An Adaptive Coarse Space for P.L. Lions Algorithm and Optimized Schwarz Methods

  • Ryadh Haferssas
  • Pierre Jolivet
  • Frédéric NatafEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 116)


Optimized Schwarz methods (OSM) are very popular methods which were introduced in Lions (On the Schwarz alternating method. III: a variant for nonoverlapping subdomains. In: Chan TF, Glowinski R, Périaux J, Widlund O (eds) Third international symposium on domain decomposition methods for partial differential equations, Houston, TX, March 20–22, 1989. SIAM, Philadelphia, PA, 1990) for elliptic problems and in Després (C R Acad Sci Paris 1(6):313–316, 1990) for propagative wave phenomena. We build here a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm (St-Cyr et al., SIAM J Sci Comput 29(6):2402–2425 (electronic), 2007) and by identifying the problematic modes using two different generalized eigenvalue problems instead of only one as in Spillane et al. (C R Math Acad Sci Paris 351(5–6):197–201, 2013) and Spillane et al. (Numer Math 126(4):741–770, 2014) for the ASM (Additive Schwarz method), BDD [balancing domain decomposition (Mandel, Comm Appl Numer Methods 9:233–241, 1992)] or FETI [finite element tearing and interconnection (Farhat and Roux, Int J Numer Meth Eng 32:1205–1227, 1991)] methods.


Domain Decomposition Domain Decomposition Method Saddle Point Problem Generalize Eigenvalue Problem Finite Element Space 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ryadh Haferssas
    • 1
  • Pierre Jolivet
    • 2
  • Frédéric Nataf
    • 1
    Email author
  1. 1.Laboratoire Jacques-Louis LionsParisFrance
  2. 2.Toulouse Institute of Computer Science ResearchToulouseFrance

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