The hybrid boundary node method accelerated by fast multipole expansion technique for 3D elasticity

CMES - Computer Modeling in Engineering and Sciences

Volumn 70, Issue 2, 2010, Pages 123-151

  Wang, Qiao ^a   Miao, Yu ^a   Zheng, Junjie ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

3D elasticity; Fast multipole method; Hybrid boundary node method; Meshless method; Modified variational principle; Moving least squares approximation

Indexed keywords

3D ELASTICITY; FAST MULTIPOLE METHOD; HYBRID BOUNDARY NODE METHOD; MESH-LESS METHODS; MOVING LEAST SQUARES APPROXIMATION; VARIATIONAL PRINCIPLES;

BOUNDARY ELEMENT METHOD; DATA STRUCTURES; ELASTICITY; EXPANSION; THREE DIMENSIONAL; TREES (MATHEMATICS); VARIATIONAL TECHNIQUES;

LEAST SQUARES APPROXIMATIONS;

EID: 79952495385     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. Atluri, S.N. (2004): The Meshless Local Petrov-Galerkin (MLPG) Method for Domain & Boundary Discretizations, Tech Science Press, 665 pages.
2. Atluri, S.N.; Han, Z.D.; Rajendran, A.M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach, CMES: Computer Modeling in Engineering & Science, vol. 6, no. 6, pp. 491-514.
3. Atluri, S.N.; Han, Z.D.; Shen, S. (2003): Meshless Local Petrov-Galerkin (MLPG) approaches for weakly-singular traction & displacement boundary integral equations, CMES: Computer Modeling in Engineering & Science, vol. 4, no. 5, pp. 507-517.
4. Atluri, S.N.; Kim, H.G.; Cho, J.Y. (1999): A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Computational Mechanics, vol. 24, pp. 348-372. (Pubitemid 30546709)
5. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006a): Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method for Elasticity Problems, CMES: Computer Modeling in Engineering & Sciences, vol. 14, no. 3, pp. 141-152. (Pubitemid 44562740)
6. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006b): Meshless Local Petrov-Galerkin (MLPG) Mixed Finite Difference Method for Solid Mechanics, CMES: Computer Modeling in Engineering & Sciences, vol. 15, no. 1, pp. 1-16. (Pubitemid 44562735)
7. Atluri, S.N.; Shen S.P. (2002a): The meshless local Petrov-Galerkin (MLPG) method. Tech. Science Press, 440 pages.
8. Atluri, S.N.; Shen S.P. (2002b): The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element and boundary element methods, CMES: Computer Modeling in Engineering & Science, vol. 3, no. 1, pp. 11-52.
9. Atluri, S.N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, vol. 22, pp. 117- 127. (Pubitemid 128620889)
10. Atluri, S.N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, vol. 22, pp. 117- 127. (Pubitemid 128620889)
11. Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless method: an overview and recent development. Computer Methods in Applied Mechanics and Engineering, vol. 139, pp. 3-47. (Pubitemid 126382692)
12. Belytschko, T.; Lu, Y.Y.; Gu, L. (1994): Element free Galerkin methods. International Journal for Numerical Methods in Engineering, vol. 37, pp. 229-256.
13. Chati, M.K.; Mukherjee, S.; Mukherjee, Y.X. (1999): The boundary node method for three-dimensional linear elasticity. International Journal for Numerical Methods in Engineering, vol. 46, pp. 1163-1184.
14. DeFigueredo, T.G.B.; Brebbia, C.A. (1989): A new hybrid displacement variational formulation of BEM for elastostatics. In Advances in Boundary Elements, Brebbia CA, Conner JJ (eds), vol. 1. Southampton: Computational Mechanics Publications, pp. 47-57.
15. Fu, Y.H.; Klimkowski, K.J.; Rodin, G.J.; et al. (1998): A fat solution method for three dimensional many-particle problems of linear elasticity. International Journal for Numerical Methods in Engineering, vol. 42, pp. 1215-1229. (Pubitemid 128500013)
16. Greegard, L. (1988): The Rapid Evaluation of Potential Fields in Particle Systems. Cambridge, MIT Press.
17. Greengard, L.; Rokhlin, V. (1987): A fast algorithm for particles simulations. Journal of Computational Physics, vol. 73, pp. 325-348.
18. Greengard, L.; Rokhlin, V. (1997): A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica, vol. 6, pp. 229-269.
19. Hayami, K.; Sauter, S.A. (1998a): Cost estimation of the panel clustering method applied to 3-D elastostatics. In: Brebbia CA, eds. Proceedings of the Second European Boundary Element Method Symposium, EUROBEM 98. Southampton: Computational Mechanics Publications, pp. 33-42.
