A research group has successfully developed a wave-based acoustics simulation that can make highly accurate time-domain estimations of acoustics in large-scale interior spaces (such as concert halls) at kilohertz frequencies. The group included Professor SAKAGAMI Kimihiro and Assistant Professor OKUZONO Takeshi of Kobe University’s Graduate School of Engineering, and Researcher YOSHIDA Takumi (of Hazama Ando Corporation and concurrently a PhD. student at Kobe University’s Graduate School of Engineering).

This proposed method could be utilized as a high level acoustic design tool that accurately reflects the effect of sound absorption, which is the principal method for controlling the acoustics of an architectural space. It is also hoped that this method will have applications in acoustics Virtual Reality (VR) technology.

The results of this research were published online in the international journal ‘Buildings’ on January 23, 2022.

Main points

  • The research group developed a new wave-based acoustics simulation method that can predict, highly efficiently and accurately, the impulse responses inside architectural spaces such as concert halls and theaters.
  • Sound absorption is the principal method for controlling the acoustics of a room. The proposed method will result in sound field predictions, visualization and auralization(*1) that reflect the effects of sound absorption more accurately.
  • The researchers conducted an investigation into the proposed method’s fundamental performance. By using 512 CPU cores on a parallel computer system, the new method can parse impulse responses with a 3 second time length, including frequency components up to 3kHz, within 2.5 hours when assessing a 2271m3 auditorium. This indicates the new method’s suitability as an architectural acoustic design tool.

Research Background

Computational acoustic simulation technologies are extremely powerful tools for designing the acoustics of various architectural spaces (such as concert halls). These simulations predict the impulse responses(*2) inside the space, enabling architects and acoustical consultants to design a comfortable acoustic environment that suits the venue’s purpose. Geometrical acoustics analysis is commonly utilized as an acoustic simulation method when designing room acoustics. This method can quickly estimate indoor acoustic environments, however it processes wave phenomena such as the sound diffraction or interference in a simple manner, which leads to issues with prediction accuracy. On the other hand, there is another method called wave acoustics analysis that can appropriately predict wave phenomena by solving the wave equation; a differential equation that describes sound propagation. Wave acoustics analysis is a more reliable method than geometrical acoustics analysis, with expected applications as a tool for high level acoustic design. However, wave acoustics analysis of an architectural space’s acoustic environment requires an extremely high level of computational resources, and this severely limits the range of spaces and frequencies to which it can currently be applied. Therefore, there is demand for the development of more efficient methods.

To design an acoustic environment suitable for the space’s purpose, it is necessary to manipulate the acoustics through the appropriate use of sound absorbing materials. This is a big issue because the realization of accurate acoustic design depends on the ability to precisely model via simulation the frequency-dependent characteristics of sound absorbers.

This research group successfully developed a method of highly effectively and accurately estimating the acoustics of a large-scale architectural space at a kilohertz frequency range based on a wave acoustics analysis technique called the time-domain Finite Element Method (FEM)(*3). The developed method can estimate the impulse responses of large-scale architectural spaces (including broadband frequency components) in a single calculation, taking into consideration the frequency-dependent characteristics of sound absorption materials.

Research Methodology

In order to make a high-accuracy estimate of the acoustic wave propagation inside an architectural space using wave acoustics analysis, it is necessary to discretize(*4) spaces with sufficiently smaller-sized elements than the acoustic wavelength of interest. As a general rule of thumb, the required size of the elements is less than one tenth of the wavelength. In addition, it is also necessary to use the time integration method to minutely discretize the time in order to calculate the sound propagation, which changes from moment to moment. This spatiotemporal discretization is restricted by the tremendous computational resources required to estimate the acoustic environment of a large architectural space up to the high-range frequencies. This research group used a theoretical analysis to minimize the error caused by the spatiotemporal discretization, developing a new time domain FEM-based calculation scheme that can produce highly accurate analyses. Compared to conventional FEM techniques, the proposed method can discretize space and time into much larger elements and time intervals. Even when using a computer with a 1CPU core, more accurate and high speed assessments of an acoustic environment can be made than with the conventional method (Figure 1).

