A new space–time energetic formulation for wave propagation analysis in layered media by BEMs

In this paper, considering a Dirichlet–Neumann problem for 1D wave propagation analysis in layered media reformulated in terms of boundary integral equations, we compare two classical weak formulations for the boundary element method with a new space–time energetic formulation. Continuity and coerciveness of the bilinear form corresponding to this last formulation are proved. Several numerical results will be presented, pointing out the numerical properties of the derived linear systems. Instability phenomena arising using one of the classical techniques can be prevented choosing suitable time steps in the discretization phase, of course with a higher computational cost with respect to the new procedure, which appears to be unconditionally stable.