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DAESA—A Matlab Tool for Structural Analysis of Differential-Algebraic Equations: Theory

Authors:

Nedialko S. Nedialkov,

Guangning TanAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 41, Issue 2

Article No.: 9, Pages 1 - 20

https://doi.org/10.1145/2689664

Published: 04 February 2015 Publication History

Abstract

daesa, <u>D</u>ifferential-<u>A</u>lgebraic <u>E</u>quations <u>S</u>tructural <u>A</u>nalyzer, is a Matlab tool for structural analysis of differential-algebraic equations (DAEs). It allows convenient translation of a DAE system into Matlab and provides a small set of easy-to-use functions. daesa can analyze systems that are fully nonlinear, high-index, and of any order. It determines structural index, number of degrees of freedom, constraints, variables to be initialized, and suggests a solution scheme. The structure of a DAE can be readily visualized by this tool. It also can construct a block-triangular form of the DAE, which can be exploited to solve it efficiently in a block-wise manner.

This article describes the theory and algorithms underlying the code.

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N. S. Nedialkov, J. D. Pryce, and G. Tan. 2015. Algorithm 948: DAESA—A Matlab tool for structural analysis of differential-algebraic equations: Software. ACM Trans. Math. Softw. 41, 2, Article 12, 15 pages. DOI http://dx.doi.org/10.1145/2689664.

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N. S. Nedialkov, G. Tan, and J. D. Pryce. 2014. Exploiting fine block triangularization and quasilinearity in differential-algebraic equation systems. arXiv:1411.4128.

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Cited By

Tan GNedialkov NPryce J(2022)Conversion methods for improving structural analysis of differential-algebraic equation systemsBIT10.1007/s10543-017-0655-z57:3(845-865)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-017-0655-z
McKenzie RPryce J(2022)Structural analysis based dummy derivative selection for differential algebraic equationsBIT10.1007/s10543-016-0642-957:2(433-462)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-016-0642-9
Wang CWan LXiong TXie YWang SDing JChen L(2021)Hierarchical Structural Analysis Method for Complex Equation-Oriented ModelsMathematics10.3390/math92126609:21(2660)Online publication date: 21-Oct-2021
https://doi.org/10.3390/math9212660
Show More Cited By

Index Terms

DAESA—A Matlab Tool for Structural Analysis of Differential-Algebraic Equations: Theory
1. Computing methodologies
  1. Modeling and simulation
    1. Simulation support systems
2. Mathematics of computing
  1. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 41, Issue 2

January 2015

173 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2732672

Editor:
Michael A. Heroux
Sandia National Laboratories, USA

Issue’s Table of Contents

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 February 2015

Accepted: 01 August 2013

Revised: 01 April 2013

Received: 01 July 2012

Published in TOMS Volume 41, Issue 2

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Ontario Research Fund
Leverhulme Trust
Natural Sciences and Engineering Research Council of Canada

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Cited By

Tan GNedialkov NPryce J(2022)Conversion methods for improving structural analysis of differential-algebraic equation systemsBIT10.1007/s10543-017-0655-z57:3(845-865)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-017-0655-z
McKenzie RPryce J(2022)Structural analysis based dummy derivative selection for differential algebraic equationsBIT10.1007/s10543-016-0642-957:2(433-462)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-016-0642-9
Wang CWan LXiong TXie YWang SDing JChen L(2021)Hierarchical Structural Analysis Method for Complex Equation-Oriented ModelsMathematics10.3390/math92126609:21(2660)Online publication date: 21-Oct-2021
https://doi.org/10.3390/math9212660
Tang JRao Y(2020)A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic EquationsMathematics10.3390/math81120578:11(2057)Online publication date: 18-Nov-2020
https://doi.org/10.3390/math8112057
Ahrens IUnger B(2020)The Pantelides algorithm for delay differential-algebraic equationsTransactions of Mathematics and Its Applications10.1093/imatrm/tnaa0034:1Online publication date: 30-Sep-2020
https://doi.org/10.1093/imatrm/tnaa003
Qin XTang JFeng YBachmann BFritzson P(2016)Efficient index reduction algorithm for large scale systems of differential algebraic equationsApplied Mathematics and Computation10.1016/j.amc.2015.11.091277:C(10-22)Online publication date: 20-Mar-2016
https://dl.acm.org/doi/10.1016/j.amc.2015.11.091
Tan GNedialkov NPryce J(2016)Symbolic-Numeric Methods for Improving Structural Analysis of Differential-Algebraic Equation SystemsMathematical and Computational Approaches in Advancing Modern Science and Engineering10.1007/978-3-319-30379-6_68(763-773)Online publication date: 11-Aug-2016
https://doi.org/10.1007/978-3-319-30379-6_68
McKenzie RPryce J(2016)Solving Differential-Algebraic Equations by Selecting Universal Dummy DerivativesMathematical and Computational Approaches in Advancing Modern Science and Engineering10.1007/978-3-319-30379-6_60(665-676)Online publication date: 11-Aug-2016
https://doi.org/10.1007/978-3-319-30379-6_60
Nedialkov NPryce JTan G(2015)Algorithm 948ACM Transactions on Mathematical Software10.1145/270058641:2(1-14)Online publication date: 4-Feb-2015
https://dl.acm.org/doi/10.1145/2700586
Tan GNedialkov NPryce J(2015)A Simple Method for Quasilinearity Analysis of DAEsInterdisciplinary Topics in Applied Mathematics, Modeling and Computational Science10.1007/978-3-319-12307-3_64(445-450)Online publication date: 4-Jul-2015
https://doi.org/10.1007/978-3-319-12307-3_64
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