1993 Fiscal Year Annual Research Report

関数方程式の応用解析と数値解析

Research Project

Project/Area Number	05640251
Research Institution	The University of Electro-Communications
Principal Investigator	牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)
Co-Investigator(Kenkyū-buntansha)	田村明久電気通信大学, 電気通信学部, 講師 (50217189) 加古孝電気通信大学, 電気通信学部, 教授 (30012488) 田端正久電気通信大学, 電気通信学部, 教授 (30093272) 内藤敏機電気通信大学, 電気通信学部, 教授 (60004446) 渡辺二郎電気通信大学, 電気通信学部, 教授 (90011535)
Keywords	分数巾の収束率 / 水の波線形問題の近似 / 劣微分作用素の固有値問題 / 線形関数微分方程の解半群 / 3次精度上流型有限要素近似 / 高レイノルズ数円柱回り流れ / 抵抗性磁気流体作用素 / 凸最小最大問題
Research Abstract	1.研究代表者を中心として得られた知見 (1)正定値自己共役作用素を近似する有界自己共役作用素列の分数巾の収束率と一様有界性近似作用素の列の収束率が近似作用素の分数巾の列の収束率に適切に反映されることを示し、この結果から分数巾の列のある意味での一様有界性がしたがうことを示した。(2)水の波線形非定常問題の有限要素離散化問題の収束性と誤差評価の方法の抽象的展開 (1)の結果を手がかりにして、研究を展開した。支配作用素が一階の擬微分作用素であることから生ずる興味ある知見を得た。(3)スチェクロフ作用素を用いた透過境界条件の設定とその数値的取り扱い外部領域におけるポアッソン問題などの有限要素近似問題に適用しその方法を正当化した。(4)軸対称容器内の水の波固有値問題の有限要素計算理論解析結果の正しさを確認するとともに、理論の適用出来ない場合の問題点を整理した。 2.分担者が著しい成果を収めた研究課題(分担者名) (1)凸汎関数に対する劣微分作用素の固有値問題の列における解の列の収束性(渡辺二郎、海津總)。(2)積分半群の理論の追究とその線形関数微分方程式の解半群への応用(内藤敏機)。(3)3次精度上流型有限要素近似による自動搬送車廻りの気流解析(田端正久)。(4)高レイノルズ数円柱回り流れにおける流脈線のシミュレーションと近似流脈線の誤差評価(田端正久)。(5)抵抗性磁気流体作用素のスペクトル的性質の解明とその近似解法(加古孝)。(6)ある種の凸最小最大問題に対する再帰的アルゴリズム(田村明久)。 3.電気通信大学数値解析研究会の継続開催と研究資料「電気通信大学数値解析研究会講演題目集」の作成本年度21回に亘っておおむね金曜午前に実施し、3月4日には一日研究会「恩故知新の集い」を開催した。研究資料には1977年から現在にいたるこの研究会とその前身の会での講演題目を収録した。

Research Products
(16 results)

All Other

All Publications (16 results)

[Publications] T.Ushijima,M.Matsuki: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Lecture Note of Mathematics,Springer. 1540. 361-380 (1993)
[Publications] T.Ushijima,R.Fu,M.Matsuki: "Numerical analysis of linear water wave problem and eigenvalue problem of Steklov type" Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics(Ed.by Z.-C.Shi and T.Ushijima). 5. 168-183 (1993)
[Publications] M.Matsuki,T.Ushijima: "A note on the fractional powers of operators approximating a positive definite selfadjoint operator" Journal of the Faculty of Science,The University of Tokyo,Sec.IA,Mathematics. 40. 517-528 (1993)
[Publications] M.Matsuki,T.Ushijima: "Error estimation of Newmark's method for conservative second order linear evolution equation" Proceedings of the Japan Academy,Ser.A. 69. 219-223 (1993)
[Publications] 符儒徳、牛島照夫: "軸対称容器内の水の波固有値問題の有限要素計算-収束率の数値的測定-" 日本応用数理学会論文誌. 3. 257-277 (1993)
[Publications] S.Kaizu,A.Nishiyama,G.Watanabe: "Convergence of solutions of nonlinear eigenvalue problems" Advances in Mathematical Sciences and Applications. 3. 353-366 (1993/94)
[Publications] T.Naito: "Dual semigroups associated with linear functional differential equations with infinite delay" Proc.Equadiff 91,Barcelona,World Sientific. 781-785 (1993)
[Publications] H.Kanayama,K.Toshigami,Y.Tashiro,M.Tabata,S.Fujima: "Finite element analysis of air flow around an automatic guided vehicle" Journal of Wind Engineering and Industrial Aerodynamics. 46&47. 801-810 (1993)
[Publications] M.Tabata,S.Fujima,K.Itakura: "Numerical simulation of streamlines emerging from the surface of a circular cylinder in high-Reynolds-number flows" Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics(Ed.by Z.-C.Shi and T.Ushijima). 5. 146-154 (1993)
[Publications] S.Fujima,M.Tabata: "Extension to three dimensional problems of the upwind finite element scheme based on the choice of up-and down-wind points" Computational Methods in Applied Mechanics and Engineering. (掲載予定). (1994)
[Publications] 加古孝: "MHD数値シミュレーションと数値解析" シミュレーション. 12. 91-98 (1993)
[Publications] 加古孝: "抵抗性MHDモデル方程式のスペクトルの数値計算" Advances in Numerical Methods for Large Sparce Sets of Linear Equations(Ed.by M.Natori and T.Nodera). 9. 62-68 (1993)
[Publications] T.Kako: "Spectral and numerical analysis of resistive linearized magnetohydrodynamic operators" Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics(Ed.by Z.-C.Shi and T.Ushijima). 5. 60-66 (1993)
[Publications] A.Tamura: "Transformation from arbitrary matchings to stable matchings" Journal of Combinatorial Theory,Series A. 62. 310-323 (1993)
[Publications] K.Sekitani,A.Tamura,Y.Yamamoto: "A recursive algorithm for a class of convex min-max problems" Asia-Pacific Journal of Operational Research. 10. 93-108 (1993)
[Publications] K.Fukuda,A.Tamura,T.Tokuyama: "A theorem on the average number of surfaces in arrangements and oriented matroids" Geometriae Dedicata. 47. 129-142 (1993)

