Large scale simulation of quantum-mechanical molecular dynamics for nano-polycrystalline diamond

Hoshi, Takeo; Iitaka, Toshiaki; Fyta, Maria

doi:10.1088/1742-6596/215/1/012118

Cited by 2 publications

(7 citation statements)

References 13 publications

(24 reference statements)

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“…A more realistic situation with the tennanometer simulation cell sizes in the three directions requires million-atom MD simulation, ten times larger than that in the present result. 10 In summary, (i) a high parallel efficiency was achieved in ten-million-atom order-N electronic structure calculations on the K computer with approximately 10 5 processor cores. Important computational issues were addressed for communication, memory size, and file reading/writing.…”

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confidence: 96%

“…For example, the initial structure for the simulation of Fig. 2 contains defects among the sp 3 domains, 10) as ''seeds'' of the sp 2 -sp 3 domain boundary. The resultant structure in Fig.…”

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confidence: 99%

“…The calculations were carried out in a couple of MD steps, with a TB-form Hamiltonian, 9 for amorphous-like conjugated polymer, poly-(9,9 dioctil-fluorene) (aPF) with N=10,629,120 atoms 5 and sp 2sp 3 nano-composite carbon solid (NCCS) with N=10,321,920 atoms (See Ref. 10 for a related study).…”

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“…The system is a resultant structure of the our previous finitetemperature MD simulation with a periodic boundary condition. 10 The simulation is a preliminary research for the formation process of the nano-polycrystalline diamond (NPD), a novel ultra-hard materials. 18,19 The NPD is produced directly from graphitic materials and consists of 10-nm-scale diamond-structure domains with a characteristic lamella-like structure.…”

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confidence: 99%

“…The structure is a '2D-like' one, because the periodic cell length in the perpendicular direction to the paper (2nm) is much smaller than the other two cell lengths, 17 nm or more. 10 The artificial '2Dlike' situation affect severely the resultant atomic structure and makes a difficulty for a direct comparison between the simulation and experiment. A more realistic situation with the ten-nanometer simulation cell sizes in the three directions requires million-atom MD simulation, ten times larger than that in the present result.…”

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Ten-Million-Atom Electronic Structure Calculations on the K Computer with a Massively Parallel Order-NTheory

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A massively parallel order-N electronic structure theory was developed by interdisciplinary research between physics, applied mathematics, and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was realized on the K computer with up to 98,304 processor cores. The mathematical foundation is a novel linear algebraic algorithm for generalized shifted linear equations. The calculation was carried out using our code ''ELSES'' (www.elses.jp) with modelled (tight-binding-form) systems based on ab initio calculations. (2) A postcalculation analysis method, called the -orbital crystalline orbital Hamiltonian population ( -COHP) method, is presented, since this method is ideal for huge electronic structure data distributed among massive nodes. The analysis method is demonstrated in an sp 2 -sp 3 nanocomposite carbon solid, with the original visualization software ''VisBAR''. The present research indicates the general aspects of computational physics with current or next-generation supercomputers.KEYWORDS: order-N electronic structure theory, numerical linear algebra, massive parallel computation, sp 2 -sp 3 nanocomposite carbon solid, crystalline orbital Hamiltonian populationA common issue in current computational physics is the theory for large calculations with modern massively parallel supercomputers, such as the K computer. Large calculations should accompany a large-data analysis theory, as a postcalculation procedure, so as to obtain a physical conclusion from huge numerical data distributed among massive computer nodes. Interdisciplinary research studies between physics, applied mathematics and computer science are thus crucial and such a study is sometimes called ''application-algorithm-architecture co-design''.The present paper is devoted to theories, for both largescale calculation and large-data analysis, as order-N electronic structure theories suitable for modern massively parallel computers.Order-N electronic structure theories are those in which the computational time is proportional to the number of atoms in the system N and are promising for large-scale calculation. The reference list for the order-N theories can be found, for example, in Ref. 1. Recently, several novel linear algebraic algorithms, with Krylov subspace, have been developed for the order-N theory, i.e., the generalized shifted conjugate-orthogonal conjugate-gradient method, [1][2][3] generalized Lanczos method, 1) generalized Arnoldi method, 1) Arnoldi ðM; W; GÞ method, 4) multiple Arnoldi method, 5) and generalized shifted quasi-minimal-residual method. 3) Their common foundation is the ''generalized shifted linear equation'', or the set of linear equationswhere z is a (complex) energy value and H and S denote the Hamiltonian and overlap matrices in the linear-combinationof-atomic-orbital (LCAO) representation, respectively. The matrices are sparse real-symmetric M Â M matrices, and S is positive definite. The vector b is the input and the vector x is the solution vector. Equation (1) is solved, iterativ...

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Ten-Million-Atom Electronic Structure Calculations on the K Computer with a Massively Parallel Order-NTheory

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Linear Algebra and Charge Self-consistent Tight-binding Method for Large-scale Electronic Structure Calculations

Fujiwara,

Yamamoto,

Hoshi

et al. 2010

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We review our recently developed electronic structure calculation methods for the dynamics of large-scale solids, liquids or soft materials with an efficient algorithm of linear algebra. The Hamiltonian of electronic structures is based on the 'atomic superposition and electron delocalization molecular orbitals theory' (ASED), using the Mulliken charge density. Very crucial algorithms of the linear algebra are the generalized Lanczos method and the generalized shifted COCG (conjugate orthogonal conjugate gradient) method for general eigen-value problems. The shift equation and the seed switching method are essential for the shifted COCG method and reduce the computational cost much. We, then, present some applications to electronic structure calculations with MD simulation, such as the fracture propagation in nano-scale Si crystals and the proton transfer in water.

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Large scale simulation of quantum-mechanical molecular dynamics for nano-polycrystalline diamond

Cited by 2 publications

References 13 publications

Ten-Million-Atom Electronic Structure Calculations on the K Computer with a Massively Parallel Order-NTheory

Ten-Million-Atom Electronic Structure Calculations on the K Computer with a Massively Parallel Order-NTheory

Linear Algebra and Charge Self-consistent Tight-binding Method for Large-scale Electronic Structure Calculations

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