  A coupling approach is presented to combine a wave-based method to the
standard finite element method. This coupling methodology is presented here for
the Helmholtz equation but it can be applied to a wide range of wave
propagation problems. While wave-based methods can significantly reduce the
computational cost, especially at high frequencies, their efficiency is
hindered by the need to use small elements to resolve complex geometric
features. This can be alleviated by using a standard Finite-Element Model close
to the surfaces to model geometric details and create large, simply-shaped
areas to model with a wave-based method. This strategy is formulated and
validated in this paper for the wave-based discontinuous Galerkin method
together with the standard finite element method. The coupling is formulated
without using Lagrange multipliers and results demonstrate that the coupling is
optimal in that the convergence rates of the individual methods are maintained.
