Results on meshless collocation techniques

Engineering Analysis with Boundary Elements

Volumn 30, Issue 4, 2006, Pages 247-253

  Ling, Leevan ^a   Opfer, Roland ^b   Schaback, Robert ^b  

^a NATIONAL SUN YAT SEN UNIVERSITY   (Taiwan)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Asymptotic feasibility; Kansa's methods; Matrix free algorithm

Indexed keywords

ADAPTIVE ALGORITHMS; ASYMPTOTIC STABILITY; PROBLEM SOLVING; TEST FACILITIES;

ASYMPTOTIC FEASIBILITY; DATA-DEPENDENT MESHLESS SELECTION; MESHLESS COLLOCATION TECHNIQUES; PDE BOUNDARY VALUE PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 33644890498     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2005.08.008     Document Type: Article

References (18)

1. N. Aronszajn Theory of reproducing kernels Trans Am Math Soc 68 1950 337 404
2. Satya N, Atluri, Shengping Shen. The meshless local Petrov-Galerkin (MLPG) method. Encino, CA: Tech Science Press; 2002.
3. F.A. de Paula, and J.C.F. Telles A comparison between point collocation and Galerkin for stiffness matrices obtained by boundary elements Eng Anal Bound Elem 6 3 1989 123 128
4. G.E. Fasshauer Newton iteration with multiquadrics for the solution of nonlinear PDEs Comput Math Appl 43 3-5 2002 423 438
5. C. Franke, and R. Schaback Solving partial differential equations by collocation using radial basis functions Appl Math Comput 93 1 1998 73 82
6. Carsten Franke, and R. Schaback Convergence order estimates of meshless collocation methods using radial basis functions Adv Comput Math 8 4 1998 381 399
7. M.A. Golberg C.S. Chen The dual reciprocity method and radial basis functions 2000 Elsevier Amsterdam [Eng Anal Bound Elem 2000;24(7-8)]
8. Y.C. Hon, and R. Schaback On unsymmetric collocation by radial basis functions Appl Math Comput 119 2-3 2001 177 186
9. Kansa EJ. Application of Hardy's multiquadric interpolation to hydrodynamics. In: Proceedings of 1986 simulations conference, vol. 4; 1986. p. 111-7.
10. E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates Comput Math Appl 19 8-9 1990 127 145
11. Jichun Li, Alexander H.D. Cheng, and Ching-Shyang Chen A comparison of efficiency and error convergence of multiquadric collocation method and finite element method Eng Anal Bound Elem 27 3 2003 251 257
12. Leevan Ling, and M.R. Trummer Multiquadratic collocation method with integral formulation for boundary layer problems Comput Math Appl 48 5-6 2004 927 941
13. N. Mai-Duy, and T. Tran-Cong Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks Int J Numer Methods Fluids 37 2001 65 86
14. R. Schaback Native Hilbert spaces for radial basis functions I M.D. Buhmann D.H. Mache M. Felten M.W. Müller New developments in approximation theory International series of numerical mathematics vol. 132 1999 Birkhäuser Boston 255 282
15. R. Schaback On the versatility of meshless kernel methods S.N. Atluri D.E. Beskos D. Polyzos Advances in computational and experimental engineering and sciences vol. 428 2003
16. A.S.M. Wong, Y.C. Hon, T.S. Li, S.L. Chung, and E.J. Kansa Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme Comput Math Appl 37 8 1999 23 43
17. Zong Min Wu Hermite-Birkhoff interpolation of scattered data by radial basis functions Approx Theory Appl 8 2 1992 1 10
18. D.L. Young, S.C. Jane, C.Y. Lin, C.L. Chiu, and K.C. Chen Solutions of 2D and 3D Stokes laws using multiquadrics method Eng Anal Bound Elem 28 10 2004 1233 1243