Article | Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015 | Internalized State-Selection: Generation and Integration of Quasi-Linear Differential-Algebraic Equations
GÃ¶m menyn

Title:
Internalized State-Selection: Generation and Integration of Quasi-Linear Differential-Algebraic Equations
Author:
Christoph Höger: Institute of Software Engineering and Theoretical Computer Science, TU Berlin, Germany Andreas Steinbrecher: Department of Mathematics, TU Berlin, Germany
DOI:
10.3384/ecp1511899
Year:
2015
Conference:
Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015
Issue:
118
Article no.:
010
Pages:
99-107
No. of pages:
9
Publication type:
Abstract and Fulltext
Published:
2015-09-18
ISBN:
978-91-7685-955-1
Series:
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:

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In modeling and simulation of dynamical processes frequently higher index differential-algebraic equations (DAEs) arise. Since an attempt to solve higher-index DAEs directly yields several numerical problems, a regularization in combination with a robust and efficient integration is required. \qualidaes\ is a DAE solver designed to make explicit use of such a regularization. It allows for the solution of over-determined quasi-linear DAEs of the form $M(x,t)\dot{x}=f(x,t)$, $0=g(x,t)$. Such DAEs arise naturally if a quasi-linear DAE is regularized by augmentation with the set of its (hidden) constraints. General DAEs can be brought into the quasi-linear form. To this end, \modelica\ equations can be transformed into the specific input format expected by \qualidaes. This transformation can be implemented in a functional style and yields a non-trivial result. Additionally it provides an on-the-fly solution for the occurrence of higher-order derivatives.

Keywords: Differential-Algebraic Equations; Quasi-Linear; Modelica; Translation; Regularization; Solver; QUALIDAES

## Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015

Author:
Christoph Höger, Andreas Steinbrecher
Title:
Internalized State-Selection: Generation and Integration of Quasi-Linear Differential-Algebraic Equations
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## Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015

Author:
Christoph Höger, Andreas Steinbrecher
Title:
Internalized State-Selection: Generation and Integration of Quasi-Linear Differential-Algebraic Equations
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