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Séminaires EDP 2018-2019



    • Jeudi 21 mars 14:00-15:00 - Félix Kpadonou - ENSTA ParisTech

      F. Kpadonou : Efficient preconditioner for H-matrix accelerated Boundary Element Method for 3D wave propagation problems

      Résumé : We are concerned in this talk with the improvement of the efficiency of iterative solver treating of 3D frequency domain (acoustic and elastic) wave propagation problems through Boundary Element Method (BEM). Since the fundamental solutions involved in the integral equations are of non-local support, the discretization with the BEM yields to some linear systems with fully-populated matrices and therefore memory storage consuming.
      \mathcal{H}-matrix (Hierarchical matrix) technique offers an alternative data-sparse representation to these matrices. This representation is based on a hierarchical partitioning of the system matrix and the use of low-rank approximations for some blocks which are a priori known as low-rank admissible. We propose an algebraic preconditioner for the \mathcal{H}-matrix based iterative solver. The preconditioner is not defined explicitly. Indeed, only its application to a given vector is required and obtained as the solution of a linear system, also computed through an iterative solver. As a result, one deals with a two-level iterative solver. The efficiency of the proposed preconditioner will be shown with some numerical tests. This work is done in collaboration with Stéphanie Chaillat and Patrick Ciarlet.

      Lieu : Salle G210, bât. Germain

    • Jeudi 28 mars 14:00-15:00 - Marco Montemurro - ENSAM Bordeaux

      M. Montemurro : A new topology optimization method based on Non-Uniform Rational B-Splines Hyper-surfaces

      Résumé : This talk focuses on a new Topology Optimisation (TO) method, developed at the Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) laboratory, which is based on a smart coupling between the well- established Solid Isotropic Material Penalisation (SIMP) strategy and the Non-Uniform Rational B-Splines (NURBS) geometric entities formalism. The resulting method is called “NURBS-based SIMP method” and it is implemented into the code SANTO (SIMP And NURBS for Topology Optimisation).
      This TO method has been developed in order to go beyond the restrictions related to the classical SIMP approach : the accent is put on the general nature of the proposed strategy, on its robustness and, of course, on its advantages when compared to the classic SIMP method.
      Among these advantages a special attention is dedicated to the intrinsic CAD compatibility of the solutions provided by the NURBS-based SIMP approach. This is due to the interesting properties of the NURBS entities and to the fact that, at each iteration, a geometric description of the topology boundary is always available. Moreover, unlike the SIMP approach, the optimised topology does not depend upon the quality of the mesh of the FE model and the continuity of the pseudo-density field is implicitly ensured by the NURBS blending function properties. Therefore no numerical artefacts, like filtering techniques, must be implemented to avoid topology discontinuity.
      In particular the following features will be highlighted during the presentation :
      - Topology representation. The topology description relies on a purely geometric entity (i.e. the NURBS surface/hyper-surface) defined over the computational domain and it is unrelated to the underlying mesh.
      - Variables Saving and Implicitly Defined Filter Zone. Thanks to the local support property of NURBS blending functions, a single control point (and the respective weight) affects the fictitious density field only in a well-defined portion of the computational domain. Unlike to the classical SIMP approach, there is no need to define a further filter zone, because the NURBS local support establishes an implicit relationship among contiguous elements.
      - Importance of the NURBS Weights. The influence of the NURBS weights on the final optimum topology is investigated. Including the NURBS weights among the design variables implies, on the one hand, improved quality of the solution (in terms of objective and constraint functions) and, on the other hand, a smoother boundary.
      - Performances and Robustness. The presented algorithms systematically provides solutions, which exhibit equivalent or better performances, if compared to those obtained through a commercial software as Altair OptiStruct®.
      - Results provision, consistency and CAD-compatibility. The advantages of NURBS entities are fully exploited in terms of their CAD compatibility : a suitable post-processing phase can be implemented and utilised in order to straightforwardly obtain the final optimised geometry for 2D and 3D problems.
      - Effective handling of geometric constraints. Thanks to the properties of NURBS blending functions some important geometric constraints like the minimum and maximum length scale can be satisfied implicitly by tuning the discrete parameters involved into the definition of the NURBS entities without imposing further (often too complex) optimisation constraints.

      Lieu : Salle G210, bât. Germain

    • Jeudi 4 avril 14:00-15:00 - Fabien Crauste - Université de Bordeaux

      F. Crauste : Modélisation Mathématique en Immunologie

      Résumé : La réponse immunitaire consiste en un ensemble de processus biologiques mis en oeuvre par l’organisme pour répondre à une infection. Beaucoup de ces processus sont spécifiques et caractérisés par d’importantes régulations, tant moléculaires que cellulaires. Je présenterai un ensemble de travaux réalisés en collaboration avec des immunologistes sur la modélisation mathématique de la réponse spécifique T CD8, c’est à dire impliquant des lymphocytes T de type CD8. En particulier, j’aborderai le développement et la validation d’un modèle de la cinétique de la réponse T CD8 (qui se développe à travers l’activation de cellules naïves, l’expansion d’une population de cellules cytotoxiques, puis la contraction de la population de cellules et la génération d’une mémoire immunitaire). Je discuterai ensuite la prise en compte de la variabilité inter-individuelle caractéristique de la réponse T CD8, via l’utilisation de modèles non-linéaires à effets mixtes. Enfin, je présenterai un modèle mathématique multi-échelles de la réponse immunitaire couplant des dynamiques moléculaires et cellulaires, et permettant de s’intéresser aux conséquences cellulaires d’événements moléculaires précoces.

      Lieu : Salle G210, bât. Germain

    • Jeudi 11 avril 14:00-15:00 - Yves Capdebosq - Université Paris-Diderot

      Y. Capdebosq : A propos d’approches statistiques récentes appliquées aux problèmes inverses

      Lieu : Salle G210, bât. Germain.Travail en collaboration avec G.S. Alberti (Gênes) et Yannick Privat (Strasbourg). De nombreux progrès ont été effectués, en imagerie, en combinant des méthodes déterministes avec de l’apprentissage. Cela a suscité un intérêt renouvelé pour les méthodes statistiques. Dans cet exposé, je discuterai de l’interprétation que l’on peut faire de l’une de ces méthodes.

    • Jeudi 18 avril 14:00-15:00 - Louis Garrigue - Univ. Paris Dauphine

      L. Garrigue : Unique continuation for the Hohenberg-Kohn theorem

      Résumé : Density functional theory is a very active field of research, and is of great importance in today’s science. It is founded by the Hohenberg-Kohn theorem, a strinking result stating that all the information of a quantum mechanical system is contained in its ground-state one-body density only. In 1983, Lieb remarked that the rigorous proof relies on a unique continuation property for many-body (magnetic) Schrödinger operators. We will introduce the Hohenberg-Kohn theorem, show why it reduces to a strong unique continuation problem, and explain how our Carleman estimate involving fractional Laplacians solves it. Based on

      Lieu : Salle G210, bât. Germain

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Les séminaires ont lieu le jeudi, bâtiment Sophie Germain, en salle G210 de 14h à 15h.

Ce séminaire hebdomadaire s’ajoute aux Journées EDP concentrées autour d’un thème, avec plusieurs conférences dans la journée.

Contact : Tahar Boulmezaoud et Pierre Gabriel.

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