Efficient and Accurate Sound Propagation Using Adaptive Rectangular Decomposition

Abstract

Accurate sound rendering can add significant realism to complement visual display in interactive applications, as well as facilitate acoustic predictions for many engineering applications, like accurate acoustic analysis for architectural design. Numerical simulation can provide this realism most naturally by modeling the underlying physics of wave propagation. However, wave simulation has traditionally posed a tough computational challenge. In this paper, we present a technique which relies on an adaptive rectangular decomposition of 3D scenes to enable efficient and accurate simulation of sound propagation in complex virtual environments. It exploits the known analytical solution of the Wave Equation in rectangular domains, and utilizes an efficient implementation of the Discrete Cosine Transform on Graphics Processors (GPU) to achieve at least a 100-fold performance gain compared to a standard Finite-Difference Time-Domain (FDTD) implementation with comparable accuracy, while also being 10-fold more memory efficient. Consequently, we are able to perform accurate numerical acoustic simulation on large, complex scenes in the kilohertz range. To the best of our knowledge, it was not previously possible to perform such simulations on a desktop computer. Our work thus enables acoustic analysis on large scenes and auditory display for complex virtual environments on commodity hardware.

An efficient GPU-based time domain solver for the acoustic wave equation

“…In particular, ours is the first solver that can run a 1 second long bandlimited simulation of 1650 Hz for both auralization and visualization purposes, on scenes with realistically complex geometry and air volume in the range of 7, 500 m 3 within 18 minutes on a desktop computer. The single-threaded optimized CPU-based ARD solver presented by Raghuvanshi et al [6] takes 4 hours 40 minutes and the CPU-based high-order FDTD solver based upon Sakamoto et al [4] takes 20 days to run the same simulation on a desktop machine 2 .…”

“…Our formulation is based on the adaptive rectangular decomposition (ARD) technique proposed by Raghuvanshi et al [6]. ARD results in little numerical dispersion error as compared to finite difference methods, allowing for execution on a very coarse grid, approaching the Nyquist limit.…”

“…ARD results in little numerical dispersion error as compared to finite difference methods, allowing for execution on a very coarse grid, approaching the Nyquist limit. This leads to substantial speedups [6]. The ARD technique assumes an isotropic, homogeneous, dissipation-free medium.…”

“…It has been demonstrated recently that impulse responses computed using ARD can be used for perceptually plausible auralizations in interactive applications such as computer games [7]. These reasons, along with the fact that it has been demonstrated to work for both auralization [7,8] and visualization purposes [6], motivated our choice of this technique. For auralization and visualization videos, please checkout the supplementary materials or the link [9].…”

“…In this section, we give an overview of adaptive rectangular decomposition (ARD) solver [6] and highlight its benefits over prior solvers for the acoustic wave equation for uniform medium. Our GPU-based wave equation solver is built upon the ARD solver.…”