Computer-assisted proofs for the global solution structures of heat convection problems

• Project/Area Number: 18540127
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu University
• Principal Investigator: WATANABE Yoshitaka Kyushu University, 情報基盤研究開発センター, 准教授 (90243972)
• Co-Investigator(Kenkyū-buntansha): NAGATOU Kaori 九州大学, 数理学研究院, 准教授 (40326426)
• Co-Investigator(Renkei-kenkyūsha): NAGATOU Kaori 九州大学, 数理学研究院, 准教授 (40326426)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,310,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥510,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 熱対流問題 / 計算機援用証明 / 精度保証付き数値計算 / 3次元熱対流問題 / 非自己共役固有値問題 / 対称性破壊分岐点 / 分岐点

Research Abstract

Rayleigh-Benard問題を記述するOberbeck-Boussinesq方程式の解空間の大域的構造を計算機援用により2次元および3次元問題に対して解明した.

Research Products

• [Journal Article] A computer-assisted instability proof for the Orr-Sommerfeld problemwith Poiseuille flow (2009)
  • Author(s): Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao,
  • Journal Title: Journal of Applied Mathematics and Mechanics(ZAMM) Vol.89, No.1 Pages: 5-18
  • Peer Reviewed
• [Journal Article] A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid (2009)
  • Author(s): Yoshitaka Watanabe
  • Journal Title: Journal of Computational and Applied Mathematics Vol.223 Pages: 983-966
  • Peer Reviewed
• [Journal Article] A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Benard problems (2009)
  • Author(s): Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe and Takaaki Nishida
  • Journal Title: Numerische Mathematik Vol.111, No.3 Pages: 389-406
  • Peer Reviewed
• [Journal Article] A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Benard problems (2009)
  • Author(s): Myoungnyoun Kimm, et al.
  • Journal Title: Numerische Mathematik 111 Pages: 389-406
  • Peer Reviewed
• [Journal Article] A computer- assisted instability proof for the Orr-Sommerfeld problemwith Poiseuille flow (2009)
  • Author(s): Yoshitaka Watanabe, et al.
  • Journal Title: Z. Angew. Math. Mech. 89 Pages: 5-18
  • Peer Reviewed
• [Journal Article] A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid (2009)
  • Author(s): Yoshitaka Watanabe
  • Journal Title: Journal of Computational and Applied Mathematics 223 Pages: 953-966
  • Peer Reviewed
• [Journal Article] 並行Poiseuille流れの不安定性に対する計算機援用証明 (2008)
  • Author(s): 渡部善隆, Michael Plum, 中尾充宏
  • Journal Title: 京都大学数理解析研究所講究録 Vol.1614 Pages: 11-19
• [Journal Article] Some computer assisted proofs on the bifurcation structure of solutions for the Rayleigh-Benard problem (2007)
  • Author(s): 渡部善隆
  • Journal Title: 京都大学数理解析研究所講究録 Vol.1536 Pages: 87-96
• [Journal Article] Validated computation for infinite dimensional eigenvalue problems (2007)
  • Author(s): Kaori Nagatou
  • Journal Title: IEEE Computer Society
  • Peer Reviewed
• [Journal Article] Validated computation for infinite dimensional eigenvalue problems (2007)
  • Author(s): K. Nagatou
  • Journal Title: IEEE Computer Society E2821(CD)
  • Peer Reviewed
• [Journal Article] Numerical verification of stationary solutions for Navier-Stokes problems (2007)
  • Author(s): Kaori Nagatou, et al.
