Conversion methods for improving structural analysis of differential-algebraic equation systems

被引:0
作者
Guangning Tan
Nedialko S. Nedialkov
John D. Pryce
机构
[1] McMaster University,School of Computational Science and Engineering
[2] McMaster University,Department of Computing and Software
[3] Cardiff University,School of Mathematics
来源
BIT Numerical Mathematics | 2017年 / 57卷
关键词
Differential-algebraic equations; Structural analysis; Modeling; Symbolic computation; 34A09; 65L80; 41A58; 68W30;
D O I
暂无
中图分类号
学科分类号
摘要
Structural analysis (SA) of a system of differential-algebraic equations (DAEs) is used to determine its index and which equations to be differentiated and how many times. Both Pantelides’s algorithm and Pryce’s Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varSigma $$\end{document}-method are equivalent: if one of them finds correct structural information, the other does also. Nonsingularity of the Jacobian produced by SA indicates success, which occurs on many problems of interest. However, these methods can fail on simple, solvable DAEs and give incorrect structural information including the index. This article investigates Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varSigma $$\end{document}-method’s failures and presents two conversion methods for fixing them. Under certain conditions, both methods reformulate a DAE system on which the Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varSigma $$\end{document}-method fails into a locally equivalent problem on which SA is more likely to succeed. Aiming at achieving global equivalence between the original DAE system and the converted one, we provide a rationale for choosing a conversion from the applicable ones.
引用
收藏
页码:845 / 865
页数:20
相关论文
共 30 条
[1]  
Barrio R(2005)Performance of the Taylor series method for ODEs/DAEs Appl. Math. Comput. 163 525-545
[2]  
Barrio R(2006)Sensitivity analysis of ODEs/DAEs using the Taylor series method SIAM J. Sci. Comput. 27 929-1947
[3]  
Campbell SL(1995)Solvability of general differential-algebraic equations SIAM J. Sci. Comput. 16 257-270
[4]  
Griepentrog E(1998)Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems Math. Comput. Simul. 48 133-150
[5]  
Carpanzano E(2004)Symbolic numeric index analysis algorithm for differential-algebraic equations Indus. Eng. Chem. Res. 43 3886-3894
[6]  
Maffezzoni C(2004)Index reduction for differential-algebraic equations by minimal extension ZAMM J. Appl. Math. Mech. Z. für Angew. Math. Mech. 84 579-597
[7]  
Chowdhry S(1993)Index reduction in differential-algebraic equations using dummy derivatives SIAM J. Sci. Comput. 14 677-692
[8]  
Krendl H(2005)Solving differential-algebraic equations by Taylor series (I): computing Taylor coefficients BIT Numer. Math. 45 561-591
[9]  
Linninger AA(2008)Solving differential-algebraic equations by Taylor series (III): the DAETS code JNAIAM J. Numer. Anal. Indus. Appl. Math. 3 61-80
[10]  
Kunkel P(2015)Algorithm 948: DAESA—a Matlab tool for structural analysis of differential-algebraic equations: software ACM Trans. Math. Softw. 41 12:1-12:14