Effects of the convergence tolerance of iterative methods used in the boundary element method on the calculation results of sound fields in rooms

• Published in: Applied acoustics 2020-01, Vol.157, p.106997, Article 106997
• Main Authors: Yasuda, Yosuke, Saito, Kota, Sekine, Hidehisa
• Format: Article
• Language: English
• Subjects: Absorption; Boundary element method; Diffuseness; Iterative method; Reverberation decay; Stopping criteria
• ISSN: 0003-682X; 1872-910X
• DOI: 10.1016/j.apacoust.2019.08.003

We investigated the effects of convergence tolerance of iterative methods used in the boundary element method (BEM) on the accuracy of the calculation results of sound fields in rooms via numerical experiments. In particular, we focused on the relation of the sound absorption and diffuseness in rooms to the convergence of each type of calculation results such as frequency responses, reverberation decay curves, and sound pressure level distributions. The results led to the following conclusions: 1) When all room surfaces are absorbing, the smaller the mean sound absorption coefficient is, the slower the convergence is. 2) When the mean sound absorption coefficients are similar, the more unevenly the sound absorbing surfaces distribute, the slower the convergence is. 3) Even if there is similarity in the unevenness of the sound absorption distribution and complexity of the room shape, the difference in the relative arrangement between the sound absorbing and diffusive surfaces affects the convergence of the results. 4) The reverberation length is not related to the convergence of the calculated reverberation decay curve. 5) The convergence of the calculation results correlates with the mean value of the finite differences of the frequency response. Finally, we recommend convergence tolerance values for each considered type of calculation results. Moreover, we confirmed the results via a numerical analysis of a real room.