1999 Fiscal Year Annual Research Report

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

Research Project

Project/Area Number	10555023
Research Institution	Nihon University
Principal Investigator	中村正彰日本大学, 理工学部, 助教授 (00017419)
Co-Investigator(Kenkyū-buntansha)	田端正久九州大学, 数理学研究科, 教授 (30093272) 大森克史富山大学, 教育学部, 教授 (20110231) 今井仁司徳島大学, 工学部, 教授 (80203298) 張紹良東京大学, 工学部, 助教授 (20252273) 森正武京都大学, 数理解析研究所, 所長 (20010936)
Keywords	computation mechanics / domain decomposition / precondition / simulation / スペクトル法 / spinodal decomposition / fluid dynamics / 無限精度
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. 1.今年度は二重指数関数型変換を中心として研究を行い,また振動型積分に対する自動計算サブルーチンの開発を行った. 2.数値シミュレーション手法を検討することで,偏微分方程式系のアトラクターを任意の精度(任意の次数)で近似する手法の確立に成功した.また,このアトラクターのリャプノフ指数の数値計算にも成功した. 3.偏微分方程式の超高精度数値シミュレーションを行い自由境界問題や逆問題に適用してその有効性を確認した. 4.超高精度数値シミュレーションの並列計算による高速化をPVMを用いて実現した.具体的には,主要な計算部分である,ガウスの消去法の多倍長計算の並列計算に成功した. 5.流速が一次有限要素と同程度の近似精度の計算スキームで行われるとき,流脈線の計算にはホイン法を用いるのが,精度と計算効率の観点から最適であることを示した. 6.地球マントル対流の数値シミュレーションを行うために,有限要素コードを作成した.3次元計算を実行し,まず,流速,圧力,温度が理論値とおりの収束精度が得られることを確認した.

Research Products
(25 results)

All Other

All Publications (25 results)

