On the initial estimate of interface forces in FETI methods |
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Authors: | Pierre GosseletChristian Rey Daniel J Rixen |
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Affiliation: | a Laboratoire de Modélisation Matériaux et Structures, Université Paris VI/CNRS, 8 rue du Capitaine Scott, 75015 Paris, France b Laboratoire de Mécanique et Technologie, ENS Cachan/CNRS/Université Paris VI, 61, Avenue du Président Wilson, 94235 Cachan Cedex, France c T.U. Delft, Faculty of Design, Engineering and Production, Engineering Dynamics, Mekelweg 2, 2628 CD Delft, The Netherlands |
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Abstract: | The balanced domain decomposition (BDD) method and the finite element tearing and interconnecting (FETI) method are two commonly used non-overlapping domain decomposition methods. Due to strong theoretical and numerical similarities, these two methods are generally considered as being equivalently efficient. However, for some particular cases, such as for structures with strong heterogeneities, FETI requires a large number of iterations to compute the solution compared to BDD. In this paper, the origin of the poor efficiency of FETI in these particular cases is traced back to bad initial estimates of the interface stresses. To improve the estimation of interface forces, a novel strategy for splitting interface forces between neighboring substructures is proposed. The additional computational cost incurred is not significant. This yields a new initialization for the FETI method and restores numerical efficiency which makes FETI comparable to BDD even for problems where FETI was performing poorly. Various simple test problems are presented to discuss the efficiency of the proposed strategy and to illustrate the so-obtained numerical equivalence between the BDD and FETI solvers. |
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Keywords: | 28 60 63 80 |
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