  The discretisation of boundary integral equations for the scalar Helmholtz
equation leads to large dense linear systems. Efficient boundary element
methods (BEM), such as the fast multipole method (FMM) and $\Hmat$ based
methods, focus on structured low-rank approximations of subblocks in these
systems. It is known that the ranks of these subblocks increase linearly with
the wavenumber. We explore a data-sparse representation of BEM-matrices valid
for a range of frequencies, based on extracting the known phase of the Green's
function. Algebraically, this leads to a Hadamard product of a frequency matrix
with an $\Hmat$. We show that the frequency dependency of this $\Hmat$ can be
determined using a small number of frequency samples, even for geometrically
complex three-dimensional scattering obstacles. We describe an efficient
construction of the representation by combining adaptive cross approximation
with adaptive rational approximation in the continuous frequency dimension. We
show that our data-sparse representation allows to efficiently sample the full
BEM-matrix at any given frequency, and as such it may be useful as part of an
efficient sweeping routine.
