Large-scale electronic-structure calculations with multigrid acceleration

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 ${\mathrm{C}}_{60}$ 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.