Abstract
Spectral element methods allow for effective implementation of numerical techniques for partial differential equations on parallel architectures. We present two implementations of the parallel algorithm where the communications are performed using MPI. In the first implementation, each processor deals with one element. It leads to a natural parallelization. In the second implementation certain number of spectral elements are allocated to each processor. In this article, we describe how communications are implemented and present results and performance of the code on two architectures: a PC-Cluster and an IBM-SP3.
Keywords
- Parallel Algorithm
- Conjugate Gradient Method
- Point Discretization
- Spectral Element
- Domain Decomposition Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
V. I. Agoshkov, Poincaré-Steklov’s operators and domain decomposition methods in finite dimensional spaces, First International Symposium on Domain Decomposition Method for Partial Differential Equations, R. Glwinski, G.H. Golub, G. A. Meurant and J. Périaux eds., SIAM, Philadelphia, pp. 73–112 (1988). 392
C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques, Paris, Springer Verlag (1992). 392
A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations, Oxford University Press, Ofxord (1999). 392
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© 2003 Springer-Verlag Berlin Heidelberg
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Airiau, S., Azaïez, M., Belgacem, F.B., Guivarch, R. (2003). Parallelization of Spectral Element Methods. 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_26
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DOI: https://doi.org/10.1007/3-540-36569-9_26
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