Extremely Scalable Algorithm for 108-atom Quantum Material Simulation on the Full System of the K Computer

Hoshi, Takeo; Imachi, Hiroto; Kumahata, Kiyoshi; Terai, Masaaki; Kengo, Miyamoto; Minami, Kazuo; Shoji, Fumiyoshi

doi:10.1109/scala.2016.009

Cited by 7 publications

(12 citation statements)

References 25 publications

(45 reference statements)

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“…EigenKernel is a middleware for the various solvers in ScaLAPACK, ELPA, and EigenExa and their hybrids. Although we have developed a massively parallel electronic state calculation method without eigenvalue problem [16], [17], [27], we still need eigenvalue solver, so as to obtain eigenpairs in the discussion of electronic property.…”

Section: Resultsmentioning

confidence: 99%

Numerical aspect of large-scale electronic state calculation for flexible device material

Hoshi

Imachi

Kuwata

et al. 2019

Japan J. Indust. Appl. Math.

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Numerical aspects of large-scale electronic state calculation are explored on flexible organic device materials. Physical theory, numerical method and real application studies are discussed in the context of application-algorithmarchitecture co-design. An application study was carried out for disordered organic thin film. Participation ratio, a measure for the spatial extension of electronic wavefunction is focused on, since it is crucial for device property. A data scientific research is reported for a classification problem of disordered The present research was partially supported by JST-CREST project of 'Development of an Eigen-Supercomputing Engine using a Post-Petascale Hierarchical Model', Priority Issue 7 of the post-K project and KAKENHI funds (16KT0016,17H02828). Oakforest-PACS was used through the JHPCN Project (jh170058-NAHI) and through Interdisciplinary Computational Science Program in Center for Computational Sciences, University of Tsukuba. The K computer was used in the HPCI System Research Projects (hp180079, hp180219). Several computations were carried out also on the facilities of the Supercomputer Center,

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Section: Resultsmentioning

confidence: 99%

Numerical aspect of large-scale electronic state calculation for flexible device material

Hoshi

Imachi

Kuwata

et al. 2019

Japan J. Indust. Appl. Math.

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“…This mini-application can be used for real researches, as in Ref. [7], if the matrix data are prepared as files in the Matrix Market format.…”

Section: Features Of Eigenkernelmentioning

confidence: 99%

“…Here we focus on a middleware for the generalized eigenvalue problem (GEP) with real-symmetric coefficient matrices, since GEP forms the numerical foundation of electronic state calculations. Some of the authors developed a prototype of such middleware on the K computer in 2015-2016 [6,7]. After that, the code appeared at GITHUB as EigenKernel ver.…”

Section: Introductionmentioning

confidence: 99%

EigenKernel

Tanaka

Imachi

Fukumoto

et al. 2019

Japan J. Indust. Appl. Math.

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An open-source middleware named EigenKernel was developed for use with parallel generalized eigenvalue solvers or large-scale electronic state calculation to attain high scalability and usability. The middleware enables the users to choose the optimal solver, among the three parallel eigenvalue libraries of ScaLAPACK, ELPA, EigenExa and hybrid solvers constructed from them, according to the problem specification and the target architecture. The benchmark was carried out on the Oakforest-PACS supercomputer and reveals that ELPA, EigenExa and their hybrid solvers show better performance, when compared with pure ScaLAPACK solvers. The benchmark on the K computer is also used for discussion. In addition, a preliminary research for the performance prediction was investigated, so as to predict the elapsed time T as the function of the number of used nodes P (T = T (P)). The prediction is based on Bayesian inference in the Markov Chain Monte Carlo (MCMC) method and the test calculation indicates that the method is applicable not only to performance interpolation but also to extrapolation. Such a middleware is of crucial importance for application-algorithm-architecture co-design among the current, next-generation (exascale), and future-generation (post-Moore era) supercomputers.

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“…One of our recent motivations to address the k-th eigenvalue problem is electronic transport calculations of organic device materials using a quantum wave (wave packet) dynamics method [13,30]. In this method, an exited electronic wave (of an excited electron or a hole) is simulated by real-time dynamics with an effective time-dependent Schrödinger-type equation, and the wave function of the HO state or states near the HO state is set as the initial state of the wave.…”

Section: B Physical Background Of the K-th Eigenvalue Problemmentioning

confidence: 99%

“…Recently, a one-million-dimensional generalized eigenvalue problem was solved by a dense eigensolver [12] using the full K computer. The elapsed time was 5516 seconds to compute all eigenpairs [13], indicating the practical size limit of eigenpair computation by a dense eigensolver. Therefore, a strong need for methodologies that can be applied to larger materials and matrices has become apparent.…”

Section: Introductionmentioning

confidence: 99%

Solution of the k-th eigenvalue problem in large-scale electronic structure calculations

Hoshi

Sogabe

Miyatake

et al. 2018

Journal of Computational Physics

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We consider computing the k-th eigenvalue and its corresponding eigenvector of a generalized Hermitian eigenvalue problem of n × n large sparse matrices. In electronic structure calculations, several properties of materials, such as those of optoelectronic device materials, are governed by the eigenpair with a material-specific index k. We present a three-stage algorithm for computing the k-th eigenpair with validation of its index. In the first stage of the algorithm, we propose an efficient way of finding an interval containing the k-th eigenvalue (1 k n) with a non-standard application of the Lanczos method. In the second stage, spectral bisection for large-scale problems is realized using a sparse direct linear solver to narrow down the interval of the k-th eigenvalue. In the third stage, we switch to a modified shift-and-invert Lanczos method to reduce bisection iterations and compute the k-th eigenpair with validation. Numerical results with problem sizes up to 1.5 million are reported, and the results demonstrate the accuracy and efficiency of the three-stage algorithm.

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Extremely Scalable Algorithm for 108-atom Quantum Material Simulation on the Full System of the K Computer

Cited by 7 publications

References 25 publications

Numerical aspect of large-scale electronic state calculation for flexible device material

Numerical aspect of large-scale electronic state calculation for flexible device material

EigenKernel

Solution of the k-th eigenvalue problem in large-scale electronic structure calculations

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