Work

On Generation of Node Distributions for Meshless PDE Discretizations

Year: 2019

Type: article

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.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/18m1231456

Authors: Jure Slak, Gregor Kosec

Institutions: University of Ljubljana, Jožef Stefan Institute

Language: English

Topic: Numerical methods in engineering

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, Javna Agencija za Raziskovalno Dejavnost RS

Awards: Scientific Computing, Multi-analysis of fretting fatigue using physical and virtual experiments