In the context of time harmonic acoustic wave propagation, the Discontinuous Galerkin Finite Element Method (DG-FEM) and the Boundary Element Method (BEM) are nowadays classical numerical techniques. On one hand, the DG-FEM is really appropriate to deal with highly heterogeneous media. In comparison with continuous Finite Elements Method (FEM), this method is well adapted to direct solver since its connectivity diagram is significantly smaller than the one of classical FEM. However, it suffers of numerical pollution: the numerical wave does not propagate at the correct velocity. This can be very problematic when this method is used on very large computational domain or at high frequency. On the other hand, the BEM is one of the most efficient method to deal with homogeneous media, especially when accelerated by a multipole method or thanks to the Adaptive Cross Approximation. Moreover, this method is really less affected by numerical pollution. However, BEM is not adapted to heterogeneous media. In this talk, we would like to present a DG-FEM whose shape functions are defined thanks to a BEM. This new numerical discretization method benefits from the advantages of BEM and DG-FEM: low pollution effect, ability to deal with highly heterogeneous media. Numerous simulations will show the efficiency and the accuracy of the method on large domains.