Advertisement

On Optimal Coarse Spaces for Domain Decomposition and Their Approximation

  • Martin J. GanderEmail author
  • Laurence HalpernEmail author
  • Kévin Santugini-RepiquetEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)

Abstract

We consider a general second order elliptic model problem.

References

  1. 1.
    F. Chaouqui, M.J. Gander, K. Santugini-Repiquet, On nilpotent subdomain iterations. Domain Decomposition Methods in Science and Engineering XXIII (Springer, Berlin, 2016)Google Scholar
  2. 2.
    V. Dolean, F. Nataf, R. Scheichl, N. Spillane, Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps. Comput. Methods Appl. Math. 12(4), 391–414 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    J. Galvis, Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media. Multiscale Model. Simul. 8(4), 1461–1483 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Galvis, Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high contrast media: reduced dimension coarse spaces. Multiscale Model. Simul. 8(5), 1621–1644 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    M.J. Gander, Optimized Schwarz methods. SIAM J. Numer. Anal. 44(2), 699–731 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    M. Gander, L. Halpern, Méthode de décomposition de domaine. Encyclopédie électronique pour les ingénieurs (2012)Google Scholar
  7. 7.
    M.J. Gander, F. Kwok, Optimal interface conditions for an arbitrary decomposition into subdomains, in Domain Decomposition Methods in Science and Engineering XIX (Springer, Berlin, 2011), pp. 101–108CrossRefGoogle Scholar
  8. 8.
    M.J. Gander, A. Loneland, SHEM: an optimal coarse space for RAS and its multiscale approximation. Domain Decomposition Methods in Science and Engineering XXIII (Springer, Berlin, 2016), pp. 313–321Google Scholar
  9. 9.
    M.J. Gander, L. Halpern, K. Santugini-Repiquet, Discontinuous coarse spaces for DD-methods with discontinuous iterates, in Domain Decomposition Methods in Science and Engineering XXI (Springer, Berlin, 2014), pp. 607–615zbMATHGoogle Scholar
  10. 10.
    M.J. Gander, L. Halpern, K. Santugini-Repiquet, A new coarse grid correction for RAS/AS, in Domain Decomposition Methods in Science and Engineering XXI (Springer, Berlin, 2014), pp. 275–283zbMATHGoogle Scholar
  11. 11.
    M.J. Gander, A. Loneland, T. Rahman, Analysis of a new harmonically enriched multiscale coarse space for domain decomposition methods. arXiv:1512.05285 (preprint, 2015)Google Scholar
  12. 12.
    A. Heinlein, A. Klawonn, J. Knepper, O. Rheinbach, Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2d. Electron. Trans. Numer. Anal. 48, 156–182 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    R. Scheichl, Robust coarsening in multiscale PDEs, in Domain Decomposition Methods in Science and Engineering XX, ed. by R. Bank, M. Holst, O. Widlund, J. Xu. Lecture Notes in Computational Science and Engineering, vol. 91 (Springer, Berlin, 2013), pp. 51–62Google Scholar
  14. 14.
    N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein, R. Scheichl, Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps. Numer. Math. 126(4), 741–770 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Geneva, Section of MathematicsGenevaSwitzerland
  2. 2.LAGAUniversité Paris 13VilletaneuseFrance
  3. 3.Bordeaux INP, IMBTalenceFrance

Personalised recommendations