A stable transient BEM for diffuser scattering

Boundary Element Methods (BEM) may be used to model scattering from hard rigid surfaces such as diffusers. They have the advantage over volumetric methods that only the surface need be meshed and the surface velocity potential found. Unlike the more widely used single frequency methodology, transient BEM discretizes integral equations to produce an iterative system that is marched on in time from known initial conditions to calculate how the velocity potential varies over time. This iterative process can be unstable, and this is one reason why transient BEM is not more widely used. Previous works on transient BEMs have focused on idealised surfaces, such as spheres and plates. However, little is published on the performance of these methods for more complex surfaces of interest, such as Schroeder Diffusers. Consequently, this paper presents an implicit scheme suitable for a surface comprising thin and solid sections. Such an implicit scheme has the benefits of not constraining time-step duration to the smallest surface detail, and brings stability benefits. Numerical integration is carried out efficiently and accurately by conversion to contour integrals. Accuracy and stability is investigated by comparison to a verified single frequency BEM