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Construction of efficient structure-preserving methods for partial differential equations and its applications

Research Project

Project/Area Number 26390126
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Computational science
Research InstitutionThe University of Tokyo

Principal Investigator

Matsuo Takayasu  東京大学, 大学院情報理工学系研究科, 教授 (90293670)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords数値解析 / 偏微分方程式 / 構造保存解法
Outline of Final Research Achievements

This research aims at improving existing structure-preserving methods so that the become more efficient and practical methods for applications. Through this research, we established "efficient structure-preserving methods based on discontinuous Galerkin methods", "an analysis method for structure-preserving methods based on dynamical systems theory", "introduction of moving meshes", and "new structure-preserving methods for partial differential equations with a mixed derivative". Through these findings we gained a new, stronger framework of structure-preserving methods.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (20 results)

All 2017 2016 2015 2014

All Journal Article (8 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 1 results,  Acknowledgement Compliant: 4 results) Presentation (12 results) (of which Int'l Joint Research: 3 results,  Invited: 1 results)

  • [Journal Article] A novel discrete variational derivative method using ``average-difference methods''2016

    • Author(s)
      D. Furihata, S. Sato, T. Matsuo
    • Journal Title

      JSIAM Letters

      Volume: 8 Issue: 0 Pages: 81-84

    • DOI

      10.14495/jsiaml.8.81

    • NAID

      130005434752

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A note on the adaptive conservative/dissipative discretization for evolutionary partial differential equations2015

    • Author(s)
      Yuto Miyatake, Takayasu Matsuo
    • Journal Title

      J. Comput. Appl. Math.

      Volume: 274 Pages: 79-87

    • DOI

      10.1016/j.cam.2014.06.027

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A local discontinuous Galerkin method based on variational structure2015

    • Author(s)
      Y. Aimoto, T. Matsuo, and Y. Miyatake
    • Journal Title

      Discrete Cont. Dyn. Sys. Ser. S

      Volume: 8 Issue: 5 Pages: 817-832

    • DOI

      10.3934/dcdss.2015.8.817

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] An analysis on the asymptotic behavior of multistep linearly implicit schemes for the Duffing equation2015

    • Author(s)
      S. Sato, T. Matsuo, H. Suzuki and D. Furihata
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 45-48

    • DOI

      10.14495/jsiaml.7.45

    • NAID

      130005073354

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Lyapunov-Type Theorem for Dissipative Numerical Integrators with Adaptive Time-Stepping2015

    • Author(s)
      S. Sato, T. Matsuo, H. Suzuki and D. Furihata
    • Journal Title

      SIAM J. Numer. Anal.

      Volume: 53 Issue: 6 Pages: 2505-2518

    • DOI

      10.1137/140996719

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A stabilization of multistep linearly implicit schemes for dissipative systems2014

    • Author(s)
      T. Matsuo, D. Furihata
    • Journal Title

      J. Comput. Appl. Math.

      Volume: 264 Pages: 38-48

    • DOI

      10.1016/j.cam.2013.12.028

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] A multi-symplectic numerical integrator for the two-component Camassa–Holm equation2014

    • Author(s)
      D. Cohen, T. Matsuo and X. Raynaud
    • Journal Title

      J.. Nonl. Math. Phys.

      Volume: 21 Issue: 3 Pages: 442-453

    • DOI

      10.1080/14029251.2014.936763

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] A general framework for finding energy dissipative/conservative H1-Galerkin schemes and their underlying H1-weak forms for nonlinear evolution equations2014

    • Author(s)
      Yuto Miyatake, Takayasu Matsuo
    • Journal Title

      BIT Numer. Math.

