2002 年度実績報告書

巨大領域のための有限要素法と領域分割計算ならびに関連事項

研究課題

研究課題/領域番号	14340031
研究機関	電気通信大学
研究代表者	牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)
研究分担者	小山大介電気通信大学, 電気通信学部, 助手 (60251708) 加古孝電気通信大学, 電気通信学部, 教授 (30012488) 竹田辰興電気通信大学, 電気通信学部, 教授 (60272746) 藤間昌一茨城大学, 理学部, 助教授 (00209082) 田端正久九州大学, 大学院・数理学研究院, 教授 (30093272)
キーワード	国際研究者交流 / 基本解近似解法 / 水の波散乱シミュレータ / 無限領域ヘルムホルツ問題 / 円外帰着波動ノイマン境界条件問題 / ニューラルネットワーク変分同化法 / 無限領域向有限要素法 / 有限要素流体計算
研究概要	1.研究代表者を中心として得られた知見円外帰着波動問題のFSM近似(FSM=Fundamental Solution Method、基本解近似解法)の数学解析と数値計算を実施した。三次元一定水深水域における柱状障碍物外部の水の波の高精度計算の一環として、円形柱状島外部の水の波散乱シミュレータの作成を、円外帰着波動ノイマン境界条件問題のFSM近似解を用い、研究協力者千葉文浩、大關雅己らの協力を得て開始した。 2.分担者が著しい成果を収めた研究課題の例(分担者名) (1)ニューラルネットワーク変分同化法による逆問題解法(竹田辰興)。(2)無限領域におけるヘルムホルツ方程式の数値解法の開発と、その応用としての音声生成問題(加古孝)。(3)精度保証法の技法を用いた有限要素法の射影誤差の定量的見積り法の開発(山本野人)。(4)金属の焼き鈍し時の結晶粒界の運動を記述する平均曲率流方程式の自己相似解の完全な分類(中村健一)。(5)三次元Helmholtz問題への仮想領域法の適用における事前誤差評価の導出と対応する数値実験による確認(小山大介)。(6)密度依存ナビエ・ストークス方程式の密度方程式への保存型風上近似法の適用、ならびに、ナビエ・ストークス方程式へ特性有限要素法の適用(田端正久)。(7)3次元渦電流解析の領域分割法に対するA一φ法の適用とその基本部分プログラムの作成(金山寛)。(8)混ざらない非圧縮性の2流体問題の有限要素近似における正則化ヘビサイド関数を用いた界面の収束性証明(大森克史、藤間昌一)。(9)ルンゲ・クッタ型解法の時間発展偏微分方程式への適用(小藤俊幸)。 3.海外共同研究者である中国北京清華大学韓厚徳教授を2002年7月26日〜8月16日電気通信大学に招聘し、共同研究を実施した。 4.2003年1月8日〜10日に研究打ち合わせ会「横浜研究会」を、KKRホテルポートピア横浜で開催した。分担者の他に専門家を招待して講演を依頼した。会期中に海洋科学技術センターを訪問し、世界最高速ハイパフォーマンスコンピュータシステム地球シミュレータを見学、情報収集ならびに研究連絡を実施した。

研究成果

(21件)

すべてその他

すべて文献書誌 (21件)

