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