Skip to main content

Topological Index Analysis and Its Application to Multi-Physical Systems in System Simulation Software

  • Conference paper
  • First Online:
Progress in Industrial Mathematics: Success Stories

Part of the book series: SEMA SIMAI Springer Series ((ICIAM2019SSSS,volume 5))

Abstract

This work is devoted to the topological analysis of multi-physical networks stemming from automated modeling processes in system simulation software. A special focus is on the methodical treatment of multi-physical networks, which can be utilized to develop robust and user-friendly simulation tools. In the multi-physical case, the already available topological criteria of different physics have to be merged and reinterpreted. A general receipt for their analysis is described in terms of a representative example, a fluid-solid network which is thermally coupled. The theoretical results are put in context to a practical realization in a simulation software in terms of modeling and coupling concepts, which help to improve the useability of system simulation software for software application engineers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    https://www.avl.com/de/cruise-m.

References

  1. Arnold, M.: Modular time integration of block-structured coupled systems without algebraic loops. In: Progress in Differential-Algebraic Equations. Springer, Berlin (2014)

    Google Scholar 

  2. Bartel, A., Günther, M.: PDAEs in refined electrical network modeling. SIAM Rev. 60(1), 56–91 (2018)

    Article  MathSciNet  Google Scholar 

  3. Bartel, A., Günther, M.: Multirate schemes, an answer of numerical analysis to a demand from applications. Preprint BUW-IMACM 19/12, Institute of Mathematical Modelling, Analysis and Computational Mathematics, Bergische Universität Wuppertal, Germany (2019)

    Google Scholar 

  4. Baum, A.-K., Kolmbauer, M.: Solvability and topological index criteria for thermal management in liquid flow networks. Technical Report RICAM-Report 2015–21, Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, 2015

    Google Scholar 

  5. Baum, A.-K., Kolmbauer, M., Offner, G.: Topological solvability and DAE-index conditions for mass flow controlled pumps in liquid flow networks. Electr. Trans. Num. Anal. 46, 395–423 (2017)

    MathSciNet  MATH  Google Scholar 

  6. Baum, A.-K., Kolmbauer, M., Offner, G.: Topological index analysis applied to coupled flow networks. In: Applications of Differential-Algebraic Equations: Examples and Benchmarks. Differential-Algebraic Equations Forum. Springer, Cham (2018)

    Google Scholar 

  7. Biggs, N.: Algebraic Graph Theory. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1974)

    Book  Google Scholar 

  8. Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, 2nd edn. SIAM Publications, Philadelphia (1996)

    MATH  Google Scholar 

  9. Deo, N.: Graph Theory with Applications to Engineering and Computer Science. Prentice-Hall Series in Automatic Computation. Prentice-Hall of India, Delhi (1974)

    Google Scholar 

  10. Diestel, R.: Graduate Texts in Mathematics: Graph Theory. Springer, Heidelberg (2000)

    Google Scholar 

  11. FMU. Functional Mock-up Interface. https://fmi-standard.org/

  12. Gomes, C., Thule, C., Broman, D., Larsen, P., Vangheluwe, H.: Co-simulation: a survey. ACM Comput. Surv. 51(3), 49:1–49:33 (2018)

    Google Scholar 

  13. Grundel, S., Jansen, L., Hornung, N., Clees, T., Tischendorf, C., Benner, P.: Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. In: Progress in Differential-Algebraic Equations, pp. 183–205. Springer, Berlin (2014)

    Google Scholar 

  14. Kübler, R., Schiehlen, W.: Modular simulation in multibody system dynamics. Multibody Syst. Dyn. 4(2), 107–127 (2000)

    Article  Google Scholar 

  15. Mehrmann, V.: Index Concepts for Differential-Algebraic Equations, pp. 676–681. Springer, Berlin (2015)

    Google Scholar 

  16. Thulasiraman, K., Swamy, M.N.S.: Graphs: Theory and Algorithms. Wiley, New York (2011)

    MATH  Google Scholar 

  17. Tischendorf, C.: Topological index calculation of differential-algebraic equations in circuit simulation. Surv. Math. Ind. 8, 187–199 (1999)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgement

Part of this work has been supported within the framework “FTI Struktur” of the Upper Austrian government.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Kolmbauer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kolmbauer, M., Offner, G., Pöchtrager, B. (2021). Topological Index Analysis and Its Application to Multi-Physical Systems in System Simulation Software. In: Cruz, M., Parés, C., Quintela, P. (eds) Progress in Industrial Mathematics: Success Stories. SEMA SIMAI Springer Series(), vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-61844-5_10

Download citation

Publish with us

Policies and ethics