A comparison between the high-frequency Boundary Element Method and Surface-Based Geometrical Acoustics

The audible frequency range covers many octaves in which the wavelength changes from being large with respect to dominant features of a space to being comparatively much smaller. This makes numerical prediction of a space's acoustic response, e.g. for auralisation, extremely challenging if all frequencies are to be represented accurately. Different classes of algorithm give the best balance of accuracy to computational cost in different frequency bands - 'wave solvers' such as Boundary Element Method (BEM) at low frequencies and Geometrical Acoustics (GA) methods at high frequencies. But combining their output data can be an awkward process due to their very different formulations. This is particularly important for early reflections, which give crucial spatial perceptual cues. Hence there is a need for a unified full audible bandwidth algorithm for early reflections. This paper will describe ongoing research to develop such an algorithm by exploiting synergies between high-frequency BEM and GA. It will describe how appropriately chosen oscillatory basis functions in BEM can produce leading-order GA behaviour at high frequencies and explore how interactions between these compare to the same interactions arising in a surface-based Geometrical Acoustics scheme.