Numerically stable explicit time-domain finite element method for room acoustics simulation using an equivalent impedance model

Abstract

This article presents a numerically stable explicit time-domain finite element method (TD-FEM) for room acoustic simulation using an equivalent impedance model. Performance over a conventional explicit TD-FEM is demonstrated using numerical experiments. Both explicit TD-FEMs were based on simultaneous first-order ordinary differential equations. The conventional method has a stability problem derived from backward difference approximation of time derivative of sound pressure related to a dissipation term for treating absorption at a boundary. The numerically stable explicit TD-FEM avoids the stability problem through the combined use of first-order forward and backward difference approximation. A completely explicit algorithm is obtainable using a lumped dissipation matrix. Numerical results demonstrate that the proposed explicit TD-FEM is stable for changing impedance values at boundary surfaces. In addition, numerical dissipation and dispersion error analyses revealed that both explicit TD-FEMs have small dissipation error. Moreover, the proposed method has slightly lower accuracy than the conventional explicit TDFEM. However, the proposed method is computationally more efficient than the conventional method for acoustics simulation of rooms with smaller impedance values at boundaries.