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Parallel Structure-Preserving Algorithms: Theory and Numerical Verification

Research Project

Project/Area Number 16K17550
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Computational science
Research InstitutionOsaka University (2018-2020)
Nagoya University (2016-2017)

Principal Investigator

Miyatake Yuto  大阪大学, サイバーメディアセンター, 准教授 (60757384)

Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords数値解析 / 偏微分方程式 / 行列計算 / 常微分方程式 / 数値解法 / 数値線形代数 / 微分方程式
Outline of Final Research Achievements

Long time simulation becomes important in many research fields. Structure-preserving algorithms have been proved to be effective, but it is a challenging task to develop algorithms that are both accurate and efficient. In this study, parallel structure-preserving algorithms are developed that balance the high accuracy and efficiency. Moreover, new algorithms for matrix computation are also developed, which further improves the efficiency of the proposed parallel algorithms.

Academic Significance and Societal Importance of the Research Achievements

現代の科学技術計算では,計算機の発展より遥かに速いスピードで現場のニーズが多様化・大規模化しており,これまで以上に計算の品質とコストの両立が困難になっている.このような問題に対し,特定の分野や方程式,計算機環境に特化した研究が主流だが,本研究では,より数理的な立場から,高い汎用性を維持して品質とコストが両立するような数値解法の開発に成功したものである.このような考え方は,数値解析や高性能計算分野で新しい研究スタイルの基盤となり,さらには既存解法を遥かに凌ぐ数値解法が次々と生成されることが期待される.

Report

(6 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (48 results)

All 2021 2020 2019 2018 2017 2016 Other

All Journal Article (18 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 18 results,  Open Access: 6 results,  Acknowledgement Compliant: 1 results) Presentation (29 results) (of which Int'l Joint Research: 17 results,  Invited: 3 results) Remarks (1 results)

  • [Journal Article] A fully discrete curve-shortening polygonal evolution law for moving boundary problems2021

    • Author(s)
      Sakakibara Koya、Miyatake Yuto
    • Journal Title

      Journal of Computational Physics

      Volume: 424 Pages: 109857-109857

    • DOI

      10.1016/j.jcp.2020.109857

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Estimation of ordinary differential equation models with discretization error quantification2021

    • Author(s)
      T. Matsuda and Y. Miyatake
    • Journal Title

      SIAM/ASA Journal on Uncertainty Quantification

      Volume: 9 Issue: 1 Pages: 302-331

    • DOI

      10.1137/19m1278405

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Algorithms for the computation of the matrix logarithm based on the double exponential formula2020

    • Author(s)
      Tatsuoka Fuminori、Sogabe Tomohiro、Miyatake Yuto、Zhang Shao-Liang
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 373 Pages: 112396-112396

    • DOI

      10.1016/j.cam.2019.112396

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A parallelizable energy-preserving integrator MB4 and its application to quantum-mechanical wavepacket dynamics2020

    • Author(s)
      Sakai Tsubasa、Kudo Shuhei、Imachi Hiroto、Miyatake Yuto、Hoshi Takeo、Yamamoto Yusaku
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 38 Issue: 1 Pages: 105-123

    • DOI

      10.1007/s13160-020-00430-2

    • NAID

      210000183552

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Adaptive SOR methods based on the Wolfe conditions2019

    • Author(s)
      Y. Miyatake, T. Sogabe, S.-L. Zhang
    • Journal Title

      Numerical Algorithms

      Volume: 84 Issue: 1 Pages: 117-132

    • DOI

      10.1007/s11075-019-00748-0

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relation between the T-congruence Sylvester equation and the generalized Sylvester equation2019

    • Author(s)
      Y. Satake, M. Oozawa, T. Sogabe, Y. Miyatake, T. Kemmochi, S.-L. Zhang
    • Journal Title

      Applied Mathematics Letters

      Volume: 96 Pages: 7-13

    • DOI

      10.1016/j.aml.2019.04.007

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Structure-preserving model reduction for dynamical systems with a first integral2019

    • Author(s)
      Miyatake Yuto
    • Journal Title

      Japan J. Indust. Appl. Math.

      Volume: 36 Issue: 3 Pages: 1021-1037

    • DOI

      10.1007/s13160-019-00378-y

    • NAID

      210000186688

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Modified Strang splitting for semilinear parabolic problems2019

    • Author(s)
      K. Nakano, T. Kemmochi, Y. Miyatake, T. Sogabe, S.-L. Zhang
    • Journal Title

      JSIAM Letters

      Volume: 11 Issue: 0 Pages: 77-80

    • DOI

      10.14495/jsiaml.11.77

    • NAID

      130007771371

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schr?dinger equation2019

    • Author(s)
      Y. Miyatake, T. Nakagawa, T. Sogabe, S.-L. Zhang
    • Journal Title

      Journal of Computational Dynamics

      Volume: 6 Issue: 2 Pages: 361-383

    • DOI

      10.3934/jcd.2019018

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Continuous Stage Runge-Kutta Methods and Their Structure-Preservation Properties2018

