2001 年度実績報告書

領域分割法による数値シミュレーション手法の開発とその数学的検証

研究課題

研究課題/領域番号	13555021
研究機関	日本大学
研究代表者	中村正彰日本大学, 理工学部, 教授 (00017419)
研究分担者	田端正久九州大学, 数理学研究科, 教授 (30093272) 池田勉竜谷大学, 理工学部, 教授 (50151296) 今井仁司徳島大学, 工学部, 教授 (80203298) 張紹良東京大学, 工学系研究科, 助教授 (20252273) 森正武東京電機大学, 工学部, 教授 (20010936)
キーワード	numerical simulation / computation mechanics / domain decomposition / precondition / fluid dynamics / spinodal decomposition / numerical integration / infinnite precision
研究概要	本年度の研究計画に基づき研究を実施し,次のような成果を得た. ・数値シミュレーションの新手法のための計算法開発高速高精度計算手法の開発と応用。高精度数値シミュレーションの逆問題への応用に成功した。大型計算の前処理法の解析数値積分法の解析. ・以下の非線形問題の数学的および数値解約解析に成功した. 相分離系を記述する江口・沖松村方程式の1次元非自明定常解の存在を予測し証明した。地球マントル対流の数値シミュレーション用有限要素コードを作成した。燃焼合成反応の数理モデルの数値シミュレーションの解析. Navier-Stokes方程式の摩擦型境界条件問題. ・有限要素法,差分法を用いた各種流体問題の解析に成果をあげた. 各種風車の数値シミュレーション多相流れの解析

研究成果

(26件)

すべてその他

すべて文献書誌 (26件)

[文献書誌] Takao Hanada, N.Ishimura, Masa Aki Nakamura: "Numerical analysis of Eguchi-Oki-Matsumura equations II"the proceedings of the fifth China-China joint-seminar on numerical mathematics. (to appear). (2002)
[文献書誌] T.Hanada, H.Imai, N.Ishimura, M.Nakamura: "Eguchi-Oki-Matsumura equations for phase separation: Numerically guided approach"the proceedings of international conference on inverse problems. (to appear). (2002)
[文献書誌] H.Suito, H.Kawarada: "Shape Optimization for an Acoustic Problem"Proceedings of 12th International Conference on Domain Decomposition Methods in Science and Engineering. 445-453 (2001)
[文献書誌] H.Kawarada, H.Suito: "Multi-phase flow reaction"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 39-56 (2001)
[文献書誌] M.Mori, M.Sugihara: "The double exponential transformation in numerical analysis"Journal of Comput.Appl.Math.. 127. 287-296 (2001)
[文献書誌] M.Mori: "Optimality of the double exponential transformation in numerical analysis"Sugaku Exposition. 14,No.1. 103-1* (2001)
[文献書誌] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"Japan Journal of Industrial and Applied Mathematics. 18. 567-585 (2001)
[文献書誌] Y.Mizuyama, M.Tabata: "Lagrangian finite element analysis of the free surface of an incompressible dielect liquid under an electric field"Theoretical Applied Mechanics. 50. 403-410 (2001)
[文献書誌] M.Tabata, S.Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. 14. 155-174 (2001)
[文献書誌] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. (to appear). (2002)
[文献書誌] M.Tabata, A.Suzuki: "Mathematical modeling and numerical simulation of Earth's mantle convection"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 219-231 (2001)
[文献書誌] 池田勉, 長山雅晴: "燃焼合成反応におけるヘリカル波"応用数理. 11,No.2. 40-48 (2001)
[文献書誌] M.Nagayama, T.Ikeda, T.Ishiwata, N.Tamura, M.Ohyanagi: "Three-dimensional numerical simulation of helically propagating combustion waves"J.of Material Synthesis and Processing. 9,No.3. 153-163 (2001)
[文献書誌] T.Nishida, T.Ikeda, H.Yoshihara: "Pattern formation of heat convection problems"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 209-218 (2001)
[文献書誌] M.Kan, T.Kawamura, K.Kuwahara: "Numerical Study of the Sand Movement around a Cylindrical Body Standing on the Sand"JSME International Journal Series B. 44,No.3. 427-433 (2001)
[文献書誌] M.Iwata, T.Kawamura, N.I.Wakayama: "Three-Dimensional Numerical Study of the Magnetic Effect on the Air Flow at an Intake"Theoretical and AppliedMechanics. 50. 289-294 (2001)
[文献書誌] T.Hayashi, S.Yamashita, H.Yamada, T.Kawamura: "Experimental and Numerical Study of the Flow around the Rotating Savonius Rotor"Proceedings of Europian Wind Energy Conference. 398-401 (2001)
[文献書誌] S.Saitoh, M.Mori: "representation of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)
[文献書誌] K.Ohmori: "Convergence of the interface in the finite element approximation for two-fluid flows"Lecture Notes in Pure and Applied Mathematics,the Navier-Stokes Equations: Theory and Numerical Methods. 223. 279-293 (2001)
[文献書誌] H.Fujita: "Non-stationary Stokes flows under leak boundary conditions of friction type"Journal of computing Mathematics. 19-1. 1-8 (2001)
[文献書誌] S.Komurasaki, T.Kawamura, K.Kuwahara: "Simulation of Thermal Convection in a Stratified Fluid Flow"AIAA paper. 2002-0877. 1-10 (2002)
[文献書誌] B.Yu, G.-C.Feng, S.-L.Zhang: "The aggregate constraint homotopy method for nonconvex nonlinear programming"Nonlinear Anal.. 45-7. 839-847 (2001)
[文献書誌] 花田孝郎, 石村直之, 中村正彰: "相分離問題におけるEOM方程式の数値解析"第51回理論応用力学講演会講演論文集. 639-640 (2002)
[文献書誌] 檜山聡, 篠田大輔, 藤間昌一: "高次モルタル型領域分割法とその並列計算"第51回理論応用力学講演会講演論文集. 501-502 (2002)
[文献書誌] H.Fujita, N.Saito, T.Suzuki: "Operator Theory and Numerical Methods"Elsevier. 309 (2001)
[文献書誌] 河村哲也, 菅牧子, 桑原邦郎, 小紫誠子: "環境流体シミュレーション"朝倉書店. 199 (2001)

