On Generation of Node Distributions for Meshless PDE Discretizations

Abstract

In this paper we present an algorithm that is able to generate locally regular node layouts with spatially variable nodal density for interiors of arbitrary domains in two, three, and higher dimensions. It is demonstrated that the generated node distributions are suitable to use in the RBF-FD method, which is demonstrated by solving thermo-fluid problem in two and three dimensions. Additionally, local minimal spacing guarantees are proven for both uniform and variable nodal densities. The presented algorithm has time complexity $O(N)$ to generate $N$ nodes with constant nodal spacing and $O(N \log N)$ to generate variably spaced nodes. Comparison with existing algorithms is performed in terms of node quality, time complexity, execution time, and PDE solution accuracy.