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非線形複雑系の3次元数値計算

Research Project

Project/Area Number 07555343
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section展開研究
Research Field Engineering fundamentals
Research InstitutionRyukoku University

Principal Investigator

池田 勉  龍谷大学, 理工学部, 教授 (50151296)

Co-Investigator(Kenkyū-buntansha) 三村 昌泰  東京大学, 大学院・数理科学研究科, 教授 (50068128)
友枝 謙二  大阪工業大学, 工学部, 教授 (60033916)
岡本 久  京都大学, 数理解析研究所, 教授 (40143359)
今井 仁司  徳島大学, 工学部共通講座, 教授 (80203298)
高橋 大輔  龍谷大学, 理工学部, 助教授 (50188025)
中村 正彰  日本大学, 理工学部, 助教授 (00017419)
木田 重雄  核融合科学研究所, 理論・シミュレーション研究センター, 教授 (70093234)
河原田 秀夫  千葉大学, 工学部, 教授 (90010793)
四ツ谷 晶二  龍谷大学, 理工学部, 教授 (60128361)
Project Period (FY) 1995 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥5,200,000)
Fiscal Year 1997: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1996: ¥3,900,000 (Direct Cost: ¥3,900,000)
Keywords反応拡散系の並列計算 / バクテリアコロニー / 水の波 / 渦層の巻き上げ / 渦構造の同定 / 管状渦と剪断流 / SOR法の収束率 / 浸透領域 / 並列計算 / 領域分割法 / 前処理付き共役勾配法 / 自由境界問題 / 水面波の分岐 / らせん渦線 / 渦線の巻き込み / 変孔質媒体流 / 可視化技術 / 共役勾配法 / 反応拡散系 / 進行脈動波解 / 反応-興奮系 / 多孔性媒質中の流体 / 導電性流体の熱対流
Research Abstract

研究代表者池田は,反応拡散方程式系の並列計算スキームの有限要素法によるコーディングを完成した.これは領域分割法と前処理付き共役勾配法に基づくものである.領域を分割することにより生成される内部界面では整合しない三角形分割も許されるモルタル法のような手法もあるが,我々は分かり易さを前面に押し出す方針を採用した.その結果,三角形分割は内部界面において整合条件を満たさなければならないが,通常の有限要素法と同一の数値計算結果が得られるという特徴を備えている.大腸菌のある種の変異株が,複雑な過程を経て,形成するストライプ・スポット状のパターンの並列計算を行い,並列スキームがほぼ予定通りに機能することを確認した.研究分担者三村は,反応拡散系と界面ダイナミクスの数理解析を分担し,発熱反応拡散系に現れる時空間パターンの特異極限解析と計算機シミュレーション,競争拡散系に現れる棲み分けパターンを捉えるための界面ダイナミクス法の導出,活性抑制因子反応拡散系に現れるパルスダイナミクスの数理解析,バクテリアコロニーの時空間パターンのモデル化とその計算機シミュレーションを行った.
渦と乱流場に関しては,岡本が水の波の数値計算および渦層の巻き上げの数値計算において重要な貢献を行い,木田が渦構造の同定と抽出,管状渦と剪断流の3次元相互作用の2点を中心に詳細な研究を行った.高橋はすべての独立変数と従属変数を離散化する超離散化法の理論を交通流モデルおよびソリトン系に応用することに成功した.今井は自由境界問題の高精度数値解法の開発と応用,ポアソン方程式の差分離散化法およびSOR法の収束率などの研究を,友枝は多孔質媒体を流れる流体によって形成される浸透領域のダイナミクスなどの研究を推進した.

Report

(3 results)
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • 1995 Annual Research Report
  • Research Products

    (52 results)

All Other

All Publications (52 results)

  • [Publications] 丸尾 彰: "ある非線形放物型方程式の整合差分近似とその画像修復への応用" 日本応用数理学会論文誌. 7・4. 389-402 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Ikeda: "Global structure of travelling pulse solutions in some reaction-diffusion systems" to appear in The Proceedings of International Conference on Asymptotics in Nonliner Diffusion Systems towards the understanding of singularitias in dissipative structurs. (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Ikeda: "Parallel computation of interfacial dynamics" Gakuto International Series Mathematical Sciences and Applications. 11. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Ikeda: "Parallel computation of reaction-diffusion phenemena" to appear in The Proceedings of the Third China-Japan Joint Seminar on Numerical Mathematics.

    • Related Report
      1997 Annual Research Report
  • [Publications] 森下 博: "代用電荷法によるポアソン方程式の数値計算" 情報処理学会論文誌. 38. 1483-1491 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Kabeya: "Number of zeros of solutions to singular initial value problems" to appear in Tohoku J.Math.

    • Related Report
      1997 Annual Research Report
  • [Publications] D.Takahashi: "Box and ball system with a carrier and ultradiscrete modified KdV equation" J.Phys.A. 30. 733-739 (1977)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hitoshi IMAI: "Conputations to Free Boundary Problems" 統計数理研究所共同研究リポート. 105. 129-142 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Okamoto: "Interfacial progressive water waves:a singularity-theoretic view" Tohoku Math.J. 49. 33-57 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Fujita: "Stability analysis of Navier-Stokes flows in annvli" Math.Meth.Appl.Sci. 20. 959-978 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Sakajo: "An application of Draghicescu's fast summation method to vortex sheet motion." to appear in J.Phys.Soc.Japan. 67. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Okamoto: "Exact solutions of the Navier-Stokes equations via Leray's scheme." Japan J.Indus.Appl.Math. 14. 169-197 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 河原田 秀夫: "Variational Inequalities for Navier-Stokes Flows Coupled with Potential Flow through Porous Media:Theory and Numerical Simulation" The proceedings of DDM-8(Beijin). 403-410 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Miura: "Identification of tubular vortices in coniplex flows" J.Phys Soc.Japan. 66. 1331-1334 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kawahara,G: "1998 Wrap,Tilt and Stretch of Vorticity Lines around a Strong Thin Straight Vortex Tube in a Simple Shear Flow" J.Fiuid Mech.

