Development of a High-Performance Eigensolver on a Peta-Scale Next-Generation Supercomputer System

Imamura, Toshiyuki; Yamada, S.; Machida, Masahiko

doi:10.15669/pnst.2.643

Cited by 49 publications

(37 citation statements)

References 8 publications

(8 reference statements)

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“…A narrow-band reduction algorithm coupled with a band divide and conquer approach was also described and successfully implemented in the new EigenExa library. [21,25] If orthogonality is not an issue then the eigenvectors can also be computed as the null spaces of shifted banded matrices [56,57]. Finally, even the tridiagonalization of the banded matrix (steps (IIIb) and (Va)) may be subdivided further [43,44,58].…”

Section: The Eigenvalue Problemmentioning

confidence: 99%

“…[25,21] As mentioned above, this library incorporates a narrow-band reduction and a band divide and conquer method, thus modifying steps (III)-(V) above. Another very recent benchmark [74] for the K computer, a 640,000 core, SPARC64 processor based distributed-memory computer, shows very promising results for this new approach.…”

Section: Recent Developments In Parallel Eigenvalue Solversmentioning

confidence: 99%

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The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

Marek

Blüm

Johanni

et al. 2014

J. Phys.: Condens. Matter

232

261

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Abstract. Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N 3 ) with the size of the investigated problem, N (e.g., the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the ELPA library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the ScaLAPACK library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g., Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPIOpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem sizes arising in the electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a ELPA -Eigenvalue Solutions for Electronic Structure Theory 2 matrix of dimension 260,000, scalability up to 295,000 CPU cores has been shown on BlueGene/P.

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Section: The Eigenvalue Problemmentioning

confidence: 99%

Section: Recent Developments In Parallel Eigenvalue Solversmentioning

confidence: 99%

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

Marek

Blüm

Johanni

et al. 2014

J. Phys.: Condens. Matter

232

261

View full text Add to dashboard Cite

show abstract

“…The parallelization of the transformation was optimized for massively parallel computing on the K computer . We also implemented the eigen_sx routine of EigenExa and the locally optimal block preconditioned conjugated gradient (LOBPCG) algorithm into the Platypus‐QM unit, to accelerate the computation of eigenvalue problems.…”

Section: Methodsmentioning

confidence: 99%

Development of massive multilevel molecular dynamics simulation program, platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

Takano

Nakata²,

Yonezawa

et al. 2016

J Comput Chem

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A massively parallel program for quantum mechanical‐molecular mechanical (QM/MM) molecular dynamics simulation, called Platypus (PLATform for dYnamic Protein Unified Simulation), was developed to elucidate protein functions. The speedup and the parallelization ratio of Platypus in the QM and QM/MM calculations were assessed for a bacteriochlorophyll dimer in the photosynthetic reaction center (DIMER) on the K computer, a massively parallel computer achieving 10 PetaFLOPs with 705,024 cores. Platypus exhibited the increase in speedup up to 20,000 core processors at the HF/cc‐pVDZ and B3LYP/cc‐pVDZ, and up to 10,000 core processors by the CASCI(16,16)/6‐31G** calculations. We also performed excited QM/MM‐MD simulations on the chromophore of Sirius (SIRIUS) in water. Sirius is a pH‐insensitive and photo‐stable ultramarine fluorescent protein. Platypus accelerated on‐the‐fly excited‐state QM/MM‐MD simulations for SIRIUS in water, using over 4000 core processors. In addition, it also succeeded in 50‐ps (200,000‐step) on‐the‐fly excited‐state QM/MM‐MD simulations for the SIRIUS in water. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

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“…Peta-scale systems are defined as systems which are able to provide peta-FLOPS, millions of billions of FLoating OPerations per Second, computational power [1,2]. They can be described as the increasingly massive and dynamic networks of interconnected diverse processors and components (i.e.…”

Section: Simulation and Peta-scale Systemsmentioning

confidence: 99%

Manycore simulation for peta-scale system design: Motivation, tools, challenges and prospects

Zarrin

Aguiar

Barraca

2017

Simulation Modelling Practice and Theory

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThe architecture design of peta-scale computing systems is complex and presents lots of difficulties to designs, as current tools lack support for relevant features of future scenarios. Novel systems must be designed with great care and tools, such as manycore architecture simulators, must be adapted accordingly. However, current simulation tools are very slow, often specific-purposeoriented, suffer from various issues and are rarely able to simulate thousands of cores. The emergence of peta-scale systems and the upcoming manycore era brings nevertheless new challenges to computing systems and architectures, adding further difficulties and requirements on the development of the corresponding simulators. Furthermore, the design of architecture simulators for manycore systems involve methods and techniques from various interdisciplinary research areas, which in turn brings more challenges in different aspects. As system complexity grows, the growth of the simulation capacity is being outpaced (reaching the so called simulation wall). In this paper, we present the challenges for simulating future large scale manycore environments, and we investigate the adequacy of current modeling and simulation tools, methodologies and techniques. The aim of this work is to highlight how current approaches can best deal with the identified problems, smoothing the challenges of research in future peta-scale systems.

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Development of a High-Performance Eigensolver on a Peta-Scale Next-Generation Supercomputer System

Cited by 49 publications

References 8 publications

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

Development of massive multilevel molecular dynamics simulation program, platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

Manycore simulation for peta-scale system design: Motivation, tools, challenges and prospects

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