  • Journal Title: Journal of Computational and Applied Mathematics 199 Pages: 445-451
  • NAID: 120000981497
• [Journal Article] Performance comparison of vector calculations between Itanium2 and other processors (2006)
  • Author(s): Takeshi Nanri, Yoshitaka Watanabe and Hiroyuki Sato,
  • Journal Title: Proceedings of International Workshop on Innovative Architecture Pages: 141-146
  • Peer Reviewed
• [Journal Article] Rayleigh-Benard問題の大域分岐構造に対する精度保証付き数値計算 (2006)
  • Author(s): 渡部善隆
  • Journal Title: 京都大学数理解析研究所講究録 Vol.1505 Pages: 101-105
• [Journal Article] A numerical verification for the Kolmogorov flows of incompressible viscous fluid, Proceedings of the international Conference on Numerical Analysis and Applied Mathematics 2006 (2006)
  • Author(s): Yoshitaka Watanabe
  • Journal Title: ICNAAM-2006 Extended Abstracts Pages: 535-539
  • Peer Reviewed
• [Journal Article] Some computer assisted proofs on three dimensional heat convection problems (2006)
  • Author(s): Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe and Takaak Nishida
  • Journal Title: Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications (NOLTA 2006) Pages: 427-430
• [Journal Article] A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid (2006)
  • Author(s): Yoshitaka Watanabe
  • Journal Title: Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications (NOLTA 2006) Pages: 431-434
• [Journal Article] Nobito Yamamoto and Takaaki Nishida, A numerical verification of bifurcation points for nonlinear heat convection problems (2006)
  • Author(s): Mitsuhiro T. Nakao, Yoshitaka Watanabe
  • Journal Title: The proceedings of 2nd International conference "From Scientific Computing to Computational Engineering"(2nd IC-SCCE) Pages: 8-8
  • Peer Reviewed
• [Journal Article] A numerical verification for the Kolmogorov flows of Imcompressible viscous fluid (2006)
  • Author(s): Yoshitaka Watanabe
  • Journal Title: Proceedings of International Conference of Numerical Analysis and Applied Mathematics 2006 (ICNAAM 2006) Pages: 535-539
• [Journal Article] A numerical verification method for two-coupled elliptic partial differential equations
  • Author(s): Yoshitaka Watanabe
  • Journal Title: Japan Journal of Industrial and Applied Mathematics (採録決定)
  • NAID: 10028168961
  • Peer Reviewed
• [Journal Article] Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Benard problem
  • Author(s): Yoshitaka Watanabe and Mitsuhiro T. Nakao
  • Journal Title: Japan Journal of Industrial and Applied Mathematics (採録決定)
  • NAID: 10028169295
  • Peer Reviewed
• [Presentation] A verified eigenvalue excluding method for the Orr-Sommerfeld problem with Poiseuille flow (2009)
  • Author(s): Yoshitaka Watanabe
  • Organizer: International Workshop on Numerical Verification and its Applications 2009(INVA2009)
  • Place of Presentation: Hotel Breeze Bay Marina, Miyako Island, Japan
  • Year and Date: 2009-03-24
• [Presentation] A verified eigenvalue exeluding method for the Orr-Sommerfeld problem with Poiseuille flow (2009)
  • Author(s): Yoshitaka Watanabe
  • Organizer: International Workshop on Numerical Verification and its Applications 2009
