A Two Level Domain Decomposition Preconditionner Based on Local Dirichlet to Neumann Maps

Frédéric Nataf (1) , Hua Xiang (1, 2) , Victorita Dolean (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 School of Mathematics and Statistics [Wuhan]
3 JAD - Laboratoire Jean Alexandre Dieudonné

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. In this work we construct the coarse grid space using the low frequency modes of the subdomain DtN (Dirichlet-Neumann) maps, and apply the obtained two-level preconditioner to the linear system arising from an overlapping domain decomposition. Our method is suitable for the parallel implementation and its efficiency is demonstrated by numerical examples on problems with high heterogeneities.

Domaines: Analyse numérique [math.NA]

Frédéric Nataf, Hua Xiang, Victorita Dolean. A Two Level Domain Decomposition Preconditionner Based on Local Dirichlet to Neumann Maps. 2010. ⟨hal-00526550⟩