  We construct an asymptotic approximation to the solution of a transmission
problem for a body containing a region occupied by many small inclusions. The
cluster of inclusions is characterised by two small parameters that determine
the nominal diameter of individual inclusions and their separation within the
cluster. These small parameters can be comparable to each other. Remainder
estimates of the asymptotic approximation are rigorously justified. Numerical
illustrations demonstrate the efficiency of the asymptotic approach when
compared with benchmark finite element algorithms.
