Relationship between dispersion error and accuracy of room acoustics parameter in time-domain finite-element room acoustics simulation

摘要

The time-domain finite-element method (TD-FEM) is a powerful wave-based numerical method for room acoustics simulation. However, it is well known that this method incurs an inherent error, called dispersion error, due to both spatial and time discretizations. To obtain a reliable result, discretization of both space and time, which maintain the dispersion error within acceptable level, is required, although the level for room acoustics applications such as calculating of the room acoustical parameters still remains unclear. Further, sufficiently fine spatial and time discretizations for reducing the error make the computation expensive. For efficient use of the method in practical applications, the balance between accuracy and computational cost needs to be considered. For the purpose, this paper presents the relationships between the dispersion errors and accuracy of room acoustical parameters in TD-FE analysis with fourth-order accuracy. Five room acoustical parameters of a sound field in a rectangular room with volume of 62 m~3 were computed at frequencies from 250 Hz to 1 kHz, using TD-FEM with FE meshes of different spatial resolutions and with different time resolutions. Also, the dispersion errors in each analysis were theoretically estimated by dispersion error analysis in three dimensions. Results showed that the use of FE meshes having dispersion error below 0.52 % is recommended to yield the reasonable results at given frequency range.