ISBN 9783843902731

978-3-8439-0273-1, Reihe Informationstechnik

Konrad Kowalczyk
Boundary and medium modelling using compact finite difference schemes in simulations of room acoustics for audio and architectural design applications

240 Seiten, Dissertation Queen’s University Belfast (2008), Softcover, A5

Zusammenfassung / Abstract

Simulation of acoustic spaces with the aim of developing virtual immersive applications and architectural design applications is one of the key areas in the field of audio signal processing. In this book, a complete method for simulating room acoustics using compact finite difference time domain (FDTD) schemes is presented.

A family of compact explicit and implicit schemes approximating the wave equation is analysed in terms of stability, accuracy, and computational efficiency. The most accurate and isotropic schemes based on a rectilinear nonstaggered grid are identified, and the optimally efficient explicit schemes are indicated.

Novel FDTD formulations of frequency-independent and frequency-dependent boundaries of a locally reacting surface type are proposed, including a full treatment of corners and boundary edges. In particular, it is proposed to model generally frequency-dependent boundaries by local incorporation of a digital impedance filter (DIF), and the resulting formulae for compact explicit schemes are provided. In addition, a numerical boundary analysis (NBA) procedure is proposed as a technique for analytic evaluation of the numerical reflectance of the presented boundary models. The digital impedance filter model is also extended to model controllable surface diffusion based on the concept of phase grating diffusers.

Results obtained from numerical experiments and numerical boundary analysis confirm the high accuracy of the proposed boundary models, the reflectance of which is shown to closely approximate locally reacting surface theory for different angles of incidence and various impedances. Furthermore, the results indicate that boundary formulations based on the identified accurate and isotropic schemes are also very accurate in terms of numerical reflectance, and outperform directly related methods such as Yee's scheme and the standard digital waveguide mesh. In addition, one particular scheme - referred to as the interpolated wideband scheme - is suggested as the best FDTD scheme for most audio applications.