Mixed constraint preconditioning in computational contact mechanics

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 45-48, 2008, Pages 3922-3931

  Ferronato, Massimiliano ^a   Janna, Carlo ^a   Gambolati, Giuseppe ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Contact mechanics; Iterative methods; Penalty formulation; Preconditioning

Indexed keywords

CONJUGATE GRADIENT METHOD; CONTROL THEORY; FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; LAWS AND LEGISLATION; MECHANICS; POROUS MATERIALS; ROBUST CONTROL; SPEED;

3-D PROBLEMS; CONSTRAINT PRECONDITIONER; CONTACT MECHANICS; CONTACT PROBLEMS; CONTACT SURFACES; EIGENSPECTRUM; FINITE ELEMENTS; GEOMECHANICS; GLOBAL DOMAINS; INCOMPLETE CHOLESKY DECOMPOSITION; ITERATIVE METHODS; ITERATIVE SOLUTIONS; NUMERICA L RESULTS; PENALTY FORMULATION; PENALTY FORMULATIONS; PENALTY PARAMETERS; POROUS MEDIUMS; POSITIVE DEFINITE; PRECONDITIONED CONJUGATE GRADIENT; PRECONDITIONED MATRIX; PRECONDITIONER; PRECONDITIONERS; PRECONDITIONING; TEST CASES;

IMAGE STORAGE TUBES;

EID: 50049116600     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.03.008     Document Type: Article

References (42)

