  This paper is devoted to the computation of compact binaries composed of one
black hole and one neutron star. The objects are assumed to be on exact
circular orbits. Standard 3+1 decomposition of Einstein equations is performed
and the conformal flatness approximation is used. The obtained system of
elliptic equations is solved by means of multi-domain spectral methods. Results
are compared with previous work both in the high mass ratio limit and for one
neutron star with very low compactness parameter. The accuracy of the present
code is shown to be greater than with previous codes. Moreover, for the first
time, some sequences containing one neutron star of realistic compactness are
presented and discussed.
