  The excitation of a black hole by infalling matter or radiation has been
studied for a long time, mostly in linear perturbation theory. In this paper we
study numerically the response of a Schwarzschild black hole to an incoming
gravitational wave pulse. We present a numerically well-posed initial boundary
value problem for the generalized conformal field equations in which a wave
profile for the ingoing wave is specified at an outer time-like boundary which
then hits an initially static and spherically symmetric black hole. The
non-linear interaction of the black hole with the gravitational wave leads to
scattered radiation moving back out. The clean separation between initial state
and incoming radiation makes this setup ideal to study scattering problems. The
use of the conformal field equations allows us to trace the response of the
black hole to null infinity where we can read off the scattered gravitational
waves and compute the Bondi-Sachs mass and the gravitational flux through
$\mathscr{I}$. In this way we check the Bondi-Sachs mass loss formula directly
on null infinity. We also comment on comparisons with quasinormal modes.
