Enriched Reproducing Kernel Approximation: Reproducing Functions With Discontinuous Derivatives

Lecture Notes in Computational Science and Engineering

Volumn 43, Issue , 2005, Pages 93-107

  Joyot, Pierre ^a   Trunzler, Jean ^a,b   Chinesta, Fransisco ^b  

^a Technopole Izarbel   (France)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION TECHNIQUES; DISCONTINUOUS DERIVATIVES; MESH-LESS METHODS; PARTICLE APPROXIMATIONS; REPRODUCING KERNEL; REPRODUCING KERNEL PARTICLE METHOD;

COMPUTER SCIENCE;

EID: 84880347158     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-27099-x_6     Document Type: Article

References (17)

1. N. Aluru. A point collocation method based on reproducing kernel approximations. Int. J. Numer. Meths. Eng., 47:1083-1121, 2000.
2. G. T. B. Nayrolles and P. Villon. Generalizing the finite element method: Diffuse approximation and diffuse elements computational mechanics. Journal of Computational Mechanics, 10(5):307-318, 1992.
3. I. Babuška and J. Melenk. The partition of unity method. Int. J. Numer. Meths. Eng., 40:727-758, 1997.
4. T. Belytschko, Y. Kronggauz, D. Organ, and M. Fleming. Meshless methods: an overview and recent developments. Comput. Meths. Appl. Mech. Engrg., 139:3-47, 1996.
5. J. Chen, C. Pan, C. Roque, and H.P.Wang. A lagrangian reproducing kernel particle method for metal forming. Comput. Mech., 22:289-307, 1998.
6. M. Fleming, Y. Chu, B. Moran, and T. Belytschko. Enriched element-free galerkin methods for crack tip fields. Int. J. Numer. Meths. Eng., 40, 1997.
7. R. Gingold and J. Monaghan. Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices Royal Astronomical Society, 181:375-389, 1977.
8. W. Han and X. Meng. Error anlysis of the reproducing kernel particle method. Comput. Meths. Appl. Mech. Engrg., 190:6157-6181, 2001.
9. H. Ji, D. Chopp, and J. Dolbow. A hybrid extended finite/level set method for modeling phase transformtions. Int. J. Numer. Meths. Eng., 54:1209-1233, 2002.
10. Y. Kronggauz and T. Belytschko. Efg approximation with discontinuous derivatives. Int. J. Numer. Meths. Eng., 41:1215-1233, 1998.
11. W. Liu, S. Jun, S. Li, J. Adee, and T. Belytschko. Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Meths. Eng., 38:1655-1679, 1995.
12. J. M. Melenk and I. Babuška. The partition of unity finite element method: Basic theory and applications. Comput. Meths. Appl. Mech. Engrg., 139:289-314,1996.
13. N. Moës and T. Belytschko. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 69:813-833, 2002.
14. J. Sethian. Evolution, implementation and application of level set and fast marching methods for advancing fronts. J. Comput. Phys., 169:503-555, 2001.
15. T. Strouboulis, K. Corps, and I. Babuška. The generalized finite elment method. Comput. Meths. Appl. Mech. Engrg., 190:4081-4193, 2001.
16. N. Sukumar, D. Chopp, N. Moës, and T. Belytschko. Modeling holes and inclusions by level sets in the extended finite-element method. Comput. Meths. Appl. Mech. Engrg., 190:6183-6200, 2001.
17. G. Ventura, J. Xu, and T. Belytschko. A vector level set method and new discontinuity approximations for crack growth by efg. Int. J. Numer. Meths. Eng., 54:923-944, 2002.