In this paper, a room acoustics simulation using a finite difference approximation on a face-centered cubic (FCC) grid with finite volume impedance boundary conditions is presented. The finite difference scheme is accelerated on an Nvidia Tesla K20 graphics processing unit (GPU) using the CUDA programming language. A performance comparison is made between 27-point finite difference schemes on a cubic grid and the 13-point scheme on the FCC grid. It is shown that the FCC scheme runs faster on the Tesla K20 GPU and has less numerical dispersion than best 27-point schemes on the cubic grid. Implementation details are discussed.

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Implicit finite difference schemes for the 3-D wave equation using a 27-point stencil on the cubic grid are presented, for use in room acoustics modelling and artificial reverberation. The system of equations that arises from the implicit formulation is solved using the Jacobi iterative method. Numerical dispersion is analysed and computational efficiency is compared to second-order accurate 27-point explicit schemes. Timing results from GPU implementations demonstrate that the proposed algorithms scale over their explicit counterparts as expected: by a factor of M + 2, where M is a fixed number of Jacobi iterations (eight can be sufficient in single precision). Thus, the accuracy of the approximation can be improved over explicit counterparts with only a linear increase in computational costs, rather than the quartic (in operations) and cubic (in memory) increases incurred when oversampling the grid. These implicit schemes are advantageous in situations where less than 1% dispersion error is desired.

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