Lagrangian formulation of domain decomposition methods: A unified theory |
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Authors: | Fré dé ric Magoulè s,Franç ois-Xavier Roux |
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Affiliation: | 1. Institut Elie Cartan de Nancy, Université Henri Poincaré, BP 239, 54506 Vandoeuvre-les-Nancy Cedex, France;2. High Performance Computing Unit, ONERA, 29 av. de la Division Leclerc, BP 72, 92322 Châtillon Cedex, France |
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Abstract: | Domain decomposition methods based on one Lagrange multiplier have been shown to be very efficient for solving ill-conditioned problems in parallel. Several variants of these methods have been developed in the last ten years. These variants are based on an augmented Lagrangian formulation involving one or two Lagrange multipliers and on mixed type interface conditions between the sub-domains. In this paper, the Lagrangian formulations of some of these domain decomposition methods are presented both from a continuous and a discrete point of view. |
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Keywords: | Domain decomposition Lagrange multipliers Saddle point problem Augmented Lagrangian Interface conditions |
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