  Background: The symmetry-unrestricted Hartree-Fock-Bogoliubov (HFB)
simulation is important for describing various quantum many-body systems.
However, the HFB problem in Cartesian coordinate space is numerically
challenging.
  Purpose: For describing ground states without imposing axial symmetry and
looking ahead to future extension for dynamics with full time dependence, we
present a numerically efficient implementation of the three-dimensional (3D)
HFB code.
  Methods: We develop a 3D Skyrme HFB code based on the mixed-basis
representation (HFBmix) which consists of two harmonic-oscillator (HO) bases in
the x- and y-directions, and finite-difference (FD) basis in the z-direction in
solving the nuclear 3D HFB problem.
  Results: The results show very well agreement among all the three codes
(HFBmix, HO3D, and hfodd). Especially for the HF calculations, the differences
in total energies are on the order of a few keV for the lightest O and Mg
nuclei. The HFBmix is applied to spherical, prolate, and triaxial systems, and
gives the same quadrupole moments for the deformed nuclei as those of the
HO-based calculations. Feasibility of the HFBmix is demonstrated in the fission
isomer and barrier calculations of 240Pu.
  Conclusions: The HFBmix is useful for solving the nuclear 3D HFB problem for
its numerical efficiency. Future work will include the analysis of deformed
drip-line systems and systematic potential-energy surface calculation for
fission-path analysis as well as the time-dependent extension of the HFBmix
code for dynamics calculations.
