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

Wave-based acoustic simulation offers, in theory, a complete solution to the problem of room auralisation. In practice, however, the computational requirements of such simulations, in terms of both computation time and memory usage are very large even for moderately-sized rooms. In this article, a family of implicit finite-difference schemes is described that can enable simulation over the full audio bandwidth up to 20 kHz. When optimised against a wideband error criterion, the schemes' improved numerical accuracy allows a coarse grid resolution to be used, in turn leading to reduced computational times and memory usage compared with commonly used explicit methods. The schemes are complemented by provably stable admittance boundaries over a general staircased geometry. Various numerical examples illustrate the stability, accuracy and performance results achieved with the optimised schemes.