Multiresolution reproducing kernel particle methods

Computational Mechanics

Volumn 20, Issue 4, 1997, Pages 295-309

  Liu, W K ^a   Hao, W ^a   Chen, Y ^a   Jun, S ^a   Gosz, J ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3843107971     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050252     Document Type: Article

References (34)

1. Babuska, I.; Melenk, J. M. (1995) The partition of unity finite element method. University of Maryland Technical Note BN-1185
2. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994a): Element free galerkin methods. Int. J. Num. Meth. Eng. 37, 229-256
3. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994b): A new implementation of the element free galerkin method. Comp. Meth. Appl. Mech. Eng. 113, 397-414
4. Belytschko, T.; Krongauz, Y.; Fleming, M.; Organ, D.; Liu, W. K. (1996): Smoothing and accelerated computations in the element free galerkin method. Comput. Appl. Math. 74, 111-126
5. Chen, Y. (1995): Multiresolution, multiple field, and generalized reproducing kernel particle methods. Ph.D Thesis, Northwestern University
6. Chen, J. S.; Pan, C.; Wu, C. T.; Liu, W. K. (1996): Reproducing kernel particle methods for large deformation analysis of non-linear structures. Comp. Meth, Appl. Mech. Eng. 139, 195-228
7. Daubechies, I. (1992): Ten lectures on Wavelets, Volume 61. Society for Industrial and Applied Mathematics
8. Duarte, C. A.; Oden, J. T. (1995): Hp clouds - a meshless method to solve boundary-value problems. TICAM Report 95-05
9. Fried, I.; Johnson, A. R. (1988): A note on elastic energy density function for largely deformed compressible rubber solids. Comp. Meth. Appl. Mech. Eng. 69, 53-64
10. Glowinski, R.; Lawton, W. M.; Ravachol, M.; Tenenbaum, E. (1990): Wavelets solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension. Comp. Meth. Appl. Sci. Eng. Glowinski, R.; Lichnewsky, A. (eds) SIAM, Philadelphia, 55-120
11. Jun, S. (1996): Multiresolution reproducing kernel particle methods for large deformation problems. Ph.D Thesis, North-western University
12. Keller, J. B.; Givoli, D. (1989): Exact non-reflecting boundary conditions. J. Comput. Physics 82, 172-192
13. Kurdila, A. J.; Sun, T.; Grama, P.; Ko, J. (1995): Affine fractal interpolation functions and wavelet-based finite elements. Comput. Mech. 17(3), 169-185
14. Li, S.; Liu, W. K. (1996): Moving least square reproducing kernel method, part ii: Fourier analysis. Comp. Meth. Appl. Mech. Eng., 139, 159-194
15. Libersky, L.; Petschek, A. G. (1990): Smooth particle hydrodynamics with strength of materials. Proceedings of the next Free-Lagrange Conference Jackson Lake Lodge, Moran, Wyoming
16. Liu, W. K. (1992): Lecture Notes on Advanced Finite Element Method. Northwestern University
17. Liu, W. K. (1995): An introduction to wavelet reproducing kernel particle methods. USACM Bulletin 8(1), 3-16
18. Liu, W. K.; Oberste-Brandenburg, C. (1993): Reproducing kernel and wavelet particle methods. Aerospace Structures; Nonlinear Dynamics and System Response, In: Cusumano, J. P.; Pierre, C.; Wu, S. T. (eds): AD33 ASME, 39-56
19. Liu, W. K.; Chen, Y. (1995): Wavelet and multiple scale reproducing kernel methods. Int. J. Num. Meth. Fluids 21, 901-931
20. Liu, W. K.; Adee, J.; Jun, S. (1993): Reproducing kernel and wavelet particle methods for elastic and plastic problems. Adv. Comput. Meth. Mat. Mod. Benson, D. J.; Asaro, R. A. (eds): AMD 180 and PVP 268 ASME, 175-190
21. Liu, W. K.; Chang, C. T.; Chen, Y.; Uras, R. A. (1995): Multiresolution reproducing kernel particle methods in acoustic problems. Acoustics, Vibrations, and Rotating Machines (ASME DE-Vol.84-2, Part B), 881-900
22. Liu, W. K.; Jun, S.; Zhang, Y. F. (1995): Reproducing kernel particle methods. Int. J. Num. Meth. Fluids 20, 1081-1106
23. Liu, W. K.; Jun, S.; Li, S.; Adee, J.; Belytschko, T. (1995): Reproducing kernel particle methods for structural dynamics. Int. J. Num. Meth. Eng. 38, 1655-1679
24. Liu, W. K.; Chen, Y.; Chang, C. T.; Belytschko, T. (1996): Advances in multiple scale kernel particle methods. Comput. Mech. 18(2), 73-111
25. Liu, W. K.; Chen, Y.; Jun, S.; Chen, J. S.; Belytschko, T.; Pan, C.; Uras, R. A.; Chang, C. T. (1996): Overview and applications of the reproducing kernel particle methods. Arch. Comput. Meth. Eng. State of the art reviews 3, 3-80
26. Liu, W. K.; Chen, Y.; Uras, R. A.; Chang, C. T. (1996): Generalized multiple scale reproducing kernel particle methods. Comp. Meth. Appl. Mech. Eng., 139, 91-158
27. Liu, W. K.; Jun, S.; Sihling, D. T.; Chen, Y.; Hao, W. (1997): Multiresolution reproducing kernel particle method for computational fluid dynamics. Presented at the 3rd US-Japan Symposium on Finite Element Methods in Large-scale Computational Fluid Dynamics International Journal for Numerical Methods in Fluids 24, 1391-1415
28. Liu, W. K.; Li, S.; Belytschko, T. (1997): Moving least square reproducing kernel method, part i: Methodology and convergence Comp. Meth. Appl. Mech. Eng. 143, 113-154
29. Malvern, L. E. (1969): Introduction to the Mechanics of a Continuous Medium. Prentice-Hall Inc.
30. Monaghan, J. J. (1988): An introduction to smooth particle hydrodynamics. Com. Phys. Comm. 48, 89-96
31. Oñate, E.; Idelsohn, S.; Zienkiewicz, O. C. (1995): Finite point methods in computational mechanics. Int. Cent. Num. Meth. Eng.
32. Oswald, P. (1994): Multilevel finite element approximation. Theory and Applications. Teubner, Stuttgart
33. Shodja, H. M.; Mura, T.; Liu, W. K. (1995): Multiresolution analysis of a micromechanical model. In: Comput. Meth. Micromech. Ghosh, S.; Ostoja-Starzewski, M. (ed.): AMD 212/MD 62 ASME, 33-54
34. Yagawa, G.; Yamada, T.; Kawai. (1995): Some remarks on free mesh method: A kind of meshless finite element method. (To be presented at ICES-95)