Modelling wave propagation phenomena in time domain by using the symmetric Galerkin BEM and the Convolution Quadrature Method

Abstract

AbstractThe boundary element method (BEM) is known to be well suited to treat wave propagation phenomena. Here, a 3‐d elastodynamic body is under consideration. For a numerical treatment of the underlying boundary integral equations appropriate time and spatial discretizations have to be introduced. The time discretization is done via the Convolution Quadrature Method (CQM) as proposed by Lubich while a symmetric Galerkin scheme is applied in space.Unfortunately, the symmetric Galerkin boundary element method (SGBEM) requires the use of the second boundary integral equation involving a hypersingular kernel. Therefore, an appropriate regularization of the hypersingular bilinear form has to be established.Finally, a numerical study show that the presented approach yields good convergence rates as well as good numerical stability properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)