- Volume 18 Issue 1
DOI QR Code
ADVANCED DOMAIN DECOMPOSITION METHOD BY LOCAL AND MIXED LAGRANGE MULTIPLIERS
- Kwak, Junyoung (DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING, SEOUL NATIONAL UNIVERSITY) ;
- Chun, Taeyoung (LIGNEX1) ;
- Cho, Haeseong (DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING, SEOUL NATIONAL UNIVERSITY) ;
- Shin, Sangjoon (DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING, SEOUL NATIONAL UNIVERSITY) ;
- Bauchau, Olivier A. (DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF MICHIGAN-SHANGHAI JIAO TONG UNIVERSITY JOINT INSTITUTE)
- Received : 2013.10.29
- Accepted : 2013.12.17
- Published : 2014.03.25
This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.
Supported by : National Research Foundation of Korea (NRF)
- C. Farhat, F.-X. Roux, A Method of Finite Element Tearing and Interconnecting and Its Parallel Solution Algorithm, International Journal for Numerical Methods in Engineering, 32 (1991), 1205-1227. https://doi.org/10.1002/nme.1620320604
- C. Farhat, J. Mandel, F.-X. Roux, Optimal Convergence Properties of the FETI Domain Decomposition Method, Computer Methods and Applied Mechanics and Engineering, 115 (1994), 367-388.
- C. Farhat, P. S. Chen, J. Mandel, F.-X. Roux, The Two-level FETI Method. Part I: an Optimal Iterative Solver for Biharmonic Systems, Computer Methods and Applied Mechanics and Engineering, 155 (1998), 129-151. https://doi.org/10.1016/S0045-7825(97)00146-1
- C. Farhat, P. S. Chen, J. Mandel, F.-X. Roux, The Two-level FETI Method. Part II: Extension to Shell Problems, Parallel Implementation and Performance Results, Computer Methods and Applied Mechanics and Engineering, 155 (1998), 153-179. https://doi.org/10.1016/S0045-7825(97)00145-X
- C. Farhat, K. Pierson, M. Lesoinne, The Second Generation FETI Methods and their Application to the Parallel Solution of Large-scale Linear and Geometrically Non-linear Structural Analysis Problems, Computer Methods in Applied Mechanics and Engineering, 184 (2000), 333-374. https://doi.org/10.1016/S0045-7825(99)00234-0
- C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, D. Rixen, FETI-DP: a Dual-primal Unified FETI method PartI: A Faster Alternative to the Two-level FETI Method, International Journal for Numerical Methods in Engineering, 50 (2001), 1523-1544. https://doi.org/10.1002/nme.76
- O.A. Bauchau, A. Epple, and C.L. Bottasso, Scaling of constraints and augmented Lagrangian formulations in multibody dynamics simulations, Journal of Computational and Nonlinear Dynamics, 4 (2009), 1-9.
- O.A. Bauchau, Parallel computation approaches for flexible multibody dynamics simulations, Journal of the Franklin Institute, 347(2010), 53-68. https://doi.org/10.1016/j.jfranklin.2009.10.001
- J.Y. Kwak, H.S. Cho, S.J. Shin, and O.A. Bauchau, Development of finite element domain decomposition method using local and mixed lagrange multipliers, Journal of the Computational Structural Engineering Institute of Korea, 25 (2012), 469-476. https://doi.org/10.7734/COSEIK.2012.25.6.469
- J.Y. Kwak, T.Y. Chun, S.J. Shin, and O.A. Bauchau, Domain decomposition approach to flexible multibody dynamics simulation, Computational Mechanics, 53 (2014), 147-158. doi: 10.1007/s00466-013-0898-8 https://doi.org/10.1007/s00466-013-0898-8
- K.C. Park, C.A. Felippa, and U.A. Gumaste, A localized version of the method of Lagrange multipliers and its applications, Computational Mechanics, 24 (2000), 476-490. https://doi.org/10.1007/s004660050007
- K.J. Bathe, Finite Element Procedures, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1996.