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On structure-preserving numerical methods on complex domains

Research Project

Project/Area Number 20760052
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionThe University of Tokyo

Principal Investigator

MATSUO Takayasu  The University of Tokyo, 大学院・情報理工学系研究科, 准教授 (90293670)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords数理工学 / 数値解析 / シミュレーション / 保存・散逸スキーム / 微分方程式 / 離散変分法 / 微分方程式の数値解法
Research Abstract

In this research, we aimed at extending the discrete variational derivative method to finite element framework, and got the following results.
First, we showed that in the spatially one-dimensional case a finite-element version of the discrete variational derivative method can be formulated only with H^1 elements, and in fact applied the new framework to several typical partial differential equations. Then we extended the framework to spatially two-/three-dimensional cases, where we applied the method to the Ginzburg-Landau equation and confirmed the scheme in fact successfully works. Finally, we introduced a new technique to linearize the resulting schemes, and checked by numerical experiments that computational complexity can be decreased.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (17 results)

All 2011 2010 2009 2008 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (8 results) Book (2 results) Remarks (1 results)

  • [Journal Article] Conservative numerical schemes for the Ostrovsky equation2010

    • Author(s)
      T.Yaguchi, T.Matsuo, M.Sugihara
    • Journal Title

      J.Comput.Appl.Math.

      Volume: 234 Pages: 1036-1048

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Hamiltonian-conserving Galerkin Scheme for the Camassa--Holm Equation2010

    • Author(s)
      T.Matsuo
    • Journal Title

      J.Comput.Appl.Math.

      Volume: 234 Pages: 1258-1266

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Degasperis--Procesi方程式に対する保存則を保つ差分スキーム2010

    • Author(s)
      宮武勇登, 松尾宇泰
    • Journal Title

      日本応用数理学会論文誌

      Volume: 20 Pages: 219-240

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations2009

    • Author(s)
      T.Matsuo, H.Yamaguchi
    • Journal Title

      J.Comput.Phys.

      Pages: 4346-4358

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations2009

    • Author(s)
      T.Matsuo, H.Yamaguchi
    • Journal Title

      J.Comput.Phys. 228

      Pages: 4346-4358

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dissipative/conservative Galerkin method using discrete partial derivative for nonlinear evolution equations2008

    • Author(s)
      T.Matsuo
    • Journal Title

      J.Comput.Appl.Math. 218

      Pages: 506-521

    • Related Report
      2010 Final Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Numerical integration of the time-dependent Ginzburg-Landau equations2010

    • Author(s)
      T.Matsuo
    • Organizer
      TRAGIC2010
    • Place of Presentation
      Launceston (Australia)
    • Year and Date
      2010-12-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Conservative Finite Difference Schemes for the Degasperis--Procesi Equation2010

    • Author(s)
      Y.Miyatake, T.Matsuo
    • Organizer
      ICCAM2010
    • Place of Presentation
      Leuven (Belgium)
    • Year and Date
      2010-07-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dissipative finite-element schemes for the time-dependent Ginzburg-Landau equations2010

    • Author(s)
      T.Matsuo
    • Organizer
      Tokyo Workshop on structure-preserving methods
    • Related Report
      2010 Final Research Report
  • [Presentation] Numerical integration of the time-dependent Ginzburg-Landau equations2010

    • Author(s)
      T.Matsuo
    • Place of Presentation
      TRAGIC
    • Related Report
      2010 Final Research Report
  • [Presentation] A dissipative linearly-implicit scheme for the Ginzburg-Landau equation2009

    • Author(s)
      T.Matsuo, E.Torii
    • Organizer
      ICNAAM2009
    • Place of Presentation
      Crete, Greece
    • Year and Date
      2009-09-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Some new linearly-implicit conservative schemes for nonlinear dispersive equations2009

    • Author(s)
      T.Matsuo
    • Organizer
      SciCADE2009
    • Place of Presentation
      北京, 中国
    • Year and Date
      2009-05-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Challenge for multi-dimensional cases III : Galerkin approach2009

    • Author(s)
      T.Matsuo
    • Organizer
      Workshop on structure-preserving methods for PDEs
    • Place of Presentation
      東京
    • Year and Date
      2009-03-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] A Hamiltonian-conserving Galerkin scheme for the Camassa-Holm equation2008

    • Author(s)
      T.Matsuo
    • Organizer
      ICCAM2008
    • Place of Presentation
      Ghent, Belgium
    • Year and Date
      2008-07-07
    • Related Report
      2008 Annual Research Report
  • [Book] Discrete Variational Derivative Method : A Structure-Preserving Method for Partial Differential Equations2011

    • Author(s)
      D.Furihata, T.Matsuo
    • Total Pages
      376
    • Publisher
      CRC Press
    • Related Report
      2010 Annual Research Report
  • [Book] Discrete Variational Derivative Method2010

    • Author(s)
      D.Furihata, T.Matsuo
    • Total Pages
      800
    • Publisher
      CRC Press
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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