January 19th – Laurent Monasse: A 3D conservative coupling between a compressible flow and a fragmenting structure

Laurent Monasse: January 19 December at 3pm, A415 Inria Paris. We will present a conservative method for three-dimensional inviscid fluid-structure interaction problems. Body-fitted methods are not well-suited for large displacements or fragmentation of the structure, since they involve possibly costly remeshing of the fluid domain. We use instead an immersed boundary technique through the modification of the finite volume fluxes in the vicinity of the solid. The method is tailored to yield the exact conservation of mass, momentum and energy of the system and exhibits consistency properties. In the event of fragmentation, void can appear due to the velocity of crack opening. In order to ensure stability in the presence of void, we resort locally to the Lax-Friedrichs flux near cracks. Since both fluid and solid methods are explicit, the coupling scheme is designed to be explicit too. The computational cost of the fluid and solid methods lies mainly in the evaluation of fluxes on the fluid side and of forces and torques on the solid side. It should be noted that the coupling algorithm evaluates these only once every time step, ensuring the computational efficiency of the coupling. We also analyze a corner instability of the conservative explicit immersed boundary method in the case of a Roe flux, explain its origin and propose a way to fix the issue.

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January 5th – Agnieszka Miedlar: Moving eigenvalues and eigenvectors by simple perturbations

Agnieszka Miedlar: Thursday 8 December at 3pm, A415 Inria Paris. Abstract: In the context of iterative solvers moving the eigenvalue or the eigenpair may be of particular importance in several cases, e.g., deflation techniques, increasing the spectral gap or determining the set of linearly independent eigenvectors. It can also be used for reducing the imaginary parts of the eigenvalues without chainging the matrix exponential; this can enhance the computation of $\exp(A)$. Exploiting the classical perturbation analysis for eigenvalue problems [Golub and Van Loan 2012] we study the following problem.

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December 8th – Luca Formaggia: Hybrid dimensional Darcy flow in fractured porous media, some recent results on mimetic discretization

Luca Formaggia: Thursday 8 December at 3pm, A415 Inria Paris. Fractures can alter greatly the characteristics of porous media. Their diverse scale distribution makes it often impossible to resort to averaging or homogenisation techniques to account for their presence. Thus, different models have been devised to account for the presence of fractures in porous media explicitly. We here present the general problem, together with a recent result of well-posedness for an hybrid dimensional mixed formulation of Darcy flow in fractured porous media, and an analysis of a mimetic finite difference scheme adopted for its numerical solution.

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(English) Internal Seminar: Paola Antonietti

Jeudi 22 Septembre, a 15h, salle Jacques Louis Lions, Inria Paris. Paola ANTONIETTI: Fast solution techniques for high order Discontinuous Galerkin methods We present two-level and multigrid algorithms for the efficient solution of the linear system of equations arising from high-order discontinuous Galerkin discretizations of second-order elliptic problems. Starting from the classical framework in geometric multigrid analysis, we define a smoothing and an approximation property, which are used to prove uniform convergence of the resulting multigrid schemes with respect to the discretization parameters and the number of levels, provided the number of smoothing steps is chosen sufficienly large.  A discussion on the effects of employing inherited or noninherited sublevel solvers is also presented as well the extension of the proposed techniques to agglomeration-based multigrid solvers. Numerical experiments confirm the theoretical results.

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19 Nov. 2015 – Géraldine Pichot: Algorithmes de génération de champs aléatoires Gaussiens stationnaires

Séminaire interne de l’équipe SERENA, Jeudi 19 Novembre 2015, 16h à 17h, Batiment 13: Géraldine Pichot: Algorithmes de génération de champs aléatoires Gaussiens stationnaires Résumé: Les équations gouvernant les phénomènes d’écoulement et de transport en milieux géologiques font intervenir des coefficients physiques caractérisant ces milieux, tels que la  perméabilité et la porosité. Devant l’impossibilité d’imager précisément les milieux géologiques, ces paramètres sont classiquement modélisées par des champs aléatoires Gaussiens stationnaires dont les paramètres sont données par l’expérimentation. Dans l’objectif d’étudier l’impact de la variabilité de ces coefficients sur les phénomènes étudiés, il est nécessaire de générer un grand nombre de ces champs aléatoires. Un algorithme de simulation efficace est alors nécessaire. Dans cet exposé, je présenterai différents algorithmes de simulations basés sur l’approche classique de « circulant embedding » permettant de générer de tels champs sur une grille régulière. La parallélisation de ces algorithmes sera discutée. Je présenterai également quelques résultats de simulations pour différentes fonctions de covariance. Ce travail est effectué en collaboration avec Jocelyne Erhel et Mestapha Oumouni (INRIA, Rennes).

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