Conference article

Contributions to the Efficient and Parallel Jacobian Evaluation and its Application in OpenModelica

Willi Braun
University of Applied Sciences Bielefeld, Germany

Martin Schroschk
Center for Information Services and High Performance Computing, TU Dresden, Germany

Vitalij Ruge
Siemens AG, Energy Sector, Erlangen, Germany

Andreas Heuermann
University of Applied Sciences Bielefeld, Germany

Bernhard Bachmann
University of Applied Sciences Bielefeld, Germany

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Published in: Proceedings of the American Modelica Conference 2020, Boulder, Colorado, USA, March 23-25, 2020

Linköping Electronic Conference Proceedings 169:17, s. 159-167

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Published: 2020-11-03

ISBN: 978-91-7929-900-2

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


Many algorithms related to Modelica-based simulations heavily rely on the efficient provision of Jacobian matrices. Besides the accuracy of the derivative information, the performance of the derivative evaluation is also of great interest, since it can have a large share in the total simulation time. In this paper, we propose two complementary approaches basing on identification of constant parts and parallelization to accelerate Jacobian evaluation. Furthermore, the implementations of these techniques in the open-source Modelica tool OpenModelica are discussed. The gained speedup in Jacobian evaluation is demonstrated on benchmark models of the ScalableTestSuite.


Jacobian Evaluation, Symbolic Differentiation, Derivatives Computation, Coloring, Sparsity, Parallelization, Modelica, OpenModelica


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