[Publications] N.Ishimura amd M.Nakamura: "Nonexistence of monotonic solutions of some third order ODE relative to the Kuramoto-Sivashinsky equation,"Tiwanese journal of mathematics. (to appear). (2000)
[Publications] T.Hanada,M.Nakamura and C.Shima: "Numerical analysis of Eguchi-Oki-Matsumura equations."Gakuto Internatonal Series,Mathematical Sciences and Applicatio:Advances of numerical mathematics in Japan and China. 12. 213-222 (1999)
[Publications] H.Imai,N.Ishimura and T.Ushijima: "A Crystalline Motion of Spiral-Shaped Curves with Symmetry"Journal of Mathematical Analysis and Applications,. 240. 115-127 (1999)
[Publications] T.Ooura and M.Mori: "A robust double exponential formula for Fourier-type integrals"J.Comput.Appl.Math.. 112. 229-241 (1999)
[Publications] H.Imai,T.Takeuchi and M.Kushida;: "ON NUMERICAL SIMULATION OF PARTIAL DIFFERENTIAL EQUATIONS IN INFINITE PRECISION,"Advances in Mathematical Sciences and Applications. 9. 1007-1016 (1999)
[Publications] H.Imai,N.Ishimura and T.Ushijima: "MOTION OF SPIRALS BY CRYSTALLINE CURVATURE,"Mathematical Modelling and Numerical Analysis,. 33. 797-806 (1999)
[Publications] T.Sakuragi and K.Ohmori: "Casting simulations using the CIP-Galerkin method,"Computational Fluid Dynamics Journal. 8. 34-42 (1999)
[Publications] B.Yu,G.-C.Feng and S.-L.Zhang: "The aggregate constaint homotopy method for nonconvex noulinear programming"Nonlinear Analysis:Theory,Methods&Applications. (to appear). (2000)
[Publications] S.-L.Zhang,Y.Oyanagi and M.Sugihara: "Necessary and Sufficient Conditions for Convergence of Orthomin(k) on Singular and Inconsistent Linear Systems"Numerische Mathematik. (to appear). (2000)
[Publications] M.Tabata and A.Suzuki: "A stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell,"Comp.Meth.Appl.Mech.Engrg. (to appear).
[Publications] N.Saito and H.Fujita: "Remarks on traces of H^1 function defined in a domain with coeners."Journal of Mathematical Science of the University of Tokyo,. (to appear). (2000)
[Publications] T.Yamada: "On fast iterative solvers for Image-based finite element method,"USNCCM99. Books of abstrcts. 273-273 (1999)
[Publications] H.Imai,T.Takeuchi,M.Nakamura and N.Ishimura: "A DIRECT APPROACH TO AN INVERSE PROBLEM"GAKUTO International Series,Mathematical Sciences and Applications,Advances in numerical mathematics in Japan and China. 12. 223-232 (1999)
[Publications] S.Komurasaki,T.Kawamura and K.Kuwahara: "Formation of a Fire Tornado and Its Breakdown"Theoretical and Applied Mechanics. 48. 331-338 (1999)
[Publications] M.Kan and T.Kawamura: "Numerical Formation of the Barchan Sand Dune"Theoretical and Applied Mechanics. 48. 349-354 (1999)
[Publications] A.Suzuki,M.Tabata,and S.Honda: "Numerical solution of an unsteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)
[Publications] K.Itakura and M.Tabata: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)
[Publications] M.Tabata: "Slip boundary conditions and rigid body movements in finite element analysis."Gakuto International Series, Mathematical Sciences and Applications:Advances in Numerical Mathematics in Japan and China. 12. 117-124 (1999)
[Publications] 阿部邦美,緒方秀教,杉原正顯,張紹良,三井斌友: "特異な係数行列をもつ連立一次方程式に対するCR法の収束性"日本応用数理学会論文誌. 9. 1-13 (1999)
[Publications] 菅牧子、河村哲也、岩津玲磨: "低マッハ数近似による熱対流の数値シミュレーション"日本機械学会論文集(B編). 65巻629号. 108-115 (1999)
[Publications] 菅牧子、河村哲也、林農: "砂面上に立てられた円柱まわりの流れと砂の動きの数値的研究"日本機械学会論文集(B編). 65巻629号. 124-129 (1999)
[Publications] 河村哲也、諸星ゆき、神近牧男: "鳥取砂丘上の風速場の3次元数値シミュレーション"日本砂丘学会誌. 46巻2号. (掲載予定)
[Publications] 菅牧子,河村哲也: "典型的な砂丘地形の形成過程の数値シミュレーション"日本砂丘学会誌. 46巻2号. (掲載予定)
[Publications] 藤田宏: "応用数学の流れを見る -山口先生を偲んで-"応用数理学会学会誌. vol.10,No.2. 55-61 (2000)
[Publications] Eds.H.Kawarada,M.Nakamura and C.Z.Shi: "Advances in numerical mathematics in Japan and China: the fourth Japan China joint-seminar on numerical mathematics"Gakko Tosho. 200 (1999)

1999 Fiscal Year Annual Research Report

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

Principal Investigator

中村 正彰 日本大学, 理工学部, 助教授 (00017419)

Research Products

[Publications] N.Ishimura amd M.Nakamura: "Nonexistence of monotonic solutions of some third order ODE relative to the Kuramoto-Sivashinsky equation,"Tiwanese journal of mathematics. (to appear). (2000)

[Publications] T.Hanada,M.Nakamura and C.Shima: "Numerical analysis of Eguchi-Oki-Matsumura equations."Gakuto Internatonal Series,Mathematical Sciences and Applicatio:Advances of numerical mathematics in Japan and China. 12. 213-222 (1999)

[Publications] H.Imai,N.Ishimura and T.Ushijima: "A Crystalline Motion of Spiral-Shaped Curves with Symmetry"Journal of Mathematical Analysis and Applications,. 240. 115-127 (1999)

[Publications] T.Ooura and M.Mori: "A robust double exponential formula for Fourier-type integrals"J.Comput.Appl.Math.. 112. 229-241 (1999)

[Publications] H.Imai,T.Takeuchi and M.Kushida;: "ON NUMERICAL SIMULATION OF PARTIAL DIFFERENTIAL EQUATIONS IN INFINITE PRECISION,"Advances in Mathematical Sciences and Applications. 9. 1007-1016 (1999)

