Compactly supported radial basis functions for shallow water equations

Authors:
S. M. Wong;Y. C. Hon;M. A. Golberg
Affiliations:
School of Science and Technology, Open University of Hong Kong, Hong Kong;Department of Mathematics, City University of Hong Kong, Hong Kong;University Circle, 2025 Las Vegas, NV 89119, USA
Venue:
Applied Mathematics and Computation
Year:
2002

Citing 3
Cited 4

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Error estimates for interpolation by compactly supported radial basis functions of minimal degree

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Solving partial differential equations by collocation using radial basis functions

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Overlapping domain decomposition method by radial basis functions

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Numerical experiments on the condition number of the interpolation matrices for radial basis functions

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Numerical simulation of Saint-Venant equations with turbulence using radial basis functions: application to Lake Bouregreg

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An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions

Journal of Computational Physics

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Abstract

This paper presents the application of the compactly supported radial basis functions (CSRBFs) in solving a system of shallow water hydrodynamics equations. The proposed scheme is derived from the idea of piecewise polynomial interpolation using a function of Euclidean distance. The compactly supported basis functions consist of a polynomial which are non-zero on [0,1) and vanish on [1, ∞). This reduces the original resultant full matrix to a sparse matrix. The operation of the banded matrix system could reduce the ill-conditioning of the resultant coefficient matrix due to the use of the global radial basis functions. To illustrate the computational efficiency and accuracy of the method, the difference between the globally and CSRBF schemes is compared. The resulting banded matrix has shown improvement in both ill-conditioning and computational efficiency. The numerical solutions are verified with the observed data. Excellent agreement is shown between the simulated and the observed data.