Journal
PHYSICAL REVIEW B
Volume 82, Issue 7, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.82.075131
Keywords
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Funding
- Fujitsu Laboratory
- Nissan Motor Co., Ltd.
- Nippon Sheet Glass Co., Ltd.
- MEXT, Japan
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An efficient low-order scaling method is presented for large-scale electronic structure calculations based on the density-functional theory using localized basis functions, which directly computes selected elements of the density matrix by a contour integration of the Green's function evaluated with a nested dissection approach for resultant sparse matrices. The computational effort of the method scales as O[N(log(2) N)(2)], O(N-2), and O(N-7/3) for one-, two-, and three-dimensional systems, respectively, where N is the number of basis functions. Unlike O(N) methods developed so far the approach is a numerically exact alternative to conventional O(N-3) diagonalization schemes in spite of the low-order scaling, and can be applicable to not only insulating but also metallic systems in a single framework. It is also demonstrated that the well separated data structure is suitable for the massively parallel computation, which enables us to extend the applicability of density-functional calculations for large-scale systems together with the low-order scaling.
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