ROOM ACOUSTICS MODELLING USING GPU-ACCELERATED FINITE DIFFERENCE AND FINITE VOLUME METHODS ON A FACE-CENTERED CUBIC GRID

ABSTRACTIn this paper, a room acoustics simulation using a finite differenceapproximation on a face-centered cubic (FCC) grid with finite vol-ume impedance boundary conditions is presented. The finite dif-ference scheme is accelerated on an Nvidia Tesla K20 graphicsprocessing unit (GPU) using the CUDA programming language.A performance comparison is made between 27-point finite differ-ence schemes on a cubic grid and the 13-point scheme on the FCCgrid. It is shown that the FCC scheme runs faster on the Tesla K20GPU and has less numerical dispersion than best 27-point schemeson the cubic grid. Implementation details are discussed.1. INTRODUCTIONRoom acoustics simulations are important for architectural acous-tics, auralising virtual spaces, and artificial reverberation. Tra-ditionally, these simulations have been carried out using image-source [1] and ray-tracing methods [2], requiring simplifying as-sumptions about room geometry or wave behaviour. Finite ele-ment and boundary element methods [3, 4] have the potential tosimulate full wave behaviour for complex room geometries, butthese methods are not easily parallelisable and thus are less suitedto implementation on graphics processing units (GPUs). Othermethods offering full 3-D acoustical simulations such as the finitedifference (FD) [5,6] and finite volume (FV) methods [7] can becomputationally heavy, but are well-suited for GPU programmingdue to their explicit formulations [8, 9]. Computation times canbe long for large spaces at audio rates like 44.1 kHz, even withstate of the art GPU cards [10], so computational efficiency in thenumerical scheme is critical.Within FD methods there are many choices for FD operatorsand grids on which to approximate solutions to the 3-D wave equa-tion [11]. The computational efficiencies of FD schemes differ anddetermining the most suitable candidate for room acoustics simu-lations has been the subject of many studies [11–14]. The inter-polated wideband scheme (IWB) scheme, employing a 27-pointstencil on the cubic grid, has been shown to be computationallyefficient at minimising wave speed error [13] and has been used inGPU-accelerated simulations [8,15,16]. Another candidate, andthe focus of this paper, is a 13-point scheme which can be usedon the cubic grid (the close-cubic packed (CCP) scheme) [13] oron the face-centered cubic grid (FCC) [12, 14, 17, 18]. The 13-point FD scheme on the FCC grid has recently been shown to bemore computationally efficient than 27-point schemes on the cubic