[文献書誌] USHIJIMA, Teruo: "Equi-distant collocation method for periodic functions with kernel expression"Proceedings of Fifth China-Japan Joint Seminar on Numerical Mathematics. 220-226 (2002)
[文献書誌] USHIJIMA, Teruo, CHIBA, Fumihiro: "A fundamental solution method for the reduced wave problem in a domain exterior to a disc"Proceedings of the International Conference on Recent Advances in Computational Mathematics. (to appear).
[文献書誌] USHIJIMA, Teruo, CHIBA, Fumihiro: "Error estimates for a fundamental solution method applied to reduced wave problems in a domain exterior to a disc"Proceedings of the Sixth Japan-China Joint Seminar. (to appear).
[文献書誌] Tatsuoki Takeda, Ali Liaqat, Makoto Fukuhara: "Neural network with residual minimization training as a general inverse solver"Proceedings of the International Workshop on Modern Science and Technology 2002. 145-150 (2002)
[文献書誌] Xiao Feng Ma, Tatsuoki Takeda: "Asymmetric Abel inversion by neural network for reconstruction of plasma density distribution"Nuclear Instruments and Methods in Physics Research. Vol.492,No.1-2. 178-189 (2002)
[文献書誌] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Optimal estimation of parameters of dynamical systems by neural network collocation method"Computer Physics Communications. Vol.150,No.3. 215-234 (2003)
[文献書誌] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Applying neural network collocation method to an incompletely known dynamical system via weak constraint data assimilation"Monthly Weather Review 2003. (to appear).
[文献書誌] H.M.Nasir, T.Kako, D.Koyama: "A mixed-type finite element approximation for radiation problems using fictitious domain method"Journal of Computational and Applied Mathematics. Vol.152. 377-392 (2003)
[文献書誌] CHIBA, Fumihiro, KAKO, Takashi: "Newmark's method and discrete energy applied to resistive MHD equation"Vietnam Journal of Mathematics. (to appear).
[文献書誌] KAKO, Takashi, NASIR, Haniffa Mohamed: "Domain decomposition method applied to a coupling vibration problem between shell and acoustics"Domain Decomposition Methods in Science and Engineering Thirteenth International Conference on Domain Decomposition. 487-493 (2002)
[文献書誌] Tohiyuki Koto: "Stability of Runge-Kutta methods for delay integro-differential equations"Journal of Computational and Applied Mathematics. Vol.145,No.2. 483-492 (2002)
[文献書誌] Toshiyuki Koto: "Stability analysis of numerical methods for delay integro-differential equations"京都大学数理解析研究所講究録. Vol.1265. 189-199 (2002)
[文献書誌] Yamamoto, N., Hayakawa, K.: "Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains"Proceedings of the Sixth Japan-China Joint Seminar. (to appear).
[文献書誌] Toshiko Ogiwara, Ken-Ichi Nakamura: "Asymptotic behavior of solutions to a model of spiral crystal growth"数理解析研究所講究録. 1258「非線形拡散系とその周辺」. 72-84 (2002)
[文献書誌] Toshiko Ogiwara, Ken-Ichi Nakamura: "Asymptotic behavior of solutions for nonlinear diffusion equations"Proceedings of the second international conference on nonlinear analysis and convex analysis. (to appear). (2003)
[文献書誌] Ken-Ichi Nakamura, Hisashi Okamoto, Hiroki Yagisita: "Blow-up solutions appearing in the vorticity dynamics with linear strain"Journal of Mathematical Fluid Mechanics. (to appear).
[文献書誌] D.Koyama: "A controllability method with an artificial boundary condition for the exterior Helmholtz problem"Japan Journal of Industrial and Applied Mathematics. Vol.20,No.1. 117-145 (2003)
[文献書誌] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. Vol.92. 161-177 (2002)
[文献書誌] Hiroshi KANAYAMA, Daisuke TAGAMI, Koichiro IMOTO: "Effectiveness of the A-phi method for 3-D eddy current problems"Theoretical and Applied Mechanics. Vol.51. 411-417 (2002)
[文献書誌] Hiroshi KANAYAMA, Ryuji SHIOYA, Daisuke TAGAMI, Satoshi MATSUMOTO: "3-D eddy current computation for a transformer tank"COMPEL. Vol.21,No.4. 554-562 (2002)
[文献書誌] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interfaces"Computational Fluid Dynamics Journal. (to appear).

2002 年度 実績報告書

巨大領域のための有限要素法と領域分割計算ならびに関連事項

研究代表者

牛島 照夫 電気通信大学, 電気通信学部, 教授 (10012410)

研究成果

[文献書誌] USHIJIMA, Teruo: "Equi-distant collocation method for periodic functions with kernel expression"Proceedings of Fifth China-Japan Joint Seminar on Numerical Mathematics. 220-226 (2002)

[文献書誌] USHIJIMA, Teruo, CHIBA, Fumihiro: "A fundamental solution method for the reduced wave problem in a domain exterior to a disc"Proceedings of the International Conference on Recent Advances in Computational Mathematics. (to appear).

