IJPAM: Volume 52, No. 1 (2009)

ON THE NEWTON'S ALGORITHM FOR
THE DATA ASSIMILATION PROBLEM:
AN APPLICATION IN HYDROLOGY

Pierre Ngnepieba$^1$, Francois-Xavier Le Dimet$^2$,
Andrew Jones, Jr.$^3$, Victor Shutyaev$^4$
$^{1,3}$Department of Mathematics
Florida A&M University
Tallahassee, Florida, 32307, USA
$^1$e-mail: [email protected]
$^3$e-mail: [email protected]
$^2$Laboratoire Jean-Kuntzmann
Université de Joseph Fourier Grenoble and INRIA
Grenoble, FRANCE
e-mail: [email protected]
$^4$Institute of Numerical Mathematics
Russian Academy of Sciences
Gubkina 8, Moscow, 119991, RUSSIA
e-mail: [email protected]


Abstract.The problem of data assimilation for a nonlinear evolution model is considered with the aim to identify the initial and/or boundary conditions. An approach to solve the data assimilation process is described. This approach is based on the Newton's Method. An application to the data assimilation problem in hydrology is presented. Numerical results are given.

Received: March 8, 2009

AMS Subject Classification: 65N30

Key Words and Phrases: Newton's Method, data assimilation, infiltration, optimality system, adjoint, Hessian, Richards equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 1