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

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...

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Bibliographic Details
Published in:Applied Mathematical Modelling Vol. 60; p. 447
Main Authors: Zheng, H, Yang, Z, Zhang, Ch, Tyrer, M
Format: Journal Article
Language:English
Published: New York Elsevier BV 01.08.2018
Subjects:
Algorithms
Band structure
Basis functions
Collocation methods
Computation
Crystals
Derivatives
Eigenvalues
Elastic waves
Finite difference method
Finite element method
Geometry
Mathematical analysis
Mathematical models
Numerical analysis
Propagation
Radial basis function
Shape functions
Wave propagation
ISSN:1088-8691, 0307-904X
Online Access:Get full text
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Summary: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.
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ISSN:1088-8691
0307-904X
DOI:10.1016/j.apm.2018.03.023