  We propose a boundary element method for problems of time-harmonic acoustic
scattering by multiple obstacles in two dimensions, at least one of which is a
convex polygon. By combining a Hybrid Numerical Asymptotic (HNA) approximation
space on the convex polygon with standard polynomial-based approximation spaces
on each of the other obstacles, we show that the number of degrees of freedom
required in the HNA space to maintain a given accuracy needs to grow only
logarithmically with respect to the frequency, as opposed to the (at least)
linear growth required by standard polynomial-based schemes. This method is
thus most effective when the convex polygon is many wavelengths in diameter and
the small obstacles have a combined perimeter comparable to the problem
wavelength.
