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

Christine Bernardi (1) , Tomas Chacon-Rebollo (2) , Eliseo Chacòn Vera (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 EDAN - Departamento de Ecuaciones Differenciales y Analysis numérico [Sevilla]

We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H¹₀ (Ω) derived by Raviart-Thomas[22] and complemented with the detailed work on polygonal domains developed by Grisvard [17]. We compute the action of the Lagrange multipliers using the natural H^1/2₀₀ 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]. Numerical results that confirm our theoretical analysis are presented.

Domaines: Analyse numérique [math.NA]

Christine Bernardi, Tomas Chacon-Rebollo, Eliseo Chacòn Vera. A FETI method with a mesh independent condition number for the iteration matrix. Computer Methods in Applied Mechanics and Engineering, 2008, 197 (issues-13-16), pp.1410-1429. ⟨10.1016/j.cma.2007.11.019⟩. ⟨hal-00170169⟩