  We compare the accuracy of two cluster extensions of Dynamical Mean-Field
Theory in describing d-wave superconductors, using as a reference model a
saddle-point t-J model which can be solved exactly in the thermodynamic limit
and at the same time reasonably describes the properties of high-temperature
superconductors. The two methods are Cellular Dynamical Mean-Field Theory,
which is based on a real-space perspective, and Dynamical Cluster
Approximation, which enforces a momentum-space picture by imposing periodic
boundary conditions on the cluster, as opposed to the open boundary conditions
of the first method. We consider the scaling of the methods for large cluster
size, but we also focus on the behavior for small clusters, such as those
accessible by means of present techniques, with particular emphasis on the
geometrical structure, which is definitely a relevant issue in small clusters.
