Skip to main content
Log in

Least squares approach for initial data recovery in dynamic data-driven applications simulations

  • Published:
Computing and Visualization in Science

Abstract

In this paper, we consider the initial data recovery and the solution update based on the local measured data that are acquired during simulations. Each time new data is obtained, the initial condition, which is a representation of the solution at a previous time step, is updated. The update is performed using the least squares approach. The objective function is set up based on both a measurement error as well as a penalization term that depends on the prior knowledge about the solution at previous time steps (or initial data). Various numerical examples are considered, where the penalization term is varied during the simulations. Numerical examples demonstrate that the predictions are more accurate if the initial data are updated during the simulations.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bear J.: Dynamics of Fluids in Porous Media. Elsevier, Amsterdam (1972)

    MATH  Google Scholar 

  2. Bear, J.: Modeling transport phenomena in porous media. In: Environmental Studies (Minneapolis, MN, 1992) vol. 79 of IMA Vol. Math. Appl., pp. 27–63 Springer, New York (1996)

  3. Chavent, G., Jaffré, J.: Mathematical Models and Finite Elements for Reservoir Simulation. no. 17 in Studies in Mathematics and its Applications. North-Holland, Amsterdam (1986)

  4. Deutsch C.V., Journel A.G.: GSLIB: Geostatistical Software Library and User’s Guide. 2nd edn. Oxford University Press, New York (1998)

    Google Scholar 

  5. Douglas C., Shannon C., Efendiev Y., Ewing R., Ginting V., Lazarov R., Cole M., Jones G., Johnson C., Simpson J.: A Note on Data-Driven Contaminant Simulation. Lecture Notes in Computer Science, vol. 3038, pp. 701–708. Springer, Berlin (2004)

    Google Scholar 

  6. Douglas, C.C., Efendiev, Y., Ewing, R., Lazarov, R., Cole, M.R., Johnson, C.R., Jones, G.: Virtual telemetry middleware for dddas. Computational Sciences—ICCS 2003. In: Sllot, P.M.A., Abramson, D., Dongarra, J.J., Zomaya, A.Y., Gorbachev, Yu. E. (eds.) vol. 4, pp. 279–288 (2003)

  7. Douglas C.C., Shannon C., Efendiev Y., Ewing R., Ginting V., Lazarov R., Cole M.R., Jones G., Johnson C.R., Simpson J.: Using a virtual telemetry methodology for dynamic data driven application simulations. In: Darema, F. (eds) Dynamic Data Driven Applications Systems, Kluwer, Amsterdam (2004)

    Google Scholar 

  8. Ewing, R.E. (eds): The Mathematics of Reservoir Simulation, vol. 1. of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1983)

    Google Scholar 

  9. Wackernagle H.: Multivariate Geostatistics: An Introduction with Applications. Springer, New York (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Lazarov.

Additional information

Communicated by Gabriel Wittum.

Research of the authors is partially supported by NSF grant ITR-0540136 and by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Douglas, C., Efendiev, Y., Ewing, R. et al. Least squares approach for initial data recovery in dynamic data-driven applications simulations. Comput. Visual Sci. 13, 365–375 (2010). https://doi.org/10.1007/s00791-011-0154-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00791-011-0154-8

Keywords

Navigation