  The boundary element method (BEM) is an efficient numerical method for
simulating harmonic wave scattering. It uses boundary integral formulations of
the Helmholtz equation at the interfaces of piecewise homogeneous domains. The
discretisation of its weak formulation leads to a dense system of linear
equations, which is typically solved with an iterative linear method such as
GMRES. The application of BEM to simulating wave scattering at large-scale
geometries is only feasible when compression and preconditioning techniques
reduce the computational footprint. Furthermore, many different boundary
integral equations exist that solve the same boundary value problem. The choice
of preconditioner and boundary integral formulation is often optimised for a
specific configuration, depending on the geometry, material characteristics,
and driving frequency. On the one hand, the design flexibility for the BEM can
lead to fast and accurate schemes. On the other hand, efficient and robust
algorithms are difficult to achieve without expert knowledge of the BEM
intricacies. This study surveys the design of boundary integral formulations
for acoustics and their acceleration with operator preconditioners. Extensive
benchmarking provide valuable information on the computational characteristics
of several hundred different models for multiple scattering and transmission of
acoustic wave fields.
