Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase

VandeVondele, Joost; Borštnik, Urban; Hutter, Jürg

doi:10.1021/ct200897x

Cited by 159 publications

(198 citation statements)

References 81 publications

(184 reference statements)

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“…All other MPI communication is performed either within the global row processor group or the global column processor group. We note that a similar conversion procedure also can be found in other electronic structure software packages such as SIESTA [6] and CP2K [16] when ScaLA-PACK is used.…”

Section: Computation Of the Electron Densitymentioning

confidence: 89%

“…On the other hand, several DFT software packages based on contracted basis functions have achieved high parallel performance using linear scaling techniques for insulating systems. Examples include CP2K [16] and CONQUEST, [17] in which linear scaling is achieved based on parallel sparse matrix multiplication. [18][19][20] CP2K has demonstrated calculations on 96,000 water molecular scaling to 46,656 cores.…”

Section: Introductionmentioning

confidence: 99%

“…[18][19][20] CP2K has demonstrated calculations on 96,000 water molecular scaling to 46,656 cores. [16] CONQUEST has demonstrated scaling to over 2,000,000 atoms on 4,096 cores. [17] The recently developed discontinuous Galerkin density functional theory (DGDFT) [21] aims at reducing the number of basis functions per atom while maintaining accuracy comparable to that of the planewave basis set.…”

Section: Introductionmentioning

confidence: 99%

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DGDFT: A massively parallel method for large scale density functional theory calculations

Lin

Yang

2015

The Journal of Chemical Physics

100

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We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field (SCF) iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. It minimizes the number of degrees of freedom required to represent the solution to the Kohn-Sham problem for a desired level of accuracy. In particular, DGDFT can reach the planewave accuracy with far fewer numbers of degrees of freedom. By using the pole expansion and selected inversion (PEXSI) technique to compute electron density, energy and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of two-dimensional (2D) phosphorene systems with 3,500-14,000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

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Section: Computation Of the Electron Densitymentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DGDFT: A massively parallel method for large scale density functional theory calculations

Lin

Yang

2015

The Journal of Chemical Physics

100

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“…Nevertheless, we can make some preliminary comparisons on the basis of already-published work, particularly that by the developers of CP2K, who have applied hybrid parallelism to their code, 35 and in particular to the sparse matrix algebra with the DBSCR library. 36 Several fundamental differences exist between these codes: firstly, CP2K uses Gaussian basis sets augmented with plane-waves, and thus a larger number of functions per atom than the number typically used by ONETEP, where a minimal number of in-situ optimised functions are used; secondly, CP2K applies thresholding to determine the truncation of its representation of the density kernel matrix, in contrast to the approach used in ONETEP, where all nonzero elements of intermediate matrices are retained until the final result of an optimisation step is used to update the current kernel.…”

Section: Large Systemsmentioning

confidence: 99%

Hybrid MPI-OpenMP Parallelism in the ONETEP Linear-Scaling Electronic Structure Code: Application to the Delamination of Cellulose Nanofibrils

Wilkinson

Hine

Skylaris

2014

J. Chem. Theory Comput.

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We present a hybrid MPI-OpenMP implementation of Linear-Scaling Density Functional Theory within the ONETEP code. We illustrate its performance on a range of high performance computing (HPC) platforms comprising shared-memory nodes with fast interconnect.Our work has focused on applying OpenMP parallelism to the routines which dominate the computational load, attempting where possible to parallelise different loops from those already parallelised within MPI. This includes 3D FFT box operations, sparse matrix algebra operations, calculation of integrals, and Ewald summation. Whilst the underlying numerical methods are unchanged, these developments represent significant changes to the algorithms used within ONETEP to distribute the workload across CPU cores. The new hybrid code exhibits much-improved strong scaling relative to the MPI-only code, and permits calculations with a much higher ratio of cores to atoms. These developments result in a significantly shorter time to solution than was possible using MPI alone, and facilitate the application of the ONETEP code to systems larger than previously feasible. We illustrate this with benchmark calculations from an amyloid fibril trimer containing 41,907 atoms. We use the code to * To whom correspondence should be addressed † School of Chemistry, University of Southampton, Southampton, SO17 1BJ, UK ‡ TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom 1 study the mechanism of delamination of cellulose nano-fibrils when undergoing sonification, a process which is controlled by a large number of interactions that collectively determine the structural properties of the fibrils. Many energy evaluations were needed for these simulations and as these systems comprise up to 21,276 atoms this would not have been feasible without the developments described here.

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“…However, the variational optimization of the DM is very inefficient for accurate DFT calculations 3,11 , which require many basis functions per atom. Therefore, the applications of DMbased LS methods have been limited to minimal-basis tight-binding problems.…”

Section: Introductionmentioning

confidence: 99%

Efficient Linear-Scaling Density Functional Theory for Molecular Systems

Khaliullin

VandeVondele

Hutter

2013

J. Chem. Theory Comput.

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Despite recent progress in linear scaling (LS) density function theory (DFT), the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate nonself-consistent approach. We demonstrate that, even for challenging condensed-phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those previously treated. Efficient linear-scaling density functional theory for molecular systems Despite recent progress in linear scaling (LS) density function theory (DFT) the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate non-self-consistent approach. We demonstrate that even for challenging condensed phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those treated before.

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Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase

Cited by 159 publications

References 81 publications

DGDFT: A massively parallel method for large scale density functional theory calculations

DGDFT: A massively parallel method for large scale density functional theory calculations

Hybrid MPI-OpenMP Parallelism in the ONETEP Linear-Scaling Electronic Structure Code: Application to the Delamination of Cellulose Nanofibrils

Efficient Linear-Scaling Density Functional Theory for Molecular Systems

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