Article | Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany | Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0

Title:
Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0
Author:
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
DOI:
10.3384/ecp12076185
Download:
Full text (pdf)
Year:
2012
Conference:
Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany
Issue:
076
Article no.:
018
Pages:
185-196
No. of pages:
12
Publication type:
Abstract and Fulltext
Published:
2012-11-19
ISBN:
978-91-7519-826-2
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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

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

Author:
Johan Åkesson, Willi Braun, Petter Lindholm, Bernhard Bachmann
Title:
Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0
DOI:
10.3384/ecp12076185
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] DĂĽrrbaum 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.; Ă…kesson; 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.

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

Author:
Johan Åkesson, Willi Braun, Petter Lindholm, Bernhard Bachmann
Title:
Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0
DOI:
10.3384/ecp12076185
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