  • Place of Presentation: 沖縄県宮古市
  • Year and Date: 2009-03-24
• [Presentation] A computer-assisted stability proof for the Orr-Sommerfeld problem with Poiseuille flow (2009)
  • Author(s): Yoshitaka Watanabe
  • Organizer: International workshop on verified computations and related topics, University of Karlsruhe (TH), Germany. COE Lecture Note
  • Place of Presentation: Faculty of Mathematics, Kyushu University(Vol.15)
  • Year and Date: 2009-03-08
• [Presentation] ある非自己共役作用素の複素固有値の除外に対する数値的検証法 (2008)
  • Author(s): 渡部善隆, 中尾充宏, Michael Plum, 長藤かおり
  • Organizer: 応用数学合同研究集会報告集
  • Place of Presentation: 龍谷大学(163-166)
• [Presentation] Orr-Sommerfeld方程式の固有値に対する計算機援用非存在証明 (2008)
  • Author(s): 渡部善隆
  • Organizer: 基盤(S)合同研究集会「流れ問題のための高品質数値解法と計算機援用解析学」
  • Place of Presentation: KKRホテル金沢
• [Presentation] Validated computations for elliptic systems of FitzHugh-Nagumo type (2008)
  • Author(s): Kaori Nagatou, Yoshitaka Watanabe, Shigeki Yamamoto and Takehiko Kinoshita
  • Organizer: 13th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics(SCAN 2008)
  • Place of Presentation: El Paso, USA
• [Presentation] FitzHugh-Nagumo型反応拡散方程式系に対する数値的検証法 (2008)
  • Author(s): 長藤かおり, 渡部善隆, 山本成樹, 木下武彦
  • Organizer: 日本数学会2008年度秋季総合分科会
  • Place of Presentation: 東京工業大学
• [Presentation] FitzHugh-Nagumo型反応拡散方程式系に対する精度保証付き数値計算 (2008)
  • Author(s): 渡部善隆, 長藤かおり, 山本成樹, 木下武彦
  • Organizer: 日本応用数理学会2008年度年会
  • Place of Presentation: 東京大学
• [Presentation] 無限次元非線形システムの精度保証付きパラメータ同定技法について (2008)
  • Author(s): 中尾充宏, 渡部善隆
  • Organizer: 産業技術数理研究センター第4回ワークショップ
  • Place of Presentation: 九州大学
• [Presentation] 科学技術計算の品質保証 (2008)
  • Author(s): 渡部善隆
  • Organizer: 先駆的科学計算に関するフォーラム2008~高精度・多倍長計算~
  • Place of Presentation: 九州大学
• [Presentation] 解けたらうれしい線形方程式(Vol.13) (2008)
  • Author(s): 渡部善隆
  • Organizer: 計算工学講演会論文集
  • Place of Presentation: 仙台市民会館
• [Presentation] Computer assisted proofs of solutions for nonlinear heat convection problems (2008)
  • Author(s): Yoshitaka Watanabe
  • Organizer: International Workshop on Numerical Verification and its Applications(INVA2008)
  • Place of Presentation: Tokyo Dai-ichi Hotel Okinawa Grand Mer Resort
• [Presentation] 並行Poiseuille流れの不安定性に対する計算機援用証明 (2007)
  • Author(s): 渡部 善隆
  • Organizer: 研究集会・計算科学の基盤技術としての高速アルゴリズムとその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-11-14
• [Presentation] A computer-assisted instability proof for the plane Poiseuille flow (2007)
  • Author(s): 渡部善隆, Michael Plum, 長藤かおり, 中尾充宏
  • Organizer: 応用数学合同研究集会報告集
  • Place of Presentation: 龍谷大学
• [Presentation] A computer-assisted instability proof for the plane Poiseuille flow (2007)
  • Author(s): 渡部善隆, Michael Plum, 長藤かおり, 中尾充宏
  • Organizer: 応用数学合同研究集会報告集
  • Place of Presentation: 龍谷大学(198-199)
• [Presentation] センター計算機群に対する実アプリケーションに即した性能評価 (2007)
  • Author(s): 渡部善隆
  • Organizer: RIITフォーラム2007(2007年度九州大学情報基盤研究開発センター研究発表会)
  • Place of Presentation: 九州大学留学生センター国際ホール
• [Presentation] Some computer-assisted proofs for nonlinear heat convection problems.(Program and Abstracts) (2007)
  • Author(s): Yoshitaka Watanabe
