Improved multiquadric approximation for partial differential equations

Engineering Analysis with Boundary Elements

Volumn 18, Issue 1, 1996, Pages 9-17

  Golberg, M A ^a   Chen, C S ^b   Karur, S R ^c  

^a University of Nevada ^*  (United States)

^b UNIVERSITY OF NEVADA   (United States)

^c WASHINGTON UNIVERSITY   (United States)

Author keywords

Boundary element method; Cross validation; Dual reciprocity method; Fundamental solutions; Multiquadrics; Particular solutions

Indexed keywords

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; FUNCTIONS; INTERPOLATION; NUMERICAL METHODS;

CROSS VALIDATION TECHNIQUE; DUAL RECIPROCITY METHOD (DRM); MULTIQUADRICS; RADIAL BASIS FUNCTIONS (RBF);

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0030181559     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(96)00033-1     Document Type: Article

References (22)

1. Brebbia, C. A. & Nardini, D. Dynamic analysis in solid mechanics by an alternative boundary element procedure. Soil Dyn. Earthq. Engng, 1983, 2, 228-233.
2. Partridge, P. W., Brebbia, C. A. & Wrobel, L. C. The Dual Reciprocity Boundary Element Mehod. Computational Mechanics Publications, Southampton, Elsevier, London, 1992.
3. Golberg, M, A., & Chen, C. S. The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations. Boundary Elements Communications, 1994, 5, 57-61.
4. Golberg, M. A. The numerical evaluation of particular solutions in the EBM - a review. Boundary Elements Communications, 1995, 6, 99-106.
5. Chen, C. S. The method of fundamental solutions for non-linear thermal explosions. Commun. Num. Meth. Engng, 1995, 11, 675-681.
6. Karur, S. R. & Ramachandran, P. A. Augmented thin plate spline approximation in DRM. Boundary Elements Communications, 1995, 6, 55-58.
7. Franke, R. Scattered data interpolation: tests of some methods. Math. Comput., 1982, 48, 181-200.
8. Powell, M. J. D. The uniform covergence of thin plate spline interpolation in two dimensions. Numerische Mathematik, 1994, 68 (1), 107-128.
9. Madych, W. R. & Nelson, S. A. Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation. J. Approxim. Theory, 1992, 70 (1), 94-114.
10. Milroy, M. J., Vickers, G. W. & Bradley, C. An adaptive radial basis function approach to modeling scattered data. J. Appl. Sci. Comput. (submitted).
11. Chen, C. S. & Golberg, M. A. A domain embedding method and the quasi-Monte Carlo method for Poisson's equation. In Boundary Elements XVII, ed. C. A. Brebbia, S. Kim, T. A. Osswald & H. Power. Computational Mechanics Publications, Southampton, 1995, pp. 115-122.
12. Golberg, M. A. The method of fundamental solutions for Poisson's equation (II). Engng Anal. Boundary Elem., 1995, 16, 205-213.
13. Hardy, R. L. Multiquadric equations of topography and other irregular surfaces. J. Geophvs. Res., 1971, 76, 1905-1915.
14. Micchelli, C. A. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx., 1986, 2, 11-22.
15. Tarwater, A. E. A parameter study of Hardy's multiquadric method for scattered data interpolation. Lawrence Livermore National Laboratory, Technical Report UCRL-563670, 1985.
16. Kansa, E. J. Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics -I. Computers Math. Applic., 1990, 19, 127-145.
17. 2 in multiquadric interpolation. Comput. Math. Appl., 1991, 21, 29-42.
18. Myers, R. H. Classical and Modern Regression with Applications. Duxbury Press, Boston, 1986.
19. Bogomolny, A. Fundamental solutions method for elliptic boundary value problems. SIAM J. Numer. Anal., 1985, 22, 644-669.
20. Cheng, R. S. C. Delta-trigonometric and spline methods using the single-layer potential representation. PhD dissertation, University of Maryland, 1987.
21. Atkinson, K. E. The numerical evaluation of particular solutions for Poisson's equation. IMA J. Num. Anal., 1985, 5, 319-338.
22. Cameron, A. D., Casey, J. A. & Simpson, G. B. Benchmark Tests for Thermal Analysis. NAFEMS Publications, Glasgow, 1986.