A Coarse Space Construction Based on Local Dirichlet to Neumann Maps

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 maps, and apply the obtained two-level preconditioner (the additive Schwarz method together with the new coarse grid) to the extended or the original 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 for both manual and automatic partitionings