Incidence directivity analysis for a hemisphere region with an absorbing surface on a rigid wall

We have conducted the incidence directivity analysis of sound fields using post-processing of the Fast Multipole Boundary Element Method (FMBEM). This analysis can be applied to observe the directivity at a receiving region, which leads to evaluate sound-field diffuseness. However, it has a limitation that the receiving region must be in a space not including any boundary surface, due to the theory of plane wave expansions. On the other hand, it is generally important to evaluate the incidence directivity on a boundary surface, such as on a test sample area in a reverberation room. In this study, we propose a new approach to the incidence directivity analysis for a hemisphere receiving region on a rigid surface, assuming that a mirror image of the sound field is adjoined to the original field. This approach removes the limitations of plane wave expansions and enables the analysis for a boundary surface in the hemisphere region. We apply this method to analyze the incidence directivity on an absorbing surface in two types of reverberation rooms with rectangular and irregular shapes. Numerical results demonstrate the effects of the absorption conditions and the room geometry on the incidence directivity.