Differential quadrature Trefftz method for Poisson-type problems on irregular domains

Engineering Analysis with Boundary Elements

Volumn 32, Issue 5, 2008, Pages 413-423

  Wu, Xionghua ^a   Du, Huijing ^a   Kong, Weibin ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

Differential quadrature method; Dual reciprocity method; Irregular domains; Poisson type problem; Trefftz method

Indexed keywords

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; HOMOGENIZATION METHOD; PROBLEM SOLVING;

DIFFERENTIAL QUADRATURE METHOD; DUAL RECIPROCITY METHOD; IRREGULAR DOMAINS; POISSON-TYPE PROBLEMS; TREFFTZ METHOD;

POISSON EQUATION;

EID: 42949165410     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2007.10.001     Document Type: Article

References (35)

1. Nardini D., and Brebbia C.A. A new approach to free vibration analysis using boundary elements. In: Brebbia C.A. (Ed). Boundary element methods in engineering proceedings. Fourth international seminar, Southampton (1982), Springer, Berlin 312-326
2. Wang H., and Qin Q.H. A meshless method for generalized linear or nonlinear Poisson-type problems. Eng Anal Boundary Elem 30 (2006) 515-521
3. Goldberg MA, Chen CS. Discrete Projection Methods for Integral Equations. Southampton, Boston: Computational Mechanics Publications;1997.
4. Tsai C.C. Meshless BEM for three-dimensional stokes flows. Comput Modeling Eng Sci 3 1 (2001) 117-128
5. Golberg M.A., Muleshkov A.S., Chen C.S., and Cheng A.H.-D. Polynomial particular solutions for certain partial differential operators. Numer Methods Partial Differential Equations 19 (2003) 112-133
6. Reutskiy S.Y., and Chen C.S. Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions. Int J Numer Methods Eng 67 (2006) 1811-1829
7. Muleshkov A.S., Golberg M.A., and Chen C.S. Particular solutions for axisymmetric Helmholtz-type operators. Eng Anal Boundary Elem 29 (2005) 1066-1076
8. Cheng A.H.-D., Chen C.S., Golberg M.A., et al. BEM for thermoelasticity and elasticity with body force-a revisit. Eng Anal Boundary Elem 25 (2001) 377-387
9. Cheng A.H.-D. Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions. Eng Anal Boundary Elem 24 (2000) 531-538
10. Bellman R., and Casti J. Differential quadrature and long term integration. J Math Anal Appl 34 (1971) 235-238
11. Li C., and Wu X.H. A new linearized method for Benjamin-Bona-Mahony equations. Numer Methods Partial Differential Equations 20 (2004) 948-961
12. Wu Y., and Wu X.H. Linearized and rational approximation method for solving non-linear Burgers's equation. Int J Numer Methods Fluids 45 (2004) 509-525
13. Wu X.H., and Shen Y. Differential quadrature domain decomposition method for a class of parabolic equations. Comput Math Appl 48 12 (2004) 1819-1832
14. Wu X.H., and Kong W.B. A highly accurate linearized method for free boundary problems. Comput Math Appl 50 (2005) 1241-1250
15. Wu X.H., and Ding Z.H. Differential quadrature method for pricing American options. Numer Methods Partial Differential Equations 18 (2002) 711-725
16. Civan F. Solving multivariable models by the quadrature and cubature methods. Numer Methods Partial Differential Equations 10 (1994) 545-567
17. Escobar F.H., Jongkittinarukom K., and Civan F. Cubature solution of the poisson equation. Commun Numer Methods Eng 13 (1997) 453-465
18. Bert C.W., and Malik M. Differential quadrature method in computational mechanics: a review. Appl Mech Rev 49 (1996) 1-28
19. Wu X.H., and Liu S.T. Differential quadrature domain decomposition method for problems on a triangular domain. Numer Methods Partial Differential Equations 21 (2005) 574-585
20. Ren Y., and Wu X. Boundary reduction technique and triangular differential quadrature domain decomposition method for polygonal region. Eng Anal Boundary Elem 30 (2006) 435-440
21. Herrera I. Trefftz method. In: Brebbia C.A. (Ed). Topics in boundary element research (1984), Springer, Berlin 225-253
22. Jin W.G., Cheung Y.K., and Zienkiewicz Q.C. Application of the Trefftz method in plane elasticity problems. Int J Numer Methods Eng 30 (1990) 1147-1161
23. Cheung Y.K., Jin W.G., and Zienkiewicz Q.C. Solution of Helmholtz equation by Trefftz method. Int J Numer Methods Eng 32 (1991) 63-78
24. Trefftz E. Ein gegenstuck zum ritzschen verfahren. Proceedings of second International Congress on Applied Mechanics, Zurich; 1926. p. 131-7.
25. Cho H.A., Golberg M.A., Muleshkov A.S., and Li X. Trefftz methods for time dependent partial differential equations. Comput Mater Continua 1 (2004) 1-37
26. Golberg M.A., and Chen C.S. The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: Golberg M.A. (Ed). Boundary integral methods-numerical and mathematical aspects (1998), Computational Mechanics Publications 103-176
27. Kitagawa T. Asymptotic stability of the fundamental solution method. J Comput Appl Math 38 (1991) 263-269
28. Li Z.C., Lu T.T., Huang H.T., and Cheng A.H.-D. The Trefftz method and other boundary methods, a comparison. Numer Methods Partial Differential Equations 23 (2007) 93-144
29. Chen W., and Tanaka M. A meshless, integration-free and boundary-only RBF technique. Comput Math Appl 43 (2002) 379-391
30. Chen W., and Hon Y.C. Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz, and convectionCdiffusion problems. Comput Methods Appl Mech Eng 192 (2003) 1859-1875
31. Yu D.H. Natural boundary integral method and its applications (2002), Science Press, Beijing
32. Canuto C., Hassaini M.Y., Quarteroni A., and Zang T.A. Spectral methods in fluid dynamics (1988), Springer, Berlin
33. Ramachandram P.A. Method of fundamental solutions: singular value decomposition analysis. Commu Numer Methods Eng 18 (2002) 789-801
34. Tee T.W., and Trefethen L.N. A rational spectral collocation method with adaptively transformed Chebyshev grid points. SIAM J Sci Comput 28 (2006) 1798-1811
35. Berrut J.-P., and Trefethen L.N. Barycentric Lagrange interpolation. SIAM Rev 46 (2004) 501-517