Article | Proceedings of the 10<sup>th</sup> International Modelica Conference; March 10-12; 2014; Lund; Sweden | Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
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Title:
Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
Author:
Lena Scholz: Technical University Berlin, Department of Mathematics, Berlin, Germany Andreas Steinbrecher: Technical University Berlin, Department of Mathematics, Berlin, Germany
DOI:
10.3384/ecp140961171
Download:
Full text (pdf)
Year:
2014
Conference:
Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Issue:
096
Article no.:
123
Pages:
1171-1178
No. of pages:
8
Publication type:
Abstract and Fulltext
Published:
2014-03-10
ISBN:
978-91-7519-380-9
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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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.

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

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

Author:
Lena Scholz, Andreas Steinbrecher
Title:
Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
DOI:
http://dx.doi.org/10.3384/ecp140961171
References:

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

Author:
Lena Scholz, Andreas Steinbrecher
Title:
Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
DOI:
http://dx.doi.org/10.3384/ecp140961171
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