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This article is concerned with the presentation of a time-domain BEM approach applied to the solution of the scalar wave equation for 2D problems. The basic idea is quite simple: the basic variables of the problem at time tn (potential and flux) are computed with the results related to the potential and to its time derivative at time tn-1 playing the role of "initial conditions". This time-marching scheme needs the computation of the potential and its time derivative at all boundary nodes and internal points, as well as the entire discretization of the domain. The convolution integrals of the standard time-domain BEM formulation, however, are not computed; the matrices assembled, only at the initial time interval, are those related to the potential, flux and to the potential time derivative. Two examples are presented and discussed at the end of the article, in order to verify the accuracy and potentialities of the proposed formulation. [ABSTRACT FROM AUTHOR]

There exist quite a number of published papers showing that BEM/FEM coupling in time domain is a robust procedure leading to great computer time savings for infinite domain analyses. However, in many cases, the procedures presented so far have considered only constant time interpolation for BEM tractions, otherwise one may have (mainly in bounded domains) strong oscillations which invalidate the results. In this paper, such a limitation is overcome by employing the linear θ method which consists, basically, of computing the response at the time tn+1 from the response previously computed at the time tn+θ, θ⩾ 1.0. This procedure is implicitly incorporated into the BEM algorithm in the coupled BEM/FEM process presented here, i.e. the response is calculated directly at time tn+1. Proceeding this way, it becomes possible to adopt the Newmark scheme in the FEM algorithm. Two examples are presented in order to validate the formulation. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this paper. Copyright © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]