  I describe the current status of a collaboration with J.D. Romano, R.H.
Price, and W. Krivan to model the geometry of and gravitational radiation
emitted by a binary system of compact objects in the regime where
non-perturbative gravitational effects exist, but the rate of inspiral is still
small relative to the orbital frequency. The method of looking for a stationary
spacetime which approximates the evolving solution is initially being tested on
a simpler model with an additional translational symmetry. This report consists
of a general description of the method, followed by summaries of three
techniques in varying stages of development: the simplification of the Einstein
equations in the presence of two commuting Killing vectors which form a
non-orthogonally-transitive symmetry group, the boundary conditions appropriate
to the balance of ingoing and outgoing radiation needed to reconcile a
stationary radiating solution with conservation of energy, and the treatment of
gravitational waves far from the sources as linearized perturbations to the
Levi-Civita spacetime. The poster presentation with which this paper is
associated is available on line at http://www-itp.unibe.ch/~whelan/poster.ps.gz
and the current status of the project is described at
http://www-itp.unibe.ch/~whelan/qsbi.html
