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
Download article
Published in: Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools
Linköping Electronic Conference Proceedings 24:14, p. 151–163
Published: 2007-07-18
ISBN: 978-91-7519-822-4
ISSN: 1650-3686 (print), 1650-3740 (online)
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.
[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
[10] M. Otter: Objektorientierte Modellierung Physikalischer Systeme (Teil 4) – Transformationsalgorithmen. In: at Automatisierungstechnik; Oldenbourg Verlag München; 1999
[11] M. Otter; B. Bachmann: Objektorientierte Modellierung Physikalischer Systeme (Teil 5;6) – Singuläre Systeme. In: at Automatisierungstechnik; Oldenbourg Verlag München; 1999
[12] R. Fletcher: Practical Methods of Optimization John Wiley & Sons; 1995
[13] J. Stoer; R. Burlisch: Einführung 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
