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In both room and city acoustics, the simulation of sound propagation is stillchallenging. The handling of diffraction is still topic of current research, especiallythe diffraction of higher orders. Due to the large scale of the environmentcompared to the typical wavelengths of sound, Geometrical Acoustic (GA)simulation methods are used rather than exact wave theoretical simulationmethods. These GA methods handle sound as particles instead of waves (waveparticledualism as known from optics). Based on this restriction, wave effects suchas diffraction have to be modelled explicitly.In this work, a diffraction formulation called Uncertainty relation Based Diffraction(UBD) by Stephenson is investigated and extended. The UBD is based onHeisenberg's uncertainty relation and the Fraunhofer diffraction theory. The greatadvantage of this formulation is that the straight forward propagation technique ofparticles can be used and integrated as a module in the simulation. However, it willbe shown that some assumptions of former publications are not well founded, suchthat alternative formulations are presented. Good agreements with the wavetheoretical reference methods are shown in almost all cases. In addition to formerpublications, the UBD method is extended to 3D.Unfortunately, the usage of the UBD diffraction module causes a split-up ofparticles, such that the computation time increases exponentially. To overcome thissplit-up, the reunification of particles is aspired. Quantized Pyramidal Beam Tracing(QPBT) and the Sound Particle Radiosity (SPR) aim at this reunification. It will beshown that SPR is both more efficient and more accurate than QPBT. However, thememory effort of the SPR yields a major bottleneck. First optimizations to decreasethe memory effort will be presented to overcome this issue.
