An energy approach to space-time Galerkin BEM for wave propagation problems

In this paper we consider Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations (BIEs) with retarded potential. In the first part, starting from a natural energy identity, a space-time weak formulation for the BIEs related to 1D problems is presented, and continuity and coerciveness properties of the related bilinear form are proved. Then, a theoretical analysis of an extension of the introduced formulation for 2D problems is proposed. At last, various numerical results will be presented, discussed and compared with those obtained with the classical Galerkin Boundary Element Method (BEM), showing unconditional stability of the energy approach.