An integrated-RBF technique based on Galerkin formulation for elliptic differential equations

Engineering Analysis with Boundary Elements

Volumn 33, Issue 2, 2009, Pages 191-199

  Mai Duy, N ^a   Tran Cong, T ^a  

^a UNIVERSITY OF SOUTHERN QUEENSLAND   (Australia)

Author keywords

Domain decomposition; Galerkin formulation; Integrated RBFNs; Multiple boundary conditions; Neumann boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DOMAIN DECOMPOSITION METHODS; FEEDFORWARD NEURAL NETWORKS; PROBABILITY DENSITY FUNCTION; RADIAL BASIS FUNCTION NETWORKS; SOLUTIONS;

DOMAIN DECOMPOSITION; GALERKIN FORMULATION; INTEGRATED RBFNS; MULTIPLE BOUNDARY CONDITIONS; NEUMANN BOUNDARY CONDITIONS;

GALERKIN METHODS;

EID: 56949100259     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2008.05.001     Document Type: Article

References (24)

1. Brebbia C.A., and Dominguez J. Boundary elements-an introductory course (1992), Computational Mechanics Publications, Southampton
2. Fasshauer GE. Meshfree approximation methods with Matlab, vol. 6. Interdisciplinary mathematical sciences, Singapore: World Scientific Publishers; 2007.
3. Schaback R. Error estimates and condition numbers for radial basis function interpolation. Adv Comput Math 3 (1995) 251-264
4. Ling L., and Kansa E.J. A least-squares preconditioner for radial basis functions collocation methods. Adv Comput Math 23 (2005) 31-54
5. Shu C., Ding H., and Yeo K.S. Computation of incompressible Navier-Stokes equations by local RBF-based differential quadrature method. Comput Model Eng Sci 7 2 (2005) 195-206
6. Sarler B., and Vertnik R. Meshfree explicit local radial basis function collocation method for diffusion problems. Comput Math Appl 51 8 (2006) 1269-1282
7. Wendland H. Scattered data approximation (2005), Cambridge University Press, Cambridge
8. Ingber M.S., Chen C.S., and Tanski J.A. A mesh free approach using radial basis functions and parallel domain decomposition for solving three-dimensional diffusion equations. Int J Numer Methods Eng 60 13 (2004) 2183-2201
9. Divo E., and Kassab A. Iterative domain decomposition meshless method modeling of incompressible viscous flows and conjugate heat transfer. Eng Anal Boundary Elem 30 6 (2006) 465-478
10. Mai-Duy N., and Tanner R.I. A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. Int J Numer Methods Heat Fluid Flow 17 2 (2007) 165-186
11. Mai-Duy N., and Tran-Cong T. A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains. Numer Methods Partial Different Eq 23 5 (2007) 1192-1210
12. Wendland H. Meshless Galerkin methods using radial basis functions. Math Comput 68 (1999) 1521-1531
13. Wendland H. Numerical solution of variational problems by radial basis functions. In: Chui C.K., and Schumaker L.L. (Eds). Approximation Theory IX, vol. II: Computational Aspects (1999), Vanderbilt University Press, Tennessee 361-368
14. Hu H.-Y., Li Z.-C., and Cheng A.H.-D. Radial basis collocation methods for elliptic boundary value problems. Comput Math Appl 50 1-2 (2005) 289-320
15. Fletcher C.A.J. Computational Galerkin methods (1984), Springer, New York
16. Zienkiewicz O.C., and Taylor R.L. The finite element method-Volume 1: The basis. 5th ed. (2000), Butterworth Heinemann, Oxford
17. Mai-Duy N., and Tran-Cong T. Approximation of function and its derivatives using radial basis function networks. Appl Math Modell 27 (2003) 197-220
18. Kansa E.J., Power H., Fasshauer G.E., and Ling L. A volumetric integral radial basis function method for time-dependent partial differential equations: I. Formulation. Eng Anal Boundary Elem 28 (2004) 1191-1206
19. Mai-Duy N., and Tran-Cong T. Numerical solution of differential equations using multiquadric radial basis function networks. Neural Netw 14 2 (2001) 185-199
20. Ling L., and Trummer M.R. Adaptive multiquadric collocation for boundary layer problems. J Comput Appl Math 188 2 (2006) 265-282
21. Shu C., and Wu Y.L. Integrated radial basis functions-based differential quadrature method and its performance. Int J Numer Methods Fluids 53 6 (2007) 969-984
22. Sarra S.A. Integrated multiquadric radial basis function approximation methods. Comput Math Appl 51 8 (2006) 1283-1296
23. Trefethen L.N. Spectral methods in MATLAB (2000), SIAM, Philadelphia
24. N. Mai-Duy, T. Tran-Cong, A multidomain integrated radial basis function collocation method for elliptic problems, Numer Methods Partial Different Eq, in press