Conference article

Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0

Johan Åkesson
Lund University, Department of Automatic Control, Lund/Modelon AB, Lund, Sweden

Willi Braun
University of Applied Sciences Bielefeld, Bielefeld, Germany

Petter Lindholm
Lund University, Department of Mathematics, Lund, Sweden

Bernhard Bachmann
University of Applied Sciences Bielefeld, Bielefeld, Germany

Download articlehttp://dx.doi.org/10.3384/ecp12076185

Published in: Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Linköping Electronic Conference Proceedings 76:18, p. 185-196

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Published: 2012-11-19

ISBN: 978-91-7519-826-2

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

Abstract

Derivatives; or Jacobians; are commonly required by numerical algorithms. Access to accurate Jacobians often improves the performance and robustness of algorithms; and in addition; efficient implementation of Jacobian computations can reduce the overall execution time. In this paper; we present methods for computing Jacobians in the context of the Functional Mock-up Interface (FMI); and Modelica. Two prototype implementations; in Jmodelica.org and OpenModelica are presented and compared in industrial benchmarks.

Keywords

Functional Mock-up Interface; Analytic Jacobians; Automatic Differentiation; JModelica.org; OpenModelica

References

[1] A. Griewank A.Walther. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation; Second Edition. SIAM; 2008.

[2] The Functional Mock-up Interface for Model Exchange 1.0; http://functional-mockup-interface.org/specifications/FMI_for_ModelExchange_v1.0.pdf; January 2010.

[3] The Functional Mock-up Interface for Co-simulation 1.0; http://functional-mockup-interface.org/specifications/FMI_for_CoSimulation_v1.0.pdf; October 2010.

[4] R. Tarjan. “Depth-first search and linear graph algorithms.” SIAM J. Computing; 1:2; pp. 146–160; 1972. doi: 10.1137/0201010.

[5] D. H. Al-Omari K. E. Sabri. “New graph coloring algorithms.” American Journal of Mathematics and Statistics; 2006.

[6] T. F. Coleman J. J. More. “Estimation of sparse Jacobian matrices and graph coloring problems.” Society for Industrial and Applied Mathematics; 1983.

[7] Dürrbaum A.; Klier W.; Hahn H.: Comparison of Automatic and Symbolic Differentiation in Mathematical Modeling and Computer Simulation of Rigid-Body Systems. In: Multibody System Dynamics. Springer Netherlands; 2002.

[8] Y. B. Gol’dshtein. “Portrait of the inverse of a sparse matrix.” Cybernetics and Systems Analysis; 28; pp. 514–519; 1992. doi: 10.1007/BF01124985.

[9] BraunW; Gallardo Yances S; Link K; Bachmann B. Fast Simulation of Fluid Models with Colored Jacobians . In: Proceedings of the 9th Modelica Conference; Munich; Germany; Modelica Association; 2012.

[10] Braun W; Ochel L; Bachmann B. Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler. In: Proceedings of the 8th Modelica Conference; Dresden; Germany; Modelica Association; 2011.

[11] Casella; F.; Donida; D.; Åkesson; J. Object-Oriented Modeling and Optimal Control: A Case Study in Power Plant Start-Up. In: Proceedings of the 18th IFAC World Congress; Milan; Italy; 2011.

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