A-priori mesh grading for the numerical calculation of the head-related transfer functions

TL;DR

This paper introduces an a-priori mesh grading algorithm that reduces computational costs in calculating head-related transfer functions (HRTFs) via the boundary element method, while maintaining accuracy and localization performance.

Contribution

The study proposes a novel mesh preprocessing technique that varies element sizes based on a grading function, improving efficiency in HRTF numerical calculations.

Findings

Mesh grading reduces computational costs significantly.

The method maintains high numerical accuracy in HRTF calculations.

Localization performance predictions are improved with graded meshes.

Abstract

Head-related transfer functions (HRTFs) describe the directional filtering of the incoming sound caused by the morphology of a listener's head and pinnae. When an accurate model of a listener's morphology exists, HRTFs can be calculated numerically with the boundary element method (BEM). However, the general recommendation to model the head and pinnae with at least six elements per wavelength renders the BEM as a time-consuming procedure when calculating HRTFs for the full audible frequency range. In this study, a mesh preprocessing algorithm is proposed, viz., a-priori mesh grading, which reduces the computational costs in the HRTF calculation process significantly. The mesh grading algorithm deliberately violates the recommendation of at least six elements per wavelength in certain regions of the head and pinnae and varies the size of elements gradually according to an a-priori defined grading function. The evaluation of the algorithm involved HRTFs calculated for various geometric objects including meshes of three human listeners and various grading functions. The numerical accuracy and the predicted sound-localization performance of calculated HRTFs were analyzed. A-priori mesh grading appeared to be suitable for the numerical calculation of HRTFs in the full audible frequency range and outperformed uniform meshes in terms of numerical errors, perception based predictions of sound-localization performance, and computational costs.