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

Area of Science:

• Acoustics
• Computational Physics
• Numerical Analysis

Background:

• Discrete mathematical models require solution verification to ensure computational reliability.
• Current head-related transfer functions (HRTFs) often lack robust numerical error assessment, hindering wave-based model validation.
• Understanding error sources is crucial for accurate computational acoustics.

Purpose of the Study:

• To quantify pinna-related high-frequency computational errors in HRTFs.
• To assess the reliability of finite-difference wave-based simulations for HRTF computation.
• To establish a foundation for solution verification in acoustic simulations.

Main Methods:

• Systematic review of error sources in wave-based simulations.
• Code verification using known and manufactured formal solutions for the wave equation.
• Asymptotic prediction of pinna acoustics using regression models and convergence studies on sub-millimeter grids.

Main Results:

• Computational errors in HRTFs increase with frequency.
• Significant frequency-dependent variations observed across different computational grids.
• Asymptotic estimates for pinna acoustics were successfully predicted.

Conclusions:

• Numerical uncertainty in HRTF computations is frequency-dependent and increases at higher frequencies.
• Finite-difference models require careful grid selection and verification for reliable HRTF prediction.
• This work provides a methodology for assessing numerical errors in acoustic simulations.