A robust preconditioning technique for the extended finite element method

International Journal for Numerical Methods in Engineering

Volumn 85, Issue 13, 2011, Pages 1609-1632

  Menk, Alexander ^a,b   Bordas, Stéphane P A ^c  

^a ROBERT BOSCH GMBH   (Germany)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

^c CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Condition number; Cracks; Domain decomposition; Iterative solvers; Material interfaces; Preconditioner; X FEM

Indexed keywords

CONDITION NUMBERS; DOMAIN DECOMPOSITIONS; ITERATIVE SOLVERS; MATERIAL INTERFACES; PRECONDITIONERS; X-FEM;

CRACKS; DOMAIN DECOMPOSITION METHODS; NUMBER THEORY; NUMERICAL METHODS; STIFFNESS; STIFFNESS MATRIX;

FINITE ELEMENT METHOD;

EID: 79951933574     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3032     Document Type: Article

References (23)

1. Braess D. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press: Cambrdige, 2001.
2. Belytschko T, Liu W, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000.
3. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4):993-1013.
4. Melenk J, Babuška I The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):289-314.
5. Bordas S, Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures. Engineering Fracture Mechanics 2006; 73(9):1176-1201.
6. Béchet E, Minnebo H, Moës N, Burgardt B. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. International Journal for Numerical Methods in Engineering 2005; 64(8):1033-1056.
7. Farhat C, Roux F. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering 1991; 32(6):1205-1227.
8. Wyart E, Duflot M, Coulon D, Martiny P, Pardoen T, Remacle J, Lani F. Substructuring FE-XFE approaches applied to three-dimensional crack propagation. Journal of Computational and Applied Mathematics 2008; 215(2):626-638.
9. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):131-150.
10. Sukumar N, Chopp D, Moës N, Belytschko T. Modeling holes and inclusions by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering 2001; 190(47):6183-6200.
11. Fries T. A corrected X-FEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering 2008; 75(5):503-532.
12. Menk A, Bordas S. Numerically determined enrichment functions for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. International Journal for Numerical Methods in Engineering; DOI: 10.1002/nme.2858.
13. Kerfriden P, Allix O, Gosselet P. A three-scale domain decomposition method for the 3D analysis of debonding in laminates. Computational Mechanics 2009; 44(3):343-362.
14. Gosselet P, Rey C. Non-overlapping domain decomposition methods in structural mechanics. Archives of Computational Methods in Engineering 2006; 13(4):515-572.
15. Simone A, Duarte C, Van der Giessen E. A generalized finite element method for polycrystals with discontinuous grain boundaries. International Journal for Numerical Methods in Engineering 2006; 67:1122-1145.
16. Budyn E, Zi G, Moës N, Belytschko T. A method for multiple crack growth in brittle materials without remeshing. International Journal for Numerical Methods in Engineering 2004; 61:1741-1770.
17. Golub G, Van Loan C. Matrix Computations. Johns Hopkins University Press: Baltimore, MD, 1996.
18. Natarajan S, Mahapatra D, Bordas S. Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework. International Journal for Numerical Methods in Engineering; DOI: 10.1002/nme.2798.
19. Natarajan S, Bordas S, Mahapatra D. Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping. International Journal for Numerical Methods in Engineering 2009; 80(1):103-134.
20. Bordas S, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics 2008; 75(5):943-960.
21. Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics 2007; 39(6):743-760.
22. Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering 2007; 196(29-30):2777-2799.
23. Song J, Areias P, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 2006; 67:868-893.