Large-Scale Parallel Numerical Computing Technology Research Team

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

Publications

1. Toshiyuki Imamura, Susumu Yamada, and Masahiko Machida:
   "A High Performance SYMV Kernel on a Fermi-core GPU"
   Lecture Note in Computer Science 7851, Springer Verlag (to appear in 2013)
2. Toshiyuki Imamura, Susumu Yamada, and Masahiko Machida:
   "Eigen-K: high performance eigenvalue solver for symmetric matrices developed for K compute"
   The 7th Workshop on Parallel Matrix Algorithms and Applications, PMAA2012, London, UK, June, 2012
3. Susumu Yamada, Yasuhiro Idomura ,Toshiyuki Imamura, and Masahiko Machida:
   "High performance Krylov subspace method for asymmetric linear system on fusion plasma simulation code GT5D"
   The 7th Workshop on Parallel Matrix Algorithms and Applications, PMAA2012, London, UK, June, 2012
4. Susumu Yamada, Yasuhiro Idomura, Toshiyuki Imamura, and Masahiko Machida:
   "Convergence property of Krylov subspace methods for asymmetric linear system on fusion plasma simulation code GT5D"
   The Proceedings in 31th Annual Conference JSST2012, International Conference on Simulation Technology, Kobe, Japan, Sep. 2012
5. Toshiyuki Imamura, Susumu Yamada, Masahiko Machida:
   "Preliminary Report for a High Precision Distributed Memory Parallel Eigenvalue Solver"
   The Proceedings in the International Conference for High Performance Computing, Networking, Storage and Analysis, SC12, Salt Lake City, US, Nov. 2012