Modelica—A language for equation-based physical modeling and high performance simulation

  • Peter Fritzson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1541)


A new language called Modelica for hierarchical physical modeling is developed through an international effort. Modelica 1.0 [http://] was announced in September 1997. It is an object-oriented language for modeling of physical systems for the purpose of efficient simulation. The language unifies and generalizes previous object-oriented modeling languages and techniques.

Compared to the widespread simulation languages available today this language offers two important advances: 1) non-causal modeling based on differential and algebraic equations; 2) multidomain modeling capability, i.e. it is possible to combine electrical, mechanical, thermodynamic, hydraulic etc. model components within the same application model.

A class in Modelica may contain variables (i.e. instances of other classes), equations and local class definitions. The multi-domain capability is partly based on a notion of connectors, which are classes just like any other entity in Modelica.

Simulation models can be developed using a graphical editor for connection diagrams. Connections are established just by drawing lines between objects picked from a class library. The Modelica model is translated into a set of constants, variables and equations. Equations are sorted and converted to assignment statements when possible. Strongly connected sets of equations are solved by calling a symbolic and/or numeric solver. The C/C++ code generated from Modelica models is quite efficient.

High performance parallel simulation code can be obtained either at the coarse-grained level by identifying fairly independent submodels which are simulated in parallel, or at the fine-grained level by parallelizing on clustered expression nodes in the equation graph. Preliminary results using the coarse-grained approach have been obtained in an application on simulating an autonomous aircraft watching car traffic.


Assignment Statement Graphical Editor Reusable Component Connector Class Connection Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Mats Andersson: Object-Oriented Modeling and Simulation of Hybrid Systems. Ph.D. thesis ISRN LUTFD2/TFRT-1043-SE, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, December 1994.Google Scholar
  2. [2]
    Hilding Elmqvist, Dag Brück, and Martin Otter: Dymola—User’s Manual. Dynasim AB, Research Park Ideon, Lund, Sweden, 1996, http://www.Dynasim.seGoogle Scholar
  3. [3]
    Hilding Elmqvist, Sven-Erik Mattsson: Modelica— The Next Generation Modeling Language—An International Design Effort. In Proceedings of First World Congress of System Simulation, Singapore, September 1–3 1997.Google Scholar
  4. [4]
    Peter Fritzson, Lars Viklund, Dag Fritzson, Johan Herber. High-Level Mathematical Modelling and Programming, IEEE Software, 12(4):77–87, July 1995, Scholar
  5. [5]
    Peter Fritzson, Vadim Engelson. Modelica—A Unified Object-Oriented Language for System Modeling and Simulation, In Proceedings of ECOOP-98, Brussels, July 1998, LNCS 1445, Springer Verlag.Google Scholar
  6. [6]
    Dag Fritzson, Patrik Nordling. Solving Ordinary Differential Equations on Parallel Computers Applied to Dynamic Rolling Bearing Simulation. In Parallel Programming and Applications, P. Fritzson, L. Finmo, eds., IOS Press, 1995Google Scholar
  7. [7]
    A.C. Hindmarsh. ODEPACK, A Systematized Collection of ODE Solvers, Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (Vol. 1 of IMACS Transactions on Scientific Computation), pp. 55–64, also Scholar
  8. [8]
    Modelica Home Page. Scholar
  9. [9]
    ObjectMath Home Page. Scholar
  10. [10]
    Martin Otter, C. Schlegel, and Hilding Elmqvist. Modeling and Real-time Simulation of an Automatic Gearbox using Modelica. In Proceedings of ESS’97— European Simulation Symposium, Passau, Oct. 19–23, 1997.Google Scholar
  11. [11]
    Clemens Szyperski. Component Software—Beyond Object-Oriented Programming. Addison-Wesley, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Peter Fritzson
    • 1
  1. 1.PELAB, Dept. of Computer and Information ScienceLinköping UniversityLinköpingSweden

Personalised recommendations