Non-overlapping domain decomposition methods in structural mechanics

Pierre Gosselet (1) , Christian Rey (1)

1 LMT - Laboratoire de Mécanique et Technologie

The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family of large ill-conditioned linear systems. In this paper we study strategies to efficiently solve to linear system based on non-overlapping domain decomposition methods. We present a review of most employed approaches and their strong connections. We outline their mechanical interpretations as well as the practical issues when willing to implement and use them. Numerical properties are illustrated by various assessments from academic to industrial problems. An hybrid approach, mainly designed for multifield problems, is also introduced as it provides a general framework of such approaches.

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Pierre Gosselet, Christian Rey. Non-overlapping domain decomposition methods in structural mechanics. Archives of Computational Methods in Engineering, 2007, 13 (4), pp.515-572. ⟨10.1007/BF02905857⟩. ⟨hal-00277626v2⟩