Large-Scale Electronic-Structure Calculations Based on the Adaptive Finite-Element Method

The adaptive finite-element method proposed in our previous work [Phys. Rev. B 54 (1996) 7602] is extended to fully self-consistent calculations of realistic materials. Our method is highly adaptive, sparse, parallel, and suited for the O(N) methods, thanks to the localized finite-element basis functions. Accurate ionic forces can also be calculated within practical time usage. Applications to the structural properties of diamond, c-BN, and the C 60 molecule, and molecular dynamics within O(N 3 ) scaling are shown first, followed by detailed error analyses. Then the O(N) method based on the orbital formulation is realized within our approach.