2001 年度 実績報告書

領域分割法による数値シミュレーション手法の開発とその数学的検証

研究代表者

中村 正彰 日本大学, 理工学部, 教授 (00017419)

研究成果

[文献書誌] Takao Hanada, N.Ishimura, Masa Aki Nakamura: "Numerical analysis of Eguchi-Oki-Matsumura equations II"the proceedings of the fifth China-China joint-seminar on numerical mathematics. (to appear). (2002)

[文献書誌] T.Hanada, H.Imai, N.Ishimura, M.Nakamura: "Eguchi-Oki-Matsumura equations for phase separation: Numerically guided approach"the proceedings of international conference on inverse problems. (to appear). (2002)

[文献書誌] H.Suito, H.Kawarada: "Shape Optimization for an Acoustic Problem"Proceedings of 12th International Conference on Domain Decomposition Methods in Science and Engineering. 445-453 (2001)

[文献書誌] H.Kawarada, H.Suito: "Multi-phase flow reaction"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 39-56 (2001)

[文献書誌] M.Mori, M.Sugihara: "The double exponential transformation in numerical analysis"Journal of Comput.Appl.Math.. 127. 287-296 (2001)

[文献書誌] M.Mori: "Optimality of the double exponential transformation in numerical analysis"Sugaku Exposition. 14,No.1. 103-1* (2001)

[文献書誌] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"Japan Journal of Industrial and Applied Mathematics. 18. 567-585 (2001)

[文献書誌] Y.Mizuyama, M.Tabata: "Lagrangian finite element analysis of the free surface of an incompressible dielect liquid under an electric field"Theoretical Applied Mechanics. 50. 403-410 (2001)

[文献書誌] M.Tabata, S.Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. 14. 155-174 (2001)

[文献書誌] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. (to appear). (2002)

[文献書誌] M.Tabata, A.Suzuki: "Mathematical modeling and numerical simulation of Earth's mantle convection"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 219-231 (2001)

[文献書誌] 池田勉, 長山雅晴: "燃焼合成反応におけるヘリカル波"応用数理. 11,No.2. 40-48 (2001)

[文献書誌] M.Nagayama, T.Ikeda, T.Ishiwata, N.Tamura, M.Ohyanagi: "Three-dimensional numerical simulation of helically propagating combustion waves"J.of Material Synthesis and Processing. 9,No.3. 153-163 (2001)

[文献書誌] T.Nishida, T.Ikeda, H.Yoshihara: "Pattern formation of heat convection problems"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 209-218 (2001)

[文献書誌] M.Kan, T.Kawamura, K.Kuwahara: "Numerical Study of the Sand Movement around a Cylindrical Body Standing on the Sand"JSME International Journal Series B. 44,No.3. 427-433 (2001)

[文献書誌] M.Iwata, T.Kawamura, N.I.Wakayama: "Three-Dimensional Numerical Study of the Magnetic Effect on the Air Flow at an Intake"Theoretical and AppliedMechanics. 50. 289-294 (2001)

[文献書誌] T.Hayashi, S.Yamashita, H.Yamada, T.Kawamura: "Experimental and Numerical Study of the Flow around the Rotating Savonius Rotor"Proceedings of Europian Wind Energy Conference. 398-401 (2001)

[文献書誌] S.Saitoh, M.Mori: "representation of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)

[文献書誌] K.Ohmori: "Convergence of the interface in the finite element approximation for two-fluid flows"Lecture Notes in Pure and Applied Mathematics,the Navier-Stokes Equations: Theory and Numerical Methods. 223. 279-293 (2001)

[文献書誌] H.Fujita: "Non-stationary Stokes flows under leak boundary conditions of friction type"Journal of computing Mathematics. 19-1. 1-8 (2001)

[文献書誌] S.Komurasaki, T.Kawamura, K.Kuwahara: "Simulation of Thermal Convection in a Stratified Fluid Flow"AIAA paper. 2002-0877. 1-10 (2002)

[文献書誌] B.Yu, G.-C.Feng, S.-L.Zhang: "The aggregate constraint homotopy method for nonconvex nonlinear programming"Nonlinear Anal.. 45-7. 839-847 (2001)

[文献書誌] 花田孝郎, 石村直之, 中村正彰: "相分離問題におけるEOM方程式の数値解析"第51回理論応用力学講演会講演論文集. 639-640 (2002)

[文献書誌] 檜山聡, 篠田大輔, 藤間昌一: "高次モルタル型領域分割法とその並列計算"第51回理論応用力学講演会講演論文集. 501-502 (2002)

[文献書誌] H.Fujita, N.Saito, T.Suzuki: "Operator Theory and Numerical Methods"Elsevier. 309 (2001)

[文献書誌] 河村哲也, 菅牧子, 桑原邦郎, 小紫誠子: "環境流体シミュレーション"朝倉書店. 199 (2001)

2001 年度実績報告書

中村正彰日本大学, 理工学部, 教授 (00017419)