Conference article

Internalized State-Selection: Generation and Integration of Quasi-Linear Differential-Algebraic Equations

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

Andreas Steinbrecher
Department of Mathematics, TU Berlin, Germany

Download articlehttp://dx.doi.org/10.3384/ecp1511899

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

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

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Published: 2015-09-18

ISBN: 978-91-7685-955-1

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

Abstract

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

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