PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2007 | 17 | 3 | 395-402
Tytuł artykułu

Analysis of patch substructuring methods

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergencerate than both the algebraic and the geometric one. We complement our results by numerical experiments.
Rocznik
Tom
17
Numer
3
Strony
395-402
Opis fizyczny
Daty
wydano
2007
Twórcy
  • Section de Mathématiques, Université de Genève, 1211 Genève, Switzerland
  • LAGA, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France
  • Applied Mathematics and Systems Laboratory, Ecole Centrale Paris, 92295 Châtenay-Malabry Cedex, France
  • High Performance Computing Research Unit ONERA, 92322 Chatillon, France
Bibliografia
  • Chevalier P. and Nataf F. (1998): Symmetrized method with optimized second-order conditions for the Helmholtz equation. Contemporary Mathematics, Vol. 218, pp. 400-407.
  • Gander M. J. (2006): Optimized Schwarz methods. SIAM Journal on Numerical Analysis, Vol. 44, No. 2, pp. 699-731.
  • Japhet C. (1998): Optimized Krylov-Ventcell method. Application to convection-diffusion problems. Proceedings of the 9th International Conference Domain Decomposition Methods, Bergen, Norway, pp. 382-389.
  • Le Tallec P. (1994): Domain decomposition methods in computational mechanics, In: Computational Mechanics Advances, (J. Tiney Oden, Ed.). North-Holland, Amsterdam, Vol. 1, No. 2, pp. 121-220.
  • Lions P. -L. (1988): On the Schwarz alternating method. I. Proceedings of the 1st International Symposium Domain Decomposition Methods for Partial Differential Equations, Philadelphia, PA: SIAM, pp. 1-42.
  • Lions P. -L. (1990): On the Schwarz alternating method. III: A variant for nonoverlapping subdomains. Proceedings of the 3rd International Symposium Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, R. Glowinski, J. P'eriaux and O. Widlund (edors), Philadelphia, PA: SIAM, pp. 202-223.
  • Magoulès F., Ivanyi P. and Topping B. H. V. (2004a): Non-overlapping Schwarz methods with optimized transmission conditions for the Helmholtz equation. Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 45-47, pp. 4797-4818.
  • Magoulès F., Roux F. -X. and Salmon S. (2004b): Optimal discrete transmission conditions for a non-overlapping domain decomposition method for the Helmholtz equation. SIAM Journal on Scientific Computing, Vol. 25, No. 5, pp. 1497-1515.
  • Magoulès F., Roux F. -X. and Series L. (2005): Algebraic way to derive absorbing boundary conditions for the Helmholtz equation. Journal of Computational Acoustics, Vol. 13, No. 3, pp. 433-454.
  • Magoulès F., Roux F. -X. and Series L. (2006): Algebraic approximation of Dirichlet-to-Neumann maps for the equations of linear elasticy. Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 29-32, pp. 3742-3759.
  • Quarteroni A. and Valli A. (1999): Domain Decomposition Methods for Partial Differential Equations. Oxford: Oxford University Press.
  • Saad Y. (1996): Iterative Methods for Linear Systems. Boston: PWS Publishing.
  • Schwarz H. (1870): Uber einen Grenzubergang durch alternierendes Verfahren. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, Vol. 15, pp. 272-286.
  • Smith B., Bjorstad P. and Gropp W. (1996): Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge: Cambridge University Press.
  • Toselli A. and Widlund O. B. (2004): Domain Decomposition Methods: Algorithms and Theory. Berlin: Springer
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv17i3p395bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.