  We have developed a set of techniques for performing large scale ab initio
calculations using multigrid accelerations and a real-space grid as a basis.
The multigrid methods permit efficient calculations on ill-conditioned systems
with long length scales or high energy cutoffs. The technique has been applied
to systems containing up to 100 atoms, including a highly elongated diamond
cell, an isolated C$_{60}$ molecule, and a 32-atom cell of GaN with the Ga
d-states in valence. The method is well suited for implementation on both
vector and massively parallel architectures.
