Boundary and coupled boundary-finite element methods for transient wave-structure interaction
Provides rigorous numerical analysis for transient wave-structure interaction, benefiting computational acoustics and structural mechanics communities.
The paper develops time-domain boundary integral and coupled BEM/FEM formulations for acoustic scattering by elastic obstacles, proving well-posedness, stability, and second-order convergence in time, with numerical experiments confirming the theoretical rates.
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 is used for time evolution in the pure BIE formulation and combined with time stepping in the coupled BEM/FEM scenario. Second order convergence in time is proven for BDF2-CQ and numerical experiments are provided for both BDF2 and Trapezoidal Rule CQ showing second order behavior for the latter as well.