Regularization of DAEs based on the Signature method
- 196 Downloads
Automated modeling of multi-physics dynamical systems often results in large-scale high-index differential-algebraic equations (DAEs). Since direct numerical simulation of such systems leads to instabilities and possibly non-convergence of numerical methods, a regularization or remodeling is required. In many simulation environments, a structural analysis based on the sparsity pattern of the system is used to determine the index and an index-reduced system model. Here, usually the Pantelides algorithm in combination with the Dummy Derivative Method is used. We present a new approach for the regularization of DAEs that is based on the Signature method (\(\varSigma \)-method).
KeywordsDifferential-algebraic equation Regularization Structural analysis \(\varSigma \)-method Index reduction
Mathematics Subject Classification65L80 34A09 37M05
We would like to thank two anonymous referees for their careful reading and for thoughtful suggestions for the improvement of the paper.
- 1.Altmeyer, R., Steinbrecher, A.: Regularization and Numerical Simulation of Dynamical Systems Modeled with Modelica. Institut für Mathematik, TU Berlin, Preprint 29–2013 (2013)Google Scholar
- 7.Fritzson, P.: Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley-IEEE Press, New York (2004)Google Scholar
- 17.Nedialkov, N., Pryce, J., Tan, G.: DAESA: a Matlab tool for structural analysis of DAEs: Software. Technical report CAS-12-01-NN, Department of Computing and Software, McMaster University, Hamilton (2012)Google Scholar
- 18.Nilsson, H.: Type-based structural analysis for modular systems of equations. In: Proceedings of the 2nd International Workshop on Equation-Based Object-Oriented Languages and Tools 029, 71–81 (2008)Google Scholar
- 21.Scholz, L., Steinbrecher, A.: A combined structural-algebraic approach for the regularization of coupled systems of DAEs. Institut für Mathematik, TU Berlin, Preprint 30–2013 (2013)Google Scholar
- 22.Scholz, L., Steinbrecher, A.: Efficient numerical integration of dynamical systems based on structural-algebraic regularization avoiding state selection. In: Proceedings of the 10th International Modelica Conference (2014)Google Scholar
- 23.Scholz, L., Steinbrecher, A.: Structural-algebraic regularization for coupled systems of DAEs. Submitted to BIT Numerical Mathematics (2014)Google Scholar
- 25.Zeng, Y., Wu, X., Cao, J.: An improved KM algorithm for computing structural index of DAE system. In: 12th International Symposium on Distributed Computing and Applications to Business, Engineering and Science (DCABES), IEEE, pp. 95–99 (2013)Google Scholar