20. Hayami, K.; Sauter, S.A. (1998b): Panel clustering for 3-D elastostatics using spherical harmonics. In: Kassab A, Brebbia CA and Chopro M, eds. Proceedings of boundary elements. Southampton: Computational Mechanics Publications, pp. 289-298.
21. Kulkarni, S.S.; Telekunta, S.; Mukherjee, S. (2003): Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory. Computational Mechanics, vol. 32, pp. 240-249.
22. Liu, Y.J.; Nishimura, N. (2006): The fast multipole boundary element method for potential problems: A tutorial. Engineering Analysis with Boundary Elements, vol. 30, pp. 371-381.
23. Liu, Y.J.; Nishimura, N.; Otani, Y.; Takahashi, T.; Chen, X.L.; Munakata, H. (2005): A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model. Journal of Applied Mechanics, vol. 72, pp.115-128. (Pubitemid 40308601)
24. Miao, Y.; Wang, Q.; Liao, B.H.; Zheng, J.J. (2009): A Dual Hybrid Boundary Node Method for 2D elastodynamics Problems. CMES: Computer Modeling in Engineering and Sciences, vol. 53, no. 1, pp. 1-22.
25. Miao, Y.; Wang, Y.H. (2006): Meshless analysis for three-dimensional elasticity with singular hybrid boundary node method. Applied Mathematics and Mechanics, vol. 27, no. 6, pp. 673-681. (Pubitemid 44054229)
26. Miao, Y.; Wang, Y.H.; Yu, F. (2005): Development of hybrid boundary node method in two-dimensional elasticity. Engineering Analysis with Boundary Elements, vol. 29, pp. 703-712. (Pubitemid 40851818)
27. Mukherjee, Y.X.; Mukherjee, S. (1997): The boundary node method for potential problems. International Journal for Numerical Methods in Engineering, vol. 40, pp. 797-815. (Pubitemid 127549025)
28. Nabors, K.; Korsmeyer, F.T.; Leighton, F.T.; White, J. (1994): Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory. SIAM Journal on Scientific Computing, vol. 15, pp. 713-735.
29. Nishida, T.; Hayami, K. (1997): Application of the fast multipole to the 3D BEM analysis of electron guns. In Boundary Elements XIX, Marchettia M, Brebbia CA, Aliabadi MH (eds). Southampton: Computational Mechanics Publications, pp. 613-622.
30. Peirce, A.P.; Napier, J.A.L. (1995): A spectral multipole method for efficient solutions of large scale boundary element models in elastostatics. International Journal for Numerical Methods in Engineering, vol. 38, pp. 4009-4034.
31. Popov, V.; Power, H. (2001): An O(N) Taylor series multipole boundary element methods for three-dimensional elasticity problems. Engineering Analysis with Boundary Elements, vol. 25, pp. 7-18. (Pubitemid 32196008)
32. Rokhlin, V. (1985): Rapid solution of integral equations of classical potential theory. Journal of Computational Physics, vol. 60, pp. 187-207.
33. Saad, Y.; Schultz, M.H. (1986): GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear system. SIAM Journal on Scientific and Statistical Computing, vol. 7, pp.856-869.
34. Yoshida, K.; Nishimura, N.; Kobayashi, S. (2001): Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D. International Journal for Numerical Methods in Engineering, vol. 50, pp. 525-547. (Pubitemid 32138355)
35. Zhang, J.M.; Tanaka, M. (2007): Systematic study of thermal properties of CNT composites by the fast multipole hybrid boundary node method. Engineering Analysis with Boundary Element, vol. 31, pp. 388-401. (Pubitemid 46428532)
36. Zhang, J.M.; Tanaka, M. (2008): Fast HdBNM for large-scale thermal analysis of CNT-reinforced composites. Computational Mechanics, vol. 41, pp. 777-787. (Pubitemid 351311848)
37. Zhang, J.M.; Tanaka, M.; Endo, M. (2005): The hybrid boundary node method accelerated by fast multipole expansion technique for 3D potential problems. International Journal for Numerical Methods in Engineering, vol. 63, pp. 660-680. (Pubitemid 40815371)
38. Zhang, J.M.; Tanaka, M.; Matsumoto, T. (2004): Meshless analysis of potential problems in three dimensions with the hybrid boundary node method. International Journal for numerical methods in Engineering, vol. 59, pp. 1147-1160.
39. Zhang, J.M.; Yao, Z.H. (2001): Meshless regular hybrid boundary node method. CMES: Computer Modeling in Engineering and Sciences, vol. 2, pp. 307-318.
40. Zhang, J.M.; Yao, Z.H. (2004): The regular hybrid boundary node method for three-dimensional linear elasticity. Engineering Analysis with Boundary Element, vol. 28, pp. 525-534.