Optimised implicit finite-difference schemes for the wave equation with admittance boundary conditionsa)

Area of Science:

• Acoustics
• Computational physics
• Numerical methods

Background:

• Wave-based acoustic simulation provides accurate room auralisation but faces high computational costs.
• Existing explicit methods often require excessive computation time and memory, limiting their practical application.

Purpose of the Study:

• To develop computationally efficient implicit finite-difference schemes for full-bandwidth room auralisation.
• To reduce the computational time and memory usage of acoustic simulations.

Main Methods:

• Development of a family of implicit finite-difference schemes.
• Optimization of schemes against a wideband error criterion for improved numerical accuracy.
• Implementation of stable admittance boundaries for general staircased geometries.

Main Results:

• Achieved full audio bandwidth simulation up to 20 kHz.
• Demonstrated reduced computational times and memory usage compared to explicit methods.
• Validated stability, accuracy, and performance through numerical examples.

Conclusions:

• Optimized implicit finite-difference schemes offer a practical solution for computationally demanding room auralisation.
• Coarse grid resolutions are feasible due to improved numerical accuracy, enhancing efficiency.
• The developed methods are stable and accurate for complex geometries.