  Time-domain Boundary Element Methods (BEM) have been successfully used in
acoustics, optics and elastodynamics to solve transient problems numerically.
However, the storage requirements are immense, since the fully populated system
matrices have to be computed for a large number of time steps or frequencies.
In this article, we propose a new approximation scheme for the Convolution
Quadrature Method (CQM) powered BEM, which we apply to scattering problems
governed by the wave equation. We use $\mathcal{H}^2$-matrix compression in the
spatial domain and employ an adaptive cross approximation (ACA) algorithm in
the frequency domain. In this way, the storage and computational costs are
reduced significantly, while the accuracy of the method is preserved.
