  Consider the scattering of a time-harmonic acoustic incident wave by a
bounded, penetrable, and isotropic elastic solid, which is immersed in a
homogeneous compressible air or fluid. The paper concerns the numerical
solution for such an acoustic-elastic interaction problem in three dimensions.
An exact transparent boundary condition (TBC) is developed to reduce the
problem equivalently into a boundary value problem in a bounded domain. The
perfectly matched layer (PML) technique is adopted to truncate the unbounded
physical domain into a bounded computational domain. The well-posedness and
exponential convergence of the solution are established for the truncated PML
problem by using a PML equivalent TBC. An a posteriori error estimate based
adaptive finite element method is developed to solve the scattering problem.
Numerical experiments are included to demonstrate the competitive behavior of
the proposed method.
