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The research on homogenization, elasitic problems and the algorithms for numerical simulations of flows of liquids and development

Research Project

Project/Area Number 11640098
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 InstitutionIBARAKI UNIVERSITY

Principal Investigator

KAIZU Satoshi  Ibaraki University, Faculty of Education, Professor, 教育学部, 教授 (80017409)

Co-Investigator(Kenkyū-buntansha) KAWASHITA Mishio  Ibaraki University, College of Education, Associate Professor, 教育学部, 助教授 (80214633)
ONISHI Kazuei  Ibaraki University, Faciulty of Science, Professor, 理学部, 教授 (20078554)
SOGA Hidco  Ibaraki University, College of Education, Professor, 教育学部, 教授 (40125795)
FUJIMA Shoichi  Ibaraki University, Faculty of Science, Associate Professor, 理学部, 助教授 (00209082)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2000: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1999: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordstwo-layers problem / the density-dependent Stokes problem / generalized boundary problems / the adjoint method / energy fecay of the Rayleigh surface waves / numeric construction of free boundaries / superosition of plane waves in the half-space / convergent finite element scheme to the Stokes equation / 有限要素スキームの誤差解析 / 有限要素法 / 非適合有限要素 / 移動境界問題 / 数値計算法 / 圧縮性粘性流体 / 時間大域解 / 表面波の散乱理論 / 逆問題
Research Abstract

(1) Algorithm for numeric scheme on liquids flows : First, a theorem on errors of between the exact boundaries and numeric construction of boundaries are proposed by colleague and examined by numerically. Second, convergent finite element scheme for multi-flows miscible among different liquids, are proposed and proved. The governed equations are the Navier-Stokes equation for the first topic and the Stokes equation for the second one.
(2) The Laplace equation is considered as the corresponding scalar equation to the Navier-Stokes equation, in order to treat in a unified way under the notion of the generalized boundary value probleml for elliptic partial differential equations by using the variational calculus. The approach is verified by numerical examples.
(3) Among elastic waves, the Rayleigh surface waave is researched. In particular, the propagation of the Rayleigh surface wave is interested by us, and some estimates on decay of the local energy of the Rayleigh waves are obtained in many types of regions.
(4) Generally in the total space, it is well known that waves are represented as superposition of plane waves. In this research, it is showd that, in the half-space region, a concrete form of superposition to elastic waves are obtained. This expression is expected to be applied to the construction of the Fourier transformation in the half-space.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] M.Kawashita and H.Soga: "Properties of Elastic Symbols and Construction of Solutions of the Dirichlet Problems"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kawashita: "Strong solutions of Cauchy problems for compressible Navier-Stokes equations"数理解析研究所講究録. 1123. 100-106 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 藤間昌一: "A domain decomposition finite element scheme for flow problems- Choice of elements"数理解析研究所講究録. 1129. 9-22 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kawashita and G.Nakamura: "The poles of the resolvent for the exterior Neumann problem fo anisotropic elasticity"SIAM J.of Math.Anal,. 31. 701-725 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohura,K.Kobayashi and K.Onishi: "Numerical solution of an under-determined problem of the Laplace equation"J.of Applied Mechanics, JSCE. 2. 185-189 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 登坂宣好,大西和榮,山本昌宏: "偏微分方程式の逆解析;逆問題の数理と解法.,"東京大学出版会. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 磯祐介,大西和榮,登坂宣好: "工学系の基礎数学"彰国社. (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Mishio Kawashita and Gen Nakamura: "The poles of the resolvent for the exterior Neumann problem fo anisotropic elasticity"SIAM J.of Math.Anal. 31. 701-725 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Mishio Kawashita, Y.Kurylev and Hideo Soga: "Harmonic momentsand and an inverse problem for the heat equation"SIAM J.of Math.Anal.. 32. 522-537 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohura, K.Kobayashi and K.Onishi: "Numerical solution of an under-determined problem of the Laplace equation"J.of Applied Mechanics, JSCE. 2. 185-189 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Shirota, G.Nakamura and K.Onishi: "Impedance computed tomo-electrocardiography"Proceedings of Japan-Korea Joint Scientfic Seminar on Inverse problems and related topics, Chapman Hall, Res.Notes in Math.. 419. 155-164 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Q.Wang, Y.Ohura, and K.Onishi: "Numerical solution of under-determined 2D Laplace equation with internal information.."ISIP 2000 Abstracts, International Symposium on Inverse Problems in Engineering Mechanics, March 7-10, 2000, Nagano, Japan. 216-219 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Q.Wang and K.Onishi: "Inverse boundary value problems of the Laplace equation."Hydraulic Engineering Software VIII, Proceedings of the 8th International Conference on Hydraulic Engineering Software, WIT Press, June 12-14, 2000, Lisbon, Portugal. 425-436 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Shirota, K.Kobayashi, and K.Onishi: "Cognitive problems in seepage and viscous fluid flows."Computational Methods and Water Res ources IV, Fourth International Conference on Computer Methods and Water Resources, Lebanese American University, Byblos (Jbeil), Lebanon, 1997.6.16-18., WIT Press, Southampton. 183-192 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Onishi and Y.Ohura: "Direct method of solution for solution for general boundary value problem of the Laplace equation."Boundary Elements XXII (Eds ; C>A.Brebbia and H.Power), International Series on Advances in Boundary Elements., Vol.8, Proceedings of the 2 2nd International Conference on Boundary Element Method, September 4-6, 2000, Cambridge University, UK, WIT Press, Southampton. 203-210 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kawashita and H.Soga: "Properties of Elastic Symbols and Construction of Solutions of the Dirichlet Problems"The Japan-Korean Seminar.. 第1巻(予定). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Kawashita: "Strong solutions of Cauchy problems for compressible Navier-Stokes equations"数理解析研究所講究録. 1123. 100-106 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 藤間昌一: "A domain decomposition finite element scheme for flow problems-Choice of elements"数理解析研究所講究録. 1129. 9-22 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 王青川,大浦洋子,代田健二,大西和栄: "不足決定系2次元Laplace方程式の境界要素解"BTEC論文集. 第9巻. 57-61 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] 林圭佐,繁田岳美,大西和栄: "2次元Poisson方程式の外部境界値問題の反復解法"境界要素法論文集. 第16巻. 127-132 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] 大西和栄,大浦洋子: "ラプラス方程式境界値逆問題の直接解法"BEM・テクノロジー・コンファレンス論文集,日本計算数理工学会. 10巻. 49-53 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ohura: "Numerical solution of an under-determined problem of the Laplace equation"Journal of Applied Mechanics. 2. 185-189 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 藤間昌一: "A domain-decomposition finite-element scheme for flow problems"京都大学数理解析研究所講究録,「計算力学の新解法と領域分割法」. 1129. 9-22 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Kawashita: "On global solutions of Cauchy problems for compressible Navier-Stokes equations"Nonlinear Analysis,to apper. (出版予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Kawashita: "The polo of the resolvent for the exterior Neumann problems of anisotropic elasticity"SIAM Journal on Matlomatical Analysis. (出版予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 登坂 宣好: "逆問題の数理と解法"東京大学出版会. 294 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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