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A two level domain decomposition preconditioner based on local Dirichlet-to-Neumann maps. (English. Abridged French version) Zbl 1206.35092
Summary: Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. In this Note 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.

MSC:
35J25 Boundary value problems for second-order elliptic equations
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
Software:
METIS
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