A robust two-level domain decomposition preconditioner for systems of PDEs

Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, Robert Scheichl

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.

Original languageEnglish
Pages (from-to)1255-1259
Number of pages5
JournalComptes Rendus Mathematique
Issue number23-24
Early online date9 Nov 2011
Publication statusPublished - 31 Dec 2011


  • domain decomposition methods
  • coarse spaces
  • partial differential equations

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