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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
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordssparse matrix computation / QCD / shifted system of equation / parallel computation / GMRES / preconditioning / approximate inverse / minimal residual method / 行列計算 / シュールコンプリメント / 並列計算 / グリッドコンピューティング
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.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (43 results)

All 2006 2005 2004 2003 Other

All Journal Article (36 results) Book (1 results) Publications (6 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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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)

    • NAID

      110006223882

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Computing the Preconditioner for Schur Complement2005

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

      ANZIAM J. 46(E)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] A new adaptive restart for GMRES(m) method2005

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

      ANZIAM J. 46(E)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [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

    • NAID

      110002950893

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

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

      ANZIAM J. Vol.46(E)

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

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

      ANZIAM J. Vol.46(E)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Breakdown-Free ML(k)BiCGStab Algorithm for non-Hermitian Linear Systems2005

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

      LMCS 3483

      Pages: 978-988

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Homogenization on disconnected selfsimilar fractal sets in R2005

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

      Tokyo J.of Math. 28・1

      Pages: 127-138

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Meromorphic solution of a Raccati differential equation with a doubly periodic coefficient2005

    • Author(s)
      Shun Shimomura
    • Journal Title

      J.Math.Anal.Appl. 304

      Pages: 644-651

    • Related Report
      2005 Annual Research Report
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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

    • NAID

      110002712302

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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

    • NAID

      130004951792

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 残差ノルムの収束判定を利用したGMRES(【less than or equal】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 45・8

      Pages: 2055-2067

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Ritz値を考慮したGMRES(m)法の適応的なリスタート2004

    • Author(s)
      張 臨傑, 野寺 隆
    • Journal Title

      情報処理学会論文誌 45・11(ACS7)

      Pages: 303-312

    • NAID

      110002712302

    • Related Report
      2004 Annual Research Report
  • [Journal Article] New adaptive GMRES(m) algorithm with choosing a suitable restart cycle m2004

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

      LNCS 3019

      Pages: 1105-1113

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 2階ILU分解による行列の前処理とその応用について2004

    • Author(s)
      山口 遼一, 野寺 隆
    • Journal Title

      情処研報 2004・81

      Pages: 169-174

    • NAID

      110002914130

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 自動リスタート過程を持つGMRES(m)法の性能評価2004

    • Author(s)
      張 臨傑, 野寺 隆
    • Journal Title

      情処研報 2004・81

      Pages: 175-180

    • NAID

      110002932520

    • Related Report
      2004 Annual Research Report
  • [Journal Article] ピボットブレイクダウンを回避するML(κ)BiCGStab法2004

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

      HPCS2004・Proceedings (予稿集)

      Pages: 71-72

    • Related Report
      2004 Annual Research Report
  • [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
    • Related Report
      2005 Final Research Report Summary
  • [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
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Publications] 田中 祐, 野寺 隆: "最小残差法による前処理を用いたGMRES(m)法について"京都大学数理解析研究所講究録. 1320. 190-200 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Inoue, T.Nodera: "The GMRES(m) methods with block factorization preconditioning"5th International Congress on Industrial and Applied Mathematics, Sydney Australia. 103 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 森屋 健太郎, 野寺 隆: "反復中に直交空間を再構成するML(k)BiCGStab法"情報処理学会・情処研報. 2003・83. 7-12 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Moriya, T.Nodera: "New adaptive GMRES(m) algorithm with choosing a suitable restart cycle m"Fifth International Conference on Parallel Processing and Applied Mathematics. Poland. 41-42 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 渡辺 智敦, 野寺 隆: "対角閾値を用いた前処理行列の構成"日本応用数理学会2003年度年会講演予稿集. 310-311 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 張 臨傑, 野寺 隆: "Ritz値を使ったGMRES法の収束性の評価について"情報処理学会・情処研報. 2003・102. 13-18 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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