Séminaire Calcul Scientifique et Modélisation

Responsables : Christele Etchegaray et Martin Parisot

Le 19 janvier 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Thibault Bourgeron

Dynamique adaptative de population sexuée, structurée en âge, induite par un changement d'environnement

On présentera des équations aux dérivées partielles modélisant l'adaptation d'une population sexuée à un (changement d')environnement par recombinaison et sélection. La reproduction sexuée est modélisée par l'opérateur infinitésimal, qui n'est ni linéaire ni monotone. On montrera l'existence d'éléments propres sans la théorie de Krein-Rutman (qui n'est pas applicable à ce problème). Ensuite on expliquera comment la méthodologie de l'approximation WKB peut être adaptée à ces équations. Dans un certain rapport des échelles phénotypiques elle permet d'obtenir un développement de la densité de population à l'équilibre par rapport à la variance génétique créée à chaque génération. La structure en âge fait apparaître des effets non linéaires (mur de mortalité). Les résultats seront illustrés par des simulations numériques.

Le 2 février 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Florian Blachère

Schémas numériques d'ordre élevé et préservant l'asymptotique pour l'hydrodynamique radiative

Le but de ce travail est de construire un schéma volumes finis explicite d'ordre élevé pour des systèmes de lois de conservation avec terme source qui peuvent dégénérer vers des équations de diffusion sous des conditions de compatibilités. Cette dégénérescence est observée en temps long et/ou lorsque le terme source devient prépondérant. Par exemple, ce comportement peut être observé sur le modèle d'Euler isentropique avec friction, ou sur le modèle M1 pour le transfert radiatif ou encore avec l'hydrodynamique radiative. On propose une théorie générale afin de développer un schéma d'ordre un préservant l'asymptotique (au sens de Jin) pour suivre la dégénérescence. On montre qu'il est stable et consistant sous une condition CFL hyperbolique classique dans le régime de transport comme proche de la diffusion pour tout maillage 2D non structuré. De plus, on justifie qu'il préserve aussi l'ensemble des états admissibles, ce qui est nécessaire pour conserver des solutions physiquement et mathématiquement valides. Cette construction se fait en utilisant le schéma non-linéaire de Droniou et Le Potier pour discrétiser l'équation de diffusion limite. Des résultats numériques sont présentés pour valider le schéma dans tous les régimes.

Le 16 février 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Julien Dambrine

The Dirichlet-to-Neumann operator with a level-set representation of the interface

The motion of surfaces with a velocity depending on the Dirichlet-to-Neumann operator for a given elliptic problem appear in various practical applications ranging from the motion of cells to the geometrical optimisation of mechanical structures. The level-set framework is particularly interesting in this context of moving surfaces. In this work we focus on the computation of the Dirichlet-to-Neumann operator calculation for the Laplace equation, following the ideas developed by C.Kublik et. al. in [1] for the computation of the bulk solution. [1] Catherine Kublik, Nicolay M. Tanushev, Richard Tsai, An implicit interface boundary integral method for Poisson's equation on arbitrary domains, JCP, 2013.

Le 9 mars 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

salle Ada Lovelace (Inria)

George Tzagkarakis

Compressive sensing: Chasing information in shadows

In recent years, compressive sensing (CS) has attracted considerable attention in areas of applied mathematics, computer science, and electrical engineering by suggesting that it may be possible to surpass the traditional limits of sampling theory. CS is based on the fundamental fact that many natural signals can be represented using only a few non-zero coefficients in a suitable basis or dictionary. Nonlinear optimization can then enable accurate recovery of such signals from a highly reduced set of measurements. In this talk, we overview the basic theory underlying CS, and demonstrate its efficiency in emerging applications (e.g., medical image processing). Specifically, we focus on the key concepts of sparsity and other low-dimensional signal models, in order to treat the central question of how to accurately recover a high-dimensional signal from a small set of measurements, whilst providing performance guarantees for a variety of sparse recovery algorithms.

