Optimized Schwarz Methods for Elliptic Optimal Control Problems

  • Bérangère Delourme
  • Laurence Halpern
  • Binh Thanh Nguyen
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


The present paper deals with the design of optimized Robin-Schwarz methods for the algorithm of optimal control proposed in Benamou (SIAM J Numer Anal 33(6):2401–2416, 1996). In both overlapping and non-overlapping cases, a full analysis of the problem is provided, and is illustrated with numerical tests.


  1. 1.
    J.-D. Benamou, A domain decomposition method with coupled transmission conditions for the optimal control of systems governed by elliptic partial differential equations. SIAM J. Numer. Anal. 33(6), 2401–2416 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    J.-D. Benamou, B. Després, A domain decomposition method for the Helmholtz equation and related optimal control problems. J. Comput. Phys. 136(1), 68–82 (1997)MathSciNetCrossRefGoogle Scholar
  3. 3.
    D. Bennequin, M.J. Gander, L. Halpern, A homographic best approximation problem with application to optimized Schwarz waveform relaxation. Math. Comput. 78(265), 185–223 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    D. Bennequin, M.J. Gander, L. Gouarin, L. Halpern, Optimized Schwarz waveform relaxation for advection reaction diffusion equations in two dimensions. Numer. Math. 134(3), 513–567 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    B. Delourme, L. Halpern, Optimized Schwarz method for control problems (in preparation)Google Scholar
  6. 6.
    M.J. Gander, Optimized Schwarz methods. SIAM J. Numer. Anal. 44(2), 699–731 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    M.J. Gander, F. Magoulès, F. Nataf, Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 24(1), 38–60 (2002)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M.J. Gander, L. Halpern, F. Magoulès, An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation. Int. J. Numer. Methods Fluids 55(2), 163–175 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Translated from the French by S.K. Mitter, Die Grundlehren der mathematischen Wissenschaften, Band 170 (Springer, New York, 1971)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Bérangère Delourme
    • 1
  • Laurence Halpern
    • 1
  • Binh Thanh Nguyen
    • 1
  1. 1.University Paris 13VilletaneuseFrance

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