Numerical and perceptual evaluations of finite-difference time-domain simulations for room acoustics applications

Abstract

The finite-difference time-domain (FDTD) method has been and continues to be widely used as a computational room acoustic modeling technique. In that context, the method aims to numerically solve the wave equation in enclosed spaces. One impediment to the efficiency of the method is its large computational cost due to the volumetric discretization of the simulation domain. Although its performance can significantly be improved by using graphics processing units (GPUs), the accuracy of the FDTD-computed solutions remains limited by the numerical errors that the method entails. This dissertation focuses on the analysis of the discretization error which not only limits the numerical accuracy of the simulation results, but also the perceptual accuracy by giving raise to audible artefacts in the auralizations. Also considering some of the key elements which constitute an immersive audio application, the analysis is carried out in the context of binaural synthesis and head-related transfer function (HRTF) prediction. Publications I and II explore to what extent the numerical accuracy of the FDTD solutions is limited by the discretization error in the prediction of HRTFs for the simple case of a single sphere model and for the more complex case of a two-sphere model. The results, similar for both models, show that more accurate HRTF predictions can be obtained by using a series of grids instead of running a single simulation over a small grid. The perceptual accuracy of the FDTD computations is explored in Publications IV and V in the context of binaural auralizations. More specifically, Publication IV investigates spherical receiver arrays minimizing the audible artefacts induced by the discretization error. The results show that increasing the receiver density for a fixed array size, which increases the robustness of the array, does not necessarily render the error inaudible in the auralizations. In Publication V, perceptual detection thresholds for the numerical error are measured in binaural auralizations of two acoustically different rooms. The results show that the perceptual detection threshold is generally lower for the most reverberant room and greatly depends on the source signal. It is the most noticeable with an impulse as source signal, and almost unnoticeable with speech. The capability of an FDTD solver in predicting complex room acoustic scenarios is also evaluated in Publication III, by comparing FDTD-simulated results with both measurement data and the results from another well-established wave-based method. While the two numerical methods are in agreement, large deviations between the measurement data and the simulated results indicate that typical material data-sets poorly represent the behaviour of real materials in a room.