A Combination of the Sound Particle Simulation Method and the Radiosity Method

Abstract

In room and urban acoustics, ray tracing as well as, for the reverberation tail, radiosity based simulation methods are in use. Any implementation of diffraction into the sound particle simulation method, i.e. a variant of ray tracing, causes a split-up of sound particles and an explosion of computation time. To prevent that, a re-unification effect of sound energies has to be achieved as known from the radiosity method. For this purpose, the discretization of the walls into small patches is applied to the sound particle simulation method. This combination is called the sound particle radiosity method. In the main part of this paper the efficiency of the presented sound particle radiosity in investigated by deriving a statistical re-unification formula as a function of the main quantization parameter: the patch size. Furthermore the error due to quantization is described as a function of the patch size. It is shown, that smaller patches increase accuracy, but larger patches increase the efficiency. The smearing of echograms due to the receiver size mainly masks the quantization error when the receiver size is at least 10 times the patch size. This investigation, restricted to 2D, serves as a feasibility test for quantized pyramidal beam tracing.