Improved finite element domain decomposition method using local and mixed Lagrange multipliers

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Volumn , Issue , 2013, Pages

  Kwak, JunYoung ^a   Cho, Haeseong ^a   Shin, Sang Joon ^a   Bauchau, Olivier A ^b  

^a Seoul National University   (South Korea)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

AUGMENTED LAGRANGIAN FORMULATIONS; COMPUTATIONAL ALGORITHM; COMPUTATIONAL ROBUSTNESS; DECOMPOSITION METHODS; EFFICIENCY CHARACTERISTIC; FINITE-ELEMENT DOMAINS; IMPROVED CONVERGENCE; PARALLEL COMPUTER;

ALGORITHMS; DOMAIN DECOMPOSITION METHODS; EFFICIENCY; LAGRANGE MULTIPLIERS; NUMERICAL METHODS; STRUCTURAL DYNAMICS;

COMPUTATIONAL EFFICIENCY;

EID: 84880779485     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2013-1611     Document Type: Conference Paper

References (18)

1. K.-J. Bathe., Finite Element Procedures in Engineering Analysis, Prentice Hall, 1996, ISBN 0-13-301458-4.
2. S. Duff, J. K. Reid, "The Multifrontal Solution of Indefinite Sparse Symmetric Linear Equations, " ACM Trans. Math. Software, 1973, pp. 302-325.
3. B.M. Irons, "A Frontal Solution Program for Finite Element Analysis, " International Journal for Numerical Methods in Engineering, Vol. 2, 1970, pp. 5-32.
4. J.H. Kim, S.J. Kim, "Multifrontal Solver Combined with Graph Partitioners, " AIAA Journal, Vol. 37, 1999, pp. 964-970
5. Y. Saad, M.H. Schultz, "A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, " Journal on Scientific and Statistical Computing, Vol. 7, 1986, pp. 856-869.
6. 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, Vol. 32, 1991, pp. 1205-1227.
7. 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, Vol. 155, 1998, pp. 129-151.
8. 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, Vol. 155, 1998, pp. 153-179.
9. C. Farhat, M. Lesoinne, K. Pierson, "A Scalable Dual-primal Domain Decomposition Method, " Numerical Linear Algebra with Applications, Vol. 7, 2000, pp. 687-714.
10. 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, Vol. 50, 2001, pp. 1523-1544.
11. O.A. Bauchau, A. Epple, C.L. Bottasso, Scaling of Constraints and Augmented Lagrangian Formulations in Multibody Dynamics Simulations, Journal of Computational and Nonlinear Dynamics, Vol. 4, 2009.
12. O.A. Bauchau, Parallel Computation Approaches for Flexible Multibody Dynamics Simulations, Journal of the Franklin Institute, Vol. 347, 2010, pp. 53-68.
13. J.Y. Kwak, T.Y. Chun, S.J. Shin, O.A., Bauchau, "Computational Approaches for Large Scale Structural Analysis using Domain Decomposition Technique, " Proceedings of the 52nd Structures, Structural Dynamics, and Materials Conference, Denver, CO, April 4-7, 2011.
14. K.C. Park, C.A. Felippa, and U.A. Gumaste, "A localized version of the method of Lagrange multipliers and its applications, " Computational Mechanics, Vol. 24, 2000, pp. 476-490.
15. C. Farhat, J. Mandel, F.-X. Roux, "Optimal Convergence Properties of the FETI Domain Decomposition Method, " Computer Methods and Applied Mechanics and Engineering, Vol. 115, 1994, pp. 367-388.
16. M. Fortin, R. Glowinski, "Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, " North-Holland, Amsterdam, The Netherlands, 1983.
17. P. Gill, W. Murray, M. Saunders, "Sequential Quadratic Programming Methods for Nonlinear Programming, " Computer Methods in Applied Mechanics and Engineering, Vol. 71, 1988, pp. 183-195.
18. 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, Vol. 184, 2000, pp. 333-374