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,
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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