A Domain Decomposition Method Derived from the Primal Hybrid Formulation for 2nd Order Elliptic Problems

C. Bernardi (), T. Chacón Rebollo () and E. Chacón Vera ()
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C. Bernardi: C.N.R.S. et université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions
T. Chacón Rebollo: Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas
E. Chacón Vera: Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 365-372 from Springer

Abstract: Abstract We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H 0 1 (Ω) derived by Raviart-Thomas [17] and complemented with the detailed work on polygonal domains developed by Grisvard [11]. We compute the action of the Lagrange multipliers using the natural H 00 1/2 scalar product. Our analysis allows to deal with cross points and floating subdomains in a natural manner. 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 given by (1 + log(H/h))2 shown by Mandel-Tezaur in [14]. Numerical results that confirm our theoretical analysis are presented in [2] or [4].

Keywords: Condition Number; Domain Decomposition; Conjugate Gradient Method; Domain Decomposition Method; Cross Point (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_43

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