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A FETI method with a mesh independent condition number for the iteration matrix

 

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Opened Access A FETI method with a mesh independent condition number for the iteration matrix
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Author: Bernardi, Christine
Chacón Rebollo, Tomás
Chacón Vera, Eliseo
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2008-02-15
Published in: Computer Methods in Applied Mechanics and Engineering, 197 (13-16), 1410-1429.
Document type: Article
Abstract: We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H1 0 (Ω) derived by Raviart-Thomas [22] P.-A. Raviart, J.-M. Thomas, Primal Hybrid Finite Element Metho and complemented with the detailed work on polygonal domains developed by Grisvard [17] P. Grisvard, Singularities in Boundary value problems. Recherches en Mathématiques Appliquées, 22. Masson, 1992.. We compute the action of the Lagrange multipliers using the natural H 1/2 00 scalar product, therefore no consistency error appears. As a byproduct, we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning. This result improves the standard asymptotic bound for this condition number shown by Mandel-Tezaur in [19] J. Mandel, R. Tezaur, Convergence of a substructuring method with Lagrange multipliers. Numer. Math., 73 (1996), 473–487. Numerical results that confirm our theoretical analysis are presented. Nous proposons une nouvelle approche des méthodes FETI: la décomposition de domaine fait appel aux multiplicateurs de Lagrange tels qu’introduits par Raviart-Thomas [22] P.-A. Raviart, J.-M. Thomas, Primal Hybrid Finite Element Methods for second o...
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Cite: Bernardi, C., Chacón Rebollo, T. y Chacón Vera, E. (2008). A FETI method with a mesh independent condition number for the iteration matrix. Computer Methods in Applied Mechanics and Engineering, 197 (13-16), 1410-1429.
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URI: http://hdl.handle.net/11441/43300

DOI: 10.1016/j.cma.2007.11.019

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