An investigation of wave propagation with high wave numbers via the regularized LBIEM

CMES - Computer Modeling in Engineering and Sciences

Volumn 20, Issue 2, 2007, Pages 85-98

  Chen, H B ^a   Fu, D J ^a   Zhang, P Q ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Helmholtz equation; Local boundary integral equation method; Modified basis function; Moving least square approximation; Regularization

Indexed keywords

ERROR ANALYSIS; HARMONIC ANALYSIS; HELMHOLTZ EQUATION; INTEGRAL EQUATIONS;

FREQUENCY DEPENDENT BASIS FUNCTIONS; HARMONIC WAVE PROPAGATION; MOVING LEAST SQUARE APPROXIMATION (MLSA);

WAVE PROPAGATION;

EID: 34547738493     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., vol. 22, pp. 117-127.
2. Babuska, I.; Melenk, J. M. (1997): The partition of unity method, Int. J. Numer. Methods Eng., vol. 40, pp. 727-758.
3. Bouillard, Ph.; Suleau, S. (1998): Element-Free Galerkin solutions for Helmholtz problems: Formulation and numerical assessment of the pollution effect. Comput. Meth. Appl. Mech. Eng., vol. 162, pp. 317-335.
4. Chen, H. B.; Lu, P.; Huang, M. G.; Williams, F. W. (1998): An effective method for finding values on and near boundaries in the elastic BEM. Comput. Struct., vol. 69, pp. 421-431.
5. Chen, H. B.; Lu, P.; Schnack, E. (2001): Regularized algorithms for the calculation on and near boundary in 2D elastic BEM. Eng. Anal. Bound. Elem., vol 25, pp. 851-876.
6. Chen, H. B.; Yu. D. H.; Schnack, E. (2003): A simple a-posteriori error estimation for adaptive mesh refinement in elastic BEM, Comput. Mech., vol. 30, pp. 343-354.
7. Ciskowski, R. D.; Brebbia, C. A. (1991): Boundary Element Methods in Acoustics. Computational Mechanics Publications, Southampton.
8. Chen, W. (2002): Meshfree boundary particle method applied to Helmholtz problems. Eng. Anal. Bound. Elem., vol. 26, pp. 577-581.
9. Chen, W; Hon, Y. C. (2003): Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz, and convection-diffusion problems. Comput. Meth. Appl. Mech. Eng., vol 192, pp. 1859-1875.
10. Deraemaeker, A.; Babuska, I.; Bouillard, P. (1999): Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Int. J. Numer. Methods Eng., vol. 46, pp. 471-499.
11. Guo, X. F.; Chen, H. B.; Wang, N. Y.; Zhang, P. Q. (2006a): Meshless regularized local boundary integral equation method to 2D potential problems. The Journal of University of Science and Technology of China; 36(6): 635-640 (in Chinese).
12. Guo, X. F.; Chen, H. B. (2006b): Dual error indicators for the local boundary integral equation method in 2D potential problems, Eng. Anal. Bound. Elem., vol. 30, pp. 702-708.
13. Han, Z. D.; Atluri, S. N. (2003): Truly Meshless Local Petrov-Galerkin (MLPG) solutions of traction & displacement BIEs. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 665-678.
14. Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (2005): Meshless Local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations. CMES: Computer Modeling in Engineering & Sciences, vol. 10, pp. 1-12.
15. Ihlenburg, F.; Babuska, I. (1995a): Finite element solution of the Helmholtz equation with high wave number part I: the h-version of the FEM. Comput. Math. Appl., vol. 30, pp. 9-37.
16. Ihlenburg, F.; Babuska, I. (1995b): Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation. Int. J. Numer. Methods Eng., vol. 38, pp. 3745-3774.
17. Sellountos, E. J.; Vavourakis, V.; Polyzos, D. (2005): A new Singular/Hypersingular MLPG(LBIE) method for 2D elastostatics. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 35-47.
18. Sladek, J.; Sladek, V.; Atluri, S. N. (2002a): Application of the local boundary integral equation method to boundary-value problems. Int. Appl. Mech., vol. 38, pp. 1025-1047.
19. Sladek, J.; Sladek, V.; Keer, R. V. (2002b): Global and local Trefftz boundary integral formulations for sound vibration. Adv. Eng. Softw., vol. 33, pp. 469-476.
20. Sladek, J.; Sladek, V.; Zhang, C. Z. (2005): A meshless local boundary integral equation method for dynamic anti-plane shear crack problem in functionally graded materials. Eng. Anal. Bound. Elem., vol. 29, pp. 334-342.
21. Sladek, V.; Sladek, J.; Tanaka, M. (2005): Local integral equations and two meshless polynomial interpolations with application to potential problems in nonhomogeneous media, CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 69-83.
22. Sladek, V.; Sladek, J.; Atluri, S. N.; Van Keer, R. (2000): Numerical integration of singularities in meshless implementation of local boundary integral equations. Comput. Mech., vol. 25, pp. 394-403.
23. Suleau, S.; Deraemaeker, A.; Bouillard, Ph. (2000a): Dispersion and pollution of meshless solutions for the Helmholtz equation. Comput. Meth. Appl. Mech. Eng., vol. 190, pp. 639-657.
24. Suleau, S.; Bouillard, Ph. (2000b): One-dimensional dispersion analysis for the elementfree Galerkin method for the Helmholtz equation. Int. J. Numer. Methods Eng., vol. 47, pp. 1169-1188.
25. Uras, R. A.; Chang, C. T.; Chen, Y.; Liu, W. K. (1997): Multiresolution reproducing kernel particle methods in acoustics. J. Comput. Acoust., vol. 5, pp. 71-94.
26. Zhu, T.; Zhang, J. D.; Atluri, S. N. (1998): A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Comput. Mech., vol. 21, pp. 223-235.
27. Zhu, T.; Zhang, J. D.; Atluri, S. N. (1999): A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems. Eng. Anal. Bound. Elem., vol. 23, pp. 375-389.