Figure 1. Graphs comparing the proposed method and conventional methods’ predicted sound pressure level for a small cubic room to the reference values.

The proposed method is more consistent with the reference than the conventional method. Using 1/7 of the conventional method’s required memory, it can perform calculations 76% faster.

In addition, incorporating an auxiliary differential equation method into the proposed method enables the accurate modelling of the frequency-dependent absorption characteristics of sound absorbers. Figure 2 shows a comparison between the proposed method’s model accuracy for the absorption characteristics of three types of sound absorbers and their theoretical values. Each of the three materials were modelled with high accuracy. The proposed method can, in a single calculation, estimate the impulse response inside the space over a broadband frequency range, taking into consideration the absorption characteristics.

Figure 2. Modelling accuracy for three sound absorption materials.

Comparison between the theoretical values (black line) and the proposed method (red line): The materials are from left: glass-wool, needle felt and a glass-wool backed micro-perforated panel. The absorption coefficient on the Y axis indicates the acoustic absorption material’s performance. The closer the value to 1, the better the absorption.

Finally, the researchers incorporated a Domain Decomposition Method (DDM)-based large-scale parallel computation algorithm into the proposed method. This enabled them to make high speed estimations of the acoustic environments of large-scale architectural spaces. DDM is a method that makes high speed computing possible by dividing the computation model into multiple subdomains. Then, each subdomain’s calculations are carried out simultaneously by multiple parallel nodes or processors. In this study, the researchers used a hybrid parallel computation technique with a 512 CPU core to analyze impulse responses with a 3 second time length, including frequency components up to 3kHz, for a 2271m3 auditorium. The proposed method successfully calculated the impulse responses within 2.5 hours, indicating its suitability for use as an architectural acoustics design tool. Figure 3 shows a visualization of acoustic wave propagation inside an auditorium (left figure) and examples of acoustic parameters (right figures). These parameters are used to evaluate the room acoustics, which were calculated from the impulse responses. The calculated impulse responses can be turned into listenable sounds by auralizing them. It is then possible to experience a 3D sound field using spatial audio reproduction systems. 

Figure 3. Acoustic wave propagation inside an auditorium (left) and the values for each acoustic parameter (right)

Reverberation time is how long a sound echoes in the space. C50 is an indicator used to evaluate the clarity of speech.

Further Research

To further develop this research, the group will try conducting performance evaluations and impulse response predictions for full audible frequencies using cloud-computing environments. At the same time, they will also improve the method’s usability by evaluating its applicability to real-life acoustic design practices. Furthermore, its application to acoustics Virtual Reality (VR) technology is also being considered.


*1 Auralization
Technology that can produce an audible sound file from a value obtained via simulations and measurements etc.
*2 Impulse response (of the interior of a room/space)
A time-series waveform related to sound pressure, including the transmission characteristics between the sound source and sound receiving point. It is used to evaluate sound fields from room acoustic parameters (such as reverberation time) and to auralize sounds.
*3 Time-domain Finite Element Method (FEM)
A numerical analysis method for solving partial differential equations. In this study, the spatial domain of the wave equation (which describes acoustic propagation) was partitioned into very small domains called finite elements, and the temporal development of sound waves was calculated using the time integration method.
*4 Discretization
This is the process in applied mathematics of transferring continuous variables or functions into discrete counterparts. This makes it possible to obtain numerical values for aspects that are continuous in the real world, such as time and space.


This research was supported in part by a Kajima Foundation Scientific Research Grant.

Journal Information

A Parallel Dissipation-Free and Dispersion-Optimized Explicit Time-Domain FEM for Large-Scale Room Acoustics Simulation
Takumi Yoshida, Takeshi Okuzono and Kimihiro Sakagami