Fdtd/k-dwm Simulation of 3d Room Acoustics on General Purpose Graphics Hardware Using Compute Unified Device Architecture (cuda)

Computer-based modelling is becoming standard practice in modern room acoustics. Its applications range from prediction of design parameters, visualization of sound propagation and auralisation [1]. Traditional architectural acoustic modelling methods, such as Ray-Tracing [2] and Image-Source models [3], draw on geometrical assumptions and therefore may be confidently applied only to an explicit class of design problems. Wave-based methods, on the other hand, attempt to solve the acoustic wave equation under specific boundary conditions, and are therefore more precise in predicting sound propagation, albeit at a much higher computational cost. Common methods such as Boundary Element [4] and Finite Element [5] analyses are considered highly accurate; however they impose two major limitations: a) their computational requirements grow exponentially with frequency, thus rendering them inadequate for wide band problems; and b) traditionally, their solution correspond to a steady-state analysis which neglects discrete timedomain transient responses. Throughout the past decade much attention has been shifted towards numerical time domain methods, particularly the Finite Difference Time Domain (FDTD) [6] and the Digital Waveguide Mesh (DWM) [7]. Even as being able to provide discrete time-space approximations to the N-dimensional wave equation, these methods have two major drawbacks. First, the entire acoustic space must be modelled resulting in large computational domains, hence higher calculation times. Second, as finite difference approximations are employed, these methods exhibit dispersion errors that increase with frequency and vary with direction of propagation [8]; thus imposing a high-frequency calculation limit. Various methods for reducing these errors have been studied, most noticeably by considering non-rectangular mesh topologies [9], [10], by spatial interpolation and frequency warping [11]. One feasible trade-off is to oversample the mesh, consequently extending the high frequency limit at the expense of a considerably large computational problem. Evidently, a way to efficiently solve such large problems at reasonable calculation times would diminish the aforementioned restrictions.