    • Author(s)
      宮武 勇登
    • Journal Title

      Bulletin of the Japan Society for Industrial and Applied Mathematics

      Volume: 28 Issue: 3 Pages: 15-22

    • DOI

      10.11540/bjsiam.28.3_15

    • NAID

      130007552790

    • ISSN
      2432-1982
    • Year and Date
      2018-09-26
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems2018

    • Author(s)
      Miyatake Yuto、Sogabe Tomohiro、Zhang Shao-Liang
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 342 Pages: 58-69

    • DOI

      10.1016/j.cam.2018.04.013

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Solution of the k -th eigenvalue problem in large-scale electronic structure calculations2018

    • Author(s)
      Lee Dongjin、Hoshi Takeo、Sogabe Tomohiro、Miyatake Yuto、Zhang Shao-Liang
    • Journal Title

      Journal of Computational Physics

      Volume: 371 Pages: 618-632

    • DOI

      10.1016/j.jcp.2018.06.002

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Note on Computing the Matrix Fractional Power Using the Double Exponential Formula2018

    • Author(s)
      立岡 文理、曽我部 知広、宮武 勇登、張 紹良
    • Journal Title

      Transactions of the Japan Society for Industrial and Applied Mathematics

      Volume: 28 Issue: 3 Pages: 142-161

    • DOI

      10.11540/jsiamt.28.3_142

    • NAID

      130007487583

    • ISSN
      2424-0982
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On a relationship between the T-congruence Sylvester equation and the Lyapunov equation2018

    • Author(s)
      Oozawa Masaya、Sogabe Tomohiro、Miyatake Yuto、Zhang Shao-Liang
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 329 Pages: 51-56

    • DOI

      10.1016/j.cam.2017.05.044

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Discrete Gradient Method for Differential Equations Can Be a Generator of Linear Solvers2017

    • Author(s)
      宮武 勇登、曽我部 知広、張 紹良
    • Journal Title

      Transactions of the Japan Society for Industrial and Applied Mathematics

      Volume: 27 Issue: 3 Pages: 239-249

    • DOI

      10.11540/jsiamt.27.3_239

    • NAID

      130006100066

    • ISSN
      2424-0982
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Geometric numerical integrators for Hunter-Saxton-like equations2017

    • Author(s)
      Miyatake Yuto、Cohen David、Furihata Daisuke、Matsuo Takayasu
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 34 Issue: 2 Pages: 441-472

    • DOI

      10.1007/s13160-017-0252-1

    • NAID

      210000160223

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Energy-preserving H1-Galerkin schemes for the Hunter-Saxton equation2017

    • Author(s)
      Y. Miyatake, G. Eom, T. Sogabe, S.-L. Zhang
    • Journal Title

      J. Math. Res. Appl.

      Volume: 37 Pages: 107-118

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems2016

    • Author(s)
      Y. Miyatake, J. C. Butcher
    • Journal Title

      SIAM J. Numer. Anal.

      Volume: 54 Issue: 3 Pages: 1993-2013

    • DOI

      10.1137/15m1020861

    • NAID

      120005905587

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Adjoint-based computation of the exact Hessian-vector multiplication2020

    • Author(s)
      S. Ito, T. Matsuda, Y. Miyatake
    • Organizer
      Adjoint-based computation of the exact Hessian-vector multiplication
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Second-order adjoint方程式に基づくヘッセ行列の計算について2020

    • Author(s)
      伊藤伸一, 松田孟留, 宮武勇登
    • Organizer
      日本応用数理学会2020年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Adjoint-based algorithm for computing the exact Hessian-vector multiplication2020

    • Author(s)
      Y. Miyatake
    • Organizer
      ANZIAM2020
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantifying discretisation errors by isotonic regression and its application to estimating ODE models2019

    • Author(s)
      T. Matsuda, Y. Miyatake
    • Organizer
      Geometric Numerical Integration of Differential Equations
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Estimation of ODE models with quantifying discretization error2019

    • Author(s)
      T. Matsuda, Y. Miyatake
    • Organizer
      SciCADE2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the equivalence between SOR-type methods for linear systems and Itoh-Abe-type discrete gradient methods for gradient systems2019

    • Author(s)
      Y. Miyatake, T. Sogabe, S.-L. Zhang
    • Organizer
      SciCADE2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantifying and reducing forward uncertainty in estimating parameters of initial value problems2019

    • Author(s)
      T. Matsuda, Y. Miyatake
    • Organizer
      SIAM: East Asian Section Conference 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] On an interval truncation method of the double exponential formula for the matrix logarithm2019

    • Author(s)
      F. Tatsuoka, T. Sogabe, Y. Miyatake, S.-L. Zhang
    • Organizer
      SIAM: East Asian Section Conference 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Reducing the effect of discretization errors in estimating ODE models by iteratively reweighted least squares2019

    • Author(s)
      T. Matsuda, Y. Miyatake
    • Organizer
      ANZIAM 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Estimating ODE models by iteratively reweighted least squares2019

