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.

Due to high computational costs, the physics governed by the wave equation in 3-D is often modelled via discrete-time numerical simulations conducted in 2-D scenarios. Results are normally generalized to 3-D rather straightforwardly, overlooking the fact that the propagation of a point-like impulse in 2-D exhibits the so-called afterglow phenomenon, which consists on the fact that non-null field values are measured after the arrival of the first wavefront. This letter analyzes the consequences of this phenomenon, both theoretically and numerically, and presents a simple method to compensate for it. Verification of this method is presented using various discrete-time numerical schemes.