Centers & Labs

RIKEN Advanced Institute for Computational Science

Large-Scale Parallel Numerical Computing Technology Research Team

Team Leader: Toshiyuki Imamura (Ph.D.)
Toshiyuki  Imamura(Ph.D.)

The Large-scale Parallel Numerical Computing Technology Research Team conducts research and development of a large scale, highly parallel and high-performance numerical software library for the K computer. Simulation programs require various numerical algorithms for the solution of linear systems, eigenvalue problems, fast Fourier transforms, and non-linear equations. In order to take advantage of the full potential of the K computer, we must select algorithms and develop a numerical software library based on the concepts of high parallelism, high performance, high precision, resiliency, and scalability. We achieve this through close collaboration among computational science (simulation), computer science (hardware and software) and numerical mathematics. Our goal is to establish a fundamental technique to develop numerical software libraries, called KMATHLIB, for next generation supercomputer systems based on strong cooperation within AICS.

Research Subjects

  • In order to fully utilize the K-computer, we need to select a numerical library which uses appropriate parallel algorithms according to the parallelism (Note, it is unacceptable to use lower parallel numerical libraries for a highly parallel application code). We conduct to develop from a high performance library, which performs on a lower parallel environment, research a highly parallelized numerical method, and equip a numerical library package on the K-computer such as a sparse linear solver, an eigenvalue solver, and a three-dimensional fast Fourier transform.
  • On the K-computer, 6 dimensional mesh/torus network called Tofu is adopted. 4 dimensions out of 6 dimensions are assigned to a user application, and 3D view is possible. Since suitable process mapping for general applications and a numerical library on a Tofu network is different in many cases, efficient network use is not achieved. We conduct to build a higher dimension mapping theory by using suitable folding and network topology theory of a two dimensional domain.
  • Like the K computer, a system which has 100,000 nodes, since the total number of the parts connected on the system also increases, it becomes difficult to hold a failure rate low. It may break down during execution of a simulation. We conduct to research checkpoint restart to a numerical library and an algorithmic fault detection which detects a "soft error" by an algorithm, and avoid the unexpected program termination.
  • Development of High Precision numerical libraries and its framework

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.
  1. Toshiyuki Imamura, Takeshi Fukaya, Yusuke Hirota, Susumu Yamada and Masahiko Machida.:
    "CAHTR: Communication-Avoiding Householder TRidiagonalization"
    Proc. ParCo2015, Advances in Parallel Computing, Vol. 27: Parallel Computing: On the Road to Exascale, pp. 381-390, 2016.
  2. Yusuke,Hirota.,and Toshiyuki Imamura.:
    "Divide-and-Conquer Method for Banded Generalized Eigenvalue Problems"
    Journal of Information Processing Computing System, Vol.52,Nov,20,2015.
  3. Kawamura,Takuma.,Idomura,Yasuhiro.,Miyamura,Hiroko.,Imamura,Toshiyuki.,and Takemiya,Hiroshi.:
    "Visualization technique for large-scale data by particle-based volume rendering"
    Transactions of ISCIE,Vol.28, No.5,pp.221-227,May,15,2015.
  4. Seikichi,Matsuoka.,Shinsuke,Satake.,Yasuhiro,Idomura.,and Toshiyuki,Imamura.:
    "Quality and Performance of a Pseudo-Random Number Generator in Massively Parallel Plasma Particle Simulations"
    Proceedings of ANS MC2015 - Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method
  5. Takeshi,Fukaya., and Toshiyuki,Imamura.:
    "Performance evaluation of the EigenExa eigensolver on Oakleaf-FX: tridiagonalization versus pentadiagonalization"
    Parallel and Distributed Processing Symposium Workshop (IPDPSW), 2015 IEEE International, pp. 960-969, May 25 2015
  6. T,Imamura.:
    "The EigenExa Library – High Performance & Scalable Direct Eigensolver for Large-Scale Computational Science"
    International Supercomputing Conference (ISC14), Leipzig, June (2014). (invited talk)
  7. D,Mukunoki., T,Imamura., and D,Takahashi.:
    "Fast Implementation of General Matrix-Vector Multiplication (GEMV) on Kepler GPUs"
    23rd Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP 2015), March 2015 (2015).
  8. T,Fukaya., Y,Nakatsukasa., Y,Yanagisawa., and Y,Yamamoto.: CholeskyQR2.:
    "A Simple and Communication-Avoiding Algorithm for Computing a Tall-Skinny QR Factorization on a Large-Scale Parallel System"
    Proceedings of the 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA), (2014).
  9. T,Miyoshi., K,Kondo., and T,Imamura.:
    "The 10,240-member ensemble Kalman filtering with an intermediate AGCM"
    Geophysical Research Letters, Vol.41 (2014)
  10. Y,Idomura., M,Nakata., S,Yamada., M,Machida., T,Imamura., T,Watanabe., M,Nunami., H,Inoue., S,Tsutsumi., I,Miyoshi., and N,Shida.:
    "Communication-overlap techniques for improved strong scaling of gyrokinetic Eulerian code beyond 100k cores on the K-computer"
    International Journal of High Performance Computing Applications, 28(1) 73-86 (2014), SAGE publications, doi: 10.1177/1094342013490973

Lab Members

Principal Investigator

Toshiyuki Imamura
Team Leader

Core Members

Yiyu Tan
Research Scientist
Yusuke Hirota
Postdoctoral Researcher
Yoshiharu Ohi
Postdoctoral Researcher
Daichi Mukunoki
Postdoctoral Researcher
Daisuke Takahashi
Senior Visiting Scientist
Tetsuya Sakurai
Senior Visiting Scientist
Yoshio Okamoto
Visiting Scientist
Franz Franchetti
Visiting Scientist
Takeshi Fukaya
Visiting Scientist

Contact information


Email: imamura.toshiyuki [at]