# Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation
## 4 Binaural Room-Acoustics Auralization in a Large-Scale Auditorium
### Objective Analysis of Auditorium Room Acoustics  
This section presents objective room-acoustics analysis results for the auditorium. Before presenting the results of such an analysis, we first present the practicality of the present massively parallel wave-based solver to large-scale room-acoustics simulation from computational cost aspects. The present massively parallel wave-based solver achieved remarkable computational speed, with computational times of 12,777 s and 12,028 s, respectively, for Cond. 1 and Cond. 2. Furthermore, we show room-acoustics evaluation findings related to acoustic disturbance and receiver's directivity in early and late time, using FOA signals. Figure 10a-d show simulated FOA signals at a receiver R3 of Cond. 1. Here, \(A_{0,0}\) is the omnidirectional component and \(A_{1,-1}\), \(A_{1,0}\), and \(A_{1,1}\) are the bidirectional components in \(y\)-, \(z\)-, and \(x\)-directions. A repetition of intense reflected sounds is apparent; it seems likely to promote flutter echoes in \(A_{1,-1}\) because of the low absorptivity of the side walls. Figure 11a-d show FOA signals at R3 for Cond. 2 with additional sidewall sound absorbers. As shown in Figure 11b, adding sidewall sound absorbers decreases repetition of intense reflected sounds, thereby suppressing flutter echoes. The contribution of adding sidewall sound absorbers is also apparent for the other components. Naturally, the direct sound shows the largest amplitude for the component \(A_{1,1}\), which is the bidirectional component in the \(x\)-direction, compared to other components. Figure 12a-d further show the receiver's horizontal directivity in early and late times at R3 and R4 for Cond. 1 and Cond. 2. The horizontal directivities \(D(\phi)\) are defined here as the summation of incident plane wave energy calculated using  
\[D(\phi)=\int_{t_{s}}^{t_{e}}|\sum_{l=0}^{1}\sum_{m=-l}^{l}A_{l,m}(t)Y_{l,m}( \phi,\theta)|^{2}\mathrm{d}t, \tag{38}\]  
where \(t_{s}\) and \(t_{e}\) are set to 0 and 50 ms for early time and 50 ms and \(\infty\) for late time. Time 0 means the direct sound arriving time denoted in ISO3382-1 [38]. The horizontal case is calculated with \(\theta=90^{\circ}\). In addition, in Figure 12, \(\phi=0\) and \(\phi=90^{\circ}\) coincide with \(x\)-axis and \(y\)-axis directions. From this, for the receiver's R3 and R4, the source respectively locates in directions of 180\({}^{\circ}\) and 202\({}^{\circ}\). It is apparent for the receiver R3 that early time directivities indicate the source location for both conditions, where \(D(\phi)\)s take the peak  
Figure 9: Source signal: **(a)** waveform and **(b)** spectrum. values at \(\phi=180^{\circ}\). In addition, the early directivities at R4 for both conditions present that their peak values track the sound source location corresponding to receiver location change from R3. Here, the peaks of \(D(\phi)\)s were found to be \(\phi=190^{\circ}\) for Cond. 1 and \(\phi=199^{\circ}\) for Cond. 2, which are slightly different directions of the exact source direction of \(202^{\circ}\) because the early time sounds at R4 include the reflected sound from the side wall located in the direction of \(\phi=90^{\circ}\). Cond. 2 presents better sound source localization than Cond. 1 by virtue of the installation of side wall absorbers. Effects of the side wall absorbers are also observed for both receivers because the incident energy decreases in both early and late directivities. Especially late directivities show a large effect by the added side wall absorbers. For Cond. 1, \(y\) directional components (\(\phi=90^{\circ}\) and \(270^{\circ}\)) are outstanding at both receivers. However, late directivities of Cond. 2 point to the source directions. Those FOA signal analysis results can be expected from the sound absorber configuration, demonstrating the feasibility of the present auditorium acoustics simulation.