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2005 Fiscal Year Final Research Report Summary

Constraction of the lattice gauge computation tools for large scale cluster computars

Research Project

Project/Area Number 15540136
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKeio University

Principal Investigator

NODERA Takashi  Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (50156212)

Co-Investigator(Kenkyū-buntansha) MAEJIMA Makoto  Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (90051846)
TANI Atsushi  Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (90118969)
TAMURA Yozo  Keio Univ., Faculty of Sci.and Tech., Associate Professor, 理工学部, 助教授 (50171905)
SHIMOMURA Shun  Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (00154328)
OHNO Yoshio  Keio Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (20051865)
Project Period (FY) 2003 – 2005
Keywordssparse matrix computation / QCD / shifted system of equation / parallel computation / GMRES / preconditioning / approximate inverse / minimal residual method
Research Abstract

Quantum Chromo dynamics (QCD) is the quantum theory of working together with quarks and gluons. It should make clear the physics of strong force from low to high energies. The direct attack it is known to be the lattice approach. This theory is called to be Lattice QCD (LQCD).
One important example is simulations in Lattice QCD with Neuberger fermions. The most important problem in this research is to find an approximate solution to the large linear systems of equations. From parallel computational point of view, iterative Krylov solvers are admired for approximately solving such the large linear systems of equations. In addition to the design of the toolkit, we have presented our approach to make up the different combinations of Krylov space generation and its preconditioning along with the orthogonality condition imposed on the residual at each step give rise to the different algorithms.
Generally, Krylov subspace methods have to be used with preconditiong, The use of approximate inverses have become a good alternative to implicit preconditioners due to their parallel nature. The main application is developed for the subspace of matrices with a given sparsity pattern which constructed iteratively by augmenting the set of non-zero entries in each column. We are developed three types of parallel approximate inverse preconditioner as follows,
(i)Newton type, (ii)Minimal residual type, (iii)Sherman-Morrison type
The effectiveness of the above sparse preconditioners was also shown with some numerical experiments of other PDE problems.
Our present work will be continued to cover up more general numerical problems and their analysis.

  • Research Products

    (28 results)

All 2006 2005 2004 2003

All Journal Article (27 results) Book (1 results)

  • [Journal Article] A new scheme of computing the approximate inverse preconditioner for the reduced linear systems,2006

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      Journal of Computational and Applied Mathematics (Elsevior) (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Speed up of the preconditioner with Sherman-Morrison formula using parallelization,2006

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      RIMS Kokyuroku (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The computation of the approximate inverse by parallelizing the Sherman Morrison formula,2006

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      Journal of IPSJ (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Operator semi-selfsimilar processes and their space-scaling matrices,2006

    • Author(s)
      T.Saigo, Y.Tamura
    • Journal Title

      Statistics and Probability Letters (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Breakdown-Free ML(k)BiCGStab Algorithm for non-Hermitian Linear Systems2005

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      LNCS 3483

      Pages: 978-988

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Computing the Preconditioner for Schur Complement2005

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      ANZIAM J. 46(E)

      Pages: C394-C408

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A new adaptive restart for GMRES(m) method2005

    • Author(s)
      L.Zhang, T.Nodera
    • Journal Title

      ANZIAM J. 46(E)

      Pages: C409-C425

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 準直交ランチョス法による大規模固有値問題の解法2005

    • Author(s)
      梅垣 悠, 野寺 隆
    • Journal Title

      情処研報 2005・57

      Pages: 1-6

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Homogenization on disconnected selfsimilar fractal sets in2005

    • Author(s)
      H.Takahashi, Y.Tamura
    • Journal Title

      Tokyo J. of Math. 28・1

      Pages: 127-138

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Computing the Preconditioner for Schur Complement,2005

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      ANZIAM J. Vol.46(E)

      Pages: C394-C408

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A new adaptive restart for GMRES(m) method,2005

    • Author(s)
      L.Zhang, T.Nodera
    • Journal Title

      ANZIAM J. Vol.46(E)

      Pages: C409-C425

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Breakdown-Free ML(k)BiCGStab Algorithm for non-Hermitian Linear Systems,2005

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      LNCS (Springer) No.3483

      Pages: 978-988

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] finite difference schemes for a certain nonlinear parabolic systems,2005

    • Author(s)
      H.Morioka, A.Tani
    • Journal Title

      Journal of Math.Anal.and Appl. Vol.304

      Pages: 644-651

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Meromorphic solutions of a Riccati differential equation with a doubly periodic coefficient2005

    • Author(s)
      S.Shimomura
    • Journal Title

      Journal of Math.Anal.and Appl. Vol.304

      Pages: 644-651

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations,2005

    • Author(s)
      O.E.Barndorff-Nielsen, M.Maejima, K.Sat0
    • Journal Title

      Bernoulli Vol.12, No.1

      Pages: 1-33

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] 3D interactive modeling system of noodles,2005

    • Author(s)
      Y.Tanaka, K.Nakamaru, Y.Ohno
    • Journal Title

      The Journal of the Institute of Image Information and Television Engineering Vol.59, No.10

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Homogenization on disconnected selfsimilar fractal sets in R,2005

    • Author(s)
      H.Takahashi, Y.Tamura
    • Journal Title

      Tokyo J.Math. Vol.28, No.1

      Pages: 127-138

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] 残差ノルムの収束判定を利用したGMRES(≦m_<max>)法2004

    • Author(s)
      森屋 健太郎, 野寺 隆
    • Journal Title

      情報処理学会論文誌 48・8

      Pages: 2055-2067

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] New adaptive GMRES(m) algorithm with choosing a suitable restart cycle m,2004

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      LNCS (Springer) No.3019

      Pages: 1105-1113

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] GMRES(≦m_<max>) method using the convergence test of the restart,2004

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      Journal of IPSJ Vol.45, No.8

      Pages: 2055-2067

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] An adaptive restart of GMRES(m) method by using Ritz value,2004

    • Author(s)
      L.Zhang, T.Nodera
    • Journal Title

      Transaction of IPSJ Vol.45, No.SIG11(ACS7)

      Pages: 303-312

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Adaptive GMRES(≦m_<max>) for using the convergence of residual,2004

    • Author(s)
      K.Moriya, T.Nodera
    • Journal Title

      RIMS Kokyuroku No.1362

      Pages: 104-112

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Existence of a week solution in an infinite viscoelastic strip with a semi-infinite crack2004

    • Author(s)
      H.Ito, A.Tani
    • Journal Title

      Math.Models and Methods in Appl.Sci. Vol.14

      Pages: 975-986

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Lower estimates for the Growth of the fourth and the second Painleve transcendents,2004

    • Author(s)
      S.Shimomura
    • Journal Title

      Proceedings of the Edinburgh Mathematical Society Vol.47

      Pages: 231-249

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Trimed Sums,2004

    • Author(s)
      M.Maejima
    • Journal Title

      Statistical Math. Vol.52, No.1

      Pages: 45-62

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Generation of stroke direction for NPR and its application to suiboku-ga style rendering,2004

    • Author(s)
      K.Kawasaki, K.Nakamaru, Y.Ohno
    • Journal Title

      Journal of the society of Arts and Science Vol.3, No.4

      Pages: 235-243

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Some Levy process, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes,2003

    • Author(s)
      M.Maejima, K.Sato
    • Journal Title

      Math.Kyoto Univ. (JMKYAZ) Vol.43, No.3

      Pages: 609-539

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] 破壊現象の数理(数理解析を中心として)2005

    • Author(s)
      谷 温之, 野寺 隆 編
    • Total Pages
      171
    • Publisher
      マセマティカ
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2007-12-13  

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