Galerkin Method In Time Domain BEM Analysis

Abstract

The Galerkin method for time domain boundary element analysis is presented in this paper and used, for the first time in the published literature, as an alternative procedure to improve the stability of the traditional time domain BEM formulation. The comparative analysis between the standard point collocation and Galerkin methods carried out in this paper shows better stability for the latter than for the former. In applications where the time marching process is likely to present instabilities, the Galerkin method should be preferred rather than the standard point collocation method, at the expense of increasing the computational cost which in any case is not significant when late time results are required. INTRODUCTION Most of the papers dealing with time domain BEM formulations which have been published in the past 30 years, employ point collocation methods. In a great deal of the currently available works on transient elastodynamics or scalar wave propagation analysis one finds reports concerning examples where the numerical analysis has either been disturbed by the presence of noise or became invalid as a consequence of an unstable behaviour. As early as 1978, Cole et al ' found the transient dynamic formulation to be unstable, leading to a building up of errors as the time stepping progressed. In 1983, Mansur^ established the general BEM formulation for scalar wave equation. After studying a onedimensional rod under a Heaviside type forcing function, he pointed out that time steps smaller than 0.6L/C (L is the element length, c is the wave propagation speed) may lead to excessive noise which may cause instability and that, on the other hand, large time steps may introduce errors due to violation of the causality condition. Thus the time step value must lie within an interval whose lower and upper limits depend on the problem being studied and the Transactions on Modelling and Simulation vol 20, © 1998 WIT Press, www.witpress.com, ISSN 1743-355X