Séminaire

14h: Gabriel Peyré "Computational Optimal Transport for Data Sciences"

Abstract: Optimal transport (OT) has become a fundamental mathematical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is a recent wave of activity on the use of OT-related methods in fields as diverse as computer vision, computer graphics, statistical inference, machine learning and image processing. In this talk, I will review an emerging class of numerical approaches for the approximate resolution of OT-based optimization problems. This offers a new perspective for the application of OT in imaging sciences (to perform color transfer or shape and texture morphing) and machine learning (to perform clustering, classification and generative models in deep learning). More information and references can be found on the website of our book "Computational Optimal Transport" https://optimaltransport.github.io/

15h30: Frédéric Alauzet "A connectivity-change moving mesh algorithm to efficiently handle large displacements of body-fitted geometries in adaptive CFD simulations"

Abtract: Numerical simulations involving three-dimensional moving geometries with large displacements on unstructured meshes are of great value to industry, but remain very time-consuming and lack of robustness. In a first part, this talk presents a robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations. The algorithm removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, allows to preserve the initial quality of the mesh throughout the simulation. An Arbitrary Lagrangian Eulerian (ALE) compressible flow solver is integrated into this process. This solver relies on a local enforcement of the Discrete Geometrical Conservation Law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid-structure interaction (FSI). In the latter case, the six degrees of freedom (6-DOF) approach for rigid bodies is considered. In a second part, the extension of anisotropic metric-based mesh adaptation to time-dependent problems with body-fitted moving geometries is discussed. Indeed, mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. This presentation establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space-time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations.