Modeling head- and pinna-related transfer functions using boundary elements and finite differences with volume penalization

Abstract Head-related transfer functions (HRTFs) describe the free-field sound transmission to the ears and are fundamental to most virtual and augmented reality systems. However, measuring HRTFs is time-consuming and error-prone, making wave-based simulations of HRTFs an appealing alternative. This paper compares a finite-difference time-domain (FDTD) method incorporating a volume penalization approach for modeling rigid boundaries with an established fast multipole boundary element method (fmBEM). The simulation models are verified by comparing them with the analytical solution for diffraction around a rigid sphere. Additionally, the grid requirements for representing rigid walls in the FDTD framework are analyzed. The models are validated using measurements of an outer ear and are compared in simulations of a complete head. Both methods show good agreement with analytical solutions and measured data close to the order of magnitude of just noticeable differences. Due to its higher computational cost, the FDTD method is particularly suitable for interior problems and smaller volumes. However, its applicability can be extended using range extrapolation methods.