A. Aimi, M. Diligenti, C. Guardasoni and S. Panizzi
A space-time energetic formulation for wave propagation analysis by BEMs
Received: 25 February 2008
Mathematics Subject Classification (2000): 65N38
In this paper we consider one-dimensional wave propagation problems,
with suitable boundary conditions, reformulated using space-time
boundary integral equations with retarded potential. In the first
part, special attention is devoted to a formulation based on a
natural energy identity that leads to a space-time weak
formulation of the corresponding boundary integral equations with
robust theoretical properties. Continuity and coerciveness of the
bilinear form related to energetic formulation are proved.
Then we compare the new energetic weak formulation with different others time-domain boundary element method procedures applied to wave propagation analysis in layered media. The paper concludes with several numerical tests to demonstrate the effectiveness of the introduced technique in the numerical solution of Dirichlet-Neumann problems in their integral formulation, pointing out the numerical properties of the derived linear systems.