Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 5-8, 2011, Pages 850-866

  Kerfriden, P ^a   Gosselet, P ^b   Adhikari, S ^c   Bordas, S P A ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Damage propagation; Hyperreduction; Model order reduction (MOR); Newton Krylov solver; Projected conjugate gradient; Proper orthogonal decomposition (POD)

Indexed keywords

CONJUGATE GRADIENT; DAMAGE PROPAGATION; HYPERREDUCTION; MODEL ORDER REDUCTION (MOR); NEWTON/KRYLOV SOLVER; PROPER ORTHOGONAL DECOMPOSITIONS;

ADAPTIVE ALGORITHMS; CONJUGATE GRADIENT METHOD;

TOPOLOGY;

EID: 78650676597     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.10.009     Document Type: Article

References (30)

1. Lemaître J., Chaboche J.-L. Mechanics of Solid Materials 1990, Cambridge University Press.
2. Lubineau G., Ladevèze P., Marsal D. Towards a bridge between the micro- and mesomechanics of delamination for laminated composites. Compos. Sci. Technol. 2007, 66(6):698-712.
3. Jefferson A.D., Bennett T. A model for cementitious composite materials based on micro-mechanical solutions and damage-contact theory. Comput. Struct. 2009, 10.1016/j.compstruc.2008.09.006.
4. Franceschini G., Bigoni D., Regitnig P., Holzapfel G.A. Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J. Mech. Phys. Solids 2006, 54(12):2592-2620.
5. Moës N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing. Int. J. Engrg. Sci. 1999, 46:131-150.
6. Bordas S., Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures. Engrg. Fract. Mech. 2006, 73(9):1176-1201.
7. Fish J., Shek K., Pandheeradi M., Shephard M.S. Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Comput. Methods Appl. Mech. Engrg. 1997, 148:53-73.
8. 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Comput. Methods Appl. Mech. Engrg. 2000, 183:309-330.
9. Gosselet P., Rey C. Non-overlapping domain decomposition methods in structural mechanics. Arch. Comput. Methods Engrg. 2006, 13:515-572.
10. Ladevèze P., Passieux J.C., Néron D. The latin multiscale computational method and the proper generalized decomposition. Comput. Methods Appl. Mech. Engrg. 2009, 199(21):1287-1296.
11. Karhunen K. Über lineare methoden in der wahrscheinlichkeitsrechnung. Ann. Academiæ Scientiarum Fennicæ Series A1, Math. Phys. 37 1947, 37:1-79.
12. Loeve M. Probability Theory 1963, Van Nostrand, Princeton. third ed.
13. Ladevèze P., Nouy A. On a multiscale computational strategy with time and space homogenization for structural mechanics. Comput. Methods Appl. Mech. Engrg. 2003, 192:3061-3087.
14. Yvonnet J., He Q.C. The reduced model multiscale method (r3m) for the non-linear homogenization of hyperelastic media at finite strains. J. Comput. Phys. 2007, 223(1):341-368.
15. Pebrel J., Rey C., Gosselet P. A nonlinear dual domain decomposition method: application to structural problems with damage. Int. J. Multiscale Comput. Engrg. 2008, 6(3).
16. Kerfriden P., Allix O., Gosselet P. A three-scale domain decomposition method for the 3D analysis of debonding in laminates. Comput. Mech. 2009, 44(3):343-362.
17. Chinesta F., Ammar A., Cueto E. Proper generalized decomposition of multiscale models. Int. J. Numer. Methods Engrg. 2009, 10.1002/nme.2794.
18. Ryckelynck D., Benziane D.M. Multi-level a priori hyper-reduction of mechanical models involving internal variables. Comput. Methods Appl. Mech. Engrg. 2010, 199(17-20):1134-1142.
19. Liang Y.C., Lee H.P., Lim S.P., Lin W.Z., Lee K.H., Wu C.G. Proper orthogonal decomposition and its applications - Part I: Theory. J. Sound Vib. 2002, 252(3):527-544.
20. Sirovich L. Turbulence and the dynamics of coherent structures. Part I: Coherent structures. Q. Appl. Math. 1987, 45:561-571.
21. Niroomandi S., Alfaro I., Cueto E., Chinesta F. Real-time deformable models of non-linear tissues by model reduction techniques. Comput. Methods Programs Biomed. 2008, 91(3):223-231.
22. Ryckelynck D. A priori hyperreduction method: an adaptive approach. J. Comput. Phys. 2005, 202(1):346-366.
23. Ryckelynck D. Hyper-reduction of mechanical models involving internal variables. Int. J. Numer. Methods Engrg. 2008, 77(1):75-89.
24. Markovinovic R., Jansen J.D. Accelerating iterative solution methods using reduced-order models as solution predictors. Int. J. Numer. Methods Engrg. 2006, 68:525-554.
25. Risler F., Rey C. Iterative accelerating algorithms with Krylov subspaces for the solution to large-scale nonlinear problems. Numer. Algorithms 2000, 23:1-30.
26. Allix O., Kerfriden P., Gosselet P. On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework. Int. J. Numer. Methods Engrg. 2010, 10.1002/nme.2884.
27. Schellenkens J.C.J., De Borst R. On the numerical integration of interface elements. Int. J. Numer. Methods Engrg. 1993, 36(1):43-66.
28. Allix O., Corigliano A. Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens. Int. J. Fract. 1996, 77:11-140.
29. Dostál Z. Conjugate gradient method with preconditioning by projector. Int. J. Comput. Math. 1988, 23(3):315-323.
30. P. Gosselet, Méthodes de décomposition de domaine et méthodes d'accélération pour les problèmes multichamps en mécanique non-linéaire, Ph.D. Thesis, Université Paris 6, 2003.