Duality-based domain decomposition with natural coarse-space for variational inequalities

Journal of Computational and Applied Mathematics

Volumn 126, Issue 1-2, 2000, Pages 397-415

  Dostál, Zdeněk ^a   Gomes Neto, Francisco A M ^b   Santos, Sandra A ^b  

^a VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONSTRAINT THEORY; PARALLEL ALGORITHMS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

DUALITY-BASED DOMAIN DECOMPOSITION; NATURAL COARSE SUBSPACES; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

EID: 0034503705     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00368-4     Document Type: Article

References (30)

1. O. Axelsson, A class of iterative methods for finite element equations, Comput. Methods Appl. Mech. Eng. 9 (1976) 127-137.
2. O. Axelsson, Iterative Solution Methods, Cambridge Univ. Press, Cambridge, 1995.
3. O. Axelsson, V.A. Barker, Finite Element Solution of Boundary Value Problems, Academic Press, London, 1984.
4. R.H. Bielschowsky, A. Friedlander, F.A.M. Gomes, J.M. Martínez, M. Raydan, An adaptive algorithm for bound constrained quadratic minimization, Investigación Operativa 7 (1,2) (1997) 67-102.
5. F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991.
6. A.R. Conn, N.I.M. Gould, Ph.L. Toint, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal. 28 (1991) 545-572.
7. Z. Dostál, Conjugate gradient method with preconditioning by projector, Int. J. Comput. Math. 23 (1988) 315-324.
8. Z. Dostál, Duality based domain decomposition with inexact subproblem solver for contact problems, in: M.H. Alibiadi, C. Alessandri (Eds.), Contact Mechanics II, Wessex Inst. of Technology, Southampton, 1995, pp. 461-468.
9. Z. Dostál, Duality based domain decomposition with proportioning for the solution of free boundary problems, J. Comput. Appl. Math. 63 (1995) 203-208.
10. Z. Dostál, Box constrained quadratic programming with proportioning and projections, SIAM J. Optim. 7 (1997) 871-887.
11. Z. Dostál, On preconditioning and penalized matrices, Numer. Linear Algebra with Appl. 6 (1999) 109-114.
12. Z. Dostál, A. Friedlander, S.A. Santos, Augmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraints, Technical Report RP 74/96, IMECC-UNICAMP, University of Campinas, October 1996.
13. Z. Dostál, A. Friedlander, S.A. Santos, Solution of coercive and semicoercive contact problems by FETI domain decomposition, Contemp. Math. 218 (1998) 82-93.
14. Z. Dostál, A. Friedlander, S.A. Santos, Augmented Lagrangians with adaptive precision control for quadratic programming with equality constraints, Comput. Optim. Appl. 14 (1) (1999) 1-17.
15. Z. Dostál, V. Vondrák, Duality based solution of contact problems with Coulomb friction, Arch. Mech. 49 (1997) 453-460.
16. G. Duvant, J.L. Lions, Inequalities in Mechanics and Physics, Springer, Berlin, 1976.
17. C. Farhat, P. Chen, F.-X. Roux, The dual Schur complement method with well posed local Neumann problems, SIAM J. Sci. Statist. Comput. 14 (1993) 752-759.
18. C. Farhat, M. Gérardin, On the general solution by a direct method of a large scale singular system of linear equations: application to the analysis of floating structures, Int. J. Numer. Methods Eng. 41 (1997) 675-696.
19. C. Farhat, J. Mandel, F.-X. Roux, Optimal convergence properties of the FETI domain decomposition method, Comput. Methods Appl. Mech. Eng. 115 (1994) 365-385.
20. C. Farhat, F.-X. Roux, An unconventional domain decomposition method for an efficient parallel solution of large-scale finite element systems, SIAM J. Sci. Statist. Comput. 13 (1992) 379-396.
21. A. Friedlander, J.M. Martínez, On the maximization of concave quadratic function with box constraints, SIAM J. Optim. 4 (1994) 177-192.
22. A. Friedlander, J.M. Martínez, M. Raydan, A new method for large scale box constrained quadratic minimization problems, Optim. Methods Software 5 (1995) 57-74.
23. A. Friedlander, J.M. Martínez, S.A. Santos, A new trust region algorithm for bound constrained minimization, Appl. Math. Optim. 30 (1994) 235-266.
24. S. Fučík, A. Kufner, Nonlinear Differential Equations, Elsevier, Amsterdam, 1980.
25. R. Glowinski, J.L. Lions, R. Trémolieres, Analyse Numérique des Inéquations Variationnelles, Vols. 1-2, Dunod, Paris, 1976.
26. G.H. Golub, C.F. Van Loan, Matrix Computation, The John Hopkins Univ. Press, Baltimore, 1985.
27. I. Hlaváček, J. Haslinger, J. Nečas, J. Lovíšek, Solution of Variational Inequalities in Mechanics, Springer, Berlin, 1988.
28. N. Kikuchi, J.T. Oden, Contact Problems in Elasticity, SIAM, Philadelphia, 1988.
29. F.-X. Roux, Spectral analysis of interface operator, in: D.E. Keyes et al. (Eds.), Proceedings of the fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1992, pp. 73-90.
30. F.-X. Roux, C. Farhat, Parallel implementation of direct solution strategies for the coarse grid solvers in 2-level FETI method, Contemp. Math. 218 (1998) 158-173.