Calculation of impulse responses and acoustic parameters in a hall by the finite-difference time-domain method

Abstract

Impulse responses in a hall were calculated by the finite-difference time-domain (FDTD) method, and typical room acoustic parameters were obtained from the responses. The calculated parameters were compared with those actually measured in the hall. In the FDTD calculation, the impedance boundary condition was modeled by an equivalent mechanical system comprising masses, springs, and dampers. To calculate the impulse responses, the normal acoustic impedance of the interior finishing materials of the various surfaces in the hall were measured by applying the impedance-tube method, and the model of the room boundary condition was determined for the respective parts. A comparison between the calculated and measured values showed that the values of reverberation time RT, definition D 50 , clarity C 80 , and center time T s were in good agreement in the middle-frequency bands. However, in low-frequency bands, large discrepancies were observed because of the difficulties in determining and modeling the boundary conditions.

An efficient GPU-based time domain solver for the acoustic wave equation

“…In recent work, Sakamoto et al [4] show that FDTD calculations of room-acoustic impulse responses on a grid with s = 6 − 10 agree well with measured values on a real hall in terms of room acoustic parameters such as reverberation time. Remember that grid size h = λ min /s.…”

“…In particular, ours is the first solver that can run a 1 second long bandlimited simulation of 1650 Hz for both auralization and visualization purposes, on scenes with realistically complex geometry and air volume in the range of 7, 500 m 3 within 18 minutes on a desktop computer. The single-threaded optimized CPU-based ARD solver presented by Raghuvanshi et al [6] takes 4 hours 40 minutes and the CPU-based high-order FDTD solver based upon Sakamoto et al [4] takes 20 days to run the same simulation on a desktop machine 2 .…”

“…Finite difference solvers, in order to maintain low errors, require the spatial discretization to contain 6−10 samples per wavelength for the highest usable frequency of interest [3,4,5]. Errors manifest themselves as numerical dispersion, where higher frequencies travel slower on the numerical grid than lower frequencies, leading to phase errors [5].…”

“…For comparison in this paper, we have chosen a sixth-order accurate solver with d = 3 and β = 1 180h 2 {2, −27, 270, −490, 270, −27, 2}, since it has smaller numerical dispersion error than a second-order accurate scheme. Recently, FDTD has been applied to medium-sized scenes in 3D for room acoustic computations by Sakamoto et al [3,4]. The authors calculated typical room acoustic parameters and compared the calculated parameters with the actual measured values in the scene.…”

“…Whether this numerical dispersion is tolerable for auralization and computation of room acoustic parameters is an open research problem. Once such thresholds have been established through listening tests, a direct comparison between IWB-FDTD, FDTD based upon work of Sakamoto et al [4] and ARD, would become possible. For this paper, our comparisons are restricted to FDTD based upon Sakamoto et al [4] and ARD.…”