  We discuss techniques for accelerating the self consistent field (SCF)
iteration for solving the Kohn-Sham equations. These techniques are all based
on constructing approximations to the inverse of the Jacobian associated with a
fixed point map satisfied by the total potential. They can be viewed as
preconditioners for a fixed point iteration. We point out different
requirements for constructing preconditioners for insulating and metallic
systems respectively, and discuss how to construct preconditioners to keep the
convergence rate of the fixed point iteration independent of the size of the
atomistic system. We propose a new preconditioner that can treat insulating and
metallic system in a unified way. The new preconditioner, which we call an
elliptic preconditioner, is constructed by solving an elliptic partial
differential equation. The elliptic preconditioner is shown to be more
effective in accelerating the convergence of a fixed point iteration than the
existing approaches for large inhomogeneous systems at low temperature.
