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BIT Numerical Mathematics

, Volume 37, Issue 3, pp 678–686 | Cite as

An accelerated domain decomposition procedure based on robin transmission conditions

  • J. Douglas
  • C. -S. Huang
Article

Abstract

A domain decomposition procedure based on Robin transmission conditions applicable to elliptic boundary problems was first introduced by P. L. Lions and later discussed by a number of authors. In all of these discussions, the weighting of the flux and the trace of the solution were independent of the iterative step number. For some model problems we introduce a cycle of weights and prove that an acceleration of the convergence rate similar to that occurring for alternating-direction iteration using a cycle of pseudo-time steps results. In some discrete cases, the cycle length can be taken to be independent of the mesh spacing.

AMS subject classification

65N55 

Key words

Domain decomposition elliptic boundary problem Robin transmission condition acceleration of convergence 

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References

  1. 1.
    B. DesprésMéthodes de décomposition de domaines pour les problèmes de propagation d'ondes en régime harmonique. Ph.D. thesis, Université Paris IX Dauphine, UER Mathématiques de la Décision, 1991.Google Scholar
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    J. Douglas, Jr., P. J. Paes Leme, J. E. Roberts, and J. Wang,A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods, Numer. Math., 65 (1993), pp. 95–108.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    P. L. Lions.On the Schwarz alternating method III: a variant for nonoverlapping subdomains, in Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., pp. 202–223, SIAM, Philadelphia, PA, 1990.Google Scholar

Copyright information

© BIT Foundation 1997

Authors and Affiliations

  • J. Douglas
    • 1
  • C. -S. Huang
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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