## Wendy Kress (MPI Leipzig)

We consider the wave equation in a time domain boundary integral
formulation. For the numerical solution , to obtain a stable time
discretization, we employ the convolution quadrature method in time,
which has been developed by Lubich.

In space, a Galerkin boundary element method is considered. The
resulting Galerkin matrices of the original method are fully populated
and the computational complexity is proportional to *N log*^{2}N M^{2},
where *M* is the number of spatial unknowns and *N* is the number of
time steps.

We present two ways of reducing these costs. The first is an a-priori
cutoff strategy, which allows to replace a substantial part of the
matrices by *0*. The second is a panel clustering approximation, which
further reduces the computational cost by approximating subblocks by low
rank matrices.

The perturbed problem is analysed and stability results are given.

It is shown that the resulting computational complexity is reduced to
*N log*^{2}N M^{1+s} where *s ∼ 1/2* depending on the order of the
Galerkin method used in space.

This is joint work with S. Sauter and W. Hackbusch.