Numerical results for the wave propagation problem with space-time boundary element method

The aim of the present contribution is the analysis of one-dimensional wave propagation problems, rewritten as BIEs directly in space-time domain, thus avoiding the use of the Laplace transform and of its inversion: the transformation back to time domain employs particular procedure corresponding to a linear multi-step method for ordinary differential equations [Becache, 1993, Lubich, 1988a, Lubich, 1988b, Bamberger and Duong, 1986a]. Some different approximation techniques will be used, analyzing and comparing the numerical properties of the derived linear systems: the first comes from a classical weak formulation of the corresponding BIE, the second from a new energetic weak formulation which has a more robust theoretical background. An alternative weak formulation of the BIEs is the one presented in [Bamberger and Duong, 1986a], [Bamberger and Duong, 1986b], which is based on the Laplace-Fourier transform of the differential problem and its inversion