Conference article

Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler

Willi Braun
Bielefeld University of Applied Sciences, Department of engineering and mathematics, Germany

Lennart Ochel
Bielefeld University of Applied Sciences, Department of engineering and mathematics, Germany

Bernhard Bachmann
Bielefeld University of Applied Sciences, Department of engineering and mathematics, Germany

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Published in: Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany

Linköping Electronic Conference Proceedings 63:56, p. 495-501

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Published: 2011-06-30

ISBN: 978-91-7393-096-3

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


Jacobian matrices are used in a wide range of applications - from solving the original DAEs to sensitivity analysis. Using Automatic Differentiation the necessary partial derivatives can be provided efficiently within a Modelica-Tool. This paper describes the corresponding implementation work within the OpenModelica Compiler (OMC) to create a symbolic derivative module. This new OMC-feature generates symbolically partial derivatives in order to calculate Jacobian matrices with respect to different variables. Applications presented here; are the generation of linear models of non-linear Modelica models and the usage of the Jacobian matrix in DASSL for simulating a model.


Symbolic Jacobian; Automatic Differentiation; Linearization; DASSL; OpenModelica


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