format des présentations : 30mn

Programme de la matinée (10h30 - 12h30) :

Introduction par Alain Dervieux

Hubert Alcin (équipe TROPICS, INRIA Sophia)
"Sur la consistance multigrille des grilles grossières algébriques"

Anca Belme (équipe TROPICS, INRIA Sophia)
"Fully anisotropic goal-oriented mesh adaptation for unsteady flows"

Thierry Coupez (Ecole des Mines ParisTech, Centre de Mise en Forme des Matériaux)
"Adaptation anisotrope et level set"

Programme de l'après midi (14h - 15h30) :

Joseph Charles (équipe NACHOS, INRIA Sophia)
"Numerical study of basis expansions and time integration methods for the numerical resolution of the time-domain Maxwell equations"

Mohammed El Bouajaji (équipe NACHOS, INRIA Sophia)
"High-Order Discontinuous Galerkin Method for the Time-Harmonic Maxwell Equations"

Elie Hachem (Ecole des Mines ParisTech, Centre de Mise en Forme des Matériaux)
"Méthode éléments finis stabilisés en aérothermie"

Hubert Alcin (équipe TROPICS, INRIA Sophia)
"Sur la consistance multigrille des grilles grossières algébriques"

Pour le traitement des équations aux derivées partielles, les méthodes de décomposition de domaine ont pris une place prépondérante. Cependant certaines, comme par exemple la méthode de Schwarz additive ne sont pas scalables sans l’introduction d’une sequence appelée “grille grossière” dans l’algorithme. Ces méthodes utilisent en général des bases grossières simplifiées qui ne permettent pas au problème grossier de converger vers la solution continue. Il en résulte un moins bon demarrage de la convergence. La consistance de la grille grossière peut être examinée à travers les opérateurs de transfert entre les deux niveaux. Dans le cas général, on peut utiliser les fonctions de base multi-niveau non-structurées. Ces propriétés sont vérifiées sur une première série de problèmes bidimensionnels elliptiques avec un préconditionnement de type Schwarz Additif Restreint et des maillages non-structurés comportant de forts étirements.

Anca Belme (équipe TROPICS, INRIA Sophia)
"Fully anisotropic goal-oriented mesh adaptation for unsteady flows"

This work presents a new algorithm for combining a fully anisotropic goal-oriented mesh adaptation with the transient fixed point method for unsteady problems. The minimization of the error on a functional provides both the density and the anisotropy (stretching) of the optimal mesh. This method is used for specifying the mesh for a time sub-interval from the state and the adjoint. The global transient fixed point iterates the re-evaluation of meshes and the states over the whole time interval until convergence. Applications to unsteady blast-wave Euler flows are presented.

Thierry Coupez (Ecole des Mines ParisTech, Centre de Mise en Forme des Matériaux)
"Adaptation anisotrope et level set"

"Anisotropic mesh adaptation and convected Level Set" Very convincing results with anisotropic mesh adaptation have been already obtained in the past years by deriving the metric field from a posteriori interpolation error analysis and hessian reconstruction. We propose here a different route to make the metric field directly at the node of the mesh. We introduce the length distribution tensor and show that only a 1d error analysis along the edges is sufficient. We will show the possibilities of this technique on geometrical interpolation problems by combination with a Level Set representation, moving free surfaces and interfaces. We will show the efficiency of the anisotropic adaptive process to the fluid buckling simulation.

12h30 - 14h : Déjeuner

Joseph Charles (équipe NACHOS, INRIA Sophia)
"Numerical study of basis expansions and time integration methods for the numerical resolution of the time-domain Maxwell equations"

We consider a discontinuous Galerkin time-domain (DGTD) method for the solution of the unsteady Maxwell equations modelling electromagnetic wave propagation. A numerical study comparing different polynomial interpolation methods for efficiency and convergence purposes is presented here. This work is a preliminary step for a more general framework aiming at developing an arbitrary high order DGTD method using tetrahedral meshes for the numerical simulation of tridimensional propagation problems. In particular, we seek to design a numerical methodology which combines a mesh refinement (h-refinement) where the regularity of the solution varies with an enrichment of the approximation order (p-enrichment) where the solution is regular.

Mohammed El Bouajaji (équipe NACHOS, INRIA Sophia)
"High-Order Discontinuous Galerkin Method for the Time-Harmonic Maxwell Equations"

This work is concerned with the numerical solution of the first order time-harmonic Maxwell equations on simplicial meshes and heterogeneous media. We are interested in discontinuous Galerkin (DG) methods based on a high-order polynomial interpolation and a centered or upwind approximation to estimate the numerical fluxes at interfaces between neighboring elements. The DG method allows distributing the interpolation orders p in a non-uniform manner and to use non-conforming meshes. The ultimate objective of this study is to develop a hp-adaptive method. A first step towards this goal is to propose a p-adaptivity criterion for an effective distribution of p on a given mesh.

Elie Hachem (Ecole des Mines ParisTech, Centre de Mise en Forme des Matériaux)
"Méthode éléments finis stabilisés en aérothermie"

15h30 : Fin du séminaire