Higher-order Finite Difference Time Domain Algorithms for Room Acoustic Modelling

The acoustic qualities of indoor spaces are fundamental to the intelligibility of speech, the quality of musical performances, and perceived noise levels. Computationally heavy wave-based acoustic modelling algorithms have gained momentum in the field of room acoustic modelling, as ever-increasing computational power makes their use more feasible. Most notably the Finite Difference Time Domain (FDTD) method is often employed for rendering the low- and mid-frequency part of room impulse responses (RIRs). However, this algorithm has known disadvantages, most prominently dispersion error, which renders a large part of the simulated RIR invalid. This thesis is concerned with the implementation and analysis of higher-order FDTD stencils as a means to improve the current state-of-art FDTD methods that solve the room acoustic wave equation. A detailed analysis of dispersive properties, stability, and required grid spacing of current and higher-order stencils is presented, and has been verified using a GPU implementation of the different algorithms. It is argued that the 4th-order stencil gives the best result in terms of output quality versus computational effort. In addition, this thesis focusses on the derivation of absorbing boundaries for the 4th-order scheme, its stability analysis, and detailed analysis of absorptive properties compared to established boundary models for 2nd-order schemes. The newly proposed 4th-order scheme and its boundaries are tested in two case studies: a large shoebox model, in order to test the validity against a common benchmark and a complex acoustic space. For the latter study, impulse responses were measured in the National Centre for Early Music in York, UK, and computationally generated using the current state-of-the-art as well as the proposed 4th-order FDTD algorithm and boundaries. It is shown that the 4th-order stencil gives at least as good as, or better results than those achieved using the 2nd-order stencil, at lower computational costs.