A moving IRBFN-based integration-free meshless method

Phong B H Le, Timon Rabczuk, Nam Mai-Duy, Thanh Tran-Cong

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

A novel approximation method using integrated radial basis function networks (IRBFN) coupled with moving least square (MLS) approximants, namely moving integrated radial basis function networks (MIRBFN), is proposed in this work. In this method, the computational domainω is divided into finite sub-domains ω1 which satisfy point-wise overlap condition. The local function interpolation is constructed by using IRBFN supported by all nodes in subdomain ω1.The global function is then constructed by using Partition of Unity Method (PUM), where MLS functions play the role ofpartition of unity.As a result, the proposed method is locally supported and yields sparse and banded interpolation matrices. The computational efficiency are excellently improved in comparison with that ofthe original global IRBFN method.In addition, the present method possesses the Kronecker-d property, which makes it easy to impose the essential boundary conditions. The proposed method is applicable to randomly distributed datasets and arbitrary domains.In this work, the MIRBFN method is implemented in the collocation of a first-order system formulation [Le, Mai-Duy, Tran-Cong, and Baker (2010)] to solve PDEs governing various problems including heat transfer, elasticity of bothcompressible and incompressible materials, and linear static crack problems.The numerical results show that the present method offers highorder of convergence and accuracy.

Original languageEnglish
Pages (from-to)63-109
Number of pages47
JournalCMES - Computer Modeling in Engineering and Sciences
Volume61
Issue number1
Publication statusPublished - 2010 Oct 11
Externally publishedYes

Fingerprint

Radial basis function networks
Radial Basis Function Network
Meshless Method
Moving Least Squares
Interpolation
Partition of Unity Method
Computational efficiency
Square Functions
Elasticity
Interpolation Function
First-order System
Boundary conditions
Collocation
Approximation Methods
Heat transfer
Cracks
Computational Efficiency
Heat Transfer
Overlap
Crack

Keywords

  • Collocation method
  • Crack
  • Elasticity
  • First order system
  • Local IRBF
  • Locking
  • Meshless
  • Moving IRBF
  • RBF

ASJC Scopus subject areas

  • Computer Science Applications
  • Software
  • Modelling and Simulation

Cite this

Le, P. B. H., Rabczuk, T., Mai-Duy, N., & Tran-Cong, T. (2010). A moving IRBFN-based integration-free meshless method. CMES - Computer Modeling in Engineering and Sciences, 61(1), 63-109.

A moving IRBFN-based integration-free meshless method. / Le, Phong B H; Rabczuk, Timon; Mai-Duy, Nam; Tran-Cong, Thanh.

In: CMES - Computer Modeling in Engineering and Sciences, Vol. 61, No. 1, 11.10.2010, p. 63-109.

Research output: Contribution to journalArticle

Le, PBH, Rabczuk, T, Mai-Duy, N & Tran-Cong, T 2010, 'A moving IRBFN-based integration-free meshless method', CMES - Computer Modeling in Engineering and Sciences, vol. 61, no. 1, pp. 63-109.
Le PBH, Rabczuk T, Mai-Duy N, Tran-Cong T. A moving IRBFN-based integration-free meshless method. CMES - Computer Modeling in Engineering and Sciences. 2010 Oct 11;61(1):63-109.
Le, Phong B H ; Rabczuk, Timon ; Mai-Duy, Nam ; Tran-Cong, Thanh. / A moving IRBFN-based integration-free meshless method. In: CMES - Computer Modeling in Engineering and Sciences. 2010 ; Vol. 61, No. 1. pp. 63-109.
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