Internal seminar of the SERENA team, Thursday 03 December, 4pm-5pm in building 13: Francois Clément: Safe and Correct Programming for Scientific Computing Abstract: The increasing complexity of algorithms for modern scientific computing  makes it a major challenge to implement them in the traditional imperative languages that are popular in the community. The idea is to  explore the usage of formal tools from computing science, and in particular from the functional programming school, to design and  implement generic tools that may ease the development of scientific computing software. In this lecture, we will focus on: Sklml, an easy coarse grain parallelization compiler system; Ref-indic, a generic inversion platform for adaptive parameter  estimation; a comprehensive mechanical proof of correctness of a C program as a  PDE solver. Basic examples of the use of OCaml, Sklml, and Coq will be given.

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Internal seminar of the SERENA team, Thursday 19 November, 4pm-5pm in building 13: Jérôme Jaffré: Discrete reduced models for flow in porous media with fractures  and barriers Abstract: Flow in porous media is strongly influenced by the presence of fractures which can have higher or lower permeabilities (barriers). Depending on the goal of the study there are many models which take into account this influence. In this lecture we will focus on discrete fracture models, that are models where each fracture can be described individually, and reduced fracture models, where a fracture is reduced to an $(n-1)$ surface in an $n$-dimensional model. We will begin with one-phase flow models and continue with two-phase flow taking into account the change of rock types between the matrix rock and the fractures.

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Internal seminar of the SERENA team, Thursday 12 November, 3pm-4pm in building 13: Elyes Ahmed: Space-time domain decomposition method for two-phase flow equations Abstract: We consider a simplified model of two-phase flow model through a heterogeneous meduim. Focusing on the capillary forces motion, we consider the Optimized Schwarz method with non-linear Robin conditions in the context of non-linear degenerate parabolic problem which is approximated in a domain shared in two homogeneous parts, each of them being a different rock type, each rock is characterized by its relative permeability and capillary curves functions of the phase saturations. We then propose a hybridized finite volume scheme for the approximation of the multi-domain solution. It relies on the Optimized Robin-Schwarz algorithm with a finite volume discretization of the subdomain problems. The existence of a weak solution for the Robin subdomain problems involved in the OSWR method is proved using the convergence of a finite volume approximation. Numerical results for three-dimensional problems are presented to illustrate the performance of the method.

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