1992 Fiscal Year Annual Research Report

科学技術における数値的手法の総合的研究

Research Project

Project/Area Number	02302011
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)	四ツ谷晶二龍谷大学, 理工学部, 教授 (60128361) 森正武東京大学, 工学部, 教授 (20010936) 細野雄三京都産業大学, 工学部, 教授 (50008877) 中尾充宏九州大学, 理学部, 助教授 (10136418) 菊地文雄東京大学, 教養学部, 教授 (40013734)
Keywords	水の波線形非定常問題 / 移流拡散差分スキーム / スチエクロフ作用素 / 電磁場問題の有限要素近似 / 植物性プランクトン藻類等の数理モデル / 精度保証付き数値計算 / 超並列高速計算 / 半線形楕円型偏徴分方程式
Research Abstract	1,研究代表者を中心として得られた知見 (1)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抽象的展開支配作用素が一階の擬徴分作用素であることから生ずる興味ある知見を得、さらにスチェクロフ作用素の構成的近似と言う観点から研究を展開した。(2)移流拡散差分スキーム空間一次元等間隔五点差分公式・時間方向にルンゲ・クッタ型前進差分公式の場合に二乗可積分ノルムでの安定条件を研究し、誤差評価を得た。三次および四次のルンゲ・クッタ公式の場合に対しても安定となることが解った。(3)外部領域問持の有限要素近以台が有界な非斉次項を持つポァッソン方程式を、非斉次項の境界を仮想境界として、そこで非局所境界条件を与えた問題に変換して有限要素計算する方法を正当化した。(4)角を持つ領域におけるラプラス方程式の数値解法スチェクロフ作用素の手法により角の近くで斉次境界条件を満たす場合に正則領域の問題に変換して非局境界条件付きの問題の有限要素近似問題とする方法を正当化した。 2.分担者が著しい成果を収めた研究課題(分担者名)(1)電磁場問題の有限要素数値解析における共変要素の導入(菊地文雄)。(2)非線形偏徴分方程式の解に対する精度保証付き数値計算法(中尾充宏)。(3)超並列高速計算の実用化(野木達夫)。(4)植物性プランクトンおよび藻類等の定常分布の数理モデル(細野雄三)(4)関数値再配置理論の展開と変分問題への適用(俣野博)。(5)Cahn-hilliard方程式の差分解法(森正武)。(6)半線形楕円型偏徴分方程式の解の構造(四ツ谷晶二)。 3.応用数学合同研究発表会の開催他の五つの総合研究(研究代表者、榎本彦衛慶應大学、有川節夫九州大学、三井斌友名古屋大学、西田孝明京都大学、佐藤雅彦東北大学、各名授)と合同で京都大学に於いて実施した。

Research Products
(34 results)

All Other

All Publications (34 results)