1. Wriggers P., and Zavarise G. Computational contact mechanics. In: Stein E., de Borst R., and Hughes T.J.R. (Eds). Encyclopedia of Computational Mechanics vol. 2 (2004), John Wiley & Sons 195-226
2. Saad Y., and van der Vorst H.A. Iterative solution of linear systems in the 20th century. J. Comput. Appl. Math. 123 (2000) 1-33
3. Dickinson J.K., and Forsyth P.A. Preconditioned conjugate gradient methods for three-dimensional linear elasticity. Int. J. Numer. Methods Engrg. 37 (1994) 2211-2234
4. Hladik I., Reed M.B., and Swoboda G. Robust preconditioners for linear elasticity FEM analyses. Int. J. Numer. Methods Engrg. 40 (1997) 2109-2127
5. Graham E., and Forsyth P.A. Preconditioning methods for very ill-conditioned three-dimensional linear elasticity problems. Int. J. Numer. Methods Engrg. 44 (1999) 77-99
6. C. Janna, A. Comerlati, G. Gambolati, A comparison of projection and direct solvers for finite elements in elastostatics, Adv. Engrg. Software, in press.
7. Chan S.H., Phoon K.K., and Lee F. A modified Jacobi preconditioner for solving ill-conditioned Biot's consolidation equations using symmetric quasi-minimal residual method. Int. J. Numer. Anal. Methods Geomech. 25 (2001) 1001-1025
8. Gambolati G., Pini G., and Ferronato M. Numerical performance of projection methods in finite element consolidation models. Int. J. Numer. Anal. Methods Geomech. 25 (2001) 1429-1447
9. Gambolati G., Pini G., and Ferronato M. Direct, partitioned and projected solution to finite element consolidation models. Int. J. Numer. Anal. Methods Geomech. 26 (2002) 1371-1383
10. Mroueh H., and Shahrour I. Use of sparse iterative methods for the resolution of three-dimensional soil/structure interaction problems. Int. J. Numer. Anal. Methods Geomech. 23 (1999) 1961-1975
11. Saad Y. ILUT: a dual threshold incomplete ILU factorization. Numer. Linear Algebra Appl. 1 (1994) 387-402
12. Saint-George P., Warzee G., Notay Y., and Beauwens R. Problem-dependent preconditioners for iterative solvers in FE elastostatics. Comput. Struct. 73 (1999) 33-43
13. Li N., Saad Y., and Chow E. Crout version of ILU for general sparse matrices. SIAM J. Sci. Comput. 25 (2003) 716-728
14. Benzi M., and Tůma M. A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J. Sci. Comput. 19 (1998) 968-994
15. Benzi M., Cullum J., and Tůma M. Robust approximate inverse preconditioning for the conjugate gradient method. SIAM J. Sci. Comput. 22 (2000) 1318-1332
16. Augarde C.E., Ramage A., and Staudacher J. Element-based preconditioners for elasto-plastic problems in geotechnical engineering. Int. J. Numer. Methods Engrg. 71 (2007) 757-779
17. Dostal Z. On preconditioning and penalized matrices. Numer. Linear Algebra Appl. 6 (1999) 109-114
18. Luksan L., and Vlcek J. Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems. Numer. Linear Algebra Appl. 5 (1998) 219-247
19. Keller C., Gould N.I.M., and Wathen A.J. Constraint preconditioning for indefinite linear systems. SIAM J. Matrix Anal. Appl. 21 (2000) 1300-1317
20. Bergamaschi L., Gondzio J., and Zilli G. Preconditioning indefinite systems in interior point methods for optimization. Comput. Optim. Appl. 28 (2004) 149-171
21. Bergamaschi L., Gondzio J., Venturin M., and Zilli G. Inexact constraint preconditioners for linear systems arising in interior point methods. Comput. Optim. Appl. 36 (2007) 137-147
22. Silvester D.J., Elman H.C., Kay D., and Wathen A.J. Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. J. Comput. Appl. Math. 128 (2001) 261-279
23. Elman H.C., Silvester D.J., and Wathen A.J. Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations. Numer. Math. 90 (2002) 665-688
24. Toh K.C., Phoon K.K., and Chan S.H. Block preconditioners for symmetric indefinite linear systems. Int. J. Numer. Methods Engrg. 60 (2004) 1361-1381
25. Bergamaschi L., Ferronato M., and Gambolati G. Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations. Comput. Methods Appl. Mech. Engrg. 196 (2007) 2647-2656
26. L. Bergamaschi, M. Ferronato, G, Gambolati, Mixed constraint preconditioners for the iterative solution of FE coupled consolidation equations, J. Comput. Phys., submitted for publication.
27. Wriggers P. Contact Mechanics (2005), Springer, Berlin
28. Bertsekas D.P. Constrained Optimization and Lagrange Multiplier Methods (1984), Academic Press, New York
29. Avery P., Rebel G., Lesoinne M., and Farhat C. A numerically scalable dual-primal substructuring method for the solution of contact problems. I: the frictionless case. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2403-2426
30. Dostal Z., Gomes F.A.M., and Santos S.A. Solution of contact problems by FETI domain decomposition with natural coarse space projection. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1611-1627
31. Dostal Z. Inexact semi-monotonic augmented Lagrangians with optimal feasibility convergence for quadratic programming with simple bounds and equality constraints. SIAM J. Numer. Anal. 45 (2007) 500-513
32. Luenberger D.G. Linear and Nonlinear Programming. second ed. (1984), Addison-Wesley, Reading, MA
33. Simo J.C., and Laursen T.A. An augmented Lagrangian treatment of contact problems involving friction. Comput. Struct. 42 (1992) 97-116
34. Zavarise G., and Wriggers P. A superlinear convergent augmented Lagrangian procedure for contact problems. Engrg. Comput. 16 (1999) 88-119
35. Durazzi C., and Ruggiero V. Indefinitely preconditioned conjugate gradient method for large sparse equality and inequality constrained quadratic problems. Numer. Linear Algebra Appl. 10 (2003) 673-688
36. Bängtsson E., and Neytcheva M. Numerical simulations of glacial rebound using preconditioned iterative solution methods. Appl. Math. 50 (2005) 183-201
37. Kraus J. Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Numer. Linear Algebra Appl. 13 (2006) 49-70
38. Benzi M., Golub G., and Liesen J. Numerical solution of saddle point problems. Acta Numer. 14 (2005) 1-137
39. Axelsson O., and Neytcheva M. Eigenvalue estimates for preconditioned saddle point matrices. Numer. Linear Algebra Appl. 13 (2006) 339-360
40. Ferronato M., Gambolati G., Janna C., and Teatini P. Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs. Int. J. Numer. Anal. Methods Geomech. 32 (2008) 633-657
41. Dongarra J.J., Duff I.S., Sorensen D.C., and van der Vorst H.A. Numerical Linear Algebra for High-performance Computers (1998), SIAM, Philadelphia (PA)
42. HSL. Harwell Subroutine Library Archive, Aea Technology, Engineering Software, CCLRC, 2004. .