Boundary and coupled boundary-finite element methods for transient wave-structure interaction

We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well-posedness along with stability and error bounds with explicit time dependence are established. Full discretization is achieved coupling boundary and finite elements; convolution quadrature (CQ) is used for time evolution in the pure boundary integral equation formulation and combined with time stepping in the coupled boundary-finite element method (BEM-FEM) scenario. Second-order convergence in time is proved for BDF2-CQ and numerical experiments are provided for both BDF2 and trapezoidal rule CQ showing second-order behaviour for the latter as well.