Conference article

Operational Semantics for a Modular Equation Language

Christoph Höger
Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, Germany

Download articlehttp://dx.doi.org/10.3384/ecp13090002

Published in: Proceedings of the 4th Analytic Virtual Integration of Cyber-Physical Systems Workshop; December 3; Vancouver; Canada

Linköping Electronic Conference Proceedings 90:2, s. 5-12

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Published: 2013-11-13

ISBN: 978-91-7519-451-6

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

Abstract

Current equation–based object–oriented modeling languages offer great means for composition of models and source code reuse. Composition is limited to the source level; though: There is currently no way to compose precompiled model fragments. In this work we present t(n;p); a language which aims to overcome this deficiency. By using automatic differentiation directly in the language semantics; t(n;p)offers the ability to implement index-reduction and causalisation of equation-terms without knowing their source-level representation. The semantics of t(n;p)allow for calculation of arbitrary-order partial and total derivatives of pre-compiled terms.

Keywords

Composition; Equation; DAE; Separate Compilation; Automatic Differentiation

References

[1] Torsten Blochwitz; M Otter; M Arnold; C Bausch; C Clauß; H Elmqvist; A Junghanns; J Mauss; M Monteiro; T Neidhold; et al. The functional mockup interface for tool independent exchange of simulation models. In Modelica’2011 Conference; March; pages 20–22; 2011.

[2] David Broman and Jeremy G. Siek. Modelyze: a gradually typed host language for embedding equation-based modeling languages. Technical Report UCB/EECS-2012-173; EECS Department; University of California; Berkeley; Jun 2012.

[3] Sébastien Furic. Enforcing model composability in modelica. In Proceedings of the 7th International Modelica Conference; Como; Italy; pages 868–879; 2009.

[4] George Giorgidze and Henrik Nilsson. Mixed-level embedding and jit compilation for an iteratively staged dsl. In Proceedings of the 19th international conference on Functional and constraint logic programming; WFLP’10; pages 48–65; Berlin; Heidelberg; 2011. Springer-Verlag.

[5] Christoph Höger. Separate compilation of causalized equations -work in progress. In François E. Cellier; David Broman; Peter Fritzson; and Edward A. Lee; editors; EOOLT; volume 56 of Linköping Electronic Conference Proceedings; pages 113–120. Linköping University Electronic Press; 2011.

[6] Dan Kalman. Doubly recursive multivariate automatic differentiation. Mathematics magazine; 75(3):187–202; 2002. doi: 10.2307/3219241

[7] Jerzy Karczmarczuk. Functional differentiation of computer programs. In ACM SIGPLAN Notices; volume 34; pages 195–203. ACM; 1998.

[8] Sven Erik Mattsson and Gustaf Söderlind. Index reduction in differential-algebraic equations using dummy derivatives. SIAM Journal on Scientific Computing; 14(3):677–692; 1993. doi: 10.1137/0914043

[9] A. Mehlhase. A Python Package for Simulating Variable-Structure Models with Dymola. In Inge Troch; editor; Proceedings of MATHMOD 2012; Vienna; Austria; feb 2012. IFAC. submitted.

[10] Constantinos C Pantelides. The consistent initialization of differential-algebraic systems. SIAM Journal on Scientific and Statistical Computing; 9(2):213–231; 1988. doi: 10.1137/0909014

[11] John D Pryce. A simple structural analysis method for daes. BIT Numerical Mathematics; 41(2):364–394; 2001. doi: