Time Domain Boundary Element Methods for Acoustic Scattering

Doktorsavhandling, 2008

In room acoustics, numerical computation of scattering phenomena is an important subject, since it is needed to accurately predict the influence of reflectors, the audience, balconies, etc, on the perceived acoustic quality of auditoria. The large physical volumes of auditoria and the wide frequency content of music and speech, together with the complicated geometries involved however, makes predictions in room acoustics a challenging task from a computational point of view. In Paper A, an exact analytical method for computing scattering phenomena in simple situations, the boss-model, is compared with measurements. Paper B presents a semi-analytical method, the time domain boundary element method, which may be used to extend the boss model in Paper A to arbitrary geometries. In the thesis, connections between the two papers are established by comparing the two methods through numerical implementations. The appendices contain details and starting points for extensions of the theory. The time domain boundary element method is implemented using Hermite field interpolation in space and time, while the boundary is discretized using curved triangles, which in turn are defined by interpolating quadric surfaces associated with each node. With this approach, both field and geometry are continuous across boundary elements and time intervals. Moreover, hyper- and strongly singular integrals that appear in the regularization process required for numerical implementation are calculated using vector potentials. In Paper A it is shown that the boss model agrees well with measurements. Initial implementations of the theory of time domain boundary element models in Paper B moreover show promising correlations with analytical benchmark solutions.