Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection

Lena Scholz
Technical University Berlin, Department of Mathematics, Berlin, Germany

Andreas Steinbrecher
Technical University Berlin, Department of Mathematics, Berlin, Germany

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp140961171

Ingår i: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Linköping Electronic Conference Proceedings 96:123, s. 1171-1178

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Publicerad: 2014-03-10

ISBN: 978-91-7519-380-9

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


Differential-algebraic equations naturally arise in the modeling of dynamical processes; in particular using MODELICA as modeling language. In general; the model equations can be of higher index; i.e.; they can contain hidden constraints which lead to instabilities and order reductions in the numerical integration. Therefore; a regularization or remodeling of the model equations is required. One way to obtain the required information on the hidden constraints is a structural analysis based on the sparsity pattern of the system. For the determination of a regular index-reduced system formulation then; usually; a crucial step is the so-called state selection. In this paper; we will present a new approach for the remodeling of dynamical systems that uses the information obtained from the structural analysis to construct a regularized overdetermined system formulation. This overdetermined system can then be solved using specially adapted numerical integrators; in such a way that the state selection can be performed within the numerical integrator during runtime of the simulation.


DAEs; regularization; structural analysis; overdetermined system; state selection


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