Multigrid methods and data assimilation ― Convergence study and first experiments on non-linear equations

Emilie Neveu 1 Laurent Debreu 1 François-Xavier Le Dimet 1
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In order to limit the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term and the discretization errors on the efficiency of the coarse grid correction step introduced by the multigrid method. We show that even if for a perfect numerical model the optimal control problem leads to the solution of an elliptic system, discretization errors introduce implicit diffusion that can alter the success of the multigrid methods. Then we test the multigrids configuration and the influence of the algorithmic parameters on a non-linear Burgers equation to show that the algorithm is robust and converges much faster than the monogrid one.
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Emilie Neveu, Laurent Debreu, François-Xavier Le Dimet. Multigrid methods and data assimilation ― Convergence study and first experiments on non-linear equations. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2011, 14, pp.63-80. ⟨hal-01299425⟩

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