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Mathematical Reliability of Parallel Computations with Indefinite-order Operations

Research Project

Project/Area Number 18K18719
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 12:Analysis, applied mathematics, and related fields
Research InstitutionKyoto University

Principal Investigator

Fujiwara Hiroshi  京都大学, 情報学研究科, 准教授 (00362583)

Co-Investigator(Kenkyū-buntansha) 吉川 仁  京都大学, 情報学研究科, 准教授 (90359836)
Project Period (FY) 2018-06-29 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2018: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Keywords数値解析学 / 並列計算 / 信頼性 / 科学・技術数値計算 / 数値解析 / ハイパフォーマンスコンピューティング
Outline of Final Research Achievements

We discussed the reliability of parallel execution of numerical schemes. The main target in numerical computations is solving systems of linear equations, and we treated the Gauss-Seidel iteration in the current research. The results are (1) construction of a mathematical model of parallel execution status, (2) proving a sufficient condition for convergence, and (3) constructing a counter example where
the serial computation converges and the parallel execution diverges. Practicality of the proposed criteria is also shown by applying it to computation appeared in science and technology.

Academic Significance and Societal Importance of the Research Achievements

数値計算は,現代社会を支える基盤技術であり,その理論的な信頼性の担保は必須である.従来,このような分野は理論数値解析学で扱われてきたが,昨今の急速な計算機ハードウエアの高性能化,特に並列計算環境の進歩との乖離も否めない.特に処理速度のみに着目して無秩序な並列化がおこなわれると,従来理論・手法では信頼性があったものが正しく動かず,数値計算が支える生活や技術開発の停滞が危惧される.この点に対し,本研究では数値計算の「正しさ」の枠組みを再考するとともに,大学学部教育での問題意識の提示,実用性,昨今のデータ科学における「再現性」との共通点など,多様な話題を包含する研究テーマである.

Report

(3 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • Research Products

    (22 results)

All 2020 2019 2018 Other

All Journal Article (7 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 6 results,  Open Access: 3 results) Presentation (14 results) (of which Int'l Joint Research: 7 results,  Invited: 4 results) Remarks (1 results)

  • [Journal Article] Numerical Reconstruction of Radiative Sources in an Absorbing and Nondiffusing Scattering Medium in Two Dimensions2020

    • Author(s)
      Fujiwara Hiroshi、Sadiq Kamran、Tamasan Alexandru
    • Journal Title

      SIAM Journal on Imaging Sciences

      Volume: 13 Issue: 1 Pages: 535-555

    • DOI

      10.1137/19m1282921

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium2019

    • Author(s)
      Fujiwara Hiroshi、Sadiq Kamran、Tamasan Alexandru
    • Journal Title

      Inverse Problems

      Volume: 36 Issue: 1 Pages: 015005-015005

    • DOI

      10.1088/1361-6420/ab4d98

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Numerical Realization of a New Generation Tomography Algorithm Based on the Cauchy-type Integral Formula2019

    • Author(s)
      Hiroshi Fujiwara, Alexandru Tamasan
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 28 Pages: 413-424

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Cauchy 型積分によるメッシュレス X 線計算機断層撮影法2019

    • Author(s)
      藤原宏志,Alexandru Tamasan
    • Journal Title

      計算数理工学論文集

      Volume: 19 Pages: 1-6

    • NAID

      40022338115

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Design and implementation of multiple-precision arithmetic environment in MATLAB for reliable numerical computations2019

    • Author(s)
      Fujiwara Hiroshi
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 36 Issue: 3 Pages: 1089-1100

    • DOI

      10.1007/s13160-019-00385-z

    • NAID

      210000182436

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical experiments on analyticity of solutions to fractional differential equations2018

    • Author(s)
      H. Fujiwara, N. Higashimori, and H. Imai
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 27 Pages: 169-180

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] 連立一次方程式に対する定常反復法の並列計算に関する一考察2018

    • Author(s)
      藤原宏志
    • Journal Title

      数理解析研究所講究録

      Volume: 2094 Pages: 122-130

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Presentation] Numerical realizations of X-ray computerized tomography by Cauchy-type boundary integration2020

    • Author(s)
      Hiroshi Fujiwara, Tamasan Alexandru
    • Organizer
      RIMS 共同研究 (公開型)「偏微分方程式による逆問題解析とその周辺」
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Cauchy 型積分によるメッシュレス X 線計算機断層撮影法2019

    • Author(s)
      藤原宏志, TAMASAN, Alexandru
    • Organizer
      日本計算数理工学会シンポジウム2019
    • Related Report
      2019 Annual Research Report
  • [Presentation] 超音波スピーカーにより生成される局所可聴音場再現のための数値解析2019

    • Author(s)
      若原孝浩, 吉川仁
    • Organizer
      第22回応用力学シンポジウム, 第65回理論応用力学講演会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Large Scale Traffic Noise Simulation by Time-Domain FMBEM2019

    • Author(s)
      Makoto Shoji, Hitoshi Yoshikawa, Kazuo Kashiyama
    • Organizer
      The 7th Asian Pacific Congress on Computational Mechanics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical Computation of the 2D Stationary Radiative Transport Equation on Graded Meshes2018

    • Author(s)
      H.Fujiwara
    • Organizer
      Japan-Taiwan Joint Workshop on Scientific Computing and Related Topics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 多倍長計算環境exflibの最新計算環境への対応と普及2018

    • Author(s)
      藤原宏志
    • Organizer
      日本応用数理学会年会2018年度 年会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Multiple-Precision Arithmetic on MATLAB and Related Software for Reliable Computations2018

    • Author(s)
      Hiroshi Fujiwara
    • Organizer
      China-Japan-Korea Conference 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Finite Volume Method for Photon Propagation in Biomedical Tissue2018

    • Author(s)
      H. Fujiwara
    • Organizer
      CoMFoS18
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 多角形メッシュによる生体内の近赤外伝播の効率的な数値計算法2018

    • Author(s)
      藤原宏志
    • Organizer
      第25回医用近赤外線分光法研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] Advantageous of the Finite Volume Method in Numerical Computation for Light Propagation in Biological Tissue2018

    • Author(s)
      H.Fujiwara
    • Organizer
      International Conference on Complex Medial Engineering 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 多角形要素をもちいる不連続Galerkin法の収束性の検証2018

    • Author(s)
      藤原宏志
    • Organizer
      ODE-JP 2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Numerical Computation of the Radiative Transport Equation on Nonconformal Meshes2018

    • Author(s)
      H. Fujiwara
    • Organizer
      East Asia Section of SIAM, 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 超音波スピーカーにより作り出される局所的な可聴音場の再現に関する数値解析2018

    • Author(s)
      若原孝浩, 吉川仁
    • Organizer
      日本機会学会第31回計算力学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] ハイブリッド並列を用いた時間域多重極境界要素法による大規模音場解析2018

    • Author(s)
      高木 貴弘, 吉川 仁, 高橋 徹, 樫山 和男
    • Organizer
      第21回応用力学シンポジウム
    • Related Report
      2018 Research-status Report
  • [Remarks] extend precision floating-point arithmetic library

    • URL

      http://www-an.acs.i.kyoto-u.ac.jp/~fujiwara/exflib

    • Related Report
      2019 Annual Research Report

URL: 

Published: 2018-07-25   Modified: 2021-02-19  

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