Abstract
A non-overlapping domain decomposition method based on augmented Lagrangian with a penalty term was introduced in the previous works by the authors [6, 7], which is a variant of the FETI-DP method. In this paper we present a further study focusing on the case of small penalty parameters in terms of condition number estimate and practical efficiency. The full analysis of the proposed method can be found in [8].
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References
I. Babuška, The finite element method with penalty. Math. Comput. 27, 221–228 (1973)
E. Burman, P. Zunino, A domain decomposition method based on weighted interior penalties for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 44, 1612–1638 (2006)
C. Farhat, F.-X. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Methods Eng. 32, 1205–1227 (1991)
C. Farhat, M. Lesoinne, K. Pierson, A scalable dual-primal domain decomposition method. Numer. Linear Algebra Appl. 7, 687–714 (2000)
R. Glowinski, P. Le Tallec, Augmented Lagrangian interpretation of the nonoverlapping Schwarz alternating method, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (Houston, TX, 1989) (SIAM, Philadelphia, 1990), pp. 224–231
C.-O. Lee, E.-H. Park, A dual iterative substructuring method with a penalty term. Numer. Math. 112, 89–113 (2009)
C.-O. Lee, E.-H. Park, A dual iterative substructuring method with a penalty term in three dimensions. Comput. Math. Appl. 64, 2787–2805 (2012)
C.-O. Lee, E.-H. Park, A dual iterative substructuring method with a small penalty parameter. Submitted (2013)
J. Mandel, R. Tezaur, On the convergence of a dual-primal substructuring method. Numer. Math. 88, 543–558 (2001)
Acknowledgement
The work of the first author was supported by NRF-2011-0015399. The second author was supported in part by Korea Research Council of Fundamental Science and Technology (KRCF) research fellowship for young scientists.
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Lee, CO., Park, EH. (2016). A Domain Decomposition Method Based on Augmented Lagrangian with an Optimized Penalty Parameter. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_58
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DOI: https://doi.org/10.1007/978-3-319-18827-0_58
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