Massively parallel linear-scaling algorithm in an ab initio local-orbital total-energy method

Shellman, Spencer; Lewis, James P.; Glaesemann, Kurt R.; Sikorski, K.; Voth, Gregory A.

doi:10.1016/s0021-9991(03)00069-x

Cited by 12 publications

(12 citation statements)

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“…There are numerous implementations of these methods: the original papers [163,165,166,238]; the generalised versions [164,199,240,241]; in parallel [242,243]; with ultra-soft pseudopotentials [36]. A real-space implementation of similar ideas [202] uses exact inversion of the overlap, thus not forming a strict linear scaling method (though the cubic scaling part will have a small prefactor).…”

Section: Direct and Iterative Approachesmentioning

confidence: 99%

“…Scaling on up to 512 processors and 85,000 atoms was demonstrated, and an extensive analysis of scaling was made, noting that as the volume assigned to each processor decreases relative to a boundary area (due to localisation radii) the amount of communication will change from depending on the number of processors (as N −1/3 proc ) to depending on the volume of the boundary. The same approach has been used for an implementation of orbital minimisation [164] within an ab initio tight binding method [243], though MPI and OpenMP parallelisation are shared; the resulting code was demonstrated on up 1,024 processors and 6,000 atoms.…”

Section: Parallelisation and Sparse Matricesmentioning

confidence: 99%

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\mathcal{O}(N) methods in electronic structure calculations

2012

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Abstract. Linear scaling methods, or O(N ) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N , in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.

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Section: Direct and Iterative Approachesmentioning

confidence: 99%

Section: Parallelisation and Sparse Matricesmentioning

confidence: 99%

\mathcal{O}(N) methods in electronic structure calculations

2012

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“…Because these integral tables depend only on the atom type, their r c values, and the type of DFT exchange-correlation functional used, the integral tables only need to be generated once, for a given number of atomic species, rather than calculating integrals ''on-the-fly'' during an MD simulation. This pre-generation process lends itself to parallelization via spreading the integrals out over multiple processors based on integral types [23,30]. This parallelization is particularly important, since the number of integrals needed for each database grows as order N 3 with the number of atom types in the database.…”

Section: Localized Pseudo-atomic Orbitals and Basis Setsmentioning

confidence: 99%

“…For large systems such as the 10-mer DNA (644 atoms), we have implemented a variational linear-scaling technique to solve for the total energies and forces from the sparse Hamiltonian and overlap matrices [31]. Furthermore, we have developed a massively-parallel algorithm using message passing interface (MPI) to manipulate extremely large sparse matrices required for linear-scaling algorithms and have exhibited simulations of up to 6000 atoms [30]. The use of local-orbitals in the FIREBALL method yields a very sparse Hamiltonian matrix, which facilitates using a linearscaling algorithm to obtain the electronic band-structure energy.…”

Section: Amorphous Chalcogenidesmentioning

confidence: 99%

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Advances and applications in the FIREBALLab initio tight‐binding molecular‐dynamics formalism

Lewis

Jelı́nek

Ortega

et al. 2011

Physica Status Solidi (b)

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231

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One of the outstanding advancements in electronic-structure density-functional methods is the Sankey-Niklewski (SN) approach [Sankey and Niklewski, Phys. Rev. B 40, 3979 (1989)]; a method for computing total energies and forces, within an ab initio tight-binding formalism. Over the past two decades, several improvements to the method have been proposed and utilized to calculate materials ranging from biomolecules to semiconductors. In particular, the improved method (called FIREBALL) uses separable pseudopotentials and goes beyond the minimal sp 3 basis set of the SN method, allowing for double numerical (DN) basis sets with the addition of polarization orbitals and d-orbitals to the basis set. Herein, we report a review of the method, some improved theoretical developments, and some recent application to a variety of systems.ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction With the increase in computational power, greater efforts have been made by the electronicstructure community to optimize the performance of quantum mechanical methods. Quantum mechanical methods have become increasingly reliable as a complementary tool to experimental research. A variety of methods exist ranging in complexity from semi-empirical methods to density-functional theory (DFT) methods to highly-accurate methods going beyond the one-electron picture. Judicious approximations enable the computational materials science community to more efficiently examine a wider range of materials questions.Otto F. Sankey was one of the early visionaries by, firstly, demonstrating that molecular-dynamics (MD) simulations can be coupled efficiently with electronic-structure methods to optimize structures and evaluate energetics of materials [1]. Secondly, his judicious approximations in the

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