Modelling of Wave Propagation using Spectral Finite Elements

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)