  Covariant density functional theory is solved in 3D lattice space by
implementing the preconditioned conjugate gradient method with a filtering
function (PCG-F). It considerably improves the computational efficiency
compared to the previous inverse Hamiltonian method (IHM). This new method is
then applied to explore the tetrahedral shape of $^{110}$Zr in the full
deformation space. The ground state of $^{110}$Zr is found to have a
tetrahedral shape, but the deformations $\beta_{31}$ and $\beta_{33}$ greatly
soften the potential energy surface. This effect is analysed with the
microscopic evolution of the single-particle levels near the Fermi surface
driven by the deformation.
