2003 Fiscal Year Annual Research Report

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

Research Project

Project/Area Number	14340031
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)	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)
Keywords	国際研究者交流 / ディリクレ境界条件円外帰着波動問題 / 基本解近似解法誤差評価 / 音声生成問題有限要素数値シミュレーション / 三次元ヘルムホルツ問題の仮想領域法・有限要素近似 / 2流体問題質量保存有限要素スキーム / レーリー・ベナール方程式の有限要素スキーム / ニュラルネットワーク
Research Abstract	1.研究代表者を中心として得られた知見ディリクレ境界条件円外帰着波動問題の基本解近似解法において、波源点と拘束点を円周上に等間隔同位相に配置した場合の選点法においては、誤差が波源点の数に対して指数的に減少することを示した。 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)微分方程式定式化による時系列データの補間・予測問題のニューラルネットワーク解法(竹田辰興)。(2)音声生成問題の有限要素法による数値シミュレーション、特に複素固有値の変分公式の導出とその適用(加古孝)。(3)2次元非凸領域ポアソン方程式に対する三角形一次要素誤差評価定数上界の精度保証付き決定(山本野人)。(4)周期的または概周期的空間構造を持つ不均質媒質中を伝播する1次元フロント波の実効速度に及ぼす空間非一様性の影響(中村健一)。(5)三次元ヘルムホルツ問題の仮想領域法・有限要素近似の一様離散inf-sup条件の十分条件の精密化(小山大介)。(6)温度に依存する諸係数を持つレーリー・ベナール方程式に対する誤差評価付きの有限要素スキームの作成(田端正久)。(7)A-φ法による時間調和渦電流問題に対する階層型領域分割法の並列環境における有効性の実証(金山寛)。(8)非混合・非圧縮2流体問題に対するラグランジュ乗数・質量保存・有限要素スキームの導出と理論解析ならびに数値実験(大森克史、藤間昌一)。(9)ルンゲ・クッタ法の偏微分方程式と遅延微分方程式に対する適用(小藤俊幸)。(10)一定角速度回転容器中の滑り境界条件非圧縮性粘性流体運動の定常流れに収束する必要十分条件(渡邊二郎)。 3.2004年2月19日〜20日に研究打ち合わせ会「調布研究会」を、電気通信大学で開催した。分担者の他に専門家を招待して講演を依頼した。

Research Products
(25 results)

All Other

All Publications (25 results)

