In many numerical implementations of the Cauchy formulation of
Einstein's field equations one encounters artificial boundaries which
raises the issue of specifying boundary conditions. Such conditions
should be compatible with the constraints, yield a well posed
initial-boundary value formulation and incorporate some physically
desirable properties like, for instance, minimizing reflections of
gravitational radiation.

Motivated by the problem in General Relativity, we analyze a model
problem, consisting of a formulation of Maxwell's equations on a
spatially compact region of spacetime with timelike boundaries. The
form in which the equations are written is such that their structure
is very similar to the Einstein-Christoffel symmetric hyperbolic
formulations of Einstein's field equations. For this model problem, we
specify a family of Sommerfeld-type constraint-preserving boundary
conditions and show that the resulting initial-boundary value
formulations are well posed. We also comment on the generalization of
these results to Einstein's field equations.