[文献書誌] USHIJIMA, Teruo, CHIBA, Fumihiro: "Error estimates for a fundamental solution method applied to reduced wave problems in a domain exterior to a disc"Proceedings of the Sixth Japan-China Joint Seminar. (to appear).

[文献書誌] Tatsuoki Takeda, Ali Liaqat, Makoto Fukuhara: "Neural network with residual minimization training as a general inverse solver"Proceedings of the International Workshop on Modern Science and Technology 2002. 145-150 (2002)

[文献書誌] Xiao Feng Ma, Tatsuoki Takeda: "Asymmetric Abel inversion by neural network for reconstruction of plasma density distribution"Nuclear Instruments and Methods in Physics Research. Vol.492,No.1-2. 178-189 (2002)

[文献書誌] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Optimal estimation of parameters of dynamical systems by neural network collocation method"Computer Physics Communications. Vol.150,No.3. 215-234 (2003)

[文献書誌] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Applying neural network collocation method to an incompletely known dynamical system via weak constraint data assimilation"Monthly Weather Review 2003. (to appear).

[文献書誌] H.M.Nasir, T.Kako, D.Koyama: "A mixed-type finite element approximation for radiation problems using fictitious domain method"Journal of Computational and Applied Mathematics. Vol.152. 377-392 (2003)

[文献書誌] CHIBA, Fumihiro, KAKO, Takashi: "Newmark's method and discrete energy applied to resistive MHD equation"Vietnam Journal of Mathematics. (to appear).

[文献書誌] KAKO, Takashi, NASIR, Haniffa Mohamed: "Domain decomposition method applied to a coupling vibration problem between shell and acoustics"Domain Decomposition Methods in Science and Engineering Thirteenth International Conference on Domain Decomposition. 487-493 (2002)

[文献書誌] Tohiyuki Koto: "Stability of Runge-Kutta methods for delay integro-differential equations"Journal of Computational and Applied Mathematics. Vol.145,No.2. 483-492 (2002)

[文献書誌] Toshiyuki Koto: "Stability analysis of numerical methods for delay integro-differential equations"京都大学数理解析研究所講究録. Vol.1265. 189-199 (2002)

[文献書誌] Yamamoto, N., Hayakawa, K.: "Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains"Proceedings of the Sixth Japan-China Joint Seminar. (to appear).

[文献書誌] Toshiko Ogiwara, Ken-Ichi Nakamura: "Asymptotic behavior of solutions to a model of spiral crystal growth"数理解析研究所講究録. 1258「非線形拡散系とその周辺」. 72-84 (2002)

[文献書誌] Toshiko Ogiwara, Ken-Ichi Nakamura: "Asymptotic behavior of solutions for nonlinear diffusion equations"Proceedings of the second international conference on nonlinear analysis and convex analysis. (to appear). (2003)

[文献書誌] Ken-Ichi Nakamura, Hisashi Okamoto, Hiroki Yagisita: "Blow-up solutions appearing in the vorticity dynamics with linear strain"Journal of Mathematical Fluid Mechanics. (to appear).

[文献書誌] D.Koyama: "A controllability method with an artificial boundary condition for the exterior Helmholtz problem"Japan Journal of Industrial and Applied Mathematics. Vol.20,No.1. 117-145 (2003)

[文献書誌] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. Vol.92. 161-177 (2002)

[文献書誌] Hiroshi KANAYAMA, Daisuke TAGAMI, Koichiro IMOTO: "Effectiveness of the A-phi method for 3-D eddy current problems"Theoretical and Applied Mechanics. Vol.51. 411-417 (2002)

[文献書誌] Hiroshi KANAYAMA, Ryuji SHIOYA, Daisuke TAGAMI, Satoshi MATSUMOTO: "3-D eddy current computation for a transformer tank"COMPEL. Vol.21,No.4. 554-562 (2002)

[文献書誌] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interfaces"Computational Fluid Dynamics Journal. (to appear).

2002 年度実績報告書

牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)