Index Reduction Methods for Differential-Algebraic Equation Models by Discrete Optimization Techniques

• Project/Area Number: 20560057
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyoto University
• Principal Investigator: IWATA Satoru Kyoto University, 数理解析研究所, 教授 (00263161)
• Co-Investigator(Renkei-kenkyūsha): TAKAMATSU Mizuyo 中央大学, 理工学部, 助教 (70580059)
• Research Collaborator: TISCHENDORF Caren Koln大学, 教授
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 微分代数方程式 / 行列束 / 離散最適化 / 非線形回路 / 混合解析 / アルゴリズム / 数値計算 / モデル化

Research Abstract

Large-scale dynamical systems, such as integrated circuits and chemical plants, are naturally described by differential-algebraic equations (DAEs). However, numerical solution of DAEs is often much more difficult than that of ODEs. This research focuses on DAEs arising in circuit simulation and establishes an efficient method to obtain a differential-algebraic equation model that is the easiest to solve numerically.

Research Products

• [Journal Article] On the Kronecker canonical form of mixed matrix pencils (2011)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: SIAM J.Matrix Analysis and Applications 32 Pages: 44-71
  • Peer Reviewed
• [Journal Article] On the Kronecker Canonical Form of Mixed Matrix Pencils (2011)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: SIAM J.Matrix Anal.Appl. Volume: 32 Pages: 44-71
  • Peer Reviewed
• [Journal Article] Index characterization of differential -algebraic equations in hybrid analysis for circuit simulation (2010)
  • Author(s): M.Takamatsu, S.Iwata
  • Journal Title: International J.Circuit Theory and Applications 38 Pages: 419-440
  • Peer Reviewed
• [Journal Article] Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation (2010)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: Math.Programming 121 Pages: 105-121
  • Peer Reviewed
• [Journal Article] Index Minimization of Differential-Algebraic Equations in Hybrid Analysis for Circuit Simulation (2010)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: Mathematical Programming 121 Pages: 105-121
  • Peer Reviewed
• [Journal Article] Index Characterization of Differential-Algebraic Equations in Hybrid Analysis for Circuit Simulation (2010)
  • Author(s): M.Takamatsu, S.Iwata
  • Journal Title: Int. J. Circuit Theory Appl. 38 Pages: 419-440
  • Peer Reviewed
• [Journal Article] Computing the degrees of all cofactors in mixed polynomial matrices (2009)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: SIAM J.Discrete Math. 23 Pages: 647-660
  • Peer Reviewed
• [Journal Article] Computing the Degree of All Cofactors in Mixed Polynomial Matr ces (2009)
  • Author(s): S. Iwata, M. Takamatsu
  • Journal Title: SIAM Journal on Discrete Mathematics 23 Pages: 647-660
  • Peer Reviewed
• [Journal Article] Index Minimization of Differential-Algebraic Equtions in Hybrid Analsis for Circuit Simulation (2009)
  • Author(s): S. Iwat, M. Takamatsu
  • Journal Title: Mathemtaical Programming (印刷中)(掲載確定)
  • Peer Reviewed
• [Journal Article] Index reduction for differential-algebraic equations by substitution method (2008)
  • Author(s): M.Takamatsu, S.Iwata
  • Journal Title: Linear Algebra and Its Applications 429 Pages: 2268-2277
  • Peer Reviewed
• [Journal Article] Index Reduction for Differential-Algebraic Equations by Substitution Method (2008)
  • Author(s): M Takamats, S Iwata
  • Journal Title: Linear Algebra and Its Application 429 Pages: 2268-2277
  • Peer Reviewed
• [Journal Article] Tractability index of hybrid equations for circuit simulation
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Journal Title: Math.Computation to appear
  • Peer Reviewed
• [Journal Article] Tractability Index of Hybrid Equations for Circuit Simulation
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Journal Title: Mathematics of Computation Volume: (掲載決定)
  • Peer Reviewed
• [Presentation] 混合多項式行列の小行列式の最大次数を計算する組合せ緩和法 (2010)
  • Author(s): 岩田覚, 高松瑞代
  • Organizer: 日本OR学会秋季研究発表会
  • Place of Presentation: 福島
  • Year and Date: 2010-09-17
• [Presentation] Structural characterization on index of DAEs in hybrid analysis for general circuits (2009)
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Organizer: SIAM Workshop on Combinatorial Scientific Computing
  • Place of Presentation: Monterey, (USA)
  • Year and Date: 2009-10-30
• [Presentation] Structural Characterization on Index of DAEs in Hybrid Analysis for General Circuits (2009)
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Organizer: SIAM Workshop on Combinatorial Scientific Computing (CSC09)
  • Place of Presentation: Monterey, CA
  • Year and Date: 2009-10-30
• [Presentation] Hybrid Analysis of Nonlinear Time-Varying Circuits Providing DAEs with at Most Index 1 (2009)
  • Author(s): S. Iwata, M. Takamatsu, C. Tischendorf
  • Organizer: International Conference on Scientific Computing in Electrical Engineering
  • Place of Presentation: Espoo, Finland
  • Year and Date: 2009-10-02
• [Presentation] 混合行列束のKronecker標準形の組合せ論的解析 (2009)
  • Author(s): 岩田覚, 高松瑞代
  • Organizer: 日本OR学会秋季研究発表会
  • Place of Presentation: 長崎
  • Year and Date: 2009-09-10
• [Presentation] Matroidal characterization on index of DAEs in hybrid analysis for general circuits (2009)
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Organizer: The Sixth Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: Budapest,(ハンガリー)
  • Year and Date: 2009-05-17
• [Presentation] Hybrid analysis of nonlinear time-varying circuits providing DAEs with at most index one (2008)
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Organizer: The Seventh International Conference on Scientific Computing in Electrical Engineering
  • Place of Presentation: Espoo,(フィンランド)
  • Year and Date: 2008-10-02
• [Presentation] 非線形時変RLC回路における混合方程式の指数の解析 (2008)
  • Author(s): 岩田覚, 高松瑞代, Caren Tischendorf
  • Organizer: 日本応用数理学会年会
  • Place of Presentation: 柏
  • Year and Date: 2008-09-17