Patrick Täuber
ABSTRACT
This paper is concerned with the tearing method according to François Cellier. Tearing is used to reduce the dimension of algebraic loops, which inevitably arise in the modelling of scientific systems using differential-algebraic equations, as far as possible to achieve an efficient simulation. However, the original tearing method according to Cellier is not suitable for the application in practice, since restrictions on the solvability of equations for variables, and other features, which appear in reality, are not considered. In this work, different changes to the method are introduced and tested, which make it possible to use Cellier Tearing in practice. In addition, the modeller can influence the selection of tearing variables. Modifications of the integrated heuristic are presented, whose efficiency is statistically evaluated at the end of this work. With these changes and the new heuristics, Cellier's method becomes a very suitable way to optimize the efficiency of simulation in practice.
- Carpanzano, E.; Girelli, R.: The Tearing Problem: Definition, Algorithm and Application to Generate Efficient Computational Code from DAE Systems. In: Proceedings of 2nd Mathmod Vienna, IMACS Symposium on Mathematical Modelling, 1997Google Scholar
- Carpanzano, E.: Order Reduction of General Nonlinear DAE Systems by Automatic Tearing. In: Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences 6:2 (2000), S. 145--168Google Scholar
- Cellier, F. E.; Kofman, E.: Continuous System Simulation. 1. Auflage. Berlin, Heidelberg: Springer, 2006. -- ISBN 978-0-387-30260-7 Google ScholarDigital Library
- Modelica Association: Modelica Homepage. www.modelica.org. Version: July 2014Google Scholar
- Ollero, P.; Amselem, C.: Decomposition algorithm for chemical process simulation. In: Chemical engineering research and design 61:5 (1983), S. 303--307Google Scholar
- Open Source Modelica Consortium: OpenModelica Homepage. www.openmodelica.org. Version: July 2014Google Scholar
- Steward, D. V.: Partitioning and Tearing Systems of Equations. In: Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis 2:2 (1965), S. 345--365Google Scholar
- Tarjan, R. E.: Depth-First Search And Linear Graph Algorithms. In: Journal of Computation 1:2 (1972), S. 146--160Google Scholar
- Waurich, V.: Untersuchung und Bewertung von Tearing-Algorithmen, Technische Universität Dresden, Diplomarbeit, 2013Google Scholar
Index Terms
- Practical realization and adaptation of Cellier's tearing method
Recommendations
Dynamic tearing: efficiency enhancement of tearing methods by consideration of solvability criteria during runtime
EOOLT '16: Proceedings of the 7th International Workshop on Equation-Based Object-Oriented Modeling Languages and ToolsCommon tearing methods try to find static tearing variables. This means that selected tearing variables are used for the entire simulation, which also means that all inner equations are used for the entire simulation. Hence, the tearing method sets up ...
Reshuffling: a symbolic pre-processing algorithm for improved robustness, performance and parallelization for the simulation of differential algebraic equations
EOOLT '14: Proceedings of the 6th International Workshop on Equation-Based Object-Oriented Modeling Languages and ToolsThis paper presents a novel algorithm, named Reshuffling, for manipulating a system of differential-algebraic equations (DAE). An algorithm is introduced to rearrange edges in the graph representation of the DAE in order to resolve cycles. The algorithm ...
Comments