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Research on mathematical analysis of finite difference methods and its numerical simulations based on fictitious domain and distributions

Research Project

Project/Area Number 14540103
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 InstitutionChiba University

Principal Investigator

KOSHIGOE Hideyuki  Chiba University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70110294)

Co-Investigator(Kenkyū-buntansha) SUITO Hiroshi  Okayama University, Waste Management Research Center, Associate Professor, 廃棄物マネジメント研究センター, 助教授 (10302530)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
KeywordsFictitious Domain / Distribution / Finite Difference Method / Transmission Condition / Direct Method / Environmental Mathematics / Numerical Simulation / Optimization / 接地逆転 / transmission / 沿岸生態系 / 自由表面 / 数値計算法 / 脳脊髄液流動
Research Abstract

1. Numerical calculation of finite difference methods based on fictitious domain and distributions
Our formulation for numerical calculation in finite difference method is to find the locally integrable function satisfying the partial differential equations in the sense of distribution. This idea leads naturally to the expression of Dirichlet-Neumann map on the fictitious boundary. We proved that numerical solutions defined by locally integrable functions are convergent to the genuine solution in the sense of the Schwartz distribution. Moreover we proposed new numerical algorithm which use the fast Fourier transform. This is based on the combination with the Fourier transform and the eigenvalues and eigenvectors of the coefficient matrix of Poisson's equation. From this idea we constructs a numerical method which we call the successive elimination of lines, and contribute to the numerical calculation for the transmission problem.
2. Applied mathematical problem and its numerical simulation
The numerical method we developed here is possible to apply to various problems in environmental mathematics. One is the modeling and simulation for surface inversions which depend on the temperature and atmosphere in urban. And we showed the numerical simulation of the singular temperature in the town. Two is the research on the coastal pollution by spilled oil when it occurs in the case of the tanker accident. We showed it through the numerical simulation based on the fictitious domain method. Third is the numerical simulation in medical treatments. We showed a numerical simulation of the cerebrospinal fluid.
As above mentiond, we researched mathematical analysis of finite difference methods from view points of fictitious domain and distribution, and established the numerical algorithm which is able to apply to various environmental mathematics. Our papers were published and research results were presented at international conferences.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (26 results)

All 2005 2004 Other

All Journal Article (15 results) Publications (11 results)

  • [Journal Article] Numerical calculation of an atmospheric temperature appearing in the weather of the surface inversion2005

    • Author(s)
      T.Shiraishi
    • Journal Title

      GAKUTO International Series, Mathematical Science and Applications 23

      Pages: 229-237

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] FFTを併用した2次元キャビティ流れの数値計算2005

    • Author(s)
      小島 智子
    • Journal Title

      応用数学合同研究集会報告集

      Pages: 161-164

    • 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] Numerical Simulation of Underground Water Flow around Landfill Sites2005

    • Author(s)
      H.Suito
    • Journal Title

      Proceeding of Tenth International Waste Management and Landfill Symposium

      Pages: 425-426

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 流通過程における多目的最適化問題2005

    • Author(s)
      七澤洋平
    • Journal Title

      Journal of Logistics and Informatics Vol.2, No.1[3]

      Pages: 13-20

    • 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] Numerical calculation of an atmospheric temperature appearing in the weather of the surface inversion2005

    • Author(s)
      SHIRAISHI, Takashi
    • Journal Title

      GAKUTO International Series, Mathematical Sciences and Applications Vol.23

      Pages: 229-237

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Applied mathematics combination research meeting report collection2005

    • Author(s)
      Kojima, Tomoko
    • Journal Title

      Numeric calculation of cavity flow that uses FFT together by two dimensions

      Pages: 161-164

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical Simulation of Underground Water Flow around Land fill Sites2005

    • Author(s)
      SUITO, Hiroshi
    • Journal Title

      Proceedings of Tenth International Waste Management and Landfill Symposium

      Pages: 425-426

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multipurpose optimization problem in circulation process2005

    • Author(s)
      Nanasawa, Yohei
    • Journal Title

      Journal of Logistics and Infomatics Vol.2, No.1[3]

      Pages: 13-20

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical Simulation of Underground Water Flow around Landfill Sites2005

    • Author(s)
      H.Suito
    • Journal Title

      Proceedings of Tenth International Waste Management and Landfill Symposium

      Pages: 425-426

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Direct solver on FFT and SEL for diffraction problems with distribution2004

    • Author(s)
      H.Koshigoe
    • Journal Title

      Lecture Notes in Computer Science 3037 Part II

      Pages: 105-112

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Direct solver for an inverse problem of the type of the transmission2004

    • Author(s)
      H.Koshigoe
    • Journal Title

      Lecture Series on Computer and Computational Science Vol.1

      Pages: 274-278

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 関数を用いた直接法による大気温逆転現象の数値計算2004

    • Author(s)
      江原誠, 白石卓巳, 大井章弘, 腰越秀之
    • Journal Title

      応用数学合同研究集会報告集

      Pages: 159-160

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Numerical simulation of spilled oil by fictitious domain method2004

    • Author(s)
      H.Suito, H.Kawarada
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics Vol.21,No.2

      Pages: 219-236

    • NAID

      10018379989

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Hybridized fuzzy and GAs distributed optimization method2004

    • Author(s)
      H.Suito, H.Kawarada
    • Journal Title

      Journal of Logistics and Informatics Vol.1,No.1

      Pages: 17-26

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 流出原油による沿岸汚染の数値シミュレーション2004

    • Author(s)
      水藤寛, 荒川貴信, 河原田秀夫
    • Journal Title

      計算工学講演会論文集 Vol.9,No.1

      Pages: 517-518

    • Related Report
      2004 Annual Research Report
  • [Publications] H.Koshigoe: "Direct Method for Solving a Transmission Problem with a Discontinuous Coefficient and the Dirac Distribution"Computational Science - ICCS 2003. Part III. 388-398 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Koshigoe: "Direct Solver on FFT and SEL for Diffraction Problems with Distribution"Computational Science - ICCS 2004. Part II(to appear). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 大井 章弘: "FFTを用いた2層拡散方程式系の数値計算-気温の逆転現象-"応用数学合同研究集会報告集. 147-150 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Suito: "Numerical Simulation of Spilled Oil by Fictitious Domain Method"Japan Journal of Industrial and Applied Mathematics. Vol.21,No.2(to appear). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 水藤 寛: "湧昇循環装置によって誘起される湖沼内流れの数値シミュレーション"岡山大学環境理工学部紀要. 65-68 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] E.Baba: "Waves and Tidal Flat Ecosystems"Springer. 164 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Koshigoe: "Numerical Calculation of Electric Potentials Governed by Transmission Equations"Proceedings of European Symposium on Numerical Methods in Electromagnetics, Toulouse, France. 401-407 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Koshigoe: "A generalization of the method of lines and its applicatio to Robin problems"Proceedings of Fifth China-Japan Seminar on Numerical Mathematics, Science Press Beijing/New York. 47-56 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 平山幸史: "境界値決定問題の数値計算-Succesive elimination of linesの方法-"応用数学合同研究集会報告集. 249-252 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 水藤寛: "仮想領域法による脳脊髄液流動の数値シミュレーション"京都大学数理解析研究所講究録. 1265. 184-188 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Kawarada: "Effect of Spilled Oil on Coastal Ecosystems"Proceedings of Fifth China-Japan Seminar on Numerical Mathematics, Science Press Beijing/New York. 168-180 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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