[Publications] USHIJIMA, Teruo, CHIBA, Fumihiro: "A fundamental solution method for the reduced wave problem in a domain exterior to a disc"Journal of Computational and Applied Mathematics. Vol.152. 545-557 (2003)
[Publications] USHIJIMA, Teruo, CHIBA, Fumihiro: "Error estimates for a fundamental solution method applied to reduced wave problems in a domain exterior to a disc"Journal of Computational and Applied Mathematics. Vol.159. 137-148 (2003)
[Publications] 西崎誉, 牛島照夫, 半田恭介: "翼の等角写像の有限要素計算による同定"航空宇宙技術研究所、航空宇宙数値シュミレーション技術シンポジウム2003. (収録見込み).
[Publications] 千葉文浩, 牛島照夫: "円外帰着波動問題基本解近似解法への多倍長数値計算の適用"数理解析研究所講究録「数値解析と新しい情報技術」. (収録見込み).
[Publications] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Optimal estimation of parameters of dynamical systems by neural network collocation method"Computer Physics Communications. Vol.150. 215-234 (2003)
[Publications] 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. Vol.131. 1696-1714 (2003)
[Publications] NASIR, Haniffa Mohamed, KAKO, Takashi, KOYAMA, Daisuke: "A mixed type finite element approximation for radiation problems using fictitious domain method"Journal of Computational and Applied Mathematics. Vol.152. 377-392 (2003)
[Publications] N.Yamamoto, K.Hayakawa: "Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains"Journal of Computational and Applied Mathematics. Vol.159. 173-183 (2003)
[Publications] Y.Watanabe, N.Yamamoto, M.T.Nakao, T.Nishida: "A numerical verification of nontrivial solutions for the heat convection problem"Journal of Mathematical Fluid Mechanics. Vol.6. 1-20 (2004)
[Publications] T.Koto: "Partitioned Runge-Kutta methods for partial differential equations"京都大学数理解析研究所講究録. Vol.1320. 60-70 (2003)
[Publications] T.Koto: "Stability of θ-methods for delay integro-differential equations"J.Comput.Appl.Math.. Vol.161. 393-404 (2003)
[Publications] 岡本久, 中村健一, 柳下浩紀: "Navier-Stokes方程式の非有界な解は爆発し得る"数理解析研究所講究録. Vol.1322. 102-106 (2003)
[Publications] Ken-Ichi Nakamura: "Bounds for effective speeds of traveling fronts in spatially periodic media"数理解析研究所講究録. Vol.1330. 79-87 (2003)
[Publications] Toshiko Ogiwara, Ken-Ichi Nakamura: "Spiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral crystal growth"Publications of Research Institute for Mathematical Sciences. Vol.39, No.4(in press).
[Publications] Bendong Lou, Matano Hiroshi, Ken-Ichi Nakamura: "Traveling waves in a band domain with quasi-periodically undulating boundaries"数理解析研究所講究録. (to appear).
[Publications] D.Koyama: "Application of a fictitious domain method to 3D Helmholtz problems"数理解析研究所講究録. No.1320. 37-46 (2003)
[Publications] 渡辺二郎: "On incompressible viscous fluid flows with slip boundary conditions"Journal of Computational and Applied Mathematics. Vol.159 No.1. 161-172 (2003)
[Publications] M.Tabata: "Finite element approximation to infinite Prandtl number Boussinesq equations with temperature dependent coefficients-thermal convection problems in a spherical shell"Future Generation Computer Systems. (to appear).
[Publications] Hiroshi KANAYAMA, Hongjie ZHENG, Natsuki MAENO: "A domain decomposition method for large-scale 3-D nonlinear magnetostatic problems"Theoretical and Applied Mechanics. Vol.52. 247-254 (2003)
[Publications] Hiroshi KANAYAMA, Daisuke TAGAMI, Koichiro IMOTO, Sin-ichiro SUGIMOTO: "Finite element computation of magnetic field problems with the displacement current"Journal of Computational and Applied Mathematics. Vol.159. 77-84 (2003)
[Publications] Hiroshi KANAYAMA, Daisuke TAGAMI, Koichiro IMOTO, Shin-ichiro SUGOMOTO: "3-D eddy current computation using the A-φ method for a transformer tank"Sixth International Symposium on Electric and Magnetic Fields from Numerical Models to Industrial Applications. 47-50 (2003)
[Publications] K.Ohmori, S.Fujima, Y.Fujita: "Convergence of the interface for inter facial transport phenomena"Math.J.Toyama Univ.. Vol.26. 109-129 (2003)
[Publications] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interface"International Journal of Computational Fluid Dynamics. (to appear).
[Publications] 大森克史, 奥村弘: "ラグランジュ乗数を用いた質量保存型有限要素法による移動界面問題の解析"第17回数値流体力学シンポジウム講演論文集. C9-2. 1-2 (2003)
[Publications] 三井斌友, 小藤俊幸, 齊藤善弘: "微分方程式による計算科学入門"共立出版. 214 (2004)

2003 Fiscal Year Annual Research Report

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

Principal Investigator

牛島 照夫 電気通信大学, 電気通信学部, 教授 (10012410)

Research Products

[Publications] USHIJIMA, Teruo, CHIBA, Fumihiro: "A fundamental solution method for the reduced wave problem in a domain exterior to a disc"Journal of Computational and Applied Mathematics. Vol.152. 545-557 (2003)

[Publications] USHIJIMA, Teruo, CHIBA, Fumihiro: "Error estimates for a fundamental solution method applied to reduced wave problems in a domain exterior to a disc"Journal of Computational and Applied Mathematics. Vol.159. 137-148 (2003)

[Publications] 西崎誉, 牛島照夫, 半田恭介: "翼の等角写像の有限要素計算による同定"航空宇宙技術研究所、航空宇宙数値シュミレーション技術シンポジウム2003. (収録見込み).

[Publications] 千葉文浩, 牛島照夫: "円外帰着波動問題基本解近似解法への多倍長数値計算の適用"数理解析研究所講究録「数値解析と新しい情報技術」. (収録見込み).

