Fast multipole accelerated boundary element methods for room acoustics

The direct and indirect boundary element methods, accelerated via the fast multipole method, are applied to numerical simulation of room acoustics for large rooms of volume $\sim 150$ $m^{3}$ and frequencies up to 5 kHz on a workstation. As the parameter $kD$ (wavenumber times room diameter) is large, stabilization of the previously developed FMM algorithms is required for accuracy. A stabilization scheme is one of the key contribution 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 million elements. The performance of different boundary integral formulations was compared, and their rates of convergence using a preconditioned flexible GMRES were found to be substantially different. These promising results suggest a path to efficient simulations of room acoustics via high performance boundary element methods.