Skip to main content

Parameter Estimation in Multispecies Transport Reaction Systems Using Parallel Algorithms

  • Chapter
Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology

Part of the book series: Water Science and Technology Library ((WSTL,volume 23))

Abstract

The authors present a general approach to estimate parameters in reactive multispecies transport models. The basic idea is to treat the discretized model equations as nonlinear constraints of a large finite-dimensional optimization problem. Multiple shooting in time is a specific feature of the discretization. The resulting constrained least squares problem is solved by a generalized Gauss-Newton method. Parallelism on several levels is exploited in the algorithmn. A practical parameter estimation problem from contaminant hydrology is considered and successfully solved. The reliability of the parameter estimates is confirmed by the results of a sensitivity analysis. A more detailed description of the presented methods and results can be found in [9].

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. G. Bock. Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, volume Nr. 183. Bonner Mathematische Schriften, 1987.

    Google Scholar 

  2. H. G. Bock, E. Eich, and J. Schiöder. Numerical solution of constrained least squares boundary value problems in differential-algebraic equations. In K. Strehmel, editor, Numerical Treatment of Differential Equations. BG Teubner, Leipzig, 1988.

    Google Scholar 

  3. H. G. Bock, J. Schiöder, and V. H. Schulz. Numerik großer differentiell-algebraischer Gleichungen: Simulation und Optimierung”. In H. Schuler, editor, Prozeßsimulation. VCH-Verlag, Weinheim, 1994.

    Google Scholar 

  4. J. V. Gallitzendörfer and H. G. Bock. Parallel algorithms for optimization boundary value problems in DAE. In H. Langendörfer, editor, Praxisorientierte Parallelverarbeitung. Hanser, München, 1994.

    Google Scholar 

  5. P. Knabner. Mathematische Modelle für den Transport gelöster Stoffe in sorbieren-den porösen Medien. Schwerpunktprogramm der Deutschen Forschungsgemeinschaft: Anwendungsbezogene Optimierung und Steuerung Report No. 121, Universität Augsburg, 1988.

    Google Scholar 

  6. W. Schäfer. Numerische Modellierung mikrobiell beeinflußter Stofftransportvorgänge im Grundwasser. Oldenbourg Verlag; Schriftenreihe Wasser, Abwasser, 1992.

    Google Scholar 

  7. Volker H. Schulz. Ein effizientes Kollokationsverfahren zur numerischen Behandlung von Mehrpunktrandwertaufgaben in der Parameteridentifizierung und optimalen Steuerung. Master’s thesis, Universität Augsburg, 1990.

    Google Scholar 

  8. Stephen J. Wright. Stable parallel algorithms for two-point boundary value problems. SIAM J. Sci. Stat Comput., 13(3):742–764, 1992.

    Article  Google Scholar 

  9. M. W. Zieße, H. G. Bock, J. V. Gallitzendörfer, and J. P. Schiöder. Parameter Estimation in Multispecies Transport Reaction Systems Using Parallel Algorithms. Preprint 95 – 26 (SFB 359), IWR, Universität Heidelberg, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Kluwer Academic Publishers

About this chapter

Cite this chapter

Zieße, M.W., Bock, H.G., Gallitzendörfer, J.V., Schlöder, J.P. (1996). Parameter Estimation in Multispecies Transport Reaction Systems Using Parallel Algorithms. In: Gottlieb, J., DuChateau, P. (eds) Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology. Water Science and Technology Library, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1704-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1704-0_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7263-2

  • Online ISBN: 978-94-009-1704-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics