On generation of node distributions for meshless PDE discretizations
Numerical Analysis
2020-05-12 v3 Data Structures and Algorithms
Numerical Analysis
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 2D and 3D. Additionally, local minimal spacing guarantees are proven for both uniform and variable nodal densities. The presented algorithm has time complexity to generate nodes with constant nodal spacing and to generate variably spaced nodes. Comparison with existing algorithms is performed in terms of node quality, time complexity, execution time and PDE solution accuracy.
Cite
@article{arxiv.1812.03160,
title = {On generation of node distributions for meshless PDE discretizations},
author = {Jure Slak and Gregor Kosec},
journal= {arXiv preprint arXiv:1812.03160},
year = {2020}
}