  We present an efficient method to solve scattering problems in
two-dimensional open billiards with two leads and a complicated scattering
region. The basic idea is to transform the scattering region to a rectangle,
which will lead to complicated dynamics in the interior, but simple boundary
conditions. The method can be specialized to closed billiards, and it allows
the treatment of interacting particles in the billiard. We apply this method to
quantum echoes measured recently in a microwave cavity, and indicate, how it
can be used for interacting particles.
