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.

中文翻译：

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用于室内声学的快速多极加速边界元方法

通过快速多极方法加速的直接和间接边界元方法应用于工作站上体积约 150 m ³和频率高达 5 kHz的房间的室内声学数值模拟。由于参数kD（波数乘以房间直径）很大，因此需要稳定先前开发的快速算法以提高准确性。稳定方案是本文的主要贡献之一。使用众所周知的鞋盒形状房间的图像源解决方案来验证计算。执行 L 形房间的计算以说明捕获衍射的能力。还展示了模拟室内挡板和边界开口（门/窗）的能力。最大的案例有kD >1100 具有大小为 6 × 10 ⁶元素的离散化。比较了不同边界积分公式的性能，发现它们使用预处理灵活广义最小残差方法的收敛速度有很大不同。这些有希望的结果表明了通过高性能边界元方法有效模拟室内声学的途径。