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Comparison of the Dirichlet-Neumann and Optimal Schwarz Method on the Sphere

  • J. Côté
  • M. J. Gander
  • L. Laayouni
  • S. Loisel
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)

Summary

We investigate the performance of domain decomposition methods for solving the Poisson equation on the surface of the sphere. This equation arises in a global weather model as a consequence of an implicit time discretization.We consider two different types of algorithms: the Dirichlet-Neumann algorithm and the optimal Schwarz method. We show that both algorithms applied to a simple two subdomain decomposition of the surface of the sphere converge in two iterations. While the Dirichlet-Neumann algorithm achieves this with local transmission conditions, the optimal Schwarz algorithm needs non-local transmission conditions. This seems to be a disadvantage of the optimal Schwarz method. We then show however that for more than two subdomains or overlapping subdomains, both the optimal Schwarz algorithm and the Dirichlet Neumann algorithm need non-local interface conditions to converge in a finite number of steps. Hence the apparent advantage of Dirichlet-Neumann over optimal Schwarz is only an artifact of the special two subdomain decomposition.

Keywords

Poisson Equation Relaxation Parameter Transmission Condition Domain Decomposition Method Jacobi Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J. Côté
    • 1
  • M. J. Gander
    • 2
  • L. Laayouni
    • 2
  • S. Loisel
    • 2
  1. 1.Recherche en prévision numériqueMeteorological Service of CanadaCanada
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontreal

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