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2014 | 12 | 10 | 1602-1614
Tytuł artykułu

The behavior of domain decomposition methods when the overlapping length is large

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
10
Strony
1602-1614
Opis fizyczny
Daty
wydano
2014-10-01
online
2014-06-21
Twórcy
Bibliografia
  • [1] R. A. Adams. Sobolev Spaces. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65.
  • [2] D. Bennequin, M. J. Gander, and L. Halpern. A homographic best approximation problem with application to optimized Schwarz waveform relaxation. Math. Comp., 78(265):185–223, 2009. http://dx.doi.org/10.1090/S0025-5718-08-02145-5
  • [3] Filipa Caetano, Martin J. Gander, Laurence Halpern, and Jérémie Szeftel. Schwarz waveform relaxation algorithms with nonlinear transmission conditions for reaction-diffusion equations. In Domain decomposition methods in science and engineering XIX, volume 78 of Lect. Notes Comput. Sci. Eng., pages 245–252. Springer, Heidelberg, 2011.
  • [4] L. C. Evans. Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998.
  • [5] M. J. Gander. A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations. Numer. Linear Algebra Appl., 6(2):125–145, 1999. Czech-US Workshop in Iterative Methods and Parallel Computing, Part 2 (Milovy, 1997). http://dx.doi.org/10.1002/(SICI)1099-1506(199903)6:2<125::AID-NLA152>3.0.CO;2-4
  • [6] M. J. Gander and L. Halpern. Optimized Schwarz waveform relaxation methods for advection reaction diffusion problems. SIAM J. Numer. Anal., 45(2):666–697 (electronic), 2007. http://dx.doi.org/10.1137/050642137
  • [7] M. J. Gander, L. Halpern, and F. Nataf. Optimal convergence for overlapping and non-overlapping Schwarz waveform relaxation. In Eleventh International Conference on Domain Decomposition Methods (London, 1998), pages 27–36 (electronic). DDM.org, Augsburg, 1999.
  • [8] M. J. Gander, L. Halpern, and F. Nataf. Optimized Schwarz methods. In Domain decomposition methods in sciences and engineering (Chiba, 1999), pages 15–27 (electronic). DDM.org, Augsburg, 2001.
  • [9] Martin J. Gander. Optimized Schwarz methods. SIAM J. Numer. Anal., 44(2):699–731 (electronic), 2006. http://dx.doi.org/10.1137/S0036142903425409
  • [10] L. Halpern and J. Szeftel. Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation. Math. Comp., 78(266):865–889, 2009. http://dx.doi.org/10.1090/S0025-5718-08-02164-9
  • [11] Jung-Han Kimn. A convergence theory for an overlapping Schwarz algorithm using discontinuous iterates. Numer. Math., 100(1):117–139, 2005. http://dx.doi.org/10.1007/s00211-004-0572-3
  • [12] P.-L. Lions. On the Schwarz alternating method. I. In First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), pages 1–42. SIAM, Philadelphia, PA, 1988.
  • [13] P.-L. Lions. On the Schwarz alternating method. II. Stochastic interpretation and order properties. In Domain decomposition methods (Los Angeles, CA, 1988), pages 47–70. SIAM, Philadelphia, PA, 1989.
  • [14] P.-L. Lions. On the Schwarz alternating method. III. A variant for nonoverlapping subdomains. In Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (Houston, TX, 1989), pages 202–223. SIAM, Philadelphia, PA, 1990.
  • [15] Sébastien Loisel and Daniel B. Szyld. On the geometric convergence of optimized Schwarz methods with applications to elliptic problems. Numer. Math., 114(4):697–728, 2010. http://dx.doi.org/10.1007/s00211-009-0261-3
  • [16] S. Mizohata. The theory of partial differential equations. Cambridge University Press, New York, 1973. Translated from the Japanese by Katsumi Miyahara.
  • [17] E. Zeidler. Nonlinear functional analysis and its applications. II/B. Springer-Verlag, New York, 1990. Nonlinear monotone operators, Translated from the German by the author and Leo F. Boron. http://dx.doi.org/10.1007/978-1-4612-0981-2
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0431-0
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