Fast multipole accelerated boundary element methods for room acoustics

Abstract

Direct and indirect boundary element methods, accelerated via the fast multipole method, are applied to numerical simulation of room acoustics for rooms of volume ∼150 m3 and frequencies up to 5 kHz on a workstation. As the parameter kD (wavenumber times room diameter) is large, stabilization of the previously developed fast algorithms is required for accuracy. A stabilization scheme is one of the key contributions of this paper. The computations are validated using well-known image source solutions for shoebox shaped rooms. Computations for L-shaped rooms are performed to illustrate the ability to capture diffractions. The ability to model in-room baffles and boundary openings (doors/windows) is also demonstrated. The largest case has kD > 1100 with a discretization of size 6 × 106 elements. The performance of different boundary integral formulations was compared, and their rates of convergence using a preconditioned flexible generalized minimal residual method were found to be substantially different. These promising results suggest a path to efficient simulations of room acoustics via high performance boundary element methods.

High potential of small-room acoustic modeling with 3D time-domain finite element method

“…Both methods in a different domain also have unique strengths and weaknesses. FEM (Otsuru et al, 2000;Otsuru et al, 2001;Okamoto et al, 2007;Aretz and Vorländer, 2014;Okuzono and Sakagami, 2018;Murillo et al, 2019;Hoshi et al, 2020;Yatabe and Sugahara, 2022) and BEM (Yasuda et al, 2016;Yasuda et al, 2020;Gumerov and Duraiswami, 2021;Cardoso Soares et al, 2022) are standard selection as a numerical method in the former frequency-domain simulations. Frequency-domain (FD) methods have an inherent benefit for use in modeling sound absorbers (Cox and Peter, 2017) such as porous-type and resonant-type materials accurately: they can deal naturally with complex-valued frequency-dependent quantities such as specific acoustic admittance.…”

Benchmarking of finite-difference time-domain method and fast multipole boundary element method for room acoustics

“…The frequency domain BEM is known as a convenient numerical method for unbounded acoustic problems as its integral equation inherently satisfies the Sommerfeld radiation condition [11]. The fast multipole method (FMM) [12] enables BEM to handle large acoustic models at high frequencies, thus making it more efficient in solving large bounded problems such as room acoustics [13,14,15]. As a classical time-domain simulation method, FDTD has shown good capabilities in a wide range of acoustic applications including room acoustic simulations [1,16,17].…”

Analysis of Instantaneous Acoustic Fields Using Fast Inverse Laplace Transform

“…Numerical simulation methods for acoustic fields include the finite element method, the boundary element method, the finite-difference time-domain (FDTD) method, and geometric acoustics [6][7][8][9][10][11]. The FDTD method, which was developed for electromagnetic field analysis, can be used to analyze time evolution problems from the perspective of wave acoustics [1,[6][7][8].…”