GPU-accelerated rectangular decomposition for sound propagation modeling in 2D

Adaptive Rectangular Decomposition (ARD) is an efficient technique for modeling the sound propagation. This technique reduces the computational overhead and memory requirements by using non-dispersive sub-rectangular domains suitable for parallel computation. In order to use this technique, the scene should be decomposed into large inscribed rectangles. For large and complex scenes, it is not feasible to find an optimal set of large rectangles and thus an approximation should be used. In this paper, we present a GPU-accelerated algorithm for searching an adequate rectangular decomposition of a 2D scene in a reasonable time. Our algorithm performs a fast parallel search in the entire domain. As a result, large and complex scenes can be decomposed in seconds and it enables them to be numerically modeled in parallel using ARD.

I. Introduction

The equation that describes the complete wave nature of sound in the time and space domain is called the acoustic wave equation and it is given by

$$\begin{equation*} \frac{\partial^{2}p(\mathrm{x},t)}{\partial t^{2}}-c^{2}\nabla^{2}p(\mathrm{x},\ t)=f(\mathrm{x},\ t) \tag{1} \end{equation*}$$ where the operator is the Laplacian in the three dimensional space, is the sound pressure in the space and time domain, the speed of sound is and is the forcing term corresponding to an acoustic source present in the scene. This equation explains wave phenomena such as interference and diffraction that are observed in the reality [1]. Analytic solutions of the wave equation exist in few problems in physical acoustics hence solutions require assumptions and simplifications [2], [3]. If the sound field is too complicated to handle in an analytic way, then a numerical approach would be effective.