1993 Fiscal Year Annual Research Report

関数方程式の応用解析と数値解析

Principal Investigator

牛島 照夫 電気通信大学, 電気通信学部, 教授 (10012410)

Research Products

[Publications] T.Ushijima,M.Matsuki: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Lecture Note of Mathematics,Springer. 1540. 361-380 (1993)

[Publications] T.Ushijima,R.Fu,M.Matsuki: "Numerical analysis of linear water wave problem and eigenvalue problem of Steklov type" Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics(Ed.by Z.-C.Shi and T.Ushijima). 5. 168-183 (1993)

[Publications] M.Matsuki,T.Ushijima: "A note on the fractional powers of operators approximating a positive definite selfadjoint operator" Journal of the Faculty of Science,The University of Tokyo,Sec.IA,Mathematics. 40. 517-528 (1993)

[Publications] M.Matsuki,T.Ushijima: "Error estimation of Newmark's method for conservative second order linear evolution equation" Proceedings of the Japan Academy,Ser.A. 69. 219-223 (1993)

[Publications] 符儒徳、牛島照夫: "軸対称容器内の水の波固有値問題の有限要素計算-収束率の数値的測定-" 日本応用数理学会論文誌. 3. 257-277 (1993)

[Publications] S.Kaizu,A.Nishiyama,G.Watanabe: "Convergence of solutions of nonlinear eigenvalue problems" Advances in Mathematical Sciences and Applications. 3. 353-366 (1993/94)

[Publications] T.Naito: "Dual semigroups associated with linear functional differential equations with infinite delay" Proc.Equadiff 91,Barcelona,World Sientific. 781-785 (1993)

[Publications] H.Kanayama,K.Toshigami,Y.Tashiro,M.Tabata,S.Fujima: "Finite element analysis of air flow around an automatic guided vehicle" Journal of Wind Engineering and Industrial Aerodynamics. 46&47. 801-810 (1993)

[Publications] M.Tabata,S.Fujima,K.Itakura: "Numerical simulation of streamlines emerging from the surface of a circular cylinder in high-Reynolds-number flows" Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics(Ed.by Z.-C.Shi and T.Ushijima). 5. 146-154 (1993)

[Publications] S.Fujima,M.Tabata: "Extension to three dimensional problems of the upwind finite element scheme based on the choice of up-and down-wind points" Computational Methods in Applied Mechanics and Engineering. (掲載予定). (1994)

[Publications] 加古 孝: "MHD数値シミュレーションと数値解析" シミュレーション. 12. 91-98 (1993)

[Publications] 加古 孝: "抵抗性MHDモデル方程式のスペクトルの数値計算" Advances in Numerical Methods for Large Sparce Sets of Linear Equations(Ed.by M.Natori and T.Nodera). 9. 62-68 (1993)

[Publications] T.Kako: "Spectral and numerical analysis of resistive linearized magnetohydrodynamic operators" Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics(Ed.by Z.-C.Shi and T.Ushijima). 5. 60-66 (1993)

[Publications] A.Tamura: "Transformation from arbitrary matchings to stable matchings" Journal of Combinatorial Theory,Series A. 62. 310-323 (1993)

[Publications] K.Sekitani,A.Tamura,Y.Yamamoto: "A recursive algorithm for a class of convex min-max problems" Asia-Pacific Journal of Operational Research. 10. 93-108 (1993)

[Publications] K.Fukuda,A.Tamura,T.Tokuyama: "A theorem on the average number of surfaces in arrangements and oriented matroids" Geometriae Dedicata. 47. 129-142 (1993)

牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)

[Publications] 加古孝: "MHD数値シミュレーションと数値解析" シミュレーション. 12. 91-98 (1993)

[Publications] 加古孝: "抵抗性MHDモデル方程式のスペクトルの数値計算" Advances in Numerical Methods for Large Sparce Sets of Linear Equations(Ed.by M.Natori and T.Nodera). 9. 62-68 (1993)