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The discontinuous enrichment method for elastic wave propagation in the medium‐frequency regime
Author(s) -
Zhang Lin,
Tezaur Radek,
Farhat Charbel
Publication year - 2006
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.1619
Subject(s) - superposition principle , finite element method , mathematical analysis , displacement field , mathematics , discontinuous galerkin method , displacement (psychology) , vibration , lagrange multiplier , polynomial , dimension (graph theory) , degrees of freedom (physics and chemistry) , wave propagation , physics , mathematical optimization , pure mathematics , acoustics , psychology , quantum mechanics , psychotherapist , thermodynamics
The discontinuous enrichment method (DEM) is specified and developed for the solution of two‐dimensional elastic wave propagation problems in the frequency domain. The classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions. The continuity of the solution across the element interfaces is weakly enforced by suitable Lagrange multipliers. Higher‐order rectangular DEM elements are constructed and benchmarked against the standard higher‐order polynomial Galerkin elements for two‐dimensional problems in the medium frequency regime. In general, it is found that for such applications, DEM can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom. This highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium. Copyright © 2006 John Wiley & Sons, Ltd.