Numerical comparison of least square-based finite-difference (LSFD) and radial basis function-based finite-difference (RBFFD) methods

Authors:
C. Shu;H. Ding;N. Zhao
Affiliations:
Department of Mechanical Engineering National University of Singapore Singapore 119260;Department of Mechanical Engineering National University of Singapore Singapore 119260;Department of Aerodynamics Nanjing University of Aeronautics and Astronautics 29 Yudao Jie, Nanjing 210016, P.R. China
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 1
Cited 1

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Scattered node compact finite difference-type formulas generated from radial basis functions

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Abstract

In this paper, two mesh-free methods, i.e., least square-based finite difference (LSFD) and radial basis function-based finite difference (RBFFD), are compared numerically in terms of their accuracy and efficiency. These two mesh-free methods are based on different approximation schemes, that is, the least square approximation and radial basis function (RBF) approximation. The two mesh-free methods exhibit very different behaviors in many ways. In this study, we examine the performance of the two methods by applying them to two example problems: Poisson equation and two-dimensional incompressible viscous lid-driven cavity flow, and some interesting findings are observed.