On the accuracy of finite-difference time-domain simulations of head-related transfer functions as a function of model complexity

Wave-based numerical tools such as finite-difference time-domain (FDTD) solvers are useful for modeling several acoustic properties and interactions. While these numerical tools are widely used in acoustics, there seems to be less attention to assessing the quality of the produced outputs. However, in order to ensure that the obtained results are reliable, the quantification of the errors present in the simulation results is an essential step. There exists a mathematical process known as solution verification which aims at assessing the accuracy of the computed solutions. A relevant application for the FDTD method is the simulation of head-related transfer functions (HRTFs), since these are relatively complex to acoustically measure on humans. This paper aims at applying the solution verification process on HRTF modeling using the FDTD method to evaluate the accuracy of the simulated HRTF magnitudes with increased human head/torso model complexity. The FDTD-simulated HRTFs are also compared with respect to the similarity/dissimilarity of their spectrum and with respect to the relevance of these spectral variations on sound source localization. The results show that asymptotically extrapolating the FDTD-simulated HRTFs from a series of simulations provides more accurate HRTF predictions when compared to using single FDTD simulations ran on sub-millimeter grids, regardless of the model complexity. Results also demonstrate that the accuracy of the FDTD-simulated HRTF predictions decreases with increased model complexity. The localization performance predictions showed that the largest localization errors were obtained with models with the lowest complexities. Significant differences in predicted sound source localization performance were found between FDTD-simulated results.