A Transient Boundary Element Method for Acoustic Scattering from Mixed Regular and Thin Rigid Bodies

Abstract

Boundary Element Methods (BEMs) may be used to predict the scattering of sound by obstacles, which has accelerated the prototyping of new room acoustic treatments such as diffusers. Unlike the more popular frequency domain method, the time domain BEM is usually solved in an iterative manner which means it can exhibit instability, a crucial impediment to its widespread use. These instabilities are primarily associated with the resonance of cavities formed by closed surface sections, but may also be caused by discretisation or integration error corrupting physical damped resonances. Regular BEM implementations cannot model objects with thin sections due to a phenomenon known as Thin Shape Breakdown. This paper develops an algorithm which combines an accepted approach for modelling thin plates with the Combined Field Integral Equation which eradicates cavity resonances, thereby permitting models of mixed regular and thin bodies. Accuracy and stability are tested by comparison to verified frequency domain BEMs, examination of the transient response, and pole decomposition. This is done for a simple obstacle and a Schroeder diffuser, which comprises a series of wells separated by thin fins. The approach is successful but universal stability cannot be guaranteed for the diffuser. It is suggested that instability is caused by the lightly damped resonances of the wells being corrupted into divergent behaviour by numerical errors.