Implementation and application of complete radiation boundary conditions: A demonstration

The radiation of energy to the far field is a fundamental feature of many problems in acoustics. Efficient numerical algorithms for simulating sound propagation in the time domain must therefore include convergent near-field domain truncation procedures. For problems modeled by uniform or stratified far fields, complete radiation boundary conditions provide a provably optimal domain truncation algorithm. In particular, they are spectrally convergent in boundary condition order and can be placed quite close to scatterers or other inhomogeneities. However, the mathematical description of the radiation conditions looks complicated in comparison with less-efficient methods, such as perfectly matched layers or simple damping. In this demonstration, we show how complete radiation conditions can be implemented in a standard discontinuous Galerkin code as easily as other schemes. In fact, the implementation is shown to simply involve a single extra element with a nonstandard differentiation matrix.