Applicability of an explicit time-domain finite-element method on room acoustics simulation

Abstract

IntroductionRecently the time-domain finite-element method (TD-FEM) is becoming an efficient wave-based numerical method for wideband room acoustics simulation up to several kilohertz frequencies, with the drastic advancement of computer technology [1,2]. However, a cost-efficient simulation up to high frequencies using the method is still considered to be a difficult task, due to the high computational cost. A dispersion error, which is an inherent discretization error coming from spatial and time discretizations of a computational domain, is one of the reasons for the high computational cost. Because of the error, a spatial discretization requirement known as a rule of thumb is imposed in a mesh generation process to yield reliable results. Also, a time discretization error must be considered in a time-domain analysis. These requirements engender the solution of large-scale problems with many degrees of freedom (DOF) and many time steps for a simulation at high frequencies.Many dispersion reduction methods have been developed to increase the computational efficiency [1][2][3][4][5][6]. The authors have also proposed some dispersion-reduced TD-FEM based on an implicit method to solve the large-scale problems efficiently [1,2]. Also, there exists an explicit TD-FEM with a simple dispersion reduction technique called modified integration rules (MIR) [5], in which fourth-order accuracy with respect to the dispersion error can be obtained for the idealized case using square or cubic finite elements (FEs). This explicit method is very attractive for realizing an efficient room acoustics simulation because it does not need a solution of a linear system of equations at each time step. However, as presented in the literature [5], the explicit method does not consider a dissipation term for treating an absorption at boundaries, which is important for room acoustics simulation.When a sound field inside a room with an finite impedance boundary is analyzed using this explicit method, a time derivative of sound pressure related to the dissipation term has to be approximated by a less-accurate backward difference even though time derivatives of other physical quantities are approximated by a second-order accurate

A Review of Finite Element Methods for Room Acoustics

“…Okuzono et al [113] attempted to address the poor efficiency of the FEM at high frequencies, by reducing the pollution effect using MIR. A 3D problem with real-valued impedances was studied and solved in the time domain using an implicit method and an explicit method.…”

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

“…( 9) by the second-order accurate central difference andṗ in Eq. ( 9) by the first-order accurate backward difference lead to the following explicit scheme as [16] p…”

“…More recently, in Ref. [16], the authors presented an explicit TD-FEM using MIR with the dissipation term for room acoustics simulations, and showed the efficiency in term of computational time over an implicit TD-FEM using MIR. However, this study was conducted in limited numerical conditions without a dispersion error analysis and a stability analysis, as a first stage of the research.…”

The Lattice Boltzmann Method Using Parallel Computation: A Great Potential Solution for Various Complicated Acoustic Problems

“…In these methods, waves' physical phenomena are modeled mathematically in the form of partial differential equations and solved numerically. The numerical methods included in the wave-based methods and which are often used are the finite-differences time-domain method (FDTD) [1][2][3][4], the finite element method (FEM) [5,6], and the finite volume method (FVM) [7,8]. These methods have heavy computational loads, especially FEM, which need a large matrices solver.…”