# Synergies between the high-frequency boundary element method and geometric room acoustic modelling techniques

**Speaker:** Jonathan Hargreaves, Acoustics Research Centre, University of Salford, Manchester

**Title:** Synergies between the high-frequency boundary element method and geometric room acoustic modelling techniques

**Abstract: **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 purposes, extremely challenging if all frequencies are required to be represented accurately, and different classes of algorithm give the best balance of accuracy to computational cost in different frequency bands. At low frequencies, wave effects such as diffraction and interference are essential, but methods that model the underlying PDEs directly have a computational cost that scales with problem size and frequency, thereby limiting them to small or low frequency scenarios. At high frequencies, geometric ray and sound-beam energy descriptions are more efficient, but the maximum accuracy they can achieve is limited by how well the geometric assumption represents sound propagation in a given scenario; this comprises their accuracy at low frequencies in particular. Hence it is often necessary to operate two algorithms in parallel handling the different bandwidths. Due to their differing formulations however, combing the output data can be a rather arbitrary process.

There is therefore a need for a unified full audible bandwidth algorithm, for deterministic early reflections at least; at later time the wave field becomes chaotic and the computational cost of this will likely outweigh the benefits. This talk will discuss some first steps taken in that direction by examining synergies between the Boundary Element Method (BEM) and geometric approaches. Specifically, it will focus on how the use of appropriately chosen oscillatory basis functions in BEM can produce leading-order geometric behaviour at high frequencies. A new boundary integral equation, that we are calling ‘Wave Matching’, will be introduced, and some rather remarkable properties that it possesses will be discussed. How this might ultimately produce a single unified full-bandwidth algorithm for early-time will be outlined.