[Publications] Ali Liaqat, Makoto Fukuhara, Tatsuoki Takeda: "Optimal estimation of parameters of dynamical systems by neural network collocation method"Computer Physics Communications. Vol.150. 215-234 (2003)

[Publications] 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. Vol.131. 1696-1714 (2003)

[Publications] NASIR, Haniffa Mohamed, KAKO, Takashi, KOYAMA, Daisuke: "A mixed type finite element approximation for radiation problems using fictitious domain method"Journal of Computational and Applied Mathematics. Vol.152. 377-392 (2003)

[Publications] N.Yamamoto, K.Hayakawa: "Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains"Journal of Computational and Applied Mathematics. Vol.159. 173-183 (2003)

[Publications] Y.Watanabe, N.Yamamoto, M.T.Nakao, T.Nishida: "A numerical verification of nontrivial solutions for the heat convection problem"Journal of Mathematical Fluid Mechanics. Vol.6. 1-20 (2004)

[Publications] T.Koto: "Partitioned Runge-Kutta methods for partial differential equations"京都大学数理解析研究所講究録. Vol.1320. 60-70 (2003)

[Publications] T.Koto: "Stability of θ-methods for delay integro-differential equations"J.Comput.Appl.Math.. Vol.161. 393-404 (2003)

[Publications] 岡本久, 中村健一, 柳下浩紀: "Navier-Stokes方程式の非有界な解は爆発し得る"数理解析研究所講究録. Vol.1322. 102-106 (2003)

[Publications] Ken-Ichi Nakamura: "Bounds for effective speeds of traveling fronts in spatially periodic media"数理解析研究所講究録. Vol.1330. 79-87 (2003)

[Publications] Toshiko Ogiwara, Ken-Ichi Nakamura: "Spiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral crystal growth"Publications of Research Institute for Mathematical Sciences. Vol.39, No.4(in press).

[Publications] Bendong Lou, Matano Hiroshi, Ken-Ichi Nakamura: "Traveling waves in a band domain with quasi-periodically undulating boundaries"数理解析研究所講究録. (to appear).

[Publications] D.Koyama: "Application of a fictitious domain method to 3D Helmholtz problems"数理解析研究所講究録. No.1320. 37-46 (2003)

[Publications] 渡辺 二郎: "On incompressible viscous fluid flows with slip boundary conditions"Journal of Computational and Applied Mathematics. Vol.159 No.1. 161-172 (2003)

[Publications] M.Tabata: "Finite element approximation to infinite Prandtl number Boussinesq equations with temperature dependent coefficients-thermal convection problems in a spherical shell"Future Generation Computer Systems. (to appear).

[Publications] Hiroshi KANAYAMA, Hongjie ZHENG, Natsuki MAENO: "A domain decomposition method for large-scale 3-D nonlinear magnetostatic problems"Theoretical and Applied Mechanics. Vol.52. 247-254 (2003)

[Publications] Hiroshi KANAYAMA, Daisuke TAGAMI, Koichiro IMOTO, Sin-ichiro SUGIMOTO: "Finite element computation of magnetic field problems with the displacement current"Journal of Computational and Applied Mathematics. Vol.159. 77-84 (2003)

[Publications] Hiroshi KANAYAMA, Daisuke TAGAMI, Koichiro IMOTO, Shin-ichiro SUGOMOTO: "3-D eddy current computation using the A-φ method for a transformer tank"Sixth International Symposium on Electric and Magnetic Fields from Numerical Models to Industrial Applications. 47-50 (2003)

[Publications] K.Ohmori, S.Fujima, Y.Fujita: "Convergence of the interface for inter facial transport phenomena"Math.J.Toyama Univ.. Vol.26. 109-129 (2003)

[Publications] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interface"International Journal of Computational Fluid Dynamics. (to appear).

[Publications] 大森克史, 奥村弘: "ラグランジュ乗数を用いた質量保存型有限要素法による移動界面問題の解析"第17回数値流体力学シンポジウム講演論文集. C9-2. 1-2 (2003)

[Publications] 三井斌友, 小藤俊幸, 齊藤善弘: "微分方程式による計算科学入門"共立出版. 214 (2004)

牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)

[Publications] 渡辺二郎: "On incompressible viscous fluid flows with slip boundary conditions"Journal of Computational and Applied Mathematics. Vol.159 No.1. 161-172 (2003)