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.

在径向基函数（RBF）方法中，点的分布和数量对准确性，稳定性和计算成本有重大影响。帕多瓦分布在方形计算域和二维空间中作为Lagrange多项式插值的最佳点。使用映射将此点分布应用于矩形和圆形域。在这项研究中，帕多瓦点首次在三维空间中使用。将该分布的结果与其他分布进行了比较，例如斐波那契，三角形网格的顶点上的点，规则网格上的点以及边界上的额外点，Halton和Sobol及其组合。使用RBF方法和紧密支持的径向基函数（CS-RBF）及其组合，使用帕多瓦点求解偏微分方程（PDE）。数值结果表明，在大多数情况下，帕多瓦分布的中心点数最少，获得的精度最高。此外，帕多瓦（Padua）点与其他分布的结合可提高准确性。本文的引人注目的结果是这些点可以用于更高的维度并获得准确的结果。