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An accelerated domain decomposition procedure based on robin transmission conditions

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.

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References

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Douglas, J., Huang, C.S. An accelerated domain decomposition procedure based on robin transmission conditions. Bit Numer Math 37, 678–686 (1997). https://doi.org/10.1007/BF02510246

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  • DOI: https://doi.org/10.1007/BF02510246

AMS subject classification

  • 65N55

Key words

  • Domain decomposition
  • elliptic boundary problem
  • Robin transmission condition
  • acceleration of convergence