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Generic Construction and Efficient Evaluation of Flow Network DAEs and Their Derivatives in the Context of Gas Networks

  • Tom StreubelEmail author
  • Christian Strohm
  • Philipp Trunschke
  • Caren Tischendorf
Conference paper
Part of the Operations Research Proceedings book series (ORP)

Abstract

We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function \(f\) and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of \(f\) can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF).

Keywords

Compressed sparse row format Algorithmic differentiation abs-normal form Piecewise linear tangent approximation Piecewise smooth 

Notes

Acknowledgements

This work was supported by the German Federal Ministry of Education and Research (BMBF) within the Research Campus MODAL (fund number 05M14ZAM) and by the Deutsche Forschungsgemeinschaft through the Collaborative Research Centre TRR154 Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks.

References

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Tom Streubel
    • 1
    • 2
    Email author
  • Christian Strohm
    • 2
  • Philipp Trunschke
    • 1
    • 2
  • Caren Tischendorf
    • 2
  1. 1.Department of OptimizationZuse Institute BerlinBerlinGermany
  2. 2.Department of MathematicsHumboldt University of BerlinBerlinGermany

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