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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 38
Edited by: B.H.V. Topping
Paper VIII.5

Parallel Iterative Solvers for Finite Element Analysis

R. Valkenberg, G. Warzee, P. Saint-Georges, R. Beauwens and Y. Notay

Universite Libre de Bruxelles (Free University of Brussels), Brussels, Belgium

Full Bibliographic Reference for this paper
R. Valkenberg, G. Warzee, P. Saint-Georges, R. Beauwens, Y. Notay, "Parallel Iterative Solvers for Finite Element Analysis", in B.H.V. Topping, (Editor), "Advances in Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, pp 373-381, 1996. doi:10.4203/ccp.38.8.5
The purpose of this contribution is to show the performances of three parallel preconditioners developed for stress analysis. The problem is the solution of large linear systems of algebraic equations, which arise in the finite element discretizations of linear elastic structures, the computation being made by a parallel iterative method. During the last few years, a general theory has been developed for the study of additive and multiplicative Schwarz methods. We apply the additive Schwarz theory, as a preconditioner which is by nature parallel. Other widely used preconditioners are based on incomplete Cholesky factorizations (IC), but for the problems treated here a reduction stage to a Stieltjes form is required in order to obtain an IC factorizable matrix. The parallelization of the IC preconditioner is performed by replication of boundary unknowns on two or more subdomains. The last preconditioner is based on the Schur complement method which consists in solving the boundary problem obtained after elimination of the internal unknowns. These three preconditioners are based on domain decomposition schemes.

Numerical analyses on regular and irregular meshes show the performances of the three methods and the influences of different parameters such as the amount of overlap, the number of subdomains or the decomposition method.

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