The mosaic of high performance domain Decomposition Methods for Structural Mechanics: Formulation, interrelation and numerical efficiency of primal and dual methods

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 35-36, 2003, Pages 3799-3830

  Fragakis, Yannis ^a   Papadrakakis, Manolis ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS;

DOMAIN DECOMPOSITION METHOD (DDM);

MECHANICS;

STRUCTURAL ANALYSIS;

EID: 0042424804     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00374-8     Document Type: Article

References (26)

1. Farhat C. Roux F.-X. A method of finite element and interconnecting and its parallel solution algorithm Int. J. Numer. Meth. Engrg. 32 1991 1205-1227
2. Mandel J. Balancing domain decomposition Commun. Appl. Numer. Meth. 9 1993 233-241
3. Y. Fragakis, M. Papadrakakis, A unified framework for formulating domain decomposition methods in structural mechanics, Technical Report, National Technical University of Athens, Greece, March 2002. Available from
4. Y. Fragakis, M. Papadrakakis, A family of new FETI methods for structural mechanics, in: Proceedings of the Fifth World Congress on Computational Mechanics (WCCMV), Vienna, Austria, July 7-12, 2002. Available from
5. Farhat C. Roux F.-X. Implicit parallel processing in structural mechanics Comput. Mech. Adv. 2 1994 1-124
6. Park K.C. Justino M.R.Jr. Felippa C.A. An algebraically partitioned FETI method for parallel structural analysis: Algorithm description Int. J. Numer. Meth. Engrg. 40 1997 2717-2737
7. Justino M.R.Jr. Park K.C. Felippa C.A. An algebraically partitioned FETI method for parallel structural analysis: Implementation and numerical performance evaluation Int. J. Numer. Meth. Engrg. 40 1997 2739-2758
8. Rixen D. Farhat C. Tezaur R. Mandel J. Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver Int. J. Numer. Meth. Engrg. 46 1999 501-534
9. Rixen D. Farhat C. A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems Int. J. Numer. Meth. Engrg. 44 4 1999 489-516
10. Bhardwaj M. Day D. Farhat C. Lesoinne M. Pierson K. Rixen D. Application of the FETI method to ASCI problems: Scalability results on one-thousand processors and discussion of highly heterogeneous problems Int. J. Numer. Meth. Engrg. 47 2000 513-536
11. Klawonn A. Widlund O.B. FETI and Neumann-Neumann iterative substructuring methods: Connection and new results Commun. Pure Appl. Math. 54 2001 57-90
12. LeTallec P. Vidrascu M. Solving large scale structural problems on parallel computers using domain decomposition techniques Papadrakakis M. Parallel Solution Methods in Computational Mechanics 1997 John Wiley - Sons New York
13. Bitzarakis S. Papadrakakis M. Kotsopoulos A. Parallel solution techniques in computational structural mechanics Comput. Methods Appl. Mech. Engrg. 148 1997 75-104
14. Farhat C. Mandel J. The two-level FETI method for static and dynamic plate problems-part I: An optimal iterative solver for biharmonic systems Comput. Methods Appl. Mech. Engrg. 155 1998 129-152
15. Farhat C. Chen P.S. Mandel J. Roux F.X. The two-level FETI method-part II: Extension to shell problems, parallel implementation and performance results Comput. Methods Appl. Mech. Engrg. 155 1998 153-180
16. Farhat C. Lesoinne M. LeTallec P. Pierson K. Rixen D. FETI-DP: A dual-primal unified FETI method-part I: A faster alternative to the two-level FETI method Int. J. Numer. Meth. Engrg. 50 2001 1523-1544
17. Farhat C. Lesoinne M. Pierson K. A scalable dual-primal domain decomposition method Numer. Linear Alg. Appl. 7 7-8 2000 687-714
18. Farhat C. Pierson K. Lesoinne M. The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems Comput. Methods Appl. Mech. Engrg. 184 2000 333-374
19. Charmpis D.C. Papadrakakis M. Enhancing the performance of the FETI method with preconditioning techniques implemented on clusters of networked computers Comput. Mech. 30 2002 12-28
20. Farhat C. Mandel J. Roux F.-X. Optimal convergence properties of the FETI domain decomposition method Comput. Methods Appl. Mech. Engrg. 115 1994 365-385
21. Farhat C. Chen P.-S. Risler F. Roux F.X. A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers Int. J. Numer. Meth. Engrg. 42 1998 257-288
22. LeTallec P. Mandel J. Vidrascu M. A Neumann-Neumann domain decomposition algorithm for solving plate and shell problems SIAM J. Numer. Anal. 35 1998 836-867
23. Papadrakakis M. Fragakis Y. An integrated geometric-algebraic method for solving semi-definite problems in structural mechanics Comput. Methods Appl. Mech. Engrg. 190 49-50 2001 6513-6532
24. M. Sharp, C. Farhat, TOPDOMDEC-A totally object oriented program for visualization, domain decomposition and parallel processing, User's manual, PGSoft and University of Colorado, Boulder, USA, 1994
25. Argyris J. Tenek L. Papadrakakis M. Apostolopoulou C. Postbuckling performance of the TRIC natural mode triangular shell element for isotropic and laminated composite shells Comput. Methods Appl. Mech. Engrg. 166 1998 211-231
26. D. Rixen, Choosing the coarse grid when applying FETI to heterogeneous structures, Presentation at the 13th International Conference on Domain Decomposition Methods, Lyon, France, October 9-12, 2000