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Modelling of Wave Propagation using Spectral Finite Elements
Author(s) -
Hennings Bianca,
Lammering Rolf
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010003
Subject(s) - legendre polynomials , finite element method , classification of discontinuities , spectral element method , mathematics , mathematical analysis , mass matrix , matrix (chemical analysis) , diagonal , spectral method , lagrange polynomial , stiffness matrix , mixed finite element method , geometry , physics , structural engineering , engineering , materials science , neutrino , nuclear physics , polynomial , composite material
For the analysis of wave propagation at high frequencies, the spectral finite element method (SFEM) is under investigation. In contrast to the conventional finite element method high‐order shape functions are used. They are composed of Lagrange polynomials with nodes at the Gauß‐Lobatto‐Legendre points. The Gauß‐Lobatto‐Legendre integration scheme is applied in order to obtain a diagonal mass matrix. So, the resulting system equations can be solved efficiently. In the numerical examples, spectral finite elements with shape functions of different order are applied to a plane strain problem. The numerical examples cover structures without and with stiffness discontinuities. It is shown that the results agree well with analytical solutions. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)