Methods and Algorithms for Scientific Computing

On Generation of Node Distributions for Meshless PDE Discretizations


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.


  1. node generation algorithms
  2. variable density discretizations
  3. meshless methods for PDEs
  4. RBF-FD

MSC codes

  1. 65D99
  2. 65N99
  3. 65Y20
  4. 68Q25

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A3202 - A3229
ISSN (online): 1095-7197


Submitted: 10 December 2018
Accepted: 19 August 2019
Published online: 15 October 2019


  1. node generation algorithms
  2. variable density discretizations
  3. meshless methods for PDEs
  4. RBF-FD

MSC codes

  1. 65D99
  2. 65N99
  3. 65Y20
  4. 68Q25



Funding Information

Research Foundation Flanders : G018916N

Funding Information

Young Researcher program : PR-08346

Funding Information

Javna Agencija za Raziskovalno Dejavnost RS : P2-0095

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