[Publications] H.Imai,N.Ishimura and T.Ushijima: "MOTION OF SPIRALS BY CRYSTALLINE CURVATURE,"Mathematical Modelling and Numerical Analysis,. 33. 797-806 (1999)

[Publications] T.Sakuragi and K.Ohmori: "Casting simulations using the CIP-Galerkin method,"Computational Fluid Dynamics Journal. 8. 34-42 (1999)

[Publications] B.Yu,G.-C.Feng and S.-L.Zhang: "The aggregate constaint homotopy method for nonconvex noulinear programming"Nonlinear Analysis:Theory,Methods&Applications. (to appear). (2000)

[Publications] S.-L.Zhang,Y.Oyanagi and M.Sugihara: "Necessary and Sufficient Conditions for Convergence of Orthomin(k) on Singular and Inconsistent Linear Systems"Numerische Mathematik. (to appear). (2000)

[Publications] M.Tabata and A.Suzuki: "A stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell,"Comp.Meth.Appl.Mech.Engrg. (to appear).

[Publications] N.Saito and H.Fujita: "Remarks on traces of H^1 function defined in a domain with coeners."Journal of Mathematical Science of the University of Tokyo,. (to appear). (2000)

[Publications] T.Yamada: "On fast iterative solvers for Image-based finite element method,"USNCCM99. Books of abstrcts. 273-273 (1999)

[Publications] H.Imai,T.Takeuchi,M.Nakamura and N.Ishimura: "A DIRECT APPROACH TO AN INVERSE PROBLEM"GAKUTO International Series,Mathematical Sciences and Applications,Advances in numerical mathematics in Japan and China. 12. 223-232 (1999)

[Publications] S.Komurasaki,T.Kawamura and K.Kuwahara: "Formation of a Fire Tornado and Its Breakdown"Theoretical and Applied Mechanics. 48. 331-338 (1999)

[Publications] M.Kan and T.Kawamura: "Numerical Formation of the Barchan Sand Dune"Theoretical and Applied Mechanics. 48. 349-354 (1999)

[Publications] A.Suzuki,M.Tabata,and S.Honda: "Numerical solution of an unsteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)

[Publications] K.Itakura and M.Tabata: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)

[Publications] M.Tabata: "Slip boundary conditions and rigid body movements in finite element analysis."Gakuto International Series, Mathematical Sciences and Applications:Advances in Numerical Mathematics in Japan and China. 12. 117-124 (1999)

[Publications] 阿部邦美,緒方秀教,杉原正顯,張紹良,三井斌友: "特異な係数行列をもつ連立一次方程式に対するCR法の収束性"日本応用数理学会論文誌. 9. 1-13 (1999)

[Publications] 菅牧子、河村哲也、岩津玲磨: "低マッハ数近似による熱対流の数値シミュレーション"日本機械学会論文集(B編). 65巻629号. 108-115 (1999)

[Publications] 菅牧子、河村哲也、林農: "砂面上に立てられた円柱まわりの流れと砂の動きの数値的研究"日本機械学会論文集(B編). 65巻629号. 124-129 (1999)

[Publications] 河村哲也、諸星ゆき、神近牧男: "鳥取砂丘上の風速場の3次元数値シミュレーション"日本砂丘学会誌. 46巻2号. (掲載予定)

[Publications] 菅牧子,河村哲也: "典型的な砂丘地形の形成過程の数値シミュレーション"日本砂丘学会誌. 46巻2号. (掲載予定)

[Publications] 藤田宏: "応用数学の流れを見る -山口先生を偲んで-"応用数理学会学会誌. vol.10,No.2. 55-61 (2000)

[Publications] Eds.H.Kawarada,M.Nakamura and C.Z.Shi: "Advances in numerical mathematics in Japan and China: the fourth Japan China joint-seminar on numerical mathematics"Gakko Tosho. 200 (1999)

中村正彰日本大学, 理工学部, 助教授 (00017419)