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.
Similar content being viewed by others
References
Bear J.: Dynamics of Fluids in Porous Media. Elsevier, Amsterdam (1972)
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)
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)
Deutsch C.V., Journel A.G.: GSLIB: Geostatistical Software Library and User’s Guide. 2nd edn. Oxford University Press, New York (1998)
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)
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)
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)
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)
Wackernagle H.: Multivariate Geostatistics: An Introduction with Applications. Springer, New York (1998)
Author information
Authors and Affiliations
Corresponding author
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
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00791-011-0154-8