  We make use of the metric version of the conformal Einstein field equations
to construct anti-de Sitter-like spacetimes by means of a suitably posed
initial-boundary value problem. The evolution system associated to this
initial-boundary value problem consists of a set of conformal wave equations
for a number of conformal fields and the conformal metric. This formulation
makes use of generalised wave coordinates and allows the free specification of
the Ricci scalar of the conformal metric via a conformal gauge source function.
We consider Dirichlet boundary conditions for the evolution equations at the
conformal boundary and show that these boundary conditions can, in turn, be
constructed from the 3-dimensional Lorentzian metric of the conformal boundary
and a linear combination of the incoming and outgoing radiation as measured by
certain components of the Weyl tensor. To show that a solution to the conformal
evolution equations implies a solution to the Einstein field equations we also
provide a discussion of the propagation of the constraints for this
initial-boundary value problem. The existence of local solutions to the
initial-boundary value problem in a neighbourhood of the corner where the
initial hypersurface and the conformal boundary intersect is subject to
compatibility conditions between the initial and boundary data. The
construction described is amenable to numerical implementation and should allow
the systematic exploration of boundary conditions.
