Repositorio de producción científica de la Universidad de Sevilla

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

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

Citas

buscar en

Estadísticas
Icon
Exportar a
Autor: Bernardi, Christine
Chacón Rebollo, Tomás
Chacón Vera, Eliseo
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2008-02-15
Publicado en: Computer Methods in Applied Mechanics and Engineering, 197 (13-16), 1410-1429.
Tipo de documento: Artículo
Resumen: 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 order eliptic equations. Math. Comp., 31 (1977), 391-413 et au traitement des domaines polygonaux dù á Grisvard [17] P. Grisvard, Singularities in Boundary value problems. Recherches en Mathématiques Appliquées, 22. Masson, 1992. Ces multiplicateurs utilisent le produit scalaire de H 1/2 00, de sorte qu’aucune erreur de consistance n’apparaît. En outre, nous prouvons que le nombre de condition de la matrice liée à chaque itération est indépendant de la taille du maillage, ce qui améliore le résultat de Mandel-Tezaur [19] J. Mandel, R. Tezaur, Convergence of a substructuring method with Lagrange multipliers. Numer. Math., 73 (1996), 473–487; par suite, aucun préconditionnement n’est nécessaire. Nous présentons des expériences numériques qui...
[Ver más]
Cita: 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.
Tamaño: 2.802Mb
Formato: PDF

URI: http://hdl.handle.net/11441/43300

DOI: 10.1016/j.cma.2007.11.019

Ver versión del editor

Mostrar el registro completo del ítem


Esta obra está bajo una Licencia Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internacional

Este registro aparece en las siguientes colecciones