A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals

Hui Zheng, Zhang Chuanzeng, Yuesheng Wang, Jan Sladek, Vladimir Sladek

Research output: Contribution to journalArticle

32 Citations (Scopus)


In this paper, a meshfree or meshless local radial basis function (RBF) collocation method is proposed to calculate the band structures of two-dimensional (2D) anti-plane transverse elastic waves in phononic crystals. Three new techniques are developed for calculating the normal derivative of the field quantity required by the treatment of the boundary conditions, which improve the stability of the local RBF collocation method significantly. The general form of the local RBF collocation method for a unit-cell with periodic boundary conditions is proposed, where the continuity conditions on the interface between the matrix and the scatterer are taken into account. The band structures or dispersion relations can be obtained by solving the eigenvalue problem and sweeping the boundary of the irreducible first Brillouin zone. The proposed local RBF collocation method is verified by using the corresponding results obtained with the finite element method. For different acoustic impedance ratios, various scatterer shapes, scatterer arrangements (lattice forms) and material properties, numerical examples are presented and discussed to show the performance and the efficiency of the developed local RBF collocation method compared to the FEM for computing the band structures of 2D phononic crystals.
Original languageEnglish
Pages (from-to)997-1014
Number of pages18
JournalJournal of Computational Physics
Early online date4 Nov 2015
Publication statusPublished - 15 Jan 2016
Externally publishedYes



  • Local RBF collocation method
  • Meshfree or meshless method
  • Two-dimensional phononic crystals
  • Band structures
  • Anti-plane transverse elastic waves

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