Scalar wave equation by the boundary element method: a D-BEM approach with non-homogeneous initial conditions

Abstract

This work is concerned with the development of a D-BEM approach to the solution of 2D scalar wave propagation problems. The time-marching process can be accomplished with the use of the Houbolt method, as usual, or with the use of the Newmark method. Special attention was devoted to the development of a procedure that allows for the computation of the initial conditions contributions. In order to verify the applicability of the Newmark method and also the correctness of the expressions concerned with the computation of the initial conditions contributions, four examples are presented and the D-BEM results are compared with the corresponding analytical solutions.

Boundary element method formulations for the solution of the scalar wave equation in one-dimensional problems

“…The computation of the initial conditions contributions, in the case of the D-BEM formulation, is carried out by following the approach presented by [6]. The procedure is summarized below:…”

“…n and, for the third case, x f = x k?1 . After substituting (6) and (10) in Eq. (13), it can be rewritten as:…”

“…As mentioned before, the Houbolt method has been widely used with both D-BEM and DR-BEM formulations, see Carrer and Mansur [6] and [1].…”

“…The acceleration is assumed to vary linearly inside each cell. Once the spatial discretization has been carried out, the resulting matrices can be assembled, thus generating an enlarged system of equations, typical from D-BEM formulations, [6], written below:…”

“…It is important to mention that although other time-marching schemes were recently proposed, see [5,7,23], the search for acceleration approximations is a task that still deserves attention. The presence of non-homogeneous initial conditions is taken into account by following the procedure presented by Carrer et al [6]. For a more complete discussion concerning dynamic analysis by the BEM, the reader is referred to Beskos [3] and Manolis and Polyzos [16].…”