RESUMEN
A common approach when employing discrete mathematical models is to assess the reliability and credibility of the computation of interest through a process known as solution verification. Present-day computed head-related transfer functions (HRTFs) seem to lack robust and reliable assessments of the numerical errors embedded in the results which makes validation of wave-based models difficult. This process requires a good understanding of the involved sources of error which are systematically reviewed here. The current work aims to quantify the pinna-related high-frequency computational errors in the context of HRTFs and wave-based simulations with finite-difference models. As a prerequisite for solution verification, code verification assesses the reliability of the proposed implementation. In this paper, known and manufactured formal solutions are used and tailored for the wave equation and frequency-independent boundary conditions inside a rectangular room of uniform acoustic wall-impedance. Asymptotic estimates for pinna acoustics are predicted in the frequency domain based on regression models and a convergence study on sub-millimeter grids. Results show an increasing uncertainty with frequency and a significant frequency-dependent change among computations on different grids.
RESUMEN
The scattering around the human pinna that is captured by the Head-Related Transfer Functions (HRTFs) is a complex problem that creates uncertainties in both acoustical measurements and simulations. Within the simulation framework of Finite Difference Time Domain (FDTD) with axis-aligned staircase boundaries resulting from a voxelization process, the voxelization-based uncertainty propagating in the HRTF-captured sound field is quantified for one solid and two surface voxelization algorithms. Simulated results utilizing a laser-scanned mesh of Knowles Electronics Manikin for Acoustic Research (KEMAR) show that in the context of complex geometries with local topology comparable to grid spacing such as the human pinna, the voxelization-related uncertainties in simulations emerge at lower frequencies than the generally used accuracy bandwidths. Numerical simulations show that the voxelization process induces both random error and algorithm-dependent bias in the simulated HRTF spectral features. Frequencies fr below which the random error is bounded by various dB thresholds are estimated and predicted. Particular shortcomings of the used voxelization algorithms are identified and the influence of the surface impedance on the induced errors is studied. Simulations are also validated against measurements.