Beugungssimulation ohne Rechenzeitexplosion: Die Methode der quantisierten Pyramidenstrahlen : ein neues Berechnungsverfahren für Raumakustik und Lärmimmissionsprognose ; Vergleiche, Ansätze, Lösungen
In room acoustics and noise immission prognosis, basically three algorithms for the computation of sound fields are in use. These are, in the order of reflection where they are efficient: the mirror image source method ray tracing methods (ray or beam tracing), among these tracing and recursive splitting of pyramidal beams ("pyrs"), and, sometimes to simulate the late reverberation, the radiosity method basing on the radiation interchange of pairs or surface patches. But, caused by their nature, the mean deficit of these geometrical and energetic methods is not to take wave effects as diffraction into account. But, with diffraction, the number of rays and computation time would explode exponentially. It was the aim, by introduction of diffraction modules, to extend those methods to lower frequencies respectively longer wavelengths where the room may be large but is not very large compared with wavelengths and to find a new uniform and universal algorithm to allow arbitrary combinations of reflections and diffractions, but without explosion of computation time. The idea for the solution: rays must be re-unified! This is achieved by quantization of solid angles as well as room surface into small patches and summing up of pyr energies arriving at the patches within certain time intervals. Both means: quantization of the space of mirror image sources. Pyrs whose vertices fall into cells of that mirror image source space are shifted to their center points, projected back to the original room, but not split up by the surface patches into smaller and smaller pyrs but, according to their overlap with the patches, their energies are interpolated and distributed to previously created quantized pyrs whose shapes are defined by aiming at the patches. To make pyr tracing efficient, a previous sub-division of the room's surface into convex walls and many small patches and a sub-division of the volume into convex sub-rooms is necessary. This is accomplished by the introduction of "transparent walls" between the sub-rooms. Thereby, a considerable simplification of the otherwise complicated pyr clipping procedure (polygon-polygon-intersections) is achieved, moreover, an elegant discovering of diffraction events at surface patches near to the edges on those transparent walls. Inspired by the uncertainty relation, for that purpose, an energetic ray diffraction model has been developed working with "deflection-angle-probability-density-functions" whose values are the higher the closer the ray passes an edge. Now, a huge amount of quantized pyrs are traced quasi-parallel in a kind of energy interchange procedure where the number of beams converges against a maximum value which may be set up by the user. Thus, quantized pyramidal beam tracing is a combination of the radiosity with the mirror image source method. With typical room acoustical applications, computation times may lie in the order of minutes up to some hours with modern PC. However, the required RAM is very high: 100MB-100GB. So, the goal has been reached. However, the algorithms proposed still have to be implemented and validated.
info:eu-repo/classification/ddc/530, Schallausbreitung, Beugung, Numerisches Verfahren, Physik, Raumakustik, numerische Akustik, Lärmimmissionsprognose, Simulation, Algorithmen, Pyramidenstrahlen
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