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

  • C. Douglas
  • Y. Efendiev
  • R. Ewing
  • V. Ginting
  • R. Lazarov
  • M. Cole
  • G. Jones
Article

DOI: 10.1007/s00791-011-0154-8

Cite this article as:
Douglas, C., Efendiev, Y., Ewing, R. et al. Comput. Visual Sci. (2010) 13: 365. doi:10.1007/s00791-011-0154-8

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.

Keywords

Initial data recovery Dynamic data-driven applications simulations (DDDAS) Least squares Parameters update 

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • C. Douglas
    • 4
    • 5
  • Y. Efendiev
    • 1
    • 2
  • R. Ewing
    • 1
    • 2
  • V. Ginting
    • 4
  • R. Lazarov
    • 1
    • 2
  • M. Cole
    • 3
  • G. Jones
    • 3
  1. 1.Institute for Scientific ComputationTexas A & M UniversityCollege StationUSA
  2. 2.Department of MathematicsTexas A & M UniversityCollege StationUSA
  3. 3.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  4. 4.Department of MathematicsUniversity of WyomingLaramieUSA
  5. 5.Department of Computer ScienceYale UniversityNew HavenUSA

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