Le 23 mars 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Daniele Di Petrio

An introduction to Hybrid High-Order methods

Hybrid High-Order (HHO) methods are a class of new generation numerical schemes for PDEs with several advantageous features, including: (i) support of general polytopal meshes in arbitrary space dimension; (ii) arbitrary approximation order; (iii) compliance with the physics, including robustness with respect to the variations of physical coefficients and reproduction of key continuous properties at the discrete level; (iv) reduced computational cost thanks to hybridization, static condensation, and compact stencil. This presentation contains an introduction as well as examples of applications to nonlinear problems. [1] D. A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes, Comput. Meth. Appl. Mech. Engrg., 2015, 283:1–21. DOI: 10.1016/j.cma.2014.09.009. [2] D. A. Di Pietro and R. Tittarelli, An introduction to Hybrid High-Order methods, arXiv preprint arXiv:1703.05136, March 2017. [3] D. A. Di Pietro and J. Droniou, A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes, Math. Comp., 2017. Published online. DOI: 10.1090/mcom/3180. [4] D. A. Di Pietro and J. Droniou, Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems, Math. Models Methods Appl. Sci., 2017. Published online. DOI: 10.1142/S0218202517500191. [5] D. A. Di Pietro and S. Krell, A Hybrid High-Order method for the steady incompressible Navier–Stokes problem, arXiv preprint arXiv:1607.08159, July 2016.

Le 6 avril 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Marion Darbas

Ondes électromagnétiques et deux applications en imagerie cérébrale: modélisation et résolution numérique.

Je présenterai dans cet exposé des résultats liés à deux applications en imagerie cérébrale qui utilisent la propagation des ondes électromagnétiques. Chacune d'entre elles nous amène à résoudre un problème inverse. La première concerne l'électroencéphalographie chez le nouveau-né et la localisation de sources épileptiques. La seconde pose la question du diagnostic d'accidents vasculaires cérébraux par imagerie micro-ondes. Les équations mises en jeu sont les équations de Maxwell. J'aborderai des questions de modélisation, d'analyse de sensibilité des mesures et la résolution numérique des problèmes direct et inverse.

Le 27 avril 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Philippe Moireau

Observer strategies for inverse problems associated with wave-like equations

In this talk, we present the theory of asymptotic observers on the exemplary case of wave-like equations. We show how this approach allows to use heterogeneous types of data in order to reconstruct a trajectory, estimate the initial conditions or identify some parameters. We present a complete analysis and numerical analysis of the strategy. The question of the data sampling and the impact of noise is also studied. Finally, we illustrate the approaches on various practical cases, from the wave equation in bounded of unbounded domain to elastodynamics models.

Le 11 mai 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Jean-Pierre Croisille

Numerical approximation of propagation problems on the sphere

In this talk, we present recent progress on the design of a compact scheme for convective equations on the sphere. In numerical climatology, the simplest system consists of the shallow water equations on the rotating earth, in linear or nonlinear form. We show that a centered eulerian scheme presents attractive properties for this purpose. This kind of scheme can be considered as a discrete counterpart of the equations with a minimal numerical diffusion. This property is essential to preserve the accuracy of the approximation in space after a large number of time iterations. We will present the main properties of the spatial and temporal approximation as well as numerical results obtained with this approach on a series of tests cases of the literature.

Le 1er juin 2017 à 11:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Cécile Carrère

Sans titre

Le 15 juin 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

salle Ada Lovelace (Inria)

Adrien Loseille

A unified framework for advanced mesh generation and adaptation

This presentation gives a unified framework to address many issues in mesh generation and mesh adaptation from surface, volume to anisotropic meshing. After reviewing the design of so-call metric-based error estimates to control and prescribe strechings and orientations from solutions of PDEs, we will show how to recast all classical meshing operators (insertion, collapse, swaps, …) to a unique cavity-based operator. We will demonstrate that this methodology addresses efficiently surface (re)meshing, non-manifold geometry, adaptive anisotropic (re)meshing, structured boundary layer (re)meshing, hybrid mesh generation, ...These concepts will be illustrated on CFD simulations.

