Article | Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools: Berlin; Germany; July 30; 2007; conjunction with ECOOP | Robust Initialization of Differential Algebraic Equations

Title:
Robust Initialization of Differential Algebraic Equations
Author:
Bernhard Bachmann: Dept. Mathematics and Engineering, University of Applied Sciences, Bielefeld, Germany Peter Aronsson: MathCore Engineering AB, Linköping, Sweden Peter Fritzson: PELAB Programming Environments Lab, Department of Computer Science, Linköping University, Linköping, Sweden
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Year:
2007
Conference:
Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools: Berlin; Germany; July 30; 2007; conjunction with ECOOP
Issue:
024
Article no.:
014
Pages:
151‚Äď163
No. of pages:
13
Publication type:
Abstract and Fulltext
Published:
2007-07-18
ISBN:
978-91-7519-822-4
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


This paper describes a new solution method applied to the problem initializing DAEs using the Modelica language. Modelica is primarily an ob-ject-oriented equation-based modeling language that allows specification of mathematical models of complex natural or man-made systems. Major features of Modelica are the mul-tidomain modeling capability and the reusability of model components corresponding to physical objects; which allow to build and simulate highly complex systems. However; initializing such models has been quite cumbersome; since initial equations have to be provided at the system level; where the user needs to know details on the underlying transformation and index-reduction algorithms; that in general are applied to simulate a Mode-lica model.

Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools: Berlin; Germany; July 30; 2007; conjunction with ECOOP

Author:
Bernhard Bachmann, Peter Aronsson, Peter Fritzson
Title:
Robust Initialization of Differential Algebraic Equations
References:

[1] Peter Fritzson; et al. The Open Source Modelica Project. In Proceedings of The 2nd International Modelica Conference; 18-19 March; 2002. Munich; Germany See also: http://www.ida.liu.se/projects/OpenModelica.


[2] Peter Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1; 940 pp.; ISBN 0-471-471631; Wiley-IEEE Press; 2004.


[3] The Modelica Association. The Modelica Language Specification Version 2.2; March 2005. http://www.modelica.org.


[4] The OpenModelica Users Guide; version 0.6; June 2005. www.ida.liu.se/projects/OpenModelica


[5] The OpenModelica System Documentation; version 0.6; June 2006. www.ida.liu.se/projects/OpenModelica


[6] K. E. Brenan; S. L. Campbell; and L. R. Petzold; Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations; Elsevier; New York; 1989.


[7] B. Bachmann et. al. (Modelica Association): Modelica - A Unified Object-Oriented Language for Physical Systems Modeling - Language Specification. 2002.


[8] P. Fritzson; P. Aronsson; P. Bunus; V. Engelson; L. Saldamli; H. Johansson; A. Karström: The Open Source Modelica Project. In: 2nd Modelica Conference 2002; Oberpfaffenhofen; 2002


[9] S.-E. Mattson; H. Olson; H. Elmqvist: Dynamic Selection of States in Dymola. In: 1st Modelica Workshop 2000; Lund; Sweden; 2000


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[11] M. Otter; B. Bachmann: Objektorientierte Modellierung Physikalischer Systeme (Teil 5;6) ‚Äď Singul√§re Systeme. In: at Automatisierungstechnik; Oldenbourg Verlag M√ľnchen; 1999


[12] R. Fletcher: Practical Methods of Optimization John Wiley & Sons; 1995


[13] J. Stoer; R. Burlisch: Einf√ľhrung in die numerische Mathematik. Springer Verlag; 1994


[14] S.E. Mattsson; G. Söderlind: Index reduction in differential-algebraic equations using dummy derivatives. SIAM Journal of Scientific and Statistical Computing; Vol. 14; 1993. 162


[15] K.E. Brenan.; S.L. Campbell; L.R. Petzold: Numerical Solution of Initial Value Problems in Differential Algebraic Equations. North-Holland; Amsterdam; 1989


[16] C.C. Pantelides: The Consistent Initialization of Differential-Algebraic Systems; SIAM Journal of Scientific and Statistical Computing; 1988.


[17] L.R. Petzold: A description of DASSL: A differential / algebraic system solver. Sandia National Laboratories; Albuquerque; 1982


[18] H. Elmqvist: A Structured Model Language for Large Continuous Systems; PhD dissertation; Department of Automatic Control; Lund Institute of Technology; Lund; Schweden; 1978


[19] R.E. Tarjan: Depth First Search and Linear Graph Algorithms. SIAM Journal of Comp.; Nr. 1; 1972

Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools: Berlin; Germany; July 30; 2007; conjunction with ECOOP

Author:
Bernhard Bachmann, Peter Aronsson, Peter Fritzson
Title:
Robust Initialization of Differential Algebraic Equations
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