      Volume: 54 Issue: 4 Pages: 1119-1154

    • DOI

      10.1007/s10543-014-0483-3

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 後退誤差解析に基づく多段陰的線形スキームの安定化と最適化2017

    • Author(s)
      松尾宇泰, 徐立元
    • Organizer
      日本応用数理学会第13回研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Annual Research Report
  • [Presentation] Some recent and open issues on finite-difference based structure-preserving methods2016

    • Author(s)
      T. Matsuo
    • Organizer
      Geometric Numerical Integration and Its Applications
    • Place of Presentation
      オーストラリア・ビクトリア州
    • Year and Date
      2016-12-05
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 平均化作用素を用いた新たな離散変分法の離散保存則2016

    • Author(s)
      降籏大介, 佐藤峻, 松尾宇泰
    • Organizer
      第45回数値解析シンポジウム
    • Place of Presentation
      霧島ホテル(鹿児島県霧島市)
    • Year and Date
      2016-06-08
    • Related Report
      2016 Annual Research Report
  • [Presentation] Structure-preserving integration of the Benjamin type equations2015

    • Author(s)
      T. Matsuo, K. Kinugasa, and Y. Miyatake
    • Organizer
      SciCADE2015
    • Place of Presentation
      ポツダム(ドイツ)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] A Structure-preserving Numerical Integrator Based on the Hodograph Transform for the Short-pulse Equation2015

    • Author(s)
      T. Matsuo
    • Organizer
      ICIAM2015
    • Place of Presentation
      北京(中国)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Invariants-preserving numerical integrators for the nonlinear Schroedinger equation2015

    • Author(s)
      T. Matsuo
    • Organizer
      Kyoto
    • Place of Presentation
      京都(京都市生涯学習総合センター)
    • Year and Date
      2015-03-26 – 2015-03-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 離散不等式の解析と非線形シュレディンガー方程式に対する ある保存差分スキームの理論解析2015

    • Author(s)
      小島広樹, 松尾宇泰, 降籏大介
    • Organizer
      応用数理学会2013年度研究部会連合発表会
    • Place of Presentation
      京都(京都大学)
    • Year and Date
      2015-03-19 – 2015-03-20
    • Related Report
      2014 Research-status Report
  • [Presentation] 散逸系に対する可変刻み構造保存解法の漸近挙動解析2015

    • Author(s)
      佐藤峻, 松尾宇泰, 鈴木秀幸, 降籏大介
    • Organizer
      日本応用数理学会2015年研究部会連合発表会
    • Place of Presentation
      中野(明治大学)
    • Year and Date
      2015-03-06 – 2015-03-07
    • Related Report
      2014 Research-status Report
  • [Presentation] 陽的ルンゲ・クッタ法をもとにした高速なエネルギー保存解法2015

    • Author(s)
      小島広樹, 松尾宇泰
    • Organizer
      日本応用数理学会2015年研究部会連合発表会
    • Place of Presentation
      中野(明治大学)
    • Year and Date
      2015-03-06 – 2015-03-07
    • Related Report
      2014 Research-status Report
  • [Presentation] Discrete inequalities for central-difference type operators2014

    • Author(s)
      T. Matsuo
    • Organizer
      FoCM2014
    • Place of Presentation
      Montevideo(Uruguay)
    • Year and Date
      2014-12-15 – 2014-12-17
    • Related Report
      2014 Research-status Report
  • [Presentation] 散逸系に対する線形多段離散勾配スキームの漸近挙動解析2014

    • Author(s)
      佐藤峻, 松尾宇泰, 降籏大介
    • Organizer
      日本応用数理学会2014年度年会
    • Place of Presentation
      六本木(政策研究大学院大学)
    • Year and Date
      2014-09-03 – 2014-09-05
    • Related Report
      2014 Research-status Report
  • [Presentation] Hunter–Saxton方程式の離散化における境界条件の扱いについて2014

    • Author(s)
      宮武勇登, David Cohen, 降籏大介, 松尾宇泰
    • Organizer
      数値解析シンポジウム2014
    • Place of Presentation
      石垣島(ホテル日航八重山)
    • Year and Date
      2014-06-11 – 2014-06-13
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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