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Identification of parameters of the advection-reaction-diffusion equation solved with Discontinuous Galerkin methods: application to plant root growth

Peynaud E.. 2016. Perpignan : Université de Perpignan, 1 p.. Emerging Trends in Applied Mathematics and Mechanics Conference (ETAMM 2016), 2016-05-30/2016-06-03, Perpignan (France).

It is well known that plant root systems are difficult to study in situ. Modelling is not only useful to study and simulate root growth, but also to design new experiments and help to decide what kind of data should be appropriate or not. The density modelling approach consists in following the evolution in time and space of the root density in a volume of soil. This leads to an advection-reaction-diffusion like-equation or to a system. Up to now, there is no specific field experiments to directly measure or estimate some of the model parameters. That is why, we rely on field root density data to identify those parameters by solving an inverse problem, a nonlinear least square minimization problem. The forward problem is approximated on an unstructured mesh. Since it is well known that Lagrange finite elements suffer from a lack of stability especially for a dominant advection, and motivated by the treatment of discontinuous parameters (e.g. for stratified soils), we implemented a Discontinuous Galerkin (DG) method for the space approximation. The inverse problem is solved using a Levenberg-Marquardt method. In this presentation we intend to show some simulations of root growth. Then we address the problem of identifying the parameters and we present some numerical experiments to emphasize that this problem needs a particular attention. (Texte intégral)

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