A moving IRBFN-based galerkin meshless method

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

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A novel meshless method based on Radial Basis Function networks (RBFN) and variational principle (global weak form) is presented in this paper. In this method, the global integrated RBFN is localized and coupled with the moving least square method via the partition of unity concept. As a result, the system matrix is symmetric, sparse and banded. The trial and test functions satisfy the Kroneckerdelta property, i.e. Φi(xj) = δij. Therefore, the essential boundary conditions are imposed in strong form as in the FEMs. Moreover, the proposed method is applicable to scattered nodes and arbitrary domains. The method is examined with several numerical examples and the results indicate that the accuracy and the rate of convergence of the proposed method are superior to those of the EFG method using linear basis functions. In addition, the method does not exhibit any volumetric locking near the limit of incompressible material.

Original languageEnglish
Pages (from-to)25-52
Number of pages28
JournalCMES - Computer Modeling in Engineering and Sciences
Volume66
Issue number1
Publication statusPublished - 2010 Dec 13
Externally publishedYes

Fingerprint

Radial basis function networks
Meshless Method
Galerkin methods
Galerkin Method
Radial Basis Function Network
Boundary conditions
Finite element method
Volumetric Locking
Moving Least Squares
Partition of Unity
Test function
Least Square Method
Variational Principle
Linear Function
Basis Functions
Rate of Convergence
Numerical Examples
Arbitrary
Vertex of a graph

Keywords

  • Crack
  • Elasticity
  • Local IRBF
  • Meshless
  • Moving IRBF
  • Partition of unity
  • RBF
  • Superconvergence

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 galerkin meshless method. CMES - Computer Modeling in Engineering and Sciences, 66(1), 25-52.

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

In: CMES - Computer Modeling in Engineering and Sciences, Vol. 66, No. 1, 13.12.2010, p. 25-52.

Research output: Contribution to journalArticle

Le, PBH, Rabczuk, T, Mai-Duy, N & Tran-Cong, T 2010, 'A moving IRBFN-based galerkin meshless method', CMES - Computer Modeling in Engineering and Sciences, vol. 66, no. 1, pp. 25-52.
Le PBH, Rabczuk T, Mai-Duy N, Tran-Cong T. A moving IRBFN-based galerkin meshless method. CMES - Computer Modeling in Engineering and Sciences. 2010 Dec 13;66(1):25-52.
Le, Phong B H ; Rabczuk, Timon ; Mai-Duy, Nam ; Tran-Cong, Thanh. / A moving IRBFN-based galerkin meshless method. In: CMES - Computer Modeling in Engineering and Sciences. 2010 ; Vol. 66, No. 1. pp. 25-52.
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