  We present a multigrid algorithm for self consistent solution of the
Kohn-Sham equations in real space. The entire problem is discretized on a real
space mesh with a high order finite difference representation. The resulting
self consistent equations are solved on a heirarchy of grids of increasing
resolution with a nonlinear Full Approximation Scheme, Full Multigrid
algorithm. The self consistency is effected by updates of the Poisson equation
and the exchange correlation potential at the end of each eigenfunction
correction cycle. The algorithm leads to highly efficient solution of the
equations, whereby the ground state electron distribution is obtained in only
two or three self consistency iterations on the finest scale.
