A massively-parallel electronic-structure calculations based on real-space density functional theory

Iwata, Junichi; Takahashi, Daisuke; Oshiyama, Atsushi; Boku, Taisuke; Shiraishi, Kenji; Okada, Susumu; Yabana, Kazuhiro

doi:10.1016/j.jcp.2009.11.038

Cited by 136 publications

(103 citation statements)

References 47 publications

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“…For example, a well preconditioned blocked Davidson scheme is superior even for augmented plane wave based all-electron DFT, with k/n % 3-10% [9]. To our knowledge, iterative strategies such as (ii) and (iii) usually still require at least one O(N 3 ) operation, at least in practice [14,6,27,29,30,9] (subspace diagonalization, re-orthonormalization, matrix inversion at the outset, etc.). (iv) A straightforward path to push the crossover point between (1) and all other, O(N) type operations out is to reduce n, the basis size itself.…”

Section: Introductionmentioning

confidence: 99%

Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations

et al. 2011

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a b s t r a c tThe computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many contexts, for example in electronic structure calculations. If a significant portion of the eigensystem is required then typically direct eigensolvers are used. The central three steps are: reduce the matrix to tridiagonal form, compute the eigenpairs of the tridiagonal matrix, and transform the eigenvectors back. To better utilize memory hierarchies, the reduction may be effected in two stages: full to banded, and banded to tridiagonal. Then the back transformation of the eigenvectors also involves two stages. For large problems, the eigensystem calculations can be the computational bottleneck, in particular with large numbers of processors. In this paper we discuss variants of the tridiagonal-to-banded back transformation, improving the parallel efficiency for large numbers of processors as well as the per-processor utilization. We also modify the divide-and-conquer algorithm for symmetric tridiagonal matrices such that it can compute a subset of the eigenpairs at reduced cost. The effectiveness of our modifications is demonstrated with numerical experiments.

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Section: Introductionmentioning

confidence: 99%

Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations

et al. 2011

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“…In Example 3, the test matrix is derived from realspace density functional calculations [12,13]. It is a standard eigenvalue problem Ax = λx, where A is a real [13].…”

Section: Examplementioning

confidence: 99%

“…It is a standard eigenvalue problem Ax = λx, where A is a real [13]. Although s is significantly smaller than the matrix size n, our method roughly estimates the eigenvalue count.…”

Section: Examplementioning

confidence: 99%

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Parallel stochastic estimation method of eigenvalue distribution

2010

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Some kinds of eigensolver for large sparse matrices require specification of parameters that are based on rough estimates of the desired eigenvalues. In this paper, we propose a stochastic estimation method of eigenvalue distribution using the combination of a stochastic estimator of the matrix trace and contour integrations. The proposed method can be easily parallelized and applied to matrices for which factorization is infeasible. Numerical experiments are executed to show that the method can perform rough estimates at a low computational cost.

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“…In this study, we have performed first-principles electronic structure calculations for Si QDs in the sizes of 1 to 7 nm diameters by using a recently developed realspace finite-difference pseudopotential code suitable for massively parallel computers [6]. We have investigated the system size dependence of the density of states (DOS), the band gaps, and the charging energies of the Si QDs.…”

Section: Introductionmentioning

confidence: 99%

Large-Scale First-Principles Electronic Structure Calculations for Nano-Meter Size Si Quantum Dots

Iwata

Oshiyama

Shiraishi

2010

e-J. Surf. Sci. Nanotechnol.

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We have studied the system size dependence of the density of states, band gap, and the charging energy of the large size Si quantum dots of 2.2 to 7.6 nm diameters by first-principles electronic structure calculations. The largest model examined in this study consists of over 10,000 Si atoms, and we performed such large calculations by using recently developed real-space density-functional theory code suitable for massively parallel computers. The density of states of 6 nm-diameter Si quantum dot is almost the same as that of the bulk Si. The band gaps of the Si quantum dots have been calculated by the ∆SCF method with local-density approximation, and we have found that the difference between the ∆SCF band gap and the Kohn-Sham eigenvalue gap is equal to the inverse of the dot radius. Consequently the ∆SCF band gap converges to the Kohn-Sham eigenvalue gap in the infinitely large size limit with the local-density approximation.

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A massively-parallel electronic-structure calculations based on real-space density functional theory

Cited by 136 publications

References 47 publications

Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations

Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations

Parallel stochastic estimation method of eigenvalue distribution

Large-Scale First-Principles Electronic Structure Calculations for Nano-Meter Size Si Quantum Dots

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