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Absorbing boundary conditions and optimized Schwarz waveform relaxation

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Abstract

We show here how the formalism, introduced by B. Engquist and A. Majda for absorbing boundary conditions, is a powerful tool to produce absorbing boundary layers and Schwarz waveform relaxation algorithms, when coupled with best approximation. The demonstration is given on the advection diffusion equation, but the ideas apply also to hyperbolic problems.

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References

  1. P. D’Anfray, L. Halpern, and J. Ryan, New trends in coupled simulations featuring domain decomposition and metacomputing, M2AN, Math. Model. Numer. Anal., 36 (2002), pp. 953–970.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Bennequin, M. J. Gander, and L. Halpern, Optimized Schwarz Waveform Relaxation methods for convection reaction diffusion problems, technical report 2004-24, LAGA, Université Paris 13, 2004. http://www.math.univ-paris13.fr/prepub/pp2004/pp2004-24.html.

  3. B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31 (1977), pp. 629–651.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. J. Gander, L. Halpern, C. Japhet, and V. Martin, Advection diffusion problems with pure advection approximation in subregions, in Proceedings of the 16th International Conference on Domain Decomposition Methods, New York, January 2005, to appear in Lecture Notes in Computational Science and Engineering, Springer. http://www.ddm.org.

  5. L. Halpern, Artificial boundary conditions for the linear advection diffusion equation, Math. Comp., 46 (1986), pp. 425–438.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Halpern, Optimized sponge layers, optimized Schwarz Waveform Relaxation algorithms for convection-diffusion problems and best approximation, in Proceedings of the 16th International Conference on Domain Decomposition Methods, New York, January 2005, to appear in Lecture Notes in Computational Science and Engineering, Springer. http://www.ddm.org.

  7. L. Halpern and J. Rauch, Absorbing boundary conditions for diffusion equations, Numer. Math., 71 (1995), pp. 185–224.

    Article  MATH  MathSciNet  Google Scholar 

  8. V. Martin, Méthodes de décomposition de domaines de type relaxation d’ondes pour des équations de l’océanographie, Thése Université Paris 13, Décembre 2003.

  9. V. Martin, An optimized Schwarz Waveform Relaxation method for the unsteady convection diffusion equation in two dimensions, Appl. Numer. Math., 52 (2005), pp. 401–428.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LAGA-Institut Galilée, Université Paris 13, Avenue J. B. Clément, 93430, Villetaneuse, France

    L. Halpern

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  1. L. Halpern
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Correspondence to L. Halpern.

Additional information

Dedicated to Björn Engquist on the occasion of his 60th birthday.

AMS subject classification (2000)

65F20

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Halpern, L. Absorbing boundary conditions and optimized Schwarz waveform relaxation . Bit Numer Math 46 (Suppl 1), 21–34 (2006). https://doi.org/10.1007/s10543-006-0090-z

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  • DOI: https://doi.org/10.1007/s10543-006-0090-z

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