  We present a multi-domain spectral method to compute initial data of binary
systems in General Relativity. By utilizing adapted conformal coordinates, the
vacuum region exterior to the gravitational sources is divided up into two
subdomains within which the spectral expansion of the field quantities is
carried out. If a component of the binary is a neutron star, a further
subdomain covering the star's interior is added. As such, the method can be
used to construct arbitrary initial data corresponding to binary black holes,
binary neutron stars or mixed binaries. In particular, it is possible to
describe a black hole component by the puncture ansatz as well as through an
excision technique. First examples are given for binary black hole excision
data that fulfill the requirements of the quasi-stationary framework, which
combines the Conformal Thin Sandwich formulation of the constraint equations
with the Isolated Horizon conditions for black holes in quasi-equilibrium.
These numerical solutions were obtained to extremely high accuracy with
moderate computational effort. Moreover, the method proves to be applicable
even when tending toward limiting cases such as large mass ratios of the binary
components.
