Optimized Schwarz Method for Poisson’s Equation in Rectangular Domains

  • José C. GarayEmail author
  • Frédéric MagoulèsEmail author
  • Daniel B. SzyldEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


An analysis of the convergence properties of Optimized Schwarz methods applied as solvers for Poisson’s Equation in a bounded rectangular domain with Dirichlet (physical) boundary conditions and Robin transmission conditions on the artificial boundaries is presented. To our knowledge this is the first time that this is done for multiple subdomains forming a 2D array in a bounded domain.



The author J. C. Garay was supported in part by the U.S. Department of Energy under grant DE-SC0016578. The author D. B. Szyld was supported in part by the U.S. National Science Foundation under grant DMS-1418882 and the U.S. Department of Energy under grant DE-SC0016578.


  1. 1.
    D. Bennequin, M.J. Gander, L. Gouarin, L. Halpern, Optimized Schwarz waveform relaxation for advection reaction diffusion equations in two dimensions. Numer. Math. 134, 513–567 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    V. Dolean, P. Jolivet, F. Nataf, An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation (SIAM, Philadelphia, 2015)CrossRefGoogle Scholar
  3. 3.
    M.J. Gander, Optimized Schwarz methods. SIAM J. Numer. Anal. 44, 699–731 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 4th edn. (Prentice Hall, Englewood Cliffs, 2003)Google Scholar
  5. 5.
    F. Magoulés, A.-K.C. Ahamed, R. Putanowicz, Optimized Schwarz method without overlap for the gravitational potential equation on cluster of graphics processing unit. Int. J. Comput. Math. 93, 955–980 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Temple UniversityPhiladelphiaUSA
  2. 2.CentraleSupélecChâtenay-MalabryFrance

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