Development of a 2D boundary element method to model Schroeder acoustic diffusers

Acoustic diffusers are used in the treatment of critical listening environments, and their performance is efficiently predicted by the Boundary Element Method (BEM). Schroeder diffusers are highly effective due to diffusion lobes produced by phase delays from different depth wells. The initial aim of this work was to further develop and optimise a 2D BEM code by Rocchi & Smith (2013) for modelling Schroeder diffusers, through improved computation methods and algorithms. In particular, an analytical integral of the Green's function for diagonal matrix elements was implemented, and the numerical integration methods for all other elements was refined. Computation time decreased by a factor of 50, and average error for the test case of an infinite cylinder reduced by a factor or 200. Intelligent discretisation methods also reduced the number of elements needed for accurate results. The performance of Quadratic Residue Diffusers (QRDs) and QRD modifications was investigated, including the e‚Äövú¬µects of design dimensions, acoustic field type and repeating periods. A systematic approach was used to model the performance of over 40 common diffusers. The superior performance of Quadratic Residue Diffusers (QRDs) with larger sequences was confirmed when modelled in a plane wave acoustic field. However, the performance of QRDs with large sequences decreased significantly when modelled in a point source acoustic field. Preliminary tests of a novel fractal QRD design displayed promising results.