Le 29 juin 2017 à 11:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

George Klonaris

Morphodynamics in a beach with submerged breakwaters

The main scope of this work is to contribute to the understanding of the complex hydrodynamic and morphodynamic processes that take place in coastal zones protected by single or multiple submerged breakwaters. The morphological response of such a system was studied both numerically and experimentally. In particular, a compound numerical model was developed in order to simulate the wave propagation, the wave-induced currents, the coastal sediment transport, the bed erosion and accretion, and finally describe the cross-shore profile and the coastline evolution in the lee of a system of permeable submerged breakwaters. The behaviour of such a system has not been described so far in a general and quantitatively consistent manner. The integrated model includes the combination of a higher order Boussinesq-type wave model with a sediment transport and a geomorphological model. Laboratory experiments were also performed focusing on measuring the morphology evolution of a sandy sloping beach in the lee of a permeable submerged breakwater. A thorough validation of the model is presented in order to check the efficiency of its various modules. Finally, the effect of some significant geometric and wave parameters was studied numerically in order to draw some guidelines for the optimal design of the aforementioned structures.

Le 7 juillet 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

salle Ada Lovelace (Inria)

Guglielmo Scovazzi

The shifted Nitsche method: A new approach to embedded boundary conditions

Embedded boundary methods obviate the need for continual re-meshing in many applications involving rapid prototyping and design. Unfortunately, many finite element embedded boundary methods for incompressible flow are also difficult to implement due to the need to perform complex cell-cutting operations at boundaries. We present a new, stable, and simple embedded boundary method, which we call “the shifted Nitsche method.” The proposed method eliminates the need to perform cell cutting, and demonstrate it on large-scale incompressible flow problems, solid mechanics, shallow water flows.

Le 6 octobre 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Kevin Santugini

Two-Dimensionnal Runge-Kutta Methods of order $3$ or above

Runge Kutta methods are well known high order methods for ODEs. In scalar advection problems with a single family of characteristics, any high order Runge-Kutta method can be used to compute high order solutions that don't diffuse by following characteristics. This is known as the method of lines. When the advection equation is no longer scalar, two (or more) families of characteristics may appear. By putting the unknowns at the intersection between the characteristics of these two different families, designing a Two-Dimensional Runge-Kutta method of order $2$ is hardly more difficult. But going beyond order $2$, designing Two-Dimensional Runge-Kutta methods of order $3$ or above is far more difficult.

Le 19 octobre 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Fabien Marche

En eaux peu profondes: modélisation et simulations numériques

Je ferai un tour d'horizon de travaux récents effectués en collaboration avec A. Duran et D.Lannes concernant la modélisation, l'analyse numérique et la simulation des ondes de surfaces à partir des asymptotiques shallow water pour écoulements à surface libre. Je vous présenterai des modèles « optimisés » récents (faiblement dispersifs fortement non-linéaires) ainsi que les formulations discrètes associées en éléments finis discontinus qui ont été proposées récemment. J'évoquerai la possibilité de surmonter l'hypothèse classique d'irrotationalité des écoulements.

Le 9 novembre 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Ulrich Razafison

Simulations numériques de lois de conservations avec contraintes non locales sur le flux : application au trafic piéton

Dans cet exposé, nous nous placerons dans le cadre du trafic piéton et nous présenterons un modèle permettant de décrire la chute de capacité (c'est-à-dire le flux de piétons maximal par unité de temps) d'une sortie de salle lors d'une évacuation. Le modèle repose sur une loi de conservation et la capacité de la sortie est décrite par une contrainte sur le flux, qui est supposée non locale dans le sens où cette contrainte dépend de la solution du modèle elle-même. La chute de capacité se produit pour les hautes densités de piétons exprimant la congestion de la sortie. Par des simulations numériques, nous montrerons que le modèle est capable de reproduire deux effets liés à la chute de la capacité et qui ont déjà été observés et reproduits expérimentalement : l'effet ''Faster-Is-Slower" qui stipule qu'une augmentation de la vitesse des piétons peut entraîner une augmentation du temps d'évacuation, et une variante du "paradoxe de Braess" qui indique que placer un obstacle avant la sortie peut faire diminuer la pression des piétons sur la sortie et entraîner une diminution du temps d'évacuation.

