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 frequency-independent 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.