Solve partial differential equations by meshless subdomains method combined with RBFs

Applied Mathematics and Computation

Volumn 174, Issue 1, 2006, Pages 700-709

  Zhang, Yun Xin ^a   Tan, Yong Ji ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

General Galerkin method; Meshless; PDEs; RBF; Subdomains method

Indexed keywords

GALERKIN METHODS; INTEGRAL EQUATIONS; RADIAL BASIS FUNCTION NETWORKS;

GENERAL GALERKIN METHOD; MESHLESS; PDES; RBF; SUBDOMAINS METHOD;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33344475702     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.04.110     Document Type: Article

References (23)

1. E.J. Kansa Multiquadrica scattered data approximation scheme with applications to computational fluid dynamics II Comput. Math. Appl. 19 1990 147 161
2. A. Quarteroni, and A. Valli Domain Decomposition Methods for Partial Differential Equations 1999 Oxford University Press
3. Beatson, J.B. Cherrie, and T. Mouat Fast solution of the radial basis function interpolation methods: domain decomposition methods SIAM J. Sci. Comput. 22 2000 1717 1740
4. Y.C. Hon, and Zongmin Wu Additive Schwarz domain decomposition with radial basis approximation Int. J. Appl. Math. 4 2002 81 98
5. Y.C. Hon, Jichun Li, Domain decomposition for radial basis meshless methods, Numer. Meth. Partial Diff. Eqs. (In Review) (2003).
6. X. Zhou, Y.C. Hon, and Jichun Li Overlapping domain decomposition method by radial basis functions Appl. Numer. Math. 44 1-2 2003 241 255
7. Leevan Ling, Edward J. Kansa, A least-squares preconditioner for radial basis functions collocation methods, Advances in Comput. Math. 2003, preprint.
8. Gregory E. Fasshauer Approximate moving least-squares approximation with compactly supported radial weights, numerical algorithms Lecture Notes in Comput. Sci. Eng. 26 2002 105 116
9. Robert Schaback, and Holger Wendland Adaptive greedy techniques for approximate solution of large RBF systems Numer. Algorithms 2000
10. Leevan Ling, Manfred R. Trummer, Multiquadric collocation method with integral formulation for boundary layer problems, Comput. Math. Appl., 2003, preprint.
11. Mira Bozzini, Licia Lenarduzzi, R. Rossini, Robert Schaback, Interpolation by basis functions of different scales and shapes, 2001.
12. E.J. Kansa, and Y.C. Hon Circumventing the ill-conditioning problem with multiquadric radial basis functions: application to elliptic partial differential equations Comput. Math. Appl. 39 2000 123 137
13. 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 1999 23 43
14. C.J.S. Alves, C.S. Chen, and B. Sǎler The method of fundamental solutions for solving Poisson problems Int. Ser. Adv. Boundary Elements, Bounday Elements XXIV 13 2002 67 76
15. W. Chen, and M. Tanaka A meshless, exponential convergence, integration-free, and boundary-only RBF technique Comput. Math. Appl. 43 2002 379 391
16. Robert Schaback, and Holger Wendland Using compactly supported radial basis functions to solve partial differential equations C. Chen C.A. Brebbia D.W. Pepper Boundary Element Technology XIII 1999 WitPress Southampton, Boston 311 324
17. Holger Wendland Meshless Galerkin methods using radial basis functions Math. Comput. 68 228 2002 1521 1531
18. Zhang yun-xin, Tan yong-ji, Solve PDEs using meshless Petrov-Galerkin methods with RBFs, submitted for publication.
19. Z. Wu, and R. Schaback Local error estimates for radial basis function interpolation of scattered data IMA J. Numer. Anal. 13 1993 13 27
20. M.J.D. Powell The theory of radial basis function approximation in 1990 W. Light Advances in Numerical Analysis vol. II 1992 Oxford Science Publications Oxford
21. W.R. Madych, and S.A. Nelson Multivariate interpolation and conditionally positive definite functions Math. Comp. 54 1990 211 230
22. R. Schaback, and H. Wendland Characterization and construction of radial basis functions N. Dyn D. Leviatan D. Levin Eilat Proceedings 2000 Cambridge University Press
23. L. Mai-Cao, T. Tran-Cong, Solving time-dependent PDEs with a meshless IRBFN-based Method, International Workshop on MeshFree Methods, 2003.