Le 23 novembre 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Pas de séminaire Modélisation et Analyse des phénomènes dispersifs\, 70 ans de J.-C. Saut

Sans titre

Le 30 novembre 2017 à 11:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Birte Schmidtmann

Reconstruction Techniques and Riemann Solvers for Finite Volume Methods / Techniques de Reconstructions et Solveurs de Riemann pour les Méthodes de Type Volumes Finis

We are interested in the numerical solution of hyperbolic conservation laws on the most local compact stencil consisting of only nearest neighbors. In the Finite Volume setting, in order to obtain higher order methods, the main challenge is the reconstruction of the interface values. These are crucial for the definition of the numerical flux functions, also referred to as the Riemann solver of the scheme. Often, the functions of interest contain smooth parts as well as discontinuities. Treating such functions with high-order schemes may lead to undesired oscillations. However, what is required is a solution with sharp discontinuities while maintaining high-order accuracy in smooth regions. One possible way of achieving this is the use of limiter functions in the MUSCL framework which switch the reconstruction to lower order when necessary. Another possibility is the third-order variant of the WENO family, called WENO3. In this work, we will recast both methods in the same framework to demonstrate the relation between Finite Volume limiter functions and the way WENO3 performs limiting. We present a new limiter function, which contains a decision criterion that is able to distinguish between discontinuities and smooth extrema. Our newly-developed limiter function does not require an artificial parameter, instead, it uses only information of the initial condition. We compare our insights with the formulation of the weight-functions in WENO3. The weights contain a parameter ε, which was originally introduced to avoid the division by zero. However, we will show that ε has a significant influence on the behavior of the reconstruction and relating the WENO3 weights to our decision criterion allows us to give a clarifying interpretation. In a second part, we will review some well-known Riemann solvers and introduce a family of incomplete Riemann solvers which avoid solving the eigensystem. Nevertheless, these solvers still reproduce all waves with less dissipation than other methods such as HLL and FORCE, requiring only an estimate of the globally fastest wave speeds in both directions. Therefore, the new family of Riemann solvers is particularly efficient for large systems of conservation laws when no explicit expression for the eigensystem is available. Joint work with: M. Torrilhon (RWTH Aachen University), B. Seibold (Temple University, Philadelphia), Rémi Abgrall (University of Zurich), Pawel Buchmüller (Universität Düsseldorf )

Le 7 décembre 2017 à 14:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Simon Labarthe

A mathematical model of the human gut microbiota in its environment

The human gut harbors a complex bacterial community that maintains a symbiotic relationship with its host. An increasing number of studies highlight its implication in the maintain of the host's health, but also in various disorders such as inflammatory bowel disease, allergic or metabolic disorders. We propose to integrate in the same model different micriobiological or biophysical informations related to the microbiota structure and functions and to the gut environment. A population dynamics model of functional microbial populations involved in fibre degradation is coupled to a fluid mechanic model of the intestinal fluids. This model is simplified through asymptotic analysis and is used to study the mechanisms that impact the spatial structure of the gut microbiota.

Le 21 décembre 2017 à 11:00

Séminaire de Calcul Scientifique et Modélisation

Salle 2

Tommaso Taddei

Model order reduction methods for Data Assimilation: simulation-based approaches for state estimation, and damage identification

I present work toward the development of Model Order Reduction (MOR) techniques to integrate (i) parameterized mathematical models, and (ii) experimental observations, for prediction of engineering Quantities of Interest (QOIs). More in detail, I present two Simulation-Based approaches — the PBDW approach to state estimation, and the SBC approach for damage identification — that map observations to accurate estimates of the QOI, without estimating the parameters of the model. PBDW and SBC rely on recent advances in MOR to speed up computations in the limit of many model evaluations, and/or to compress prior knowledge about the system coming from the parameterized model into low-dimensional and more manageable forms. In the last part of the talk, motivated by the extension of PBDW and SBC to Fluid Mechanics problems, I present a MOR technique for long-time integration of parameterized turbulent flows. The approach corrects the standard Galerkin formulation by incorporating prior information about the attractor, and relies on an a posteriori error indicator to estimate the error in mean flow prediction.

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Séminaire Calcul Scientifique et Modélisation

Institut de Mathématiques de Bordeaux UMR 5251