This research is concerned with developing efficient computer models for coupling wave propagation exterior to and interior of a bounded heterogenous configuration. Finite element computer models (FEMs) are well suited for general shape inhomogeneous media. However, FEMs require bounded regions for triangulation of the media. Hence, for a mathematical wave propagation model described in unbounded media, standard FEMs require artificial truncation of the unbounded region. Further the truncation requires approximation of the radiation condition. Boundary element computer models (BEMs) for wave propagation do not require such artificial truncations, and the BEM solution ansatz automatically satisfies the radiation condition in the model. However, BEMs require the fundamental solution of the wave propagation models, and hence BEMs are generally restricted to constant coefficient PDE models.
In this work, for simulation of time-harmonic acoustic wave propagation in the heterogeneous media, we couple the interior and exterior computer models by combining and implementing a high-order isoparametric FEM with a spectral BEM. This is achieved through an unknown function on an artificial smooth boundary that couples the interior FEM and exterior BEM solutions. For the Galerkin isoparametric FEM in the interior domain, with non-smooth and curved smooth boundaries, we use high-order spline basis functions to reduce the cost for high frequency models. For the unbounded domain model exterior to the artificial smooth boundary, we use a spectral BEM to reduce the number of interface matrix entries and to obtain high-order convergence of the exterior solution. We demonstrate the approach and its parallel performance for a class of two dimensional smooth and non-smooth configurations.