A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry

Hui Zheng, Zhenjun Yang, Chuanzeng Zhang, Mark Tyrer

    Research output: Contribution to journalArticle

    19 Citations (Scopus)
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    Abstract

    A numerical algorithm based on the local radial basis function collocation method (LRBFCM) is developed to efficiently compute the derivatives of primary field quantities. Instead of a direct calculation of the derivatives by partial differentiation of the shape functions as in traditional numerical approaches, the derivative calculation in the present work is performed using a simple finite difference scheme with an introduced fictitious node. The developed algorithm is geometrically very flexible and can be easily applied to the continuity and boundary conditions of arbitrary geometries, which require an accurate derivative computation of the primary field quantities. The developed LRBFCM are applied to phononic crystals with scatterers of arbitrary geometry, which has not yet been reported before to the authors’ knowledge. A few examples for anti-plane elastic wave propagation are modelled to validate the developed LRBFCM. A comparison with finite element modelling shows that the present method is efficient and flexible.
    Original languageEnglish
    Pages (from-to)447-459
    Number of pages13
    JournalApplied Mathematical Modelling
    Volume60
    Early online date21 Mar 2018
    DOIs
    Publication statusPublished - Aug 2018

    Bibliographical note

    NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematical Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematical Modelling, [60, (2018)] DOI: 10.1016/j.apm.2018.03.023

    © 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

    Keywords

    • Phononic crystals
    • Radial basis functions
    • Eigenvalue problems
    • Band structures
    • Elastic wave propagation
    • Interface conditions

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