An explicit time-domain finite element method for room acoustics simulations: Comparison of the performance with implicit methods

Abstract

This paper presents the applicability of an explicit time-domain finite element method (TD-FEM) using a dispersion reduction technique called modified integration rules (MIR) on room acoustics simulations with a frequencyindependent finite impedance boundary. First, a dispersion error analysis and a stability analysis are performed to derive the dispersion relation and the stability condition of the present explicit TD-FEM for three-dimensional room acoustics simulations with an infinite impedance boundary. Secondly, the accuracy and efficiency of the explicit TD-FEM are presented by comparing with implicit TD-FEM using MIR through room acoustics simulations in a rectangular room with infinite impedance boundaries. Thirdly, the stability condition of the explicit TD-FEM is investigated numerically in the case with finite impedance boundaries. Finally, the performance of the explicit TD-FEM in room acoustics simulations with finite impedance boundaries is demonstrated in a comparison with the implicit TD-FEM. Although the stability of the present explicit TD-FEM is dependent on the impedance values given at boundaries, the explicit TD-FEM is computationally more efficient than the implicit method from the perspective of computational time for acoustics simulations of a room with larger impedance values at boundaries.

Time domain room acoustic simulations using the spectral element method

“…(10) efficiently, an explicit time stepping method is preferred. 51 Explicit time stepping comes with conditional stability, which sets an upper bound on the time step size ∆t. In the proposed numerical scheme there are two mechanisms at play which influence the maximum allowable time step.…”

Modeling continuous source distributions in wave-based virtual acoustics

“…The emulation of sources in time domain wavebased virtual and architectural acoustics (such as the finite difference time domain method or FDTD 1-3 , finite volume methods 4,5 , finite element methods 6 and other varieties 7 ) has a long history [8][9][10][11][12][13] , and follows even earlier work on the representation of sources in electromagnetic simulation 14 . Time domain volumetric wave-based method, operating over a full 3D spatial grid are the focus here, though frequency-domain wave-based methods employing sources have also been proposed using boundary element techniques 15,16 .…”

Locally implicit time-domain finite element method for sound field analysis including permeable membrane sound absorbers

“…A first-order ordinary differential equation (ODE)-based TD-FEM [7,8] has been proposed recently as an alternative method to the standard implicit TD-FEM. First-order ODEbased TD-FEM shows an explicit algorithm.…”