Pinna-related transfer functions and lossless wave equation using finite-difference methods: Verification and asymptotic solution

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.