# Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation
## 5 Conclusions  
The proposed binaural room-acoustics auralization method uses a highly scalable wave-acoustics-based solver that is applicable to large-scale room-acoustics problems under a cloud HPC environment. The binaural room-acoustics auralization is based on a hybrid technique using Ambisonics and HRTF. The Ambisonics encoding uses room impulse responses computed using a wave-based solver based on dispersion-optimized explicit TD-FEM. Detailed procedures of computing expansion coefficients of spherical harmonics using spatial differentiation of shape function of FEs are also proposed. This paper first presented examination of the scalability of the present parallel wave-based solver on an HPC cloud environment to address the question of solver efficiency when computing room impulse responses for practical room-acoustics problems. Two room-acoustics problems with different problem sizes and geometrical complexities were selected: a meeting room-acoustics simulation and a classroom-acoustics simulation. The parallel performance examination involved using up to 6144 CPU cores on the HPC cloud environment and computing room impulse responses, including frequency components up to  
Figure 15: BRIRs for Cond. 1 at (**a**) R3 and (**b**) (R4). 6 kHz. Results showed that the present parallel wave-based solver is an efficient means of simulating room acoustics under the HPC cloud environment. It can compute room impulse responses rapidly. It was possible to compute room impulse responses with 217 s for a meeting room having 35,00,000 DOFs when using 6144 CPU cores. For a classroom problem having 100,000,000 DOFs, the computational time was only 613 s. Results also demonstrated the high scalability of the present parallel wave-based solver. The speedup increased almost linearly with an increasing number of CPU cores used. Next, we demonstrated the potential of the proposed binaural room-acoustics auralization method via an auditorium acoustics simulation up to 5 kHz having 750,000,000 DOFs. This problem size is the largest ever reported for an architectural acoustics problem with FEM-based room-acoustics solvers. By this simulation, we demonstrated how room acoustics change with two acoustics treatments: The first treatment produces flutter echoes. Another is an acoustic treatment suppressing flutter echoes with additional sound absorbers installed on side walls. The plausibility of the proposed binaural room-acoustics auralization method was first demonstrated by comparing the first-order Ambisonics signals, the receiver's directivity, and four room acoustical parameters between the two conditions. The findings indicated behavior consistent with those expected from the two acoustic treatments. In addition, the binaural room-acoustics auralization showed that auditory impression corresponds to the objective analysis. It is also notable that the parallel wave-based solver can simulate the room acoustics of this huge model within 13,000 s using 6144 cores. As a subsequent stage of the present study, we expect to examine the proposed binaural auralization method with measurements, with expansion to high-order Ambisonics. The following supporting information can be downloaded online. We supply the audio data (WAV files) explained in Section 4.3 as supplemental materials where BRIRs, Japanese, and English speeches at all receivers in two absorption conditions are arranged. Those can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13052832/s1](https://www.mdpi.com/article/10.3390/app13052832/s1)]([https://www.mdpi.com/article/10.3390/app13052832/s1](https://www.mdpi.com/article/10.3390/app13052832/s1)). Specifically, we provide a zip file for which the first level comprises three folders: \"bri\", \"japanese\" and \"english\", the second comprises two absorption conditions: \"condition 1\" and \"condition 2\", and the last level with receiver names R1-R6. Conceptualization, T.Y. ; Funding acquisition, T.O. ; Investigation, T.Y. ; Methodology, T.Y. ; Project administration, K.S. ; Resources, T.O. ; Software, T.Y.