[Publications] M.Matsuki,T.Ushijima: "An iegenvalue problem for a system of finite difference equations approximating a linear wave equaiton" Japan Journal of Industrial and Applied Mathematics. 9. 91-116 (1992)
[Publications] T.Ushijima,MMatsuki: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Proc.Int.Conf.on Functional Anaysis and Related Topics. (1993)
[Publications] R.Fu,T.Uxhijima: "Finite element analysis of free vibration of liquid-filled axisymmetric tanks" Acta Mathematicae Applicatae Sinica.
[Publications] K.Sugihara,M Iri: "Construction of the Voronoi diagram for¨one million¨generators in single-precision arithmetic" Proceedings of the IEEE. 80. 1471-1484 (1992)
[Publications] M.Iri: "How to generate realistic sample problems for network optimization" Lecture Notes in Computer Science. 650. 342-350 (1992)
[Publications] F.Kikuchi,M.Hara,T.wada: "A mixed finite element method for 3-D analysis of resonators" Sci.papers Coll.Arts&Sci.,Univ.Tokyo. 42. 111-129 (1993)
[Publications] F.kikuchi: "Numerical analysis of electrostatic and magnetostatic problems" Sugaku Expositions. 6. (1993)
[Publications] 金山寛,池口修一,松木直美,遠藤研二,菊地文雄: "辺要素を用いた3次元非線形磁場解析" シュミレーション. 11. 212-220 (1992)
[Publications] T.Yamada,F.Kikuchi: "An arbitrary Lagrangian-Eulerian finite element method for incompressible hyperelasticity" Computer Methods in Applied Mechanics and Engineering. (1993)
[Publications] A.Kohda,Y.Shinogara: "Numerical Analysis of the quasiperiodic solutions to Duffing type equations" Japan J.Indust.Appl.Math.
[Publications] T.Sakurai,H.sugiura,T.Torii: "Factorization of a polynomial by rational hermite interpolation" Numerical Algorithm. 3. 411-418 (1992)
[Publications] H.sugiura,T.Torii: "Polynomial interpolation on quasiequidistributed nodes on unit circle" SIAM J.Numer Anal.29. 1154-1165 (1992)
[Publications] T.Torii,T.Sakurai,H.sugiura: "An application of Sunzi's teorem for solving algebraic equations" Proc.1st China-Japan Joint Seminar on Numerical Mathematics.
[Publications] T.Hasegawa,H.Sugiura,T.Torii: "Positivity of the weights of extended Clenshaw-Clenshaw-Curtis quadrature rules" Math.Comp.
[Publications] M.T.Nakao: "A numerical verification method for the existence of weak solutions for nonlinear boundry value problems" Journal of Mathematical Analysis and Applications. 164. 489-507 (1992)
[Publications] 小田中紳二,広木彰,材木幸二,野木達夫: "分割作用素法を用いた超並列計算による3次元デバイスシミュレーション" 信学技報,SDM92-91,VLD92-66. 45-51 (1992)
[Publications] T.nogi: "ADENA computer IV" Mem.Fac.Eng.kyoto Univ.55. (1993)
[Publications] E.Beretta,A.fasano,Y.hosono: "Equilibrim of a phytoplankton population in alaboratory controlled system" Surveys on Mathematics for Industry. 1. 283-336 (1992)
[Publications] E.beretta,A.Fasano,Y.Hosono,Kolmanovski: "The stability analysis of the phytoplankton vertical steady states in a laboratory test tube." Math.Methods in Applied Sciences. 1. 283-336 (1992)
[Publications] B.Ilyas,Hosono: "Existence of travelling wave solutions for the epidemic model" Acta Humanistica et Scientifica Universitatis Sangio kyotiensis. 21. (1993)
[Publications] M.Kuwamua,S.I.Ei,M.Mimura: "Very slow dynamics for some reaction-deffusion system with activator-inhibitor type" Japan J.Indust.Appl.Math.9. 35-77 (1992)
[Publications] T.Mimura,T.Tsujikawa,R.Kobayashi: "Formation of band-type electric patterns in Characean cells" J.Math.Biol.30. 513-545 (1992)
[Publications] T.Sekimura,M.Mimura: "Amodel for celluar pattern formation in Dictyostelium slug" Forma. 7. 27-37 (1992)
[Publications] T.Ikeda,M.Mimura: "An interfacial approach to regional segregation of two competing species mediated by a predator" J.Math.Biol.
[Publications] E.Beretta,A.Fasaon,Y.Hosono,Kolmaonvski: "The stability analysis of the phytoplankton vertical steady states in a laboratory test tube." Math Methods in Applied Sciences. 1. 283-336 (1992)
[Publications] B.Ilyas,Y.Hosono: "Existence of travelling wave solutions for the epidemic model" Acta Humanistica et Scientifica Universitatis Sangio Kyotiensis. 21. (1993)
[Publications] M.Kuwamua,S.I.Ei,M.mimura: "Very slow dynamics for some reaction-diffusion system with activator-inhibitor type" Japan J.Indust.Appl.Math.9. 35-77 (1992)
[Publications] T.Mimura,T.Tsujikawa,R.Kobyashi: "Formation of band-type electric patterns in Characean cells" J.Math.Biol.30. 513-545 (1992)
[Publications] T.Sekimura,M.Mimura: "A model for celluar pattern formation in Dictyostelium slug" Forma. 7. 27-37 (1992)
[Publications] T.Ikeda,M.Mimura: "An interfacial approach to regional segregation of two competing species mediated by a predator" J.Math.Biol.
[Publications] S.yotsutani: "Chemical interfacial reagtion models with radial symmetry" Nonlinar Diffusion Equations and their Epuilibrium states. 561-572 (1992)
[Publications] N.Kawano,E.Yanagida,S.Yotutani: "Structure theorems for positive radial solutions to Δu+k(|x|)u^p=O in R^n" Funkcial.Ekvac.
[Publications] N.kawano,E.Yanagida,S.Yotsutani: "Structure theorems for positive radial solutions to div(|Du|^<m-2>Du)+K(|X|)u^q=O in R^n" J.Math.Soc.Japan.
[Publications] E.Yanagida,S.Yotsutani: "Existence of nodal fast-decay solution to Δu+K(|x|)|u|^<p-1>u=O in R^n" Nonlinear Analysis.

1992 Fiscal Year Annual Research Report

科学技術における数値的手法の総合的研究

Principal Investigator

牛島 照夫 電気通信大学, 電気通信学部, 教授 (10012410)

Research Products

[Publications] M.Matsuki,T.Ushijima: "An iegenvalue problem for a system of finite difference equations approximating a linear wave equaiton" Japan Journal of Industrial and Applied Mathematics. 9. 91-116 (1992)

[Publications] T.Ushijima,MMatsuki: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Proc.Int.Conf.on Functional Anaysis and Related Topics. (1993)

[Publications] R.Fu,T.Uxhijima: "Finite element analysis of free vibration of liquid-filled axisymmetric tanks" Acta Mathematicae Applicatae Sinica.

[Publications] K.Sugihara,M Iri: "Construction of the Voronoi diagram for¨one million¨generators in single-precision arithmetic" Proceedings of the IEEE. 80. 1471-1484 (1992)

[Publications] M.Iri: "How to generate realistic sample problems for network optimization" Lecture Notes in Computer Science. 650. 342-350 (1992)

[Publications] F.Kikuchi,M.Hara,T.wada: "A mixed finite element method for 3-D analysis of resonators" Sci.papers Coll.Arts&Sci.,Univ.Tokyo. 42. 111-129 (1993)

[Publications] F.kikuchi: "Numerical analysis of electrostatic and magnetostatic problems" Sugaku Expositions. 6. (1993)

[Publications] 金山 寛,池口 修一,松木 直美,遠藤 研二,菊地 文雄: "辺要素を用いた3次元非線形磁場解析" シュミレーション. 11. 212-220 (1992)

[Publications] T.Yamada,F.Kikuchi: "An arbitrary Lagrangian-Eulerian finite element method for incompressible hyperelasticity" Computer Methods in Applied Mechanics and Engineering. (1993)

[Publications] A.Kohda,Y.Shinogara: "Numerical Analysis of the quasiperiodic solutions to Duffing type equations" Japan J.Indust.Appl.Math.

[Publications] T.Sakurai,H.sugiura,T.Torii: "Factorization of a polynomial by rational hermite interpolation" Numerical Algorithm. 3. 411-418 (1992)

[Publications] H.sugiura,T.Torii: "Polynomial interpolation on quasiequidistributed nodes on unit circle" SIAM J.Numer Anal.29. 1154-1165 (1992)

[Publications] T.Torii,T.Sakurai,H.sugiura: "An application of Sunzi's teorem for solving algebraic equations" Proc.1st China-Japan Joint Seminar on Numerical Mathematics.

[Publications] T.Hasegawa,H.Sugiura,T.Torii: "Positivity of the weights of extended Clenshaw-Clenshaw-Curtis quadrature rules" Math.Comp.

[Publications] M.T.Nakao: "A numerical verification method for the existence of weak solutions for nonlinear boundry value problems" Journal of Mathematical Analysis and Applications. 164. 489-507 (1992)

[Publications] 小田中 紳二,広木 彰,材木 幸二,野木 達夫: "分割作用素法を用いた超並列計算による3次元デバイスシミュレーション" 信学技報,SDM92-91,VLD92-66. 45-51 (1992)

[Publications] T.nogi: "ADENA computer IV" Mem.Fac.Eng.kyoto Univ.55. (1993)

[Publications] E.Beretta,A.fasano,Y.hosono: "Equilibrim of a phytoplankton population in alaboratory controlled system" Surveys on Mathematics for Industry. 1. 283-336 (1992)

[Publications] E.beretta,A.Fasano,Y.Hosono,Kolmanovski: "The stability analysis of the phytoplankton vertical steady states in a laboratory test tube." Math.Methods in Applied Sciences. 1. 283-336 (1992)

[Publications] B.Ilyas,Hosono: "Existence of travelling wave solutions for the epidemic model" Acta Humanistica et Scientifica Universitatis Sangio kyotiensis. 21. (1993)

[Publications] M.Kuwamua,S.I.Ei,M.Mimura: "Very slow dynamics for some reaction-deffusion system with activator-inhibitor type" Japan J.Indust.Appl.Math.9. 35-77 (1992)

[Publications] T.Mimura,T.Tsujikawa,R.Kobayashi: "Formation of band-type electric patterns in Characean cells" J.Math.Biol.30. 513-545 (1992)

[Publications] T.Sekimura,M.Mimura: "Amodel for celluar pattern formation in Dictyostelium slug" Forma. 7. 27-37 (1992)

[Publications] T.Ikeda,M.Mimura: "An interfacial approach to regional segregation of two competing species mediated by a predator" J.Math.Biol.

[Publications] E.Beretta,A.Fasaon,Y.Hosono,Kolmaonvski: "The stability analysis of the phytoplankton vertical steady states in a laboratory test tube." Math Methods in Applied Sciences. 1. 283-336 (1992)

[Publications] B.Ilyas,Y.Hosono: "Existence of travelling wave solutions for the epidemic model" Acta Humanistica et Scientifica Universitatis Sangio Kyotiensis. 21. (1993)

[Publications] M.Kuwamua,S.I.Ei,M.mimura: "Very slow dynamics for some reaction-diffusion system with activator-inhibitor type" Japan J.Indust.Appl.Math.9. 35-77 (1992)

[Publications] T.Mimura,T.Tsujikawa,R.Kobyashi: "Formation of band-type electric patterns in Characean cells" J.Math.Biol.30. 513-545 (1992)

[Publications] T.Sekimura,M.Mimura: "A model for celluar pattern formation in Dictyostelium slug" Forma. 7. 27-37 (1992)

[Publications] T.Ikeda,M.Mimura: "An interfacial approach to regional segregation of two competing species mediated by a predator" J.Math.Biol.

[Publications] S.yotsutani: "Chemical interfacial reagtion models with radial symmetry" Nonlinar Diffusion Equations and their Epuilibrium states. 561-572 (1992)

[Publications] N.Kawano,E.Yanagida,S.Yotutani: "Structure theorems for positive radial solutions to Δu+k(|x|)u^p=O in R^n" Funkcial.Ekvac.

[Publications] N.kawano,E.Yanagida,S.Yotsutani: "Structure theorems for positive radial solutions to div(|Du|^<m-2>Du)+K(|X|)u^q=O in R^n" J.Math.Soc.Japan.

[Publications] E.Yanagida,S.Yotsutani: "Existence of nodal fast-decay solution to Δu+K(|x|)|u|^<p-1>u=O in R^n" Nonlinear Analysis.

牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)

[Publications] 金山寛,池口修一,松木直美,遠藤研二,菊地文雄: "辺要素を用いた3次元非線形磁場解析" シュミレーション. 11. 212-220 (1992)

[Publications] 小田中紳二,広木彰,材木幸二,野木達夫: "分割作用素法を用いた超並列計算による3次元デバイスシミュレーション" 信学技報,SDM92-91,VLD92-66. 45-51 (1992)