Christoph Höger

Institute of Software Engineering and Theoretical Computer Science, TU Berlin, Germany

Andreas Steinbrecher

Department of Mathematics, TU Berlin, Germany

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

Linköping Electronic Conference Proceedings 118:10, s. 99-107

Published: 2015-09-18

ISBN: 978-91-7685-955-1

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

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.

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

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