Development of a finite element code with adaptive mesh refinement for flow problems

2008 Fiscal Year Final Research Report

• Project/Area Number: 19540138
• 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: ATSUSHI Suzuki Kyushu University, 大学院・数理学研究院, 助教 (60284155)
• Project Period (FY): 2007 – 2008
• Keywords: 解適合細分 / 階層型有限要素 / 特性有限要素法 / 部分構造反復法 / 縁取り直接解法

Research Abstract

非圧縮流れの基礎方程式であるナビエ・ストークス方程式で記述される三次元流れ問題において, 少ない計算量で高解像度の計算を実現できる計算コードを開発した. ナビエ・ストークス方程式の物質微分項に特性曲線による近似を適用して時間微分の近似を行うことで時間発展の各ステップで線形のストークス方程式を解く. 領域全体での高解像メッシュを用いることなく, 流れが急激に変化する領域において有限要素分割を細分することで効率的な計算を行う事ができる. 三次元ストークス方程式は大規模計算となるが, 部分構造反復法を改良することで効率的な並列計算が可能になった.

Research Products

• [Journal Article] An iterative substructuring method for the discretized Stokes equations by a stabilized finite element method (2009)
  • Author(s): Suzuki, A.
  • Journal Title: to appear in Proceedings of ALGORITMY 18 Pages: 41-50
  • Peer Reviewed
• [Journal Article] An iterative substructuring solver for the Stokes equations, to appear in Proceedings of the First International Conference on Parallel (2009)
  • Author(s): Suzuki, A.
  • Journal Title: Distributed and Grid Computing for Engineering, B.H.V. Topping and P. Ivanyi, (eds.), Civil-Comp Press 90 Pages: P37/1-P37/11
  • Peer Reviewed
• [Journal Article] ストークス方程式に対する平衡化前処理付き領域分割法 (2007)
  • Author(s): 鈴木厚
  • Journal Title: 計算工学講演論文集 12 Pages: 833-834
• [Journal Article] Finite element matrices in congruent subdomains and some techniques for practical problems
  • Author(s): Suzuki, A., Tabata, M.
  • Journal Title: Algorithms and Practice, Civil-Comp Press(F. Magoules ed.) (accepted) Pages: 37
  • Peer Reviewed
• [Presentation] A balancing domain decomposition method with congruent subdomains for the Stokes equations (2009)
  • Author(s): Suzuki, A.
  • Organizer: Seminarie Equations aux derives partielles, Institute de Recherche Mathematique Anancee, Universite de Strasbourg
  • Place of Presentation: Strasbourg, France
  • Year and Date: 2009-03-24
• [Presentation] An iterative substructuring method for the discretized Stokes equations by a stabilized finite element method, ALGORITMY 2009 (2009)
  • Author(s): Suzuki, A.
  • Organizer: 18th Conference on Scientific Computing Vysoke Tatry-Podbanske, Slovakia
  • Place of Presentation: Slovakia
  • Year and Date: 2009-03-17
• [Presentation] An iterative substructuring algorithm with congruent subdomains, Workshop on Numerical Methods (2009)
  • Author(s): Suzuki, A.
  • Organizer: Laboratoire Jacques-Louis Lions
  • Place of Presentation: Paris, France
  • Year and Date: 2009-01-19
• [Presentation] Preconditioned conjugate gradient solver for the Stokes equations (2009)
  • Author(s): Suzuki, A.
  • Organizer: Necas Seminar on Continuum Mechanics
  • Place of Presentation: Charles University in Prague, Czech Republic
  • Year and Date: 2009-01-05
• [Presentation] An iterative substructuring algorithm with congruent subdomains (2008)
  • Author(s): Suzuki, A.
  • Organizer: Czech-Japanese Seminar in Applied Mathematics 2008
  • Place of Presentation: Takachiho, Miyazaki, Japan.
  • Year and Date: 2008-09-03
• [Presentation] ストークス方程式に対する部分構造反復法の高速実装 (2008)
  • Author(s): 鈴木厚
  • Organizer: 第13回計算工学講演会
  • Place of Presentation: 仙台市民会館
  • Year and Date: 2008-05-21
• [Presentation] A fast domain decomposition solver for the Stokes problems (2008)
  • Author(s): Suzuki, A.
  • Organizer: Mini workshop on advanced mathematical and computational methods
  • Place of Presentation: Czech Technical University in Prague, Czech Republic.
  • Year and Date: 2008-03-10
• [Presentation] 合同名部分領域分割による有限要素方程式解法 (2007)
  • Author(s): 鈴木厚
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2007-12-18
• [Presentation] Parallel finite element solver for the Stokes equations (2007)
  • Author(s): Suzuki, A.
  • Organizer: DMHF2007 : COE Conference on the Development of Dynamic Mathematics with High Functionality
  • Place of Presentation: Fukuoka Recent Hotel, Japan.
  • Year and Date: 2007-10-04
• [Presentation] ストークス方程式の平衡化前処理付き領域分割法ソルバー (2007)
  • Author(s): 鈴木厚
  • Organizer: 日本応用数理学会2007年度年会
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-15
• [Presentation] A 3-D implementation of characteristic Galerkin method with P1-interpolation (2007)
  • Author(s): Suzuki, A.
  • Organizer: INSF2007 : International Conference on Recent Developments of Numerical Schemes for Flow Problems
  • Place of Presentation: Kyushu University, Japan
  • Year and Date: 2007-06-29