Two-scale Dirichlet-Neumann Preconditioners for Boundary Refinements

Patrice Hauret (1) , Patrick Le Tallec (2)

1 Manufacture Française des Pneumatiques Michelin
2 LMS - Laboratoire de mécanique des solides

The present work introduces simple Dirichlet-Neumann preconditioners for the solution of elasticity problems in presence of numerous small disjoint geometric refinements on the boundary of the domain, situation which typically occurs in the tire industry. Moreover, the condition number of the preconditioned system is proved to be independent of the number and the size of the small details on the boundary. Finally, as an enhancement, a second proposed preconditioner makes use of a coarse space counterbalancing the effect of essential boundary conditions on the small details, and a simple numerical academic test illustrates the increased ef- ficiency. Further details on the motivation as well as complete proofs can be found in [4, 5].

Domaines: Mécanique [physics.med-ph]

Patrice Hauret, Patrick Le Tallec. Two-scale Dirichlet-Neumann Preconditioners for Boundary Refinements. Domain Decomposition Methods in Science and Engineering XVI, 55, pp.447-454, 2007, Lecture Notes in Computational Science and Engineering, 9783540344681. ⟨10.1007/978-3-540-34469-8_56⟩. ⟨hal-00111504⟩