Parallel implementation of a least-squares spectral element solver for incompressible flow problems. Submitted to J. Supercomput., 2002. 43, 49
L. F. Pavarino and O.B. Widlund. Iterative substructuring methods for spectral element discretizations of elliptic systems. I: compressible linear elasticity. SIAM J. NUMER. ANAL., 37(2):353–374, 1999. 40
L. F. Pavarino and O.B. Widlund. Iterative substructuring methods for spectral element discretizations of elliptic systems. II: Mixed methods for linear elasticity and Stokes flow. SIAM J. NUMER. ANAL., 37(2):375–402, 1999. 40
M.M. J. Proot and M. I. Gerritsma. A least-squares spectral element formulation for the Stokes problem. J. Sci. Comp., 17(1–3):311–322, 2002. 39
M.M. J. Proot and M. I. Gerritsma. Least-squares spectral elements applied to the Stokes problem. submitted. 39
A. Quateroni and A. Valli. Domain Decomposition Methods for PartialDifferential equations. Oxford University Press, 1999. 40
Marc Snir, Steve W. Otto, Steven Huss-Lederman, David W. Walker, and Jack Dongarra. MPI: The Complete Reference. MIT Press, Cambridge, Massachusetts, 1996. 47
Yousef Saad. SPARSKIT: a basic tool-kit for sparse matrix computations (Version 2) http://www.cs.umn.edu/research/arpa/SPARSKIT/sparskit.html 46
Aad J. van der Steen. Overview of recent supercomputers, Issue 2001 National Computing Facilities Foundation, Den Haag, 2001. 47
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nool, M., Proot, M.M.J. (2003). A Parallel, State-of-the-Art, Least-Squares Spectral Element Solver for Incompressible Flow Problems. In: Palma, J.M.L.M., Sousa, A.A., Dongarra, J., Hernández, V. (eds) High Performance Computing for Computational Science — VECPAR 2002. VECPAR 2002. Lecture Notes in Computer Science, vol 2565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36569-9_3
Download citation
DOI: https://doi.org/10.1007/3-540-36569-9_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00852-1
Online ISBN: 978-3-540-36569-3
eBook Packages: Springer Book Archive