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Evaluating RBF methods for solving PDEs using Padua points distribution
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DOI：10.1016/j.aej.2020.04.047.png)
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In Radial Basis Functions (RBFs) methods, the distribution and the number of points have a significant effect on the accuracy, stability, and computational costs. Padua distribution is known as optimal points in the interpolation of Lagrange polynomials in a square-shaped computational domain and two-dimensional space. This point distribution was applied in rectangular and circular domains using mapping. In this research, for the first time, Padua points were used in three-dimensional space. The results of this distribution were compared with other distributions such as Fibonacci, points on vertices of a triangular mesh, points on regular grid plus extra points on boundaries, Halton, and Sobol and their combinations. Padua points were used to solve Partial Differential Equations (PDEs) using the RBF methods and Compactly Supported-Radial Basis Functions (CS-RBFs) and their combinations. Numerical results showed that Padua distribution in most of the cases with the lowest number of center points obtained the highest accuracy. Furthermore, Padua points in combination with other distributions increase the accuracy. The remarkable result of this paper is that these points can be used in higher dimensions and got accurate results. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Keyword:
Padua points
RBF method
CS-RBF method
Points distribution
Mapping
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