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A course space construction based on local Dirichlet-to-Neumann maps

Nataf, Frédéric and Xiang, Hua and Dolean Maini, Victorita and Spillane, Nicole (2011) A course space construction based on local Dirichlet-to-Neumann maps. SIAM Journal on Scientific Computing, 33 (4). pp. 1623-1642. ISSN 1064-8275

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    Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings.