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Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method
Author(s) -
El Kacimi A.,
Laghrouche O.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2471
Subject(s) - partition of unity , finite element method , mathematical analysis , extended finite element method , mixed finite element method , scattering , basis function , plane wave , boundary value problem , mathematics , geometry , physics , optics , thermodynamics
In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time‐harmonic elastic wave equations. The aim of the proposed work is to accurately model two‐dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd.