領域分割法による計算力学の新解法の開発とその数学的検証

2000 Fiscal Year Annual Research Report

• Project/Area Number: 10555023
• Research Institution: Nihon University
• Principal Investigator: 中村 正彰 日本大学, 理工学部, 教授 (00017419)
• Co-Investigator(Kenkyū-buntansha): 田端 正久 九州大学, 数理学研究院, 教授 (30093272) ; 今井 仁司 徳島大学, 工学部, 教授 (80203298) ; 池田 勉 竜谷大学, 理工学部, 教授 (50151296) ; 森 正武 京都大学, 数理解析研究所, 所長 (20010936) ; 張 紹良 東京大学, 工学系研究科, 助教授 (20252273)
• Keywords: computation mechanics / domain decomposition / precondition / simulation / fluid dynamics / spinodal decomposition / infinnite precision / PVM (parallel virtual machine)

Research Abstract

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.
・計算力学の新解法開発
高速計算手法の開発と応用。
PVMを用いて,ガウスの消去法の並列計算プログラムの開発に成功した。
無限精度数値シミュレーションの自由境界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的解析に成功した.
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。
流脈線の誤差解析をハウスドルフ距離を用いて行った。
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.
表面張力を考慮した2流体問題への領域分割法の適用妥当条件を得ることに成功した。
Navier-Stokes方程式の摩擦型境界条件問題.
超電導を記述するギンズブルクーランダウ方程式の解析.
・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.

Research Products

• [Publications] N.Ishimura and M.Nakamura: "Nonexistence of monotonic solutions of some third order ODE relative to the Kuramoto-Sivashinsky equation,"Tiwanese journal of mathematics. 4. 621-625 (2000)
• [Publications] T.Hanada,N.Ishimura and M.Nakamura: "Note on steady solution of the Eguchi-Oki-Matsumura equation."Proc.Japan Acad.. 76. 146-148 (2000)
• [Publications] N.Ishimura and M.Nakamura: "Note on nonexistence of monotonic steady solutions of the Kuramoto-Sivashinsky equation,"Ann.Univ.Ferrara,Sez.VII,Sc.Mat.. XLVV. (2000)
• [Publications] H.Ikeda and T.Ikeda: "bifurcation phenomena from standing pulse in some bistable reaction-diffusion systems."Journal of Dynamics and Differential Equations,. 12. 117-167 (2000)
• [Publications] T.Ikeda,H.Ikeda and M.Mimura: "Hopf bifurcation of travelling pulse in some bistable reaction-diffusion systems."Methods and Applications of Analysis,. 7,No.1. 165-194 (2000)
• [Publications] M.Mimura,M.Nagayama,H.Ikeda,and T.Ikeda: "Dynamics of travelling breathers arising in reaction-diffusion systems-ODE modelling an proach."Hiroshima Mathematical Journal,. 30,No.2. 221-256 (2000)
• [Publications] M Tabata and A.Suzuki: "A stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtle number in a spherical shell,"Comput.Methods Appl.Mech.Engrg.. 190. 387-402 (2000)
• [Publications] Tarmizi,T.Takeuchi,H.Imai and M.Kushida: "Numerical simulation of one-dimensional free boundary problems in infinite precision."Advances in Mathematical Sciences and Applications.. 10,No.2. (2000)
• [Publications] Tarmizi,T.Takeuchi,H.Imai and M.Kushida: "Numerical simulation of some one-dimensional free boundary problems in arbitrary precision."GAKUTO International Series, Mathematical Sciences and Applications.. 14. 440-452 (2000)
• [Publications] H.Imai,N.ishimura and T.Aiki: "Analysis on ohe-phase Stefan problems for semilinear parabolic equations with the Dirichlet boundary condition."GAKUTO International Series, Mathematical Sciences and Applications.. 14. 176-183 (2000)
• [Publications] 大森克史: "アダプティブ有限要素法に対するメッシュ生成法の評価."富山大学 教育学部研究論集. 30. 33-44 (2000)
• [Publications] H.Suito and H.kawarada,: "shape optimization for an acoustic problems."Proceedings of 12th international conferencs on domain decomposition methods,. 419-426 (2001)
• [Publications] M Tabata and D.Tagami: "A finite element analysis of a linerarized problem of the Navier-Stokes equations with surface tension,"SIAM journal on Numerical Analysis,. 38. 40-57 (2000)
• [Publications] M Tabata and D.Tagami: "Error estimate for finite element approximation of drag and lift in nonstationary Navier-Stokes flows."Japan Journal of Industrial and Applied Mathematics.. 17. 371-389 (2000)
• [Publications] M Tabata,: "Uniform solvability of finite element solution in approximate domains."Japan Journal of Industrial and Applied Mathematics.. (2000)
• [Publications] S.-L.Zhang,R..-H.Wang,Y.Oyanagi and W.Li,: "A kind of bbivariate cubic splines and related linear operators on Type-I triangulation."Japan Journal of Industrial and Applied Mathematics.. 17-3. 391-402 (2000)
• [Publications] S.-L.Zhang,Y.Oyanagi and M.sugihara,: "Necessary and sufficient conditions for convergences of Orthomin (k) on singular and inconsistent linear systems."Numerisch Mathematik. 87-2. 391-405 (2000)
• [Publications] T.Akiyama,H.Kasai and M.Tsutsumi,: "On the existence of the solutions of the time dependent Ginzugurg-Landau equations in R^3,"Funckciakaj Ekvacioj. 43. 255-270 (2000)
• [Publications] T.Akiyama,H.Kasai and M.Tsutsumi,: "On the Cauchy problems of the time dependent Ginzugurg-Landau equations in R^3,"GAKUTO International Series, Mathematical Sciences and Applications.. 14. 1-10 (2000)
• [Publications] N.Saito and H,Fujita: "Remarks on traces of H^1 function defined in a domain with coners."Journal of Mathematical Science of the University of Tokyo,. 7. 325-345 (2000)
• [Publications] H.Fujita,: "Non-stationary Stokes flows under leak boundary conditions of friction type,"Journal of computing Mathematics.. 19-1. 1-8 (2001)
• [Publications] M.Mori and M.Sugihara,: "The double exponential transformation in numerical analysis."Journal of Comput.Appl.Math.. (to appear). (2001)
• [Publications] M.Mori,: "Optimality of the double exponential transformation in numerical analysis."Sugaku. (to appear). (2001)
• [Publications] S.Saitoh and M.Mori,: "representation of analytic functions in terms of local values by means of the Riemann mapping function,"Complex Variables. (to appear). (2001)