    • Related Report
      1997 Annual Research Report
  • [Publications] Kenji Tomoeda: "The possibility of a support splitting caused by the absorption in some nonlinear diffusion equations" New trends of inverse and ill-posed problems,VSP.

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Nakaki: "On the heteroclinic orbit of the point vortex problem" to appear in the Proceedings of the Second World Congress of Nonlinear Analysts.

    • Related Report
      1997 Annual Research Report
  • [Publications] Naoyuki Ishimura: "Uniqueness for unbounded classical solutions of the MHD equations" Methematical Methods in the Applied Science. 20. 617-623 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Mimura: "Singular perturbation problems to a combustion equation in very long cylindrical domains" Studies in Advanced Mathematics. 3. 75-84 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Mimura: "Sakamoto:Hopf・bifurcation in a chemical reaction-diffusion system" to appear in Applied Mathematics Letter.

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Ohta: "Collision of propagating pules in a reaction-diffusion system" J.Phys.Soc Japan. 66. 1551-1558 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Kawaguchi: "Collision of travelling waves in a reaction-diffusion system with global coupling" to appear in SIAMJ.Appl.Math.

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Mimura: "Non-annihilation dynamics in a sexothermic reaction-diffusion system with mono-stable excitablity" to appear in Journal of CHAOS.

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Kan-on: "Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics" to appear in SIAMJ.Math.Anal.

    • Related Report
      1997 Annual Research Report
  • [Publications] E.N.Dancer: "Spatial segregation limit of a competition-diffusion system" Lecture Notes in Math.Institute,Vniv Leiden.

    • Related Report
      1997 Annual Research Report
  • [Publications] 高橋 大輔: "数値計算" 岩波書店, 194 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 藤井 宏: "非線型力学" 岩波書店 岩波講座「応用数学」, (1995)

    • Related Report
      1997 Annual Research Report
  • [Publications] 岡本 久: "関数解析" 岩波書店 岩波講座「現代数学の基礎」, (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tsutomu Ikeda: "Numerical simulation for nonlinear oscillation of internal layers" Lecture Notes in Numerical and Applied Analysis. 14. 66-77 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Takashi Hakamada: "Analytical approach to estimating the dimension of attractors" Applied Mathematics and Optimization. 34. 29-36 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 檜山 澄子: "Wavelet変換による海岸線データの間引き" 日本応用数理学会論文誌. 6(1). 83-99 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 周 偉東: "スペクトル選点法における最適パラメータ前処理" 日本応用数理学会論文誌. 6(3). 191-204 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Katsurada: "On the collocation points of the fundaniental solution method for the potential problem" Int.J.Comp.Math.Appl.31. 123-137 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Okamoto: "Nearly singular two-dimensional kolmogorov frows for large newline Reynolds number" J.Dynamics and Diff.Egns. 8. 203-220 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Okamoto: "The resonance of modes in the problem of capillary gravity waves" Physica D. 95. 336-350 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Shoji: "Secondary and tertiary bifurcations of capillary gravity waves" Adv.Math.Sci.Appl.6. 135-145 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Sakajo: "Numerical computation of vortex sheet roll-up in the background shear flow" Fluid Dynam.Res.17. 195-212 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.N.Beronov: "Linear two-dimensional stability of a Burgers vortex layer" Phys.Fluids. 8. 1024-1035 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Tatsuyuki Nakaki: "Numerical approximations to some nonlinear diffusion equation with strong absorption" Proceedings of the Sixth International Colloquivm on Differential Equations. 165-172 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Hitoshi Imai: "Convergence of attractors for the simplifind magnetic Benard equations" European Journal of Applied Mathematics. 7(1). 53-62 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] E.Yanagida: "Global structure of positive solutions to equations of Matukuma type" Arch.Rational Mech.Anal.124. 199-226 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Kabeya: "Existence of nodal fast-decay solutions to div (Ivul^m - ^2Vu) +K (1×1) lul^<P-1> u=O in R^n" Differential and Integral Equations. 9. 981-1004 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Kawarada: "On Penetration Phenomenon of Magnetic Field into Superconducting Materials" Advances in Mathematical Sciences and Applications Gakkoutosho,Tokyo. 6(1). 125-133 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Torii: "Combinatorial Representation of Invariants of a Soliton Cellular Autoamton" Physica D. 92. 209-220 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Tokihiro: "From Soliton Equations to Integrable Cellular Automata through a Limiting Procedure" Phys.Rev.Lett.76. 3247-3250 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T. Ikeda: "Numerical simulation for nonlinear oscillation of internal layers" Lecture Notes in Numerical and Applied Analysis. 14. 69-77 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 今井 仁司: "磁気ベナ-ル問題のカオス" 日本物理学会学会誌. 50. 697-703 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hitoshi Imai: "Magnetic Benard system and its simplified model" Lecture Notes in Numerical and Applied Analysis. 14. 79-92 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] E. Yanagida: "Existence of positive radial solutions to Δu+K(|×|)|u|^<P-1>u=O in R^n" J. Differential Equations. 115. 477-502 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H. Fjita: "Distribution theoretic opproach to fictitious domain method for Neumann problems" East-West J. Numer Math.,. 3. 111-126 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] M. Mimura: "Pattern dynamics in an exothermic reaction" Physica D. 84. 58-71 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 高橋大輔: "数値計算" 岩波書店, 194 (1996)

    • Related Report
      1995 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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