The Pseudo-Spectral Time Domain (PSTD) method is an alternative time-marching method to classical leapfrog finite difference schemes in the simulation of wave-like propagating phenomena. It is based on the fundamentals of the Fourier transform to compute the spatial derivatives of hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acoustics simulations. However, one of the first issues to be solved consists on modeling wall absorption. Unfortunately, there are no references in the technical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals to overcome this problem are presented, validated and compared to analytical solutions in different scenarios.

In recent years, computational engineering has undergone great changes due to the development of the Graphics Processing Unit (GPU) technology. For example, in room acoustics, the wave-based methods, that formerly were considered too expensive for 3-D impulse response simulations, are now chosen to exploit the parallel nature of GPU devices considerably reducing the execution time of the simulations. There exist contributions related to this topic that have explored the performance of different GPU algorithms, however, the computational analysis of a general explicit model that incorporates algorithms with different neighboring orders and a general frequency dependent impedance boundary model has not been properly developed. In this paper, we present a GPU implementation of a complete room acoustic model based on a family of explicit Finite-Difference Time-Domain (FDTD) algorithms. We first develop a strategy for implementing a Frequency Independent (FI) impedance model which is free from thread divergences and then, we extend the model adding a Digital Impedance Filter (DIF) boundary subroutine able to compute the acoustic pressure of different nodes such as corners or edges without an additional performance penalty. Both implementations are validated and deeply analyzed by performing different 3-D numerical experiments. Finally, we define a performance metric which is able to objectively measure the computing throughput of a FDTD implementation using a simple number. The robustness of this metric allows us to compare algorithms even if these have been run in different GPU cards or have been formulated with other explicit models.

Finite-Differences in the Time Domain (FDTD) are among the most accurate numerical techniques to simulate wave phenomena. The main drawback of FDTD numerical schemes is their computational cost in large scale simulations. The recently developed Fourier Pseudospectral Time-Domain (PSTD) techniques, by approximating the spatial derivatives more efficiently, have improved significantly the accuracy and time costs of the simulations of electromagnetic fields. As a step towards applying PSTD techniques to Room Acoustic problems, we present here a framework to properly deal with material modelling in terms of generic impedance boundary conditions, beyond the common Perfectly Matched Layer absorbing boundaries. We apply our results to a few representative cases (simple but reverberant rooms) and analyse its performance in terms of accuracy and computational resources. In particular we analyse whether the mild constraints that PSTD imposes on space-time discretization lead to good enough results in Room Acoustic simulations.

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