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A coupled BEM/FEM formulation for the transient interaction between anacoustic field and a piezoelectric scatterer is proposed. The scattered part ofthe acoustic wave is represented in terms of retarded layer potentials whilethe elastic displacement and electric potential are treated variationally. Thisresults in an integro-differential system. Well posedness of a general Galerkinsemi-discretization in space of the problem is shown in the Laplace domain andtranslated into explicit stability bounds in the time domain. Trapezoidal-Ruleand BDF2 Convolution Quadrature are used in combination with matching timestepping for time discretization. Second order convergence is proven for theBDF2-based method. Numerical experiments are provided for BDF2 and TrapezoidalRule based time evolution.

Boundary-Finite Element discretization of time dependent acoustic scattering by elastic obstacles with piezoelectric behavior