  An overlapped continuous model framework, for the Helmholtz wave propagation
problem in unbounded regions comprising bounded heterogeneous media, was
recently introduced and analyzed by the authors ({\tt J. Comput. Phys., {\bf
403}, 109052, 2020}). The continuous Helmholtz system incorporates a radiation
condition (RC) and our equivalent hybrid framework facilitates application of
widely used finite element methods (FEM) and boundary element methods (BEM),
and the resulting discrete systems retain the RC exactly. The FEM and BEM
discretizations, respectively, applied to the designed interior heterogeneous
and exterior homogeneous media Helmholtz systems include the FEM and BEM
solutions matching in artificial interface domains, and allow for computations
of the exact ansatz based far-fields. In this article we present rigorous
numerical analysis of a discrete two-dimensional FEM-BEM overlapped coupling
implementation of the algorithm. We also demonstrate the efficiency of our
discrete FEM-BEM framework and analysis using numerical experiments, including
applications to non-convex heterogeneous multiple particle Janus
configurations. Simulations of the far-field induced differential scattering
cross sections (DSCS) of heterogeneous configurations and orientation-averaged
(OA) counterparts are important for several applications, including inverse
wave problems. Our robust FEM-BEM framework facilities computations of such
quantities of interest, without boundedness or homogeneity or shape
restrictions on the wave propagation model.
