Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation.
V. Gavini, K. Bhattacharya and M. Ortiz.
Journal of the Mechanics and Physics of Solids, 55, 697-718 (2007).

ABSTRACT
Density-functional theory has provided insights into various materials
properties in the recent decade. However, its computational complexity has made
other aspects, especially those involving defects, beyond reach. Here, we
present a method that enables the study of multi-million atom clusters using
orbital-free density-functional theory with no spurious physics or restrictions
on geometry. The key ideas are (i) a real-space formulation, (ii) a nested
finite-element implementation of the formulation and (iii) a systematic means of
adaptive coarse-graining retaining full resolution where necessary and
coarsening elsewhere with no patches, assumptions or structure. We demonstrate
the method, its accuracy under modest computational cost and the physical
insights it offers by studying one and two vacancies in aluminum crystals
consisting of millions of atoms.