AMCA: Second Order Methods for Geophysical Flows by Francois-Xavier Le Dimet

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AD 2000 - From Simulation to Optimization
June 19-23, 2000
INRIA Sophia Antipolis
Sophia Antipolis, France

Organizers
George Corliss, Christele Faure, Andre Galligo, Andreas Griewank, Laurent Hascoet, Uwe Naumann

Second Order Methods for Geophysical Flows
by
Francois-Xavier Le Dimet
Université Joseph Fourier, Grenoble, France
Coauthors: I.M. Navon (Florida State University, USA), P. Ngnepieba (LMC and Université de Yaondé, Cameroon)

A geophysical episode is a unique situation. To retrieve it is necessary to gather all the available information ( models, data, statistics). The information is linked through a variational principle involving the derivative of the model with respect to its variables. Most of the time the variational principle uses a so-called adjoint model which is obtained after a derivation and a transposition of th direct model. The information o the second derivative is useful for several purposes:

to estimate a preconditioning of the problem.

to carry out efficient numerical methods ( Newton and related methods).

to compute the sensitivity with respect to some inputs of the model, especially the observations.

to evaluate statistical quantities such as correlation matrices.

We will show how to compute these second order quantities through a so-called second order adjoint which permits to compute the product of the Hessian matrix by a vector and how this property is used for prctical purposes. We will discuss about the automatic derivation of the second order adjoint. An application will be shown to a problem of identification for underground water. A comparison of hand written adjoint and adjoint generated by ODYSSEE will be carried out.

Date received: February 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cads-59.