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Boundary and coupled boundary-finite element methods for transient wave-structure interaction. (English) Zbl 1433.74114

Summary: 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.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
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