  • Organizer: 2007 Taiwan-Japan Joint workshop on Numerical Analysis and Scientific Computation
  • Place of Presentation: Institute of Mathematics, Academia Sinica, Nankang, Taipei, the Republic of China
• [Presentation] 並行Poiseuille流れの安定性に関する計算機援用解析 (2007)
  • Author(s): 渡部善隆
  • Organizer: 研究集会・流れ問題のための高品質数値解法と精度保証計算
  • Place of Presentation: 島根県民会館, 松江市
• [Presentation] 反応拡散方程式系の解に対する計算機援用証明 (2007)
  • Author(s): 渡部善隆
  • Organizer: 九州大学数値解析学セミナー
  • Place of Presentation: 九州大学大学院数理学研究院
• [Presentation] A computer-assited proof of solutions for an elliptic system of reaction-diffusion equations (2007)
  • Author(s): Yoshitaka Watanabe
  • Organizer: 「精度保証付き数値計算とその周辺」ワークショップ
  • Place of Presentation: 岐阜大学地域科学部
• [Presentation] ある反応拡散方程式系に対する精度保証付き数値計算, 日本数学会2007年度秋季総合分科会 (2007)
  • Author(s): 渡部善隆
  • Organizer: 応用数学分科会講演アブストラクト
  • Place of Presentation: 東北大学
• [Presentation] 対称疎行列の精度保証付き正定値判定計算におけるオーダリングの効用 (2007)
  • Author(s): 渡部善隆
  • Organizer: 日本応用数理学会2007年度年会講演予稿集
  • Place of Presentation: 北海道大学
• [Presentation] A computer-assisted proof of solutions for three dimensional nonlinear heat convection problems (2007)
  • Author(s): Yoshitaka Watanabe22 , Myoungnyoun Kim, Mitsuhiro T. Nakao and Takaaki Nishida
  • Organizer: INSF2007: International Conference on Recent Developments of Numerical Schemes for Flow Problems, Book of Abstracts(159-162)
  • Place of Presentation: Kyushu University Nishijin Plaza
• [Presentation] 疎行列に対する線形方程式の直接解法を用いた固有値・特異値計算 (2007)
  • Author(s): 渡部善隆
  • Organizer: 第2回計算科学研究ステーション研究集会
  • Place of Presentation: 電気通信大学情報工学科
• [Presentation] A computer-assisted proof of the existence of Benard cells for the heat convection problems (2007)
  • Author(s): Yoshitaka Watanabe
  • Organizer: International Workshop on Numerical Verification and its Applications(INVA2007)
  • Place of Presentation: Waseda University
• [Presentation] 疎行列に対する連立1次方程式の直接解法を援用した固有値・特異値計算 (2006)
  • Author(s): 渡部善隆
  • Organizer: 第11回情報・統計科学シンポジウム
  • Place of Presentation: 九州大学留学生会館国際ホール
• [Presentation] 3次元熱対流問題に対する解の数値的検証について (2006)
  • Author(s): 渡部善隆, Myoungnyoun Kim, 西田孝明, 中尾充宏
  • Organizer: 研究集会・流れ問題の数値解析と精度保証付き数値計算
  • Place of Presentation: ブケ東海静岡(静岡市)
• [Presentation] A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Benard problems, 12th GAMM-IMACS International Symposion on Scientific Computing (2006)
  • Author(s): Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takaaki Nishida
  • Organizer: Computer Arithmetic and Validated Numerics
  • Place of Presentation: Duisburg, Germany
• [Presentation] 非対称疎行列に対する連立1次方程式の直接解法を用いた特異値計算(70-73) (2006)
  • Author(s): 渡部善隆
  • Organizer: 第10回環瀬戸内応用数理研究部会シンポジウム講演予稿集
  • Place of Presentation: 沖縄県青年会館
• [Presentation] 計算機援用証明による熱対流問題の分岐点の存在検証 (2006)
  • Author(s): 渡部善隆, 中尾充宏, 山本野人, 西田孝明
  • Organizer: 九州大学数値解析学セミナー
  • Place of Presentation: 九州大学大学院数理学研究院
• [Remarks]
  • URL: http://www.cc.kyushu-u.ac.jp/RD/watanabe/
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/~nagatou/
• [Remarks]
  • URL: http://www.cc.kyushu-u.ac.jp/RD/watanabe/
• [Remarks]
  • URL: http://www.cc.kyushu-u.ac.jp/RD/watanabe/
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/~nagatou/