    • Author(s)
      T. Matsuda, Y. Miyatake
    • Organizer
      A3 Workshop on fluid dynamics and related topics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] ウルフ条件を利用した適応型SOR法2018

    • Author(s)
      宮武勇登, 曽我部知広, 張紹良
    • Organizer
      第47回数値解析シンポジウム
    • Related Report
      2018 Research-status Report
  • [Presentation] 保存量を持つ常微分方程式に対するモデル縮減について2018

    • Author(s)
      宮武勇登
    • Organizer
      常微分方程式の数値解法とその周辺2018
    • Related Report
      2018 Research-status Report
  • [Presentation] 常微分方程式の初期値推定における離散化誤差に由来するバイアスの軽減に向けて2018

    • Author(s)
      松田孟留, 宮武勇登
    • Organizer
      RIMS研究集会:次世代の科学技術を支える数値解析学の基盤整備と応用展開
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Energy-preserving model reduction for Poisson systems2018

    • Author(s)
      Y. Miyatake
    • Organizer
      SIAM: East Asian Section Conference 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Structure-preserving model reduction for initial value problems with a first integral2018

    • Author(s)
      Y. Miyatake
    • Organizer
      CJK2018 Joint Conference on Numerical Mathematics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] SOR法の緩和パラメータの幾何学的解釈2018

    • Author(s)
      宮武勇登, 曽我部知広, 張紹良
    • Organizer
      日本応用数理学会 第14回 研究部会連合発表会
    • Related Report
      2017 Research-status Report
  • [Presentation] 発展方程式に対して複数の保存量を再現する差分スキームの導出2017

    • Author(s)
      宮武勇登
    • Organizer
      流体方程式の構造と特異性に迫る数値解析・数値計算 II
    • Place of Presentation
      名古屋(名古屋大学)
    • Year and Date
      2017-01-30
    • Related Report
      2016 Research-status Report
  • [Presentation] Structure-preserving continuous stage Runge-Kutta methods2017

    • Author(s)
      Y. Miyatake
    • Organizer
      A3 Workshop on Fluid Dynamics and Material Science
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Finite difference schemes preserving multiple invariants for evolutionary partial differential equations2017

    • Author(s)
      D.I. McLaren, Y. Miyatake, G.R.W. Quispel
    • Organizer
      SciCADE2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the equivalence between the SOR-type methods and the Itoh-Abe discrete gradient methods2017

    • Author(s)
      Y. Miyatake, T. Sogabe, S.-L. Zhang
    • Organizer
      SIAM: East Asian Section Conference 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Iterative solvers based on the discrete gradient method for symmetric positive definite linear systems2017

    • Author(s)
      Y. Miyatake, T. Sogabe, S.-L. Zhang
    • Organizer
      19h International Conference on Finite Elements in Flow Problems - FEF 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] SOR法と離散勾配法の関係と緩和パラメータに関する考察2017

    • Author(s)
      SOR法と離散勾配法の関係と緩和パラメータに関する考察
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] 波動方程式に対するモデル縮減手法を組み込んだ確率的数値解法について2017

    • Author(s)
      宮武勇登
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Research-status Report
  • [Presentation] Dirichlet 境界条件下の偏微分方程式に対する splitting 解法の収束性劣化の改善案2017

    • Author(s)
      中野航輔, 宮武勇登, 曽我部知広, 張紹良
    • Organizer
      第46回数値解析シンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] 発展方程式に対する複数の保存量を再現する差分スキーム2016

    • Author(s)
      D. I. McLaren, 宮武勇登, G. R. W. Quispel
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      瀬田(龍谷大学)
    • Year and Date
      2016-12-15
    • Related Report
      2016 Research-status Report
  • [Presentation] Structure-preserving Galerkin methods based on variational structure2016

    • Author(s)
      Y. Miyatake
    • Organizer
      IMI-La Trobe Joint Conference ''Geometric Numerical Integration and its Applications''
    • Place of Presentation
      Melbourne
    • Year and Date
      2016-12-05
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 勾配系の数値計算に基づく線形方程式の数値解法の生成について2016

    • Author(s)
      宮武勇登, 曽我部知広, 張紹良
    • Organizer
      RIMS研究集会:現象解明に向けた数値解析学の新展開 II
    • Place of Presentation
      京都(京都大学)
    • Year and Date
      2016-10-19
    • Related Report
      2016 Research-status Report
  • [Presentation] KdV方程式に対する複数の保存量を再現する差分スキーム2016

    • Author(s)
      D. I. McLaren, 宮武勇登, G. R. W. Quispel
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州
    • Year and Date
      2016-09-12
    • Related Report
      2016 Research-status Report
  • [Presentation] An energy-preserving H1-Galerkin scheme for the Hunter-Saxton equation2016

    • Author(s)
      Y. Miyatake
    • Organizer
      SIAM: East Asian Section Conference 2016
    • Place of Presentation
      Macau
    • Year and Date
      2016-06-20
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Remarks]

    • URL

      https://yutomiyatake.github.io/

    • Related Report
      2019 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2022-01-27  

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