Numerical solution for biharmonic equation using multilevel radial basis functions and domain decomposition methods

Applied Mathematics and Computation

Volumn 186, Issue 1, 2007, Pages 246-255

  Adibi, H ^a   Es'haghi, Jaafar ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Biharmonic equation; Meshless method; Multilevel RBF; Overlapping domain decomposition; Radial basis functions

Indexed keywords

DOMAIN DECOMPOSITION METHODS; NUMERICAL METHODS; PROBLEM SOLVING;

BIHARMONIC EQUATION; GLOBAL INTERPOLANT; IRREGULAR DOMAINS; MASHLESS METHODS;

RADIAL BASIS FUNCTION NETWORKS;

EID: 33947381455     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.06.123     Document Type: Article

References (19)

1. Beatson R.K., Light W.A., and Billings S. Fast solution of the radial basis function interpolation equations: domain decomposition methods. SIAM J. Sci. Comput. 22 (2000) 1717-1740
2. Buhmann M.D. Radial Basis Functions: Theory and Implementations (2003), Cambridge University Press, Cambridge
3. Fasshauer G.E. Solving partial differential equations by collocation with radial basis functions. In: Le Mehaute A., Rabut C., and Schumaker L.L. (Eds). Surface Fitting and Multiresolution Methods (1997), Vanderbilt University Press 131-138
4. Fasshauer G.E. Newton iteration with multiquadrics for the solution of nonlinear PDEs. Comput. Math. Appl. 43 (2002) 423-438
5. Fasshauer G.E., Gartland E.G., and Jerome J.W. Newton iteration for partial differential equations and the approximation of the identity. Numer. Algorithms 25 (2000) 181-195
6. Fasshauer G.E., and Jerome J.W. Multistep approximation algorithms: Improved convergence rates through postconditioning with smoothing kernels. Adv. Comput. Math. 10 (1999) 1-27
7. Floater M.S., and Iske A. Multistep scattered data interpolation using compactly supported radial basis functions. J. Comput. Appl. Math. 73 (1996) 65-78
8. Franke R. Scattered data interpolation: tests of some methods. Math. Comput. 48 (1982) 181-200
9. Franke C., and Schaback R. Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput. 93 (1998) 73-82
10. Franke C., and Schaback R. Convergence orders of meshless collocation methods using radial basis functions. Adv. Comput. Math. 8 (1998) 381-399
11. Garbey M., and Kaper H.G. Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems. SIAM J. Numer. Anal. 34 (1997) 15131544
12. Griebel M., and Schweitzer M.A. A particle-partition of unity method for the solution of elliptic parabolic and hyperbolic PDES. SIAM J. Sci. Comput. 22 (2000) 853890
13. Hardy R.L. Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res. 176 (1971) 1905-1915
14. Hon Y.C., and Schaback R. On unsymmetric collocation by radial basis functions. Appl. Math. Comput. 119 (2001) 177-186
15. Kansa E.J. Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics-II: solutions to parabolic hyperbolic and elliptic partial differential equations. Comput. Math. Appl. 19 (1990) 147-161
16. Micchelli C.A. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx. 2 (1986) 11-22
17. Wendland H. Scattered Data Approximation (2005), Cambridge University Press, Cambridge
18. Wu Z. Hermite-Birkhoff interpolation of scattered data by radial basis functions. Approx. Theory Appl. 8 (1992) 1-10
19. Zhou X., Hon Y.C., and Li J. Overlapping domain decomposition method by radial basis functions. Appl. Numer. Math. 44 (2003) 241-255