Optimization of direct domain decomposition methods
Abstract
In this paper, the problem of parallelizing the finite element method for distributed memory computers using domain decomposition methods is addressed. We focus on direct domain decomposition methods because they are robust and well adapted to multi-level decompositions. Two important problems concerning these methods are studied: the condensation of subdomains and the resolution of the interface problem. Finally, results are presented which show that, in sequential implementation, direct domain decomposition methods are more efficient than standard LDLt-skyline solvers, and compare favorably with state-of-the-art LDLt-sparse solvers.
References
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[5]1. S. Duff, J. A. Scott. The use of multiple fronts in gaussian elimination. RAL Report RAL-94-040, Rutherford Appleton Laboratory, 1994.
[2] C. Baranger. Méthodes de résolution paralleles de grands systemes appliquees au calcul de structures par éléments finis. PhD thesis, Université de Compiegne, 1995.
[3] P. Breitkopf, G. Touzot. Architecture des logiciels et langages de modélisation. Revue Européenne des Eléments Finis, 1(3): 333- 368, 1992.
[4]1. Duff, A. Erisman, J. Reid. Direct Methods for Sparse Matrices. Oxford University Press, Oxford, England, 1987.
[5]1. S. Duff, J. A. Scott. The use of multiple fronts in gaussian elimination. RAL Report RAL-94-040, Rutherford Appleton Laboratory, 1994.
Published
2023-07-17
Issue
pp. 1-8
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Escaig, Y., & Touzot, G. (2023). Optimization of direct domain decomposition methods. Computer Assisted Methods in Engineering and Science, 3(1), 1-8. https://cames3.ippt.pan.pl/index.php/cames/article/view/1459
