Laboratoire Jacques-Louis Lions
Présentation
Le laboratoire, créé en 1969, porte le nom de son fondateur Jacques-Louis Lions. il s'agit maintenant d'une unité de recherche conjointe à l’Université Pierre et Marie Curie, à l’université Paris Diderot et au Centre National de la Recherche Scientifique.
Le Laboratoire Jacques-Louis Lions constitue le plus grand laboratoire de France et l'un des principaux au monde pour la formation et la recherche en mathématiques appliquées.
Il accueille l'activités de deux masters deuxième année ce qui représente un centaine d'étudiants. Ses activités recouvrent l’analyse, la modélisation et le calcul scientifique haute performance de phénomènes représentés par des équations aux dérivées partielles.
Fort d’environ 100 enseignants-chercheurs, chercheurs, ingénieurs, personnels administratifs permanents ou émérites, et d’autant de doctorants ou post-doctorants, il collabore avec le monde économique et avec d'autres domaines scientifiques à travers un large spectre d'applications : dynamique des fluides; physique, mécanique et chimie théoriques; contrôle, optimisation et finance; médecine et biologie; traitement du signal et des données.
Thèmes de recherche
- Equations aux dérivées partielles et équations différentielles
- Contrôle, optimisation, calcul des variations
- Calcul scientifique, simulations numériques
- Applications des mathématiques
[hal-01095566] A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations
Date: 9 2 月 2016 - 12:16
Desc: This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwell's equations, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Magnetic-to-Electric operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented.
[hal-00685974] The rain on underground porous media Part I. Analysis of a Richards model
Date: 6 4 月 2012 - 16:08
Desc: <b>Résumé:</b> L'équation de Richards modélise l'écoulement d'eau dans un milieu poreux partiellement saturé souterrain. Lorsqu'il pleut, des conditions aux limites de type Signorini doivent être imposées sur la surface. Nous étudions tout d'abord ce problème qui se traduit par une inéquation variationnelle. Nous écrivons une discrétisation par schéma d'Euler implicite en temps et éléments finis en espace. La convergence de cette discrétisation permet de véri fier que le problème est bien posé. <b>Abstract:</b> Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. We first study this problem which results into a variational inequality. We propose a discretization by an implicit Euler's scheme in time and nite elements in space. The convergence of this discretization leads to the well-posedness of the problem.<p>
[hal-00578694] Nonparametric estimation of the division rate of a size-structured population
Date: 21 Mar 2011 - 22:51
Desc: We consider the problem of estimating the division rate of a size-structured population in a nonparametric setting. The size of the system evolves according to a transport-fragmentation equation: each individual grows with a given transport rate, and splits into two offsprings of the same size, following a binary fragmentation process with unknown division rate that depends on its size. In contrast to a deterministic inverse problem approach, as in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2009), we take in this paper the perspective of statistical inference: our data consists in a large sample of the size of individuals, when the evolution of the system is close to its time-asymptotic behavior, so that it can be related to the eigenproblem of the considered transport-fragmentation equation (see \cite{PR} for instance). By estimating statistically each term of the eigenvalue problem and by suitably inverting a certain linear operator (see previously quoted articles), we are able to construct a more realistic estimator of the division rate that achieves the same optimal error bound as in related deterministic inverse problems. Our procedure relies on kernel methods with automatic bandwidth selection. It is inspired by model selection and recent results of Goldenschluger and Lepski.
[hal-01490440] Analytical Initialization of a Continuation-Based Indirect Method for Optimal Control of Endo-Atmospheric Launch Vehicle Systems
Date: 15 Mar 2017 - 12:45
Desc: In this paper, we propose a strategy to solve endo-atmospheric launch vehicle optimal control problems using indirect methods. More specifically, we combine shooting methods with an adequate continuation algorithm, taking advantage of the knowledge of an analytical solution of a simpler problem. This procedure is resumed in two main steps. We first simplify the physical dynamics to obtain an analytical guidance law which is used as initial guess for a shooting method. Then, a continuation procedure makes the problem converge to the complete dynamics leading to the optimal solution of the original system. Numerical results are presented.
[hal-00768479] Positivity-preserving schemes for Euler equations: Sharp and practical CFL conditions
Date: 13 1 月 2013 - 16:28
Desc: When one solves PDEs modelling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. For instance, the underlying physical assumptions for the Euler equations are the positivity of both den- sity and pressure variables. We consider in this paper an unstructured vertex-based tesselation in R2 . Given a MUSCL finite volume scheme and given a reconstruction method (including a limiting process), the point is to determine whether the overall scheme ensures the positivity. The present work is issued from seminal papers from Perthame and Shu (On positivity preserving finite volume schemes for Euler equations, Numer. Math. 73 (1996) 119-130) and Berthon (Robustness of MUSCL schemes for 2D unstructured meshes, J. Comput. Phys. 218 (2) (2006) 495-509). They proved in different frameworks that under assumptions on the cor- responding one-dimensional numerical flux, a suitable CFL condition guarantees that den- sity and pressure remain positive. We first analyse Berthon's method by presenting the ins and outs. We then propose a more general approach adding non geometric degrees of freedom. This approach includes an optimization procedure in order to make the CFL condition explicit and as less restric- tive as possible. The reconstruction method is handled independently by means of s- limiters and of an additional damping parameter. An algorithm is provided in order to specify the adjustments to make in a preexisting code based on a certain numerical flux. Numerical simulations are carried out to prove the accuracy of the method and its ability to deal with low densities and pressures.