  Magnetic field in the solar corona is usually extrapolated from photospheric
vector magnetogram using a nonlinear force-free field (NLFFF) model. NLFFF
extrapolation needs a considerable effort to be devoted for its numerical
realization. In this paper we present a new implementation of the
magnetohydrodynamics (MHD)-relaxation method for NLFFF extrapolation. The
magneto-frictional approach which is introduced for speeding the relaxation of
the MHD system is novelly realized by the spacetime conservation-element and
solution-element (CESE) scheme. A magnetic field splitting method is used to
further improve the computational accuracy. The bottom boundary condition is
prescribed by changing the transverse field incrementally to match the
magnetogram, and all other artificial boundaries of the computational box are
simply fixed. We examine the code by two types of NLFFF benchmark tests, the
Low & Lou (1990) semi-analytic force-free solutions and a more realistic
solar-like case constructed by van Ballegooijen et al. (2007). The results show
that our implementation are successful and versatile for extrapolations of
either the relatively simple cases or the rather complex cases which need
significant rebuilding of the magnetic topology, e.g., a flux rope. We also
compute a suite of metrics to quantitatively analyze the results and
demonstrate that the performance of our code in extrapolation accuracy
basically reaches the same level of the present best-performing code, e.g.,
that developed by Wiegelmann (2004).
