A System Theoretic Approach for the Reduction of Large-Scale Room Acoustic Models

Efficiently simulating sound density in room acoustic models poses a significant challenge since it involves the solution of large-scale systems of equations, which can result in unreasonably/unacceptably long computation times. However, in many cases, sound density measurements only need to be taken at certain points in the room rather than every point, which allows the use of Model Order Reduction (MOR) techniques. System theoretic techniques like balanced truncation (BT) are well-established and can be applied to the sound diffusion equation, offering reliable error bounds. This paper presents a low-rank BT algorithm in order to generate compact models, which can be efficiently and accurately simulated over many timesteps. The experimental results show that this method can provide extreme order reduction percentages of 99.99% and thus accelerate simulations by up to $59\times$ while maintaining a relative error of less than 0.75%.